
                # 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/level2/version4" level="2" version="4">
  <model id="id_t7ma">
    <listOfUnitDefinitions>
      <unitDefinition id="id_vtns">
        <listOfUnits>
          <unit kind="metre" exponent="1" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_67s8">
        <listOfUnits>
          <unit kind="metre" exponent="2" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_qwzn">
        <listOfUnits>
          <unit kind="litre" exponent="1" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_dpfo">
        <listOfUnits>
          <unit kind="second" exponent="1" scale="0" multiplier="86400"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_vy5t">
        <listOfUnits>
          <unit kind="mole" exponent="1" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_lqze" spatialDimensions="3" size="1" constant="true"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_dqvv" compartment="id_lqze" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_1zyi" compartment="id_lqze" initialConcentration="1000000" boundaryCondition="false" constant="false"/>
      <species id="id_c29i" compartment="id_lqze" initialConcentration="4000000" 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 contains three species but no reactions. To understand the system's behavior and identify missing mechanisms, I need to observe how the species concentrations change over time under default conditions. This will reveal if any reactions are occurring in the true system that are not present in the model.

My first action will be to request 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: 1001 rows × 4 columns. 

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

Time   id_dqvv  id_1zyi  id_c29i
0         0 1.00e+06 4.00e+06
...
6.00e+00  3.96e+03 9.79e+05 8.86e+04
...
1.20e+01  4.11e+03 9.56e+05 2.10e+04
...
1.80e+01  4.20e+03 9.34e+05 1.94e+04
...
2.40e+01  4.29e+03 9.12e+05 1.90e+04
...
3.00e+01  4.38e+03 8.92e+05 1.86e+04
...
3.60e+01  4.46e+03 8.73e+05 1.82e+04
...
4.20e+01  4.54e+03 8.54e+05 1.79e+04
...
4.80e+01  4.62e+03 8.37e+05 1.75e+04
...
5.40e+01  4.70e+03 8.20e+05 1.72e+04
...
6.00e+01  4.78e+03 8.04e+05 1.69e+04
...
6.60e+01  4.86e+03 7.88e+05 1.66e+04
...
7.20e+01  4.94e+03 7.73e+05 1.63e+04
...
7.80e+01  5.02e+03 7.59e+05 1.61e+04
...
8.40e+01  5.09e+03 7.45e+05 1.58e+04
...
9.00e+01  5.17e+03 7.32e+05 1.56e+04
...
9.60e+01  5.24e+03 7.19e+05 1.53e+04
...
1.02e+02  5.31e+03 7.07e+05 1.51e+04
...
1.08e+02  5.39e+03 6.95e+05 1.49e+04
...
1.14e+02  5.46e+03 6.84e+05 1.47e+04
...
1.20e+02  5.53e+03 6.73e+05 1.45e+04
...
1.26e+02  5.60e+03 6.62e+05 1.43e+04
...
1.32e+02  5.67e+03 6.52e+05 1.41e+04
...
1.38e+02  5.74e+03 6.42e+05 1.39e+04
...
1.44e+02  5.80e+03 6.32e+05 1.37e+04
...
1.50e+02  5.87e+03 6.23e+05 1.35e+04
...
1.56e+02  5.94e+03 6.14e+05 1.34e+04
...
1.62e+02  6.01e+03 6.05e+05 1.32e+04
...
1.68e+02  6.07e+03 5.97e+05 1.30e+04
...
1.74e+02  6.14e+03 5.89e+05 1.29e+04
...
1.80e+02  6.20e+03 5.81e+05 1.27e+04
...
1.86e+02  6.27e+03 5.73e+05 1.26e+04
...
1.92e+02  6.33e+03 5.65e+05 1.25e+04
...
1.98e+02  6.40e+03 5.58e+05 1.23e+04
...
2.04e+02  6.46e+03 5.51e+05 1.22e+04
...
2.10e+02  6.52e+03 5.44e+05 1.21e+04
...
2.16e+02  6.59e+03 5.37e+05 1.20e+04
...
2.22e+02  6.65e+03 5.31e+05 1.18e+04
...
2.28e+02  6.71e+03 5.24e+05 1.17e+04
...
2.34e+02  6.77e+03 5.18e+05 1.16e+04
...
2.40e+02  6.83e+03 5.12e+05 1.15e+04
...
2.46e+02  6.90e+03 5.06e+05 1.14e+04
...
2.52e+02  6.96e+03 5.01e+05 1.13e+04
...
2.58e+02  7.02e+03 4.95e+05 1.12e+04
...
2.64e+02  7.08e+03 4.89e+05 1.11e+04
...
2.70e+02  7.14e+03 4.84e+05 1.10e+04
...
2.76e+02  7.20e+03 4.79e+05 1.09e+04
...
2.82e+02  7.26e+03 4.74e+05 1.08e+04
...
2.88e+02  7.32e+03 4.69e+05 1.07e+04
...
3.00e+02  7.44e+03 4.59e+05 1.06e+04

## 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
I have performed the first observation experiment and analyzed the data. The data clearly shows changes in species concentrations over time, indicating that reactions are occurring in the system, which are missing from the initial SBML model.

Based on the observed changes (id_dqvv increases, id_1zyi and id_c29i decrease), I hypothesized a model with three reactions:
1. `id_1zyi` -> Sink (first order)
2. `id_c29i` -> Sink (first order)
3. `id_1zyi` + `id_c29i` -> `id_dqvv` (second order)

I estimated initial parameters for these reactions based on the early time points of the experimental data. I then constructed an SBML model with these reactions and parameters using `libsbml` and simulated it.

The next step is to compare the simulation results with the experimental data to evaluate how well the hypothesized model fits the observed behavior. The code I wrote in the previous step performs this comparison and prints the results.

Based on the comparison, I will decide on the next course of action. If the fit is poor, I might need to refine the parameters, consider different reaction structures (e.g., different orders, stoichiometries, or additional reactions), or perform more targeted experiments (like changing initial concentrations) to gain more insight into the system's dynamics.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define estimated parameters (from previous step's rough estimation)
k1_est = 0.00284
k2_est = 0.1628
k3_est = 1.65e-10

# Add parameters to the model if they don't exist
if model.getParameter("k1") is None:
    p1 = model.createParameter()
    p1.setId("k1")
    p1.setValue(k1_est)
    p1.setConstant(True)

if model.getParameter("k2") is None:
    p2 = model.createParameter()
    p2.setId("k2")
    p2.setValue(k2_est)
    p2.setConstant(True)

if model.getParameter("k3") is None:
    p3 = model.createParameter()
    p3.setId("k3")
    p3.setValue(k3_est)
    p3.setConstant(True)

# Add Reaction 1: id_1zyi -> Sink
if model.getReaction("reaction_1zyi_sink") is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)

    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)

    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)

# Add Reaction 2: id_c29i -> Sink
if model.getReaction("reaction_c29i_sink") is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)

    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)

    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)

# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
if model.getReaction("reaction_1zyi_c29i_dqvv") is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)

    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)

    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)

    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)

    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model
sim_data = simulate(updated_sbml)

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

# Ensure simulation data covers the same time points as experimental data
# This might require interpolation if time points don't match exactly,
# but the simulate function usually returns data at the same time points as the experiment.
# Let's assume time points match for now.

# Calculate difference at the last time point
last_time = exp_data['Time'].iloc[-1]
exp_last = exp_data[exp_data['Time'] == last_time].iloc[0]
sim_last = sim_data[sim_data['Time'] == last_time].iloc[0]

print(f"\nComparison at Time = {last_time}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last['id_dqvv']:.2f} | {sim_last['id_dqvv']:.2f} | {exp_last['id_dqvv'] - sim_last['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last['id_1zyi']:.2f} | {sim_last['id_1zyi']:.2f} | {exp_last['id_1zyi'] - sim_last['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last['id_c29i']:.2f} | {sim_last['id_c29i']:.2f} | {exp_last['id_c29i'] - sim_last['id_c29i']:.2f}")

# Calculate sum of squared errors (SSE) as a simple metric
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse = 0
for species_id in species_ids:
    sse += np.sum((exp_data[species_id] - sim_data[species_id])**2)

print(f"\nSum of Squared Errors (SSE): {sse:.2f}")

# Store the updated SBML for potential future use or submission
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_est)
shared_variables.add("estimated_k2", k2_est)
shared_variables.add("estimated_k3", k3_est)
```
# Observation

## Code Stdout

Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 3972.67 | 3462.46
id_1zyi | 459322.97 | 424836.85 | 34486.12
id_c29i | 10577.39 | 0.00 | 10577.39

Sum of Squared Errors (SSE): 74708634208902.02

## 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. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3)

### 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 results from the previous step show a poor fit to the experimental data, particularly for `id_dqvv` and `id_c29i`. The simulated `id_c29i` depletes completely, which is not observed in the experiment. This suggests that either the parameters are wrong, or the model structure is incorrect (e.g., missing reactions, wrong reaction orders, or incorrect stoichiometry).

To gain more insight, I will perturb the system by changing the initial concentration of one of the species. Changing the initial concentration of `id_c29i` seems like a good starting point, as its behavior in the simulation is significantly different from the experiment. This might help reveal how its concentration affects the rates of the reactions it participates in.

I will request an experiment where the initial concentration of `id_c29i` is set to a different value (e.g., half of the default) while keeping others at their default values.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_c29i": 2000000
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_2
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_2]

Total size: 1001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_2] for the full data

Time   id_dqvv  id_1zyi  id_c29i
0         0 1.00e+06 2.00e+06
...
6.00e+00  2.01e+03 9.77e+05 5.38e+04
...
1.20e+01  2.13e+03 9.54e+05 2.00e+04
...
1.80e+01  2.21e+03 9.32e+05 1.90e+04
...
2.40e+01  2.29e+03 9.11e+05 1.86e+04
...
3.00e+01  2.37e+03 8.91e+05 1.82e+04
...
3.60e+01  2.45e+03 8.71e+05 1.78e+04
...
4.20e+01  2.52e+03 8.53e+05 1.75e+04
...
4.80e+01  2.60e+03 8.35e+05 1.71e+04
...
5.40e+01  2.67e+03 8.19e+05 1.68e+04
...
6.00e+01  2.75e+03 8.02e+05 1.65e+04
...
6.60e+01  2.82e+03 7.87e+05 1.62e+04
...
7.20e+01  2.89e+03 7.72e+05 1.59e+04
...
7.80e+01  2.96e+03 7.58e+05 1.56e+04
...
8.40e+01  3.03e+03 7.44e+05 1.54e+04
...
9.00e+01  3.10e+03 7.31e+05 1.51e+04
...
9.60e+01  3.16e+03 7.18e+05 1.49e+04
...
1.02e+02  3.23e+03 7.06e+05 1.47e+04
...
1.08e+02  3.30e+03 6.94e+05 1.44e+04
...
1.14e+02  3.36e+03 6.83e+05 1.42e+04
...
1.20e+02  3.43e+03 6.72e+05 1.40e+04
...
1.26e+02  3.49e+03 6.61e+05 1.38e+04
...
1.32e+02  3.55e+03 6.51e+05 1.36e+04
...
1.38e+02  3.62e+03 6.41e+05 1.34e+04
...
1.44e+02  3.68e+03 6.32e+05 1.33e+04
...
1.50e+02  3.74e+03 6.22e+05 1.31e+04
...
1.56e+02  3.80e+03 6.13e+05 1.29e+04
...
1.62e+02  3.86e+03 6.05e+05 1.28e+04
...
1.68e+02  3.92e+03 5.96e+05 1.26e+04
...
1.74e+02  3.98e+03 5.88e+05 1.25e+04
...
1.80e+02  4.04e+03 5.80e+05 1.23e+04
...
1.86e+02  4.10e+03 5.72e+05 1.22e+04
...
1.92e+02  4.16e+03 5.65e+05 1.20e+04
...
1.98e+02  4.21e+03 5.57e+05 1.19e+04
...
2.04e+02  4.27e+03 5.50e+05 1.18e+04
...
2.10e+02  4.33e+03 5.43e+05 1.16e+04
...
2.16e+02  4.39e+03 5.37e+05 1.15e+04
...
2.22e+02  4.44e+03 5.30e+05 1.14e+04
...
2.28e+02  4.50e+03 5.24e+05 1.13e+04
...
2.34e+02  4.55e+03 5.18e+05 1.12e+04
...
2.40e+02  4.61e+03 5.12e+05 1.11e+04
...
2.46e+02  4.66e+03 5.06e+05 1.10e+04
...
2.52e+02  4.72e+03 5.00e+05 1.08e+04
...
2.58e+02  4.77e+03 4.94e+05 1.07e+04
...
2.64e+02  4.82e+03 4.89e+05 1.07e+04
...
2.70e+02  4.88e+03 4.84e+05 1.06e+04
...
2.76e+02  4.93e+03 4.78e+05 1.05e+04
...
2.82e+02  4.98e+03 4.73e+05 1.04e+04
...
2.88e+02  5.04e+03 4.68e+05 1.03e+04
...
3.00e+02  5.14e+03 4.59e+05 1.01e+04

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3)

### 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
I have now performed two experiments: one with default initial concentrations and one with a reduced initial concentration of `id_c29i`. I have also implemented a model with three reactions: `id_1zyi` -> Sink, `id_c29i` -> Sink, and `id_1zyi` + `id_c29i` -> `id_dqvv`, using parameters estimated from the initial rates of the first experiment.

The comparison of the simulation results with the experimental data from both experiments shows that the current model does not accurately capture the system's behavior, especially the dynamics of `id_c29i`. In both simulations, `id_c29i` is predicted to deplete completely, which is not observed in the experiments. The SSE values are very high, indicating a significant mismatch.

The initial rate analysis from the previous step suggested that the parameters were somewhat reasonable for the initial phase, but the long-term behavior is clearly wrong. The fact that `id_c29i` doesn't go to zero in the experiments implies either:
1. The `id_c29i` consumption rate slows down significantly at lower concentrations, more than a simple first-order decay.
2. There is a production mechanism for `id_c29i` that is missing.
3. The reaction `id_c29i` -> Sink is not present or has a much smaller rate constant.
4. The reaction `id_1zyi` + `id_c29i` -> `id_dqvv` is reversible.

Looking at the experimental data again, `id_c29i` decreases rapidly initially but then seems to level off at a non-zero concentration (around 10,000-20,000). This leveling off could be due to a production rate balancing the consumption rate, or the consumption rate becoming negligible.

Let's reconsider the reactions. The decrease in `id_1zyi` and `id_c29i` and the increase in `id_dqvv` strongly suggest the reaction `id_1zyi` + `id_c29i` -> `id_dqvv`. The initial rate analysis supported this. The decrease in `id_1zyi` even when `id_c29i` is low suggests a sink for `id_1zyi`. The decrease in `id_c29i` suggests a sink for `id_c29i` or consumption via the reaction with `id_1zyi`.

The fact that `id_c29i` doesn't go to zero is the most striking discrepancy. Let's hypothesize that the `id_c29i` -> Sink reaction is either absent or much slower than initially estimated. If it's absent, then `id_c29i` is only consumed by reacting with `id_1zyi`. However, the initial rate of `id_c29i` decrease was very high, much higher than the rate of `id_dqvv` production, which contradicts a simple 1:1 stoichiometry in the `id_1zyi` + `id_c29i` -> `id_dqvv` reaction being the *only* consumer of `id_c29i`.

Let's re-examine the initial rates more carefully.
Exp 0:
rate_dqvv ≈ 660
rate_1zyi ≈ -3500
rate_c29i ≈ -651900

Exp 2:
rate_dqvv ≈ 335
rate_1zyi ≈ -3833
rate_c29i ≈ -324367

The rate of `id_c29i` decrease is orders of magnitude larger than the rate of `id_dqvv` production. This strongly suggests there is a significant consumption pathway for `id_c29i` *other than* the reaction producing `id_dqvv`. This supports the `id_c29i` -> Sink reaction.

The problem must be with the rate constant `k2` or the reaction order for `id_c29i` -> Sink, or perhaps there's a production term for `id_c29i`. Given the leveling off, a production term seems plausible. Let's consider a simple zero-order production of `id_c29i` from a boundary species (implicitly, something outside the system maintains a constant production rate).

Hypothesis 2:
1. `id_1zyi` -> Sink (rate = k1 * [id_1zyi])
2. `id_c29i` -> Sink (rate = k2 * [id_c29i])
3. `id_1zyi` + `id_c29i` -> `id_dqvv` (rate = k3 * [id_1zyi] * [id_c29i])
4. Source -> `id_c29i` (rate = k4) - Zero-order production

Let's try to estimate parameters for this new model structure.
From Exp 0 initial rates:
Rate of `id_dqvv` formation ≈ 660. This is from R3. 660 ≈ k3 * 1e6 * 4e6 => k3 ≈ 1.65e-10 (same as before).
Rate of `id_1zyi` decrease ≈ 3500. This is from R1 + R3. 3500 ≈ k1 * 1e6 + k3 * 1e6 * 4e6 = k1 * 1e6 + 660 => k1 * 1e6 ≈ 2840 => k1 ≈ 0.00284 (same as before).
Rate of `id_c29i` decrease ≈ 651900. This is from R2 + R3 - R4. 651900 ≈ k2 * 4e6 + k3 * 1e6 * 4e6 - k4 = k2 * 4e6 + 660 - k4.
651900 ≈ k2 * 4e6 + 660 - k4

From Exp 2 initial rates:
Initial [id_1zyi] = 1e6, [id_c29i] = 2e6
Rate of `id_dqvv` formation ≈ 335. This is from R3. 335 ≈ k3 * 1e6 * 2e6 => k3 ≈ 335 / 2e12 = 1.675e-10. (Close to 1.65e-10, let's stick with 1.65e-10 for now).
Rate of `id_1zyi` decrease ≈ 3833. This is from R1 + R3. 3833 ≈ k1 * 1e6 + k3 * 1e6 * 2e6 = k1 * 1e6 + 1.65e-10 * 2e12 = k1 * 1e6 + 330. k1 * 1e6 ≈ 3833 - 330 = 3503. k1 ≈ 3503 / 1e6 = 0.003503. (This is different from 0.00284. The initial rate approximation might be problematic, or the model is still wrong).

Let's use the average k1: (0.00284 + 0.003503) / 2 ≈ 0.00317. Let's use k3 = 1.65e-10.

Now use the `id_c29i` rates to estimate k2 and k4.
Exp 0: 651900 ≈ k2 * 4e6 + 660 - k4 => 651240 ≈ k2 * 4e6 - k4
Exp 2: 324367 ≈ k2 * 2e6 + 330 - k4 => 324037 ≈ k2 * 2e6 - k4

We have a system of two linear equations for k2 and k4:
1) 4e6 * k2 - k4 ≈ 651240
2) 2e6 * k2 - k4 ≈ 324037

Subtracting (2) from (1):
(4e6 - 2e6) * k2 ≈ 651240 - 324037
2e6 * k2 ≈ 327203
k2 ≈ 327203 / 2e6 ≈ 0.1636

Substitute k2 back into (2):
2e6 * 0.1636 - k4 ≈ 324037
327200 - k4 ≈ 324037
k4 ≈ 327200 - 324037 ≈ 3163

So, estimated parameters:
k1 ≈ 0.00317
k2 ≈ 0.1636
k3 ≈ 1.65e-10
k4 ≈ 3163

Let's update the SBML model with these new parameters and the new reaction (Source -> `id_c29i`). Then simulate and compare again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define estimated parameters
k1_est = 0.00317
k2_est = 0.1636
k3_est = 1.65e-10
k4_est = 3163 # New parameter for zero-order production

# Add parameters to the model if they don't exist or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_est)
add_or_update_parameter(model, "k2", k2_est)
add_or_update_parameter(model, "k3", k3_est)
add_or_update_parameter(model, "k4", k4_est) # Add k4

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sim_data_0 = simulate(updated_sbml)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
print(f"\nTotal SSE (Exp 0 + Exp 2): {sse_0 + sse_2:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_est)
shared_variables.add("estimated_k2", k2_est)
shared_variables.add("estimated_k3", k3_est)
shared_variables.add("estimated_k4", k4_est)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 4541.19 | 2893.94
id_1zyi | 459322.97 | 384440.03 | 74882.94
id_c29i | 10577.39 | 19326.10 | -8748.71

Sum of Squared Errors (SSE) for Experiment 0: 75719945067692.92

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 2571.44 | 2571.32
id_1zyi | 458904.67 | 385215.49 | 73689.18
id_c29i | 10115.91 | 19326.08 | -9210.17

Sum of Squared Errors (SSE) for Experiment 2: 19582980083849.74

Total SSE (Exp 0 + Exp 2): 95302925151542.66

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4)

### 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 with the manually adjusted parameters show some improvement in the SSE, but the fit is still not great. The simulated `id_dqvv` and `id_1zyi` are still significantly off, and while `id_c29i` doesn't go to zero, its dynamics aren't perfectly matched.

The manual parameter tuning is difficult and inefficient. The current model structure (three first/second-order reactions and one zero-order production) seems plausible based on the species dynamics (consumption of `id_1zyi` and `id_c29i`, production of `id_dqvv`, and leveling off of `id_c29i`).

Given the remaining iterations, I should try to refine the parameters more systematically. While I don't have a built-in parameter fitting function, I can use the simulation function and the SSE calculation to guide further manual adjustments.

Let's look at the differences at the end time point again:
Exp 0:
id_dqvv: Exp (7435) vs Sim (4541) -> Sim too low (Difference ~2900)
id_1zyi: Exp (459323) vs Sim (384440) -> Sim too high (Difference ~75000)
id_c29i: Exp (10577) vs Sim (19326) -> Sim too high (Difference ~-8700)

Exp 2:
id_dqvv: Exp (5143) vs Sim (2571) -> Sim too low (Difference ~2500)
id_1zyi: Exp (458905) vs Sim (385215) -> Sim too high (Difference ~74000)
id_c29i: Exp (10116) vs Sim (19326) -> Sim too high (Difference ~-9200)

Observations:
- `id_dqvv` is consistently too low in simulations. This suggests the production rate (k3 * [id_1zyi] * [id_c29i]) is too low. Increasing k3 should help.
- `id_1zyi` is consistently too high in simulations. This suggests the consumption rate (k1 * [id_1zyi] + k3 * [id_1zyi] * [id_c29i]) is too low. Increasing k1 and/or k3 should help.
- `id_c29i` levels off too high in simulations. This suggests the production rate (k4) is too high relative to consumption (k2 * [id_c29i] + k3 * [id_1zyi] * [id_c29i]). Decreasing k4 or increasing k2 or k3 should help.

All three points suggest increasing k3. Increasing k3 will increase `id_dqvv` production, increase `id_1zyi` consumption (via R3), and increase `id_c29i` consumption (via R3), which aligns with the needed adjustments.

Let's try increasing k3 further. Current k3 = 2.0e-10. Let's try k3 = 3.0e-10.
Let's also slightly increase k1 to help with `id_1zyi` consumption. Current k1 = 0.004. Let's try k1 = 0.005.
Let's keep k2 = 0.1636 and k4 = 2000 for now and see the effect of increasing k1 and k3.

I will update the SBML model with these new parameters and simulate both experiments again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define adjusted parameters
k1_adj = 0.005 # Increased
k2_adj = 0.1636 # Keep the same
k3_adj = 3.0e-10 # Increased
k4_adj = 2000 # Keep the same

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_adj)
add_or_update_parameter(model, "k2", k2_adj)
add_or_update_parameter(model, "k3", k3_adj)
add_or_update_parameter(model, "k4", k4_adj)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sbml_doc_exp0 = libsbml.readSBMLFromString(updated_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nTotal SSE (Exp 0 + Exp 2): {total_sse:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_adj)
shared_variables.add("estimated_k2", k2_adj)
shared_variables.add("estimated_k3", k3_adj)
shared_variables.add("estimated_k4", k4_adj)
shared_variables.add("total_sse", total_sse)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 7622.93 | -187.80
id_1zyi | 459322.97 | 221263.57 | 238059.40
id_c29i | 10577.39 | 12219.82 | -1642.44

Sum of Squared Errors (SSE) for Experiment 0: 99152939248428.17

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 4091.47 | 1051.29
id_1zyi | 458904.67 | 222074.28 | 236830.39
id_c29i | 10115.91 | 12219.81 | -2103.90

Sum of Squared Errors (SSE) for Experiment 2: 42759201199985.59

Total SSE (Exp 0 + Exp 2): 141912140448413.75

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4, total_sse)

### 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
The previous parameter adjustment (increasing k1 and k3) significantly improved the fit for `id_dqvv` and `id_c29i` at the final time point, but the fit for `id_1zyi` worsened considerably. The total SSE increased. This indicates that simply increasing k1 and k3 wasn't the right approach, or the balance between the reactions is still off.

Let's re-examine the differences and the effect of each parameter:
- `id_dqvv` is produced by R3 (k3 * [id_1zyi] * [id_c29i]). Sim is now slightly high for Exp 0, low for Exp 2.
- `id_1zyi` is consumed by R1 (k1 * [id_1zyi]) and R3 (k3 * [id_1zyi] * [id_c29i]). Sim is much too low. This means consumption is too high. Either k1 or k3 (or both) are too high.
- `id_c29i` is consumed by R2 (k2 * [id_c29i]) and R3 (k3 * [id_1zyi] * [id_c29i]), and produced by R4 (k4). Sim is still too high. This means production is too high relative to consumption. Either k4 is too high, or k2/k3 are too low.

The large error in `id_1zyi` suggests that the consumption of `id_1zyi` is the main issue. Since increasing k3 helped `id_dqvv` and `id_c29i` but hurt `id_1zyi`, and increasing k1 also hurts `id_1zyi`, perhaps the values of k1 and k3 are too high.

Let's try decreasing k1 and k3 from the last values (k1=0.005, k3=3.0e-10).
Let's go back closer to the initial estimates, but maybe slightly higher than the very first ones.
Initial estimates: k1=0.00284, k3=1.65e-10.
Last attempt: k1=0.005, k3=3.0e-10.

Let's try intermediate values: k1 = 0.004, k3 = 2.0e-10.
The `id_c29i` simulation was too high, suggesting k4 is too high or k2/k3 are too low. Since we are decreasing k3, we might need to decrease k4 or increase k2. Let's try decreasing k4 slightly. Last k4 = 2000. Let's try k4 = 1500. Keep k2 = 0.1636.

New parameters:
k1 = 0.004
k2 = 0.1636
k3 = 2.0e-10
k4 = 1500

Let's update the model and simulate again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define adjusted parameters
k1_adj = 0.004 # Adjusted
k2_adj = 0.1636 # Keep the same
k3_adj = 2.0e-10 # Adjusted
k4_adj = 1500 # Adjusted

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_adj)
add_or_update_parameter(model, "k2", k2_adj)
add_or_update_parameter(model, "k3", k3_adj)
add_or_update_parameter(model, "k4", k4_adj)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sbml_doc_exp0 = libsbml.readSBMLFromString(updated_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nTotal SSE (Exp 0 + Exp 2): {total_sse:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_adj)
shared_variables.add("estimated_k2", k2_adj)
shared_variables.add("estimated_k3", k3_adj)
shared_variables.add("estimated_k4", k4_adj)
shared_variables.add("total_sse", total_sse)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 5063.85 | 2371.28
id_1zyi | 459322.97 | 299564.58 | 159758.39
id_c29i | 10577.39 | 9165.26 | 1412.12

Sum of Squared Errors (SSE) for Experiment 0: 82328830383977.44

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 2689.35 | 2453.41
id_1zyi | 458904.67 | 300296.94 | 158607.73
id_c29i | 10115.91 | 9165.26 | 950.65

Sum of Squared Errors (SSE) for Experiment 2: 26336398024113.57

Total SSE (Exp 0 + Exp 2): 108665228408091.00

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4, total_sse)

### 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
The latest parameter adjustment (k1=0.004, k3=2.0e-10, k4=1500) resulted in a lower total SSE compared to the previous attempt (k1=0.005, k3=3.0e-10, k4=2000), but it's still higher than the very first attempt (k1=0.00284, k2=0.1628, k3=1.65e-10, k4=3163) which had an SSE of ~9.5e13. The current SSE is ~1.08e14.

Let's look at the differences again:
Exp 0:
id_dqvv: Exp (7435) vs Sim (5064) -> Sim too low (~2371)
id_1zyi: Exp (459323) vs Sim (299565) -> Sim too low (~159758)
id_c29i: Exp (10577) vs Sim (9165) -> Sim too low (~1412)

Exp 2:
id_dqvv: Exp (5143) vs Sim (2689) -> Sim too low (~2453)
id_1zyi: Exp (458905) vs Sim (300297) -> Sim too low (~158608)
id_c29i: Exp (10116) vs Sim (9165) -> Sim too low (~951)

Observations:
- `id_dqvv` is consistently too low. Increase k3.
- `id_1zyi` is consistently too low. This means consumption is too high. Decrease k1 and/or k3. This contradicts the need to increase k3 for `id_dqvv`.
- `id_c29i` is consistently too low. This means consumption is too high relative to production. Decrease k2 or k3, or increase k4. This also contradicts the need to increase k3 for `id_dqvv`.

There seems to be a conflict. Increasing k3 helps `id_dqvv` but hurts `id_1zyi` and `id_c29i`. Decreasing k1 helps `id_1zyi` but doesn't directly affect `id_dqvv` or `id_c29i` (except indirectly through [id_1zyi]). Decreasing k2 helps `id_c29i` but doesn't directly affect others. Increasing k4 helps `id_c29i` but doesn't directly affect others.

The large error in `id_1zyi` is the most significant. The simulation predicts a much faster decay of `id_1zyi` than observed. This strongly suggests that the total consumption rate of `id_1zyi` in the model (k1*[id_1zyi] + k3*[id_1zyi]*[id_c29i]) is too high.

Let's try decreasing k1 significantly and slightly increasing k3 to compensate for `id_dqvv`.
Current: k1=0.004, k3=2.0e-10.
Let's try: k1 = 0.001, k3 = 2.5e-10.
Keep k2 = 0.1636.
The `id_c29i` simulation was too low. Let's try increasing k4 back towards the initial estimate. Current k4 = 1500. Initial estimate was ~3163. Let's try k4 = 2500.

New parameters:
k1 = 0.001
k2 = 0.1636
k3 = 2.5e-10
k4 = 2500

Let's update the model and simulate again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define adjusted parameters
k1_adj = 0.001 # Adjusted
k2_adj = 0.1636 # Keep the same
k3_adj = 2.5e-10 # Adjusted
k4_adj = 2500 # Adjusted

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_adj)
add_or_update_parameter(model, "k2", k2_adj)
add_or_update_parameter(model, "k3", k3_adj)
add_or_update_parameter(model, "k4", k4_adj)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sbml_doc_exp0 = libsbml.readSBMLFromString(updated_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nTotal SSE (Exp 0 + Exp 2): {total_sse:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_adj)
shared_variables.add("estimated_k2", k2_adj)
shared_variables.add("estimated_k3", k3_adj)
shared_variables.add("estimated_k4", k4_adj)
shared_variables.add("total_sse", total_sse)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 7007.09 | 428.04
id_1zyi | 459322.97 | 735485.81 | -276162.84
id_c29i | 10577.39 | 15263.91 | -4686.53

Sum of Squared Errors (SSE) for Experiment 0: 120904590851950.30

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 3990.72 | 1152.04
id_1zyi | 458904.67 | 737733.30 | -278828.63
id_c29i | 10115.91 | 15263.86 | -5147.95

Sum of Squared Errors (SSE) for Experiment 2: 66315919116869.31

Total SSE (Exp 0 + Exp 2): 187220509968819.62

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4, total_sse)

### 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 latest parameter adjustment (k1=0.001, k3=2.5e-10, k4=2500) resulted in a significantly *higher* total SSE. The simulation for `id_1zyi` is now much too high, indicating its consumption rate is too low. This confirms that decreasing k1 and increasing k3 simultaneously was not effective.

Let's analyze the errors again:
Exp 0:
id_dqvv: Sim too low (~428) - Increase k3
id_1zyi: Sim too high (~-276163) - Increase k1 and/or k3
id_c29i: Sim too high (~-4687) - Decrease k4 or increase k2 or k3

Exp 2:
id_dqvv: Sim too low (~1152) - Increase k3
id_1zyi: Sim too high (~-278829) - Increase k1 and/or k3
id_c29i: Sim too high (~-5148) - Decrease k4 or increase k2 or k3

All species suggest increasing k3. `id_1zyi` also suggests increasing k1. `id_c29i` suggests decreasing k4 or increasing k2 or k3.

The most significant error is still in `id_1zyi`. Its consumption is too slow in the model. This means k1 and k3 are likely too low. However, increasing k3 also affects `id_dqvv` and `id_c29i`.

Let's try increasing k1 and k3 again, but perhaps less drastically than the attempt in Iteration 4.
Current: k1=0.001, k3=2.5e-10, k4=2500.
Let's try: k1 = 0.003, k3 = 2.8e-10.
The `id_c29i` simulation is too high, suggesting k4 is too high or k2/k3 are too low. Since we are increasing k3, let's try decreasing k4 further. Current k4 = 2500. Let's try k4 = 1000. Keep k2 = 0.1636.

New parameters:
k1 = 0.003
k2 = 0.1636
k3 = 2.8e-10
k4 = 1000

Let's update the model and simulate again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define adjusted parameters
k1_adj = 0.003 # Adjusted
k2_adj = 0.1636 # Keep the same
k3_adj = 2.8e-10 # Adjusted
k4_adj = 1000 # Adjusted

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_adj)
add_or_update_parameter(model, "k2", k2_adj)
add_or_update_parameter(model, "k3", k3_adj)
add_or_update_parameter(model, "k4", k4_adj)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sbml_doc_exp0 = libsbml.readSBMLFromString(updated_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nTotal SSE (Exp 0 + Exp 2): {total_sse:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_adj)
shared_variables.add("estimated_k2", k2_adj)
shared_variables.add("estimated_k3", k3_adj)
shared_variables.add("estimated_k4", k4_adj)
shared_variables.add("total_sse", total_sse)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 7014.57 | 420.56
id_1zyi | 459322.97 | 403597.32 | 55725.65
id_c29i | 10577.39 | 6108.17 | 4469.22

Sum of Squared Errors (SSE) for Experiment 0: 74234833674692.05

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 3676.85 | 1465.92
id_1zyi | 458904.67 | 404981.80 | 53922.87
id_c29i | 10115.91 | 6108.16 | 4007.75

Sum of Squared Errors (SSE) for Experiment 2: 18699432914479.19

Total SSE (Exp 0 + Exp 2): 92934266589171.23

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4, total_sse)

### 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
The latest parameter adjustment (k1=0.003, k3=2.8e-10, k4=1000) resulted in a lower total SSE (~9.29e13) compared to the previous attempt (~1.87e14), and is now lower than the very first attempt (~9.5e13). This is a step in the right direction.

Let's analyze the differences at the end time point:
Exp 0:
id_dqvv: Exp (7435) vs Sim (7015) -> Sim too low (~420)
id_1zyi: Exp (459323) vs Sim (403597) -> Sim too low (~55726)
id_c29i: Exp (10577) vs Sim (6108) -> Sim too low (~4469)

Exp 2:
id_dqvv: Exp (5143) vs Sim (3677) -> Sim too low (~1466)
id_1zyi: Exp (458905) vs Sim (404982) -> Sim too low (~53923)
id_c29i: Exp (10116) vs Sim (6108) -> Sim too low (~4008)

Observations:
- All species are consistently too low in the simulations compared to the experiments.
- `id_dqvv` is produced by R3 (k3 * [id_1zyi] * [id_c29i]). Sim too low -> Increase k3.
- `id_1zyi` is consumed by R1 (k1 * [id_1zyi]) and R3 (k3 * [id_1zyi] * [id_c29i]). Sim too low -> Consumption is too high. Decrease k1 and/or k3. This contradicts the need to increase k3 for `id_dqvv`.
- `id_c29i` is consumed by R2 (k2 * [id_c29i]) and R3 (k3 * [id_1zyi] * [id_c29i]), and produced by R4 (k4). Sim too low -> Consumption is too high relative to production. Decrease k2 or k3, or increase k4. This also contradicts the need to increase k3 for `id_dqvv`.

The consistent "Sim too low" for all species is confusing. Let's re-check the interpretation.
If Sim < Exp, it means the simulated concentration is lower than the experimental one.
- `id_dqvv`: Sim too low means production is too slow. Increase k3.
- `id_1zyi`: Sim too low means consumption is too fast. Decrease k1 and/or k3.
- `id_c29i`: Sim too low means net consumption is too fast (consumption > production). Decrease k2 or k3, or increase k4.

The conflict persists: `id_dqvv` needs k3 increased, while `id_1zyi` and `id_c29i` suggest k3 should be decreased (or k1/k2 adjusted).

Let's look at the magnitude of the errors. The error in `id_1zyi` (~55000) is much larger than `id_dqvv` (~400-1400) and `id_c29i` (~4000). This suggests that the `id_1zyi` dynamics are the primary driver of the SSE.

The simulation predicts `id_1zyi` decays too quickly. This means the combined rate of R1 and R3 is too high.
Rate of `id_1zyi` consumption = k1 * [id_1zyi] + k3 * [id_1zyi] * [id_c29i].

Let's try decreasing k1 further, as it only affects `id_1zyi` consumption.
Current k1 = 0.003. Let's try k1 = 0.0005.
To compensate for the decrease in `id_1zyi` consumption via R3 (due to lower [id_1zyi] over time), we might need to slightly increase k3 to keep `id_dqvv` production up. Current k3 = 2.8e-10. Let's try k3 = 3.0e-10.
The `id_c29i` simulation was too low. Let's try increasing k4 again. Current k4 = 1000. Let's try k4 = 2000. Keep k2 = 0.1636.

New parameters:
k1 = 0.0005
k2 = 0.1636
k3 = 3.0e-10
k4 = 2000

Let's update the model and simulate again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define adjusted parameters
k1_adj = 0.0005 # Adjusted
k2_adj = 0.1636 # Keep the same
k3_adj = 3.0e-10 # Adjusted
k4_adj = 2000 # Adjusted

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_adj)
add_or_update_parameter(model, "k2", k2_adj)
add_or_update_parameter(model, "k3", k3_adj)
add_or_update_parameter(model, "k4", k4_adj)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sbml_doc_exp0 = libsbml.readSBMLFromString(updated_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nTotal SSE (Exp 0 + Exp 2): {total_sse:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_adj)
shared_variables.add("estimated_k2", k2_adj)
shared_variables.add("estimated_k3", k3_adj)
shared_variables.add("estimated_k4", k4_adj)
shared_variables.add("total_sse", total_sse)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 8262.65 | -827.52
id_1zyi | 459322.97 | 853510.44 | -394187.47
id_c29i | 10577.39 | 12205.78 | -1628.39

Sum of Squared Errors (SSE) for Experiment 0: 156353244099015.44

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 4636.53 | 506.23
id_1zyi | 458904.67 | 856640.60 | -397735.93
id_c29i | 10115.91 | 12205.71 | -2089.80

Sum of Squared Errors (SSE) for Experiment 2: 102726087154757.36

Total SSE (Exp 0 + Exp 2): 259079331253772.81

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4, total_sse)

### 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
The latest parameter adjustment (k1=0.0005, k3=3.0e-10, k4=2000) resulted in a much higher total SSE (~2.59e14). The simulation for `id_1zyi` is now drastically too high, indicating its consumption rate is far too low.

Let's analyze the differences at the end time point:
Exp 0:
id_dqvv: Exp (7435) vs Sim (8263) -> Sim too high (~-828)
id_1zyi: Exp (459323) vs Sim (853510) -> Sim too high (~-394187)
id_c29i: Exp (10577) vs Sim (12206) -> Sim too high (~-1628)

Exp 2:
id_dqvv: Exp (5143) vs Sim (4637) -> Sim too low (~506)
id_1zyi: Exp (458905) vs Sim (856641) -> Sim too high (~-397736)
id_c29i: Exp (10116) vs Sim (12206) -> Sim too high (~-2090)

Observations:
- `id_1zyi` is consistently and significantly too high. This means its consumption rate (k1*[id_1zyi] + k3*[id_1zyi]*[id_c29i]) is too low. We need to increase k1 and/or k3.
- `id_c29i` is consistently too high. This means its net consumption rate (k2*[id_c29i] + k3*[id_1zyi]*[id_c29i] - k4) is too low. We need to increase k2 or k3, or decrease k4.
- `id_dqvv` is too high in Exp 0 and too low in Exp 2. This suggests the dependence on initial conditions isn't perfectly captured, but overall production (k3*[id_1zyi]*[id_c29i]) might be slightly off.

The dominant error is `id_1zyi` being too high. This requires increasing its consumption. Both k1 and k3 contribute to this.
Let's try increasing k1 significantly, as it directly impacts `id_1zyi` consumption without involving `id_c29i`.
Current k1 = 0.0005. Let's try k1 = 0.002.
Let's also increase k3 slightly to help with `id_dqvv` and `id_c29i` consumption. Current k3 = 3.0e-10. Let's try k3 = 3.2e-10.
The `id_c29i` simulation is too high, suggesting k4 is too high or k2/k3 are too low. Since we are increasing k3, let's also increase k2 slightly. Current k2 = 0.1636. Let's try k2 = 0.2. Keep k4 = 2000.

New parameters:
k1 = 0.002
k2 = 0.2
k3 = 3.2e-10
k4 = 2000

Let's update the model and simulate again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define adjusted parameters
k1_adj = 0.002 # Adjusted
k2_adj = 0.2 # Adjusted
k3_adj = 3.2e-10 # Adjusted
k4_adj = 2000 # Keep the same

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_adj)
add_or_update_parameter(model, "k2", k2_adj)
add_or_update_parameter(model, "k3", k3_adj)
add_or_update_parameter(model, "k4", k4_adj)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sbml_doc_exp0 = libsbml.readSBMLFromString(updated_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nTotal SSE (Exp 0 + Exp 2): {total_sse:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_adj)
shared_variables.add("estimated_k2", k2_adj)
shared_variables.add("estimated_k3", k3_adj)
shared_variables.add("estimated_k4", k4_adj)
shared_variables.add("total_sse", total_sse)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 7007.09 | 428.04
id_1zyi | 459322.97 | 544804.82 | -85481.85
id_c29i | 10577.39 | 9991.20 | 586.18

Sum of Squared Errors (SSE) for Experiment 0: 58835350833816.20

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 3861.00 | 1281.76
id_1zyi | 458904.67 | 546547.37 | -87642.70
id_c29i | 10115.91 | 9991.17 | 124.73

Sum of Squared Errors (SSE) for Experiment 2: 21739283187148.45

Total SSE (Exp 0 + Exp 2): 80574634020964.64

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4, total_sse)

### 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
The latest parameter adjustment (k1=0.002, k2=0.2, k3=3.2e-10, k4=2000) resulted in a significantly lower total SSE (~8.06e13) compared to the previous attempt (~2.59e14). This is the lowest SSE achieved so far.

Let's analyze the differences at the end time point:
Exp 0:
id_dqvv: Exp (7435) vs Sim (7007) -> Sim too low (~428)
id_1zyi: Exp (459323) vs Sim (544805) -> Sim too high (~-85482)
id_c29i: Exp (10577) vs Sim (9991) -> Sim too low (~586)

Exp 2:
id_dqvv: Exp (5143) vs Sim (3861) -> Sim too low (~1282)
id_1zyi: Exp (458905) vs Sim (546547) -> Sim too high (~-87643)
id_c29i: Exp (10116) vs Sim (9991) -> Sim too low (~125)

Observations:
- `id_dqvv` is consistently too low. Increase k3.
- `id_1zyi` is consistently too high. Consumption is too low. Increase k1 and/or k3.
- `id_c29i` is consistently too low (though the error is small in Exp 2). Net consumption is too high. Decrease k2 or k3, or increase k4.

The errors in `id_dqvv` and `id_1zyi` suggest increasing k3. The error in `id_c29i` suggests decreasing k3 (or k2, or increasing k4).

The error in `id_1zyi` is still the largest. It's too high, meaning its consumption is too slow. This points to k1 and k3 being too low.
Let's try increasing k1 and k3 again.
Current: k1=0.002, k3=3.2e-10.
Let's try: k1 = 0.0025, k3 = 3.5e-10.
The `id_c29i` simulation was too low. Let's try increasing k4 slightly. Current k4 = 2000. Let's try k4 = 2200. Keep k2 = 0.2.

New parameters:
k1 = 0.0025
k2 = 0.2
k3 = 3.5e-10
k4 = 2200

Let's update the model and simulate again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define adjusted parameters
k1_adj = 0.0025 # Adjusted
k2_adj = 0.2 # Keep the same
k3_adj = 3.5e-10 # Adjusted
k4_adj = 2200 # Adjusted

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_adj)
add_or_update_parameter(model, "k2", k2_adj)
add_or_update_parameter(model, "k3", k3_adj)
add_or_update_parameter(model, "k4", k4_adj)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sbml_doc_exp0 = libsbml.readSBMLFromString(updated_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nTotal SSE (Exp 0 + Exp 2): {total_sse:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_adj)
shared_variables.add("estimated_k2", k2_adj)
shared_variables.add("estimated_k3", k3_adj)
shared_variables.add("estimated_k4", k4_adj)
shared_variables.add("total_sse", total_sse)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 7664.58 | -229.45
id_1zyi | 459322.97 | 468545.15 | -9222.18
id_c29i | 10577.39 | 10990.87 | -413.49

Sum of Squared Errors (SSE) for Experiment 0: 51990318092412.67

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 4234.32 | 908.44
id_1zyi | 458904.67 | 470185.34 | -11280.67
id_c29i | 10115.91 | 10990.85 | -874.94

Sum of Squared Errors (SSE) for Experiment 2: 14599116527852.50

Total SSE (Exp 0 + Exp 2): 66589434620265.17

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4, total_sse)

### 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
The latest parameter adjustment (k1=0.0025, k2=0.2, k3=3.5e-10, k4=2200) resulted in a significantly lower total SSE (~6.66e13) compared to the previous attempt (~8.06e13). This is the lowest SSE achieved so far. The differences at the end time point are also smaller.

Let's analyze the differences at the end time point:
Exp 0:
id_dqvv: Exp (7435) vs Sim (7665) -> Sim slightly high (~-229)
id_1zyi: Exp (459323) vs Sim (468545) -> Sim slightly high (~-9222)
id_c29i: Exp (10577) vs Sim (10991) -> Sim slightly high (~-413)

Exp 2:
id_dqvv: Exp (5143) vs Sim (4234) -> Sim too low (~908)
id_1zyi: Exp (458905) vs Sim (470185) -> Sim slightly high (~-11281)
id_c29i: Exp (10116) vs Sim (10991) -> Sim slightly high (~-875)

Observations:
- In Exp 0, all species are slightly too high in the simulation.
- In Exp 2, `id_dqvv` is too low, while `id_1zyi` and `id_c29i` are slightly too high.

Let's consider the overall trends and the largest remaining errors. The error in `id_1zyi` is still the largest, consistently too high in both experiments, although much smaller than before. This means its consumption rate is still slightly too low. This points to k1 and/or k3 being slightly too low.

`id_c29i` is also slightly too high, meaning its net consumption is too low. This points to k2 or k3 being too low, or k4 being too high.

`id_dqvv` is slightly high in Exp 0 and too low in Exp 2. This suggests the model's response to the initial concentration change of `id_c29i` isn't perfect. The production rate (k3 * [id_1zyi] * [id_c29i]) might be slightly off, or the stoichiometry could be wrong (though 1:1 seems likely given the initial rates).

Let's focus on reducing the `id_1zyi` error by increasing its consumption. Both k1 and k3 contribute. Increasing k3 also helps with `id_dqvv` (Exp 2) and `id_c29i` consumption.

Let's try increasing k1 and k3 slightly.
Current: k1=0.0025, k3=3.5e-10.
Let's try: k1 = 0.0028, k3 = 3.8e-10.
The `id_c29i` simulation was slightly too high. Let's try decreasing k4 slightly. Current k4 = 2200. Let's try k4 = 2000. Keep k2 = 0.2.

New parameters:
k1 = 0.0028
k2 = 0.2
k3 = 3.8e-10
k4 = 2000

Let's update the model and simulate again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define adjusted parameters
k1_adj = 0.0028 # Adjusted
k2_adj = 0.2 # Keep the same
k3_adj = 3.8e-10 # Adjusted
k4_adj = 2000 # Adjusted

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_adj)
add_or_update_parameter(model, "k2", k2_adj)
add_or_update_parameter(model, "k3", k3_adj)
add_or_update_parameter(model, "k4", k4_adj)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sbml_doc_exp0 = libsbml.readSBMLFromString(updated_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nTotal SSE (Exp 0 + Exp 2): {total_sse:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_adj)
shared_variables.add("estimated_k2", k2_adj)
shared_variables.add("estimated_k3", k3_adj)
shared_variables.add("estimated_k4", k4_adj)
shared_variables.add("total_sse", total_sse)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 8198.68 | -763.55
id_1zyi | 459322.97 | 427967.53 | 31355.44
id_c29i | 10577.39 | 9991.76 | 585.63

Sum of Squared Errors (SSE) for Experiment 0: 50515650570384.85

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 4481.91 | 660.85
id_1zyi | 458904.67 | 429597.99 | 29306.68
id_c29i | 10115.91 | 9991.73 | 124.18

Sum of Squared Errors (SSE) for Experiment 2: 13008770030428.54

Total SSE (Exp 0 + Exp 2): 63524420600813.39

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4, total_sse)

### 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
The latest parameter adjustment (k1=0.0028, k2=0.2, k3=3.8e-10, k4=2000) resulted in a lower total SSE (~6.35e13) compared to the previous attempt (~6.66e13). This is the lowest SSE achieved so far. The differences at the end time point are also getting smaller, especially for `id_1zyi`.

Let's analyze the differences at the end time point:
Exp 0:
id_dqvv: Exp (7435) vs Sim (8199) -> Sim slightly high (~-764)
id_1zyi: Exp (459323) vs Sim (427968) -> Sim too low (~31355)
id_c29i: Exp (10577) vs Sim (9992) -> Sim slightly low (~586)

Exp 2:
id_dqvv: Exp (5143) vs Sim (4482) -> Sim too low (~661)
id_1zyi: Exp (458905) vs Sim (429598) -> Sim too low (~29307)
id_c29i: Exp (10116) vs Sim (9992) -> Sim slightly low (~124)

Observations:
- `id_1zyi` is consistently too low in simulations. This means its consumption rate is too high. Decrease k1 and/or k3.
- `id_c29i` is consistently slightly too low. Net consumption is too high. Decrease k2 or k3, or increase k4.
- `id_dqvv` is slightly high in Exp 0 and too low in Exp 2.

The error in `id_1zyi` is still the largest. It's too low, meaning its consumption is too fast. This points to k1 and k3 being too high.
Let's try decreasing k1 and k3.
Current: k1=0.0028, k3=3.8e-10.
Let's try: k1 = 0.002, k3 = 3.5e-10.
The `id_c29i` simulation was slightly too low. Let's try increasing k4 slightly. Current k4 = 2000. Let's try k4 = 2200. Keep k2 = 0.2.

New parameters:
k1 = 0.002
k2 = 0.2
k3 = 3.5e-10
k4 = 2200

Let's update the model and simulate again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define adjusted parameters
k1_adj = 0.002 # Adjusted
k2_adj = 0.2 # Keep the same
k3_adj = 3.5e-10 # Adjusted
k4_adj = 2200 # Adjusted

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_adj)
add_or_update_parameter(model, "k2", k2_adj)
add_or_update_parameter(model, "k3", k3_adj)
add_or_update_parameter(model, "k4", k4_adj)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sbml_doc_exp0 = libsbml.readSBMLFromString(updated_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nTotal SSE (Exp 0 + Exp 2): {total_sse:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_adj)
shared_variables.add("estimated_k2", k2_adj)
shared_variables.add("estimated_k3", k3_adj)
shared_variables.add("estimated_k4", k4_adj)
shared_variables.add("total_sse", total_sse)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 7736.89 | -301.76
id_1zyi | 459322.97 | 544373.24 | -85050.27
id_c29i | 10577.39 | 10989.43 | -412.04

Sum of Squared Errors (SSE) for Experiment 0: 58781553590397.06

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 4298.38 | 844.38
id_1zyi | 458904.67 | 546277.36 | -87372.69
id_c29i | 10115.91 | 10989.39 | -873.48

Sum of Squared Errors (SSE) for Experiment 2: 21704347727556.79

Total SSE (Exp 0 + Exp 2): 80485901317953.86

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4, total_sse)

### 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
The latest parameter adjustment (k1=0.002, k2=0.2, k3=3.5e-10, k4=2200) resulted in a higher total SSE (~8.05e13) compared to the previous attempt (~6.35e13). This indicates the previous parameters (k1=0.0028, k2=0.2, k3=3.8e-10, k4=2000) were better.

Let's go back to the parameters from Iteration 11 (k1=0.0025, k2=0.2, k3=3.5e-10, k4=2200) which gave SSE ~6.66e13, and the parameters from Iteration 12 (k1=0.0028, k2=0.2, k3=3.8e-10, k4=2000) which gave SSE ~6.35e13. The latter set is currently the best.

Let's analyze the differences with the best parameters so far (k1=0.0028, k2=0.2, k3=3.8e-10, k4=2000):
Exp 0:
id_dqvv: Exp (7435) vs Sim (8199) -> Sim slightly high (~-764)
id_1zyi: Exp (459323) vs Sim (427968) -> Sim too low (~31355)
id_c29i: Exp (10577) vs Sim (9992) -> Sim slightly low (~586)

Exp 2:
id_dqvv: Exp (5143) vs Sim (4482) -> Sim too low (~661)
id_1zyi: Exp (458905) vs Sim (429598) -> Sim too low (~29307)
id_c29i: Exp (10116) vs Sim (9992) -> Sim slightly low (~124)

Observations:
- `id_1zyi` is consistently too low. Consumption is too high. Decrease k1 and/or k3.
- `id_c29i` is consistently slightly too low. Net consumption is too high. Decrease k2 or k3, or increase k4.
- `id_dqvv` is slightly high in Exp 0 and too low in Exp 2.

The error in `id_1zyi` is still the largest. It's too low, meaning its consumption is too fast. This points to k1 and k3 being too high.
Let's try decreasing k1 and k3 again, but starting from the best parameters (k1=0.0028, k3=3.8e-10).
Let's try: k1 = 0.0025, k3 = 3.6e-10.
The `id_c29i` simulation was slightly too low. Let's try increasing k4 slightly. Current k4 = 2000. Let's try k4 = 2100. Keep k2 = 0.2.

New parameters:
k1 = 0.0025
k2 = 0.2
k3 = 3.6e-10
k4 = 2100

Let's update the model and simulate again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define adjusted parameters
k1_adj = 0.0025 # Adjusted
k2_adj = 0.2 # Keep the same
k3_adj = 3.6e-10 # Adjusted
k4_adj = 2100 # Adjusted

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_adj)
add_or_update_parameter(model, "k2", k2_adj)
add_or_update_parameter(model, "k3", k3_adj)
add_or_update_parameter(model, "k4", k4_adj)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sbml_doc_exp0 = libsbml.readSBMLFromString(updated_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nTotal SSE (Exp 0 + Exp 2): {total_sse:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_adj)
shared_variables.add("estimated_k2", k2_adj)
shared_variables.add("estimated_k3", k3_adj)
shared_variables.add("estimated_k4", k4_adj)
shared_variables.add("total_sse", total_sse)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 7845.57 | -410.44
id_1zyi | 459322.97 | 468461.33 | -9138.36
id_c29i | 10577.39 | 10491.04 | 86.35

Sum of Squared Errors (SSE) for Experiment 0: 51949200828526.84

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 4317.94 | 824.82
id_1zyi | 458904.67 | 470152.03 | -11247.36
id_c29i | 10115.91 | 10491.01 | -375.10

Sum of Squared Errors (SSE) for Experiment 2: 14580718776671.38

Total SSE (Exp 0 + Exp 2): 66529919605198.22

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4, total_sse)

### 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
The latest parameter adjustment (k1=0.0025, k2=0.2, k3=3.6e-10, k4=2100) resulted in a slightly higher total SSE (~6.65e13) compared to the best so far (~6.35e13 from Iteration 12).

Let's go back to the parameters from Iteration 12 (k1=0.0028, k2=0.2, k3=3.8e-10, k4=2000) which gave the lowest SSE.

Let's analyze the differences with these parameters again:
Exp 0:
id_dqvv: Exp (7435) vs Sim (8199) -> Sim slightly high (~-764)
id_1zyi: Exp (459323) vs Sim (427968) -> Sim too low (~31355)
id_c29i: Exp (10577) vs Sim (9992) -> Sim slightly low (~586)

Exp 2:
id_dqvv: Exp (5143) vs Sim (4482) -> Sim too low (~661)
id_1zyi: Exp (458905) vs Sim (429598) -> Sim too low (~29307)
id_c29i: Exp (10116) vs Sim (9992) -> Sim slightly low (~124)

Observations:
- `id_1zyi` is consistently too low. Consumption is too high. Decrease k1 and/or k3.
- `id_c29i` is consistently slightly too low. Net consumption is too high. Decrease k2 or k3, or increase k4.
- `id_dqvv` is slightly high in Exp 0 and too low in Exp 2.

The error in `id_1zyi` is still the largest. It's too low, meaning its consumption is too fast. This points to k1 and k3 being too high.
Let's try decreasing k1 and k3 again, starting from the best parameters (k1=0.0028, k3=3.8e-10).
Let's try: k1 = 0.0026, k3 = 3.7e-10.
The `id_c29i` simulation was slightly too low. Let's try increasing k4 slightly. Current k4 = 2000. Let's try k4 = 2050. Keep k2 = 0.2.

New parameters:
k1 = 0.0026
k2 = 0.2
k3 = 3.7e-10
k4 = 2050

Let's update the model and simulate again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define adjusted parameters
k1_adj = 0.0026 # Adjusted
k2_adj = 0.2 # Keep the same
k3_adj = 3.7e-10 # Adjusted
k4_adj = 2050 # Adjusted

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_adj)
add_or_update_parameter(model, "k2", k2_adj)
add_or_update_parameter(model, "k3", k3_adj)
add_or_update_parameter(model, "k4", k4_adj)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sbml_doc_exp0 = libsbml.readSBMLFromString(updated_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nTotal SSE (Exp 0 + Exp 2): {total_sse:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_adj)
shared_variables.add("estimated_k2", k2_adj)
shared_variables.add("estimated_k3", k3_adj)
shared_variables.add("estimated_k4", k4_adj)
shared_variables.add("total_sse", total_sse)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 8029.48 | -594.35
id_1zyi | 459322.97 | 454523.94 | 4799.03
id_c29i | 10577.39 | 10241.28 | 336.11

Sum of Squared Errors (SSE) for Experiment 0: 51262174701126.65

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 4406.33 | 736.43
id_1zyi | 458904.67 | 456208.49 | 2696.18
id_c29i | 10115.91 | 10241.24 | -125.33

Sum of Squared Errors (SSE) for Experiment 2: 13851501781517.87

Total SSE (Exp 0 + Exp 2): 65113676482644.52

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4, total_sse)

### 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
The latest parameter adjustment (k1=0.0026, k2=0.2, k3=3.7e-10, k4=2050) resulted in a slightly higher total SSE (~6.51e13) compared to the best so far (~6.35e13 from Iteration 12).

Let's go back to the parameters from Iteration 12 (k1=0.0028, k2=0.2, k3=3.8e-10, k4=2000) which gave the lowest SSE.

Let's analyze the differences with these parameters again:
Exp 0:
id_dqvv: Exp (7435) vs Sim (8199) -> Sim slightly high (~-764)
id_1zyi: Exp (459323) vs Sim (427968) -> Sim too low (~31355)
id_c29i: Exp (10577) vs Sim (9992) -> Sim slightly low (~586)

Exp 2:
id_dqvv: Exp (5143) vs Sim (4482) -> Sim too low (~661)
id_1zyi: Exp (458905) vs Sim (429598) -> Sim too low (~29307)
id_c29i: Exp (10116) vs Sim (9992) -> Sim slightly low (~124)

Observations:
- `id_1zyi` is consistently too low. Consumption is too high. Decrease k1 and/or k3.
- `id_c29i` is consistently slightly too low. Net consumption is too high. Decrease k2 or k3, or increase k4.
- `id_dqvv` is slightly high in Exp 0 and too low in Exp 2.

The error in `id_1zyi` is still the largest. It's too low, meaning its consumption is too fast. This points to k1 and k3 being too high.
Let's try decreasing k1 and k3 again, starting from the best parameters (k1=0.0028, k3=3.8e-10).
Let's try: k1 = 0.0027, k3 = 3.75e-10.
The `id_c29i` simulation was slightly too low. Let's try increasing k4 slightly. Current k4 = 2000. Let's try k4 = 2025. Keep k2 = 0.2.

New parameters:
k1 = 0.0027
k2 = 0.2
k3 = 3.75e-10
k4 = 2025

Let's update the model and simulate again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define adjusted parameters
k1_adj = 0.0027 # Adjusted
k2_adj = 0.2 # Keep the same
k3_adj = 3.75e-10 # Adjusted
k4_adj = 2025 # Adjusted

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_adj)
add_or_update_parameter(model, "k2", k2_adj)
add_or_update_parameter(model, "k3", k3_adj)
add_or_update_parameter(model, "k4", k4_adj)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sbml_doc_exp0 = libsbml.readSBMLFromString(updated_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nTotal SSE (Exp 0 + Exp 2): {total_sse:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_adj)
shared_variables.add("estimated_k2", k2_adj)
shared_variables.add("estimated_k3", k3_adj)
shared_variables.add("estimated_k4", k4_adj)
shared_variables.add("total_sse", total_sse)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 8114.17 | -679.04
id_1zyi | 459322.97 | 441046.12 | 18276.86
id_c29i | 10577.39 | 10116.52 | 460.87

Sum of Squared Errors (SSE) for Experiment 0: 50793079850949.97

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 4444.19 | 698.57
id_1zyi | 458904.67 | 442700.23 | 16204.44
id_c29i | 10115.91 | 10116.49 | -0.58

Sum of Squared Errors (SSE) for Experiment 2: 13333716851043.46

Total SSE (Exp 0 + Exp 2): 64126796701993.44

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4, total_sse)

### 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
The latest parameter adjustment (k1=0.0027, k2=0.2, k3=3.75e-10, k4=2025) resulted in a slightly higher total SSE (~6.41e13) compared to the best so far (~6.35e13 from Iteration 12).

Let's go back to the parameters from Iteration 12 (k1=0.0028, k2=0.2, k3=3.8e-10, k4=2000) which gave the lowest SSE.

Let's analyze the differences with these parameters again:
Exp 0:
id_dqvv: Exp (7435) vs Sim (8199) -> Sim slightly high (~-764)
id_1zyi: Exp (459323) vs Sim (427968) -> Sim too low (~31355)
id_c29i: Exp (10577) vs Sim (9992) -> Sim slightly low (~586)

Exp 2:
id_dqvv: Exp (5143) vs Sim (4482) -> Sim too low (~661)
id_1zyi: Exp (458905) vs Sim (429598) -> Sim too low (~29307)
id_c29i: Exp (10116) vs Sim (9992) -> Sim slightly low (~124)

Observations:
- `id_1zyi` is consistently too low. Consumption is too high. Decrease k1 and/or k3.
- `id_c29i` is consistently slightly too low. Net consumption is too high. Decrease k2 or k3, or increase k4.
- `id_dqvv` is slightly high in Exp 0 and too low in Exp 2.

The error in `id_1zyi` is still the largest. It's too low, meaning its consumption is too fast. This points to k1 and k3 being too high.
Let's try decreasing k1 and k3 again, starting from the best parameters (k1=0.0028, k3=3.8e-10).
Let's try: k1 = 0.00275, k3 = 3.78e-10.
The `id_c29i` simulation was slightly too low. Let's try increasing k4 slightly. Current k4 = 2000. Let's try k4 = 2010. Keep k2 = 0.2.

New parameters:
k1 = 0.00275
k2 = 0.2
k3 = 3.78e-10
k4 = 2010

Let's update the model and simulate again.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define adjusted parameters
k1_adj = 0.00275 # Adjusted
k2_adj = 0.2 # Keep the same
k3_adj = 3.78e-10 # Adjusted
k4_adj = 2010 # Adjusted

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_adj)
add_or_update_parameter(model, "k2", k2_adj)
add_or_update_parameter(model, "k3", k3_adj)
add_or_update_parameter(model, "k4", k4_adj)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model with initial conditions from experiment 0
sbml_doc_exp0 = libsbml.readSBMLFromString(updated_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Compare simulation with experiment 0
print("Comparison with Experiment 0 (Default Initial Concentrations):")
last_time_0 = exp_data_0['Time'].iloc[-1]
exp_last_0 = exp_data_0[exp_data_0['Time'] == last_time_0].iloc[0]
sim_last_0 = sim_data_0[sim_data_0['Time'] == last_time_0].iloc[0]

print(f"Comparison at Time = {last_time_0}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_0['id_dqvv']:.2f} | {sim_last_0['id_dqvv']:.2f} | {exp_last_0['id_dqvv'] - sim_last_0['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_0['id_1zyi']:.2f} | {sim_last_0['id_1zyi']:.2f} | {exp_last_0['id_1zyi'] - sim_last_0['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_0['id_c29i']:.2f} | {sim_last_0['id_c29i']:.2f} | {exp_last_0['id_c29i'] - sim_last_0['id_c29i']:.2f}")

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 0: {sse_0:.2f}")


# Simulate the updated model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(updated_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Compare simulation with experiment 2
print("\nComparison with Experiment 2 (Perturbed Initial [id_c29i]):")
last_time_2 = exp_data_2['Time'].iloc[-1]
exp_last_2 = exp_data_2[exp_data_2['Time'] == last_time_2].iloc[0]
sim_last_2 = sim_data_exp2[sim_data_exp2['Time'] == last_time_2].iloc[0]

print(f"Comparison at Time = {last_time_2}:")
print(f"Species | Experimental | Simulation | Difference")
print(f"--------|--------------|------------|------------")
print(f"id_dqvv | {exp_last_2['id_dqvv']:.2f} | {sim_last_2['id_dqvv']:.2f} | {exp_last_2['id_dqvv'] - sim_last_2['id_dqvv']:.2f}")
print(f"id_1zyi | {exp_last_2['id_1zyi']:.2f} | {sim_last_2['id_1zyi']:.2f} | {exp_last_2['id_1zyi'] - sim_last_2['id_1zyi']:.2f}")
print(f"id_c29i | {exp_last_2['id_c29i']:.2f} | {sim_last_2['id_c29i']:.2f} | {exp_last_2['id_c29i'] - sim_last_2['id_c29i']:.2f}")

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nSum of Squared Errors (SSE) for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nTotal SSE (Exp 0 + Exp 2): {total_sse:.2f}")

# Store the updated SBML and parameters
shared_variables.add("current_sbml_model", updated_sbml)
shared_variables.add("estimated_k1", k1_adj)
shared_variables.add("estimated_k2", k2_adj)
shared_variables.add("estimated_k3", k3_adj)
shared_variables.add("estimated_k4", k4_adj)
shared_variables.add("total_sse", total_sse)
```
# Observation

## Code Stdout
Comparison with Experiment 0 (Default Initial Concentrations):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 7435.13 | 8166.25 | -731.12
id_1zyi | 459322.97 | 434451.83 | 24871.14
id_c29i | 10577.39 | 10041.64 | 535.75

Sum of Squared Errors (SSE) for Experiment 0: 50630003239005.38

Comparison with Experiment 2 (Perturbed Initial [id_c29i]):
Comparison at Time = 300.0:
Species | Experimental | Simulation | Difference
--------|--------------|------------|------------
id_dqvv | 5142.76 | 4468.02 | 674.74
id_1zyi | 458904.67 | 436099.29 | 22805.38
id_c29i | 10115.91 | 10041.61 | 74.30

Sum of Squared Errors (SSE) for Experiment 2: 13147365159220.24

Total SSE (Exp 0 + Exp 2): 63777368398225.61

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model, estimated_k1, estimated_k2, estimated_k3, estimated_k4, total_sse)

### 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
The latest parameter adjustment (k1=0.00275, k2=0.2, k3=3.78e-10, k4=2010) resulted in a slightly higher total SSE (~6.38e13) compared to the best so far (~6.35e13 from Iteration 12).

It seems I am oscillating around the minimum SSE found in Iteration 12 with parameters k1=0.0028, k2=0.2, k3=3.8e-10, k4=2000. The manual parameter tuning is getting very fine-grained and doesn't seem to be yielding significant improvements.

The current model structure (R1: id_1zyi -> Sink, R2: id_c29i -> Sink, R3: id_1zyi + id_c29i -> id_dqvv, R4: Source -> id_c29i) seems to capture the general behavior, but the fit isn't perfect. The remaining errors, particularly for `id_1zyi`, suggest that either the reaction orders are not exactly first/second order, or there are other minor reactions occurring.

Given the limited iterations remaining, further manual tuning is unlikely to find the absolute best parameters or reveal a fundamentally missing mechanism if the current structure is mostly correct. The current model with the best parameters found so far (Iteration 12) provides a reasonably good fit to the observed data, especially compared to the initial model.

Let's review the best parameters and the corresponding SSE:
k1 = 0.0028
k2 = 0.2
k3 = 3.8e-10
k4 = 2000
Total SSE = 6.35e13

The differences at the end time point with these parameters were:
Exp 0:
id_dqvv: ~-764
id_1zyi: ~31355
id_c29i: ~586

Exp 2:
id_dqvv: ~661
id_1zyi: ~29307
id_c29i: ~124

The largest remaining error is consistently in `id_1zyi`, which is simulated to decay too quickly. This suggests the consumption rate of `id_1zyi` is slightly overestimated by the model.

However, without more experimental data or a more sophisticated parameter fitting method, it's hard to pinpoint the exact cause of the remaining error. The current model structure is the most plausible explanation based on the observed dynamics.

Given the constraints, I believe the current model structure with the best-found parameters is the most accurate representation I can achieve within the remaining iterations. I will prepare to submit this model.

Before submitting, I will regenerate the SBML string with the best parameters from Iteration 12 to ensure the final submission uses these values.

## Action

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

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define the best parameters found (from Iteration 12)
k1_best = 0.0028
k2_best = 0.2
k3_best = 3.8e-10
k4_best = 2000

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_best)
add_or_update_parameter(model, "k2", k2_best)
add_or_update_parameter(model, "k3", k3_best)
add_or_update_parameter(model, "k4", k4_best)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
final_sbml = writer.writeSBMLToString(sbml_doc)

# Print the final SBML to verify (optional)
# print(final_sbml)

# Simulate the final model with initial conditions from experiment 0 to confirm SSE
sbml_doc_exp0 = libsbml.readSBMLFromString(final_sbml)
model_exp0 = sbml_doc_exp0.getModel()
# Ensure initial concentrations are default for Exp 0
model_exp0.getSpecies("id_dqvv").setInitialConcentration(0)
model_exp0.getSpecies("id_1zyi").setInitialConcentration(1000000)
model_exp0.getSpecies("id_c29i").setInitialConcentration(4000000)
writer_exp0 = libsbml.SBMLWriter()
sbml_string_exp0 = writer_exp0.writeSBMLToString(sbml_doc_exp0)
sim_data_0 = simulate(sbml_string_exp0)

# Get experimental data for experiment 0
exp_data_0 = experiment_history['iteration_0']

# Calculate SSE for experiment 0
species_ids = ['id_dqvv', 'id_1zyi', 'id_c29i']
sse_0 = 0
for species_id in species_ids:
    sse_0 += np.sum((exp_data_0[species_id] - sim_data_0[species_id])**2)
print(f"\nFinal Model SSE for Experiment 0: {sse_0:.2f}")


# Simulate the final model with initial conditions from experiment 2
sbml_doc_exp2 = libsbml.readSBMLFromString(final_sbml)
model_exp2 = sbml_doc_exp2.getModel()

# Change initial concentration for id_c29i
s_c29i = model_exp2.getSpecies("id_c29i")
s_c29i.setInitialConcentration(2000000) # Value used in experiment 2

writer_exp2 = libsbml.SBMLWriter()
sbml_string_exp2 = writer_exp2.writeSBMLToString(sbml_doc_exp2)

sim_data_exp2 = simulate(sbml_string_exp2)

# Get experimental data for experiment 2
exp_data_2 = experiment_history['iteration_2']

# Calculate SSE for experiment 2
sse_2 = 0
for species_id in species_ids:
    sse_2 += np.sum((exp_data_2[species_id] - sim_data_exp2[species_id])**2)
print(f"\nFinal Model SSE for Experiment 2: {sse_2:.2f}")

# Total SSE
total_sse = sse_0 + sse_2
print(f"\nFinal Model Total SSE (Exp 0 + Exp 2): {total_sse:.2f}")

```
## Action

### Submit
```python
import libsbml

# Load the initial model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Define the best parameters found (from Iteration 12)
k1_best = 0.0028
k2_best = 0.2
k3_best = 3.8e-10
k4_best = 2000

# Add parameters to the model or update their values
def add_or_update_parameter(model, param_id, value):
    param = model.getParameter(param_id)
    if param is None:
        param = model.createParameter()
        param.setId(param_id)
        param.setConstant(True)
    param.setValue(value)

add_or_update_parameter(model, "k1", k1_best)
add_or_update_parameter(model, "k2", k2_best)
add_or_update_parameter(model, "k3", k3_best)
add_or_update_parameter(model, "k4", k4_best)

# Add Reaction 1: id_1zyi -> Sink
rxn1 = model.getReaction("reaction_1zyi_sink")
if rxn1 is None:
    rxn1 = model.createReaction()
    rxn1.setId("reaction_1zyi_sink")
    rxn1.setReversible(False)
    reactant1_rxn1 = rxn1.createReactant()
    reactant1_rxn1.setSpecies("id_1zyi")
    reactant1_rxn1.setStoichiometry(1)
    kinetics1 = rxn1.createKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)
else: # Update kinetics if reaction exists
    kinetics1 = rxn1.getKineticLaw()
    math_ast1 = libsbml.parseL3Formula("k1 * id_1zyi")
    kinetics1.setMath(math_ast1)


# Add Reaction 2: id_c29i -> Sink
rxn2 = model.getReaction("reaction_c29i_sink")
if rxn2 is None:
    rxn2 = model.createReaction()
    rxn2.setId("reaction_c29i_sink")
    rxn2.setReversible(False)
    reactant1_rxn2 = rxn2.createReactant()
    reactant1_rxn2.setSpecies("id_c29i")
    reactant1_rxn2.setStoichiometry(1)
    kinetics2 = rxn2.createKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)
else: # Update kinetics if reaction exists
    kinetics2 = rxn2.getKineticLaw()
    math_ast2 = libsbml.parseL3Formula("k2 * id_c29i")
    kinetics2.setMath(math_ast2)


# Add Reaction 3: id_1zyi + id_c29i -> id_dqvv
rxn3 = model.getReaction("reaction_1zyi_c29i_dqvv")
if rxn3 is None:
    rxn3 = model.createReaction()
    rxn3.setId("reaction_1zyi_c29i_dqvv")
    rxn3.setReversible(False)
    reactant1_rxn3 = rxn3.createReactant()
    reactant1_rxn3.setSpecies("id_1zyi")
    reactant1_rxn3.setStoichiometry(1)
    reactant2_rxn3 = rxn3.createReactant()
    reactant2_rxn3.setSpecies("id_c29i")
    reactant2_rxn3.setStoichiometry(1)
    product1_rxn3 = rxn3.createProduct()
    product1_rxn3.setSpecies("id_dqvv")
    product1_rxn3.setStoichiometry(1)
    kinetics3 = rxn3.createKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)
else: # Update kinetics if reaction exists
    kinetics3 = rxn3.getKineticLaw()
    math_ast3 = libsbml.parseL3Formula("k3 * id_1zyi * id_c29i")
    kinetics3.setMath(math_ast3)

# Add Reaction 4: Source -> id_c29i (Zero-order production)
rxn4 = model.getReaction("reaction_source_c29i")
if rxn4 is None:
    rxn4 = model.createReaction()
    rxn4.setId("reaction_source_c29i")
    rxn4.setReversible(False)
    # No reactants for a source reaction from boundary

    product1_rxn4 = rxn4.createProduct()
    product1_rxn4.setSpecies("id_c29i")
    product1_rxn4.setStoichiometry(1)

    kinetics4 = rxn4.createKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4") # Zero-order rate
    kinetics4.setMath(math_ast4)
else: # Update kinetics if reaction exists
    kinetics4 = rxn4.getKineticLaw()
    math_ast4 = libsbml.parseL3Formula("k4")
    kinetics4.setMath(math_ast4)


# Write the updated SBML
writer = libsbml.SBMLWriter()
final_sbml = writer.writeSBMLToString(sbml_doc)
```
