
                # Interation 0

                ## Task Info
                You are investigating a biological system where all species are observable. Your goal is to discover the missing reactions. You do not need to add new species.


                ## Incomplete SBML Model. You can assess it as input_sbml_string.

                <?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level3/version1/core" xmlns:layout="http://www.sbml.org/sbml/level3/version1/layout/version1" xmlns:render="http://www.sbml.org/sbml/level3/version1/render/version1" level="3" version="1" layout:required="false" render:required="false">
  <model id="id_jqcb" substanceUnits="id_rfy5" timeUnits="id_pixl" volumeUnits="id_u0ay" areaUnits="id_jta8" lengthUnits="id_5dzf" extentUnits="id_rfy5">
    <listOfUnitDefinitions>
      <unitDefinition id="id_5dzf">
        <listOfUnits>
          <unit kind="metre" exponent="1" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_jta8">
        <listOfUnits>
          <unit kind="metre" exponent="2" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_u0ay">
        <listOfUnits>
          <unit kind="litre" exponent="1" scale="-3" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_pixl">
        <listOfUnits>
          <unit kind="second" exponent="1" scale="0" multiplier="86400"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_rfy5">
        <listOfUnits>
          <unit kind="item" exponent="1" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_z01l">
        <listOfUnits>
          <unit kind="dimensionless" exponent="0" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_ebqc" spatialDimensions="3" size="1" units="id_u0ay" constant="true"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_shpe" compartment="id_ebqc" initialConcentration="1000000" substanceUnits="id_rfy5" hasOnlySubstanceUnits="false" boundaryCondition="false" constant="false"/>
      <species id="id_55cy" compartment="id_ebqc" initialConcentration="0" substanceUnits="id_rfy5" hasOnlySubstanceUnits="false" boundaryCondition="false" constant="false"/>
      <species id="id_yiw5" compartment="id_ebqc" initialConcentration="7000000" substanceUnits="id_rfy5" hasOnlySubstanceUnits="false" boundaryCondition="false" constant="false"/>
      <species id="id_97q7" compartment="id_ebqc" initialConcentration="100000000" substanceUnits="id_rfy5" hasOnlySubstanceUnits="false" boundaryCondition="false" constant="false"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

                Format your response according to the instructions in the system message.
                
## Thoughts
The initial SBML model defines four species (`id_shpe`, `id_55cy`, `id_yiw5`, `id_97q7`) and their initial concentrations, but it contains no reactions. My goal is to identify the reactions governing the interactions between these species.

1.  **Observe the System:** The first step is to run an experiment to see how the species concentrations change over time under default conditions. This will provide the baseline data.
2.  **Simulate the Current Model:** After getting the experimental data, I will simulate the `input_sbml_string`. Since it has no reactions, the species concentrations should remain constant at their initial values.
3.  **Compare and Hypothesize:** By comparing the experimental data with the simulation of the current model, I can start forming hypotheses about the missing reactions. For example, if `id_shpe` decreases and `id_55cy` increases, there might be a reaction `id_shpe -> id_55cy`.

I will start by requesting an "observe" experiment.

## Action

### Experiment
```json
{
   "action": "observe",
   "meta_data": {}
}
```
# Observation

## Experiment Result
Experiment ID: iteration_0
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_0]

Total size: 1480 rows × 5 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_0] for the full data

Time   id_shpe  id_55cy  id_yiw5  id_97q7
0  1.00e+06        0 7.00e+06 1.00e+08
...
1.01e+00  7.27e+05 1.51e+04 1.45e+06 1.14e+08
...
2.03e+00  5.26e+05 1.11e+04 9.65e+05 1.42e+08
...
3.04e+00  3.82e+05 8.35e+03 7.21e+05 1.80e+08
...
4.06e+00  2.79e+05 6.39e+03 5.50e+05 2.27e+08
...
5.07e+00  2.04e+05 4.98e+03 4.26e+05 2.82e+08
...
6.09e+00  1.50e+05 3.96e+03 3.36e+05 3.47e+08
...
7.10e+00  1.12e+05 3.22e+03 2.72e+05 4.19e+08
...
8.11e+00  8.43e+04 2.70e+03 2.26e+05 4.99e+08
...
9.13e+00  6.44e+04 2.34e+03 1.94e+05 5.84e+08
...
1.01e+01  5.02e+04 2.10e+03 1.73e+05 6.72e+08
...
1.12e+01  4.02e+04 1.98e+03 1.61e+05 7.61e+08
...
1.22e+01  3.34e+04 1.96e+03 1.57e+05 8.49e+08
...
1.32e+01  2.89e+04 2.06e+03 1.62e+05 9.33e+08
...
1.42e+01  2.66e+04 2.31e+03 1.79e+05 1.01e+09
...
1.52e+01  2.63e+04 2.76e+03 2.10e+05 1.08e+09
...
1.62e+01  2.81e+04 3.51e+03 2.63e+05 1.14e+09
...
1.72e+01  3.27e+04 4.70e+03 3.48e+05 1.18e+09
...
1.83e+01  4.08e+04 6.48e+03 4.78e+05 1.20e+09
...
1.93e+01  5.37e+04 9.05e+03 6.66e+05 1.21e+09
...
2.03e+01  7.26e+04 1.25e+04 9.23e+05 1.21e+09
...
2.13e+01  9.84e+04 1.68e+04 1.25e+06 1.20e+09
...
2.23e+01  1.31e+05 2.17e+04 1.63e+06 1.18e+09
...
2.33e+01  1.70e+05 2.68e+04 2.04e+06 1.15e+09
...
2.43e+01  2.12e+05 3.14e+04 2.42e+06 1.12e+09
...
2.54e+01  2.54e+05 3.50e+04 2.73e+06 1.09e+09
...
2.64e+01  2.91e+05 3.73e+04 2.94e+06 1.07e+09
...
2.74e+01  3.20e+05 3.79e+04 3.03e+06 1.04e+09
...
2.84e+01  3.39e+05 3.72e+04 3.00e+06 1.01e+09
...
2.94e+01  3.46e+05 3.52e+04 2.86e+06 9.83e+08
...
3.04e+01  3.43e+05 3.25e+04 2.66e+06 9.59e+08
...
3.14e+01  3.31e+05 2.93e+04 2.41e+06 9.37e+08
...
3.25e+01  3.12e+05 2.60e+04 2.15e+06 9.17e+08
...
3.35e+01  2.88e+05 2.29e+04 1.90e+06 9.01e+08
...
3.45e+01  2.63e+05 2.00e+04 1.66e+06 8.88e+08
...
3.55e+01  2.36e+05 1.74e+04 1.45e+06 8.78e+08
...
3.65e+01  2.11e+05 1.52e+04 1.26e+06 8.72e+08
...
3.75e+01  1.88e+05 1.33e+04 1.10e+06 8.70e+08
...
3.85e+01  1.66e+05 1.18e+04 9.73e+05 8.72e+08
...
3.96e+01  1.48e+05 1.05e+04 8.66e+05 8.77e+08
...
4.06e+01  1.31e+05 9.50e+03 7.80e+05 8.86e+08
...
4.16e+01  1.18e+05 8.72e+03 7.13e+05 8.98e+08
...
4.26e+01  1.06e+05 8.13e+03 6.62e+05 9.12e+08
...
4.36e+01  9.71e+04 7.72e+03 6.25e+05 9.28e+08
...
4.46e+01  8.99e+04 7.47e+03 6.02e+05 9.46e+08
...
4.56e+01  8.46e+04 7.36e+03 5.90e+05 9.64e+08
...
4.67e+01  8.09e+04 7.38e+03 5.89e+05 9.82e+08
...
4.77e+01  7.88e+04 7.54e+03 5.99e+05 9.99e+08
...
4.87e+01  7.82e+04 7.82e+03 6.19e+05 1.01e+09
...
5.00e+01  7.94e+04 8.35e+03 6.59e+05 1.03e+09

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 20/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. ()

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 1
## Thoughts

The experimental data from `iteration_0` shows dynamic changes in all species concentrations, which confirms that there are reactions occurring.

Here's a summary of the observed trends:
*   `id_shpe`: Starts at 1.00e+06, decreases significantly, then shows some recovery, and then decreases again.
*   `id_55cy`: Starts at 0, increases to a peak, and then decreases.
*   `id_yiw5`: Starts at 7.00e+06, decreases significantly, then shows some recovery, and then decreases again.
*   `id_97q7`: Starts at 1.00e+08, increases significantly, then shows a slight decrease, and then increases again.

The initial model has no reactions. I will now simulate the `input_sbml_string` to confirm that it produces constant concentrations. Then I will start adding reactions based on the observed initial trends.

**Initial Phase (approx. T=0 to T=10-15):**
*   `id_shpe` decreases.
*   `id_55cy` increases (from 0).
*   `id_yiw5` decreases.
*   `id_97q7` increases.

This suggests that `id_shpe` and `id_yiw5` might be reactants, and `id_55cy` and `id_97q7` might be products in one or more reactions.

Let's consider a plausible initial reaction:
`R1: id_shpe + id_yiw5 -> id_55cy + id_97q7`

This reaction would explain the initial decrease in `id_shpe` and `id_yiw5`, and the initial increase in `id_55cy` and `id_97q7`.

I will add this reaction to the model and then simulate it. I'll need to assign a kinetic law and parameters. For now, I'll use mass action kinetics with a placeholder rate constant.

Steps:
1.  Simulate the current `input_sbml_string` (which has no reactions) to get a baseline.
2.  Print the head of the experimental data for reference.
3.  Add the hypothesized reaction `id_shpe + id_yiw5 -> id_55cy + id_97q7` to the SBML model.
4.  Simulate the new model.
5.  Compare the simulation results with the experimental data.

## Action

### Code
```python
import pandas as pd
import libsbml

# Print the head of the experimental data for reference
print("Experimental Data (iteration_0):")
print(experiment_history['iteration_0'].head())

# Simulate the initial empty model
print("\nSimulating the initial empty model:")
initial_simulation_df = simulate(input_sbml_string)
print(initial_simulation_df.head())
shared_variables.add("initial_simulation_df", initial_simulation_df)

# Create a new SBML model with the first hypothesized reaction
doc = libsbml.readSBMLFromString(input_sbml_string)
model = doc.getModel()

# Reaction 1: id_shpe + id_yiw5 -> id_55cy + id_97q7
r1 = model.createReaction()
r1.setId("R1")
r1.setReversible(False)
r1.setFast(False)

# Reactant: id_shpe
reactant1_r1 = r1.createReactant()
reactant1_r1.setSpecies("id_shpe")
reactant1_r1.setStoichiometry(1)
reactant1_r1.setConstant(False)

# Reactant: id_yiw5
reactant2_r1 = r1.createReactant()
reactant2_r1.setSpecies("id_yiw5")
reactant2_r1.setStoichiometry(1)
reactant2_r1.setConstant(False)

# Product: id_55cy
product1_r1 = r1.createProduct()
product1_r1.setSpecies("id_55cy")
product1_r1.setStoichiometry(1)
product1_r1.setConstant(False)

# Product: id_97q7
product2_r1 = r1.createProduct()
product2_r1.setSpecies("id_97q7")
product2_r1.setStoichiometry(1)
product2_r1.setConstant(False)

# Kinetic Law for R1 (Mass Action)
kl_r1 = r1.createKineticLaw()
k1 = kl_r1.createParameter()
k1.setId("k1_R1")
k1.setValue(1e-9) # Placeholder value, will need adjustment
k1.setUnits("litre_per_mole_per_second") # Adjust if necessary based on concentration units
math_ast_r1 = libsbml.parseL3Formula("k1_R1 * id_shpe * id_yiw5")
kl_r1.setMath(math_ast_r1)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml_v1 = writer.writeSBMLToString(doc)
shared_variables.add("model_v1_sbml", updated_sbml_v1)

print("\nSBML model_v1 created with R1: id_shpe + id_yiw5 -> id_55cy + id_97q7")
# print(updated_sbml_v1) # Optional: print the SBML string if needed for debugging

# Simulate the model with R1
print("\nSimulating model_v1:")
simulation_df_v1 = simulate(updated_sbml_v1)
print(simulation_df_v1.head())
shared_variables.add("simulation_df_v1", simulation_df_v1)

# Basic comparison (qualitative for now)
exp_data = experiment_history['iteration_0']

print("\nInitial concentrations (Experimental):")
print(exp_data.iloc[0])

print("\nConcentrations at T_approx=1 (Experimental):")
print(exp_data[exp_data['Time'] > 1.0].iloc[0])
print("\nConcentrations at T_approx=1 (Simulated with R1):")
# Find closest time point to 1.0 in simulation
sim_t1 = simulation_df_v1.iloc[(simulation_df_v1['Time']-1.0).abs().argsort()[:1]]
print(sim_t1)

```
# Observation

## Code Stdout
Experimental Data (iteration_0):
          id_shpe       id_55cy       id_yiw5       id_97q7      Time
0  1000000.000000      0.000000  7.000000e+06  1.000000e+08  0.000000
1   989881.864602  10288.616939  6.221365e+06  1.000902e+08  0.033807
2   979781.018548  15913.087690  5.608696e+06  1.002066e+08  0.067613
3   969716.179971  18879.697997  5.108448e+06  1.003484e+08  0.101420
4   959700.044932  20339.529931  4.688013e+06  1.005155e+08  0.135227

Simulating the initial empty model:
     id_shpe  id_55cy    id_yiw5      id_97q7      Time
0  1000000.0      0.0  7000000.0  100000000.0  0.000000
1  1000000.0      0.0  7000000.0  100000000.0  0.033807
2  1000000.0      0.0  7000000.0  100000000.0  0.067613
3  1000000.0      0.0  7000000.0  100000000.0  0.101420
4  1000000.0      0.0  7000000.0  100000000.0  0.135227

SBML model_v1 created with R1: id_shpe + id_yiw5 -> id_55cy + id_97q7

Simulating model_v1:
          id_shpe     id_55cy       id_yiw5       id_97q7      Time
0  1000000.000000    0.000000  7.000000e+06  1.000000e+08  0.000000
1   999763.385610  236.614390  6.999763e+06  1.000002e+08  0.033807
2   999526.835190  473.164810  6.999527e+06  1.000005e+08  0.067613
3   999290.348704  709.651296  6.999290e+06  1.000007e+08  0.101420
4   999053.926173  946.073827  6.999054e+06  1.000009e+08  0.135227

Initial concentrations (Experimental):
id_shpe      1000000.0
id_55cy            0.0
id_yiw5      7000000.0
id_97q7    100000000.0
Time               0.0
Name: 0, dtype: float64

Concentrations at T_approx=1 (Experimental):
id_shpe    7.270729e+05
id_55cy    1.509285e+04
id_yiw5    1.448171e+06
id_97q7    1.135763e+08
Time       1.014199e+00
Name: 30, dtype: float64

Concentrations at T_approx=1 (Simulated with R1):
          id_shpe      id_55cy       id_yiw5       id_97q7      Time
30  992929.313551  7070.686449  6.992929e+06  1.000071e+08  1.014199

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 19/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 2
## Thoughts

The simulation of the initial empty model confirmed that species concentrations remain constant, as expected.
The simulation of `model_v1` (with `R1: id_shpe + id_yiw5 -> id_55cy + id_97q7` and `k1_R1 = 1e-9`) shows:
*   `id_shpe` decreases (from 1e6 to 9.93e5 at T~1).
*   `id_55cy` increases (from 0 to 7.07e3 at T~1).
*   `id_yiw5` decreases (from 7e6 to 6.99e6 at T~1).
*   `id_97q7` increases (from 1e8 to 1.000071e8 at T~1).

Comparing this to the experimental data at T~1:
*   Experimental `id_shpe`: 7.27e5
*   Experimental `id_55cy`: 1.51e4
*   Experimental `id_yiw5`: 1.45e6
*   Experimental `id_97q7`: 1.14e8

The directions of change for `id_shpe`, `id_55cy`, and `id_97q7` are correct, but the magnitudes are off. `id_yiw5` also decreases as expected.
The simulated consumption of `id_shpe` and `id_yiw5` is much lower than observed, and the production of `id_55cy` and `id_97q7` is also much lower.

This suggests that the rate constant `k1_R1` (currently `1e-9`) is too small. I need to increase it.
Let's try increasing `k1_R1` significantly.
The observed change in `id_shpe` is `1e6 - 7.27e5 = 2.73e5`.
The observed change in `id_yiw5` is `7e6 - 1.45e6 = 5.55e6`.
The observed change in `id_55cy` is `1.51e4`.
The observed change in `id_97q7` is `1.14e8 - 1e8 = 1.4e7`.

The stoichiometry of R1 is 1:1:1:1.
The consumption of `id_shpe` (2.73e5) and `id_yiw5` (5.55e6) are not 1:1. This strongly suggests that R1 alone is not sufficient or the stoichiometry is different, or there are other reactions consuming `id_yiw5` more rapidly or producing `id_shpe`.
Similarly, the production of `id_55cy` (1.51e4) and `id_97q7` (1.4e7) are not 1:1.

Let's look at the ratios:
`delta_id_yiw5 / delta_id_shpe` = 5.55e6 / 2.73e5 ~= 20.3
`delta_id_97q7 / delta_id_55cy` = 1.4e7 / 1.51e4 ~= 927

This implies that `id_yiw5` is consumed much faster than `id_shpe`, and `id_97q7` is produced much faster than `id_55cy`.

Hypothesis 1: The stoichiometry of R1 is incorrect.
Perhaps `R1: id_shpe + X*id_yiw5 -> Y*id_55cy + Z*id_97q7`.
If `id_shpe` is limiting, then `X` would be around `delta_id_yiw5 / delta_id_shpe` which is ~20.
And `Y` and `Z` would relate to `delta_id_55cy / delta_id_shpe` and `delta_id_97q7 / delta_id_shpe`.
`delta_id_55cy / delta_id_shpe` = 1.51e4 / 2.73e5 ~= 0.055
`delta_id_97q7 / delta_id_shpe` = 1.4e7 / 2.73e5 ~= 51.3

This would suggest a reaction like: `1 id_shpe + 20 id_yiw5 -> 0.05 id_55cy + 50 id_97q7`. Stoichiometry must be integers, so this is not directly usable but indicates the scale.

Hypothesis 2: There are multiple reactions.
Reaction `R1: id_shpe -> id_55cy` (or involving `id_55cy` as a product)
Reaction `R2: id_yiw5 -> id_97q7` (or involving `id_97q7` as a product)
And perhaps a reaction consuming `id_shpe` and `id_yiw5`.

Let's re-examine the initial phase (T=0 to T~10-15):
*   `id_shpe` decreases.
*   `id_55cy` increases.
*   `id_yiw5` decreases.
*   `id_97q7` increases.

Consider simpler reactions first.
`R_A: id_shpe -> id_55cy`
`R_B: id_yiw5 -> id_97q7`

If `R_A` exists, then `delta_id_shpe` should be roughly `-delta_id_55cy`.
At T~1: `delta_id_shpe` = -2.73e5, `delta_id_55cy` = 1.51e4. Not a 1:1 match. `id_shpe` is consumed much more than `id_55cy` is produced. So `id_shpe` must be involved in other reactions, likely producing `id_97q7` or consuming `id_yiw5`.

If `R_B` exists, then `delta_id_yiw5` should be roughly `-delta_id_97q7`.
At T~1: `delta_id_yiw5` = -5.55e6, `delta_id_97q7` = 1.4e7. Not a 1:1 match. `id_97q7` is produced more than `id_yiw5` is consumed. So `id_97q7` must have other sources, or `id_yiw5` is consumed with a higher stoichiometry for `id_97q7` production.

Let's go back to the idea of `id_shpe + id_yiw5 -> ...` and `... -> id_55cy + id_97q7`.
The initial decrease of `id_shpe` and `id_yiw5` and increase of `id_55cy` and `id_97q7` is strong.

Let's try to adjust the rate constant `k1_R1` for `R1: id_shpe + id_yiw5 -> id_55cy + id_97q7` first.
The rate of R1 is `k1 * [id_shpe] * [id_yiw5]`.
Initial rate approx `delta_id_shpe / delta_t` = `2.73e5 / 1` = `2.73e5`.
So, `k1 * (1e6) * (7e6) approx 2.73e5`.
`k1 * 7e12 approx 2.73e5`.
`k1 approx 2.73e5 / 7e12 = (2.73/7) * 1e-7 approx 0.39 * 1e-7 = 3.9e-8`.
This is larger than the `1e-9` I used. Let's try `k1_R1 = 4e-8`.

The later phase (e.g., T > 15) shows `id_shpe` and `id_yiw5` increasing again, while `id_55cy` decreases after a peak, and `id_97q7` continues to increase but its rate of increase changes. This suggests reversible reactions or new reactions becoming dominant.

For now, let's focus on matching the initial phase better with R1.
I will update `k1_R1` to `4e-8` and re-simulate.

The complex behavior (peaks, reversals in trend) strongly suggests multiple reactions, possibly some reversible or feedback loops.
`id_55cy` peaks around T=2.3-2.8 (experimental data shows max around 3.79e+04 at T=2.74e+01, but the first peak is earlier, around T=1.32e+01, value 2.06e+03, then it goes up again to 3.7e4. The provided snippet is not enough to see the first peak clearly. Let me check the full data).

Looking at the full `experiment_history['iteration_0']`:
`id_55cy`:
T=0, val=0
T=1.01, val=1.51e4
...
T=13.2, val=2.06e3 (this is a local minimum after an initial rise, not a peak)
The data snippet was misleading. Let's re-examine the snippet.
T=0, id_55cy=0
T=1.01, id_55cy=1.51e4
T=2.03, id_55cy=1.11e4 (decreased from 1.51e4)
T=3.04, id_55cy=8.35e3 (decreased)
...
T=12.2, id_55cy=1.96e3 (minimum)
T=13.2, id_55cy=2.06e3 (starts increasing)
T=14.2, id_55cy=2.31e3
...
T=28.4, id_55cy=3.72e4 (local maximum)
T=29.4, id_55cy=3.52e4 (starts decreasing)

So, `id_55cy` rises, then falls, then rises again, then falls again. This is complex.
`id_shpe` falls, then rises, then falls.
`id_yiw5` falls, then rises, then falls.
`id_97q7` generally rises, but the rate changes.

This complexity means a single irreversible reaction `R1` will not capture the full dynamics.
However, let's first try to get the initial phase somewhat right with R1 by adjusting its rate constant.

The stoichiometry issue is still a concern.
If `R1: S + Y -> C + Q` (shpe, yiw5, 55cy, 97q7)
`delta_S` = -2.73e5 (at T=1)
`delta_Y` = -5.55e6 (at T=1)
`delta_C` = +1.51e4 (at T=1)
`delta_Q` = +1.4e7 (at T=1)

If R1 is the only reaction:
Consumption ratio `Y/S` should be 1, observed is ~20.
Production ratio `C/S` should be 1, observed is `1.51e4 / 2.73e5` ~ 0.055.
Production ratio `Q/S` should be 1, observed is `1.4e7 / 2.73e5` ~ 51.3.

This strongly indicates that the 1:1:1:1 stoichiometry for `id_shpe, id_yiw5 -> id_55cy, id_97q7` is incorrect or other reactions are dominant.

Let's consider two separate primary reactions for the initial phase:
`R_shpe_consumption: id_shpe -> ...`
`R_yiw5_consumption: id_yiw5 -> ...`
`R_55cy_production: ... -> id_55cy`
`R_97q7_production: ... -> id_97q7`

Perhaps:
`R1_new: id_shpe + id_yiw5 -> id_97q7` (to explain large `id_97q7` production and consumption of `id_shpe` and `id_yiw5`)
Rate `k1 * [id_shpe] * [id_yiw5]`.
If this reaction produces `id_97q7`, then `delta_id_shpe` ~ `delta_id_yiw5` ~ `-delta_id_97q7` (if stoich is 1:1:1).
Observed: `delta_id_shpe`=-2.7e5, `delta_id_yiw5`=-5.5e6, `delta_id_97q7`=1.4e7.
The consumption of `id_yiw5` is much larger than `id_shpe`. The production of `id_97q7` is much larger than consumption of `id_shpe`.

This suggests `id_yiw5` is a major source for `id_97q7`.
`R_A: id_yiw5 -> id_97q7` (with some stoichiometry)
And `id_shpe` is consumed, and `id_55cy` is produced.
`R_B: id_shpe -> id_55cy` (with some stoichiometry)

Let's test `R_A: id_yiw5 -> id_97q7` and `R_B: id_shpe -> id_55cy`.
For `R_A`: `s_Y * id_yiw5 -> s_Q * id_97q7`.
`delta_id_yiw5` = -5.55e6. `delta_id_97q7` = 1.4e7.
Ratio `delta_id_97q7 / (-delta_id_yiw5)` = `1.4e7 / 5.55e6` ~= 2.5.
So, maybe `id_yiw5 -> 2.5 id_97q7` (or `2 id_yiw5 -> 5 id_97q7`). Let's try `id_yiw5 -> 2 id_97q7` or `id_yiw5 -> 3 id_97q7`.
Let's try `R_A: id_yiw5 -> 2 id_97q7`.
Rate `kA * [id_yiw5]`.
`delta_id_yiw5 / delta_t = -kA * [id_yiw5]`.
`5.55e6 / 1 = kA * 7e6`. So `kA approx 5.55/7 = 0.79`.

For `R_B: id_shpe -> id_55cy`.
`s_S * id_shpe -> s_C * id_55cy`.
`delta_id_shpe` = -2.73e5. `delta_id_55cy` = 1.51e4.
Ratio `delta_id_55cy / (-delta_id_shpe)` = `1.51e4 / 2.73e5` ~= 0.055.
So, maybe `id_shpe -> 0.05 id_55cy` (or `20 id_shpe -> id_55cy`). This means `id_shpe` is consumed for other things too.
Let's try `R_B: id_shpe -> id_55cy` (1:1 stoichiometry for now).
Rate `kB * [id_shpe]`.
`delta_id_55cy / delta_t = kB * [id_shpe]`.
`1.51e4 / 1 = kB * 1e6`. So `kB approx 1.51e-2`.

If `R_B` is `id_shpe -> id_55cy`, then `id_shpe` consumed for this is `1.51e4`.
Total `id_shpe` consumed is `2.73e5`. Remaining `id_shpe` consumption is `2.73e5 - 1.51e4 = 2.58e5`.
This remaining `id_shpe` consumption must go somewhere else.

What if `id_shpe` is also converted to `id_97q7`?
`R_C: id_shpe -> id_97q7` (with some stoichiometry `s_S2 * id_shpe -> s_Q2 * id_97q7`)
If `R_A: id_yiw5 -> 2 id_97q7` (rate `kA * [id_yiw5]`)
And `R_B: id_shpe -> id_55cy` (rate `kB * [id_shpe]`)
And `R_C: id_shpe -> id_97q7` (rate `kC * [id_shpe]`)

From `R_A`: `id_97q7` produced = `2 * delta_id_yiw5_consumed_by_RA`.
If all `id_yiw5` consumption (-5.55e6) is by `R_A`, then `id_97q7` produced by `R_A` is `2 * 5.55e6 = 1.11e7`.
Total `id_97q7` produced is `1.4e7`.
Remaining `id_97q7` to be produced = `1.4e7 - 1.11e7 = 2.9e6`.
This could come from `R_C: id_shpe -> X id_97q7`.
If `id_shpe` consumed by `R_C` is `delta_id_shpe_RC`, then `X * delta_id_shpe_RC = 2.9e6`.
Total `id_shpe` consumed = `2.73e5`.
`id_shpe` consumed by `R_B` (for `id_55cy`) = `1.51e4` (assuming 1:1).
Remaining `id_shpe` for `R_C` = `2.73e5 - 1.51e4 = 2.58e5`.
So, `X * 2.58e5 = 2.9e6`. `X = 2.9e6 / 2.58e5 = 290 / 25.8 ~= 11.2`.
This suggests `R_C: id_shpe -> 11 id_97q7`.

So, the hypothesis is:
1.  `R_A: id_yiw5 -> 2 id_97q7` (Parameter `kA`)
2.  `R_B: id_shpe -> id_55cy` (Parameter `kB`)
3.  `R_C: id_shpe -> 11 id_97q7` (Parameter `kC`)

Let's estimate parameters:
`kA`: `delta_id_yiw5 / delta_t = -kA * [id_yiw5]`. `5.55e6 / 1 = kA * 7e6`. `kA = 5.55/7 ~ 0.79`.
`kB`: `delta_id_55cy / delta_t = kB * [id_shpe]`. `1.51e4 / 1 = kB * 1e6`. `kB = 1.51e-2`.
`kC`: `(1/11) * delta_id_97q7_from_RC / delta_t = kC * [id_shpe]`.
Or, `delta_id_shpe_for_RC / delta_t = kC * [id_shpe]`.
`2.58e5 / 1 = kC * 1e6`. `kC = 0.258`.

This set of reactions seems more plausible for the initial phase based on stoichiometry.
The later dynamics (oscillations/reversals) will require more, possibly reversible reactions.
For example, `id_55cy` decreases after its initial rise. This means `id_55cy` is consumed.
`id_55cy -> ?` or `id_55cy + ? -> ?`

Let's implement these three reactions and simulate.

Model `v2` will have:
*   `R_A: id_yiw5 -> 2 id_97q7` with `kA = 0.79`
*   `R_B: id_shpe -> id_55cy` with `kB = 0.0151`
*   `R_C: id_shpe -> 11 id_97q7` with `kC = 0.258`

All are mass-action kinetics based on the reactant.

The units for these first-order rate constants would be `1/time_unit`. The time unit is `day` (86400s). So `1/day`.

Let's check the species behavior again:
`id_shpe`: decreases, then increases (around T=10-20), then decreases.
`id_yiw5`: decreases, then increases (around T=10-20), then decreases.
The increase suggests production of `id_shpe` and `id_yiw5` in a later phase.
This could be from `id_55cy` or `id_97q7` converting back, or some other source.

`id_55cy`: increases, decreases, increases, decreases.
The decrease of `id_55cy` (e.g. T=1 to T=12) implies `id_55cy` is consumed.
`R_D: id_55cy -> ?`
What could `id_55cy` convert to? Perhaps back to `id_shpe`? Or to `id_yiw5`? Or something else.
If `R_D: id_55cy -> id_shpe`, this could explain the rise of `id_shpe` later.
If `R_E: id_55cy -> id_yiw5`, this could explain the rise of `id_yiw5` later.

Let's focus on the first three reactions for now and see how well they match the initial phase (T=0 to T=2).
The rise of `id_shpe` starts around T=12.2 (from 3.34e4 to 5.37e4 at T=19.3).
The rise of `id_yiw5` starts around T=12.2 (from 1.57e5 to 6.66e5 at T=19.3).
The first fall of `id_55cy` is from T=1.01 (1.51e4) to T=12.2 (1.96e3).

This fall of `id_55cy` needs to be modeled.
`R_D: id_55cy -> X`. What is X?
If `id_55cy` converts to `id_shpe` and `id_yiw5`, it could explain their later rise.
`R_D: id_55cy -> id_shpe` (rate `kD * [id_55cy]`)
`R_E: id_55cy -> id_yiw5` (rate `kE * [id_55cy]`)
Or `R_D_combined: id_55cy -> alpha*id_shpe + beta*id_yiw5`

Let's add `R_A, R_B, R_C` first.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model
doc_v2 = libsbml.readSBMLFromString(input_sbml_string) # Start from the base model
model_v2 = doc_v2.getModel()

# Reaction R_A: id_yiw5 -> 2 id_97q7
r_a = model_v2.createReaction()
r_a.setId("R_A")
r_a.setReversible(False)
r_a.setFast(False)
# Reactant
reactant_ra = r_a.createReactant()
reactant_ra.setSpecies("id_yiw5")
reactant_ra.setStoichiometry(1)
reactant_ra.setConstant(False)
# Product
product_ra = r_a.createProduct()
product_ra.setSpecies("id_97q7")
product_ra.setStoichiometry(2) # Updated stoichiometry
product_ra.setConstant(False)
# Kinetic Law
kl_ra = r_a.createKineticLaw()
param_ka = kl_ra.createParameter()
param_ka.setId("kA")
param_ka.setValue(0.79) # Estimated value
param_ka.setUnits("per_day") # Assuming time unit is day
kl_ra.setMath(libsbml.parseL3Formula("kA * id_yiw5"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v2.createReaction()
r_b.setId("R_B")
r_b.setReversible(False)
r_b.setFast(False)
# Reactant
reactant_rb = r_b.createReactant()
reactant_rb.setSpecies("id_shpe")
reactant_rb.setStoichiometry(1)
reactant_rb.setConstant(False)
# Product
product_rb = r_b.createProduct()
product_rb.setSpecies("id_55cy")
product_rb.setStoichiometry(1)
product_rb.setConstant(False)
# Kinetic Law
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createParameter()
param_kb.setId("kB")
param_kb.setValue(0.0151) # Estimated value
param_kb.setUnits("per_day")
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v2.createReaction()
r_c.setId("R_C")
r_c.setReversible(False)
r_c.setFast(False)
# Reactant
reactant_rc = r_c.createReactant()
reactant_rc.setSpecies("id_shpe")
reactant_rc.setStoichiometry(1)
reactant_rc.setConstant(False)
# Product
product_rc = r_c.createProduct()
product_rc.setSpecies("id_97q7")
product_rc.setStoichiometry(11) # Updated stoichiometry
product_rc.setConstant(False)
# Kinetic Law
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createParameter()
param_kc.setId("kC")
param_kc.setValue(0.258) # Estimated value
param_kc.setUnits("per_day")
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml_v2 = writer.writeSBMLToString(doc_v2)
shared_variables.add("model_v2_sbml", updated_sbml_v2)
print("SBML model_v2 created with R_A, R_B, R_C.")
# print(updated_sbml_v2) # For debugging

# Simulate the model_v2
print("\nSimulating model_v2:")
simulation_df_v2 = simulate(updated_sbml_v2)
shared_variables.add("simulation_df_v2", simulation_df_v2)
print(simulation_df_v2.head())

# Compare with experimental data at T_approx=1
print("\nExperimental Data (iteration_0) at T~1:")
print(exp_data[exp_data['Time'] > 1.0].iloc[0])

print("\nSimulated Data (model_v2) at T~1:")
sim_t1_v2 = simulation_df_v2.iloc[(simulation_df_v2['Time']-1.0).abs().argsort()[:1]]
print(sim_t1_v2)

# Compare with experimental data at T_approx=2
print("\nExperimental Data (iteration_0) at T~2:")
print(exp_data[exp_data['Time'] > 2.0].iloc[0])

print("\nSimulated Data (model_v2) at T~2:")
sim_t2_v2 = simulation_df_v2.iloc[(simulation_df_v2['Time']-2.0).abs().argsort()[:1]]
print(sim_t2_v2)

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model
doc_v2 = libsbml.readSBMLFromString(input_sbml_string) # Start from the base model
model_v2 = doc_v2.getModel()

# Reaction R_A: id_yiw5 -> 2 id_97q7
r_a = model_v2.createReaction()
r_a.setId("R_A")
r_a.setReversible(False)
r_a.setFast(False)
# Reactant
reactant_ra = r_a.createReactant()
reactant_ra.setSpecies("id_yiw5")
reactant_ra.setStoichiometry(1)
reactant_ra.setConstant(False)
# Product
product_ra = r_a.createProduct()
product_ra.setSpecies("id_97q7")
product_ra.setStoichiometry(2) # Updated stoichiometry
product_ra.setConstant(False)
# Kinetic Law
kl_ra = r_a.createKineticLaw()
param_ka = kl_ra.createLocalParameter() # Use local parameter
param_ka.setId("kA")
param_ka.setValue(0.79) # Estimated value
# param_ka.setUnits("per_day") # Units are tricky with SBML L3 core, often implicit or defined on model
kl_ra.setMath(libsbml.parseL3Formula("kA * id_yiw5"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v2.createReaction()
r_b.setId("R_B")
r_b.setReversible(False)
r_b.setFast(False)
# Reactant
reactant_rb = r_b.createReactant()
reactant_rb.setSpecies("id_shpe")
reactant_rb.setStoichiometry(1)
reactant_rb.setConstant(False)
# Product
product_rb = r_b.createProduct()
product_rb.setSpecies("id_55cy")
product_rb.setStoichiometry(1)
product_rb.setConstant(False)
# Kinetic Law
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter() # Use local parameter
param_kb.setId("kB")
param_kb.setValue(0.0151) # Estimated value
# param_kb.setUnits("per_day")
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v2.createReaction()
r_c.setId("R_C")
r_c.setReversible(False)
r_c.setFast(False)
# Reactant
reactant_rc = r_c.createReactant()
reactant_rc.setSpecies("id_shpe")
reactant_rc.setStoichiometry(1)
reactant_rc.setConstant(False)
# Product
product_rc = r_c.createProduct()
product_rc.setSpecies("id_97q7")
product_rc.setStoichiometry(11) # Updated stoichiometry
product_rc.setConstant(False)
# Kinetic Law
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter() # Use local parameter
param_kc.setId("kC")
param_kc.setValue(0.258) # Estimated value
# param_kc.setUnits("per_day")
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml_v2 = writer.writeSBMLToString(doc_v2)
shared_variables.add("model_v2_sbml", updated_sbml_v2)
print("SBML model_v2 created with R_A, R_B, R_C.")

# Simulate the model_v2
print("\nSimulating model_v2:")
simulation_df_v2 = simulate(updated_sbml_v2)
shared_variables.add("simulation_df_v2", simulation_df_v2)
print("Simulation model_v2 head:")
print(simulation_df_v2.head())

# Compare with experimental data at T_approx=1
print("\nExperimental Data (iteration_0) at T~1:")
print(exp_data[exp_data['Time'] > 1.0].iloc[0])

print("\nSimulated Data (model_v2) at T~1:")
sim_t1_v2 = simulation_df_v2.iloc[(simulation_df_v2['Time']-1.0).abs().argsort()[:1]]
print(sim_t1_v2)

# Compare with experimental data at T_approx=2
print("\nExperimental Data (iteration_0) at T~2:")
print(exp_data[exp_data['Time'] > 2.0].iloc[0])

print("\nSimulated Data (model_v2) at T~2:")
sim_t2_v2 = simulation_df_v2.iloc[(simulation_df_v2['Time']-2.0).abs().argsort()[:1]]
print(sim_t2_v2)
```
# Observation

## Code Stdout
SBML model_v2 created with R_A, R_B, R_C.

Simulating model_v2:
          id_shpe      id_55cy       id_yiw5       id_97q7      Time
0  1000000.000000     0.000000  7.000000e+06  1.000000e+08  0.000000
1   990809.898409   508.130846  6.815524e+06  1.004645e+08  0.033807
2   981704.254493  1011.591934  6.635909e+06  1.009183e+08  0.067613
3   972682.293427  1510.426105  6.461028e+06  1.013618e+08  0.101420
4   963743.246583  2004.675857  6.290757e+06  1.017953e+08  0.135227

Experimental Data (iteration_0) at T~1:
id_shpe    7.270729e+05
id_55cy    1.509285e+04
id_yiw5    1.448171e+06
id_97q7    1.135763e+08
Time       1.014199e+00
Name: 30, dtype: float64

Simulated Data (model_v2) at T~1:
          id_shpe       id_55cy       id_yiw5       id_97q7      Time
30  758071.503765  13376.493201  3.141502e+06  1.102311e+08  1.014199

Experimental Data (iteration_0) at T~2:
id_shpe    5.264868e+05
id_55cy    1.108505e+04
id_yiw5    9.652980e+05
id_97q7    1.424605e+08
Time       2.028398e+00
Name: 60, dtype: float64

Simulated Data (model_v2) at T~2:
         id_shpe       id_55cy       id_yiw5       id_97q7      Time
59  580002.60428  23222.118914  1.448005e+06  1.154685e+08  1.994591

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 18/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 3
## Thoughts

The simulation results for `model_v2` with reactions `R_A, R_B, R_C` are:

At T~1 (Experimental vs. Simulated `model_v2`):
*   `id_shpe`: 7.27e5 vs. 7.58e5 (Closer, good direction)
*   `id_55cy`: 1.51e4 vs. 1.34e4 (Closer, good direction)
*   `id_yiw5`: 1.45e6 vs. 3.14e6 (Simulated `id_yiw5` is higher, meaning consumption is underestimated or production is overestimated if it were produced. Here it's only consumed by R_A. So R_A rate might be too low, or initial estimate of kA was based on total change, not just R_A.)
*   `id_97q7`: 1.14e8 vs. 1.10e8 (Closer, good direction)

At T~2 (Experimental vs. Simulated `model_v2`):
*   `id_shpe`: 5.26e5 vs. 5.80e5 (Simulated is higher, consumption rate is slowing down more than in experiment or experimental consumption is accelerating)
*   `id_55cy`: 1.11e4 vs. 2.32e4 (Simulated is much higher. Experimental `id_55cy` decreases from T=1 to T=2 (1.51e4 -> 1.11e4). Simulated `id_55cy` increases (1.34e4 -> 2.32e4). This confirms `id_55cy` needs a consumption pathway.)
*   `id_yiw5`: 9.65e5 vs. 1.45e6 (Simulated `id_yiw5` is still higher. Consumption of `id_yiw5` is still underestimated.)
*   `id_97q7`: 1.42e8 vs. 1.15e8 (Simulated `id_97q7` is lower. Production is underestimated.)

**Key observations and next steps:**

1.  **`id_55cy` consumption:** The most glaring issue is `id_55cy`. Experimentally, it peaks before T=2 and starts decreasing. The model currently only produces it. We need a reaction that consumes `id_55cy`.
    *   Hypothesis: `R_D: id_55cy -> ?`
    *   What does it turn into? The later rise in `id_shpe` and `id_yiw5` (around T=12-20) could be fueled by `id_55cy`.
    *   Let's try `R_D: id_55cy -> id_shpe`. This would help `id_shpe` recover later and consume `id_55cy`.
    *   Rate for `R_D`: `kD * [id_55cy]`.
    *   When does `id_55cy` start decreasing? After T=1.01 (1.51e4), at T=2.03 it's 1.11e4. Change is `(1.11e4 - 1.51e4) = -4e3` over approx 1 day.
    *   Net rate of change of `id_55cy` = `(kB * [id_shpe]) - (kD * [id_55cy])`.
    *   At T=1, `[id_shpe]`~7.3e5, `[id_55cy]`~1.5e4.
    *   Rate of production from R_B: `0.0151 * 7.3e5 = 1.1e4`.
    *   Observed `d[id_55cy]/dt` around T=1 to T=2 is approx `-4e3`.
    *   So, `1.1e4 - (kD * 1.5e4) = -4e3`.
    *   `kD * 1.5e4 = 1.1e4 + 4e3 = 1.5e4`.
    *   `kD approx 1.0`. This seems high for a rate constant, but let's use it as a starting point.

2.  **`id_yiw5` consumption:** `id_yiw5` is consumed less in the model than in experiments.
    *   Current consumption is only by `R_A: id_yiw5 -> 2 id_97q7` with `kA = 0.79`.
    *   We could increase `kA`.
    *   Experimental `delta_id_yiw5` (T=0 to T=1) = `1.45e6 - 7e6 = -5.55e6`. Rate = `5.55e6`.
    *   Simulated `delta_id_yiw5` (T=0 to T=1) = `3.14e6 - 7e6 = -3.86e6`. Rate = `3.86e6`.
    *   The rate `kA * [id_yiw5]` needs to be higher. Average `[id_yiw5]` in first interval is `(7e6+3.14e6)/2 = 5.07e6` (sim) vs `(7e6+1.45e6)/2 = 4.22e6` (exp).
    *   Let's try to match the consumption at T=1. We need to consume `5.55e6` of `id_yiw5`.
    *   If `kA_new * Avg[id_yiw5]_exp = 5.55e6`. `kA_new * 4.22e6 = 5.55e6`. `kA_new = 5.55/4.22 ~ 1.31`.
    *   Let's try increasing `kA` from `0.79` to `1.3`.

3.  **`id_97q7` production:** `id_97q7` production is underestimated at T=2 (1.42e8 exp vs 1.15e8 sim).
    *   `id_97q7` is produced by `R_A: id_yiw5 -> 2 id_97q7` and `R_C: id_shpe -> 11 id_97q7`.
    *   If we increase `kA` (for `id_yiw5` consumption), this will also increase `id_97q7` production from `R_A`.
    *   Change from `kA=0.79` to `kA=1.3`. This is a `1.3/0.79 = 1.64` fold increase in rate from R_A.
    *   Production of `id_97q7` from R_A at T=1 (sim_v2): `2 * kA * Integral([id_yiw5]dt)`. `delta_id_yiw5` from R_A was `3.86e6`. So `id_97q7` from R_A was `2 * 3.86e6 = 7.72e6`.
    *   Production of `id_97q7` from R_C at T=1 (sim_v2): `delta_id_shpe` from R_C was `kC * Integral([id_shpe]dt)`. Total `delta_id_shpe` was `1e6 - 7.58e5 = 2.42e5`. `delta_id_shpe` for R_B was `1.34e4`. So for R_C it was `2.42e5 - 1.34e4 = 2.286e5`. `id_97q7` from R_C was `11 * 2.286e5 = 2.51e6`.
    *   Total `id_97q7` produced (sim_v2, T=1) = `7.72e6 + 2.51e6 = 1.023e7`. Matches `1.10e8 - 1e8 = 1e7`. This is consistent.

    *   If `kA` increases to `1.3`, `id_yiw5` consumption will increase. Let's assume `id_yiw5` drops to `1.45e6` (experimental value at T=1). Then `delta_id_yiw5` is `5.55e6`.
    *   `id_97q7` from new R_A would be `2 * 5.55e6 = 1.11e7`.
    *   `id_shpe` at T=1 (exp) is `7.27e5`. `delta_id_shpe` is `2.73e5`.
    *   `id_55cy` at T=1 (exp) is `1.51e4`. This is from R_B. So `id_shpe` consumed by R_B is `1.51e4`.
    *   `id_shpe` consumed by R_C is `2.73e5 - 1.51e4 = 2.58e5`.
    *   `id_97q7` from R_C is `11 * 2.58e5 = 2.838e7`.
    *   Total `id_97q7` produced (T=1, with new kA and using exp values for calculation) = `1.11e7 + 2.838e6 = 1.39e7`. (Mistake: 2.838e6 should be 2.838e6, not e7. 11 * 2.58e5 = 2.838e6)
    *   Total `id_97q7` produced = `1.11e7 (from R_A) + 2.838e6 (from R_C) = 1.3938e7`. This matches experimental `delta_id_97q7` of `1.4e7`.
    *   So, increasing `kA` to `1.3` seems appropriate. The parameters `kB=0.0151` and `kC=0.258` seem okay for the T=1 snapshot if `id_yiw5` consumption is corrected.

Let's summarize the plan for `model_v3`:
1.  Keep `R_A: id_yiw5 -> 2 id_97q7`, update `kA` from `0.79` to `1.3`.
2.  Keep `R_B: id_shpe -> id_55cy`, `kB = 0.0151`.
3.  Keep `R_C: id_shpe -> 11 id_97q7`, `kC = 0.258`.
4.  Add `R_D: id_55cy -> id_shpe` with `kD = 1.0`. (This reaction will consume `id_55cy` and produce `id_shpe`, helping with `id_55cy` dynamics and later `id_shpe` recovery).

This new reaction `R_D` might affect the `id_shpe` balance for `R_B` and `R_C` if it becomes active early.
At T=1, `[id_55cy]` is `1.5e4`. Rate of `R_D` would be `1.0 * 1.5e4 = 1.5e4`. This is a significant production of `id_shpe`.
This means `id_shpe` consumption by `R_B` and `R_C` would need to be higher to achieve the same net drop in `id_shpe`.
Net `d[id_shpe]/dt = kD*[id_55cy] - kB*[id_shpe] - kC*[id_shpe]`.
At T=1 (exp values): `1.0 * 1.51e4 - (0.0151 + 0.258) * 7.27e5 = 1.51e4 - 0.2731 * 7.27e5 = 1.51e4 - 1.985e5 = -1.834e5`.
Experimental `d[id_shpe]/dt` (from T=0 to T=1) is `(7.27e5 - 1e6)/1 = -2.73e5`.
The model with R_D would predict less consumption of `id_shpe` than observed if `kB` and `kC` are unchanged.
So, `kB` and `kC` might need to be increased if `R_D` is active from early on.

Let's re-evaluate `kB` and `kC` assuming `R_D` is active.
`d[id_shpe]/dt = kD*[id_55cy] - (kB+kC)*[id_shpe]`
`d[id_55cy]/dt = kB*[id_shpe] - kD*[id_55cy]`
`d[id_yiw5]/dt = -kA*[id_yiw5]`
`d[id_97q7]/dt = 2*kA*[id_yiw5] + 11*kC*[id_shpe]`

At T=1 (using experimental values as targets for rates):
`d[id_55cy]/dt` (exp, T=1 to T=2) = `(1.11e4 - 1.51e4)/1 = -4e3`.
So, `kB*[id_shpe_T1] - kD*[id_55cy_T1] = -4e3`.
`kB * 7.27e5 - 1.0 * 1.51e4 = -4e3`.
`kB * 7.27e5 = 1.51e4 - 4e3 = 1.11e4`.
`kB = 1.11e4 / 7.27e5 = 0.01527`. This is very close to the original `0.0151`. So `kB` is likely fine.

Now for `kC`.
`d[id_shpe]/dt` (exp, T=0 to T=1) = `-2.73e5`.
Average `[id_shpe]` = `(1e6+7.27e5)/2 = 8.635e5`. Average `[id_55cy]` = `(0+1.51e4)/2 = 7.55e3`.
`-2.73e5 = kD*Avg[id_55cy] - (kB+kC)*Avg[id_shpe]`.
`-2.73e5 = 1.0 * 7.55e3 - (0.01527+kC) * 8.635e5`.
`-2.73e5 - 7.55e3 = -(0.01527+kC) * 8.635e5`.
`-2.8055e5 = -(0.01527+kC) * 8.635e5`.
`0.01527+kC = 2.8055e5 / 8.635e5 = 0.3248`.
`kC = 0.3248 - 0.01527 = 0.3095`.
This is higher than the previous `kC = 0.258`.

So, revised parameters with `R_D`:
`kA = 1.3`
`kB = 0.0153` (approx)
`kC = 0.31` (approx)
`kD = 1.0`

Let's try these.

The later rise of `id_yiw5` is not yet accounted for. `R_D` produces `id_shpe`. If `id_55cy` also produces `id_yiw5`, say `R_E: id_55cy -> id_yiw5`, then `id_55cy` would be consumed even faster, or `kD` would be split between `id_shpe` and `id_yiw5` production.
For now, let's add `R_D` and adjust `kA, kB, kC`.

One more check: `id_97q7` production.
`d[id_97q7]/dt` (exp, T=0 to T=1) = `1.4e7`.
Model: `2*kA*Avg[id_yiw5] + 11*kC*Avg[id_shpe]`.
Avg `[id_yiw5]` (exp T0-T1) = `(7e6+1.45e6)/2 = 4.225e6`.
Avg `[id_shpe]` (exp T0-T1) = `8.635e5`.
Rate = `2 * 1.3 * 4.225e6 + 11 * 0.31 * 8.635e5`
     `= 2.6 * 4.225e6 + 3.41 * 8.635e5`
     `= 1.0985e7 + 2.9445e6`
     `= 1.39295e7`. This is very close to `1.4e7`.
This gives confidence in the new `kA` and `kC` values.

Final proposed model `v3` reactions and parameters:
1.  `R_A: id_yiw5 -> 2 id_97q7` (Mass action: `kA * id_yiw5`), `kA = 1.3`
2.  `R_B: id_shpe -> id_55cy` (Mass action: `kB * id_shpe`), `kB = 0.0153`
3.  `R_C: id_shpe -> 11 id_97q7` (Mass action: `kC * id_shpe`), `kC = 0.31`
4.  `R_D: id_55cy -> id_shpe` (Mass action: `kD * id_55cy`), `kD = 1.0`

This set of reactions should:
- Improve `id_yiw5` consumption.
- Improve `id_97q7` production.
- Introduce `id_55cy` consumption, potentially matching its peak and fall.
- Allow for `id_shpe` recovery later due to `R_D`.

The recovery of `id_yiw5` is still unaddressed. If `model_v3` is good for the first ~10-15 time units, we can then focus on the later phase.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model
doc_v3 = libsbml.readSBMLFromString(input_sbml_string) # Start from the base model
model_v3 = doc_v3.getModel()

# Parameters for model_v3
kA_v3 = 1.3
kB_v3 = 0.0153
kC_v3 = 0.31
kD_v3 = 1.0

# Reaction R_A: id_yiw5 -> 2 id_97q7
r_a = model_v3.createReaction()
r_a.setId("R_A")
r_a.setReversible(False); r_a.setFast(False)
reactant_ra = r_a.createReactant(); reactant_ra.setSpecies("id_yiw5"); reactant_ra.setStoichiometry(1); reactant_ra.setConstant(False)
product_ra = r_a.createProduct(); product_ra.setSpecies("id_97q7"); product_ra.setStoichiometry(2); product_ra.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_ka = kl_ra.createLocalParameter(); param_ka.setId("kA"); param_ka.setValue(kA_v3)
kl_ra.setMath(libsbml.parseL3Formula("kA * id_yiw5"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v3.createReaction()
r_b.setId("R_B")
r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v3)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v3.createReaction()
r_c.setId("R_C")
r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v3)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v3.createReaction()
r_d.setId("R_D")
r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v3)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml_v3 = writer.writeSBMLToString(doc_v3)
shared_variables.add("model_v3_sbml", updated_sbml_v3)
print("SBML model_v3 created with R_A, R_B, R_C, R_D.")

# Simulate the model_v3
print("\nSimulating model_v3:")
simulation_df_v3 = simulate(updated_sbml_v3)
shared_variables.add("simulation_df_v3", simulation_df_v3)
print("Simulation model_v3 head:")
print(simulation_df_v3.head())

# Compare with experimental data at T_approx=1
print("\nExperimental Data (iteration_0) at T~1:")
print(exp_data[exp_data['Time'] > 1.0].iloc[0])
print("\nSimulated Data (model_v3) at T~1:")
sim_t1_v3 = simulation_df_v3.iloc[(simulation_df_v3['Time']-1.0).abs().argsort()[:1]]
print(sim_t1_v3)

# Compare with experimental data at T_approx=2
print("\nExperimental Data (iteration_0) at T~2:")
print(exp_data[exp_data['Time'] > 2.0].iloc[0])
print("\nSimulated Data (model_v3) at T~2:")
sim_t2_v3 = simulation_df_v3.iloc[(simulation_df_v3['Time']-2.0).abs().argsort()[:1]]
print(sim_t2_v3)

# Compare with experimental data at T_approx=12 (around first minimum for id_shpe, id_yiw5, id_55cy)
print("\nExperimental Data (iteration_0) at T~12:")
print(exp_data[exp_data['Time'] > 12.0].iloc[0]) # Closest to 12.20
print("\nSimulated Data (model_v3) at T~12:")
sim_t12_v3 = simulation_df_v3.iloc[(simulation_df_v3['Time']-12.0).abs().argsort()[:1]]
print(sim_t12_v3)

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model
doc_v3 = libsbml.readSBMLFromString(input_sbml_string) # Start from the base model
model_v3 = doc_v3.getModel()

# Parameters for model_v3
kA_v3 = 1.3
kB_v3 = 0.0153
kC_v3 = 0.31
kD_v3 = 1.0

# Reaction R_A: id_yiw5 -> 2 id_97q7
r_a = model_v3.createReaction()
r_a.setId("R_A")
r_a.setReversible(False); r_a.setFast(False)
reactant_ra = r_a.createReactant(); reactant_ra.setSpecies("id_yiw5"); reactant_ra.setStoichiometry(1); reactant_ra.setConstant(False)
product_ra = r_a.createProduct(); product_ra.setSpecies("id_97q7"); product_ra.setStoichiometry(2); product_ra.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_ka = kl_ra.createLocalParameter(); param_ka.setId("kA"); param_ka.setValue(kA_v3)
kl_ra.setMath(libsbml.parseL3Formula("kA * id_yiw5"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v3.createReaction()
r_b.setId("R_B")
r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v3)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v3.createReaction()
r_c.setId("R_C")
r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v3)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v3.createReaction()
r_d.setId("R_D")
r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v3)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml_v3 = writer.writeSBMLToString(doc_v3)
shared_variables.add("model_v3_sbml", updated_sbml_v3)
print("SBML model_v3 created with R_A, R_B, R_C, R_D.")

# Simulate the model_v3
print("\nSimulating model_v3:")
simulation_df_v3 = simulate(updated_sbml_v3)
shared_variables.add("simulation_df_v3", simulation_df_v3)
print("Simulation model_v3 head:")
print(simulation_df_v3.head())

# Compare with experimental data at T_approx=1
print("\nExperimental Data (iteration_0) at T~1:")
exp_t1 = exp_data[exp_data['Time'] >= 1.0].iloc[0]
print(exp_t1)
print("\nSimulated Data (model_v3) at T~1:")
sim_t1_v3 = simulation_df_v3.iloc[(simulation_df_v3['Time']-exp_t1['Time']).abs().argsort()[:1]]
print(sim_t1_v3)

# Compare with experimental data at T_approx=2
print("\nExperimental Data (iteration_0) at T~2:")
exp_t2 = exp_data[exp_data['Time'] >= 2.0].iloc[0]
print(exp_t2)
print("\nSimulated Data (model_v3) at T~2:")
sim_t2_v3 = simulation_df_v3.iloc[(simulation_df_v3['Time']-exp_t2['Time']).abs().argsort()[:1]]
print(sim_t2_v3)

# Compare with experimental data at T_approx=12 (around first minimum for id_shpe, id_yiw5, id_55cy)
print("\nExperimental Data (iteration_0) at T~12:")
exp_t12 = exp_data[exp_data['Time'] >= 12.0].iloc[0] # experimental time point near 12
print(exp_t12)
print("\nSimulated Data (model_v3) at T~12:")
sim_t12_v3 = simulation_df_v3.iloc[(simulation_df_v3['Time']-exp_t12['Time']).abs().argsort()[:1]]
print(sim_t12_v3)

```
# Observation

## Code Stdout
SBML model_v3 created with R_A, R_B, R_C, R_D.

Simulating model_v3:
Simulation model_v3 head:
          id_shpe      id_55cy       id_yiw5       id_97q7      Time
0  1000000.000000     0.000000  7.000000e+06  1.000000e+08  0.000000
1   989071.535699   505.795422  6.699022e+06  1.007166e+08  0.033807
2   978279.225302   989.253142  6.410986e+06  1.014061e+08  0.067613
3   967620.841853  1451.184810  6.135335e+06  1.020695e+08  0.101420
4   957094.209217  1892.373998  5.871536e+06  1.027081e+08  0.135227

Experimental Data (iteration_0) at T~1:
id_shpe    7.270729e+05
id_55cy    1.509285e+04
id_yiw5    1.448171e+06
id_97q7    1.135763e+08
Time       1.014199e+00
Name: 30, dtype: float64

Simulated Data (model_v3) at T~1:
          id_shpe      id_55cy       id_yiw5       id_97q7      Time
30  723548.508551  8100.532655  1.872825e+06  1.132062e+08  1.014199

Experimental Data (iteration_0) at T~2:
id_shpe    5.264868e+05
id_55cy    1.108505e+04
id_yiw5    9.652980e+05
id_97q7    1.424605e+08
Time       2.028398e+00
Name: 60, dtype: float64

Simulated Data (model_v3) at T~2:
         id_shpe      id_55cy      id_yiw5       id_97q7      Time
59  533347.23701  8853.052715  523582.5108  1.179886e+08  1.994591

Experimental Data (iteration_0) at T~12:
id_shpe    3.431791e+04
id_55cy    1.958135e+03
id_yiw5    1.568635e+05
id_97q7    8.343848e+08
Time       1.200135e+01
Name: 355, dtype: float64

Simulated Data (model_v3) at T~12:
          id_shpe    id_55cy   id_yiw5       id_97q7       Time
355  25438.289884  558.56897  1.173315  1.247140e+08  12.001352

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 17/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 4
## Thoughts

The simulation results for `model_v3` (with `R_A, R_B, R_C, R_D` and updated parameters) are:

At T~1 (Experimental vs. Simulated `model_v3`):
*   `id_shpe`: 7.27e5 vs. 7.24e5 (Very good match)
*   `id_55cy`: 1.51e4 vs. 8.10e3 (Simulated is lower. Production by R_B might be too low, or consumption by R_D is too high/starts too early. Original `kB` was 0.0151, now 0.0153. `kD` is 1.0)
*   `id_yiw5`: 1.45e6 vs. 1.87e6 (Simulated is higher. Consumption by R_A (kA=1.3) is still a bit underestimated.)
*   `id_97q7`: 1.14e8 vs. 1.13e8 (Very good match)

At T~2 (Experimental vs. Simulated `model_v3`):
*   `id_shpe`: 5.26e5 vs. 5.33e5 (Good match)
*   `id_55cy`: 1.11e4 vs. 8.85e3 (Simulated is lower and has increased from T=1 (8.1e3 -> 8.85e3), while experimental decreased (1.51e4 -> 1.11e4). The model is capturing the decrease relative to a higher peak that would have occurred without R_D, but the absolute values and the timing of the peak are off.)
*   `id_yiw5`: 9.65e5 vs. 5.24e5 (Simulated is now lower. Consumption by R_A (kA=1.3) might be slightly overestimated for this interval, or the dynamics are more complex.)
*   `id_97q7`: 1.42e8 vs. 1.18e8 (Simulated is lower. Production is underestimated in this phase.)

At T~12 (Experimental vs. Simulated `model_v3`):
*   `id_shpe`: 3.43e4 vs. 2.54e4 (Simulated is lower. R_D producing `id_shpe` is active, but perhaps not enough, or `id_shpe` consumption is too high.)
*   `id_55cy`: 1.96e3 vs. 5.58e2 (Simulated is much lower. `id_55cy` is depleted too much by R_D.)
*   `id_yiw5`: 1.57e5 vs. 1.17e0 (Simulated `id_yiw5` is practically depleted! `kA=1.3` is too high for long term.)
*   `id_97q7`: 8.34e8 vs. 1.25e8 (Simulated `id_97q7` is vastly underestimated. This is a major issue.)

**Key issues from `model_v3`:**
1.  **`id_yiw5` depletion:** `kA=1.3` for `R_A: id_yiw5 -> 2 id_97q7` is too aggressive in the long run, leading to near-total depletion of `id_yiw5` by T=12, which is incorrect. Experimental `id_yiw5` is 1.57e5 at T=12. This means either `kA` needs to be smaller, or `id_yiw5` needs a production pathway.
2.  **`id_97q7` underproduction (long term):** The massive underestimation of `id_97q7` at T=12 (1.25e8 sim vs 8.34e8 exp) is critical. Since `id_yiw5` (a source for `id_97q7` via R_A) is depleted in the simulation, this is a major contributing factor. Also, `id_shpe` (another source via R_C) is lower in sim than exp.
3.  **`id_55cy` dynamics:** Simulated `id_55cy` is too low throughout (T=1, T=2, T=12). This suggests `kD=1.0` for `R_D: id_55cy -> id_shpe` might be too high, or `kB` (production from `id_shpe`) is too low. The experimental data shows `id_55cy` having a complex pattern (rise, fall, rise, fall). `model_v3` only has one rise (due to R_B) and one fall (due to R_D).

**Addressing `id_yiw5` depletion and `id_97q7` underproduction:**
*   The most straightforward way to prevent `id_yiw5` depletion and boost `id_97q7` is to ensure `id_yiw5` doesn't run out.
*   This implies `id_yiw5` needs a production mechanism.
*   Looking at the species that accumulate: `id_97q7`. Could `id_97q7` be involved in regenerating `id_yiw5`? Or perhaps `id_shpe`?
*   The experimental data shows `id_yiw5` decreases then *increases* (from T~12, 1.57e5, to T~28, 3.0e6), then decreases again. This *increase* phase needs to be modeled.
*   Similarly, `id_shpe` decreases then *increases* (from T~12, 3.43e4, to T~28, 3.39e5). `R_D: id_55cy -> id_shpe` contributes to this, but `id_55cy` itself is low in sim.

Let's hypothesize a reaction that produces `id_yiw5`.
What could be the source?
If `id_shpe` produces `id_yiw5`: `R_E: id_shpe -> id_yiw5`. This would further deplete `id_shpe`.
If `id_97q7` is involved: `R_E: id_97q7 -> id_yiw5`. This would consume the main product.
What about `id_55cy`? We have `R_D: id_55cy -> id_shpe`. Could `id_55cy` also produce `id_yiw5`?
`R_E: id_55cy -> id_yiw5` (rate `kE * [id_55cy]`).
This would mean `id_55cy` is a precursor to both `id_shpe` and `id_yiw5`.
If this is the case, `kD` (for `id_55cy -> id_shpe`) might need to be adjusted, or `kE` is a new parameter.
The consumption of `id_55cy` would be `(kD+kE)*[id_55cy]`.

Let's consider the period T=12 to T=28 for `id_yiw5` recovery.
`id_yiw5` goes from ~1.6e5 (T=12) to ~3.0e6 (T=28). Increase of ~2.8e6 over 16 days. Avg rate ~1.75e5/day.
During this time, `id_55cy` (exp) goes from ~2e3 (T=12) up to ~3.7e4 (T=28) and then down.
So, `id_55cy` is *increasing* when `id_yiw5` is increasing. This makes `id_55cy -> id_yiw5` less likely to be the sole driver of `id_yiw5` increase, unless `id_55cy` production (from `R_B: id_shpe -> id_55cy`) is very high.

What if `id_97q7` is involved in a reversible reaction or a feedback loop?
The problem states "You do not need to add new species."
Perhaps one of the existing reactions is reversible.
`R_A: id_yiw5 <=> 2 id_97q7`? If it's reversible, then high `id_97q7` could drive production of `id_yiw5`.
This is a common biological motif. Let's explore making `R_A` reversible.
`R_A_fwd: id_yiw5 -> 2 id_97q7` (rate `kA_f * [id_yiw5]`)
`R_A_rev: 2 id_97q7 -> id_yiw5` (rate `kA_r * [id_97q7]^2`)
Net rate for `R_A`: `kA_f * [id_yiw5] - kA_r * [id_97q7]^2`.
Previously, `kA` was `kA_f = 1.3`.
If `R_A` is reversible, then at T=12, when `id_yiw5` is low (exp: 1.57e5) and `id_97q7` is high (exp: 8.34e8), the reverse reaction could become significant.
`kA_f * 1.57e5 - kA_r * (8.34e8)^2`.
If `id_yiw5` is to be produced, then `kA_r * (8.34e8)^2 > kA_f * 1.57e5`.
`kA_r * 7e17 > 1.3 * 1.57e5 = 2.04e5`.
`kA_r > 2.04e5 / 7e17 = ~3e-13`.

This reversibility would naturally limit `id_yiw5` depletion and allow its recovery when `id_97q7` is high. It would also reduce net `id_97q7` production at high `id_97q7` levels, potentially helping to match its curve better.

**Adjusting `id_55cy` levels:**
Simulated `id_55cy` is too low.
`d[id_55cy]/dt = kB*[id_shpe] - kD*[id_55cy]`.
To increase `[id_55cy]`, we can increase `kB` or decrease `kD`.
At T=1, exp `[id_55cy]`=1.51e4, sim=8.1e3.
At T=2, exp `[id_55cy]`=1.11e4, sim=8.85e3.
At T=12, exp `[id_55cy]`=1.96e3, sim=5.58e2.
The ratio exp/sim is roughly 2-3.
If we decrease `kD` (consumption of `id_55cy`), say from 1.0 to 0.3-0.5.
Let's try `kD = 0.4`.
This would also mean that `id_shpe` production from `R_D` is slower, which might make simulated `id_shpe` lower, which is already a bit low at T=12.

Let's try `model_v4` with:
1.  `R_A: id_yiw5 <=> 2 id_97q7`. `kA_f = 1.3`. Need to choose `kA_r`.
    Let's aim for equilibrium when `id_yiw5` is around its trough (e.g., 1e5) and `id_97q7` is high (e.g., 1e9).
    `kA_f * 1e5 = kA_r * (1e9)^2`.
    `1.3 * 1e5 = kA_r * 1e18`.
    `kA_r = 1.3e5 / 1e18 = 1.3e-13`. This is a plausible magnitude.
2.  `R_B: id_shpe -> id_55cy` (`kB = 0.0153`). Keep for now.
3.  `R_C: id_shpe -> 11 id_97q7` (`kC = 0.31`). Keep for now.
4.  `R_D: id_55cy -> id_shpe` (`kD`). Let's reduce `kD` from `1.0` to `0.4` to try and raise `id_55cy` levels.

Recalculating `kB` and `kC` might be needed if `kD` changes significantly, as they were derived assuming `kD=1.0`.
Original derivation for `kB` (from `d[id_55cy]/dt`):
`kB * [id_shpe_T1] - kD_new * [id_55cy_T1] = -4e3` (target rate at T=1).
`kB * 7.27e5 - 0.4 * 1.51e4 = -4e3`.
`kB * 7.27e5 = 0.4 * 1.51e4 - 4e3 = 6.04e3 - 4e3 = 2.04e3`.
`kB = 2.04e3 / 7.27e5 = 0.0028`. This is much lower than `0.0153`.
This means if `kD` is reduced, `kB` must also be reduced to match the `id_55cy` decline. This would further lower `id_55cy` levels, which is counterproductive.

This suggests that the issue with `id_55cy` might not be a simple `kD` adjustment, or the initial rate calculation was flawed.
The experimental `id_55cy` at T=1 is 1.51e4. At T=2 it's 1.11e4.
Simulated `id_55cy` at T=1 is 8.1e3.
If `kB` is what produces `id_55cy`, and `[id_shpe]` at T=1 is ~7.2e5 (sim and exp match well).
Production rate of `id_55cy` via R_B at T=1 (sim) = `0.0153 * 7.23e5 = 1.10e4`.
Consumption rate of `id_55cy` via R_D at T=1 (sim) = `1.0 * 8.10e3 = 8.10e3`.
Net `d[id_55cy]/dt` (sim, T=1) = `1.10e4 - 8.10e3 = 2.9e3`. (Positive, so `id_55cy` is increasing).
Experimental `d[id_55cy]/dt` (T=1 to T=2) = `(1.11e4 - 1.51e4)/1 = -4e3`. (Negative).
The model has the wrong sign for `d[id_55cy]/dt` at T=1.

To get `d[id_55cy]/dt` negative at T=1, with `[id_shpe]`~7.2e5 and `[id_55cy]`~1.5e4 (target exp values):
`kB * 7.2e5 - kD * 1.5e4 = -4e3`.
If `kB = 0.0153`, then `0.0153 * 7.2e5 - kD * 1.5e4 = -4e3`.
`1.10e4 - kD * 1.5e4 = -4e3`.
`kD * 1.5e4 = 1.10e4 + 4e3 = 1.5e4`.
`kD = 1.0`. This was the value used.
So, why is simulated `[id_55cy]` at T=1 (8.1e3) lower than experimental (1.51e4)?
It must be that `id_55cy` didn't accumulate enough by T=1. This means `kB` might be too low for the *initial phase* (T=0 to T=1), or `kD` kicks in too strongly/early.

The problem is that `id_55cy` shows complex dynamics:
1. Initial rise (T=0 to T=1, from 0 to 1.51e4).
2. Fall (T=1 to T=12, from 1.51e4 to 1.96e3).
3. Rise again (T=12 to T=28, from 1.96e3 to 3.7e4).
4. Fall again (T=28 onwards).

Current model `R_B: S->C`, `R_D: C->S`. This can create a peak, but not multiple oscillations without S also oscillating significantly.
`id_shpe` (S) does oscillate (fall, rise, fall).
`R_D` (C->S) contributes to S rise.
The second rise of `id_55cy` (T=12 to T=28) happens when `id_shpe` is also rising (T=12 to T=28). This is consistent with `R_B: id_shpe -> id_55cy`.
The parameters `kB` and `kD` likely need fine-tuning.

Let's focus on `R_A` reversibility first, as `id_yiw5` depletion and `id_97q7` underproduction are major issues.
`kA_f = 1.3`, `kA_r = 1.3e-13`.
Keep `kB=0.0153`, `kC=0.31`, `kD=1.0` for now, and see how `R_A` reversibility impacts the system.

Plan for `model_v4`:
1.  Modify `R_A` to be reversible: `id_yiw5 <=> 2 id_97q7`
    *   Forward rate: `kA_f * id_yiw5` with `kA_f = 1.3`
    *   Reverse rate: `kA_r * id_97q7 * id_97q7` with `kA_r = 1.3e-13`
2.  Keep `R_B: id_shpe -> id_55cy` with `kB = 0.0153`.
3.  Keep `R_C: id_shpe -> 11 id_97q7` with `kC = 0.31`.
4.  Keep `R_D: id_55cy -> id_shpe` with `kD = 1.0`.

This change primarily addresses `id_yiw5` and `id_97q7` long-term behavior. We can then re-evaluate `id_55cy` and `id_shpe`.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model
doc_v4 = libsbml.readSBMLFromString(input_sbml_string) # Start from the base model
model_v4 = doc_v4.getModel()

# Parameters for model_v4
kA_f_v4 = 1.3
kA_r_v4 = 1.3e-13 # New parameter for reversible R_A
kB_v4 = 0.0153
kC_v4 = 0.31
kD_v4 = 1.0

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v4.createReaction()
r_a.setId("R_A")
r_a.setReversible(True) # Set to reversible
r_a.setFast(False)
# Reactant for forward, Product for reverse
reactant_ra = r_a.createReactant(); reactant_ra.setSpecies("id_yiw5"); reactant_ra.setStoichiometry(1); reactant_ra.setConstant(False)
# Product for forward, Reactant for reverse
product_ra = r_a.createProduct(); product_ra.setSpecies("id_97q7"); product_ra.setStoichiometry(2); product_ra.setConstant(False)
# Kinetic Law
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v4)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v4)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v4.createReaction()
r_b.setId("R_B")
r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v4)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v4.createReaction()
r_c.setId("R_C")
r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v4)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v4.createReaction()
r_d.setId("R_D")
r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v4)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml_v4 = writer.writeSBMLToString(doc_v4)
shared_variables.add("model_v4_sbml", updated_sbml_v4)
print("SBML model_v4 created with R_A (reversible), R_B, R_C, R_D.")

# Simulate the model_v4
print("\nSimulating model_v4:")
simulation_df_v4 = simulate(updated_sbml_v4)
shared_variables.add("simulation_df_v4", simulation_df_v4)

# Compare with experimental data at T_approx=1, T_approx=2, T_approx=12, and T_approx=28 (new point for recovery phase)
print_comparison = lambda name, time_point, exp_df, sim_df: (
    print(f"\nExperimental Data (iteration_0) at T~{name}:"),
    exp_t = exp_df[exp_df['Time'] >= time_point].iloc[0],
    print(exp_t),
    print(f"\nSimulated Data (model_v4) at T~{name}:"),
    sim_t = sim_df.iloc[(sim_df['Time'] - exp_t['Time']).abs().argsort()[:1]],
    print(sim_t)
)

print_comparison("1", 1.0, exp_data, simulation_df_v4)
print_comparison("2", 2.0, exp_data, simulation_df_v4)
print_comparison("12", 12.0, exp_data, simulation_df_v4)
print_comparison("28", 28.0, exp_data, simulation_df_v4) # Check recovery phase
print_comparison("50", 50.0, exp_data, simulation_df_v4) # Check end phase

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model
doc_v4 = libsbml.readSBMLFromString(input_sbml_string) # Start from the base model
model_v4 = doc_v4.getModel()

# Parameters for model_v4
kA_f_v4 = 1.3
kA_r_v4 = 1.3e-13 # New parameter for reversible R_A
kB_v4 = 0.0153
kC_v4 = 0.31
kD_v4 = 1.0

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v4.createReaction()
r_a.setId("R_A")
r_a.setReversible(True) # Set to reversible
r_a.setFast(False)
# Reactant for forward, Product for reverse
reactant_ra = r_a.createReactant(); reactant_ra.setSpecies("id_yiw5"); reactant_ra.setStoichiometry(1); reactant_ra.setConstant(False)
# Product for forward, Reactant for reverse
product_ra = r_a.createProduct(); product_ra.setSpecies("id_97q7"); product_ra.setStoichiometry(2); product_ra.setConstant(False)
# Kinetic Law
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v4)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v4)
# SBML L3 Formula for reversible mass action: k_f * S1*S2... - k_r * P1*P2...
# For R_A: kA_f * id_yiw5 - kA_r * id_97q7^2
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))


# Reaction R_B: id_shpe -> id_55cy
r_b = model_v4.createReaction()
r_b.setId("R_B")
r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v4)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v4.createReaction()
r_c.setId("R_C")
r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v4)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v4.createReaction()
r_d.setId("R_D")
r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v4)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml_v4 = writer.writeSBMLToString(doc_v4)
shared_variables.add("model_v4_sbml", updated_sbml_v4)
print("SBML model_v4 created with R_A (reversible), R_B, R_C, R_D.")

# Simulate the model_v4
print("\nSimulating model_v4:")
simulation_df_v4 = simulate(updated_sbml_v4)
shared_variables.add("simulation_df_v4", simulation_df_v4)

# Helper for printing comparison
def print_comparison_point(name, time_val, exp_df, sim_df):
    print(f"\n--- Comparison at T ~ {name} ---")
    # Find closest experimental data point
    exp_point = exp_df.iloc[(exp_df['Time'] - time_val).abs().argsort()[:1]].squeeze()
    print("Experimental Data:")
    print(exp_point[['Time', 'id_shpe', 'id_55cy', 'id_yiw5', 'id_97q7']])
    
    # Find closest simulation data point to the *experimental* time
    sim_point = sim_df.iloc[(sim_df['Time'] - exp_point['Time']).abs().argsort()[:1]].squeeze()
    print("\nSimulated Data (model_v4):")
    print(sim_point[['Time', 'id_shpe', 'id_55cy', 'id_yiw5', 'id_97q7']])

print_comparison_point("1.0", 1.0, exp_data, simulation_df_v4)
print_comparison_point("2.0", 2.0, exp_data, simulation_df_v4)
print_comparison_point("12.0", 12.0, exp_data, simulation_df_v4)
print_comparison_point("28.0", 28.0, exp_data, simulation_df_v4) 
print_comparison_point("50.0", 50.0, exp_data, simulation_df_v4)

```
# Observation

## Code Stderror
 Syntax error in code: invalid syntax. Maybe you meant '==' or ':=' instead of '='? (<unknown>, line 77)

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 16/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 5
## Thoughts
It seems I made a syntax error in my previous Python code block, specifically in the `print_comparison_point` helper function. The line `exp_point = exp_df.iloc[(exp_df['Time'] - time_val).abs().argsort()[:1]].squeeze()` and similar lines for `sim_point` are correct, but the error message "Syntax error in code: invalid syntax. Maybe you meant '==' or ':=' instead of '='? (<unknown>, line 77)" usually points to an issue with assignment within a lambda or an unexpected keyword.

Looking back at the previous code, the `print_comparison` lambda function was:
```python
# print_comparison = lambda name, time_point, exp_df, sim_df: (
# print(f"\nExperimental Data (iteration_0) at T~{name}:"),
# exp_t = exp_df[exp_df['Time'] >= time_point].iloc[0],  # This assignment within lambda tuple is problematic
# print(exp_t),
# print(f"\nSimulated Data (model_v4) at T~{name}:"),
# sim_t = sim_df.iloc[(sim_df['Time'] - exp_t['Time']).abs().argsort()[:1]], # Also problematic
# print(sim_t)
# )
```
Assignments (`exp_t = ...`) are not allowed directly inside a lambda like that if it's part of a tuple of expressions meant to be returned or executed for side effects. I then changed it to a full `def` function `print_comparison_point` in the action block, which should be fine.

The error message points to line 77. Let's count the lines in the previous *action* block's code:
```python
# ... (lines 1-57 are SBML model setup) ...
# print("SBML model_v4 created with R_A (reversible), R_B, R_C, R_D.") # Line 58

# print("\nSimulating model_v4:") # Line 61
# simulation_df_v4 = simulate(updated_sbml_v4) # Line 62
# shared_variables.add("simulation_df_v4", simulation_df_v4) # Line 63

# Helper for printing comparison
# def print_comparison_point(name, time_val, exp_df, sim_df): # Line 66
#     print(f"\n--- Comparison at T ~ {name} ---") # Line 67
#     # Find closest experimental data point
#     exp_point = exp_df.iloc[(exp_df['Time'] - time_val).abs().argsort()[:1]].squeeze() # Line 69
#     print("Experimental Data:") # Line 70
#     print(exp_point[['Time', 'id_shpe', 'id_55cy', 'id_yiw5', 'id_97q7']]) # Line 71
    
#     # Find closest simulation data point to the *experimental* time
#     sim_point = sim_df.iloc[(sim_df['Time'] - exp_point['Time']).abs().argsort()[:1]].squeeze() # Line 74
#     print("\nSimulated Data (model_v4):") # Line 75
#     print(sim_point[['Time', 'id_shpe', 'id_55cy', 'id_yiw5', 'id_97q7']]) # Line 76

# print_comparison_point("1.0", 1.0, exp_data, simulation_df_v4) # Line 78
# print_comparison_point("2.0", 2.0, exp_data, simulation_df_v4) # Line 79
# print_comparison_point("12.0", 12.0, exp_data, simulation_df_v4) # Line 80
# print_comparison_point("28.0", 28.0, exp_data, simulation_df_v4) # Line 81
# print_comparison_point("50.0", 50.0, exp_data, simulation_df_v4) # Line 82
```
Line 77 is blank in this reconstruction. The error message might be off by one, or there's an invisible character.
The most likely culprit is still related to how I defined or called the helper function.
The structure of `def print_comparison_point(...)` seems fine.

Let me re-check the `libsbml.parseL3Formula` for the reversible reaction:
`kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))`
This looks correct for a reversible mass-action reaction.

Perhaps the issue was an indentation error or a subtle syntax problem not immediately obvious.
I will resubmit the same code for `model_v4` construction and simulation, paying close attention to the helper function definition and its calls. I will ensure the helper function is defined correctly at the top level of the script or within a scope where it can be properly called.

The plan for `model_v4` remains the same:
1.  Modify `R_A` to be reversible: `id_yiw5 <=> 2 id_97q7`
    *   Forward rate: `kA_f * id_yiw5` with `kA_f = 1.3`
    *   Reverse rate: `kA_r * id_97q7 * id_97q7` with `kA_r = 1.3e-13`
2.  Keep `R_B: id_shpe -> id_55cy` with `kB = 0.0153`.
3.  Keep `R_C: id_shpe -> 11 id_97q7` with `kC = 0.31`.
4.  Keep `R_D: id_55cy -> id_shpe` with `kD = 1.0`.

I will simplify the printing part slightly to ensure no complex calls are causing issues, just printing heads of dataframes or specific rows after simulation.

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model
doc_v4 = libsbml.readSBMLFromString(input_sbml_string) # Start from the base model
model_v4 = doc_v4.getModel()

# Parameters for model_v4
kA_f_v4 = 1.3
kA_r_v4 = 1.3e-13 # New parameter for reversible R_A
kB_v4 = 0.0153
kC_v4 = 0.31
kD_v4 = 1.0

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v4.createReaction()
r_a.setId("R_A")
r_a.setReversible(True) # Set to reversible
r_a.setFast(False)
# Reactant for forward, Product for reverse
reactant_ra_yiw5 = r_a.createReactant()
reactant_ra_yiw5.setSpecies("id_yiw5")
reactant_ra_yiw5.setStoichiometry(1)
reactant_ra_yiw5.setConstant(False)
# Product for forward, Reactant for reverse
product_ra_97q7 = r_a.createProduct()
product_ra_97q7.setSpecies("id_97q7")
product_ra_97q7.setStoichiometry(2)
product_ra_97q7.setConstant(False)
# Kinetic Law
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter()
param_kaf.setId("kA_f")
param_kaf.setValue(kA_f_v4)
param_kar = kl_ra.createLocalParameter()
param_kar.setId("kA_r")
param_kar.setValue(kA_r_v4)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))


# Reaction R_B: id_shpe -> id_55cy
r_b = model_v4.createReaction()
r_b.setId("R_B")
r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v4)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v4.createReaction()
r_c.setId("R_C")
r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v4)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v4.createReaction()
r_d.setId("R_D")
r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v4)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml_v4 = writer.writeSBMLToString(doc_v4)
shared_variables.add("model_v4_sbml", updated_sbml_v4)
print("SBML model_v4 created with R_A (reversible), R_B, R_C, R_D.")

# Simulate the model_v4
print("\nSimulating model_v4:")
simulation_df_v4 = simulate(updated_sbml_v4)
shared_variables.add("simulation_df_v4", simulation_df_v4)
print("Simulation model_v4 head:")
print(simulation_df_v4.head())
print("Simulation model_v4 tail:")
print(simulation_df_v4.tail())


# Helper for printing comparison
def print_comparison_at_time(label, target_time_val, exp_df, sim_df):
    print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
    
    # Find closest experimental data point to target_time_val
    exp_point = exp_df.iloc[(exp_df['Time'] - target_time_val).abs().argsort()[:1]].squeeze()
    # Ensure exp_point is a Series, not DataFrame (squeeze might not be enough if only 1 row matched exactly)
    if isinstance(exp_point, pd.DataFrame):
        exp_point = exp_point.iloc[0]
        
    print("Experimental Data (closest to target time):")
    print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
    
    # Find closest simulation data point to the *actual experimental time*
    sim_point = sim_df.iloc[(sim_df['Time'] - exp_point['Time']).abs().argsort()[:1]].squeeze()
    if isinstance(sim_point, pd.DataFrame):
        sim_point = sim_point.iloc[0]

    print("Simulated Data (model_v4, closest to exp. time):")
    print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

# Perform comparisons at specified time points
time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
for label, time_val in time_points_to_compare.items():
    print_comparison_at_time(label, time_val, exp_data, simulation_df_v4)

```
# Observation

## Code Stdout
## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 15/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 6
## Thoughts
It appears my code executed without syntax errors this time, but no output was printed to the console. This usually means either the simulation failed silently, or the print statements were not reached or did not produce output for some reason. The `simulate` function might return an empty DataFrame or raise an exception that's caught by the environment.

Given that the previous error was a syntax error and this time there's no error but also no output, it's possible the simulation itself is having issues with the `model_v4` SBML string, perhaps due to the reversible reaction or parameter values leading to instability or very fast dynamics that the solver struggles with.

The `shared_variables` should contain `model_v4_sbml` and `simulation_df_v4` if the simulation call completed. If `simulation_df_v4` is empty or malformed, the subsequent print calls would either fail or print nothing useful.

Let's try to debug this by:
1.  Printing the `model_v4_sbml` string to ensure it's generated correctly.
2.  Checking if `simulation_df_v4` exists in `shared_variables` and printing its info if it does.
3.  If the simulation is indeed failing, I might need to simplify the model changes or adjust parameters. The reversibility with a squared term (`id_97q7^2`) and very small `kA_r` (1.3e-13) combined with a large `kA_f` (1.3) could potentially cause stiffness or numerical issues if concentrations vary wildly.

Let's first verify the SBML string and the result of the simulation.

The plan for `model_v4` was:
1.  `R_A: id_yiw5 <=> 2 id_97q7` (Reversible: `kA_f * id_yiw5 - kA_r * id_97q7^2`)
    *   `kA_f = 1.3`
    *   `kA_r = 1.3e-13`
2.  `R_B: id_shpe -> id_55cy` (`kB * id_shpe`), `kB = 0.0153`
3.  `R_C: id_shpe -> 11 id_97q7` (`kC * id_shpe`), `kC = 0.31`
4.  `R_D: id_55cy -> id_shpe` (`kD * id_55cy`), `kD = 1.0`

If the SBML string is fine, the issue is likely with the simulation process for this specific model.
I will add print statements to check the SBML string and the simulation output dataframe directly.

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v4)
doc_v4 = libsbml.readSBMLFromString(input_sbml_string) 
model_v4 = doc_v4.getModel()

# Parameters for model_v4
kA_f_v4 = 1.3
kA_r_v4 = 1.3e-13 
kB_v4 = 0.0153
kC_v4 = 0.31
kD_v4 = 1.0

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v4.createReaction()
r_a.setId("R_A")
r_a.setReversible(True) 
r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant()
reactant_ra_yiw5.setSpecies("id_yiw5")
reactant_ra_yiw5.setStoichiometry(1)
reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct()
product_ra_97q7.setSpecies("id_97q7")
product_ra_97q7.setStoichiometry(2)
product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter()
param_kaf.setId("kA_f")
param_kaf.setValue(kA_f_v4)
param_kar = kl_ra.createLocalParameter()
param_kar.setId("kA_r")
param_kar.setValue(kA_r_v4)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v4.createReaction()
r_b.setId("R_B")
r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v4)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v4.createReaction()
r_c.setId("R_C")
r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v4)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v4.createReaction()
r_d.setId("R_D")
r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v4)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

writer = libsbml.SBMLWriter()
updated_sbml_v4 = writer.writeSBMLToString(doc_v4)
shared_variables.add("model_v4_sbml", updated_sbml_v4)
print("SBML model_v4 created.")
# print("Model_v4 SBML string (first 500 chars):") # Potentially too long for stdout
# print(updated_sbml_v4[:500])

print("\nAttempting to simulate model_v4...")
try:
    simulation_df_v4 = simulate(updated_sbml_v4)
    shared_variables.add("simulation_df_v4", simulation_df_v4)
    print("Simulation of model_v4 completed.")
    if simulation_df_v4 is not None and not simulation_df_v4.empty:
        print("Simulation model_v4 head:")
        print(simulation_df_v4.head())
        print("Simulation model_v4 tail:")
        print(simulation_df_v4.tail())
        
        # Helper for printing comparison (re-defined for safety)
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_point = exp_df.iloc[(exp_df['Time'] - target_time_val).abs().argsort()[:1]].squeeze()
            if isinstance(exp_point, pd.DataFrame): exp_point = exp_point.iloc[0]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_point = sim_df_local.iloc[(sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1]].squeeze()
            if isinstance(sim_point, pd.DataFrame): sim_point = sim_point.iloc[0]
            print("Simulated Data (model_v4, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v4)
    else:
        print("Simulation_df_v4 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing: {e}")
    import traceback
    print(traceback.format_exc())

# Check shared_variables content
print("\nChecking shared_variables:")
if shared_variables.access("model_v4_sbml") is not None:
    print("model_v4_sbml is in shared_variables.")
else:
    print("model_v4_sbml is NOT in shared_variables.")

if shared_variables.access("simulation_df_v4") is not None:
    print("simulation_df_v4 is in shared_variables.")
    # Try to access and print info if it exists from a previous (failed) attempt
    # sim_df_check = shared_variables.access("simulation_df_v4")
    # if sim_df_check is not None:
    #    print("Info for existing simulation_df_v4 in shared_variables:")
    #    sim_df_check.info(verbose=True, show_counts=True) # This might be too verbose
    #    print(sim_df_check.head())

else:
    print("simulation_df_v4 is NOT in shared_variables (after this attempt).")

```
# Observation

## Code Stdout
SBML model_v4 created.

Attempting to simulate model_v4...
Simulation of model_v4 completed.
Simulation model_v4 head:
          id_shpe      id_55cy       id_yiw5       id_97q7      Time
0  1000000.000000     0.000000  7.000000e+06  1.000000e+08  0.000000
1   989071.535699   505.795422  6.699065e+06  1.007165e+08  0.033807
2   978279.225302   989.253142  6.411071e+06  1.014059e+08  0.067613
3   967620.841853  1451.184810  6.135461e+06  1.020693e+08  0.101420
4   957094.209217  1892.373998  5.871702e+06  1.027077e+08  0.135227
Simulation model_v4 tail:
       id_shpe   id_55cy      id_yiw5       id_97q7       Time
1475  0.261490  0.005743  1562.421784  1.249969e+08  49.864773
1476  0.258822  0.005684  1562.421785  1.249969e+08  49.898580
1477  0.256181  0.005626  1562.421786  1.249969e+08  49.932387
1478  0.253568  0.005569  1562.421787  1.249969e+08  49.966193
1479  0.250981  0.005512  1562.421788  1.249969e+08  50.000000

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v4, closest to exp. time):
Time: 1.01, shpe: 7.24e+05, 55cy: 8.10e+03, yiw5: 1.87e+06, 97q7: 1.13e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v4, closest to exp. time):
Time: 1.99, shpe: 5.33e+05, 55cy: 8.85e+03, yiw5: 5.25e+05, 97q7: 1.18e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v4, closest to exp. time):
Time: 12.00, shpe: 2.54e+04, 55cy: 5.59e+02, yiw5: 1.55e+03, 97q7: 1.25e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v4, closest to exp. time):
Time: 27.99, shpe: 1.99e+02, 55cy: 4.37e+00, yiw5: 1.56e+03, 97q7: 1.25e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v4, closest to exp. time):
Time: 50.00, shpe: 2.51e-01, 55cy: 5.51e-03, yiw5: 1.56e+03, 97q7: 1.25e+08

Checking shared_variables:
model_v4_sbml is in shared_variables.
simulation_df_v4 is in shared_variables.

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 14/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 7
## Thoughts

The simulation for `model_v4` (with reversible `R_A`) ran successfully this time, and we have output.

Let's analyze the results for `model_v4`:
Parameters: `kA_f=1.3`, `kA_r=1.3e-13`, `kB=0.0153`, `kC=0.31`, `kD=1.0`.

At T~1:
*   `id_shpe`: Exp 7.27e5, Sim 7.24e5 (Good)
*   `id_55cy`: Exp 1.51e4, Sim 8.10e3 (Sim low)
*   `id_yiw5`: Exp 1.45e6, Sim 1.87e6 (Sim high, R_A forward rate might still be a bit low, or reverse not kicking in yet)
*   `id_97q7`: Exp 1.14e8, Sim 1.13e8 (Good)

At T~2:
*   `id_shpe`: Exp 5.32e5, Sim 5.33e5 (Good)
*   `id_55cy`: Exp 1.12e4, Sim 8.85e3 (Sim low, and trend issue remains - exp decreasing, sim increasing from T=1)
*   `id_yiw5`: Exp 9.75e5, Sim 5.25e5 (Sim low, R_A forward rate might be too high for this phase, or reverse not strong enough)
*   `id_97q7`: Exp 1.41e8, Sim 1.18e8 (Sim low)

At T~12:
*   `id_shpe`: Exp 3.43e4, Sim 2.54e4 (Sim low)
*   `id_55cy`: Exp 1.96e3, Sim 5.59e2 (Sim very low)
*   `id_yiw5`: Exp 1.57e5, Sim 1.55e3 (Sim very low! Reversibility of R_A did not prevent depletion as much as hoped. `id_yiw5` is ~100x lower in sim.)
*   `id_97q7`: Exp 8.34e8, Sim 1.25e8 (Sim vastly underestimated. This is linked to `id_yiw5` depletion.)

At T~28:
*   `id_shpe`: Exp 3.32e5, Sim 1.99e2 (Sim extremely low. Experimental `id_shpe` has recovered significantly.)
*   `id_55cy`: Exp 3.76e4, Sim 4.37e0 (Sim extremely low. Experimental `id_55cy` has recovered significantly.)
*   `id_yiw5`: Exp 3.02e6, Sim 1.56e3 (Sim extremely low. Experimental `id_yiw5` has recovered significantly.)
*   `id_97q7`: Exp 1.02e9, Sim 1.25e8 (Sim vastly underestimated.)

At T~50:
*   `id_shpe`: Exp 7.94e4, Sim 2.51e-1 (Sim effectively zero.)
*   `id_55cy`: Exp 8.35e3, Sim 5.51e-3 (Sim effectively zero.)
*   `id_yiw5`: Exp 6.59e5, Sim 1.56e3 (Sim extremely low.)
*   `id_97q7`: Exp 1.03e9, Sim 1.25e8 (Sim vastly underestimated.)

**Conclusions from `model_v4`:**
1.  **Reversible `R_A` (id_yiw5 <=> 2 id_97q7):** The chosen `kA_r = 1.3e-13` was not effective enough to prevent `id_yiw5` depletion or to significantly boost its levels during the recovery phase (T>12). `id_yiw5` still crashes to very low levels (1.5e3), and `id_97q7` plateaus at a much lower level (1.25e8) than observed (1e9).
    *   The reverse rate `kA_r * [id_97q7]^2` needs to be stronger, or the forward rate `kA_f * [id_yiw5]` needs to be weaker, especially when `[id_yiw5]` is low.
    *   At T=12 (sim): `[id_yiw5]`=1.55e3, `[id_97q7]`=1.25e8.
        *   Forward flux of R_A: `1.3 * 1.55e3 = 2.015e3`.
        *   Reverse flux of R_A: `1.3e-13 * (1.25e8)^2 = 1.3e-13 * 1.5625e16 = 2.03e3`.
        *   The fluxes are nearly balanced at this low `id_yiw5` level, effectively stalling `id_yiw5` at ~1.5e3 and `id_97q7` at ~1.25e8. This is far from the experimental values.
    *   To get `id_yiw5` to recover to experimental levels (e.g., 1.57e5 at T=12, or 3e6 at T=28), the reverse reaction needs to dominate significantly when `id_yiw5` is low.
    *   If `[id_yiw5]` is 1.5e3 and `[id_97q7]` is 1e9 (target exp level for `id_97q7`), reverse flux should be much larger than forward.
        *   `kA_r * (1e9)^2 = kA_r * 1e18`.
        *   `kA_f * 1.5e3 = 1.3 * 1.5e3 = 1.95e3`.
        *   We need `kA_r * 1e18 >> 1.95e3`.
        *   If `kA_r` was, say, `1e-14` instead of `1.3e-13`, reverse flux would be `1e-14 * 1e18 = 1e4`. This is larger.
        *   The previous `kA_r` was derived to balance at `id_yiw5=1e5, id_97q7=1e9`. `1.3 * 1e5 = kA_r * (1e9)^2 => kA_r = 1.3e-13`. This should have led to `id_yiw5` stabilizing around 1e5 if `id_97q7` reached 1e9. But `id_97q7` never got that high.

2.  **`id_shpe`, `id_55cy` depletion:** These species also crash to near-zero levels in the simulation long-term, while they show recovery and sustained levels in experiments. This indicates that their production mechanisms (`R_D: id_55cy -> id_shpe` for `id_shpe`, and `R_B: id_shpe -> id_55cy` for `id_55cy`) are insufficient or their consumption is too high. Since `id_shpe` is a reactant for `id_55cy` production, and `id_55cy` for `id_shpe` production, they are coupled. If one crashes, the other likely will too.

**Strategy for `model_v5`:**

*   **Focus on `R_A` (id_yiw5 <=> 2 id_97q7):**
    *   The system needs to allow `id_97q7` to reach much higher levels (~1e9).
    *   The reverse reaction `2 id_97q7 -> id_yiw5` must become dominant enough to replenish `id_yiw5` to levels like 1e5-1e6 when `id_97q7` is high.
    *   Let's try to make `kA_r` larger. If `kA_r` is too large, `id_97q7` might not accumulate enough.
    *   Consider the equilibrium `K_eq = kA_f / kA_r = [id_97q7]^2 / [id_yiw5]`.
    *   At T=28 (exp): `[id_yiw5]`=3.02e6, `[id_97q7]`=1.02e9.
        *   `K_eq_target = (1.02e9)^2 / 3.02e6 = 1.04e18 / 3.02e6 = 3.44e11`.
    *   Current `kA_f = 1.3`. So, `kA_r_new = kA_f / K_eq_target = 1.3 / 3.44e11 = 3.78e-12`.
    *   This new `kA_r` (3.78e-12) is about 30 times larger than the previous `kA_r` (1.3e-13). This should make the reverse reaction much stronger.

*   **Addressing `id_shpe` and `id_55cy`:**
    *   Their crash is likely linked to `id_shpe` being consumed by `R_B` and `R_C`, and `id_55cy` by `R_D`.
    *   `R_C: id_shpe -> 11 id_97q7` (with `kC=0.31`) is a major drain on `id_shpe`. If `id_97q7` levels are higher due to changes in `R_A`, this might indirectly affect `id_shpe`.
    *   The parameters `kB=0.0153` (for `id_shpe -> id_55cy`) and `kD=1.0` (for `id_55cy -> id_shpe`) define a cycle.
    *   Experimental `id_shpe` recovers to ~3e5 and `id_55cy` to ~3e4 around T=28.
    *   Simulated values are near zero.
    *   Perhaps the rate of `id_shpe` consumption by `R_C` (`kC * id_shpe`) is too high in the long run when `id_shpe` levels are meant to be low but non-zero.
    *   Or, the production of `id_shpe` via `R_D` (`kD * id_55cy`) is too weak because `id_55cy` itself crashes.

    *   Let's re-evaluate `kD`. If `kD` is too high, `id_55cy` is depleted quickly. If `kD` is too low, `id_shpe` doesn't recover.
    *   The experimental ratio `[id_shpe]/[id_55cy]` during their recovery phase (e.g., T=28) is `3.32e5 / 3.76e4 ~ 8.8`.
    *   In a pseudo-steady state for `id_55cy -> id_shpe` and `id_shpe -> id_55cy` (ignoring `R_C` for a moment):
        `d[id_55cy]/dt = kB*[id_shpe] - kD*[id_55cy] = 0 => kB*[id_shpe] = kD*[id_55cy]`
        `[id_shpe]/[id_55cy] = kD/kB`.
        So, `kD/kB ~ 8.8`. With `kB=0.0153`, this implies `kD ~ 8.8 * 0.0153 = 0.1346`.
        This is much lower than the current `kD=1.0`.
    *   If `kD` is reduced to ~0.13, `id_55cy` might survive longer and build up, which in turn would help `id_shpe` build up.

Let's try `model_v5` with:
1.  `R_A: id_yiw5 <=> 2 id_97q7`. `kA_f = 1.3`, `kA_r = 3.8e-12` (increased from 1.3e-13).
2.  `R_B: id_shpe -> id_55cy`. `kB = 0.0153` (keep for now).
3.  `R_C: id_shpe -> 11 id_97q7`. `kC = 0.31` (keep for now).
4.  `R_D: id_55cy -> id_shpe`. `kD = 0.13` (decreased from 1.0).

This set of changes aims to:
*   Allow `id_yiw5` to recover and `id_97q7` to reach higher levels due to adjusted `R_A` reversibility.
*   Allow `id_55cy` and `id_shpe` to maintain higher concentrations by reducing `kD`.

The initial phase (T=0-2) might be affected by these changes, especially the `id_55cy` dynamics, as `kD` is now much smaller. The initial drop in `id_55cy` after its first peak might be less pronounced or delayed.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v5)
doc_v5 = libsbml.readSBMLFromString(input_sbml_string) 
model_v5 = doc_v5.getModel()

# Parameters for model_v5
kA_f_v5 = 1.3
kA_r_v5 = 3.8e-12 # Updated from 1.3e-13
kB_v5 = 0.0153
kC_v5 = 0.31
kD_v5 = 0.13    # Updated from 1.0

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v5.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v5)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v5)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v5.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v5)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v5.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v5)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v5.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v5)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

writer = libsbml.SBMLWriter()
updated_sbml_v5 = writer.writeSBMLToString(doc_v5)
shared_variables.add("model_v5_sbml", updated_sbml_v5)
print("SBML model_v5 created.")

print("\nAttempting to simulate model_v5...")
try:
    simulation_df_v5 = simulate(updated_sbml_v5)
    shared_variables.add("simulation_df_v5", simulation_df_v5)
    print("Simulation of model_v5 completed.")
    if simulation_df_v5 is not None and not simulation_df_v5.empty:
        print("Simulation model_v5 head:")
        print(simulation_df_v5.head())
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_point = exp_df.iloc[(exp_df['Time'] - target_time_val).abs().argsort()[:1]].squeeze()
            if isinstance(exp_point, pd.DataFrame): exp_point = exp_point.iloc[0]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_point = sim_df_local.iloc[(sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1]].squeeze()
            if isinstance(sim_point, pd.DataFrame): sim_point = sim_point.iloc[0]
            print(f"Simulated Data (model_v5, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v5)
    else:
        print("Simulation_df_v5 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v5: {e}")
    import traceback
    print(traceback.format_exc())
```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v5)
doc_v5 = libsbml.readSBMLFromString(input_sbml_string) 
model_v5 = doc_v5.getModel()

# Parameters for model_v5
kA_f_v5 = 1.3
kA_r_v5 = 3.8e-12 # Updated from 1.3e-13
kB_v5 = 0.0153
kC_v5 = 0.31
kD_v5 = 0.13    # Updated from 1.0

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v5.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v5)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v5)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v5.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v5)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v5.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v5)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v5.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v5)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

writer = libsbml.SBMLWriter()
updated_sbml_v5 = writer.writeSBMLToString(doc_v5)
shared_variables.add("model_v5_sbml", updated_sbml_v5)
print("SBML model_v5 created.")

print("\nAttempting to simulate model_v5...")
try:
    simulation_df_v5 = simulate(updated_sbml_v5)
    shared_variables.add("simulation_df_v5", simulation_df_v5)
    print("Simulation of model_v5 completed.")
    if simulation_df_v5 is not None and not simulation_df_v5.empty:
        print("Simulation model_v5 head:")
        print(simulation_df_v5.head())
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            # Find closest experimental data point to target_time_val
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            # Find closest simulation data point to the *actual experimental time*
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v5, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v5)
    else:
        print("Simulation_df_v5 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v5: {e}")
    import traceback
    print(traceback.format_exc())
```
# Observation

## Code Stdout
SBML model_v5 created.

Attempting to simulate model_v5...
Simulation of model_v5 completed.
Simulation model_v5 head:
          id_shpe      id_55cy       id_yiw5       id_97q7      Time
0  1000000.000000     0.000000  7.000000e+06  1.000000e+08  0.000000
1   989064.079516   513.277115  6.700288e+06  1.007141e+08  0.033807
2   978249.995506  1018.690558  6.413484e+06  1.014011e+08  0.067613
3   967556.380205  1516.337414  6.139033e+06  1.020621e+08  0.101420
4   956981.880319  2006.313711  5.876401e+06  1.026983e+08  0.135227

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v5, closest to exp. time):
Time: 1.01, shpe: 7.20e+05, 55cy: 1.23e+04, yiw5: 1.90e+06, 97q7: 1.13e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v5, closest to exp. time):
Time: 1.99, shpe: 5.25e+05, 55cy: 1.95e+04, yiw5: 5.59e+05, 97q7: 1.18e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v5, closest to exp. time):
Time: 12.00, shpe: 2.78e+04, 55cy: 1.55e+04, yiw5: 4.52e+04, 97q7: 1.24e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v5, closest to exp. time):
Time: 27.99, shpe: 1.64e+03, 55cy: 2.45e+03, yiw5: 4.56e+04, 97q7: 1.25e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v5, closest to exp. time):
Time: 50.00, shpe: 1.10e+02, 55cy: 1.74e+02, yiw5: 4.56e+04, 97q7: 1.25e+08

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 13/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4, model_v5_sbml, simulation_df_v5)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 8
## Thoughts

Let's analyze `model_v5` results:
Parameters: `kA_f=1.3`, `kA_r=3.8e-12`, `kB=0.0153`, `kC=0.31`, `kD=0.13`.

At T~1:
*   `id_shpe`: Exp 7.27e5, Sim 7.20e5 (Good)
*   `id_55cy`: Exp 1.51e4, Sim 1.23e4 (Sim still a bit low, but better than 8.1e3 in v4. Reducing `kD` helped `id_55cy` to be higher.)
*   `id_yiw5`: Exp 1.45e6, Sim 1.90e6 (Sim high, similar to v4)
*   `id_97q7`: Exp 1.14e8, Sim 1.13e8 (Good)

At T~2:
*   `id_shpe`: Exp 5.32e5, Sim 5.25e5 (Good)
*   `id_55cy`: Exp 1.12e4, Sim 1.95e4 (Sim is now higher than exp. Exp decreased from T1 to T2 (1.51e4 -> 1.12e4). Sim increased (1.23e4 -> 1.95e4). The reduction in `kD` (from 1.0 to 0.13) means `id_55cy` is consumed much slower by `R_D`. This has overshot `id_55cy` levels and inverted its trend in this phase.)
*   `id_yiw5`: Exp 9.75e5, Sim 5.59e5 (Sim low, similar to v4)
*   `id_97q7`: Exp 1.41e8, Sim 1.18e8 (Sim low, similar to v4)

At T~12:
*   `id_shpe`: Exp 3.43e4, Sim 2.78e4 (Sim low, but slightly better than v4's 2.54e4)
*   `id_55cy`: Exp 1.96e3, Sim 1.55e4 (Sim much higher! Exp is low. Reduced `kD` has kept `id_55cy` very high.)
*   `id_yiw5`: Exp 1.57e5, Sim 4.52e4 (Sim very low. Increased `kA_r` (from 1.3e-13 to 3.8e-12) helped `id_yiw5` from crashing to 1.5e3 (v4) to 4.5e4 (v5). This is a significant improvement, but still below exp 1.57e5.)
*   `id_97q7`: Exp 8.34e8, Sim 1.24e8 (Sim vastly underestimated. No significant improvement from v4. This is still the major issue.)

At T~28:
*   `id_shpe`: Exp 3.32e5, Sim 1.64e3 (Sim extremely low. No recovery.)
*   `id_55cy`: Exp 3.76e4, Sim 2.45e3 (Sim extremely low. No recovery.)
*   `id_yiw5`: Exp 3.02e6, Sim 4.56e4 (Sim extremely low. `id_yiw5` is stuck at the ~4.5e4 level. The new `kA_r` is not enough to drive recovery to millions.)
*   `id_97q7`: Exp 1.02e9, Sim 1.25e8 (Sim vastly underestimated.)

At T~50:
*   `id_shpe`: Exp 7.94e4, Sim 1.10e2 (Sim effectively zero.)
*   `id_55cy`: Exp 8.35e3, Sim 1.74e2 (Sim effectively zero.)
*   `id_yiw5`: Exp 6.59e5, Sim 4.56e4 (Sim extremely low, stuck.)
*   `id_97q7`: Exp 1.03e9, Sim 1.25e8 (Sim vastly underestimated, stuck.)

**Conclusions from `model_v5`:**
1.  **`R_A` (id_yiw5 <=> 2 id_97q7):** Increasing `kA_r` to `3.8e-12` helped `id_yiw5` from completely crashing (it stabilized around 4.5e4 instead of 1.5e3). However, this is still far too low compared to experimental recovery (up to 3e6). Consequently, `id_97q7` production is still stalled at 1.25e8, far below the 1e9 target. The equilibrium `[id_97q7]^2 / [id_yiw5]` set by `kA_f/kA_r` is `1.3 / 3.8e-12 = 3.42e11`.
    *   If `id_yiw5` is 4.5e4, then `[id_97q7]^2 = 3.42e11 * 4.5e4 = 1.54e16`. So `[id_97q7] = sqrt(1.54e16) = 1.24e8`. This matches the simulation.
    *   To get `id_97q7` to ~1e9, with this `K_eq`, `id_yiw5` would need to be `(1e9)^2 / 3.42e11 = 1e18 / 3.42e11 = 2.92e6`. This is the target level for `id_yiw5` recovery!
    *   So, the `K_eq` (and thus `kA_r`) is correctly set for the *target equilibrium*. The problem is that the system does not *reach* this state. `id_yiw5` is not being replenished enough to get to 2.9e6. This means the net reverse reaction `2 id_97q7 -> id_yiw5` is not strong enough, or `id_yiw5` has other consumption pathways not accounted for, or its sources are too weak.
    *   The only source for `id_yiw5` in the model is the reverse part of `R_A`. The only consumption is the forward part of `R_A`.
    *   Perhaps `kA_f` (1.3) is too high, constantly draining `id_yiw5` even when it's low. If `kA_f` were lower, `id_yiw5` might not drop as much initially, giving the reverse reaction a better chance.

2.  **`id_55cy` dynamics:** Reducing `kD` to `0.13` made `id_55cy` levels too high in the early-middle phase (e.g., T=2, T=12) and inverted its trend at T=2. The previous `kD=1.0` was better for the initial decline of `id_55cy` after its peak. The complex rise-fall-rise-fall of `id_55cy` is hard to capture with simple irreversible reactions `S->C` and `C->S`.

3.  **`id_shpe`, `id_55cy` long-term crash:** These still crash. The change in `kD` didn't prevent this. Their recovery seen in experiments is not happening. This is tied to `id_yiw5` and `id_97q7` not behaving correctly.

**Strategy for `model_v6`:**

*   **Revisit `R_A` (id_yiw5 <=> 2 id_97q7):**
    *   The `K_eq` seems right for the T=28 target. The issue is kinetics.
    *   If `id_yiw5` drops too low (e.g. to 1e4-1e5), the forward rate `kA_f * [id_yiw5]` becomes small. The reverse rate `kA_r * [id_97q7]^2` also needs `[id_97q7]` to be high.
    *   The problem might be that `id_97q7` doesn't get high enough *before* `id_yiw5` gets too low.
    *   `id_97q7` is produced by `R_A_fwd` and `R_C: id_shpe -> 11 id_97q7`.
    *   If `id_shpe` crashes, then `R_C` stops producing `id_97q7`. This is happening.
    *   So, the crash of `id_shpe` is critical.

*   **Focus on `id_shpe` and `id_55cy` recovery:**
    *   The experimental data shows `id_shpe` recovering from ~3e4 (T=12) to ~3e5 (T=28).
    *   And `id_55cy` recovering from ~2e3 (T=12) to ~3e4 (T=28).
    *   This recovery phase needs a net production for both.
    *   In our model:
        `d[id_shpe]/dt = kD*[id_55cy] - (kB+kC)*[id_shpe]`
        `d[id_55cy]/dt = kB*[id_shpe] - kD*[id_55cy]`
    *   For both to increase, we need their production terms to be larger than consumption.
    *   The current `kD=0.13` and `kB=0.0153` were based on `kD/kB ~ 8.8` for `[S]/[C]` ratio.
    *   If `id_shpe` is too low, `kB*[id_shpe]` is low, so `id_55cy` won't be produced.
    *   If `id_55cy` is too low, `kD*[id_55cy]` is low, so `id_shpe` won't be produced.
    *   The term `kC*[id_shpe]` is a major drain on `id_shpe`. `kC=0.31`. This is very large compared to `kB=0.0153`.
    *   Maybe `kC` is too high, causing `id_shpe` to deplete, which then stops `id_55cy` production, and then `id_shpe` can't recover.

    *   Let's try reducing `kC`. If `kC` is reduced, `id_97q7` production from `R_C` will decrease. This means `R_A` will be more responsible for `id_97q7` levels.
    *   Original estimation of `kC` (iteration 2-3) was based on initial rates.
        `kC = ( (d[id_shpe]/dt)_total_consumption - (d[id_shpe]/dt)_for_R_B ) / [id_shpe]`
        And also `(1/11) * (d[id_97q7]/dt)_from_RC / [id_shpe]`.
    *   If `kC` is reduced, `id_shpe` might survive better. Let's try halving `kC` to `0.15`.

*   **Re-evaluate `kD` for `id_55cy`:**
    *   With `kD=0.13`, `id_55cy` became too high at T=2 and T=12.
    *   With `kD=1.0`, `id_55cy` was too low overall.
    *   The experimental `id_55cy` drops from 1.51e4 (T=1) to 1.12e4 (T=2). `d[id_55cy]/dt ~ -4e3`.
    *   `kB*[id_shpe] - kD*[id_55cy] = -4e3`.
    *   Using T=1 values (exp `id_shpe`=7.27e5, exp `id_55cy`=1.51e4, `kB`=0.0153):
        `0.0153 * 7.27e5 - kD * 1.51e4 = -4e3`
        `1.11e4 - kD * 1.51e4 = -4e3`
        `kD * 1.51e4 = 1.51e4 => kD = 1.0`.
    *   This suggests `kD=1.0` is correct for the *initial phase* if `id_55cy` is at its experimental level.
    *   The problem with `kD=0.13` was that `id_55cy` didn't decrease after T=1.
    *   The problem with `kD=1.0` was that `id_55cy` became too low later.
    *   This implies that the relationship `kD/kB = [S]/[C]` might hold for the later recovery phase, but the early phase dynamics are different.
    *   Perhaps the model needs a more complex regulation for `id_55cy` or `id_shpe`.

Let's try a less drastic change for `kD` and focus on `kC` reduction.
If `kC` is reduced, `id_shpe` is less consumed. This might allow `id_shpe` and subsequently `id_55cy` to persist at higher levels.
If `id_shpe` stays higher, `R_C` will still contribute to `id_97q7` production.

Proposed changes for `model_v6`:
1.  `R_A: id_yiw5 <=> 2 id_97q7`. Keep `kA_f = 1.3`, `kA_r = 3.8e-12`. (The `K_eq` is targeted for T=28. If other species behave better, this might work out).
2.  `R_B: id_shpe -> id_55cy`. Keep `kB = 0.0153`.
3.  `R_C: id_shpe -> 11 id_97q7`. Reduce `kC` from `0.31` to `0.15`.
4.  `R_D: id_55cy -> id_shpe`. Let's try an intermediate `kD`. `kD=1.0` was good for early phase, `kD=0.13` for late phase ratio (but bad for early). What about `kD = 0.4`? (This was a value considered in iteration 4).

Recalculate `kB` if `kD` changes, to match `d[id_55cy]/dt` at T=1.
If `kD=0.4`:
`0.0153 * 7.27e5 - 0.4 * 1.51e4 = -4e3`
`1.11e4 - 0.604e4 = -4e3`
`0.506e4 = -4e3`. This is `5060 = -4000`, which is false.
This means `kB` needs to be adjusted if `kD` is 0.4.
`kB * 7.27e5 - 0.4 * 1.51e4 = -4e3`
`kB * 7.27e5 = 0.604e4 - 0.4e4 = 0.204e4 = 2040`.
`kB = 2040 / 7.27e5 = 0.0028`.
This `kB` is much smaller than `0.0153`. If `kB` is this small, `id_55cy` won't be produced much initially.

This is tricky. The parameters `kB` and `kD` are highly influential on `id_shpe` and `id_55cy`.
The fact that `id_55cy` has multiple peaks and troughs suggests more complex regulation than simple `S <=> C` conversion.
However, we are constrained to not add new species.

Let's stick to reducing `kC` first, as it's a major drain. Keep `kD=0.13` for now, as it was derived from the later-stage ratio. The initial phase mismatch for `id_55cy` might be a secondary issue if the long-term behavior improves.

Revised plan for `model_v6`:
1.  `R_A: id_yiw5 <=> 2 id_97q7`. `kA_f = 1.3`, `kA_r = 3.8e-12`.
2.  `R_B: id_shpe -> id_55cy`. `kB = 0.0153`.
3.  `R_C: id_shpe -> 11 id_97q7`. Reduce `kC` from `0.31` to `0.15`.
4.  `R_D: id_55cy -> id_shpe`. `kD = 0.13`.

The main hypothesis is that reducing `id_shpe`'s main consumption pathway (`R_C`) will allow `id_shpe` to survive, which in turn allows `id_55cy` to be produced and survive (due to `kD=0.13`), and this might help `R_A` achieve its target equilibrium by providing sustained `id_shpe` for `R_C`'s contribution to `id_97q7`.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v6)
doc_v6 = libsbml.readSBMLFromString(input_sbml_string) 
model_v6 = doc_v6.getModel()

# Parameters for model_v6
kA_f_v6 = 1.3
kA_r_v6 = 3.8e-12 
kB_v6 = 0.0153
kC_v6 = 0.15    # Updated from 0.31
kD_v6 = 0.13    

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v6.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v6)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v6)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v6.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v6)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v6.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v6)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v6.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v6)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

writer = libsbml.SBMLWriter()
updated_sbml_v6 = writer.writeSBMLToString(doc_v6)
shared_variables.add("model_v6_sbml", updated_sbml_v6)
print("SBML model_v6 created.")

print("\nAttempting to simulate model_v6...")
try:
    simulation_df_v6 = simulate(updated_sbml_v6)
    shared_variables.add("simulation_df_v6", simulation_df_v6)
    print("Simulation of model_v6 completed.")
    if simulation_df_v6 is not None and not simulation_df_v6.empty:
        print("Simulation model_v6 head:")
        print(simulation_df_v6.head())
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v6, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v6)
    else:
        print("Simulation_df_v6 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v6: {e}")
    import traceback
    print(traceback.format_exc())

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v6)
doc_v6 = libsbml.readSBMLFromString(input_sbml_string) 
model_v6 = doc_v6.getModel()

# Parameters for model_v6
kA_f_v6 = 1.3
kA_r_v6 = 3.8e-12 
kB_v6 = 0.0153
kC_v6 = 0.15    # Updated from 0.31
kD_v6 = 0.13    

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v6.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v6)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v6)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v6.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v6)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v6.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v6)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v6.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v6)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

writer = libsbml.SBMLWriter()
updated_sbml_v6 = writer.writeSBMLToString(doc_v6)
shared_variables.add("model_v6_sbml", updated_sbml_v6)
print("SBML model_v6 created.")

print("\nAttempting to simulate model_v6...")
try:
    simulation_df_v6 = simulate(updated_sbml_v6)
    shared_variables.add("simulation_df_v6", simulation_df_v6)
    print("Simulation of model_v6 completed.")
    if simulation_df_v6 is not None and not simulation_df_v6.empty:
        print("Simulation model_v6 head:")
        print(simulation_df_v6.head())
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            # Find closest experimental data point to target_time_val
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            # Find closest simulation data point to the *actual experimental time*
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v6, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v6)
    else:
        print("Simulation_df_v6 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v6: {e}")
    import traceback
    print(traceback.format_exc())
```
# Observation

## Code Stdout
SBML model_v6 created.

Attempting to simulate model_v6...
Simulation of model_v6 completed.
Simulation model_v6 head:
          id_shpe      id_55cy       id_yiw5       id_97q7      Time
0  1000000.000000     0.000000  7.000000e+06  1.000000e+08  0.000000
1   994428.480068   514.666298  6.700286e+06  1.006551e+08  0.033807
2   988890.253241  1024.208654  6.413479e+06  1.012840e+08  0.067613
3   983385.111254  1528.666736  6.139023e+06  1.018879e+08  0.101420
4   977912.847454  2028.079878  5.876387e+06  1.024679e+08  0.135227

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v6, closest to exp. time):
Time: 1.01, shpe: 8.47e+05, 55cy: 1.34e+04, yiw5: 1.90e+06, 97q7: 1.12e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v6, closest to exp. time):
Time: 1.99, shpe: 7.22e+05, 55cy: 2.28e+04, yiw5: 5.58e+05, 97q7: 1.16e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v6, closest to exp. time):
Time: 12.00, shpe: 1.61e+05, 55cy: 3.30e+04, yiw5: 4.39e+04, 97q7: 1.23e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v6, closest to exp. time):
Time: 27.99, shpe: 2.23e+04, 55cy: 9.12e+03, yiw5: 4.53e+04, 97q7: 1.25e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v6, closest to exp. time):
Time: 50.00, shpe: 2.20e+03, 55cy: 1.08e+03, yiw5: 4.56e+04, 97q7: 1.25e+08

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 12/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4, model_v5_sbml, simulation_df_v5, model_v6_sbml, simulation_df_v6)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 9
## Thoughts

Let's analyze `model_v6` results:
Parameters: `kA_f=1.3`, `kA_r=3.8e-12`, `kB=0.0153`, `kC=0.15` (was 0.31), `kD=0.13`.

At T~1:
*   `id_shpe`: Exp 7.27e5, Sim 8.47e5 (Sim higher. Reducing `kC` (consumption) made `id_shpe` higher, as expected.)
*   `id_55cy`: Exp 1.51e4, Sim 1.34e4 (Sim slightly low. Higher `id_shpe` should boost `id_55cy` production via `R_B`.)
*   `id_yiw5`: Exp 1.45e6, Sim 1.90e6 (Sim high, same as v5)
*   `id_97q7`: Exp 1.14e8, Sim 1.12e8 (Good. Reduced `kC` means less `id_97q7` from `R_C`, but `id_shpe` is higher, so it might balance out somewhat for initial phase.)

At T~2:
*   `id_shpe`: Exp 5.32e5, Sim 7.22e5 (Sim much higher. `id_shpe` not decreasing as fast as exp.)
*   `id_55cy`: Exp 1.12e4, Sim 2.28e4 (Sim much higher. Trend still inverted: exp decreasing, sim increasing.)
*   `id_yiw5`: Exp 9.75e5, Sim 5.58e5 (Sim low, same as v5)
*   `id_97q7`: Exp 1.41e8, Sim 1.16e8 (Sim low, same as v5)

At T~12:
*   `id_shpe`: Exp 3.43e4, Sim 1.61e5 (Sim much higher. Reduced `kC` has kept `id_shpe` significantly higher.)
*   `id_55cy`: Exp 1.96e3, Sim 3.30e4 (Sim vastly higher. `kD=0.13` is too low for this phase, `id_55cy` not consumed enough.)
*   `id_yiw5`: Exp 1.57e5, Sim 4.39e4 (Sim very low, slightly worse than v5's 4.52e4. Higher `id_shpe` didn't help `id_yiw5` recovery via `R_A`.)
*   `id_97q7`: Exp 8.34e8, Sim 1.23e8 (Sim vastly underestimated. No improvement.)

At T~28:
*   `id_shpe`: Exp 3.32e5, Sim 2.23e4 (Sim very low. Despite being higher earlier, `id_shpe` still crashes eventually.)
*   `id_55cy`: Exp 3.76e4, Sim 9.12e3 (Sim very low.)
*   `id_yiw5`: Exp 3.02e6, Sim 4.53e4 (Sim extremely low, stuck.)
*   `id_97q7`: Exp 1.02e9, Sim 1.25e8 (Sim vastly underestimated, stuck.)

At T~50:
*   `id_shpe`: Exp 7.94e4, Sim 2.20e3 (Sim very low.)
*   `id_55cy`: Exp 8.35e3, Sim 1.08e3 (Sim very low.)
*   `id_yiw5`: Exp 6.59e5, Sim 4.56e4 (Sim extremely low, stuck.)
*   `id_97q7`: Exp 1.03e9, Sim 1.25e8 (Sim vastly underestimated, stuck.)

**Conclusions from `model_v6`:**
1.  **Reducing `kC` (for `R_C: id_shpe -> 11 id_97q7`):** This made `id_shpe` higher in the initial/middle phases (T=1 to T=12), but it still crashed by T=28. This change also made `id_55cy` higher due to more substrate for `R_B`. However, it did not solve the long-term crash of `id_shpe` and `id_55cy`, nor did it help `id_yiw5` or `id_97q7` achieve their target recovery levels.
2.  **`id_yiw5` and `id_97q7`:** Still stuck at low `id_yiw5` (~4.5e4) and low `id_97q7` (~1.25e8). The `K_eq` for `R_A` is set for the target concentrations, but the system doesn't get there. The net production of `id_yiw5` (reverse `R_A`) is not enough to overcome its consumption (forward `R_A`) to lift `id_yiw5` to the ~1e6 range.
3.  **`id_55cy` dynamics:** The `kD=0.13` value makes `id_55cy` too high and its initial decrease is not captured. `kD=1.0` was better for the initial phase. This suggests `kD` might not be constant, or another reaction consuming `id_55cy` is missing or becomes active.

**The core problem remains:** The system does not recover `id_yiw5`, `id_shpe`, and `id_55cy` to their high experimental levels in the later stages (T > 20), and consequently `id_97q7` does not reach its peak.

What if the production of `id_yiw5` is not solely from reverse `R_A`?
The experimental data shows `id_yiw5` increasing from T~12 (1.57e5) to T~28 (3.02e6). This is a substantial increase.
During this same period (T=12 to T=28):
*   `id_shpe` increases from 3.43e4 to 3.32e5.
*   `id_55cy` increases from 1.96e3 to 3.76e4.
*   `id_97q7` increases from 8.34e8 to 1.02e9 (but this is already high).

Could `id_shpe` or `id_55cy` be a source for `id_yiw5`?
*   `R_E: id_shpe -> id_yiw5`? If `id_shpe` is recovering, it could fuel `id_yiw5` production.
*   `R_F: id_55cy -> id_yiw5`? If `id_55cy` is recovering, it could fuel `id_yiw5` production.

If `R_E: id_shpe -> id_yiw5` (rate `kE * [id_shpe]`) exists:
This would be another consumption pathway for `id_shpe`.
The net change in `id_yiw5` would be `(kA_r * [id_97q7]^2 + kE * [id_shpe]) - kA_f * [id_yiw5]`.
This new source `kE * [id_shpe]` could help push `[id_yiw5]` up.

Let's estimate `kE`.
From T=12 to T=28 (16 days), `delta_id_yiw5` ~ 2.86e6. Avg rate ~ 1.79e5 / day.
Avg `[id_shpe]` in this interval (exp): `(3.43e4 + 3.32e5)/2 ~ 1.83e5`.
Avg `[id_yiw5]` (exp): `(1.57e5 + 3.02e6)/2 ~ 1.59e6`.
Avg `[id_97q7]` (exp): `(8.34e8 + 1.02e9)/2 ~ 9.27e8`.

Net rate for `R_A` (using exp values and current `kA_f, kA_r`):
`kA_f * Avg[id_yiw5] - kA_r * Avg[id_97q7]^2`
`= 1.3 * 1.59e6 - 3.8e-12 * (9.27e8)^2`
`= 2.067e6 - 3.8e-12 * 8.59e17`
`= 2.067e6 - 3.26e6 = -1.193e6`.
This means `R_A` alone would provide a net production of `id_yiw5` at an average rate of `1.193e6 / day` if species were at these average experimental concentrations. This is much higher than the observed average net production rate of `1.79e5 / day`.
This calculation suggests that `kA_r` might be *too high* if these are average concentrations, or `kA_f` is too low.
The previous `K_eq` was based on point T=28. `K_eq = kA_f / kA_r = 3.42e11`.
`[id_97q7]^2 / [id_yiw5]`. At T=12 (exp): `(8.34e8)^2 / 1.57e5 = 6.95e17 / 1.57e5 = 4.4e12`.
At T=28 (exp): `(1.02e9)^2 / 3.02e6 = 1.04e18 / 3.02e6 = 3.44e11`.
The ratio `[Q]^2/[Y]` changes significantly, so the system is not at equilibrium w.r.t R_A.
At T=12, `[Q]^2/[Y]` is `4.4e12`, which is `> K_eq=3.42e11`. So reverse `R_A` should dominate, producing `id_yiw5`.
At T=28, `[Q]^2/[Y]` is `3.44e11`, which is `~ K_eq=3.42e11`. So `R_A` is near equilibrium.

The simulation gets stuck with `id_yiw5` at 4.5e4 and `id_97q7` at 1.25e8.
At this point (sim): `[Q]^2/[Y] = (1.25e8)^2 / 4.5e4 = 1.56e16 / 4.5e4 = 3.47e11`. This matches `K_eq`.
So, `R_A` reaches its equilibrium, but at the wrong concentrations.
This means the total amounts of Y and Q in the Y <=> 2Q system are not matching the experiment.
This implies that other reactions feeding into or draining Y and Q are critical.
`R_C: id_shpe -> 11 id_97q7` is a source for Q.
If `id_shpe` crashes, `R_C` stops, and `id_97q7` cannot reach its high levels. This is the current problem.

We need `id_shpe` to recover.
`d[id_shpe]/dt = kD*[id_55cy] - (kB+kC)*[id_shpe]`
If `id_shpe` is to recover (e.g. from 2e4 to 3e5), `d[id_shpe]/dt` must be positive.
`kD*[id_55cy] > (kB+kC)*[id_shpe]`.
Using `kD=0.13`, `kB=0.0153`, `kC=0.15` (from v6). `kB+kC = 0.1653`.
At T=28 (sim v6): `id_shpe`=2.23e4, `id_55cy`=9.12e3.
`0.13 * 9.12e3 = 1185`.
`0.1653 * 2.23e4 = 3686`.
`d[id_shpe]/dt` is `1185 - 3686 = -2501` (negative, so `id_shpe` is still decreasing, consistent with crash).

To make `d[id_shpe]/dt` positive during recovery (e.g. using T=28 exp values: `id_shpe`=3.32e5, `id_55cy`=3.76e4):
`0.13 * 3.76e4 = 4888`.
`0.1653 * 3.32e5 = 54880`.
`d[id_shpe]/dt` would be `4888 - 54880 = -5e4` (still very negative!).
This means the parameters `kD, kB, kC` are not suitable for `id_shpe` recovery even if `id_55cy` were high.
The consumption term `(kB+kC)*[id_shpe]` is too large, or production `kD*[id_55cy]` is too small.

The term `kC*[id_shpe]` (where `kC=0.15`) is the main part of consumption: `0.15 * 3.32e5 = 4.98e4`.
If `kC` was much smaller, e.g., `kC=0.01`. Then `kB+kC = 0.0153+0.01 = 0.0253`.
Then consumption `0.0253 * 3.32e5 = 8400`.
Production `kD*[id_55cy] = 0.13 * 3.76e4 = 4888`.
Still `4888 - 8400` is negative.

This suggests `kD` needs to be larger relative to `(kB+kC)`.
Ratio `kD / (kB+kC)` should be `> [id_shpe]/[id_55cy]`.
Exp ratio `[id_shpe]/[id_55cy]` at T=28 is `3.32e5 / 3.76e4 ~ 8.8`.
So we need `kD / (kB+kC) > 8.8`.
With `kB=0.0153`. If `kC` is small, say `0.01`, then `kB+kC = 0.0253`.
Then `kD > 8.8 * 0.0253 = 0.222`.
So, if `kC` is small (e.g. 0.01), then `kD` should be > 0.222 (e.g. 0.25 or 0.3).
This `kD` is larger than the `0.13` used.

Let's try `model_v7` with a significantly reduced `kC` and a `kD` based on this new `kC`.
1.  `R_A: id_yiw5 <=> 2 id_97q7`. `kA_f = 1.3`, `kA_r = 3.8e-12`. (No change yet)
2.  `R_B: id_shpe -> id_55cy`. `kB = 0.0153`. (No change yet)
3.  `R_C: id_shpe -> 11 id_97q7`. Drastically reduce `kC` from `0.15` to `0.02`. (This is >10x reduction from original 0.31).
4.  `R_D: id_55cy -> id_shpe`. Adjust `kD`.
    New `kB+kC = 0.0153 + 0.02 = 0.0353`.
    We need `kD / 0.0353 > 8.8` for `id_shpe` recovery.
    `kD > 8.8 * 0.0353 = 0.31`. Let's try `kD = 0.35`.
    This `kD=0.35` is between `0.13` (v5, v6) and `1.0` (v4).

This strategy aims to make `id_shpe` much more resilient by drastically cutting its main conversion to `id_97q7` via `R_C`.
This will mean `id_97q7` relies more heavily on `R_A` (from `id_yiw5`).
If `id_shpe` recovers, then `id_55cy` might recover. If `id_shpe` and `id_55cy` recover, this might provide a better "environment" for `R_A` to operate and bring `id_yiw5` and `id_97q7` to their target levels.

The initial phase (T=0-2) for `id_shpe` will be affected: `id_shpe` will decrease much slower.
Original `kB+kC` was `0.0153+0.31 = 0.3253`. New is `0.0353`. About 10x slower consumption.
This will make initial `id_shpe` much higher than experimental.
This implies that `kC` might not be a simple constant; it might be high initially and low later, or regulated.
However, with current tools, we use constant parameters.
This change might break the good fit for `id_shpe` in the early phase to fix the late phase. This is a common trade-off.

Let's check `id_55cy` initial decline with `kD=0.35`.
`d[id_55cy]/dt = kB*[id_shpe] - kD*[id_55cy]`. Target `-4e3` at T=1.
`0.0153 * id_shpe_T1 - 0.35 * 1.51e4 = -4e3`.
`0.0153 * id_shpe_T1 - 5285 = -4000`.
`0.0153 * id_shpe_T1 = 1285`.
`id_shpe_T1 = 1285 / 0.0153 = 8.4e4`.
Experimental `id_shpe_T1` is 7.27e5.
So, if `id_shpe_T1` is high (as it will be with low `kC`), then `kB*id_shpe_T1` will be large.
`0.0153 * 7.27e5 - 0.35 * 1.51e4 = 1.11e4 - 5285 = 5815`. This is positive, not -4000.
So `id_55cy` will increase at T=1, not decrease. This means `kD=0.35` is too low for the initial phase `id_55cy` drop.

This iterative adjustment of `kB, kC, kD` based on different phases is difficult.
The system likely has some form of regulation not captured by simple mass-action with constant parameters.
Perhaps one of the reactions should be reversible, e.g. `R_B` or `R_D` or `R_C`.
`R_C: id_shpe <=> 11 id_97q7`? If `id_97q7` gets very high, it could regenerate `id_shpe`.
If `R_C` is reversible: `kCf * [id_shpe] - kCr * [id_97q7]^11`. The power of 11 is very high, making it switch-like.
This is too complex to parameterize without more insight.

Let's try the current plan (low `kC`, moderate `kD`) and see if long-term recovery is prioritized.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v7)
doc_v7 = libsbml.readSBMLFromString(input_sbml_string) 
model_v7 = doc_v7.getModel()

# Parameters for model_v7
kA_f_v7 = 1.3
kA_r_v7 = 3.8e-12 
kB_v7 = 0.0153
kC_v7 = 0.02    # Updated from 0.15 (was 0.31 originally)
kD_v7 = 0.35    # Updated from 0.13 

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v7.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v7)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v7)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v7.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v7)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v7.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v7)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v7.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v7)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

writer = libsbml.SBMLWriter()
updated_sbml_v7 = writer.writeSBMLToString(doc_v7)
shared_variables.add("model_v7_sbml", updated_sbml_v7)
print("SBML model_v7 created.")

print("\nAttempting to simulate model_v7...")
try:
    simulation_df_v7 = simulate(updated_sbml_v7)
    shared_variables.add("simulation_df_v7", simulation_df_v7)
    print("Simulation of model_v7 completed.")
    if simulation_df_v7 is not None and not simulation_df_v7.empty:
        # print("Simulation model_v7 head:")
        # print(simulation_df_v7.head())
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v7, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v7)
    else:
        print("Simulation_df_v7 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v7: {e}")
    import traceback
    print(traceback.format_exc())

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v7)
doc_v7 = libsbml.readSBMLFromString(input_sbml_string) 
model_v7 = doc_v7.getModel()

# Parameters for model_v7
kA_f_v7 = 1.3
kA_r_v7 = 3.8e-12 
kB_v7 = 0.0153
kC_v7 = 0.02    # Updated from 0.15 (was 0.31 originally)
kD_v7 = 0.35    # Updated from 0.13 

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v7.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v7)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v7)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v7.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v7)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v7.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v7)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v7.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v7)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

writer = libsbml.SBMLWriter()
updated_sbml_v7 = writer.writeSBMLToString(doc_v7)
shared_variables.add("model_v7_sbml", updated_sbml_v7)
print("SBML model_v7 created.")

print("\nAttempting to simulate model_v7...")
try:
    simulation_df_v7 = simulate(updated_sbml_v7)
    shared_variables.add("simulation_df_v7", simulation_df_v7)
    print("Simulation of model_v7 completed.")
    if simulation_df_v7 is not None and not simulation_df_v7.empty:
        # print("Simulation model_v7 head:") # Hiding head to save output space
        # print(simulation_df_v7.head())
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            # Find closest experimental data point to target_time_val
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            # Find closest simulation data point to the *actual experimental time*
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v7, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v7)
    else:
        print("Simulation_df_v7 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v7: {e}")
    import traceback
    print(traceback.format_exc())
```
# Observation

## Code Stdout
SBML model_v7 created.

Attempting to simulate model_v7...
Simulation of model_v7 completed.

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v7, closest to exp. time):
Time: 1.01, shpe: 9.67e+05, 55cy: 1.28e+04, yiw5: 1.90e+06, 97q7: 1.10e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v7, closest to exp. time):
Time: 1.99, shpe: 9.40e+05, 55cy: 2.12e+04, yiw5: 5.57e+05, 97q7: 1.13e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v7, closest to exp. time):
Time: 12.00, shpe: 7.59e+05, 55cy: 3.45e+04, yiw5: 3.94e+04, 97q7: 1.16e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v7, closest to exp. time):
Time: 27.99, shpe: 5.58e+05, 55cy: 2.58e+04, yiw5: 4.10e+04, 97q7: 1.18e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v7, closest to exp. time):
Time: 50.00, shpe: 3.67e+05, 55cy: 1.70e+04, yiw5: 4.25e+04, 97q7: 1.21e+08

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 11/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4, model_v5_sbml, simulation_df_v5, model_v6_sbml, simulation_df_v6, model_v7_sbml, simulation_df_v7)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 10
## Thoughts

Let's analyze `model_v7` results:
Parameters: `kA_f=1.3`, `kA_r=3.8e-12`, `kB=0.0153`, `kC=0.02` (was 0.15), `kD=0.35` (was 0.13).

At T~1:
*   `id_shpe`: Exp 7.27e5, Sim 9.67e5 (Sim much higher. Drastically reducing `kC` made `id_shpe` decrease very slowly.)
*   `id_55cy`: Exp 1.51e4, Sim 1.28e4 (Sim slightly low.)
*   `id_yiw5`: Exp 1.45e6, Sim 1.90e6 (Sim high.)
*   `id_97q7`: Exp 1.14e8, Sim 1.10e8 (Sim slightly low. Reduced `kC` directly impacts this.)

At T~2:
*   `id_shpe`: Exp 5.32e5, Sim 9.40e5 (Sim much higher.)
*   `id_55cy`: Exp 1.12e4, Sim 2.12e4 (Sim high. `kD=0.35` is too low for initial `id_55cy` decline.)
*   `id_yiw5`: Exp 9.75e5, Sim 5.57e5 (Sim low.)
*   `id_97q7`: Exp 1.41e8, Sim 1.13e8 (Sim low.)

At T~12:
*   `id_shpe`: Exp 3.43e4, Sim 7.59e5 (Sim vastly higher. `id_shpe` is not being consumed enough.)
*   `id_55cy`: Exp 1.96e3, Sim 3.45e4 (Sim vastly higher.)
*   `id_yiw5`: Exp 1.57e5, Sim 3.94e4 (Sim very low. Still stuck.)
*   `id_97q7`: Exp 8.34e8, Sim 1.16e8 (Sim vastly underestimated. Still stuck.)

At T~28:
*   `id_shpe`: Exp 3.32e5, Sim 5.58e5 (Sim higher. `id_shpe` has remained high, not showing the experimental dip and recovery to ~3e5. It just stays high and slowly declines.)
*   `id_55cy`: Exp 3.76e4, Sim 2.58e4 (Sim lower. Experimental `id_55cy` recovered more.)
*   `id_yiw5`: Exp 3.02e6, Sim 4.10e4 (Sim extremely low, stuck.)
*   `id_97q7`: Exp 1.02e9, Sim 1.18e8 (Sim vastly underestimated, stuck.)

At T~50:
*   `id_shpe`: Exp 7.94e4, Sim 3.67e5 (Sim much higher.)
*   `id_55cy`: Exp 8.35e3, Sim 1.70e4 (Sim higher.)
*   `id_yiw5`: Exp 6.59e5, Sim 4.25e4 (Sim extremely low, stuck.)
*   `id_97q7`: Exp 1.03e9, Sim 1.21e8 (Sim vastly underestimated, stuck.)

**Conclusions from `model_v7`:**
1.  **Drastically reducing `kC` (for `R_C: id_shpe -> 11 id_97q7`):** This prevented `id_shpe` from crashing. In fact, `id_shpe` now stays too high throughout the simulation compared to experimental data (which shows a dip around T=12). This also led to `id_55cy` being generally higher.
2.  **`id_yiw5` and `id_97q7`:** Still stuck. `id_yiw5` hovers around 4e4, and `id_97q7` around 1.2e8. The fundamental issue of these two species not reaching their target recovery/peak levels persists. Even with `id_shpe` staying high, `R_C`'s contribution to `id_97q7` (with `kC=0.02`) is `0.02 * [id_shpe] * 11`. If `id_shpe` is ~5e5, this is `0.22 * 5e5 = 1.1e5` (rate of `id_97q7` production). This is small compared to the changes needed for `id_97q7`.
3.  **Initial phase mismatch:** The initial good fit for `id_shpe` (T=0-2) is now lost. `id_55cy` dynamics are also not matching the initial drop.

**The core problem is that `R_A: id_yiw5 <=> 2 id_97q7` reaches an equilibrium at concentrations far from the experimental observations for `id_yiw5` and `id_97q7` during the later phase.**
The current `K_eq = kA_f / kA_r = 1.3 / 3.8e-12 = 3.42e11`.
Simulated equilibrium: `id_yiw5` ~4e4, `id_97q7` ~1.2e8. `(1.2e8)^2 / 4e4 = 1.44e16 / 4e4 = 3.6e11`. This matches `K_eq`.
Experimental T=28: `id_yiw5` ~3e6, `id_97q7` ~1e9. `(1e9)^2 / 3e6 = 1e18 / 3e6 = 3.33e11`. This also matches `K_eq`.

So, the `K_eq` is consistent with the late-stage experimental ratio.
Why does the simulation settle at the low concentrations?
It means the "total pool" of (Y + Q/2, in molar terms for Y) in the reversible reaction `Y <=> 2Q` is too low in the simulation.
This pool is affected by:
*   Initial concentrations.
*   Other reactions producing/consuming Y (`id_yiw5`) or Q (`id_97q7`).
    *   `id_yiw5` has no other reactions in the model.
    *   `id_97q7` is also produced by `R_C: id_shpe -> 11 id_97q7`.

If `R_C` produces a lot of `id_97q7`, it should shift the `R_A` equilibrium towards more `id_yiw5`.
In `model_v7`, `id_shpe` stays high (e.g., 5e5 at T=28).
Rate of `id_97q7` production from `R_C` = `kC * [id_shpe] = 0.02 * 5e5 = 1e4` (this is rate of `id_shpe` consumption for `R_C`).
Rate of `id_97q7` species production = `11 * 1e4 = 1.1e5`.
This is a continuous influx into the `id_97q7` pool. This influx should, over time, push `id_97q7` higher, and consequently `id_yiw5` higher through the reverse `R_A`.
But `id_yiw5` and `id_97q7` are stuck.

Could the simulation time be too short? The provided data goes to T=50.
The simulation values for `id_yiw5` and `id_97q7` seem to have stabilized by T=12 and remain flat.

What if `kA_f` (forward rate of `id_yiw5` consumption by `R_A`) is too high?
If `kA_f` is high, `id_yiw5` is depleted quickly. Even if `R_C` is supplying `id_97q7`, if `id_yiw5` is kept very low by a high `kA_f`, the reverse `R_A` (`kA_r*[Q]^2`) might not be ables to build up `id_yiw5` against this strong forward flux.
Let's try reducing `kA_f`.
If `kA_f` is reduced, `K_eq = kA_f / kA_r` will change. We need to adjust `kA_r` to maintain the target `K_eq ~ 3.4e11`.
Suppose we reduce `kA_f` from `1.3` to `0.13` (10x reduction).
New `kA_r = kA_f_new / K_eq = 0.13 / 3.42e11 = 3.8e-13`. (This was close to my very first estimate for `kA_r`).
With a lower `kA_f`, `id_yiw5` will be consumed slower by `R_A`. This might allow `id_yiw5` to persist at higher levels initially, and allow the influx of `id_97q7` from `R_C` to build up `[Q]`, which then helps build up `[Y]` via reverse `R_A`.

This change (lower `kA_f` and correspondingly lower `kA_r`) will slow down the dynamics of `R_A`.

Regarding `id_shpe` and `id_55cy`:
`id_shpe` is too high in `model_v7`. This means `kC=0.02` is too low for the initial phase.
The original `kC=0.31` gave good initial `id_shpe`.
The parameter `kD` for `R_D: id_55cy -> id_shpe` also affects `id_55cy` dynamics. `kD=0.35` made `id_55cy` too high initially. `kD=1.0` was better for initial `id_55cy` drop.

This suggests that some parameters might need to be different for early vs. late phases, which points to more complex regulation.
Since we can't implement that directly, we have to find a compromise or identify if a structural change is needed (e.g., another reaction).

Let's try `model_v8` with:
1.  `R_A: id_yiw5 <=> 2 id_97q7`.
    *   `kA_f = 0.13` (reduced from 1.3).
    *   `kA_r = 3.8e-13` (recalculated to keep `K_eq` same).
2.  `R_B: id_shpe -> id_55cy`. `kB = 0.0153`.
3.  `R_C: id_shpe -> 11 id_97q7`. Return `kC` to a higher value, e.g., `kC = 0.20` (between 0.02 and 0.31). This is to bring `id_shpe` down in the initial phase.
4.  `R_D: id_55cy -> id_shpe`. Return `kD` to a higher value, e.g., `kD = 0.8` (between 0.35 and 1.0). This is to get `id_55cy` to decrease initially.

The main idea is to slow down `R_A` turnover, allowing `id_yiw5` to survive better and `id_97q7` (fed by `R_C`) to accumulate more, hopefully shifting the `R_A` equilibrium to higher concentrations for both.
The adjustments to `kC` and `kD` are attempts to improve the `id_shpe` and `id_55cy` profiles, especially early on.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v8)
doc_v8 = libsbml.readSBMLFromString(input_sbml_string) 
model_v8 = doc_v8.getModel()

# Parameters for model_v8
K_eq_target_RA = 3.42e11 # (1e9)^2 / 3e6, approx

kA_f_v8 = 0.13    # Reduced from 1.3
kA_r_v8 = kA_f_v8 / K_eq_target_RA # Recalculated: 0.13 / 3.42e11 = 3.80e-13

kB_v8 = 0.0153
kC_v8 = 0.20    # Increased from 0.02, was 0.31 originally
kD_v8 = 0.80    # Increased from 0.35, was 1.0 originally

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v8.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v8)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v8)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v8.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v8)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v8.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v8)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v8.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v8)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

writer = libsbml.SBMLWriter()
updated_sbml_v8 = writer.writeSBMLToString(doc_v8)
shared_variables.add("model_v8_sbml", updated_sbml_v8)
print("SBML model_v8 created.")

print("\nAttempting to simulate model_v8...")
try:
    simulation_df_v8 = simulate(updated_sbml_v8)
    shared_variables.add("simulation_df_v8", simulation_df_v8)
    print("Simulation of model_v8 completed.")
    if simulation_df_v8 is not None and not simulation_df_v8.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v8, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v8)
    else:
        print("Simulation_df_v8 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v8: {e}")
    import traceback
    print(traceback.format_exc())

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v8)
doc_v8 = libsbml.readSBMLFromString(input_sbml_string) 
model_v8 = doc_v8.getModel()

# Parameters for model_v8
K_eq_target_RA = 3.42e11 # (1e9)^2 / 3e6, approx

kA_f_v8 = 0.13    # Reduced from 1.3
kA_r_v8 = kA_f_v8 / K_eq_target_RA # Recalculated: 0.13 / 3.42e11 = 3.801169...e-13
# Ensure kA_r_v8 is not zero if kA_f_v8 is very small, though 0.13 is fine.
if kA_r_v8 == 0 and kA_f_v8 !=0 : # Should not happen here
    kA_r_v8 = 1e-20 # A very small number instead of zero if K_eq is huge

kB_v8 = 0.0153
kC_v8 = 0.20    # Increased from 0.02 (v7), was 0.31 originally
kD_v8 = 0.80    # Increased from 0.35 (v7), was 1.0 originally

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v8.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v8)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v8)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v8.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v8)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v8.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v8)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v8.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v8)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

writer = libsbml.SBMLWriter()
updated_sbml_v8 = writer.writeSBMLToString(doc_v8)
shared_variables.add("model_v8_sbml", updated_sbml_v8)
print("SBML model_v8 created.")

print("\nAttempting to simulate model_v8...")
try:
    simulation_df_v8 = simulate(updated_sbml_v8)
    shared_variables.add("simulation_df_v8", simulation_df_v8)
    print("Simulation of model_v8 completed.")
    if simulation_df_v8 is not None and not simulation_df_v8.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            # Find closest experimental data point to target_time_val
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            # Find closest simulation data point to the *actual experimental time*
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v8, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v8)
    else:
        print("Simulation_df_v8 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v8: {e}")
    import traceback
    print(traceback.format_exc())
```
# Observation

## Code Stdout
SBML model_v8 created.

Attempting to simulate model_v8...
Simulation of model_v8 completed.

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v8, closest to exp. time):
Time: 1.01, shpe: 8.08e+05, 55cy: 9.43e+03, yiw5: 6.14e+06, 97q7: 1.04e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v8, closest to exp. time):
Time: 1.99, shpe: 6.62e+05, 55cy: 1.18e+04, yiw5: 5.41e+06, 97q7: 1.07e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v8, closest to exp. time):
Time: 12.00, shpe: 9.31e+04, 55cy: 2.35e+03, yiw5: 1.50e+06, 97q7: 1.21e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v8, closest to exp. time):
Time: 27.99, shpe: 4.11e+03, 55cy: 1.04e+02, yiw5: 2.27e+05, 97q7: 1.24e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v8, closest to exp. time):
Time: 50.00, shpe: 5.62e+01, 55cy: 1.42e+00, yiw5: 5.60e+04, 97q7: 1.25e+08

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 10/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4, model_v5_sbml, simulation_df_v5, model_v6_sbml, simulation_df_v6, model_v7_sbml, simulation_df_v7, model_v8_sbml, simulation_df_v8)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 11
## Thoughts

Let's analyze `model_v8` results:
Parameters: `kA_f=0.13`, `kA_r` adjusted for `K_eq` (`~3.8e-13`), `kB=0.0153`, `kC=0.20`, `kD=0.80`.

At T~1:
*   `id_shpe`: Exp 7.27e5, Sim 8.08e5 (Sim high. `kC=0.20` is better than 0.02, but still not consuming `id_shpe` as fast as original 0.31.)
*   `id_55cy`: Exp 1.51e4, Sim 9.43e3 (Sim low. `kD=0.80` is better than 0.35 for initial phase, but `id_55cy` still not peaking high enough.)
*   `id_yiw5`: Exp 1.45e6, Sim 6.14e6 (Sim very high. Reducing `kA_f` drastically (1.3 -> 0.13) made `id_yiw5` consume much slower, as expected.)
*   `id_97q7`: Exp 1.14e8, Sim 1.04e8 (Sim low. Lower `kA_f` means less from `R_A_fwd`. `kC=0.20` means less from `R_C` than original.)

At T~2:
*   `id_shpe`: Exp 5.32e5, Sim 6.62e5 (Sim high.)
*   `id_55cy`: Exp 1.12e4, Sim 1.18e4 (Good match in value. Exp trend T1->T2 is decrease (1.51e4->1.12e4). Sim trend T1->T2 is increase (9.43e3->1.18e4). So, `kD=0.80` is getting closer to capturing the turnover, but the peak might be delayed/blunted in sim.)
*   `id_yiw5`: Exp 9.75e5, Sim 5.41e6 (Sim very high.)
*   `id_97q7`: Exp 1.41e8, Sim 1.07e8 (Sim low.)

At T~12:
*   `id_shpe`: Exp 3.43e4, Sim 9.31e4 (Sim high.)
*   `id_55cy`: Exp 1.96e3, Sim 2.35e3 (Good match! `kD=0.80` seems to work well for this phase for `id_55cy`.)
*   `id_yiw5`: Exp 1.57e5, Sim 1.50e6 (Sim much higher. `id_yiw5` is not dropping enough.)
*   `id_97q7`: Exp 8.34e8, Sim 1.21e8 (Sim vastly underestimated. Still stuck around 1.2e8.)

At T~28:
*   `id_shpe`: Exp 3.32e5, Sim 4.11e3 (Sim crashed! Despite being high earlier, it eventually crashed.)
*   `id_55cy`: Exp 3.76e4, Sim 1.04e2 (Sim crashed!)
*   `id_yiw5`: Exp 3.02e6, Sim 2.27e5 (Sim very low. It did come down from 1.5e6 at T=12, but got stuck at 2.2e5 instead of recovering to 3e6.)
*   `id_97q7`: Exp 1.02e9, Sim 1.24e8 (Sim vastly underestimated, stuck.)

At T~50:
*   `id_shpe`: Exp 7.94e4, Sim 5.62e1 (Crashed.)
*   `id_55cy`: Exp 8.35e3, Sim 1.42e0 (Crashed.)
*   `id_yiw5`: Exp 6.59e5, Sim 5.60e4 (Very low, stuck.)
*   `id_97q7`: Exp 1.03e9, Sim 1.25e8 (Vastly underestimated, stuck.)

**Conclusions from `model_v8`:**
1.  **Slowing `R_A` (lower `kA_f`, `kA_r`):** This kept `id_yiw5` higher for longer (e.g., 1.5e6 at T=12 vs 4e4 in v6/v7). However, `id_yiw5` still didn't recover to the experimental 3e6 at T=28; instead, it dropped and got stuck at a lower level (~2e5, then ~5e4). This also did not help `id_97q7` reach its target. `id_97q7` remains stuck at ~1.2e8.
2.  **`id_shpe` and `id_55cy`:** The adjustments to `kC` (0.20) and `kD` (0.80) gave a better profile for `id_55cy` around T=12. However, `id_shpe` was too high initially and then both `id_shpe` and `id_55cy` still crashed hard by T=28. The long-term recovery is still missing.
3.  **The fundamental issue persists:** The system settles into an equilibrium for `R_A` that is correct in terms of `K_eq` but at far too low absolute concentrations. The feed of `id_97q7` from `R_C` is not sufficient to drive the equilibrium to higher values because `id_shpe` (reactant for `R_C`) crashes.

**Root Cause Hypothesis:** The crash of `id_shpe` is the primary reason `R_C` cannot supply enough `id_97q7` to shift the `R_A` equilibrium to high `[Y]` and high `[Q]`. We need a robust mechanism for `id_shpe` to recover and be sustained at a reasonable level (e.g., ~1e5 - 3e5) during the T=20-T=50 phase.

Current `id_shpe` balance: `d[S]/dt = kD*[C] - (kB+kC)*[S]`.
For `id_shpe` to be sustained or recover, `kD*[C]` must balance or exceed `(kB+kC)*[S]`.
At T=28 (exp): `S`=3.32e5, `C`=3.76e4.
With `kB=0.0153`, `kC=0.20`, `kD=0.80` (model v8 params):
Production of S from C: `0.80 * 3.76e4 = 3.01e4`.
Consumption of S: `(0.0153 + 0.20) * 3.32e5 = 0.2153 * 3.32e5 = 7.15e4`.
Net `d[S]/dt` = `3.01e4 - 7.15e4 = -4.14e4`. So `id_shpe` would decrease, which is consistent with the crash if it ever reached these levels.

The ratio `kD / (kB+kC)` should be around `[S]/[C]` for steady state.
Exp `[S]/[C]` at T=28 is `3.32e5 / 3.76e4 ~ 8.8`.
Current `kD / (kB+kC)` = `0.80 / 0.2153 ~ 3.7`.
This is much less than 8.8. So `id_shpe` will be lower than `8.8 * id_55cy` at steady state.
To achieve the ratio of 8.8, if `kB+kC = 0.2153`, then `kD` would need to be `8.8 * 0.2153 = 1.89`.
This `kD=1.89` is very high. It would mean `id_55cy` is consumed very rapidly to produce `id_shpe`.

What if `R_D: id_55cy -> id_shpe` is not the only source of `id_shpe` recovery?
Or what if `kC` is not constant? If `kC` decreases significantly in the later stages, then `(kB+kC)` would be smaller.
E.g., if late-stage `kC` becomes effectively 0.01 (as tried in v7 for other reasons):
`kB+kC = 0.0153 + 0.01 = 0.0253`.
Then `kD` needed: `8.8 * 0.0253 = 0.22`. This `kD=0.22` is much more reasonable.

This points towards `kC` (consumption of `id_shpe` to `id_97q7`) being too high persistently.
If `kC` is high initially (e.g. ~0.3) for the initial `id_shpe` drop and initial `id_97q7` burst, but then becomes low later (e.g. ~0.01-0.05) to allow `id_shpe` to recover. This implies regulation.

Since we can't model regulated parameters easily, we must choose constant parameters.
If we choose a low `kC` (like 0.02 in v7), `id_shpe` stays too high initially.
If we choose a high `kC` (like 0.20 in v8 or 0.31 in v3), `id_shpe` crashes.

Perhaps the stoichiometry of `R_C: id_shpe -> 11 id_97q7` is too aggressive on `id_97q7` production per `id_shpe`. If it was `id_shpe -> 1 id_97q7`, then `kC` would represent a more direct rate. The high stoichiometry (11) amplifies the effect of `kC`.

Let's consider the total flux of `id_97q7` needed.
`id_97q7` goes from 1e8 to 1e9. Change of 9e8.
If `R_C` is `id_shpe -> sQ * id_97q7`.
The amount of `id_shpe` consumed to make this `id_97q7` would be `9e8 / sQ`.
If `sQ=11`, then `id_shpe` consumed is `9e8 / 11 = 8.2e7`. This is a huge amount, far more than initial `id_shpe`.
This implies `id_shpe` must be continually produced (e.g. from `id_55cy`) and then consumed by `R_C` over time.

What if `id_yiw5` itself is a source for `id_shpe` or `id_55cy`?
Or `id_97q7` is a source for them?
E.g. `R_G: id_97q7 -> id_shpe`? This would create a larger cycle.

Let's reconsider the `id_55cy` oscillations. It has two peaks.
Peak 1: around T=1-2 (value ~1.5e4)
Trough 1: around T=12 (value ~2e3)
Peak 2: around T=28 (value ~3.7e4)
Trough 2: around T=40 (value ~1e4)
This oscillatory behavior is often indicative of feedback loops or multiple interacting components.
Our simple `S -> C -> S` cycle (`R_B`, `R_D`) can give one peak.

Perhaps one of the reactions is reversible.
What if `R_B: id_shpe <=> id_55cy` is reversible?
`d[C]/dt = kF_B*[S] - kR_B*[C] - kD*[C]`
`d[S]/dt = kD*[C] + kR_B*[C] - kF_B*[S] - kC*[S]`
This makes the `S-C` module more complex.

Let's try to get `id_shpe` to recover without crashing, even if the initial phase is sacrificed.
To do this, `kD*[C]` must be comparable to `(kB+kC)*[S]` in the later stages.
Use `kC` that is low, e.g., `kC = 0.05`.
Then `kB+kC = 0.0153 + 0.05 = 0.0653`.
For `[S]/[C] ~ 8.8`, we need `kD/ (kB+kC) ~ 8.8`.
So `kD ~ 8.8 * 0.0653 = 0.57`.
This `kD` is moderate.

Try `model_v9` with:
1.  `R_A: id_yiw5 <=> 2 id_97q7`. `kA_f = 0.13`, `kA_r` based on `K_eq` (`~3.8e-13`). (Keep R_A slow for now).
2.  `R_B: id_shpe -> id_55cy`. `kB = 0.0153`.
3.  `R_C: id_shpe -> 11 id_97q7`. `kC = 0.05` (low, to help `id_shpe` survive).
4.  `R_D: id_55cy -> id_shpe`. `kD = 0.57` (to balance `id_shpe`/`id_55cy` ratio with low `kC`).

This will likely make initial `id_shpe` too high. But let's see if long-term recovery of all species occurs. If it does, we can then try to fine-tune for the initial phase or accept the compromise.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v9)
doc_v9 = libsbml.readSBMLFromString(input_sbml_string) 
model_v9 = doc_v9.getModel()

# Parameters for model_v9
K_eq_target_RA = 3.42e11 

kA_f_v9 = 0.13    
kA_r_v9 = kA_f_v9 / K_eq_target_RA 

kB_v9 = 0.0153
kC_v9 = 0.05    # Reduced to help id_shpe survive
kD_v9 = 0.57    # Adjusted to balance S/C ratio with new kC

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v9.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v9)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v9)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v9.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v9)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v9.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v9)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v9.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v9)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

writer = libsbml.SBMLWriter()
updated_sbml_v9 = writer.writeSBMLToString(doc_v9)
shared_variables.add("model_v9_sbml", updated_sbml_v9)
print("SBML model_v9 created.")

print("\nAttempting to simulate model_v9...")
try:
    simulation_df_v9 = simulate(updated_sbml_v9)
    shared_variables.add("simulation_df_v9", simulation_df_v9)
    print("Simulation of model_v9 completed.")
    if simulation_df_v9 is not None and not simulation_df_v9.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v9, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v9)
    else:
        print("Simulation_df_v9 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v9: {e}")
    import traceback
    print(traceback.format_exc())

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v9)
doc_v9 = libsbml.readSBMLFromString(input_sbml_string) 
model_v9 = doc_v9.getModel()

# Parameters for model_v9
K_eq_target_RA = 3.42e11 

kA_f_v9 = 0.13    
kA_r_v9 = kA_f_v9 / K_eq_target_RA 

kB_v9 = 0.0153
kC_v9 = 0.05    # Reduced to help id_shpe survive
kD_v9 = 0.57    # Adjusted to balance S/C ratio with new kC

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v9.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v9)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v9)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v9.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v9)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v9.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v9)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v9.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v9)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

writer = libsbml.SBMLWriter()
updated_sbml_v9 = writer.writeSBMLToString(doc_v9)
shared_variables.add("model_v9_sbml", updated_sbml_v9)
print("SBML model_v9 created.")

print("\nAttempting to simulate model_v9...")
try:
    simulation_df_v9 = simulate(updated_sbml_v9)
    shared_variables.add("simulation_df_v9", simulation_df_v9)
    print("Simulation of model_v9 completed.")
    if simulation_df_v9 is not None and not simulation_df_v9.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            # Find closest experimental data point to target_time_val
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            # Find closest simulation data point to the *actual experimental time*
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v9, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v9)
    else:
        print("Simulation_df_v9 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v9: {e}")
    import traceback
    print(traceback.format_exc())
```
# Observation

## Code Stdout
SBML model_v9 created.

Attempting to simulate model_v9...
Simulation of model_v9 completed.

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v9, closest to exp. time):
Time: 1.01, shpe: 9.39e+05, 55cy: 1.14e+04, yiw5: 6.14e+06, 97q7: 1.02e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v9, closest to exp. time):
Time: 1.99, shpe: 8.89e+05, 55cy: 1.70e+04, yiw5: 5.41e+06, 97q7: 1.04e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v9, closest to exp. time):
Time: 12.00, shpe: 5.41e+05, 55cy: 1.58e+04, yiw5: 1.50e+06, 97q7: 1.16e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v9, closest to exp. time):
Time: 27.99, shpe: 2.49e+05, 55cy: 7.30e+03, yiw5: 2.25e+05, 97q7: 1.22e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v9, closest to exp. time):
Time: 50.00, shpe: 8.54e+04, 55cy: 2.51e+03, yiw5: 5.49e+04, 97q7: 1.24e+08

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 9/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4, model_v5_sbml, simulation_df_v5, model_v6_sbml, simulation_df_v6, model_v7_sbml, simulation_df_v7, model_v8_sbml, simulation_df_v8, model_v9_sbml, simulation_df_v9)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 12
## Thoughts

Let's analyze `model_v9` results:
Parameters: `kA_f=0.13`, `kA_r` based on `K_eq` (`~3.8e-13`), `kB=0.0153`, `kC=0.05`, `kD=0.57`.

At T~1:
*   `id_shpe`: Exp 7.27e5, Sim 9.39e5 (Sim very high. `kC=0.05` is too low for initial `id_shpe` drop.)
*   `id_55cy`: Exp 1.51e4, Sim 1.14e4 (Sim low.)
*   `id_yiw5`: Exp 1.45e6, Sim 6.14e6 (Sim very high due to low `kA_f`.)
*   `id_97q7`: Exp 1.14e8, Sim 1.02e8 (Sim low.)

At T~2:
*   `id_shpe`: Exp 5.32e5, Sim 8.89e5 (Sim very high.)
*   `id_55cy`: Exp 1.12e4, Sim 1.70e4 (Sim high. `kD=0.57` not causing initial drop.)
*   `id_yiw5`: Exp 9.75e5, Sim 5.41e6 (Sim very high.)
*   `id_97q7`: Exp 1.41e8, Sim 1.04e8 (Sim low.)

At T~12:
*   `id_shpe`: Exp 3.43e4, Sim 5.41e5 (Sim vastly higher.)
*   `id_55cy`: Exp 1.96e3, Sim 1.58e4 (Sim vastly higher.)
*   `id_yiw5`: Exp 1.57e5, Sim 1.50e6 (Sim much higher.)
*   `id_97q7`: Exp 8.34e8, Sim 1.16e8 (Sim vastly underestimated. Still stuck.)

At T~28:
*   `id_shpe`: Exp 3.32e5, Sim 2.49e5 (Sim getting closer, but exp shows recovery to 3.3e5 from a lower point. Sim just declines to this.)
*   `id_55cy`: Exp 3.76e4, Sim 7.30e3 (Sim very low.)
*   `id_yiw5`: Exp 3.02e6, Sim 2.25e5 (Sim very low. Still stuck, no recovery to millions.)
*   `id_97q7`: Exp 1.02e9, Sim 1.22e8 (Sim vastly underestimated, stuck.)

At T~50:
*   `id_shpe`: Exp 7.94e4, Sim 8.54e4 (Values match! But trajectories are different. Exp `id_shpe` is after a recovery and then decline. Sim `id_shpe` is just a slow continuous decline from a very high initial level.)
*   `id_55cy`: Exp 8.35e3, Sim 2.51e3 (Sim low.)
*   `id_yiw5`: Exp 6.59e5, Sim 5.49e4 (Sim very low, stuck.)
*   `id_97q7`: Exp 1.03e9, Sim 1.24e8 (Vastly underestimated, stuck.)

**Conclusions from `model_v9`:**
1.  **Low `kC` (0.05) and adjusted `kD` (0.57):** This combination helped `id_shpe` to not crash completely. It persists at a reasonable level towards the end (T=50). However, the initial dynamics of `id_shpe` are way off (stays too high). `id_55cy` also doesn't match well.
2.  **`id_yiw5` and `id_97q7`:** Still the main problem. They are stuck at low levels (`id_yiw5` ~5e4, `id_97q7` ~1.2e8). Slowing down `R_A` (low `kA_f`) kept `id_yiw5` higher for longer initially, but it didn't lead to the desired recovery. The system still settles at the "wrong" (low concentration) equilibrium for `R_A`.
3.  **Sustained `id_shpe` did not fix `id_yiw5`/`id_97q7`:** Even though `id_shpe` did not crash in this simulation (it was ~2.5e5 at T=28 and ~8e4 at T=50), `R_C`'s contribution to `id_97q7` (rate `kC*[S]`, with `kC=0.05`) was not enough to push the `R_A` equilibrium to high `[Y]` and `[Q]`.
    *   At T=28 (sim): `id_shpe`=2.49e5. `R_C` flux of `id_shpe` = `0.05 * 2.49e5 = 1.245e4`. `id_97q7` species production rate = `11 * 1.245e4 = 1.37e5`.
    *   This influx into `id_97q7` should help. Why are they still stuck?

The `K_eq` for `R_A` is `3.42e11`.
Simulated T=50: `id_yiw5`=5.49e4, `id_97q7`=1.24e8.
`[Q]^2/[Y] = (1.24e8)^2 / 5.49e4 = 1.5376e16 / 5.49e4 = 2.8e11`. This is close to `K_eq`.
So `R_A` is near its equilibrium.

The issue is that the total amount of material in the `Y <=> 2Q` system, plus the inflow from `R_C`, is not enough to drive concentrations to the high experimental levels.

What if the stoichiometry of `R_C` is wrong? `id_shpe -> 11 id_97q7`.
This `11` means a small consumption of `id_shpe` leads to a large production of `id_97q7`.
This should be beneficial for `id_97q7` accumulation.

Could there be a missing reaction that consumes `id_97q7` or produces `id_yiw5` more directly and strongly?
The problem statement says "You do not need to add new species." This implies the 4 species are sufficient.

Let's reconsider the parameters for `R_A`.
`kA_f` and `kA_r`.
If `kA_f` is very low (as in v9, 0.13), `id_yiw5` is consumed slowly.
If `kA_r` is also low (as in v9, ~3.8e-13 to maintain `K_eq`), then `id_yiw5` is produced slowly from `id_97q7`.
This makes the whole `R_A` reaction slow to equilibrate and slow to respond.

What if `R_A` is faster?
Original `kA_f=1.3`. `kA_r` was `3.8e-12` (in v5, v6, v7) to maintain `K_eq`.
In v5, `id_yiw5` stuck at 4.5e4, `id_97q7` at 1.25e8.
The speed of `R_A` (values of `kA_f, kA_r`) vs. the speed of `R_C` (value of `kC`) might be important.

If `id_shpe` does not crash, `R_C` continuously produces `id_97q7`.
This `id_97q7` feeds into `R_A`. `2 id_97q7 -> id_yiw5`.
This `id_yiw5` is then consumed by `id_yiw5 -> 2 id_97q7`.
This looks like a futile cycle if `R_C` is the only net source into this Y/Q system.

The experimental data shows `id_yiw5` and `id_shpe` (and `id_55cy`) all recover after an initial drop.
This coordinated recovery is key.
`R_D: id_55cy -> id_shpe` helps `id_shpe` recover if `id_55cy` is present.
`R_B: id_shpe -> id_55cy` produces `id_55cy` if `id_shpe` is present.
This `S-C` cycle needs to be robust.

The parameters `kC` and `kD` are critical for `id_shpe` and `id_55cy`.
`model_v9` (low `kC=0.05`, `kD=0.57`) kept `id_shpe` from crashing but messed up initial phase.
`model_v8` (`kC=0.20`, `kD=0.80`) had better `id_55cy` at T=12, but `id_shpe` still crashed.
`model_v4` (`kC=0.31`, `kD=1.0`) had good initial `id_shpe` but `id_55cy` was low and all crashed.

Let's try to find a `kC` and `kD` that allows `id_shpe` to dip but then recover, similar to experiment.
This requires `kD*[C] - (kB+kC)*[S]` to be negative initially, then positive during recovery.
This can happen if `[C]` rises sufficiently relative to `[S]`, or if `[S]` drops low enough.

Consider the parameters from `model_v3` which gave good initial fits but crashed:
`kA=1.3` (unidirectional), `kB=0.0153`, `kC=0.31`, `kD=1.0`.
`id_shpe` at T1=7.2e5, T2=5.3e5, T12=2.5e4 (crashed).
`id_55cy` at T1=8.1e3, T2=8.8e3, T12=5.6e2 (crashed).

The issue is that `(kB+kC)` with `kC=0.31` is `0.0153+0.31 = 0.3253`. This is a strong sink for `id_shpe`.
Production `kD*[id_55cy]`. If `kD=1.0`.
For `id_shpe` to recover, `1.0*[C] > 0.3253*[S]`. Or `[C]/[S] > 0.3253`.
Exp at T=28: `[C]/[S] = 3.76e4 / 3.32e5 = 0.11`. This is less than 0.3253. So `id_shpe` would not recover.

This means the assumption `kD/(kB+kC) ~ [S]/[C]_recovery` is important.
`[S]/[C]_recovery ~ 8.8`. So `kD = 8.8 * (kB+kC)`.
If we want `id_shpe` to drop initially, `kC` must be high. Let `kC=0.25` (slightly lower than 0.31).
`kB+kC = 0.0153 + 0.25 = 0.2653`.
Then `kD_recovery = 8.8 * 0.2653 = 2.33`. This `kD` is very high.
A high `kD` will make `id_55cy` deplete very fast initially.

This suggests a structural problem or a more complex kinetic form.
What if one of the consumption reactions is saturable (Michaelis-Menten)?
E.g., if `R_C: id_shpe -> 11 id_97q7` follows `Vm * S / (Km + S)`.
If `Km` is small, it's like mass-action at low `S`, but saturates at high `S`.
If `Km` is large, it's like mass-action.

Let's reconsider the `R_A` parameters.
The fact that `id_yiw5` and `id_97q7` get stuck at an equilibrium far below experimental values, despite `R_C` providing some influx of `id_97q7` (when `id_shpe` is present), suggests that either:
1.  The influx from `R_C` is too small. (We saw `id_shpe` crashing is an issue).
2.  The `R_A` reaction itself is too slow to utilize the influx from `R_C` to shift equilibrium effectively within the simulation time, OR
3.  There's a missing significant source for `id_yiw5` or `id_97q7`, or a missing sink that keeps them low (but this would prevent recovery).

Let's try to make `R_A` faster, while keeping the same `K_eq`.
`kA_f=1.3`, `kA_r=3.8e-12` (from v5-v7). This was faster than v8/v9.
In v5 (`kC=0.31, kD=0.13`), `id_shpe` crashed, `id_yiw5` stuck at 4.5e4.
The `kD=0.13` was too low, `id_55cy` got too high.

It seems I am going in circles with `kC` and `kD`.
The core issue is the lack of robust recovery of `id_shpe`, `id_55cy`, and `id_yiw5`.
And `id_97q7` not reaching high enough levels.

What if the stoichiometry `11` in `R_C: id_shpe -> 11 id_97q7` is too high?
If it was `id_shpe -> id_97q7` (stoich 1), then `kC` would need to be ~11x larger to get same `id_97q7` production rate for a given `id_shpe` consumption.
Or, for the same `kC`, `id_shpe` consumption would be the same, but `id_97q7` production would be 11x lower. This would be worse for `id_97q7`.
So the high stoichiometry `11` should be helpful for `id_97q7`.

Is there any species that accumulates to very high levels in sim that shouldn't? No, all crash or get stuck low.

Let's try a combination:
- `R_A` fast: `kA_f=1.3`, `kA_r=3.8e-12`.
- `kC` moderate for initial drop but not too severe: `kC=0.20` (as in v8).
- `kD` moderate for initial `id_55cy` drop and later `id_shpe` recovery: `kD=0.80` (as in v8).
This is basically `model_v8` parameters, but with the faster `R_A` rates from `model_v5/v6/v7`.
Model v8 had `kA_f=0.13`. Model v5 had `kA_f=1.3`, `kA_r=3.8e-12`, `kC=0.31`, `kD=0.13`.
The difference between this new proposal and v5 is `kC` (0.20 vs 0.31) and `kD` (0.80 vs 0.13).

Model `v10` parameters:
1.  `R_A: id_yiw5 <=> 2 id_97q7`. `kA_f = 1.3`, `kA_r = 3.8e-12`.
2.  `R_B: id_shpe -> id_55cy`. `kB = 0.0153`.
3.  `R_C: id_shpe -> 11 id_97q7`. `kC = 0.20`.
4.  `R_D: id_55cy -> id_shpe`. `kD = 0.80`.

This combination has not been tried exactly. It uses the faster `R_A` kinetics, and the `kC, kD` values from `model_v8` which gave a decent `id_55cy` at T=12 but still led to `id_shpe` crash. The hope is that faster `R_A` might interact differently.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v10)
doc_v10 = libsbml.readSBMLFromString(input_sbml_string) 
model_v10 = doc_v10.getModel()

# Parameters for model_v10
kA_f_v10 = 1.3    # Faster R_A forward rate
kA_r_v10 = 3.8e-12 # Corresponding reverse rate for K_eq ~3.42e11

kB_v10 = 0.0153
kC_v10 = 0.20    # Moderate kC (from model_v8)
kD_v10 = 0.80    # Moderate kD (from model_v8)

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v10.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v10)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v10)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v10.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v10)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v10.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v10)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v10.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v10)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

writer = libsbml.SBMLWriter()
updated_sbml_v10 = writer.writeSBMLToString(doc_v10)
shared_variables.add("model_v10_sbml", updated_sbml_v10)
print("SBML model_v10 created.")

print("\nAttempting to simulate model_v10...")
try:
    simulation_df_v10 = simulate(updated_sbml_v10)
    shared_variables.add("simulation_df_v10", simulation_df_v10)
    print("Simulation of model_v10 completed.")
    if simulation_df_v10 is not None and not simulation_df_v10.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v10, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v10)
    else:
        print("Simulation_df_v10 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v10: {e}")
    import traceback
    print(traceback.format_exc())

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v10)
doc_v10 = libsbml.readSBMLFromString(input_sbml_string) 
model_v10 = doc_v10.getModel()

# Parameters for model_v10
kA_f_v10 = 1.3    # Faster R_A forward rate
kA_r_v10 = 3.8e-12 # Corresponding reverse rate for K_eq ~3.42e11

kB_v10 = 0.0153
kC_v10 = 0.20    # Moderate kC (from model_v8)
kD_v10 = 0.80    # Moderate kD (from model_v8)

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v10.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v10)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v10)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v10.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v10)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v10.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v10)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v10.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v10)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

writer = libsbml.SBMLWriter()
updated_sbml_v10 = writer.writeSBMLToString(doc_v10)
shared_variables.add("model_v10_sbml", updated_sbml_v10)
print("SBML model_v10 created.")

print("\nAttempting to simulate model_v10...")
try:
    simulation_df_v10 = simulate(updated_sbml_v10)
    shared_variables.add("simulation_df_v10", simulation_df_v10)
    print("Simulation of model_v10 completed.")
    if simulation_df_v10 is not None and not simulation_df_v10.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            # Find closest experimental data point to target_time_val
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            # Find closest simulation data point to the *actual experimental time*
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v10, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v10)
    else:
        print("Simulation_df_v10 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v10: {e}")
    import traceback
    print(traceback.format_exc())
```
# Observation

## Code Stdout
SBML model_v10 created.

Attempting to simulate model_v10...
Simulation of model_v10 completed.

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v10, closest to exp. time):
Time: 1.01, shpe: 8.08e+05, 55cy: 9.43e+03, yiw5: 1.90e+06, 97q7: 1.12e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v10, closest to exp. time):
Time: 1.99, shpe: 6.62e+05, 55cy: 1.18e+04, yiw5: 5.59e+05, 97q7: 1.16e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v10, closest to exp. time):
Time: 12.00, shpe: 9.31e+04, 55cy: 2.35e+03, yiw5: 4.47e+04, 97q7: 1.24e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v10, closest to exp. time):
Time: 27.99, shpe: 4.11e+03, 55cy: 1.04e+02, yiw5: 4.56e+04, 97q7: 1.25e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v10, closest to exp. time):
Time: 50.00, shpe: 5.62e+01, 55cy: 1.42e+00, yiw5: 4.56e+04, 97q7: 1.25e+08

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 8/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4, model_v5_sbml, simulation_df_v5, model_v6_sbml, simulation_df_v6, model_v7_sbml, simulation_df_v7, model_v8_sbml, simulation_df_v8, model_v9_sbml, simulation_df_v9, model_v10_sbml, simulation_df_v10)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 13
## Thoughts

Let's analyze `model_v10` results:
Parameters: `kA_f=1.3`, `kA_r=3.8e-12` (Fast R_A), `kB=0.0153`, `kC=0.20`, `kD=0.80`.

At T~1:
*   `id_shpe`: Exp 7.27e5, Sim 8.08e5 (Sim high)
*   `id_55cy`: Exp 1.51e4, Sim 9.43e3 (Sim low)
*   `id_yiw5`: Exp 1.45e6, Sim 1.90e6 (Sim high. Faster `kA_f` consumes `id_yiw5` more, but it starts very high.)
*   `id_97q7`: Exp 1.14e8, Sim 1.12e8 (Good match)

At T~2:
*   `id_shpe`: Exp 5.32e5, Sim 6.62e5 (Sim high)
*   `id_55cy`: Exp 1.12e4, Sim 1.18e4 (Good match in value. Trend still slightly off.)
*   `id_yiw5`: Exp 9.75e5, Sim 5.59e5 (Sim low. `kA_f=1.3` is consuming `id_yiw5` rapidly.)
*   `id_97q7`: Exp 1.41e8, Sim 1.16e8 (Sim low)

At T~12:
*   `id_shpe`: Exp 3.43e4, Sim 9.31e4 (Sim high)
*   `id_55cy`: Exp 1.96e3, Sim 2.35e3 (Good match!)
*   `id_yiw5`: Exp 1.57e5, Sim 4.47e4 (Sim very low. Faster `kA_f` depleted `id_yiw5` more than the slower `kA_f=0.13` in v8/v9.)
*   `id_97q7`: Exp 8.34e8, Sim 1.24e8 (Sim vastly underestimated. Stuck.)

At T~28:
*   `id_shpe`: Exp 3.32e5, Sim 4.11e3 (Crashed!)
*   `id_55cy`: Exp 3.76e4, Sim 1.04e2 (Crashed!)
*   `id_yiw5`: Exp 3.02e6, Sim 4.56e4 (Very low, stuck. Same as v5, v6, v7.)
*   `id_97q7`: Exp 1.02e9, Sim 1.25e8 (Vastly underestimated, stuck. Same as v5, v6, v7.)

At T~50: (Similar to T=28, all crashed or stuck low)
*   `id_shpe`: Crashed.
*   `id_55cy`: Crashed.
*   `id_yiw5`: Stuck low.
*   `id_97q7`: Stuck low.

**Conclusions from `model_v10`:**
1.  **Faster `R_A` kinetics (`kA_f=1.3`)**: This led to faster depletion of `id_yiw5` compared to models with `kA_f=0.13`. It did not solve the problem of `id_yiw5` and `id_97q7` getting stuck at low levels. The equilibrium is reached, but at the wrong absolute concentrations.
2.  **`kC=0.20`, `kD=0.80`**: These parameters provided a good match for `id_55cy` around T=12 and a reasonable (though high) `id_shpe` profile up to T=12. However, `id_shpe` and `id_55cy` still crashed by T=28.
3.  **The core issue is unchanged**: The model cannot sustain `id_shpe` and `id_55cy` in the long term, and therefore `R_C` cannot provide enough `id_97q7` to shift the `R_A` equilibrium to the high experimental concentrations of `id_yiw5` and `id_97q7`.

The system seems to require a robust source for `id_shpe` (and consequently `id_55cy`) that is active in the later stages (T > 20).
The current `R_D: id_55cy -> id_shpe` is not enough because `id_55cy` itself crashes.

Let's consider the possibility of a reaction that produces `id_shpe` or `id_55cy` from `id_yiw5` or `id_97q7`.
*   `id_yiw5 -> id_shpe`? or `id_yiw5 -> id_55cy`?
*   `id_97q7 -> id_shpe`? or `id_97q7 -> id_55cy`?

If `id_97q7` (which is supposed to be abundant) can be converted to `id_shpe`:
`R_X: id_97q7 -> id_shpe` (rate `kX * [id_97q7]`)
This would provide a source for `id_shpe` that depends on `id_97q7`. If `id_97q7` reaches high levels, `id_shpe` could be maintained.
This new reaction would add a feedback loop:
`id_shpe -> (R_C) -> id_97q7 -> (R_X) -> id_shpe`.
Also `id_shpe -> (R_A via R_C) -> id_yiw5`.

Let's try adding `R_X: id_97q7 -> id_shpe`.
If this reaction exists, it would reduce the net accumulation of `id_97q7`.
The rate `kX` needs to be chosen.
During `id_shpe` recovery (e.g. T=12 to T=28), `id_shpe` increases.
Net `d[S]/dt = kD*[C] + kX*[Q] - (kB+kC)*[S]`.
We need this to be positive.
At T=28 (exp): `S`=3.32e5, `C`=3.76e4, `Q`=1.02e9.
Using `kB=0.0153`, `kC=0.20`, `kD=0.80` (from v10):
`0.80*3.76e4 + kX*1.02e9 - (0.0153+0.20)*3.32e5 > 0`
`3.01e4 + kX*1.02e9 - 0.2153*3.32e5 > 0`
`3.01e4 + kX*1.02e9 - 7.15e4 > 0`
`kX*1.02e9 > 4.14e4`
`kX > 4.14e4 / 1.02e9 = 4.06e-5`.
This is a possible magnitude for `kX`. Let's try `kX = 5e-5`.

This new reaction `R_X` might be what's missing to sustain `id_shpe`. If `id_shpe` is sustained, `R_C` can produce `id_97q7`, which might help `R_A` reach the correct high-concentration equilibrium.

Model `v11` parameters:
1.  `R_A: id_yiw5 <=> 2 id_97q7`. `kA_f = 1.3`, `kA_r = 3.8e-12` (Fast R_A).
2.  `R_B: id_shpe -> id_55cy`. `kB = 0.0153`.
3.  `R_C: id_shpe -> 11 id_97q7`. `kC = 0.20`.
4.  `R_D: id_55cy -> id_shpe`. `kD = 0.80`.
5.  **New Reaction** `R_X: id_97q7 -> id_shpe`. `kX = 5e-5`.

This is a structural change to the model.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v11)
doc_v11 = libsbml.readSBMLFromString(input_sbml_string) 
model_v11 = doc_v11.getModel()

# Parameters for model_v11
kA_f_v11 = 1.3    
kA_r_v11 = 3.8e-12 

kB_v11 = 0.0153
kC_v11 = 0.20    
kD_v11 = 0.80    
kX_v11 = 5e-5 # New parameter for R_X

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v11.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v11)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v11)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v11.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v11)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v11.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v11)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v11.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v11)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# New Reaction R_X: id_97q7 -> id_shpe
r_x = model_v11.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v11)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v11 = writer.writeSBMLToString(doc_v11)
shared_variables.add("model_v11_sbml", updated_sbml_v11)
print("SBML model_v11 created.")

print("\nAttempting to simulate model_v11...")
try:
    simulation_df_v11 = simulate(updated_sbml_v11)
    shared_variables.add("simulation_df_v11", simulation_df_v11)
    print("Simulation of model_v11 completed.")
    if simulation_df_v11 is not None and not simulation_df_v11.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v11, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v11)
    else:
        print("Simulation_df_v11 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v11: {e}")
    import traceback
    print(traceback.format_exc())

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v11)
doc_v11 = libsbml.readSBMLFromString(input_sbml_string) 
model_v11 = doc_v11.getModel()

# Parameters for model_v11
kA_f_v11 = 1.3    
kA_r_v11 = 3.8e-12 

kB_v11 = 0.0153
kC_v11 = 0.20    
kD_v11 = 0.80    
kX_v11 = 5e-5 # New parameter for R_X

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v11.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v11)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v11)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v11.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v11)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v11.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v11)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v11.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v11)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# New Reaction R_X: id_97q7 -> id_shpe
r_x = model_v11.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v11)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v11 = writer.writeSBMLToString(doc_v11)
shared_variables.add("model_v11_sbml", updated_sbml_v11)
print("SBML model_v11 created.")

print("\nAttempting to simulate model_v11...")
try:
    simulation_df_v11 = simulate(updated_sbml_v11)
    shared_variables.add("simulation_df_v11", simulation_df_v11)
    print("Simulation of model_v11 completed.")
    if simulation_df_v11 is not None and not simulation_df_v11.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            # Find closest experimental data point to target_time_val
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            # Find closest simulation data point to the *actual experimental time*
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v11, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v11)
    else:
        print("Simulation_df_v11 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v11: {e}")
    import traceback
    print(traceback.format_exc())
```
# Observation

## Code Stdout
SBML model_v11 created.

Attempting to simulate model_v11...
Simulation of model_v11 completed.

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v11, closest to exp. time):
Time: 1.01, shpe: 8.13e+05, 55cy: 9.46e+03, yiw5: 1.90e+06, 97q7: 1.12e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v11, closest to exp. time):
Time: 1.99, shpe: 6.71e+05, 55cy: 1.19e+04, yiw5: 5.59e+05, 97q7: 1.16e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v11, closest to exp. time):
Time: 12.00, shpe: 1.21e+05, 55cy: 2.86e+03, yiw5: 4.50e+04, 97q7: 1.24e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v11, closest to exp. time):
Time: 27.99, shpe: 3.54e+04, 55cy: 7.01e+02, yiw5: 4.65e+04, 97q7: 1.26e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v11, closest to exp. time):
Time: 50.00, shpe: 3.19e+04, 55cy: 6.10e+02, yiw5: 4.76e+04, 97q7: 1.28e+08

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 7/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4, model_v5_sbml, simulation_df_v5, model_v6_sbml, simulation_df_v6, model_v7_sbml, simulation_df_v7, model_v8_sbml, simulation_df_v8, model_v9_sbml, simulation_df_v9, model_v10_sbml, simulation_df_v10, model_v11_sbml, simulation_df_v11)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 14
## Thoughts

Let's analyze `model_v11` results (added `R_X: id_97q7 -> id_shpe` with `kX = 5e-5`):
Parameters: `kA_f=1.3`, `kA_r=3.8e-12`, `kB=0.0153`, `kC=0.20`, `kD=0.80`, `kX=5e-5`.

At T~1 & T~2: (Initial phase)
*   `id_shpe`: Sim high (8.1e5 vs 7.3e5 at T1; 6.7e5 vs 5.3e5 at T2). `kC=0.20` still not consuming `id_shpe` fast enough.
*   `id_55cy`: Sim low at T1 (9.5e3 vs 1.5e4), good at T2 (1.2e4 vs 1.1e4).
*   `id_yiw5`: Sim high at T1 (1.9e6 vs 1.4e6), low at T2 (5.6e5 vs 9.7e5). `kA_f=1.3` is active.
*   `id_97q7`: Sim matches well initially.

At T~12:
*   `id_shpe`: Sim 1.2e5, Exp 3.4e4 (Sim much higher).
*   `id_55cy`: Sim 2.9e3, Exp 1.9e3 (Sim slightly high, but reasonable match).
*   `id_yiw5`: Sim 4.5e4, Exp 1.57e5 (Sim very low, stuck).
*   `id_97q7`: Sim 1.24e8, Exp 8.34e8 (Sim vastly underestimated, stuck).

At T~28: (Recovery phase)
*   `id_shpe`: Sim 3.5e4, Exp 3.3e5 (Sim very low. `R_X` did not cause robust recovery. Exp `id_shpe` is 10x higher).
*   `id_55cy`: Sim 7.0e2, Exp 3.7e4 (Sim crashed. Exp `id_55cy` is 50x higher).
*   `id_yiw5`: Sim 4.6e4, Exp 3.0e6 (Sim extremely low, stuck. Exp `id_yiw5` is ~65x higher).
*   `id_97q7`: Sim 1.26e8, Exp 1.0e9 (Sim vastly underestimated, stuck. Exp `id_97q7` is ~8x higher).

At T~50: (Long term)
*   `id_shpe`: Sim 3.2e4, Exp 7.9e4 (Sim low, but not zero. `R_X` provides some sustenance).
*   `id_55cy`: Sim 6.1e2, Exp 8.3e3 (Sim crashed).
*   `id_yiw5`: Sim 4.8e4, Exp 6.6e5 (Sim extremely low, stuck).
*   `id_97q7`: Sim 1.28e8, Exp 1.0e9 (Sim vastly underestimated, stuck).

**Conclusions from `model_v11`:**
1.  **New reaction `R_X: id_97q7 -> id_shpe`:** Adding this reaction with `kX=5e-5` did prevent `id_shpe` from crashing to absolute zero. It maintained `id_shpe` around 3e4 in the later stages. However, this level is still too low compared to the experimental recovery (to 3.3e5 at T=28) and later levels (8e4 at T=50).
2.  **Consequences of low `id_shpe`:** Because `id_shpe` remained low, `id_55cy` (produced from `id_shpe` by `R_B`) also remained very low/crashed.
3.  **`id_yiw5` and `id_97q7` still stuck:** The fundamental problem of these species not reaching their high experimental concentrations persists. The `R_A` equilibrium is reached at low concentrations. The influx of `id_97q7` from `R_C` is weak because `id_shpe` is low. The new reaction `R_X` consumes `id_97q7`, which, if anything, would make it harder for `id_97q7` to accumulate, unless `kX` is very small or `id_97q7` is extremely high.

The value of `kX=5e-5` means that if `id_97q7` were at its target of 1e9, the production rate of `id_shpe` from `R_X` would be `5e-5 * 1e9 = 5e4`.
This rate (5e4) should be enough to sustain `id_shpe` if its consumption `(kB+kC)*S` is matched.
At T=28 (exp `S`=3.3e5, `C`=3.7e4):
Consumption of `S` (using v11 params `kB=0.0153, kC=0.20`): `(0.0153+0.20)*3.3e5 = 0.2153*3.3e5 = 7.1e4`.
Production of `S` from `R_D`: `kD*[C] = 0.80*3.7e4 = 2.96e4`.
Production of `S` from `R_X` (if `Q`=1e9): `5e4`.
Total production of `S` = `2.96e4 + 5e4 = 7.96e4`.
This total production (7.96e4) is slightly higher than consumption (7.1e4). This suggests `id_shpe` *could* recover if `id_97q7` reached 1e9 and `id_55cy` was around 3.7e4.

The problem is a "chicken and egg" situation:
*   `id_shpe` needs high `id_97q7` (for `R_X`) and high `id_55cy` (for `R_D`) to recover.
*   `id_55cy` needs high `id_shpe` (for `R_B`) to recover.
*   `id_97q7` needs high `id_shpe` (for `R_C`) and/or high `id_yiw5` (for `R_A_fwd`) to become high.
*   `id_yiw5` needs high `id_97q7` (for `R_A_rev`) to recover.

Everything is interlinked and stuck in a low state.

The initial phase (T=0-2) parameters seem to require:
*   `kC` relatively high (e.g., 0.2-0.3) for `id_shpe` to drop.
*   `kD` relatively high (e.g., 0.8-1.0) for `id_55cy` to drop after its initial peak.
*   `kA_f` relatively high (e.g., 1.3) for `id_yiw5` to drop.

The later phase (T > 12) parameters seem to require:
*   `kC` relatively low for `id_shpe` to not be overly consumed.
*   `kD/(kB+kC)` ratio to be around `[S]/[C]` ratio for `id_shpe`/`id_55cy` balance.
*   `kA_r` for `R_A_rev` to be strong enough (relative to `kA_f`) to drive `id_yiw5` recovery when `id_97q7` is high.
*   `kX` for `R_X` to provide a source for `id_shpe` from `id_97q7`.

The discrepancy suggests that some parameters are not constant or there's a missing regulatory element or reaction that changes the system's behavior over time.

Since we are using constant parameters, we need a set that provides the best compromise or captures the most critical features. The most critical failure is the lack of recovery and stabilization at high levels for `Y` and `Q`.

Let's try to boost `kX` significantly. If `R_X: Q -> S` is much stronger, `id_shpe` might recover more robustly, which could then kickstart the other recoveries.
If `kX` is too high, it might deplete `id_97q7` too much.
Current `kX=5e-5`. If `Q`=1.25e8 (current stuck level), `R_X` produces `S` at rate `5e-5 * 1.25e8 = 6250`.
This is not enough to counter `id_shpe` consumption if `id_shpe` is e.g. 1e5 (`(kB+kC)*S = 0.2153*1e5 = 21530`).
Let's increase `kX` by 10-fold to `5e-4`.
Production from `R_X` (if `Q`=1.25e8) = `5e-4 * 1.25e8 = 6.25e4`.
This is a substantial production rate for `id_shpe`.

Model `v12` parameters:
1.  `R_A: id_yiw5 <=> 2 id_97q7`. `kA_f = 1.3`, `kA_r = 3.8e-12`.
2.  `R_B: id_shpe -> id_55cy`. `kB = 0.0153`.
3.  `R_C: id_shpe -> 11 id_97q7`. `kC = 0.20`. (Compromise for initial drop vs. later survival)
4.  `R_D: id_55cy -> id_shpe`. `kD = 0.80`. (Compromise for initial drop vs. later S/C balance)
5.  `R_X: id_97q7 -> id_shpe`. `kX = 5e-4` (Increased 10x).

This focuses on making `id_shpe` recovery much stronger, hoping it will cascade.
The initial phase `id_shpe` might still be too high due to `kC=0.20`.
The initial phase `id_55cy` might be okay with `kD=0.80`.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v12)
doc_v12 = libsbml.readSBMLFromString(input_sbml_string) 
model_v12 = doc_v12.getModel()

# Parameters for model_v12
kA_f_v12 = 1.3    
kA_r_v12 = 3.8e-12 

kB_v12 = 0.0153
kC_v12 = 0.20    
kD_v12 = 0.80    
kX_v12 = 5e-4 # Increased 10x from 5e-5

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v12.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v12)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v12)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v12.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v12)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v12.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v12)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v12.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v12)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = model_v12.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v12)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v12 = writer.writeSBMLToString(doc_v12)
shared_variables.add("model_v12_sbml", updated_sbml_v12)
print("SBML model_v12 created.")

print("\nAttempting to simulate model_v12...")
try:
    simulation_df_v12 = simulate(updated_sbml_v12)
    shared_variables.add("simulation_df_v12", simulation_df_v12)
    print("Simulation of model_v12 completed.")
    if simulation_df_v12 is not None and not simulation_df_v12.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v12, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v12)
    else:
        print("Simulation_df_v12 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v12: {e}")
    import traceback
    print(traceback.format_exc())

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v12)
doc_v12 = libsbml.readSBMLFromString(input_sbml_string) 
model_v12 = doc_v12.getModel()

# Parameters for model_v12
kA_f_v12 = 1.3    
kA_r_v12 = 3.8e-12 

kB_v12 = 0.0153
kC_v12 = 0.20    
kD_v12 = 0.80    
kX_v12 = 5e-4 # Increased 10x from 5e-5

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v12.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v12)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v12)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v12.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v12)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v12.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v12)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v12.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v12)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = model_v12.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v12)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v12 = writer.writeSBMLToString(doc_v12)
shared_variables.add("model_v12_sbml", updated_sbml_v12)
print("SBML model_v12 created.")

print("\nAttempting to simulate model_v12...")
try:
    simulation_df_v12 = simulate(updated_sbml_v12)
    shared_variables.add("simulation_df_v12", simulation_df_v12)
    print("Simulation of model_v12 completed.")
    if simulation_df_v12 is not None and not simulation_df_v12.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            # Find closest experimental data point to target_time_val
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            # Find closest simulation data point to the *actual experimental time*
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v12, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v12)
    else:
        print("Simulation_df_v12 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v12: {e}")
    import traceback
    print(traceback.format_exc())
```
# Observation

## Code Stdout
SBML model_v12 created.

Attempting to simulate model_v12...
Simulation of model_v12 completed.

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v12, closest to exp. time):
Time: 1.01, shpe: 8.57e+05, 55cy: 9.73e+03, yiw5: 1.90e+06, 97q7: 1.12e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v12, closest to exp. time):
Time: 1.99, shpe: 7.53e+05, 55cy: 1.27e+04, yiw5: 5.59e+05, 97q7: 1.17e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v12, closest to exp. time):
Time: 12.00, shpe: 3.74e+05, 55cy: 7.50e+03, yiw5: 4.74e+04, 97q7: 1.28e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v12, closest to exp. time):
Time: 27.99, shpe: 3.42e+05, 55cy: 6.51e+03, yiw5: 5.61e+04, 97q7: 1.39e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v12, closest to exp. time):
Time: 50.00, shpe: 3.78e+05, 55cy: 7.18e+03, yiw5: 6.95e+04, 97q7: 1.55e+08

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 6/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4, model_v5_sbml, simulation_df_v5, model_v6_sbml, simulation_df_v6, model_v7_sbml, simulation_df_v7, model_v8_sbml, simulation_df_v8, model_v9_sbml, simulation_df_v9, model_v10_sbml, simulation_df_v10, model_v11_sbml, simulation_df_v11, model_v12_sbml, simulation_df_v12)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 15
## Thoughts

Let's analyze `model_v12` results (increased `kX` for `R_X: Q -> S` by 10x to `5e-4`):
Parameters: `kA_f=1.3`, `kA_r=3.8e-12`, `kB=0.0153`, `kC=0.20`, `kD=0.80`, `kX=5e-4`.

At T~1 & T~2: (Initial phase)
*   `id_shpe`: Sim very high (8.6e5 vs 7.3e5 at T1; 7.5e5 vs 5.3e5 at T2). `kC=0.20` + strong `R_X` makes `id_shpe` high.
*   `id_55cy`: Sim low at T1 (9.7e3 vs 1.5e4), good at T2 (1.3e4 vs 1.1e4).
*   `id_yiw5`: Sim high at T1, low at T2. Similar to v11.
*   `id_97q7`: Sim matches well initially.

At T~12:
*   `id_shpe`: Sim 3.7e5, Exp 3.4e4 (Sim vastly higher. Strong `R_X` keeps `id_shpe` very high).
*   `id_55cy`: Sim 7.5e3, Exp 1.9e3 (Sim high).
*   `id_yiw5`: Sim 4.7e4, Exp 1.57e5 (Sim very low, stuck).
*   `id_97q7`: Sim 1.28e8, Exp 8.34e8 (Sim vastly underestimated, stuck).

At T~28: (Recovery phase)
*   `id_shpe`: Sim 3.4e5, Exp 3.3e5 (Excellent match for `id_shpe`! Strong `R_X` worked for `id_shpe` level).
*   `id_55cy`: Sim 6.5e3, Exp 3.7e4 (Sim very low. `id_shpe` is high, so `R_B` should produce `id_55cy`. `kD=0.80` might be consuming it too fast if `id_shpe` is not its only source, or `kB` is too low).
*   `id_yiw5`: Sim 5.6e4, Exp 3.0e6 (Sim extremely low, stuck).
*   `id_97q7`: Sim 1.39e8, Exp 1.0e9 (Sim vastly underestimated, stuck. Slightly higher than v11 due to more `id_shpe` for `R_C`, but not nearly enough).

At T~50: (Long term)
*   `id_shpe`: Sim 3.8e5, Exp 7.9e4 (Sim much higher. `id_shpe` is sustained at a high level by `R_X`).
*   `id_55cy`: Sim 7.2e3, Exp 8.3e3 (Good match for `id_55cy`! This is a consequence of sustained high `id_shpe`).
*   `id_yiw5`: Sim 6.9e4, Exp 6.6e5 (Sim extremely low, stuck. Slight increase but still very far).
*   `id_97q7`: Sim 1.55e8, Exp 1.0e9 (Sim vastly underestimated, stuck. Slight increase but still very far).

**Conclusions from `model_v12`:**
1.  **Stronger `R_X: Q -> S` (`kX=5e-4`):** This was very effective at sustaining `id_shpe` at high levels (around 3-4e5) throughout the later part of the simulation. This is a major improvement for `id_shpe`'s long-term behavior. Consequently, `id_55cy` also achieved good levels at T=50.
2.  **Initial phase for `id_shpe`:** Still problematic; `id_shpe` is too high initially because `kC=0.20` is not enough to bring it down fast, and `R_X` contributes to `id_shpe` from the start (as `id_97q7` is initially high).
3.  **`id_yiw5` and `id_97q7` are STILL THE PROBLEM:** Despite `id_shpe` being sustained at high levels (which means `R_C: S -> 11Q` is actively producing `id_97q7`), `id_yiw5` and `id_97q7` remain stuck at their low equilibrium (`Y`~5-7e4, `Q`~1.3-1.5e8).
    *   Rate of `id_97q7` production from `R_C` at T=28 (sim): `kC*[S] = 0.20 * 3.4e5 = 6.8e4` (this is `id_shpe` consumption rate). Species `id_97q7` production rate = `11 * 6.8e4 = 7.48e5`.
    *   Rate of `id_97q7` consumption by `R_X` at T=28 (sim, `Q`~1.4e8): `kX*[Q] = 5e-4 * 1.4e8 = 7e4`.
    *   Net influx to `id_97q7` pool from `R_C` and `R_X` is `7.48e5 - 7e4 = 6.78e5`. This is a substantial influx.
    *   This influx should be pushing the `R_A: Y <=> 2Q` equilibrium. Why isn't it?
    *   The `R_A` reaction: `kA_f*[Y] - kA_r*[Q]^2`. At the stuck state (Y~6e4, Q~1.4e8):
        *   Forward flux: `1.3 * 6e4 = 7.8e4`.
        *   Reverse flux: `3.8e-12 * (1.4e8)^2 = 3.8e-12 * 1.96e16 = 7.45e4`.
        *   These are nearly balanced, as expected for equilibrium.
    *   The net influx of `id_97q7` (6.78e5) must be going somewhere. In `R_A`, if `id_97q7` increases, the reverse reaction `2Q -> Y` should increase, producing `Y`. Then `Y` increases, and forward `Y -> 2Q` increases.
    *   It seems the system *is* at equilibrium for `R_A`, but this equilibrium is maintained despite the influx. This can only happen if the influx is balanced by a net consumption within the `R_A` reaction itself, meaning `kA_f*[Y]` effectively consumes what `kA_r*[Q]^2` produces from the excess `Q`.

The `K_eq` for `R_A` is `kA_f/kA_r = 1.3 / 3.8e-12 = 3.42e11`.
Experimental T=28 target: `Y`=3e6, `Q`=1e9. `Q^2/Y = (1e9)^2/3e6 = 3.33e11`. This matches.
If the simulation has `Y`=6e4, then for this `K_eq`, `Q^2 = K_eq * Y = 3.42e11 * 6e4 = 2.05e16`. So `Q = sqrt(2.05e16) = 1.43e8`. This matches the simulation's stuck `Q` level.

The system is correctly finding the equilibrium for `R_A` based on the `K_eq`. The problem is that the total amount of "material" (that can be interconverted between Y and Q) is too low.
The influx from `R_C` (producing Q) and consumption by `R_X` (consuming Q) modify this pool.
Net change to "Q equivalent" pool from `R_C` and `R_X`: `11*kC*[S] - kX*[Q]`.
At T=28 sim: `11*0.2*3.4e5 - 5e-4*1.4e8 = 7.48e5 - 7e4 = 6.78e5`. This is a net production of Q-equivalents.
This net production should increase the total Y/Q pool over time, shifting the equilibrium to higher absolute values.
The simulation runs for 50 days. Perhaps it's not long enough for this slow accumulation to take effect given the large concentrations involved?
The `id_yiw5` and `id_97q7` levels in sim are fairly flat from T=12 to T=50. This suggests it's not a matter of simulation time to reach a higher state, but that it's truly stuck.

This implies that the net influx `11*kC*[S] - kX*[Q]` might become zero or negative at the stuck state, or the model is missing a crucial element for `id_yiw5` accumulation.

What if `id_yiw5` has a direct source that is not `R_A_rev`?
E.g., `R_Y_source: id_shpe -> id_yiw5`?
Or `R_Y_source_2: id_55cy -> id_yiw5`?
If `id_shpe` is sustained high (as in v12), `id_shpe -> id_yiw5` (rate `k_sy * [S]`) could be a source.
This would add another consumption for `id_shpe`.
`dY/dt = k_sy*[S] + kA_r*[Q]^2 - kA_f*[Y]`.
`dS/dt = kD*[C] + kX*[Q] - (kB+kC+k_sy)*[S]`.

This is getting very complex with many parameters.
The initial problem description: "discover the biological mechanisms missing from your model".
The current model has 5 reactions. The true model might have a similar number or one more.

Let's reconsider the initial phase parameters.
`kC=0.20` and `kD=0.80` are compromises.
If we use `kC=0.31` and `kD=1.0` (from v3, good initial `id_shpe` drop, `id_55cy` drop).
And keep `kX=5e-4` (strong `id_shpe` recovery from `id_97q7`).
And `kA_f=1.3, kA_r=3.8e-12` (fast `R_A`).
This might give good initial phase and good `id_shpe` recovery. Will it fix Y/Q?

Model `v13` parameters:
1.  `R_A: id_yiw5 <=> 2 id_97q7`. `kA_f = 1.3`, `kA_r = 3.8e-12`.
2.  `R_B: id_shpe -> id_55cy`. `kB = 0.0153`.
3.  `R_C: id_shpe -> 11 id_97q7`. `kC = 0.31` (original best for initial `id_shpe` drop).
4.  `R_D: id_55cy -> id_shpe`. `kD = 1.0` (original best for initial `id_55cy` drop).
5.  `R_X: id_97q7 -> id_shpe`. `kX = 5e-4` (strong `id_shpe` source from `id_97q7`).

This attempts to combine good initial phase parameters for S and C with the strong S recovery mechanism.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v13)
doc_v13 = libsbml.readSBMLFromString(input_sbml_string) 
model_v13 = doc_v13.getModel()

# Parameters for model_v13
kA_f_v13 = 1.3    
kA_r_v13 = 3.8e-12 

kB_v13 = 0.0153
kC_v13 = 0.31    # Back to original estimate for good initial id_shpe drop
kD_v13 = 1.0     # Back to original estimate for good initial id_55cy drop
kX_v13 = 5e-4    # Strong id_shpe source from id_97q7

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v13.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v13)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v13)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v13.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v13)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v13.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v13)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v13.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v13)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = model_v13.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v13)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v13 = writer.writeSBMLToString(doc_v13)
shared_variables.add("model_v13_sbml", updated_sbml_v13)
print("SBML model_v13 created.")

print("\nAttempting to simulate model_v13...")
try:
    simulation_df_v13 = simulate(updated_sbml_v13)
    shared_variables.add("simulation_df_v13", simulation_df_v13)
    print("Simulation of model_v13 completed.")
    if simulation_df_v13 is not None and not simulation_df_v13.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v13, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v13)
    else:
        print("Simulation_df_v13 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v13: {e}")
    import traceback
    print(traceback.format_exc())

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v13)
doc_v13 = libsbml.readSBMLFromString(input_sbml_string) 
model_v13 = doc_v13.getModel()

# Parameters for model_v13
kA_f_v13 = 1.3    
kA_r_v13 = 3.8e-12 

kB_v13 = 0.0153
kC_v13 = 0.31    # Back to original estimate for good initial id_shpe drop
kD_v13 = 1.0     # Back to original estimate for good initial id_55cy drop
kX_v13 = 5e-4    # Strong id_shpe source from id_97q7

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v13.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v13)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v13)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v13.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v13)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v13.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v13)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v13.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v13)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = model_v13.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v13)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v13 = writer.writeSBMLToString(doc_v13)
shared_variables.add("model_v13_sbml", updated_sbml_v13)
print("SBML model_v13 created.")

print("\nAttempting to simulate model_v13...")
try:
    simulation_df_v13 = simulate(updated_sbml_v13)
    shared_variables.add("simulation_df_v13", simulation_df_v13)
    print("Simulation of model_v13 completed.")
    if simulation_df_v13 is not None and not simulation_df_v13.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            # Find closest experimental data point to target_time_val
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            # Find closest simulation data point to the *actual experimental time*
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v13, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v13)
    else:
        print("Simulation_df_v13 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v13: {e}")
    import traceback
    print(traceback.format_exc())
```
# Observation

## Code Stdout
SBML model_v13 created.

Attempting to simulate model_v13...
Simulation of model_v13 completed.

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v13, closest to exp. time):
Time: 1.01, shpe: 7.70e+05, 55cy: 8.37e+03, yiw5: 1.90e+06, 97q7: 1.13e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v13, closest to exp. time):
Time: 1.99, shpe: 6.17e+05, 55cy: 9.61e+03, yiw5: 5.59e+05, 97q7: 1.18e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v13, closest to exp. time):
Time: 12.00, shpe: 2.25e+05, 55cy: 3.56e+03, yiw5: 4.88e+04, 97q7: 1.30e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v13, closest to exp. time):
Time: 27.99, shpe: 2.23e+05, 55cy: 3.40e+03, yiw5: 5.73e+04, 97q7: 1.41e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v13, closest to exp. time):
Time: 50.00, shpe: 2.49e+05, 55cy: 3.79e+03, yiw5: 7.12e+04, 97q7: 1.57e+08

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 5/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4, model_v5_sbml, simulation_df_v5, model_v6_sbml, simulation_df_v6, model_v7_sbml, simulation_df_v7, model_v8_sbml, simulation_df_v8, model_v9_sbml, simulation_df_v9, model_v10_sbml, simulation_df_v10, model_v11_sbml, simulation_df_v11, model_v12_sbml, simulation_df_v12, model_v13_sbml, simulation_df_v13)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 16
## Thoughts

Let's analyze `model_v13` results:
Parameters: `kA_f=1.3`, `kA_r=3.8e-12`, `kB=0.0153`, `kC=0.31` (high), `kD=1.0` (high), `kX=5e-4` (strong Q->S).

At T~1 & T~2: (Initial phase)
*   `id_shpe`: Sim 7.7e5 (vs 7.3e5 exp at T1), 6.2e5 (vs 5.3e5 exp at T2). Closer to exp than v12, due to higher `kC`. Still a bit high.
*   `id_55cy`: Sim 8.4e3 (vs 1.5e4 exp at T1 - low), 9.6e3 (vs 1.1e4 exp at T2 - good). Higher `kD` makes `id_55cy` lower initially.
*   `id_yiw5`: Sim high at T1, low at T2. Similar to v11/v12.
*   `id_97q7`: Sim matches well.

At T~12:
*   `id_shpe`: Sim 2.25e5, Exp 3.4e4 (Sim vastly higher. `kX` is keeping `id_shpe` very high, `kC=0.31` not enough to bring it down to exp levels here).
*   `id_55cy`: Sim 3.56e3, Exp 1.96e3 (Sim high, but better than some previous models).
*   `id_yiw5`: Sim 4.88e4, Exp 1.57e5 (Sim very low, stuck).
*   `id_97q7`: Sim 1.30e8, Exp 8.34e8 (Sim vastly underestimated, stuck).

At T~28: (Recovery phase)
*   `id_shpe`: Sim 2.23e5, Exp 3.32e5 (Sim lower than exp. `id_shpe` has stabilized around 2.2e5 due to `R_X`, but doesn't quite reach the exp peak of 3.3e5).
*   `id_55cy`: Sim 3.40e3, Exp 3.76e4 (Sim very low. Exp `id_55cy` is 10x higher).
*   `id_yiw5`: Sim 5.73e4, Exp 3.02e6 (Sim extremely low, stuck).
*   `id_97q7`: Sim 1.41e8, Exp 1.02e9 (Sim vastly underestimated, stuck).

At T~50: (Long term)
*   `id_shpe`: Sim 2.49e5, Exp 7.94e4 (Sim much higher. `id_shpe` is sustained high by `R_X`).
*   `id_55cy`: Sim 3.79e3, Exp 8.35e3 (Sim low).
*   `id_yiw5`: Sim 7.12e4, Exp 6.59e5 (Sim extremely low, stuck).
*   `id_97q7`: Sim 1.57e8, Exp 1.03e9 (Sim vastly underestimated, stuck).

**Conclusions from `model_v13`:**
1.  **`kC=0.31`, `kD=1.0` with strong `kX=5e-4`:**
    *   Initial `id_shpe` drop is better captured than with lower `kC`.
    *   `id_shpe` is sustained at a high level (~2.2-2.5e5) due to `R_X`, preventing a full crash. This is good.
    *   However, this sustained `id_shpe` level is a bit too low for T=28 peak (exp 3.3e5) and a bit too high for T=50 (exp 7.9e4).
    *   `id_55cy` is too low throughout the mid to late stages. Even with sustained `id_shpe`, `id_55cy` doesn't recover to its experimental peak (3.7e4 at T=28). This suggests `kD=1.0` might be too high for `id_55cy` accumulation, or `kB` is too low.
2.  **`id_yiw5` and `id_97q7` are STILL THE MAJOR PROBLEM:** They remain stuck at low levels (`Y`~5-7e4, `Q`~1.3-1.6e8). Sustaining `id_shpe` (and thus `R_C` flux) did not solve this.
    *   The net influx of `id_97q7` from `R_C` ( `11*kC*[S]` ) minus consumption by `R_X` ( `kX*[Q]` ) is not effectively driving the `R_A` equilibrium to higher absolute concentrations for `Y` and `Q`.
    *   At T=28 (sim): `S`=2.23e5, `Q`=1.41e8.
        *   `R_C` source for `Q`: `11 * 0.31 * 2.23e5 = 7.60e5`.
        *   `R_X` sink for `Q`: `5e-4 * 1.41e8 = 7.05e4`.
        *   Net `Q` influx to `R_A` system = `7.60e5 - 7.05e4 = 6.895e5`. This is a large positive influx.
    *   This large influx should cause `Q` to rise, and via `R_A_rev`, `Y` to rise.
    *   The `R_A` equilibrium `Q^2/Y = K_eq = 3.42e11`.
    *   Sim T=28: `Q`=1.41e8, `Y`=5.73e4. `Q^2/Y = (1.41e8)^2 / 5.73e4 = 1.988e16 / 5.73e4 = 3.47e11`. Matches `K_eq`.
    *   The system *is* at `R_A` equilibrium. The continuous influx of `Q` (6.9e5) must be perfectly balanced by net consumption of `Q` through the `R_A` reaction itself to maintain this equilibrium. This means `kA_f*[Y] - kA_r*[Q]^2` must equal `-(net Q influx from R_C/R_X)`.
    *   So, `kA_f*[Y] - kA_r*[Q]^2 = -6.895e5`.
    *   This means `R_A` is acting as a net *sink* for `Q` (or net producer of `Y` from `Q`) at this state, which is what we want for `Y` recovery.
    *   However, `Y` is not recovering significantly. It implies that `kA_f*[Y]` (consumption of Y) is still too dominant once Y increases a bit.

This is puzzling. A continuous net influx of `Q` into the `Y <=> 2Q` system should, over time, increase both `Y` and `Q` while maintaining the `K_eq` ratio. If they are stuck, it means the influx is not "net" or the simulation isn't capturing the long-term accumulation.
The simulation runs to T=50. `Y` and `Q` are flat from T~12 onwards.

Could the `K_eq` itself be wrong? Or the structure?
The `K_eq` was derived from T=28 experimental data.
What if `R_A` is not simply `Y <=> 2Q`?

Let's reconsider the `id_55cy` levels. Exp T=28 `C`=3.76e4. Sim `C`=3.4e3.
`dC/dt = kB*[S] - kD*[C]`.
At T=28 sim: `S`=2.23e5, `C`=3.4e3.
`dC/dt = 0.0153*2.23e5 - 1.0*3.4e3 = 3412 - 3400 = 12`. (So `C` is nearly steady, but very low).
To get `C` to 3.76e4 (exp) with `S`=2.23e5 (sim):
`0.0153*2.23e5 - kD_new*3.76e4 = 0` (for steady state at exp C)
`3412 = kD_new*3.76e4 => kD_new = 3412 / 3.76e4 = 0.09`.
This `kD=0.09` is much lower than `1.0`. If `kD` is this low, `id_55cy` would accumulate much more.
This `kD=0.09` is close to the `kD=0.13` derived from `[S]/[C]` ratio if `kC` was very low.

This suggests that for `id_shpe` and `id_55cy` to achieve their late-stage recovery levels, `kD` needs to be low (around 0.1-0.2).
But a low `kD` messes up the initial `id_55cy` drop.

This points strongly to a mechanism where `kD` (or `kC`) effectively changes over time.
Since we can't do that, what if there's another reaction producing `id_55cy` in the later stages?
Or consuming `id_shpe` less?

I am running out of ideas for simple parameter tuning of the existing 5 reactions. The Y/Q system not reaching high levels despite a net influx is the biggest mystery if the model structure is correct.

Could the issue be with the `id_97q7` stoichiometry in `R_C`? `id_shpe -> 11 id_97q7`.
If it was `id_shpe -> id_97q7` (1:1), then `kC` would need to be ~11x larger for the same `id_97q7` production from `id_shpe`.
Current `kC=0.31`. If stoich was 1, `kC_eff_for_Q_prod = 0.31`.
With stoich 11, `kC_eff_for_Q_prod = 0.31 * 11 = 3.41` (in terms of `id_shpe` molecules being converted to Q-equivalents).
This high effective production of Q from S should be very powerful.

What if the problem is numerical precision with `kA_r = 3.8e-12`? Unlikely to cause it to get stuck if influx is present.

Let's try one more adjustment focusing on `id_55cy` recovery, as that might indirectly help `id_shpe` via `R_D`, and then `id_97q7` via `R_C`.
Use `kD=0.1` (very low, to maximize `id_55cy` accumulation).
Keep `kC=0.31` (for initial `id_shpe` drop).
Keep `kX=5e-4` (strong `id_shpe` source from `id_97q7`).
Keep `kA_f=1.3, kA_r=3.8e-12`.

Model `v14` parameters:
1.  `R_A: id_yiw5 <=> 2 id_97q7`. `kA_f = 1.3`, `kA_r = 3.8e-12`.
2.  `R_B: id_shpe -> id_55cy`. `kB = 0.0153`.
3.  `R_C: id_shpe -> 11 id_97q7`. `kC = 0.31`.
4.  `R_D: id_55cy -> id_shpe`. `kD = 0.1` (very low).
5.  `R_X: id_97q7 -> id_shpe`. `kX = 5e-4`.

This will likely make `id_55cy` very high throughout, and its initial drop will be gone. But the goal is to see if maximizing `id_55cy` (and thus its contribution to `id_shpe` via `R_D`) can break the Y/Q deadlock.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v14)
doc_v14 = libsbml.readSBMLFromString(input_sbml_string) 
model_v14 = doc_v14.getModel()

# Parameters for model_v14
kA_f_v14 = 1.3    
kA_r_v14 = 3.8e-12 

kB_v14 = 0.0153
kC_v14 = 0.31    
kD_v14 = 0.1     # Very low kD to boost id_55cy
kX_v14 = 5e-4    

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v14.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v14)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v14)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v14.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v14)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v14.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v14)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v14.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v14)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = model_v14.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v14)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v14 = writer.writeSBMLToString(doc_v14)
shared_variables.add("model_v14_sbml", updated_sbml_v14)
print("SBML model_v14 created.")

print("\nAttempting to simulate model_v14...")
try:
    simulation_df_v14 = simulate(updated_sbml_v14)
    shared_variables.add("simulation_df_v14", simulation_df_v14)
    print("Simulation of model_v14 completed.")
    if simulation_df_v14 is not None and not simulation_df_v14.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v14, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v14)
    else:
        print("Simulation_df_v14 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v14: {e}")
    import traceback
    print(traceback.format_exc())

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v14)
doc_v14 = libsbml.readSBMLFromString(input_sbml_string) 
model_v14 = doc_v14.getModel()

# Parameters for model_v14
kA_f_v14 = 1.3    
kA_r_v14 = 3.8e-12 

kB_v14 = 0.0153
kC_v14 = 0.31    
kD_v14 = 0.1     # Very low kD to boost id_55cy
kX_v14 = 5e-4    

# Reaction R_A: id_yiw5 <=> 2 id_97q7 (Reversible)
r_a = model_v14.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(2); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v14)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v14)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7 * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v14.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v14)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v14.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v14)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v14.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v14)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = model_v14.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v14)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v14 = writer.writeSBMLToString(doc_v14)
shared_variables.add("model_v14_sbml", updated_sbml_v14)
print("SBML model_v14 created.")

print("\nAttempting to simulate model_v14...")
try:
    simulation_df_v14 = simulate(updated_sbml_v14)
    shared_variables.add("simulation_df_v14", simulation_df_v14)
    print("Simulation of model_v14 completed.")
    if simulation_df_v14 is not None and not simulation_df_v14.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            # Find closest experimental data point to target_time_val
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            # Find closest simulation data point to the *actual experimental time*
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v14, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v14)
    else:
        print("Simulation_df_v14 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v14: {e}")
    import traceback
    print(traceback.format_exc())
```
# Observation

## Code Stdout
SBML model_v14 created.

Attempting to simulate model_v14...
Simulation of model_v14 completed.

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v14, closest to exp. time):
Time: 1.01, shpe: 7.66e+05, 55cy: 1.29e+04, yiw5: 1.90e+06, 97q7: 1.13e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v14, closest to exp. time):
Time: 1.99, shpe: 6.07e+05, 55cy: 2.14e+04, yiw5: 5.59e+05, 97q7: 1.18e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v14, closest to exp. time):
Time: 12.00, shpe: 2.22e+05, 55cy: 3.65e+04, yiw5: 4.86e+04, 97q7: 1.29e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v14, closest to exp. time):
Time: 27.99, shpe: 2.23e+05, 55cy: 3.41e+04, yiw5: 5.70e+04, 97q7: 1.40e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v14, closest to exp. time):
Time: 50.00, shpe: 2.48e+05, 55cy: 3.63e+04, yiw5: 7.08e+04, 97q7: 1.56e+08

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 4/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4, model_v5_sbml, simulation_df_v5, model_v6_sbml, simulation_df_v6, model_v7_sbml, simulation_df_v7, model_v8_sbml, simulation_df_v8, model_v9_sbml, simulation_df_v9, model_v10_sbml, simulation_df_v10, model_v11_sbml, simulation_df_v11, model_v12_sbml, simulation_df_v12, model_v13_sbml, simulation_df_v13, model_v14_sbml, simulation_df_v14)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 17
## Thoughts

Let's analyze `model_v14` results:
Parameters: `kA_f=1.3`, `kA_r=3.8e-12`, `kB=0.0153`, `kC=0.31` (high), `kD=0.1` (very low), `kX=5e-4` (strong Q->S).

At T~1 & T~2: (Initial phase)
*   `id_shpe`: Sim 7.7e5 (vs 7.3e5 exp at T1), 6.1e5 (vs 5.3e5 exp at T2). Still a bit high, but `kC=0.31` is helping bring it down.
*   `id_55cy`: Sim 1.3e4 (vs 1.5e4 exp at T1 - good), 2.1e4 (vs 1.1e4 exp at T2 - high). Very low `kD=0.1` causes `id_55cy` to accumulate more and not show the initial drop.
*   `id_yiw5` & `id_97q7`: Similar to v13.

At T~12:
*   `id_shpe`: Sim 2.2e5, Exp 3.4e4 (Sim vastly higher).
*   `id_55cy`: Sim 3.6e4, Exp 1.9e3 (Sim vastly higher. Low `kD` means `id_55cy` is not consumed).
*   `id_yiw5`: Sim 4.9e4, Exp 1.57e5 (Sim very low, stuck).
*   `id_97q7`: Sim 1.3e8, Exp 8.34e8 (Sim vastly underestimated, stuck).

At T~28: (Recovery phase)
*   `id_shpe`: Sim 2.2e5, Exp 3.3e5 (Sim lower than exp. Sustained by `R_X` but not reaching exp peak).
*   `id_55cy`: Sim 3.4e4, Exp 3.7e4 (Good match for `id_55cy`! Low `kD` allowed it to recover to this high level, supported by sustained `id_shpe`). This is a positive sign for `id_55cy`.
*   `id_yiw5`: Sim 5.7e4, Exp 3.0e6 (Sim extremely low, stuck).
*   `id_97q7`: Sim 1.4e8, Exp 1.0e9 (Sim vastly underestimated, stuck).

At T~50: (Long term)
*   `id_shpe`: Sim 2.5e5, Exp 7.9e4 (Sim much higher).
*   `id_55cy`: Sim 3.6e4, Exp 8.3e3 (Sim much higher. `id_55cy` stays high due to low `kD`).
*   `id_yiw5`: Sim 7.1e4, Exp 6.6e5 (Sim extremely low, stuck).
*   `id_97q7`: Sim 1.6e8, Exp 1.0e9 (Sim vastly underestimated, stuck).

**Conclusions from `model_v14`:**
1.  **Low `kD=0.1`:** This was very effective for achieving high `id_55cy` levels in the later stages (matching T=28 peak). However, it completely messes up the initial `id_55cy` dynamics (no drop after T=1 peak) and keeps `id_55cy` too high at T=12 and T=50.
2.  **Sustained `id_shpe` (due to `kX=5e-4` and high `id_55cy` via low `kD`):** `id_shpe` is maintained around 2.2-2.5e5. This is good for preventing a crash but doesn't match the experimental shape (dip then peak then fall).
3.  **`id_yiw5` and `id_97q7` are STILL THE UNYIELDING PROBLEM:** They remain stuck at low levels (`Y`~5-7e4, `Q`~1.3-1.6e8). Even with sustained high `id_shpe` (and thus strong `R_C` flux) AND high `id_55cy`, the Y/Q system does not shift to high concentrations.

The net influx of `Q` into the `Y <=> 2Q` system from `R_C` and `R_X` is substantial with these parameters, yet `Y` and `Q` do not accumulate to high levels.
At T=28 (sim): `S`=2.2e5, `Q`=1.4e8.
Net `Q` influx = `11*kC*[S] - kX*[Q] = 11*0.31*2.2e5 - 5e-4*1.4e8 = 7.5e5 - 7e4 = 6.8e5`.
This large influx should be driving `Y` and `Q` up.

This is extremely puzzling. If `R_A` is `Y <=> 2Q` and there's a net production of `Q` from external reactions, both `Y` and `Q` should increase over time until the external production is balanced by some consumption or the system runs out of precursors for the external production.
Here, `id_shpe` is the precursor for `R_C`'s production of `Q`. `id_shpe` is sustained.

Could the `K_eq` for `R_A` be orders of magnitude different from what I calculated?
`K_eq = kA_f / kA_r = 1.3 / 3.8e-12 = 3.42e11`.
Experimental T=28 target: `Y`=3e6, `Q`=1e9. `Q^2/Y = (1e9)^2/3e6 = 3.33e11`. This is consistent.

What if the stoichiometry of `R_A` is not `1Y <=> 2Q`?
If it's `1Y <=> 1Q`, then `K_eq = [Q]/[Y]`.
Exp T=28: `Q/Y = 1e9 / 3e6 = 333`.
Sim stuck state: `Q/Y = 1.4e8 / 5.7e4 = 2456`. These are very different.
If `R_A` was `Y <=> Q`, then `kA_f*[Y] - kA_r*[Q]`.
To get `Q/Y ~ 333` with `kA_f=1.3`, then `kA_r = kA_f / 333 = 1.3 / 333 = 0.0039`.
This is a possibility. A 1:1 reaction is simpler.

Let's test this structural change for `R_A`: `id_yiw5 <=> id_97q7` (1:1 stoichiometry).
Parameters for `R_A`: `kA_f = 1.3`. `kA_r = 0.0039`.
Keep other parameters from `v14` as they produced high `id_shpe` and `id_55cy` (though with bad initial shapes).
Model `v15` parameters:
1.  **New `R_A`: `id_yiw5 <=> id_97q7`**. `kA_f = 1.3`, `kA_r = 0.0039`.
2.  `R_B: id_shpe -> id_55cy`. `kB = 0.0153`.
3.  `R_C: id_shpe -> 11 id_97q7`. `kC = 0.31`. (High `id_97q7` production per `id_shpe` still seems necessary).
4.  `R_D: id_55cy -> id_shpe`. `kD = 0.1`.
5.  `R_X: id_97q7 -> id_shpe`. `kX = 5e-4`.

This is a significant structural hypothesis for `R_A`.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v15)
doc_v15 = libsbml.readSBMLFromString(input_sbml_string) 
model_v15 = doc_v15.getModel()

# Parameters for model_v15
kA_f_v15 = 1.3    
kA_r_v15 = 0.0039 # For R_A as Y <=> Q, K_eq = Q/Y ~ 333

kB_v15 = 0.0153
kC_v15 = 0.31    
kD_v15 = 0.1     
kX_v15 = 5e-4    

# Reaction R_A: id_yiw5 <=> id_97q7 (Reversible, new 1:1 stoichiometry)
r_a = model_v15.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(1); product_ra_97q7.setConstant(False) # Stoich changed to 1
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v15)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v15)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7")) # Kinetic law changed for 1:1

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v15.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v15)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v15.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v15)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v15.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v15)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = model_v15.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v15)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v15 = writer.writeSBMLToString(doc_v15)
shared_variables.add("model_v15_sbml", updated_sbml_v15)
print("SBML model_v15 created.")

print("\nAttempting to simulate model_v15...")
try:
    simulation_df_v15 = simulate(updated_sbml_v15)
    shared_variables.add("simulation_df_v15", simulation_df_v15)
    print("Simulation of model_v15 completed.")
    if simulation_df_v15 is not None and not simulation_df_v15.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v15, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v15)
    else:
        print("Simulation_df_v15 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v15: {e}")
    import traceback
    print(traceback.format_exc())

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v15)
doc_v15 = libsbml.readSBMLFromString(input_sbml_string) 
model_v15 = doc_v15.getModel()

# Parameters for model_v15
kA_f_v15 = 1.3    
kA_r_v15 = 0.0039 # For R_A as Y <=> Q, K_eq = Q/Y ~ 333

kB_v15 = 0.0153
kC_v15 = 0.31    
kD_v15 = 0.1     
kX_v15 = 5e-4    

# Reaction R_A: id_yiw5 <=> id_97q7 (Reversible, new 1:1 stoichiometry)
r_a = model_v15.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(1); product_ra_97q7.setConstant(False) # Stoich changed to 1
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v15)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v15)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7")) # Kinetic law changed for 1:1

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v15.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v15)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v15.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v15)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v15.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v15)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = model_v15.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v15)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v15 = writer.writeSBMLToString(doc_v15)
shared_variables.add("model_v15_sbml", updated_sbml_v15)
print("SBML model_v15 created.")

print("\nAttempting to simulate model_v15...")
try:
    simulation_df_v15 = simulate(updated_sbml_v15)
    shared_variables.add("simulation_df_v15", simulation_df_v15)
    print("Simulation of model_v15 completed.")
    if simulation_df_v15 is not None and not simulation_df_v15.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            # Find closest experimental data point to target_time_val
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            # Find closest simulation data point to the *actual experimental time*
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v15, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v15)
    else:
        print("Simulation_df_v15 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v15: {e}")
    import traceback
    print(traceback.format_exc())
```
# Observation

## Code Stdout
SBML model_v15 created.

Attempting to simulate model_v15...
Simulation of model_v15 completed.

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v15, closest to exp. time):
Time: 1.01, shpe: 7.65e+05, 55cy: 1.29e+04, yiw5: 2.10e+06, 97q7: 1.08e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v15, closest to exp. time):
Time: 1.99, shpe: 6.04e+05, 55cy: 2.14e+04, yiw5: 8.26e+05, 97q7: 1.11e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v15, closest to exp. time):
Time: 12.00, shpe: 2.11e+05, 55cy: 3.55e+04, yiw5: 3.64e+05, 97q7: 1.22e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v15, closest to exp. time):
Time: 27.99, shpe: 2.10e+05, 55cy: 3.24e+04, yiw5: 3.95e+05, 97q7: 1.32e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v15, closest to exp. time):
Time: 50.00, shpe: 2.33e+05, 55cy: 3.42e+04, yiw5: 4.40e+05, 97q7: 1.47e+08

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 3/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4, model_v5_sbml, simulation_df_v5, model_v6_sbml, simulation_df_v6, model_v7_sbml, simulation_df_v7, model_v8_sbml, simulation_df_v8, model_v9_sbml, simulation_df_v9, model_v10_sbml, simulation_df_v10, model_v11_sbml, simulation_df_v11, model_v12_sbml, simulation_df_v12, model_v13_sbml, simulation_df_v13, model_v14_sbml, simulation_df_v14, model_v15_sbml, simulation_df_v15)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 18
## Thoughts

Let's analyze `model_v15` results (changed `R_A` to `Y <=> Q` (1:1) with `kA_f=1.3, kA_r=0.0039`):
Other params: `kB=0.0153`, `kC=0.31`, `kD=0.1`, `kX=5e-4`.

At T~1 & T~2: (Initial phase)
*   `id_shpe`: Sim high (7.6e5 vs 7.3e5; 6.0e5 vs 5.3e5).
*   `id_55cy`: Sim good at T1 (1.3e4 vs 1.5e4), high at T2 (2.1e4 vs 1.1e4). Low `kD=0.1` effect.
*   `id_yiw5`: Sim high at T1 (2.1e6 vs 1.4e6), good at T2 (8.3e5 vs 9.7e5). Changing `R_A` stoich affected this.
*   `id_97q7`: Sim low (1.1e8 vs 1.14e8; 1.1e8 vs 1.4e8).

At T~12:
*   `id_shpe`: Sim 2.1e5, Exp 3.4e4 (Sim vastly higher).
*   `id_55cy`: Sim 3.5e4, Exp 1.9e3 (Sim vastly higher).
*   `id_yiw5`: Sim 3.6e5, Exp 1.57e5 (Sim higher. This is an improvement over previous ~5e4 stuck levels! `id_yiw5` is now higher).
*   `id_97q7`: Sim 1.2e8, Exp 8.34e8 (Sim vastly underestimated. Still stuck low).

At T~28: (Recovery phase)
*   `id_shpe`: Sim 2.1e5, Exp 3.3e5 (Sim lower. Sustained by `R_X` but not matching exp shape/peak).
*   `id_55cy`: Sim 3.2e4, Exp 3.7e4 (Good match! Low `kD` + sustained `id_shpe` works for `id_55cy` late stage).
*   `id_yiw5`: Sim 3.9e5, Exp 3.0e6 (Sim much higher than previous ~5e4, but still far below exp 3e6).
*   `id_97q7`: Sim 1.3e8, Exp 1.0e9 (Sim vastly underestimated, stuck).

At T~50: (Long term)
*   `id_shpe`: Sim 2.3e5, Exp 7.9e4 (Sim much higher).
*   `id_55cy`: Sim 3.4e4, Exp 8.3e3 (Sim much higher).
*   `id_yiw5`: Sim 4.4e5, Exp 6.6e5 (Sim getting closer! `id_yiw5` is now at 4.4e5 vs previous ~7e4. This is a significant improvement for `id_yiw5`).
*   `id_97q7`: Sim 1.5e8, Exp 1.0e9 (Sim vastly underestimated, stuck. `id_97q7` has slightly increased but is nowhere near).

**Conclusions from `model_v15`:**
1.  **Changing `R_A` to `Y <=> Q` (1:1 stoichiometry):** This had a noticeable positive impact on `id_yiw5` levels. `id_yiw5` is no longer stuck at very low values (4-7e4) but now reaches ~4e5. This is a big step forward for `id_yiw5`.
2.  **`id_97q7` is still the biggest problem:** It remains stuck at low levels (~1.5e8) despite the change in `R_A` and sustained `id_shpe`. The target is 1e9.
3.  **`id_shpe` and `id_55cy`:** The parameters `kC=0.31` (high) and `kD=0.1` (very low) lead to `id_shpe` being too high initially and then sustained high by `R_X`. `id_55cy` is too high throughout due to low `kD`. The shapes are not well matched, but the late-stage high levels for `id_55cy` are good.

**Focus on `id_97q7`:**
If `R_A` is `Y <=> Q` with `K_eq = Q/Y = 333`.
At T=50 sim: `Y`=4.4e5, `Q`=1.5e8. `Q/Y = 1.5e8 / 4.4e5 = 340`. This matches `K_eq`.
So `R_A` is at its equilibrium.
The influx to `Q` from `R_C` (`11*kC*[S]`) minus efflux from `R_X` (`kX*[Q]`) and efflux from `R_A_rev` (`kA_r*[Q]`) must be balanced by influx to `Q` from `R_A_fwd` (`kA_f*[Y]`).
Net `Q` production from `R_C` and `R_X`:
At T=50 sim: `S`=2.3e5, `Q`=1.5e8.
`11*kC*[S] - kX*[Q] = 11*0.31*2.3e5 - 5e-4*1.5e8 = 7.84e5 - 7.5e4 = 7.09e5`.
This is a large net production of `Q` from these two reactions.
This net production must be consumed by the net reverse flux of `R_A` (`kA_r*Q - kA_f*Y`) for `Q` to be steady.
`kA_r*Q - kA_f*Y = 0.0039*1.5e8 - 1.3*4.4e5 = 5.85e5 - 5.72e5 = 1.3e4`.
This is a small net reverse flux (Q -> Y).
This does not balance the `7.09e5` influx. So `Q` should still be increasing.
The simulation output for `id_97q7` at T=50 (1.47e8) is slightly higher than at T=28 (1.32e8). So it *is* slowly increasing, but far too slowly to reach 1e9.

The rate of `id_97q7` increase is too slow.
The main source of `id_97q7` is `R_C: S -> 11Q`. Rate `11*kC*[S]`.
The main sinks are `R_X: Q -> S` (rate `kX*[Q]`) and `R_A_rev: Q -> Y` (rate `kA_r*[Q]`).
`d[Q]/dt = 11*kC*[S] - kX*[Q] - kA_r*[Q] + kA_f*[Y]`.
To get `Q` to 1e9, we need a stronger push.

What if `kX` (for `Q->S`) is too high, draining `Q` too much?
`kX=5e-4`. If `Q`=1e9, sink rate = `5e-4*1e9 = 5e5`.
Production from `R_C` (if `S`=2e5) = `11*0.31*2e5 = 6.82e5`.
This leaves little net `Q` for `R_A` or accumulation.
Let's reduce `kX` back to `5e-5` (from v11). This will allow `Q` to accumulate more from `R_C`.
This will mean `id_shpe` is less sustained by `R_X`.

And what about the initial `id_shpe` and `id_55cy` profiles?
`kC=0.31` and `kD=0.1` are bad for initial shapes.
We need `kC` high-ish and `kD` high-ish for initial phase.
`kC=0.31`, `kD=1.0` (from v13) gave better initial `id_shpe` and `id_55cy` drop.
But `kD=1.0` made `id_55cy` crash later.

This is the constant battle.
Let's prioritize getting `id_97q7` up.
To do this, we need:
1.  Sustained `id_shpe` for `R_C`.
2.  `R_C` to be strong enough.
3.  Sinks for `id_97q7` (like `R_X` and `R_A_rev`) to not overwhelm production.

Try `model_v16`:
1.  `R_A: id_yiw5 <=> id_97q7` (1:1). `kA_f = 1.3`, `kA_r = 0.0039`. (Keep from v15, as Y improved).
2.  `R_B: id_shpe -> id_55cy`. `kB = 0.0153`.
3.  `R_C: id_shpe -> 11 id_97q7`. `kC = 0.31`. (Strong `Q` production from `S`).
4.  `R_D: id_55cy -> id_shpe`. `kD = 0.3` (Intermediate `kD`. Low `kD=0.1` gave good late `C` but bad early. High `kD=1.0` gave good early `C` but bad late. Try a mid-value).
5.  `R_X: id_97q7 -> id_shpe`. `kX = 1e-5` (Reduced `kX` significantly to let `Q` build up. `id_shpe` will rely more on `R_D`).

The hope is that with reduced `kX`, `id_97q7` can accumulate much more from the strong `R_C`. This high `id_97q7` should then drive `id_yiw5` up via `R_A_rev`.
The `kD=0.3` is a guess to balance `id_55cy`'s behavior.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v16)
doc_v16 = libsbml.readSBMLFromString(input_sbml_string) 
model_v16 = doc_v16.getModel()

# Parameters for model_v16
kA_f_v16 = 1.3    
kA_r_v16 = 0.0039 

kB_v16 = 0.0153
kC_v16 = 0.31    # Strong Q production from S
kD_v16 = 0.3     # Intermediate kD for id_55cy
kX_v16 = 1e-5    # Significantly reduced kX to let Q build up

# Reaction R_A: id_yiw5 <=> id_97q7 (Reversible, 1:1 stoichiometry)
r_a = model_v16.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(1); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v16)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v16)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v16.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v16)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v16.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v16)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v16.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v16)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = model_v16.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v16)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v16 = writer.writeSBMLToString(doc_v16)
shared_variables.add("model_v16_sbml", updated_sbml_v16)
print("SBML model_v16 created.")

print("\nAttempting to simulate model_v16...")
try:
    simulation_df_v16 = simulate(updated_sbml_v16)
    shared_variables.add("simulation_df_v16", simulation_df_v16)
    print("Simulation of model_v16 completed.")
    if simulation_df_v16 is not None and not simulation_df_v16.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v16, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v16)
    else:
        print("Simulation_df_v16 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v16: {e}")
    import traceback
    print(traceback.format_exc())

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v16)
doc_v16 = libsbml.readSBMLFromString(input_sbml_string) 
model_v16 = doc_v16.getModel()

# Parameters for model_v16
kA_f_v16 = 1.3    
kA_r_v16 = 0.0039 

kB_v16 = 0.0153
kC_v16 = 0.31    # Strong Q production from S
kD_v16 = 0.3     # Intermediate kD for id_55cy
kX_v16 = 1e-5    # Significantly reduced kX to let Q build up

# Reaction R_A: id_yiw5 <=> id_97q7 (Reversible, 1:1 stoichiometry)
r_a = model_v16.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(1); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v16)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v16)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v16.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v16)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v16.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v16)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v16.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v16)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = model_v16.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v16)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v16 = writer.writeSBMLToString(doc_v16)
shared_variables.add("model_v16_sbml", updated_sbml_v16)
print("SBML model_v16 created.")

print("\nAttempting to simulate model_v16...")
try:
    simulation_df_v16 = simulate(updated_sbml_v16)
    shared_variables.add("simulation_df_v16", simulation_df_v16)
    print("Simulation of model_v16 completed.")
    if simulation_df_v16 is not None and not simulation_df_v16.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            # Find closest experimental data point to target_time_val
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            # Find closest simulation data point to the *actual experimental time*
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v16, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v16)
    else:
        print("Simulation_df_v16 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v16: {e}")
    import traceback
    print(traceback.format_exc())
```
# Observation

## Code Stdout
SBML model_v16 created.

Attempting to simulate model_v16...
Simulation of model_v16 completed.

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v16, closest to exp. time):
Time: 1.01, shpe: 7.22e+05, 55cy: 1.13e+04, yiw5: 2.10e+06, 97q7: 1.08e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v16, closest to exp. time):
Time: 1.99, shpe: 5.29e+05, 55cy: 1.64e+04, yiw5: 8.26e+05, 97q7: 1.11e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v16, closest to exp. time):
Time: 12.00, shpe: 3.16e+04, 55cy: 4.98e+03, yiw5: 3.52e+05, 97q7: 1.17e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v16, closest to exp. time):
Time: 27.99, shpe: 4.26e+03, 55cy: 3.11e+02, yiw5: 3.54e+05, 97q7: 1.18e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v16, closest to exp. time):
Time: 50.00, shpe: 3.81e+03, 55cy: 1.95e+02, yiw5: 3.55e+05, 97q7: 1.18e+08

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 2/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4, model_v5_sbml, simulation_df_v5, model_v6_sbml, simulation_df_v6, model_v7_sbml, simulation_df_v7, model_v8_sbml, simulation_df_v8, model_v9_sbml, simulation_df_v9, model_v10_sbml, simulation_df_v10, model_v11_sbml, simulation_df_v11, model_v12_sbml, simulation_df_v12, model_v13_sbml, simulation_df_v13, model_v14_sbml, simulation_df_v14, model_v15_sbml, simulation_df_v15, model_v16_sbml, simulation_df_v16)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 19
## Thoughts

Let's analyze `model_v16` results:
Parameters: `R_A (Y<=>Q)`: `kA_f=1.3, kA_r=0.0039`. `R_B (S->C)`: `kB=0.0153`. `R_C (S->11Q)`: `kC=0.31`. `R_D (C->S)`: `kD=0.3`. `R_X (Q->S)`: `kX=1e-5`.

At T~1 & T~2: (Initial phase)
*   `id_shpe`: Sim 7.2e5 (vs 7.3e5 exp at T1 - good!), 5.3e5 (vs 5.3e5 exp at T2 - excellent!). `kC=0.31` and low `kX` gives good initial `id_shpe`.
*   `id_55cy`: Sim 1.1e4 (vs 1.5e4 exp at T1 - low), 1.6e4 (vs 1.1e4 exp at T2 - high). `kD=0.3` is intermediate.
*   `id_yiw5`: Sim high at T1, good at T2.
*   `id_97q7`: Sim low.

At T~12:
*   `id_shpe`: Sim 3.16e4, Exp 3.43e4 (Excellent match!).
*   `id_55cy`: Sim 4.98e3, Exp 1.96e3 (Sim high).
*   `id_yiw5`: Sim 3.52e5, Exp 1.57e5 (Sim higher. `R_A (1:1)` helps `id_yiw5` stay up).
*   `id_97q7`: Sim 1.17e8, Exp 8.34e8 (Sim vastly underestimated. Still stuck low).

At T~28: (Recovery phase)
*   `id_shpe`: Sim 4.26e3, Exp 3.32e5 (Sim crashed! Low `kX` was not enough to sustain `id_shpe`).
*   `id_55cy`: Sim 3.11e2, Exp 3.76e4 (Sim crashed).
*   `id_yiw5`: Sim 3.54e5, Exp 3.02e6 (Sim much higher than previous stuck ~5e4, but still far below exp 3e6. It seems to have stabilized around 3.5e5).
*   `id_97q7`: Sim 1.18e8, Exp 1.02e9 (Sim vastly underestimated, stuck).

At T~50: (Long term)
*   `id_shpe`: Sim 3.81e3, Exp 7.94e4 (Crashed).
*   `id_55cy`: Sim 1.95e2, Exp 8.35e3 (Crashed).
*   `id_yiw5`: Sim 3.55e5, Exp 6.59e5 (Sim is at 3.55e5, exp is 6.59e5. `id_yiw5` is much better than the very low stuck states, but not quite matching and not showing the earlier peak of 3e6).
*   `id_97q7`: Sim 1.18e8, Exp 1.03e9 (Vastly underestimated, stuck).

**Conclusions from `model_v16`:**
1.  **Initial Phase (T=0-12):** This model version gives the best fit so far for `id_shpe` in the initial phase, including its dip around T=12. `id_55cy` is a bit off but reasonable. `id_yiw5` is also behaving better initially with `R_A (1:1)`.
2.  **`id_shpe` Crash:** Reducing `kX` (for `R_X: Q->S`) to `1e-5` was too much; `id_shpe` could not be sustained and crashed after T=12. This then caused `id_55cy` to crash.
3.  **`id_yiw5` Improvement:** `id_yiw5` with `R_A (1:1)` now stabilizes around 3.5e5, which is a major improvement from the ~5e4 levels when `R_A` was `Y <=> 2Q`. However, it doesn't reach the experimental peak of 3e6 at T=28, nor the T=50 level of 6.6e5.
4.  **`id_97q7` is THE UNYIELDING PROBLEM:** It remains stubbornly stuck around 1.1-1.2e8, far from the 1e9 target. Even with good initial `id_shpe` (meaning `R_C` is active), `id_97q7` does not accumulate.

The fact that `id_yiw5` improved significantly when `R_A` stoichiometry changed to 1:1 is a strong hint that this structural change might be correct.
The `K_eq` for `R_A (Y<=>Q)` is `Q/Y`.
Exp T=28: `Q/Y = 1e9 / 3e6 = 333`.
Sim T=50 (v16): `Q/Y = 1.18e8 / 3.55e5 = 332`. This matches `K_eq` perfectly.
So, `R_A` is reaching its equilibrium correctly with the 1:1 stoichiometry and chosen `kA_f, kA_r`.

The problem is that the *total amount of Y+Q material* in the system is too low.
This pool is fed by `R_C: S -> 11Q` (source of Q).
It's drained by `R_X: Q -> S` (sink for Q).
If `id_shpe` crashes (as in v16 after T=12), then `R_C` stops producing `Q`.
Then the Y/Q pool cannot grow.

We need `id_shpe` to be sustained. `model_v12` (with `kX=5e-4`) sustained `id_shpe` well.
Let's combine:
*   `R_A (Y<=>Q)` 1:1 stoich with `kA_f=1.3, kA_r=0.0039` (from v15/v16 - good for Y level and Keq).
*   `kC=0.31` (from v16 - good for initial S drop).
*   `kX=5e-4` (from v12 - good for sustained S).
*   `kD` for `R_D (C->S)`: This is tricky. `kD=0.1` (v15) gave good late C but bad early. `kD=0.3` (v16) gave okayish C at T12 but S crashed. `kD=1.0` (v13) gave good initial C drop but C crashed later. `kD=0.8` (v12) gave good C at T12 when S was high.

Let's try `kD=0.6` as a compromise.
Model `v17` parameters:
1.  `R_A: id_yiw5 <=> id_97q7`. `kA_f = 1.3`, `kA_r = 0.0039`.
2.  `R_B: id_shpe -> id_55cy`. `kB = 0.0153`.
3.  `R_C: id_shpe -> 11 id_97q7`. `kC = 0.31`.
4.  `R_D: id_55cy -> id_shpe`. `kD = 0.6`.
5.  `R_X: id_97q7 -> id_shpe`. `kX = 5e-4`.

This model attempts to get:
*   Good `id_yiw5` behavior due to `R_A (1:1)`.
*   Good initial `id_shpe` drop (`kC=0.31`).
*   Sustained `id_shpe` due to strong `kX`.
*   Balanced `id_55cy` with `kD=0.6`.

If this sustains `id_shpe` at a decent level (e.g. 1-3e5), then `R_C` will continuously produce `id_97q7`.
With `R_A (1:1)`, this influx of `id_97q7` should robustly increase both `id_97q7` and `id_yiw5` towards their high experimental levels while maintaining the `Q/Y` ratio. This is my strongest hypothesis now.

I have only 2 iterations left after this one. This needs to be a good attempt.

```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v17)
doc_v17 = libsbml.readSBMLFromString(input_sbml_string) 
model_v17 = doc_v17.getModel()

# Parameters for model_v17
kA_f_v17 = 1.3    
kA_r_v17 = 0.0039 # For R_A as Y <=> Q (1:1), K_eq = Q/Y ~ 333

kB_v17 = 0.0153
kC_v17 = 0.31    # Good for initial S drop
kD_v17 = 0.6     # Compromise for C dynamics
kX_v17 = 5e-4    # Good for sustained S

# Reaction R_A: id_yiw5 <=> id_97q7 (Reversible, 1:1 stoichiometry)
r_a = model_v17.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(1); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v17)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v17)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v17.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v17)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v17.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v17)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v17.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v17)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = model_v17.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v17)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v17 = writer.writeSBMLToString(doc_v17)
shared_variables.add("model_v17_sbml", updated_sbml_v17)
print("SBML model_v17 created.")

print("\nAttempting to simulate model_v17...")
try:
    simulation_df_v17 = simulate(updated_sbml_v17)
    shared_variables.add("simulation_df_v17", simulation_df_v17)
    print("Simulation of model_v17 completed.")
    if simulation_df_v17 is not None and not simulation_df_v17.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v17, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v17)
    else:
        print("Simulation_df_v17 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v17: {e}")
    import traceback
    print(traceback.format_exc())

```

## Action

### Code
```python
import pandas as pd
import libsbml

# Load experimental data
exp_data = experiment_history['iteration_0']

# Create a new SBML model (model_v17)
doc_v17 = libsbml.readSBMLFromString(input_sbml_string) 
model_v17 = doc_v17.getModel()

# Parameters for model_v17
kA_f_v17 = 1.3    
kA_r_v17 = 0.0039 # For R_A as Y <=> Q (1:1), K_eq = Q/Y ~ 333

kB_v17 = 0.0153
kC_v17 = 0.31    # Good for initial S drop
kD_v17 = 0.6     # Compromise for C dynamics
kX_v17 = 5e-4    # Good for sustained S

# Reaction R_A: id_yiw5 <=> id_97q7 (Reversible, 1:1 stoichiometry)
r_a = model_v17.createReaction(); r_a.setId("R_A"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(1); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f_v17)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r_v17)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = model_v17.createReaction(); r_b.setId("R_B"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB_v17)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = model_v17.createReaction(); r_c.setId("R_C"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC_v17)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = model_v17.createReaction(); r_d.setId("R_D"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD_v17)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = model_v17.createReaction(); r_x.setId("R_X"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX_v17)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
updated_sbml_v17 = writer.writeSBMLToString(doc_v17)
shared_variables.add("model_v17_sbml", updated_sbml_v17)
print("SBML model_v17 created.")

print("\nAttempting to simulate model_v17...")
try:
    simulation_df_v17 = simulate(updated_sbml_v17)
    shared_variables.add("simulation_df_v17", simulation_df_v17)
    print("Simulation of model_v17 completed.")
    if simulation_df_v17 is not None and not simulation_df_v17.empty:
        
        def print_comparison_at_time(label, target_time_val, exp_df, sim_df_local):
            print(f"\n--- Comparison at T ~ {label} (target time: {target_time_val:.2f}) ---")
            # Find closest experimental data point to target_time_val
            exp_idx = (exp_df['Time'] - target_time_val).abs().argsort()[:1].iloc[0]
            exp_point = exp_df.iloc[exp_idx]
            
            print("Experimental Data (closest to target time):")
            print(f"Time: {exp_point['Time']:.2f}, shpe: {exp_point['id_shpe']:.2e}, 55cy: {exp_point['id_55cy']:.2e}, yiw5: {exp_point['id_yiw5']:.2e}, 97q7: {exp_point['id_97q7']:.2e}")
            
            # Find closest simulation data point to the *actual experimental time*
            sim_idx = (sim_df_local['Time'] - exp_point['Time']).abs().argsort()[:1].iloc[0]
            sim_point = sim_df_local.iloc[sim_idx]
            print(f"Simulated Data (model_v17, closest to exp. time):")
            print(f"Time: {sim_point['Time']:.2f}, shpe: {sim_point['id_shpe']:.2e}, 55cy: {sim_point['id_55cy']:.2e}, yiw5: {sim_point['id_yiw5']:.2e}, 97q7: {sim_point['id_97q7']:.2e}")

        time_points_to_compare = {"T=1": 1.0, "T=2": 2.0, "T=12": 12.0, "T=28": 28.0, "T=50": 50.0}
        for label, time_val in time_points_to_compare.items():
            print_comparison_at_time(label, time_val, exp_data, simulation_df_v17)
    else:
        print("Simulation_df_v17 is None or empty.")
except Exception as e:
    print(f"Error during simulation or processing for model_v17: {e}")
    import traceback
    print(traceback.format_exc())
```
# Observation

## Code Stdout
SBML model_v17 created.

Attempting to simulate model_v17...
Simulation of model_v17 completed.

--- Comparison at T ~ T=1 (target time: 1.00) ---
Experimental Data (closest to target time):
Time: 1.01, shpe: 7.27e+05, 55cy: 1.51e+04, yiw5: 1.45e+06, 97q7: 1.14e+08
Simulated Data (model_v17, closest to exp. time):
Time: 1.01, shpe: 7.67e+05, 55cy: 1.01e+04, yiw5: 2.10e+06, 97q7: 1.08e+08

--- Comparison at T ~ T=2 (target time: 2.00) ---
Experimental Data (closest to target time):
Time: 1.99, shpe: 5.32e+05, 55cy: 1.12e+04, yiw5: 9.75e+05, 97q7: 1.41e+08
Simulated Data (model_v17, closest to exp. time):
Time: 1.99, shpe: 6.10e+05, 55cy: 1.33e+04, yiw5: 8.26e+05, 97q7: 1.11e+08

--- Comparison at T ~ T=12 (target time: 12.00) ---
Experimental Data (closest to target time):
Time: 12.00, shpe: 3.43e+04, 55cy: 1.96e+03, yiw5: 1.57e+05, 97q7: 8.34e+08
Simulated Data (model_v17, closest to exp. time):
Time: 12.00, shpe: 2.14e+05, 55cy: 5.91e+03, yiw5: 3.65e+05, 97q7: 1.22e+08

--- Comparison at T ~ T=28 (target time: 28.00) ---
Experimental Data (closest to target time):
Time: 27.99, shpe: 3.32e+05, 55cy: 3.76e+04, yiw5: 3.02e+06, 97q7: 1.02e+09
Simulated Data (model_v17, closest to exp. time):
Time: 27.99, shpe: 2.10e+05, 55cy: 5.32e+03, yiw5: 3.96e+05, 97q7: 1.32e+08

--- Comparison at T ~ T=50 (target time: 50.00) ---
Experimental Data (closest to target time):
Time: 50.00, shpe: 7.94e+04, 55cy: 8.35e+03, yiw5: 6.59e+05, 97q7: 1.03e+09
Simulated Data (model_v17, closest to exp. time):
Time: 50.00, shpe: 2.34e+05, 55cy: 5.92e+03, yiw5: 4.41e+05, 97q7: 1.47e+08

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 1/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (initial_simulation_df, model_v1_sbml, simulation_df_v1, model_v2_sbml, simulation_df_v2, model_v3_sbml, simulation_df_v3, model_v4_sbml, simulation_df_v4, model_v5_sbml, simulation_df_v5, model_v6_sbml, simulation_df_v6, model_v7_sbml, simulation_df_v7, model_v8_sbml, simulation_df_v8, model_v9_sbml, simulation_df_v9, model_v10_sbml, simulation_df_v10, model_v11_sbml, simulation_df_v11, model_v12_sbml, simulation_df_v12, model_v13_sbml, simulation_df_v13, model_v14_sbml, simulation_df_v14, model_v15_sbml, simulation_df_v15, model_v16_sbml, simulation_df_v16, model_v17_sbml, simulation_df_v17)

### Allowed libraires
['numpy', 'pandas', 'libsbml', 'math', 'scipy', 'jax', 'sklearn', 'io', 'traceback']


Please construct your response according to the thoughts-action markdown format.



# Iteration 20
## Thoughts

This is the last iteration. I need to submit a model.
Let's analyze `model_v17` results:
Parameters: `R_A (Y<=>Q)`: `kA_f=1.3, kA_r=0.0039`. `R_B (S->C)`: `kB=0.0153`. `R_C (S->11Q)`: `kC=0.31`. `R_D (C->S)`: `kD=0.6`. `R_X (Q->S)`: `kX=5e-4`.

At T~1 & T~2: (Initial phase)
*   `id_shpe`: Sim 7.7e5 (vs 7.3e5 exp at T1), 6.1e5 (vs 5.3e5 exp at T2). Decent initial drop.
*   `id_55cy`: Sim 1.0e4 (vs 1.5e4 exp at T1 - low), 1.3e4 (vs 1.1e4 exp at T2 - good). `kD=0.6` is a reasonable compromise.
*   `id_yiw5`: Sim high at T1, good at T2.
*   `id_97q7`: Sim low.

At T~12:
*   `id_shpe`: Sim 2.1e5, Exp 3.4e4 (Sim vastly higher). `kX` keeps `id_shpe` high.
*   `id_55cy`: Sim 5.9e3, Exp 1.9e3 (Sim high).
*   `id_yiw5`: Sim 3.6e5, Exp 1.57e5 (Sim higher. `R_A (1:1)` helps `id_yiw5` stay up).
*   `id_97q7`: Sim 1.2e8, Exp 8.34e8 (Sim vastly underestimated. Still stuck low).

At T~28: (Recovery phase)
*   `id_shpe`: Sim 2.1e5, Exp 3.3e5 (Sim lower than exp peak, but sustained).
*   `id_55cy`: Sim 5.3e3, Exp 3.7e4 (Sim very low. `kD=0.6` not allowing enough accumulation for `id_55cy` peak).
*   `id_yiw5`: Sim 3.9e5, Exp 3.0e6 (Sim much higher than previous stuck ~5e4, but still far below exp 3e6).
*   `id_97q7`: Sim 1.3e8, Exp 1.0e9 (Sim vastly underestimated, stuck).

At T~50: (Long term)
*   `id_shpe`: Sim 2.3e5, Exp 7.9e4 (Sim much higher).
*   `id_55cy`: Sim 5.9e3, Exp 8.3e3 (Sim slightly low, but reasonable order of magnitude).
*   `id_yiw5`: Sim 4.4e5, Exp 6.6e5 (Sim getting closer! `id_yiw5` is at 4.4e5. This is the best result for `id_yiw5` so far).
*   `id_97q7`: Sim 1.5e8, Exp 1.0e9 (Sim vastly underestimated, stuck. `id_97q7` has slightly increased but is nowhere near).

**Overall Assessment of `model_v17`:**
*   **Strengths:**
    *   `R_A (Y<=>Q)` 1:1 stoichiometry significantly improved `id_yiw5` behavior, preventing deep crashes and allowing it to reach moderate levels (4.4e5 at T=50 vs exp 6.6e5).
    *   `R_X (Q->S)` with `kX=5e-4` sustains `id_shpe` at high levels, preventing its crash.
    *   Initial `id_shpe` drop is reasonably captured.
    *   `id_55cy` has a reasonable level at T=50.
*   **Weaknesses:**
    *   **`id_97q7` is the biggest failure.** It consistently stays around 1.2-1.5e8, while the experiment reaches 1e9. This is a nearly 10-fold difference.
    *   `id_shpe` profile doesn't show the experimental dip around T=12 as sharply because `R_X` keeps it high. Its sustained level (2.3e5) is higher than exp T=50 (7.9e4).
    *   `id_55cy` doesn't reach its experimental peak at T=28 (exp 3.7e4, sim 5.3e3). `kD=0.6` might be too high for this accumulation.
    *   `id_yiw5` doesn't reach its experimental peak at T=28 (exp 3.0e6, sim 3.9e5).

**Final Decision for Submission:**
Given that `id_97q7` is so far off, and it's a major species, this model is unlikely to be highly accurate. The core mechanism driving `id_97q7` to 1e9 and `id_yiw5` to 3e6 is still missing or incorrectly parameterized.
The change of `R_A` to 1:1 was a good structural insight for `id_yiw5`.
The addition of `R_X (Q->S)` was good for `id_shpe` sustainability.

The problem is likely that the net production of `id_97q7` is insufficient.
`d[Q]/dt = 11*kC*[S] + kA_f*[Y] - kA_r*[Q] - kX*[Q]`.
To increase `Q`, we need `11*kC*[S] + kA_f*[Y]` to be larger than `(kA_r+kX)*[Q]`.
At T=50 (sim v17): `S`=2.3e5, `Y`=4.4e5, `Q`=1.5e8.
Source terms for `Q`:
`11*kC*[S] = 11*0.31*2.3e5 = 7.84e5`
`kA_f*[Y] = 1.3*4.4e5 = 5.72e5`
Total source = `7.84e5 + 5.72e5 = 1.356e6`.
Sink terms for `Q`:
`kA_r*[Q] = 0.0039*1.5e8 = 5.85e5`
`kX*[Q] = 5e-4*1.5e8 = 7.5e4`
Total sink = `5.85e5 + 7.5e4 = 6.6e5`.
Net `d[Q]/dt = 1.356e6 - 6.6e5 = 6.96e5`.
This is a large positive rate of change for `id_97q7`. It *should* be increasing much faster.
Why is it stuck at 1.5e8 in the simulation if `d[Q]/dt` is so high?
The simulation output shows `id_97q7` at T=28 is 1.32e8, and at T=50 is 1.47e8. This is an increase of only 1.5e7 over 22 days. Average rate `1.5e7/22 = 6.8e5`. This matches the calculated `d[Q]/dt`.
So it *is* increasing at that rate. To reach 1e9 from 1.5e8 (change of 8.5e8) at this rate would take `8.5e8 / 6.8e5 = 1250` days. The simulation only runs for 50 days.

This means the parameters might be qualitatively correct for the interactions, but the timescale for `id_97q7` to reach its peak is much longer than the experiment duration with these parameters.
This implies that either:
a) Some rates are much faster in reality (e.g., `kC` or `kA_f` higher, or sinks `kA_r`, `kX` lower).
b) The simulation time in `simulate()` is not long enough to show the true steady state or peak for `id_97q7`. However, the experimental data *does* show `id_97q7` reaching ~1e9 by T=28-50.

If `id_97q7` is to reach ~1e9 by T=28:
Average rate of increase from T=0 (1e8) to T=28 (1e9) is `(1e9-1e8)/28 = 9e8/28 = 3.2e7 / day`.
The current model produces `id_97q7` at a rate of ~7e5/day. This is about 50x too slow.

To increase `d[Q]/dt`, we need to increase `11*kC*[S]` or `kA_f*[Y]`, or decrease `(kA_r+kX)*[Q]`.
*   `kC` is already high (0.31). `S` is sustained around 2e5.
*   `kA_f` is 1.3. `Y` gets to ~4e5.
*   `kA_r` is tied to `kA_f` by `K_eq`.
*   `kX` (sink `Q->S`) could be reduced. If `kX` is smaller, `S` might not be sustained as well.

Let's try to make `R_C` even stronger by increasing its stoichiometry for `Q` or increasing `kC`.
The stoichiometry `11` is already very high. Increasing `kC` further might make `S` drop too fast initially.

This is a tough spot for the final model. `model_v17` has some good points (Y improved, S sustained) but fails badly on Q magnitude and some shapes.
Given the time constraint, I will submit `model_v17` as it represents the most structural insights gained (R_A 1:1, R_X Q->S). The parameter values are a compromise. It's possible the true system has some parameters that are very different or additional control.

Final check on `model_v17` parameters:
`kA_f=1.3`, `kA_r=0.0039` (for `R_A: Y <=> Q`)
`kB=0.0153` (for `R_B: S -> C`)
`kC=0.31` (for `R_C: S -> 11Q`)
`kD=0.6` (for `R_D: C -> S`)
`kX=5e-4` (for `R_X: Q -> S`)

These seem like a reasonable set to try for submission, acknowledging the `id_97q7` issue.

```python
import pandas as pd
import libsbml

# This is the model chosen for submission.
# It is based on model_v17 logic.

final_sbml_doc = libsbml.readSBMLFromString(input_sbml_string) 
final_model = final_sbml_doc.getModel()

# Parameters for the final model (model_v17 parameters)
kA_f = 1.3    
kA_r = 0.0039 # For R_A as Y <=> Q (1:1), K_eq = Q/Y ~ 333

kB = 0.0153
kC = 0.31    # Good for initial S drop
kD = 0.6     # Compromise for C dynamics
kX = 5e-4    # Good for sustained S

# Reaction R_A: id_yiw5 <=> id_97q7 (Reversible, 1:1 stoichiometry)
r_a = final_model.createReaction(); r_a.setId("R_A_yiw5_ reversible_97q7"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(1); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = final_model.createReaction(); r_b.setId("R_B_shpe_to_55cy"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = final_model.createReaction(); r_c.setId("R_C_shpe_to_97q7"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = final_model.createReaction(); r_d.setId("R_D_55cy_to_shpe"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = final_model.createReaction(); r_x.setId("R_X_97q7_to_shpe"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
final_sbml = writer.writeSBMLToString(final_sbml_doc)
print("Final SBML model (model_v17 parameters) prepared for submission.")
# print(final_sbml) # Optional: print for verification if needed, but can be long.
```

## Action

### Submit
```python
import pandas as pd
import libsbml

# This is the model chosen for submission.
# It is based on model_v17 logic and parameters.

final_sbml_doc = libsbml.readSBMLFromString(input_sbml_string) 
final_model = final_sbml_doc.getModel()

# Parameters for the final model (model_v17 parameters)
kA_f = 1.3    
kA_r = 0.0039 # For R_A as Y <=> Q (1:1), K_eq = Q/Y ~ 333

kB = 0.0153
kC = 0.31    # Good for initial S drop
kD = 0.6     # Compromise for C dynamics
kX = 5e-4    # Good for sustained S

# Reaction R_A: id_yiw5 <=> id_97q7 (Reversible, 1:1 stoichiometry)
# Using more descriptive IDs for reactions
r_a = final_model.createReaction(); r_a.setId("R_A_yiw5_reversible_97q7"); r_a.setReversible(True); r_a.setFast(False)
reactant_ra_yiw5 = r_a.createReactant(); reactant_ra_yiw5.setSpecies("id_yiw5"); reactant_ra_yiw5.setStoichiometry(1); reactant_ra_yiw5.setConstant(False)
product_ra_97q7 = r_a.createProduct(); product_ra_97q7.setSpecies("id_97q7"); product_ra_97q7.setStoichiometry(1); product_ra_97q7.setConstant(False)
kl_ra = r_a.createKineticLaw()
param_kaf = kl_ra.createLocalParameter(); param_kaf.setId("kA_f"); param_kaf.setValue(kA_f)
param_kar = kl_ra.createLocalParameter(); param_kar.setId("kA_r"); param_kar.setValue(kA_r)
kl_ra.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7"))

# Reaction R_B: id_shpe -> id_55cy
r_b = final_model.createReaction(); r_b.setId("R_B_shpe_to_55cy"); r_b.setReversible(False); r_b.setFast(False)
reactant_rb = r_b.createReactant(); reactant_rb.setSpecies("id_shpe"); reactant_rb.setStoichiometry(1); reactant_rb.setConstant(False)
product_rb = r_b.createProduct(); product_rb.setSpecies("id_55cy"); product_rb.setStoichiometry(1); product_rb.setConstant(False)
kl_rb = r_b.createKineticLaw()
param_kb = kl_rb.createLocalParameter(); param_kb.setId("kB"); param_kb.setValue(kB)
kl_rb.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction R_C: id_shpe -> 11 id_97q7
r_c = final_model.createReaction(); r_c.setId("R_C_shpe_to_11_97q7"); r_c.setReversible(False); r_c.setFast(False)
reactant_rc = r_c.createReactant(); reactant_rc.setSpecies("id_shpe"); reactant_rc.setStoichiometry(1); reactant_rc.setConstant(False)
product_rc = r_c.createProduct(); product_rc.setSpecies("id_97q7"); product_rc.setStoichiometry(11); product_rc.setConstant(False)
kl_rc = r_c.createKineticLaw()
param_kc = kl_rc.createLocalParameter(); param_kc.setId("kC"); param_kc.setValue(kC)
kl_rc.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction R_D: id_55cy -> id_shpe
r_d = final_model.createReaction(); r_d.setId("R_D_55cy_to_shpe"); r_d.setReversible(False); r_d.setFast(False)
reactant_rd = r_d.createReactant(); reactant_rd.setSpecies("id_55cy"); reactant_rd.setStoichiometry(1); reactant_rd.setConstant(False)
product_rd = r_d.createProduct(); product_rd.setSpecies("id_shpe"); product_rd.setStoichiometry(1); product_rd.setConstant(False)
kl_rd = r_d.createKineticLaw()
param_kd = kl_rd.createLocalParameter(); param_kd.setId("kD"); param_kd.setValue(kD)
kl_rd.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction R_X: id_97q7 -> id_shpe
r_x = final_model.createReaction(); r_x.setId("R_X_97q7_to_shpe"); r_x.setReversible(False); r_x.setFast(False)
reactant_rx = r_x.createReactant(); reactant_rx.setSpecies("id_97q7"); reactant_rx.setStoichiometry(1); reactant_rx.setConstant(False)
product_rx = r_x.createProduct(); product_rx.setSpecies("id_shpe"); product_rx.setStoichiometry(1); product_rx.setConstant(False)
kl_rx = r_x.createKineticLaw()
param_kx = kl_rx.createLocalParameter(); param_kx.setId("kX"); param_kx.setValue(kX)
kl_rx.setMath(libsbml.parseL3Formula("kX * id_97q7"))


writer = libsbml.SBMLWriter()
final_sbml = writer.writeSBMLToString(final_sbml_doc)
# print("Final SBML model (model_v17 parameters) prepared for submission.")
# print(final_sbml) 
```
# Observation


            You have used up all interactions. Please put your final model as a string variable called `final_sbml` in your code.
            ```python
            final_sbml = ....
            ```
            It is recommended using libsbml to modify `input_sbml_string` rather than write the entire xml on your own.
            ## Parsing error
ERROR: A <reaction> object must have the required attributes 'id', 'reversible' and 'fast', and may have the optional attributes 'metaid', 'sboTerm', 'name' and 'compartment'. No other attributes from the SBML Level 3 Core namespace are permitted on a Reaction object.
Reference: L3V1 Section 4.11
 The required attribute 'id' is missing.

# Iteration 21
## Thoughts
The previous submission attempt failed due to an SBML parsing error: "A <reaction> object must have the required attributes 'id', 'reversible' and 'fast'... The required attribute 'id' is missing." This is puzzling as my libSBML code explicitly sets these attributes for every reaction.

I will reconstruct the model with the same structure and parameters as `model_v17`, which represented my best attempt at capturing the system dynamics, particularly the improved behavior of `id_yiw5` with a 1:1 stoichiometry for `R_A` and sustained `id_shpe` via `R_X`. The main outstanding issue was the magnitude of `id_97q7`.

To minimize any potential parsing issues, I will:
1.  Use very simple reaction IDs (e.g., "R1", "R2", ...).
2.  Ensure all required attributes are set for each reaction immediately after its creation.
3.  Double-check the species IDs used in reactants and products.

The parameters and reaction structure are:
*   **Reaction 1 (R_A in previous versions):** `id_yiw5 <=> id_97q7` (reversible, 1:1 stoichiometry)
    *   `kA_f = 1.3`
    *   `kA_r = 0.0039` (derived from `K_eq = kA_f / (Q_exp/Y_exp) = 1.3 / (1e9/3e6) = 1.3 / 333.33 = 0.0039`)
*   **Reaction 2 (R_B):** `id_shpe -> id_55cy` (irreversible, 1:1)
    *   `kB = 0.0153`
*   **Reaction 3 (R_C):** `id_shpe -> 11 id_97q7` (irreversible, 1:11)
    *   `kC = 0.31` (This value was chosen for a good initial drop in `id_shpe`)
*   **Reaction 4 (R_D):** `id_55cy -> id_shpe` (irreversible, 1:1)
    *   `kD = 0.6` (This was a compromise value for `id_55cy` dynamics)
*   **Reaction 5 (R_X):** `id_97q7 -> id_shpe` (irreversible, 1:1)
    *   `kX = 5e-4` (This value helped sustain `id_shpe` levels in later stages)

This set of reactions and parameters aims to balance initial phase dynamics with later-stage recovery and sustainability, with the known limitation that `id_97q7` levels might not reach the experimental peak within the typical simulation timeframe due to the rate of its net accumulation.

## Action

### Submit
```python
import libsbml

# Ensure input_sbml_string is available globally as per problem description.
# If it's not, this will fail. For the purpose of this block, assume it is.
# Example: input_sbml_string = "<?xml version..." (actual string not needed here)

final_sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
# Check if model exists
if final_sbml_doc.getNumErrors() > 0:
    print("Errors in reading input_sbml_string:")
    for i in range(final_sbml_doc.getNumErrors()):
        print(final_sbml_doc.getError(i).getMessage())
    # Fallback or error handling if input SBML is problematic
    # For now, assume it's valid and proceed.
    
final_model = final_sbml_doc.getModel()

if final_model is None:
    # This would be a critical error if the input_sbml_string is faulty
    # or does not contain a model.
    # For this submission, we assume final_model is valid.
    # Create a new model if it's absolutely necessary and input is empty
    if final_sbml_doc.getLevel() == 0: # SBMLDocument not initialized
        final_sbml_doc = libsbml.SBMLDocument(3,1)
        final_model = final_sbml_doc.createModel()
        final_model.setId("default_model")
        # Need to add compartment, units etc. if starting from scratch.
        # This path is unlikely given the problem setup.
    else: # SBMLDocument exists, but no model
        final_model = final_sbml_doc.createModel()
        final_model.setId("default_model")


# Parameters for the final model
kA_f_val = 1.3    
kA_r_val = 0.0039 
kB_val = 0.0153
kC_val = 0.31    
kD_val = 0.6     
kX_val = 5e-4    

# Reaction 1 (R_A): id_yiw5 <=> id_97q7
r1 = final_model.createReaction()
r1.setId("R1_yiw5_reversible_97q7")
r1.setReversible(True)
r1.setFast(False)

reactant_r1_yiw5 = r1.createReactant()
reactant_r1_yiw5.setSpecies("id_yiw5")
reactant_r1_yiw5.setStoichiometry(1)
reactant_r1_yiw5.setConstant(False)

product_r1_97q7 = r1.createProduct()
product_r1_97q7.setSpecies("id_97q7")
product_r1_97q7.setStoichiometry(1)
product_r1_97q7.setConstant(False)

kl_r1 = r1.createKineticLaw()
param_r1_kf = kl_r1.createLocalParameter(); param_r1_kf.setId("kA_f"); param_r1_kf.setValue(kA_f_val)
param_r1_kr = kl_r1.createLocalParameter(); param_r1_kr.setId("kA_r"); param_r1_kr.setValue(kA_r_val)
kl_r1.setMath(libsbml.parseL3Formula("kA_f * id_yiw5 - kA_r * id_97q7"))

# Reaction 2 (R_B): id_shpe -> id_55cy
r2 = final_model.createReaction()
r2.setId("R2_shpe_to_55cy")
r2.setReversible(False)
r2.setFast(False)

reactant_r2_shpe = r2.createReactant()
reactant_r2_shpe.setSpecies("id_shpe")
reactant_r2_shpe.setStoichiometry(1)
reactant_r2_shpe.setConstant(False)

product_r2_55cy = r2.createProduct()
product_r2_55cy.setSpecies("id_55cy")
product_r2_55cy.setStoichiometry(1)
product_r2_55cy.setConstant(False)

kl_r2 = r2.createKineticLaw()
param_r2_kb = kl_r2.createLocalParameter(); param_r2_kb.setId("kB"); param_r2_kb.setValue(kB_val)
kl_r2.setMath(libsbml.parseL3Formula("kB * id_shpe"))

# Reaction 3 (R_C): id_shpe -> 11 id_97q7
r3 = final_model.createReaction()
r3.setId("R3_shpe_to_11_97q7")
r3.setReversible(False)
r3.setFast(False)

reactant_r3_shpe = r3.createReactant()
reactant_r3_shpe.setSpecies("id_shpe")
reactant_r3_shpe.setStoichiometry(1)
reactant_r3_shpe.setConstant(False)

product_r3_97q7 = r3.createProduct()
product_r3_97q7.setSpecies("id_97q7")
product_r3_97q7.setStoichiometry(11)
product_r3_97q7.setConstant(False)

kl_r3 = r3.createKineticLaw()
param_r3_kc = kl_r3.createLocalParameter(); param_r3_kc.setId("kC"); param_r3_kc.setValue(kC_val)
kl_r3.setMath(libsbml.parseL3Formula("kC * id_shpe"))

# Reaction 4 (R_D): id_55cy -> id_shpe
r4 = final_model.createReaction()
r4.setId("R4_55cy_to_shpe")
r4.setReversible(False)
r4.setFast(False)

reactant_r4_55cy = r4.createReactant()
reactant_r4_55cy.setSpecies("id_55cy")
reactant_r4_55cy.setStoichiometry(1)
reactant_r4_55cy.setConstant(False)

product_r4_shpe = r4.createProduct()
product_r4_shpe.setSpecies("id_shpe")
product_r4_shpe.setStoichiometry(1)
product_r4_shpe.setConstant(False)

kl_r4 = r4.createKineticLaw()
param_r4_kd = kl_r4.createLocalParameter(); param_r4_kd.setId("kD"); param_r4_kd.setValue(kD_val)
kl_r4.setMath(libsbml.parseL3Formula("kD * id_55cy"))

# Reaction 5 (R_X): id_97q7 -> id_shpe
r5 = final_model.createReaction()
r5.setId("R5_97q7_to_shpe")
r5.setReversible(False)
r5.setFast(False)

reactant_r5_97q7 = r5.createReactant()
reactant_r5_97q7.setSpecies("id_97q7")
reactant_r5_97q7.setStoichiometry(1)
reactant_r5_97q7.setConstant(False)

product_r5_shpe = r5.createProduct()
product_r5_shpe.setSpecies("id_shpe")
product_r5_shpe.setStoichiometry(1)
product_r5_shpe.setConstant(False)

kl_r5 = r5.createKineticLaw()
param_r5_kx = kl_r5.createLocalParameter(); param_r5_kx.setId("kX"); param_r5_kx.setValue(kX_val)
kl_r5.setMath(libsbml.parseL3Formula("kX * id_97q7"))

writer = libsbml.SBMLWriter()
final_sbml = writer.writeSBMLToString(final_sbml_doc)
# print(final_sbml) # For debugging if needed
```
