
                # 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/version3" level="2" version="3">
  <model id="id_bifm">
    <listOfUnitDefinitions>
      <unitDefinition id="id_dp7b">
        <listOfUnits>
          <unit kind="mole" scale="-6"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_iz0z">
        <listOfUnits>
          <unit kind="mole" scale="-6"/>
          <unit kind="litre" exponent="-1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_n9p3">
        <listOfUnits>
          <unit kind="mole" scale="-6"/>
          <unit kind="litre" exponent="-1"/>
          <unit kind="second" exponent="-1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_va0a">
        <listOfUnits>
          <unit kind="second" exponent="-1"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_wmdb" size="1"/>
      <compartment id="id_xpsc" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_hura" compartment="id_xpsc" initialConcentration="0.1"/>
      <species id="id_0e6o" compartment="id_xpsc" initialConcentration="0.1"/>
      <species id="id_v92z" compartment="id_wmdb" initialConcentration="1.5"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

                Format your response according to the instructions in the system message.
                
## Thoughts
The first step is to understand the baseline behavior of the system. I will request an observation experiment with the default initial concentrations. This will show me how the concentrations of the species `id_hura`, `id_0e6o`, and `id_v92z` change over time in the real system. Since the provided SBML model has no reactions, simulating it would show constant concentrations. Comparing the experimental data to this trivial simulation will highlight the dynamics I need to model.

## 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_hura  id_0e6o  id_v92z
0  1.00e-01 1.00e-01 1.50e+00
...
2.00e-01  1.03e-01 2.97e-01 1.28e+00
...
4.00e-01  1.06e-01 2.99e-01 1.26e+00
...
6.00e-01  1.10e-01 3.00e-01 1.24e+00
...
8.00e-01  1.13e-01 3.01e-01 1.22e+00
...
1.00e+00  1.16e-01 3.02e-01 1.20e+00
...
1.20e+00  1.19e-01 3.02e-01 1.18e+00
...
1.40e+00  1.22e-01 3.02e-01 1.16e+00
...
1.60e+00  1.25e-01 3.01e-01 1.14e+00
...
1.80e+00  1.28e-01 3.00e-01 1.12e+00
...
2.00e+00  1.31e-01 2.99e-01 1.10e+00
...
2.20e+00  1.34e-01 2.98e-01 1.08e+00
...
2.40e+00  1.37e-01 2.97e-01 1.06e+00
...
2.60e+00  1.40e-01 2.95e-01 1.05e+00
...
2.80e+00  1.42e-01 2.93e-01 1.03e+00
...
3.00e+00  1.45e-01 2.91e-01 1.01e+00
...
3.20e+00  1.47e-01 2.89e-01 9.95e-01
...
3.40e+00  1.50e-01 2.87e-01 9.78e-01
...
3.60e+00  1.52e-01 2.85e-01 9.62e-01
...
3.80e+00  1.54e-01 2.82e-01 9.46e-01
...
4.00e+00  1.57e-01 2.80e-01 9.30e-01
...
4.20e+00  1.59e-01 2.77e-01 9.15e-01
...
4.40e+00  1.61e-01 2.75e-01 9.00e-01
...
4.60e+00  1.63e-01 2.72e-01 8.85e-01
...
4.80e+00  1.65e-01 2.69e-01 8.71e-01
...
5.00e+00  1.66e-01 2.67e-01 8.57e-01
...
5.20e+00  1.68e-01 2.64e-01 8.43e-01
...
5.40e+00  1.70e-01 2.61e-01 8.30e-01
...
5.60e+00  1.71e-01 2.58e-01 8.17e-01
...
5.80e+00  1.73e-01 2.55e-01 8.04e-01
...
6.00e+00  1.74e-01 2.53e-01 7.91e-01
...
6.20e+00  1.75e-01 2.50e-01 7.79e-01
...
6.40e+00  1.77e-01 2.47e-01 7.67e-01
...
6.60e+00  1.78e-01 2.44e-01 7.55e-01
...
6.80e+00  1.79e-01 2.41e-01 7.44e-01
...
7.00e+00  1.80e-01 2.38e-01 7.33e-01
...
7.20e+00  1.81e-01 2.35e-01 7.22e-01
...
7.40e+00  1.82e-01 2.33e-01 7.11e-01
...
7.60e+00  1.83e-01 2.30e-01 7.01e-01
...
7.80e+00  1.83e-01 2.27e-01 6.91e-01
...
8.00e+00  1.84e-01 2.24e-01 6.81e-01
...
8.20e+00  1.85e-01 2.22e-01 6.71e-01
...
8.40e+00  1.85e-01 2.19e-01 6.62e-01
...
8.60e+00  1.86e-01 2.16e-01 6.53e-01
...
8.80e+00  1.86e-01 2.13e-01 6.44e-01
...
9.00e+00  1.86e-01 2.11e-01 6.36e-01
...
9.20e+00  1.87e-01 2.08e-01 6.27e-01
...
9.40e+00  1.87e-01 2.06e-01 6.19e-01
...
9.60e+00  1.87e-01 2.03e-01 6.12e-01
...
1.00e+01  1.87e-01 1.98e-01 5.96e-01

## 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 analyzed the initial observation data. The concentrations of `id_hura` increase, while `id_0e6o` and `id_v92z` decrease. This suggests a reaction where `id_0e6o` and `id_v92z` are reactants and `id_hura` is a product.

My initial hypothesis is a single irreversible bimolecular reaction: `id_0e6o` + `id_v92z` -> `id_hura` with mass action kinetics. I will add this reaction to the SBML model with a placeholder rate constant (k1 = 0.1) and simulate it. Then I will compare the simulation results with the experimental data to see if this reaction structure can explain the observed dynamics.

I will use `libsbml` to modify the model and the `simulate` function to run the simulation. I will also calculate the sum of squared errors between the simulated and experimental data as a quantitative measure of the fit.

## Action

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

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

# Add a parameter for the rate constant
p = model.createParameter()
p.setId("k1")
p.setValue(0.1) # Initial guess for the rate constant
p.setConstant(True)

# Create a new reaction: id_0e6o + id_v92z -> id_hura
reaction = model.createReaction()
reaction.setId("reaction1")
reaction.setReversible(False)
reaction.setFast(False)

# Add reactants
reactant1 = reaction.createReactant()
reactant1.setSpecies("id_0e6o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)

reactant2 = reaction.createReactant()
reactant2.setSpecies("id_v92z")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)

# Add product
product1 = reaction.createProduct()
product1.setSpecies("id_hura")
product1.setStoichiometry(1.0)
product1.setConstant(False) # Species concentration changes

# Create Mass Action kinetic law
kinetic_law = reaction.createKineticLaw()
# Use the parameter 'k1' and the species IDs in the formula
math_ast = libsbml.parseL3Formula("k1 * id_0e6o * id_v92z")
kinetic_law.setMath(math_ast)

# Add the reaction to the model
model.addReaction(reaction)

# 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']

# Compare simulation and experiment (visually or by calculating error)
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head:")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail:")
print(sim_data.tail())

# Calculate sum of squared errors as a simple metric
# Align data points by time
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (k1=0.1): {sse}")

# Store the updated SBML for potential future use or submission
shared_variables.add("model_with_reaction1_k0_1", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100150  0.099850  1.499850  0.01
2  0.100299  0.099701  1.499701  0.02
3  0.100449  0.099551  1.499551  0.03
4  0.100598  0.099402  1.499402  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.176466  0.023534  1.423534   9.96
997   0.176500  0.023500  1.423500   9.97
998   0.176533  0.023467  1.423467   9.98
999   0.176566  0.023434  1.423434   9.99
1000  0.176600  0.023400  1.423400  10.00

Sum of Squared Errors (k1=0.1): 395.91180839648655

## 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. (model_with_reaction1_k0_1)

### 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 with the single reaction `id_0e6o` + `id_v92z` -> `id_hura` and a rate constant of 0.1 does not match the experimental data well, as indicated by the large sum of squared errors and the visual inspection of the head and tail data. Specifically, the simulated `id_0e6o` and `id_v92z` concentrations decrease much slower than observed, and `id_hura` increases slower. Also, the experimental data shows a significant initial drop in `id_0e6o` and `id_v92z` that is not captured by the simulation.

This suggests that either the rate constant is incorrect, or there are other reactions involved. The initial rapid change in `id_0e6o` and `id_v92z` might indicate a faster reaction or perhaps a reaction that doesn't involve `id_hura` as a product, or even a reversible reaction.

Let's first try to see if optimizing the rate constant for the current reaction improves the fit. I will use a simple optimization approach (though a full optimization is not feasible in this environment, I can try a few different values). Let's try a higher rate constant, say 1.0, and see if the error decreases.

I will modify the existing model stored in `shared_variables` by changing the value of the parameter `k1` and then simulate again.

## Action

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

# Retrieve the previously created SBML model
updated_sbml = shared_variables.access("model_with_reaction1_k0_1")
sbml_doc = libsbml.readSBMLFromString(updated_sbml)
model = sbml_doc.getModel()

# Find the parameter k1 and change its value
param_k1 = model.getParameter("k1")
if param_k1:
    param_k1.setValue(1.0) # Try a higher rate constant

# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml_k1_1 = writer.writeSBMLToString(sbml_doc)

# Simulate the updated model
sim_data = simulate(updated_sbml_k1_1)

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

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (k1=1.0):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (k1=1.0):")
print(sim_data.tail())


# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (k1=1.0): {sse}")

# Store the updated SBML
shared_variables.add("model_with_reaction1_k1_1", updated_sbml_k1_1)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (k1=1.0):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.101488  0.098512  1.498512  0.01
2  0.102952  0.097048  1.497048  0.02
3  0.104394  0.095606  1.495606  0.03
4  0.105813  0.094187  1.494187  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (k1=1.0):
      id_hura       id_0e6o  id_v92z   Time
996       0.2  8.208747e-08      1.4   9.96
997       0.2  8.094626e-08      1.4   9.97
998       0.2  7.982092e-08      1.4   9.98
999       0.2  7.871122e-08      1.4   9.99
1000      0.2  7.761695e-08      1.4  10.00

Sum of Squared Errors (k1=1.0): 373.7348927925264

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1)

### 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
Increasing the rate constant to 1.0 did reduce the sum of squared errors, but the fit is still poor, especially at the beginning of the time course. The simulated data still doesn't capture the rapid initial decrease in `id_0e6o` and `id_v92z` and the corresponding increase in `id_hura`. The simulated concentrations of `id_0e6o` and `id_v92z` also drop to near zero in the simulation, which is not observed in the experimental data.

This strongly suggests that the single irreversible reaction `id_0e6o` + `id_v92z` -> `id_hura` is not sufficient to explain the observed dynamics. There must be other reactions or mechanisms at play.

Looking at the experimental data again:
- `id_hura` increases over time.
- `id_0e6o` decreases initially, then seems to level off or decrease very slowly.
- `id_v92z` decreases steadily over time.

The behavior of `id_0e6o` is particularly interesting. It drops quickly and then its rate of change slows down significantly. This could indicate a reversible reaction or a reaction that consumes `id_0e6o` but also produces it, or a reaction that is limited by another factor.

Let's consider the possibility of a reversible reaction: `id_0e6o` + `id_v92z` <=> `id_hura`. This would mean `id_hura` can also react to form `id_0e6o` and `id_v92z`. This could explain why `id_0e6o` and `id_v92z` don't go to zero and why `id_hura` doesn't increase indefinitely.

I will modify the model to make the existing reaction reversible. I will add a reverse rate constant (k2) and update the kinetic law. I will start with initial guesses for both forward (k1) and reverse (k2) rate constants and simulate the model. Let's try k1=1.0 and k2=0.1 as a starting point.

## Action

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

# Retrieve the previously created SBML model (with k1=1.0)
updated_sbml = shared_variables.access("model_with_reaction1_k1_1")
sbml_doc = libsbml.readSBMLFromString(updated_sbml)
model = sbml_doc.getModel()

# Find the existing reaction
reaction = model.getReaction("reaction1")
if reaction:
    # Make the reaction reversible
    reaction.setReversible(True)

    # Add a parameter for the reverse rate constant
    p_k2 = model.createParameter()
    p_k2.setId("k2")
    p_k2.setValue(0.1) # Initial guess for the reverse rate constant
    p_k2.setConstant(True)

    # Update the kinetic law for reversibility (Mass Action)
    # Forward rate: k1 * id_0e6o * id_v92z
    # Reverse rate: k2 * id_hura
    # Net rate: k1 * id_0e6o * id_v92z - k2 * id_hura
    kinetic_law = reaction.getKineticLaw()
    math_ast = libsbml.parseL3Formula("k1 * id_0e6o * id_v92z - k2 * id_hura")
    kinetic_law.setMath(math_ast)

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

# Simulate the updated model
sim_data = simulate(updated_sbml_reversible)

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

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reversible, k1=1.0, k2=0.1):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reversible, k1=1.0, k2=0.1):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reversible, k1=1.0, k2=0.1): {sse}")

# Store the updated SBML
shared_variables.add("model_with_reversible_reaction1_k1_1_k2_0_1", updated_sbml_reversible)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reversible, k1=1.0, k2=0.1):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.101388  0.098612  1.498612  0.01
2  0.102753  0.097247  1.497247  0.02
3  0.104095  0.095905  1.495905  0.03
4  0.105414  0.094586  1.494586  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reversible, k1=1.0, k2=0.1):
       id_hura   id_0e6o   id_v92z   Time
996   0.186783  0.013217  1.413217   9.96
997   0.186783  0.013217  1.413217   9.97
998   0.186783  0.013217  1.413217   9.98
999   0.186783  0.013217  1.413217   9.99
1000  0.186783  0.013217  1.413217  10.00

Sum of Squared Errors (Reversible, k1=1.0, k2=0.1): 380.4420300327976

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1)

### 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
Making the reaction reversible with k1=1.0 and k2=0.1 did not significantly improve the fit compared to the irreversible reaction with k1=1.0. The sum of squared errors is still high, and the simulated dynamics, especially for `id_0e6o` and `id_v92z`, do not match the experimental data. The simulated `id_0e6o` and `id_v92z` still decrease too much and too quickly compared to the experiment.

The experimental data shows a very rapid initial decrease in `id_0e6o` and `id_v92z`, followed by a much slower change. This suggests a fast initial process. The reversible reaction `id_0e6o` + `id_v92z` <=> `id_hura` with mass action kinetics doesn't seem to capture this initial burst and subsequent slowdown accurately with the current parameters.

Let's re-examine the initial experimental data closely.
At Time 0: `id_hura`=0.1, `id_0e6o`=0.1, `id_v92z`=1.5
At Time 0.01: `id_hura`=0.100047, `id_0e6o`=0.229289, `id_v92z`=1.370336

Wait, the initial concentration of `id_0e6o` in the experiment is 0.1, but at Time 0.01 it jumps to 0.229289. This is an *increase*, not a decrease! My initial interpretation of the data was incorrect based on the subset shown in the previous turn. Let's look at the full data head again.

Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Okay, `id_hura` increases, `id_0e6o` increases rapidly initially then seems to level off, and `id_v92z` decreases.

This changes my hypothesis significantly.
- `id_v92z` is consumed.
- `id_hura` is produced.
- `id_0e6o` is produced, at least initially.

A reaction like `id_v92z` -> `id_hura` + `id_0e6o` could explain the consumption of `id_v92z` and production of `id_hura` and `id_0e6o`. Let's try this irreversible reaction with mass action kinetics.

I will remove the previous reaction and add a new one: `id_v92z` -> `id_hura` + `id_0e6o`. I will start with a rate constant (k3) of 0.1 and simulate.

## Action

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

# Load the original SBML model (without any added reactions)
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Add a parameter for the rate constant
p = model.createParameter()
p.setId("k3")
p.setValue(0.1) # Initial guess for the rate constant
p.setConstant(True)

# Create a new reaction: id_v92z -> id_hura + id_0e6o
reaction = model.createReaction()
reaction.setId("reaction2")
reaction.setReversible(False)
reaction.setFast(False)

# Add reactant
reactant1 = reaction.createReactant()
reactant1.setSpecies("id_v92z")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)

# Add products
product1 = reaction.createProduct()
product1.setSpecies("id_hura")
product1.setStoichiometry(1.0)
product1.setConstant(False)

product2 = reaction.createProduct()
product2.setSpecies("id_0e6o")
product2.setStoichiometry(1.0)
product2.setConstant(False)

# Create Mass Action kinetic law
kinetic_law = reaction.createKineticLaw()
# Use the parameter 'k3' and the reactant ID
math_ast = libsbml.parseL3Formula("k3 * id_v92z")
kinetic_law.setMath(math_ast)

# Add the reaction to the model
model.addReaction(reaction)

# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reaction: v92z -> hura + 0e6o, k3=0.1):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reaction: v92z -> hura + 0e6o, k3=0.1):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reaction: v92z -> hura + 0e6o, k3=0.1): {sse}")

# Store the updated SBML
shared_variables.add("model_with_reaction2_k3_0_1", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reaction: v92z -> hura + 0e6o, k3=0.1):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.101499  0.101499  1.498501  0.01
2  0.102997  0.102997  1.497003  0.02
3  0.104493  0.104493  1.495507  0.03
4  0.105988  0.105988  1.494012  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reaction: v92z -> hura + 0e6o, k3=0.1):
       id_hura   id_0e6o   id_v92z   Time
996   1.045968  1.045968  0.554032   9.96
997   1.046522  1.046522  0.553478   9.97
998   1.047075  1.047075  0.552925   9.98
999   1.047628  1.047628  0.552372   9.99
1000  1.048180  1.048180  0.551820  10.00

Sum of Squared Errors (Reaction: v92z -> hura + 0e6o, k3=0.1): 557.0137349125868

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1)

### 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 reaction `id_v92z` -> `id_hura` + `id_0e6o` with k3=0.1 also does not fit the data well. The simulated `id_0e6o` and `id_hura` increase much more than observed, and `id_v92z` decreases too slowly. The sum of squared errors is even higher than the previous attempts.

The experimental data shows `id_0e6o` increasing rapidly initially and then leveling off around 0.3. `id_hura` increases more slowly and seems to level off around 0.18. `id_v92z` decreases steadily.

The initial rapid increase in `id_0e6o` and `id_hura` and decrease in `id_v92z` suggests a reaction consuming `id_v92z` and producing `id_0e6o` and `id_hura`. The leveling off of `id_0e6o` and `id_hura` suggests either a reversible reaction or another reaction consuming them or producing `id_v92z`.

Let's reconsider the reversible reaction `id_0e6o` + `id_v92z` <=> `id_hura`. The forward reaction consumes `id_0e6o` and `id_v92z` and produces `id_hura`. The reverse reaction consumes `id_hura` and produces `id_0e6o` and `id_v92z`. This doesn't quite fit the initial increase in `id_0e6o`.

How about two separate reactions?
1. `id_v92z` -> `id_hura` + `id_0e6o` (explains initial changes)
2. Another reaction that consumes `id_0e6o` or produces `id_v92z` or consumes `id_hura` to cause the leveling off.

Let's look at the stoichiometry from the initial rapid phase.
Change in `id_hura` from 0 to 0.01s: 0.100047 - 0.1 = 0.000047
Change in `id_0e6o` from 0 to 0.01s: 0.229289 - 0.1 = 0.129289
Change in `id_v92z` from 0 to 0.01s: 1.370336 - 1.5 = -0.129664

The changes in `id_0e6o` and `id_v92z` are roughly equal in magnitude and opposite in sign, while the change in `id_hura` is much smaller. This doesn't fit a simple 1:1:1 stoichiometry like `id_v92z` -> `id_hura` + `id_0e6o`.

Let's consider the possibility that `id_0e6o` is a catalyst or enzyme, or involved in a more complex rate law. However, the task states I do not need to add new species, implying the mechanism should involve only the existing species.

Let's revisit the reversible reaction `id_0e6o` + `id_v92z` <=> `id_hura`. Perhaps the initial rapid increase in `id_0e6o` is due to the reverse reaction being very fast initially, or the forward reaction being slow initially. But the forward reaction consumes `id_0e6o`, which contradicts the initial increase.

What if the stoichiometry is different? For `id_0e6o` + `id_v92z` <=> `id_hura`, the stoichiometry is 1:1:1. What if it's something like `id_v92z` <=> `id_hura` + `id_0e6o`? This is the reaction I just tried.

Let's consider the possibility of two separate reactions involving these species.
Reaction 1: `id_v92z` -> `id_hura` (consumes v92z, produces hura)
Reaction 2: `id_v92z` -> `id_0e6o` (consumes v92z, produces 0e6o)
Reaction 3: `id_0e6o` -> `id_hura` (consumes 0e6o, produces hura)
Reaction 4: `id_hura` -> `id_0e6o` (consumes hura, produces 0e6o)
... and combinations.

The initial data suggests `id_v92z` is consumed, and `id_hura` and `id_0e6o` are produced. This points towards reactions where `id_v92z` is a reactant and `id_hura` and `id_0e6o` are products.

Let's try two irreversible reactions:
Reaction A: `id_v92z` -> `id_hura` (rate kA * id_v92z)
Reaction B: `id_v92z` -> `id_0e6o` (rate kB * id_v92z)

This would lead to:
d[id_hura]/dt = kA * id_v92z
d[id_0e6o]/dt = kB * id_v92z
d[id_v92z]/dt = -(kA + kB) * id_v92z

This would cause `id_hura` and `id_0e6o` to increase proportionally to each other (with ratio kB/kA) as long as `id_v92z` is present, and `id_v92z` would decrease exponentially. This doesn't explain the leveling off of `id_0e6o` and `id_hura`.

What if one of the reactions is reversible?
Reaction A: `id_v92z` <=> `id_hura` (rate kA1 * id_v92z - kA2 * id_hura)
Reaction B: `id_v92z` -> `id_0e6o` (rate kB * id_v92z)

This still doesn't explain the leveling off of `id_0e6o`.

Let's consider the possibility that `id_0e6o` is involved in consuming `id_v92z` or producing `id_hura`.
Reaction A: `id_v92z` -> `id_hura` (rate kA * id_v92z)
Reaction B: `id_0e6o` + `id_v92z` -> `id_hura` (rate kB * id_0e6o * id_v92z)

This would consume `id_v92z` and produce `id_hura`. It doesn't produce `id_0e6o`.

Let's go back to the initial observation: `id_v92z` decreases, `id_hura` increases, `id_0e6o` increases then levels off.

Maybe there is a reaction that produces `id_0e6o` and another that consumes it.
Reaction 1: `id_v92z` -> `id_hura` + `id_0e6o` (rate k1 * id_v92z) - This produced too much `id_0e6o` and `id_hura` in the previous simulation.
Reaction 2: `id_0e6o` -> X (where X is something that doesn't affect the observed species, or is `id_v92z` or `id_hura`)

If Reaction 2 is `id_0e6o` -> `id_v92z`:
d[id_0e6o]/dt = k1 * id_v92z - k2 * id_0e6o
d[id_v92z]/dt = -k1 * id_v92z + k2 * id_0e6o - k1 * id_v92z = k2 * id_0e6o - 2*k1 * id_v92z
d[id_hura]/dt = k1 * id_v92z

This doesn't look right.

Let's consider the stoichiometry again from the initial phase. The change in `id_0e6o` is much larger than the change in `id_hura`. This suggests that the reaction producing `id_0e6o` is faster or has a higher stoichiometric coefficient than the reaction producing `id_hura`.

What if there are two parallel reactions from `id_v92z`?
Reaction 1: `id_v92z` -> `id_0e6o` (rate k1 * id_v92z)
Reaction 2: `id_v92z` -> `id_hura` (rate k2 * id_v92z)

This would give:
d[id_0e6o]/dt = k1 * id_v92z
d[id_hura]/dt = k2 * id_v92z
d[id_v92z]/dt = -(k1 + k2) * id_v92z

This still doesn't explain the leveling off of `id_0e6o` and `id_hura`. It would lead to exponential decay of `id_v92z` and proportional increase of `id_0e6o` and `id_hura`.

Let's consider a reaction that consumes `id_0e6o`.
Reaction 1: `id_v92z` -> `id_0e6o` (rate k1 * id_v92z)
Reaction 2: `id_0e6o` -> `id_hura` (rate k2 * id_0e6o)

This would give:
d[id_0e6o]/dt = k1 * id_v92z - k2 * id_0e6o
d[id_hura]/dt = k2 * id_0e6o
d[id_v92z]/dt = -k1 * id_v92z

This looks more promising. `id_v92z` decreases exponentially. `id_0e6o` increases initially (if k1*id_v92z > k2*id_0e6o) and then might level off as `id_v92z` decreases and `id_0e6o` increases. `id_hura` increases as `id_0e6o` is consumed.

Let's try this model:
Reaction 1: `id_v92z` -> `id_0e6o` (irreversible, mass action)
Reaction 2: `id_0e6o` -> `id_hura` (irreversible, mass action)

I will add these two reactions to the original model with initial guesses for rate constants (k1=0.5, k2=0.1) and simulate.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(0.5) # Initial guess for rate constant 1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(0.1) # Initial guess for rate constant 2
p2.setConstant(True)

# Create Reaction 1: id_v92z -> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o -> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k2 * id_0e6o")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z -> 0e6o, 0e6o -> hura; k1=0.5, k2=0.1):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z -> 0e6o, 0e6o -> hura; k1=0.5, k2=0.1):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z -> 0e6o, 0e6o -> hura; k1=0.5, k2=0.1): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reactions_k1_0_5_k2_0_1", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z -> 0e6o, 0e6o -> hura; k1=0.5, k2=0.1):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100104  0.107377  1.492519  0.01
2  0.100215  0.114710  1.485075  0.02
3  0.100333  0.121999  1.477668  0.03
4  0.100459  0.129243  1.470298  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z -> 0e6o, 0e6o -> hura; k1=0.5, k2=0.1):
       id_hura   id_0e6o   id_v92z   Time
996   0.973104  0.716585  0.010311   9.96
997   0.973820  0.715920  0.010260   9.97
998   0.974536  0.715255  0.010209   9.98
999   0.975251  0.714591  0.010158   9.99
1000  0.975965  0.713928  0.010107  10.00

Sum of Squared Errors (Reactions: v92z -> 0e6o, 0e6o -> hura; k1=0.5, k2=0.1): 1005.1669833642791

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1)

### 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 model with two consecutive irreversible reactions (`id_v92z` -> `id_0e6o` and `id_0e6o` -> `id_hura`) also does not fit the data well with the chosen rate constants. The simulated `id_0e6o` and `id_hura` concentrations increase much more than observed, and `id_v92z` decreases too quickly. The sum of squared errors is very high.

The initial rapid increase in `id_0e6o` and `id_hura` and decrease in `id_v92z` is a key feature. The subsequent leveling off of `id_0e6o` and `id_hura` is another.

Let's look at the initial phase again. The change in `id_0e6o` is much larger than the change in `id_hura`. This suggests that the reaction producing `id_0e6o` is significantly faster than the reaction producing `id_hura`.

Consider the model:
Reaction 1: `id_v92z` -> `id_0e6o` (rate k1 * id_v92z)
Reaction 2: `id_0e6o` -> `id_hura` (rate k2 * id_0e6o)

If k1 is much larger than k2, `id_0e6o` would initially increase rapidly as it's produced from `id_v92z`. As `id_0e6o` concentration builds up, the second reaction starts consuming it and producing `id_hura`. The concentration of `id_0e6o` would then reach a peak and potentially decrease or level off, depending on the relative rates. `id_hura` would increase as `id_0e6o` is converted. `id_v92z` would decrease as it's consumed by the first reaction.

This structure seems plausible for explaining the observed dynamics. The initial rapid increase in `id_0e6o` and decrease in `id_v92z` would be dominated by Reaction 1. The later leveling off of `id_0e6o` and the continued increase of `id_hura` would be influenced by Reaction 2.

Let's try increasing k1 significantly and perhaps adjusting k2. Let's try k1=5.0 and k2=0.5.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(5.0) # Increased guess for rate constant 1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(0.5) # Adjusted guess for rate constant 2
p2.setConstant(True)

# Create Reaction 1: id_v92z -> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o -> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k2 * id_0e6o")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z -> 0e6o, 0e6o -> hura; k1=5.0, k2=0.5):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z -> 0e6o, 0e6o -> hura; k1=5.0, k2=0.5):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z -> 0e6o, 0e6o -> hura; k1=5.0, k2=0.5): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reactions_k1_5_k2_0_5", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z -> 0e6o, 0e6o -> hura; k1=5.0, k2=0.5):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100683  0.172473  1.426844  0.01
2  0.101718  0.241026  1.357256  0.02
3  0.103087  0.305851  1.291062  0.03
4  0.104771  0.367133  1.228096  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z -> 0e6o, 0e6o -> hura; k1=5.0, k2=0.5):
       id_hura   id_0e6o       id_v92z   Time
996   1.687856  0.012144  1.586355e-15   9.96
997   1.687916  0.012084  1.886228e-15   9.97
998   1.687977  0.012023  2.094396e-15   9.98
999   1.688037  0.011963  2.200081e-15   9.99
1000  1.688096  0.011904  2.192049e-15  10.00

Sum of Squared Errors (Reactions: v92z -> 0e6o, 0e6o -> hura; k1=5.0, k2=0.5): 2480.6830970249152

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1, model_with_two_reactions_k1_5_k2_0_5)

### 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
Increasing k1 to 5.0 and k2 to 0.5 in the consecutive reaction model (`id_v92z` -> `id_0e6o` -> `id_hura`) resulted in a much worse fit, with a very high sum of squared errors. The simulated `id_0e6o` and `id_hura` concentrations still increase too much, and `id_v92z` decreases too quickly, reaching near zero.

The experimental data shows `id_v92z` decreasing but leveling off around 0.6, not going to zero. This suggests that `id_v92z` is not fully consumed, or there's a reaction producing it, or the reaction consuming it is reversible or limited.

Let's reconsider the initial rapid increase in `id_0e6o` and `id_hura` and decrease in `id_v92z`. The stoichiometry from the initial phase (approximate changes: d[hura] ~ 0.000047, d[0e6o] ~ 0.129289, d[v92z] ~ -0.129664) suggests that for every mole of `id_v92z` consumed, roughly 1 mole of `id_0e6o` is produced, and a much smaller amount of `id_hura` is produced.

This points towards a primary reaction consuming `id_v92z` and producing `id_0e6o`, and a secondary reaction producing `id_hura`.

What if the primary reaction is reversible?
Reaction 1: `id_v92z` <=> `id_0e6o` (rate k1 * id_v92z - k2 * id_0e6o)
Reaction 2: `id_v92z` -> `id_hura` (rate k3 * id_v92z) or `id_0e6o` -> `id_hura` (rate k3 * id_0e6o)

If Reaction 2 is `id_v92z` -> `id_hura`:
d[id_v92z]/dt = -k1 * id_v92z + k2 * id_0e6o - k3 * id_v92z = (k2 * id_0e6o) - (k1 + k3) * id_v92z
d[id_0e6o]/dt = k1 * id_v92z - k2 * id_0e6o
d[id_hura]/dt = k3 * id_v92z

This could potentially explain the leveling off of `id_v92z` if the reverse reaction of R1 becomes significant. It could also explain the initial rapid increase in `id_0e6o` (if k1 is large) and a slower increase in `id_hura` (if k3 is smaller). The leveling off of `id_0e6o` would occur when k1 * id_v92z ≈ k2 * id_0e6o.

Let's try this model:
Reaction 1: `id_v92z` <=> `id_0e6o` (reversible, mass action)
Reaction 2: `id_v92z` -> `id_hura` (irreversible, mass action)

I will add these two reactions to the original model with initial guesses for rate constants (k1=5.0, k2=0.5, k3=0.1) and simulate.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(5.0) # Initial guess for forward rate constant 1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(0.5) # Initial guess for reverse rate constant 1
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(0.1) # Initial guess for rate constant 2
p3.setConstant(True)


# Create Reaction 1: id_v92z <=> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z - k2 * id_0e6o")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_v92z -> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_v92z")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k3 * id_v92z")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z <=> 0e6o, v92z -> hura; k1=5.0, k2=0.5, k3=0.1):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z <=> 0e6o, v92z -> hura; k1=5.0, k2=0.5, k3=0.1):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z <=> 0e6o, v92z -> hura; k1=5.0, k2=0.5, k3=0.1): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reactions_reversible_k1_5_k2_0_5_k3_0_1", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z <=> 0e6o, v92z -> hura; k1=5.0, k2=0.5, k3=0.1):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.101463  0.172453  1.426085  0.01
2  0.102854  0.240958  1.356189  0.02
3  0.104176  0.305731  1.290093  0.03
4  0.105435  0.366975  1.227590  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z <=> 0e6o, v92z -> hura; k1=5.0, k2=0.5, k3=0.1):
       id_hura   id_0e6o   id_v92z   Time
996   0.258587  1.312509  0.128903   9.96
997   0.258716  1.312392  0.128892   9.97
998   0.258845  1.312274  0.128880   9.98
999   0.258974  1.312157  0.128869   9.99
1000  0.259103  1.312040  0.128857  10.00

Sum of Squared Errors (Reactions: v92z <=> 0e6o, v92z -> hura; k1=5.0, k2=0.5, k3=0.1): 1768.2570742652267

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1, model_with_two_reactions_k1_5_k2_0_5, model_with_two_reactions_reversible_k1_5_k2_0_5_k3_0_1)

### 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 model with reactions `id_v92z` <=> `id_0e6o` and `id_v92z` -> `id_hura` with k1=5.0, k2=0.5, k3=0.1 still doesn't fit the data well. The simulated `id_0e6o` increases too much and doesn't level off correctly, `id_hura` increases too much, and `id_v92z` decreases too much.

Let's reconsider the model with consecutive irreversible reactions:
Reaction 1: `id_v92z` -> `id_0e6o` (rate k1 * id_v92z)
Reaction 2: `id_0e6o` -> `id_hura` (rate k2 * id_0e6o)

The dynamics are:
d[id_v92z]/dt = -k1 * id_v92z
d[id_0e6o]/dt = k1 * id_v92z - k2 * id_0e6o
d[id_hura]/dt = k2 * id_0e6o

This system describes a sequential conversion. `id_v92z` is converted to `id_0e6o`, which is then converted to `id_hura`.
- `id_v92z` will decrease exponentially.
- `id_0e6o` will initially increase (as it's produced faster than consumed), reach a peak, and then decrease (as its source `id_v92z` depletes and it's consumed by R2).
- `id_hura` will increase, initially slowly, then faster as `id_0e6o` builds up, and eventually level off as `id_0e6o` is depleted.

This general behavior (v92z decreasing, 0e6o peaking then decreasing/leveling, hura increasing and leveling) *qualitatively* matches the experimental data, except that in the experiment, `id_0e6o` seems to level off rather than decrease significantly after the peak, and `id_v92z` levels off rather than going to zero.

The fact that `id_v92z` doesn't go to zero suggests either the reaction consuming it is reversible, or there's a source of `id_v92z`, or the reaction rate slows down significantly at lower concentrations (e.g., not simple mass action, but the problem implies mass action kinetics are likely). Given the species list, a source of `id_v92z` is unlikely unless it's produced from `id_hura` or `id_0e6o`.

Let's consider the possibility that the second reaction (`id_0e6o` -> `id_hura`) is reversible.
Reaction 1: `id_v92z` -> `id_0e6o` (rate k1 * id_v92z)
Reaction 2: `id_0e6o` <=> `id_hura` (rate k2 * id_0e6o - k3 * id_hura)

Dynamics:
d[id_v92z]/dt = -k1 * id_v92z
d[id_0e6o]/dt = k1 * id_v92z - k2 * id_0e6o + k3 * id_hura
d[id_hura]/dt = k2 * id_0e6o - k3 * id_hura

This model:
- `id_v92z` still decreases exponentially to zero. This contradicts the experimental data where `id_v92z` levels off.

The leveling off of `id_v92z` is a critical feature not captured by models where `id_v92z` is only consumed by irreversible reactions. This strongly suggests that the reaction consuming `id_v92z` must be reversible, or `id_v92z` is produced by another reaction.

Let's go back to the reversible reaction `id_v92z` <=> `id_0e6o`.
Reaction 1: `id_v92z` <=> `id_0e6o` (rate k1 * id_v92z - k2 * id_0e6o)
And a reaction that produces `id_hura`. `id_hura` increases steadily. It could be produced from `id_v92z` or `id_0e6o`.

If `id_v92z` -> `id_hura` (as in the previous attempt):
d[id_v92z]/dt = -k1 * id_v92z + k2 * id_0e6o - k3 * id_v92z
d[id_0e6o]/dt = k1 * id_v92z - k2 * id_0e6o
d[id_hura]/dt = k3 * id_v92z

This model allows `id_v92z` and `id_0e6o` to reach an equilibrium (or steady state) where k1 * id_v92z ≈ k2 * id_0e6o, while `id_hura` continues to increase as long as `id_v92z` is present. However, `id_hura` also levels off in the experiment. This suggests the reaction producing `id_hura` might also be reversible or dependent on a species that depletes.

What if `id_hura` is produced from `id_0e6o`?
Reaction 1: `id_v92z` <=> `id_0e6o` (rate k1 * id_v92z - k2 * id_0e6o)
Reaction 2: `id_0e6o` -> `id_hura` (rate k3 * id_0e6o)

Dynamics:
d[id_v92z]/dt = -k1 * id_v92z + k2 * id_0e6o
d[id_0e6o]/dt = k1 * id_v92z - k2 * id_0e6o - k3 * id_0e6o = k1 * id_v92z - (k2 + k3) * id_0e6o
d[id_hura]/dt = k3 * id_0e6o

In this model:
- `id_v92z` and `id_0e6o` can reach a steady state where k1 * id_v92z = (k2 + k3) * id_0e6o. This would explain the leveling off of `id_v92z` and `id_0e6o`.
- `id_hura` would continue to increase as long as `id_0e6o` is present at a non-zero steady state. However, `id_hura` also levels off in the experiment. This suggests Reaction 2 might be reversible.

Let's try this model:
Reaction 1: `id_v92z` <=> `id_0e6o` (reversible, mass action)
Reaction 2: `id_0e6o` <=> `id_hura` (reversible, mass action)

Dynamics:
d[id_v92z]/dt = -k1 * id_v92z + k2 * id_0e6o
d[id_0e6o]/dt = k1 * id_v92z - k2 * id_0e6o - k3 * id_0e6o + k4 * id_hura = k1 * id_v92z - (k2 + k3) * id_0e6o + k4 * id_hura
d[id_hura]/dt = k3 * id_0e6o - k4 * id_hura

This system can reach a full equilibrium where all rates are zero:
k1 * id_v92z = k2 * id_0e6o
k3 * id_0e6o = k4 * id_hura

This model structure seems capable of explaining the leveling off of all three species. Let's implement this model and try some initial rate constants. Based on the initial rapid increase of `id_0e6o` relative to `id_hura`, k1 should likely be larger than k3. k2 and k4 determine the reverse rates and equilibrium points.

Let's try k1=5.0, k2=0.5, k3=0.5, k4=0.1.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(5.0) # Initial guess for forward rate constant R1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(0.5) # Initial guess for reverse rate constant R1
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(0.5) # Initial guess for forward rate constant R2
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(0.1) # Initial guess for reverse rate constant R2
p4.setConstant(True)


# Create Reaction 1: id_v92z <=> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z - k2 * id_0e6o")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o <=> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(True)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k3 * id_0e6o - k4 * id_hura")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=5.0, k2=0.5, k3=0.5, k4=0.1):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=5.0, k2=0.5, k3=0.5, k4=0.1):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=5.0, k2=0.5, k3=0.5, k4=0.1): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reversible_reactions_k1_5_k2_0_5_k3_0_5_k4_0_1", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=5.0, k2=0.5, k3=0.5, k4=0.1):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100581  0.171909  1.427510  0.01
2  0.101511  0.239593  1.358896  0.02
3  0.102767  0.303284  1.293949  0.03
4  0.104332  0.363198  1.232471  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=5.0, k2=0.5, k3=0.5, k4=0.1):
       id_hura   id_0e6o   id_v92z   Time
996   1.387449  0.284077  0.028474   9.96
997   1.387482  0.284048  0.028471   9.97
998   1.387514  0.284018  0.028468   9.98
999   1.387547  0.283989  0.028464   9.99
1000  1.387579  0.283960  0.028461  10.00

Sum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=5.0, k2=0.5, k3=0.5, k4=0.1): 1848.1651038312143

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1, model_with_two_reactions_k1_5_k2_0_5, model_with_two_reactions_reversible_k1_5_k2_0_5_k3_0_1, model_with_two_reversible_reactions_k1_5_k2_0_5_k3_0_5_k4_0_1)

### 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 model with two reversible reactions (`id_v92z` <=> `id_0e6o` and `id_0e6o` <=> `id_hura`) with the chosen rate constants (k1=5.0, k2=0.5, k3=0.5, k4=0.1) still doesn't fit the data well. The simulated concentrations, especially at the tail end, are far from the experimental values. `id_v92z` goes too low, and `id_hura` and `id_0e6o` go too high.

However, the *structure* of this model (sequential reversible conversions) seems the most promising so far, as it allows for the leveling off of all species. The issue is likely with the rate constants.

Let's look at the experimental data's approximate steady-state concentrations (around Time 10):
`id_hura` ≈ 0.187
`id_0e6o` ≈ 0.198
`id_v92z` ≈ 0.596

At equilibrium, the net rates of both reactions should be zero:
k1 * [id_v92z] - k2 * [id_0e6o] = 0  => k1/k2 = [id_0e6o] / [id_v92z] ≈ 0.198 / 0.596 ≈ 0.33
k3 * [id_0e6o] - k4 * [id_hura] = 0  => k3/k4 = [id_hura] / [id_0e6o] ≈ 0.187 / 0.198 ≈ 0.94

From the initial rapid phase, we saw that the production of `id_0e6o` is much faster than the production of `id_hura`. In our current model, the initial rate of `id_0e6o` production is dominated by k1 * [id_v92z] (since [id_0e6o] and [id_hura] are low). The initial rate of `id_hura` production is dominated by k3 * [id_0e6o]. However, initially [id_0e6o] is low.

Let's rethink the initial phase. The rapid increase in `id_0e6o` and decrease in `id_v92z` suggests a fast conversion between them. The slower increase in `id_hura` suggests it's produced from `id_0e6o` at a slower rate, or the reaction producing it is less direct.

Let's stick with the two reversible reactions:
Reaction 1: `id_v92z` <=> `id_0e6o` (k1, k2)
Reaction 2: `id_0e6o` <=> `id_hura` (k3, k4)

Based on the approximate equilibrium ratios:
k1/k2 ≈ 0.33
k3/k4 ≈ 0.94

Let's try to pick rate constants that satisfy these ratios and also reflect the initial dynamics. The initial rapid change suggests k1 should be relatively large. Let's try k1=1.0. Then k2 should be around k1 / 0.33 ≈ 1.0 / 0.33 ≈ 3.0.
For the second reaction, let's try k3=1.0. Then k4 should be around k3 / 0.94 ≈ 1.0 / 0.94 ≈ 1.06.

Let's try k1=1.0, k2=3.0, k3=1.0, k4=1.06.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(1.0) # Adjusted guess for forward rate constant R1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(3.0) # Adjusted guess for reverse rate constant R1
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(1.0) # Adjusted guess for forward rate constant R2
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(1.06) # Adjusted guess for reverse rate constant R2
p4.setConstant(True)


# Create Reaction 1: id_v92z <=> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z - k2 * id_0e6o")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o <=> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(True)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k3 * id_0e6o - k4 * id_hura")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=1.0, k2=3.0, k3=1.0, k4=1.06):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=1.0, k2=3.0, k3=1.0, k4=1.06):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=1.0, k2=3.0, k3=1.0, k4=1.06): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reversible_reactions_k1_1_k2_3_k3_1_k4_1_06", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=1.0, k2=3.0, k3=1.0, k4=1.06):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.099999  0.111764  1.488237  0.01
2  0.100113  0.122954  1.476933  0.02
3  0.100334  0.133598  1.466068  0.03
4  0.100656  0.143723  1.455621  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=1.0, k2=3.0, k3=1.0, k4=1.06):
       id_hura   id_0e6o   id_v92z   Time
996   0.324419  0.343893  1.031688   9.96
997   0.324419  0.343893  1.031688   9.97
998   0.324419  0.343893  1.031688   9.98
999   0.324419  0.343893  1.031688   9.99
1000  0.324419  0.343893  1.031688  10.00

Sum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=1.0, k2=3.0, k3=1.0, k4=1.06): 85.85541170032032

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1, model_with_two_reactions_k1_5_k2_0_5, model_with_two_reactions_reversible_k1_5_k2_0_5_k3_0_1, model_with_two_reversible_reactions_k1_5_k2_0_5_k3_0_5_k4_0_1, model_with_two_reversible_reactions_k1_1_k2_3_k3_1_k4_1_06)

### 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 model with two reversible reactions (`id_v92z` <=> `id_0e6o` and `id_0e6o` <=> `id_hura`) and rate constants k1=1.0, k2=3.0, k3=1.0, k4=1.06 shows a significantly lower sum of squared errors (85.86) compared to previous attempts. This model structure seems to be on the right track.

However, looking at the simulated data head, the initial rapid increase in `id_0e6o` is not captured well. The experimental `id_0e6o` jumps from 0.1 to 0.229 in 0.01s, while the simulation only goes from 0.1 to 0.111. This suggests that the forward rate of the first reaction (k1) might still be too low, or the reverse rate (k2) is too high, preventing a rapid initial build-up of `id_0e6o`.

Also, the simulated tail concentrations (hura ~ 0.324, 0e6o ~ 0.344, v92z ~ 1.03) are still quite different from the experimental tail concentrations (hura ~ 0.187, 0e6o ~ 0.198, v92z ~ 0.596). This indicates the equilibrium ratios k1/k2 and k3/k4 are not quite right.

Let's adjust the rate constants further.
To get a faster initial increase in `id_0e6o`, I need to increase the net forward rate of Reaction 1 (`id_v92z` <=> `id_0e6o`). I can increase k1 or decrease k2. Let's try increasing k1.

Based on the equilibrium ratios:
k1/k2 ≈ 0.198 / 0.596 ≈ 0.33
k3/k4 ≈ 0.187 / 0.198 ≈ 0.94

Let's try increasing k1 to 3.0. To maintain the ratio k1/k2 ≈ 0.33, k2 should be around 3.0 / 0.33 ≈ 9.09. Let's use 9.0.
For the second reaction, let's keep k3=1.0 and k4=1.06 for now, as the initial phase is more sensitive to the first reaction rates.

New parameters: k1=3.0, k2=9.0, k3=1.0, k4=1.06.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(3.0) # Adjusted guess for forward rate constant R1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(9.0) # Adjusted guess for reverse rate constant R1
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(1.0) # Keep k3
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(1.06) # Keep k4
p4.setConstant(True)


# Create Reaction 1: id_v92z <=> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z - k2 * id_0e6o")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o <=> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(True)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k3 * id_0e6o - k4 * id_hura")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=3.0, k2=9.0, k3=1.0, k4=1.06):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=3.0, k2=9.0, k3=1.0, k4=1.06):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=3.0, k2=9.0, k3=1.0, k4=1.06): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reversible_reactions_k1_3_k2_9_k3_1_k4_1_06", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=3.0, k2=9.0, k3=1.0, k4=1.06):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100112  0.133815  1.466073  0.01
2  0.100539  0.163501  1.435960  0.02
3  0.101238  0.189558  1.409204  0.03
4  0.102172  0.212425  1.385403  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=3.0, k2=9.0, k3=1.0, k4=1.06):
       id_hura   id_0e6o   id_v92z   Time
996   0.324426  0.343893  1.031681   9.96
997   0.324426  0.343893  1.031681   9.97
998   0.324426  0.343893  1.031681   9.98
999   0.324426  0.343893  1.031681   9.99
1000  0.324426  0.343893  1.031681  10.00

Sum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=3.0, k2=9.0, k3=1.0, k4=1.06): 88.34460836864677

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1, model_with_two_reactions_k1_5_k2_0_5, model_with_two_reactions_reversible_k1_5_k2_0_5_k3_0_1, model_with_two_reversible_reactions_k1_5_k2_0_5_k3_0_5_k4_0_1, model_with_two_reversible_reactions_k1_1_k2_3_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_3_k2_9_k3_1_k4_1_06)

### 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
Adjusting k1 and k2 to 3.0 and 9.0 respectively did not significantly improve the fit (SSE 88.34 vs 85.86). The initial rapid increase in `id_0e6o` is still not matched, and the tail concentrations are still off.

Let's re-examine the equilibrium ratios based on the experimental tail data:
k1/k2 = [id_0e6o] / [id_v92z] ≈ 0.198 / 0.596 ≈ 0.332
k3/k4 = [id_hura] / [id_0e6o] ≈ 0.187 / 0.198 ≈ 0.944

The ratios seem consistent. The issue is likely in achieving both the correct initial dynamics and the correct equilibrium simultaneously with the current rate constants.

The initial phase is dominated by the forward rates (k1 and k3) and the initial concentrations. The rapid increase in `id_0e6o` suggests k1 should be relatively high. The slower increase in `id_hura` suggests k3 might be lower than k1, or the concentration of its reactant (`id_0e6o`) is initially low.

Let's try to match the initial rate of change for `id_0e6o`.
From experiment (0 to 0.01s): d[id_0e6o]/dt ≈ (0.229289 - 0.1) / 0.01 = 12.9289
From model: d[id_0e6o]/dt = k1 * [id_v92z] - k2 * [id_0e6o] - k3 * [id_0e6o] + k4 * [id_hura]
At t=0: [id_v92z]=1.5, [id_0e6o]=0.1, [id_hura]=0.1
Initial rate = k1 * 1.5 - k2 * 0.1 - k3 * 0.1 + k4 * 0.1

Using the previous parameters k1=3, k2=9, k3=1, k4=1.06:
Initial rate = 3.0 * 1.5 - 9.0 * 0.1 - 1.0 * 0.1 + 1.06 * 0.1 = 4.5 - 0.9 - 0.1 + 0.106 = 3.606. This is much lower than the observed initial rate (12.9).

To increase the initial rate of `id_0e6o` production, k1 needs to be higher, or k2 needs to be lower. Let's try increasing k1 significantly while maintaining the k1/k2 ratio.

Let's try k1 = 10.0. To maintain k1/k2 ≈ 0.332, k2 ≈ 10.0 / 0.332 ≈ 30.12. Let's use 30.0.
For the second reaction, let's try to match the initial rate of `id_hura`.
From experiment (0 to 0.01s): d[id_hura]/dt ≈ (0.100047 - 0.1) / 0.01 = 0.0047
From model: d[id_hura]/dt = k3 * [id_0e6o] - k4 * [id_hura]
At t=0: [id_0e6o]=0.1, [id_hura]=0.1
Initial rate = k3 * 0.1 - k4 * 0.1

Using k3=1.0, k4=1.06: Initial rate = 1.0 * 0.1 - 1.06 * 0.1 = 0.1 - 0.106 = -0.006. This is negative, which is wrong. `id_hura` increases initially.

This suggests k3 * [id_0e6o] must be greater than k4 * [id_hura] initially. Since initial [id_0e6o] and [id_hura] are both 0.1, this means k3 > k4. Our current k3=1.0 and k4=1.06 violates this.

Let's use the equilibrium ratio k3/k4 ≈ 0.944. If k3 > k4, this ratio should be > 1. My calculation of the equilibrium ratio might be off due to reading the tail data. Let's look at the last few points more carefully.
Time 9.98: hura=0.187310, 0e6o=0.198206, v92z=0.597179
Time 9.99: hura=0.187312, 0e6o=0.198081, v92z=0.596813
Time 10.00: hura=0.187314, 0e6o=0.197957, v92z=0.596448

Average tail concentrations:
[id_hura] ≈ 0.1873
[id_0e6o] ≈ 0.1981
[id_v92z] ≈ 0.5972

k1/k2 ≈ 0.1981 / 0.5972 ≈ 0.3317
k3/k4 ≈ 0.1873 / 0.1981 ≈ 0.9455

Okay, the ratios are indeed less than 1 for k3/k4. This means at equilibrium, [id_hura] < [id_0e6o]. This is consistent with the tail data. My previous reasoning about k3 > k4 based on initial rates was flawed because the initial rate of R2 depends on the *produced* `id_0e6o`, not just the initial concentration.

Let's go back to the initial rate of `id_0e6o` production. We need it to be around 12.9.
Initial rate = k1 * 1.5 - k2 * 0.1 - k3 * 0.1 + k4 * 0.1 ≈ 12.9

Let's try k1 = 10.0, k2 = 30.0 (ratio ~ 0.33).
10.0 * 1.5 - 30.0 * 0.1 - k3 * 0.1 + k4 * 0.1 ≈ 12.9
15.0 - 3.0 - 0.1*k3 + 0.1*k4 ≈ 12.9
12.0 - 0.1*k3 + 0.1*k4 ≈ 12.9
-0.1*k3 + 0.1*k4 ≈ 0.9
k4 - k3 ≈ 9

Also, k3/k4 ≈ 0.9455. So k3 ≈ 0.9455 * k4.
k4 - 0.9455 * k4 ≈ 9
0.0545 * k4 ≈ 9
k4 ≈ 9 / 0.0545 ≈ 165.1

Then k3 ≈ 0.9455 * 165.1 ≈ 156.1

These rate constants seem very high. Let's re-evaluate the initial rate calculation. The simulation step is 0.01s. The change over 0.01s is influenced by the rate *during* that interval, not just at t=0. However, the t=0 rate is a good starting point.

Let's try k1=10.0, k2=30.0. This gives a ratio k1/k2 = 1/3 ≈ 0.333.
Let's try k3=1.0, k4=1.06 again, but with the new k1, k2.

New parameters: k1=10.0, k2=30.0, k3=1.0, k4=1.06.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(10.0) # Adjusted guess for forward rate constant R1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(30.0) # Adjusted guess for reverse rate constant R1
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(1.0) # Keep k3
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(1.06) # Keep k4
p4.setConstant(True)


# Create Reaction 1: id_v92z <=> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z - k2 * id_0e6o")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o <=> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(True)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k3 * id_0e6o - k4 * id_hura")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.0, k2=30.0, k3=1.0, k4=1.06):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.0, k2=30.0, k3=1.0, k4=1.06):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.0, k2=30.0, k3=1.0, k4=1.06): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reversible_reactions_k1_10_k2_30_k3_1_k4_1_06", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.0, k2=30.0, k3=1.0, k4=1.06):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100464  0.198481  1.401054  0.01
2  0.101727  0.263771  1.334502  0.02
3  0.103508  0.306987  1.289505  0.03
4  0.105622  0.335521  1.258856  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.0, k2=30.0, k3=1.0, k4=1.06):
       id_hura   id_0e6o  id_v92z   Time
996   0.324427  0.343893  1.03168   9.96
997   0.324427  0.343893  1.03168   9.97
998   0.324427  0.343893  1.03168   9.98
999   0.324427  0.343893  1.03168   9.99
1000  0.324427  0.343893  1.03168  10.00

Sum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.0, k2=30.0, k3=1.0, k4=1.06): 89.54183827374476

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1, model_with_two_reactions_k1_5_k2_0_5, model_with_two_reactions_reversible_k1_5_k2_0_5_k3_0_1, model_with_two_reversible_reactions_k1_5_k2_0_5_k3_0_5_k4_0_1, model_with_two_reversible_reactions_k1_1_k2_3_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_3_k2_9_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_10_k2_30_k3_1_k4_1_06)

### 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
Increasing k1 to 10.0 and k2 to 30.0 slightly improved the initial phase match for `id_0e6o`, but the overall SSE increased slightly (89.54). The tail concentrations are still significantly off.

The model structure with two consecutive reversible reactions (`id_v92z` <=> `id_0e6o` and `id_0e6o` <=> `id_hura`) seems correct because it allows for the observed leveling off of all species. The challenge is finding the right rate constants.

Let's focus on matching the equilibrium concentrations first, as they are determined solely by the ratios of the rate constants (k1/k2 and k3/k4).
Target ratios:
k1/k2 ≈ 0.332
k3/k4 ≈ 0.944

Let's try to set the ratios correctly and then adjust the magnitudes to fit the dynamics.
Let k1 = 0.332 * k2
Let k3 = 0.944 * k4

We need to pick a magnitude for one of the rate constants and calculate the others. The initial rapid change in `id_0e6o` suggests the first reaction is relatively fast. Let's try setting k1 to a value that gives a reasonable initial rate.

Initial rate of `id_0e6o` production ≈ 12.9.
Initial rate = k1 * 1.5 - k2 * 0.1 - k3 * 0.1 + k4 * 0.1 ≈ 12.9
Substitute k1 = 0.332 * k2 and k3 = 0.944 * k4:
0.332 * k2 * 1.5 - k2 * 0.1 - 0.944 * k4 * 0.1 + k4 * 0.1 ≈ 12.9
0.498 * k2 - 0.1 * k2 - 0.0944 * k4 + 0.1 * k4 ≈ 12.9
0.398 * k2 + 0.0056 * k4 ≈ 12.9

We have one equation with two unknowns (k2 and k4). We need another constraint. The speed at which the system approaches equilibrium is related to the magnitudes of the rate constants. Higher magnitudes mean faster dynamics.

Let's try to pick a value for k2 and calculate k1, then pick a value for k4 and calculate k3, and see if the initial rate equation is roughly satisfied.

If k2 = 1.0, then k1 ≈ 0.332.
If k4 = 1.0, then k3 ≈ 0.944.
Initial rate = 0.332 * 1.5 - 1.0 * 0.1 - 0.944 * 0.1 + 1.0 * 0.1 = 0.498 - 0.1 - 0.0944 + 0.1 = 0.4036. Too slow.

If k2 = 10.0, then k1 ≈ 3.32.
If k4 = 10.0, then k3 ≈ 9.44.
Initial rate = 3.32 * 1.5 - 10.0 * 0.1 - 9.44 * 0.1 + 10.0 * 0.1 = 4.98 - 1.0 - 0.944 + 1.0 = 4.036. Still too slow.

If k2 = 30.0, then k1 ≈ 9.96.
If k4 = 30.0, then k3 ≈ 28.32.
Initial rate = 9.96 * 1.5 - 30.0 * 0.1 - 28.32 * 0.1 + 30.0 * 0.1 = 14.94 - 3.0 - 2.832 + 3.0 = 12.108. This is close to 12.9!

Let's try these rate constants: k1=9.96, k2=30.0, k3=28.32, k4=30.0.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(9.96) # Adjusted guess for forward rate constant R1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(30.0) # Adjusted guess for reverse rate constant R1
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(28.32) # Adjusted guess for forward rate constant R2
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(30.0) # Adjusted guess for reverse rate constant R2
p4.setConstant(True)


# Create Reaction 1: id_v92z <=> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z - k2 * id_0e6o")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o <=> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(True)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k3 * id_0e6o - k4 * id_hura")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=9.96, k2=30.0, k3=28.32, k4=30.0):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=9.96, k2=30.0, k3=28.32, k4=30.0):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=9.96, k2=30.0, k3=28.32, k4=30.0): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reversible_reactions_k1_9_96_k2_30_k3_28_32_k4_30", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=9.96, k2=30.0, k3=28.32, k4=30.0):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.111068  0.188383  1.400549  0.01
2  0.135026  0.235865  1.329110  0.02
3  0.161576  0.263616  1.274808  0.03
4  0.186625  0.281397  1.231978  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=9.96, k2=30.0, k3=28.32, k4=30.0):
       id_hura   id_0e6o   id_v92z   Time
996   0.323806  0.343015  1.033178   9.96
997   0.323806  0.343015  1.033178   9.97
998   0.323806  0.343015  1.033178   9.98
999   0.323806  0.343015  1.033178   9.99
1000  0.323806  0.343015  1.033178  10.00

Sum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=9.96, k2=30.0, k3=28.32, k4=30.0): 97.7473115692306

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1, model_with_two_reactions_k1_5_k2_0_5, model_with_two_reactions_reversible_k1_5_k2_0_5_k3_0_1, model_with_two_reversible_reactions_k1_5_k2_0_5_k3_0_5_k4_0_1, model_with_two_reversible_reactions_k1_1_k2_3_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_3_k2_9_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_10_k2_30_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_9_96_k2_30_k3_28_32_k4_30)

### 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 simulation with k1=9.96, k2=30.0, k3=28.32, k4=30.0 resulted in an SSE of 97.75, which is worse than the previous best (85.86). While the initial phase for `id_0e6o` looks a bit better, the tail concentrations are still significantly off.

The model structure with two consecutive reversible reactions (`id_v92z` <=> `id_0e6o` and `id_0e6o` <=> `id_hura`) still seems the most plausible. The discrepancy likely lies in the rate constants.

Let's revisit the equilibrium ratios and try to match them more precisely.
Target ratios:
k1/k2 ≈ 0.3317
k3/k4 ≈ 0.9455

Let's try to fix the ratios and then scale the magnitudes.
Let k2 = 1.0, then k1 = 0.3317.
Let k4 = 1.0, then k3 = 0.9455.
This gives very slow dynamics (initial rate calculation in previous step was ~0.4).

We need to scale these up to match the initial dynamics. The initial rate of `id_0e6o` production is around 12.9.
Initial rate = k1 * 1.5 - k2 * 0.1 - k3 * 0.1 + k4 * 0.1 ≈ 12.9
Substitute k1 = 0.3317*k2 and k3 = 0.9455*k4:
0.3317*k2 * 1.5 - k2 * 0.1 - 0.9455*k4 * 0.1 + k4 * 0.1 ≈ 12.9
0.49755*k2 - 0.1*k2 - 0.09455*k4 + 0.1*k4 ≈ 12.9
0.39755*k2 + 0.00545*k4 ≈ 12.9

Let's assume the first reaction is significantly faster than the second, which seems implied by the rapid initial rise of `id_0e6o`. This means k1 and k2 should be larger than k3 and k4.

Let's try setting k2 = 30.0 again.
0.39755 * 30.0 + 0.00545 * k4 ≈ 12.9
11.9265 + 0.00545 * k4 ≈ 12.9
0.00545 * k4 ≈ 12.9 - 11.9265 = 0.9735
k4 ≈ 0.9735 / 0.00545 ≈ 178.62

If k4 ≈ 178.62, then k3 = 0.9455 * 178.62 ≈ 168.86.
And k1 = 0.3317 * k2 = 0.3317 * 30.0 ≈ 9.951.

Let's try these parameters: k1=9.951, k2=30.0, k3=168.86, k4=178.62.
These k3 and k4 values are very high, which would imply the second reaction is very fast. This contradicts the relatively slow increase of `id_hura` compared to the initial burst of `id_0e6o`.

Perhaps the initial rate calculation is misleading due to the discrete time steps. Let's focus on the equilibrium ratios and try scaling the magnitudes more intuitively.

Let's try to keep the k1/k2 ratio around 0.332 and k3/k4 around 0.9455.
Let's try scaling the previous best parameters (k1=1.0, k2=3.0, k3=1.0, k4=1.06) which had SSE 85.86. The ratios were k1/k2 = 1/3 ≈ 0.333 and k3/k4 = 1/1.06 ≈ 0.943. These ratios are very close to the target equilibrium ratios.

The issue with k1=1.0, k2=3.0, k3=1.0, k4=1.06 was the slow initial dynamics. To speed up the dynamics while maintaining the ratios, we need to multiply all rate constants by a scaling factor.

Let's try multiplying by 5:
k1 = 1.0 * 5 = 5.0
k2 = 3.0 * 5 = 15.0
k3 = 1.0 * 5 = 5.0
k4 = 1.06 * 5 = 5.3

Let's try these parameters: k1=5.0, k2=15.0, k3=5.0, k4=5.3.
Ratios: k1/k2 = 5/15 = 1/3 ≈ 0.333, k3/k4 = 5/5.3 ≈ 0.943. Ratios are maintained.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(5.0) # Scaled guess for forward rate constant R1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(15.0) # Scaled guess for reverse rate constant R1
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(5.0) # Scaled guess for forward rate constant R2
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(5.3) # Scaled guess for reverse rate constant R2
p4.setConstant(True)


# Create Reaction 1: id_v92z <=> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z - k2 * id_0e6o")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o <=> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(True)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k3 * id_0e6o - k4 * id_hura")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=5.0, k2=15.0, k3=5.0, k4=5.3):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=5.0, k2=15.0, k3=5.0, k4=5.3):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=5.0, k2=15.0, k3=5.0, k4=5.3): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reversible_reactions_k1_5_k2_15_k3_5_k4_5_3", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=5.0, k2=15.0, k3=5.0, k4=5.3):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.101072  0.153355  1.445573  0.01
2  0.104386  0.194913  1.400701  0.02
3  0.109318  0.227290  1.363393  0.03
4  0.115388  0.252520  1.332092  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=5.0, k2=15.0, k3=5.0, k4=5.3):
       id_hura   id_0e6o   id_v92z   Time
996   0.324427  0.343893  1.031679   9.96
997   0.324427  0.343893  1.031679   9.97
998   0.324427  0.343893  1.031679   9.98
999   0.324427  0.343893  1.031679   9.99
1000  0.324427  0.343893  1.031679  10.00

Sum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=5.0, k2=15.0, k3=5.0, k4=5.3): 95.22914355030494

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1, model_with_two_reactions_k1_5_k2_0_5, model_with_two_reactions_reversible_k1_5_k2_0_5_k3_0_1, model_with_two_reversible_reactions_k1_5_k2_0_5_k3_0_5_k4_0_1, model_with_two_reversible_reactions_k1_1_k2_3_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_3_k2_9_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_10_k2_30_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_9_96_k2_30_k3_28_32_k4_30, model_with_two_reversible_reactions_k1_5_k2_15_k3_5_k4_5_3)

### 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
Scaling the rate constants by 5 (k1=5.0, k2=15.0, k3=5.0, k4=5.3) resulted in an SSE of 95.23, still higher than the best so far (85.86 with k1=1.0, k2=3.0, k3=1.0, k4=1.06). The initial phase match improved slightly, but the tail is still off.

It seems there's a trade-off between matching the initial rapid dynamics and matching the final equilibrium. The initial phase is more sensitive to the absolute magnitudes of the forward rates, while the equilibrium is determined by the ratios.

Let's look at the initial experimental data again. The jump in `id_0e6o` from 0.1 to 0.229 in 0.01s is a change of 0.129. The jump in `id_v92z` is from 1.5 to 1.370, a change of -0.130. The change in `id_hura` is from 0.1 to 0.100047, a change of 0.000047.

The changes in `id_0e6o` and `id_v92z` are almost equal and opposite. This strongly suggests a reaction with 1:1 stoichiometry between `id_v92z` and `id_0e6o`. The change in `id_hura` is much smaller.

This reinforces the idea of two reactions:
Reaction 1: `id_v92z` <=> `id_0e6o` (fast, reversible)
Reaction 2: `id_0e6o` <=> `id_hura` (slower, reversible)

Let's try to match the initial rate of change for `id_0e6o` more closely.
Initial rate of `id_0e6o` production ≈ 12.9.
Initial rate = k1 * 1.5 - k2 * 0.1 - k3 * 0.1 + k4 * 0.1 ≈ 12.9

Let's try increasing the rates of the first reaction significantly while keeping their ratio.
Let k1 = 30.0. To maintain k1/k2 ≈ 0.332, k2 ≈ 30.0 / 0.332 ≈ 90.36. Let's use 90.0.
Now, let's see what k3 and k4 need to be to satisfy the initial rate equation and the equilibrium ratio k3/k4 ≈ 0.9455.
30.0 * 1.5 - 90.0 * 0.1 - 0.1*k3 + 0.1*k4 ≈ 12.9
45.0 - 9.0 - 0.1*k3 + 0.1*k4 ≈ 12.9
36.0 - 0.1*k3 + 0.1*k4 ≈ 12.9
-0.1*k3 + 0.1*k4 ≈ 12.9 - 36.0 = -23.1
k3 - k4 ≈ 231

Also, k3 ≈ 0.9455 * k4.
0.9455 * k4 - k4 ≈ 231
-0.0545 * k4 ≈ 231
k4 ≈ 231 / -0.0545 ≈ -4238. This is not possible as rate constants must be positive.

My assumption that the initial rate equation at t=0 is sufficient to determine the parameters might be incorrect, especially with discrete time steps.

Let's go back to the idea of scaling the previous best parameters (k1=1.0, k2=3.0, k3=1.0, k4=1.06). The SSE was 85.86. The initial `id_0e6o` was too slow. Let's try scaling by a factor larger than 5, say 10.

k1 = 1.0 * 10 = 10.0
k2 = 3.0 * 10 = 30.0
k3 = 1.0 * 10 = 10.0
k4 = 1.06 * 10 = 10.6

Let's try these parameters: k1=10.0, k2=30.0, k3=10.0, k4=10.6.
Ratios: k1/k2 = 10/30 = 1/3 ≈ 0.333, k3/k4 = 10/10.6 ≈ 0.943. Ratios are maintained.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(10.0) # Scaled guess for forward rate constant R1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(30.0) # Scaled guess for reverse rate constant R1
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(10.0) # Scaled guess for forward rate constant R2
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(10.6) # Scaled guess for reverse rate constant R2
p4.setConstant(True)


# Create Reaction 1: id_v92z <=> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z - k2 * id_0e6o")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o <=> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(True)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k3 * id_0e6o - k4 * id_hura")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.0, k2=30.0, k3=10.0, k4=10.6):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.0, k2=30.0, k3=10.0, k4=10.6):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.0, k2=30.0, k3=10.0, k4=10.6): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reversible_reactions_k1_10_k2_30_k3_10_k4_10_6", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.0, k2=30.0, k3=10.0, k4=10.6):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.104386  0.194913  1.400701  0.01
2  0.115388  0.252520  1.332092  0.02
3  0.129569  0.287521  1.282909  0.03
4  0.144930  0.308822  1.246248  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.0, k2=30.0, k3=10.0, k4=10.6):
       id_hura   id_0e6o   id_v92z   Time
996   0.324427  0.343893  1.031679   9.96
997   0.324427  0.343893  1.031679   9.97
998   0.324427  0.343893  1.031679   9.98
999   0.324427  0.343893  1.031679   9.99
1000  0.324427  0.343893  1.031679  10.00

Sum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.0, k2=30.0, k3=10.0, k4=10.6): 96.9875546979892

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1, model_with_two_reactions_k1_5_k2_0_5, model_with_two_reactions_reversible_k1_5_k2_0_5_k3_0_1, model_with_two_reversible_reactions_k1_5_k2_0_5_k3_0_5_k4_0_1, model_with_two_reversible_reactions_k1_1_k2_3_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_3_k2_9_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_10_k2_30_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_9_96_k2_30_k3_28_32_k4_30, model_with_two_reversible_reactions_k1_5_k2_15_k3_5_k4_5_3, model_with_two_reversible_reactions_k1_10_k2_30_k3_10_k4_10_6)

### 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
Scaling the rate constants by 10 (k1=10.0, k2=30.0, k3=10.0, k4=10.6) resulted in an SSE of 96.99, still not better than the best (85.86). The initial phase match for `id_0e6o` is getting closer, but the tail concentrations are consistently wrong across these scaled models.

The consistent error in the tail concentrations suggests that the equilibrium ratios k1/k2 and k3/k4 are not being met correctly by the chosen parameters, or the model structure is slightly off.

Let's re-calculate the target equilibrium ratios from the experimental data:
[id_hura] ≈ 0.1873
[id_0e6o] ≈ 0.1981
[id_v92z] ≈ 0.5972

k1/k2 = [id_0e6o] / [id_v92z] ≈ 0.1981 / 0.5972 ≈ 0.3317
k3/k4 = [id_hura] / [id_0e6o] ≈ 0.1873 / 0.1981 ≈ 0.9455

Let's try to set the rate constants to match these ratios exactly, and then scale the overall magnitude.
Let k2 = 1.0, k1 = 0.3317.
Let k4 = 1.0, k3 = 0.9455.

Now, let's scale these by a factor `s`.
k1 = 0.3317 * s
k2 = 1.0 * s
k3 = 0.9455 * s
k4 = 1.0 * s

Initial rate of `id_0e6o` production ≈ 12.9.
Initial rate = k1 * 1.5 - k2 * 0.1 - k3 * 0.1 + k4 * 0.1 ≈ 12.9
(0.3317 * s) * 1.5 - (1.0 * s) * 0.1 - (0.9455 * s) * 0.1 + (1.0 * s) * 0.1 ≈ 12.9
s * (0.3317 * 1.5 - 1.0 * 0.1 - 0.9455 * 0.1 + 1.0 * 0.1) ≈ 12.9
s * (0.49755 - 0.1 - 0.09455 + 0.1) ≈ 12.9
s * (0.403) ≈ 12.9
s ≈ 12.9 / 0.403 ≈ 31.985

Let's try scaling factor s = 32.
k1 = 0.3317 * 32 ≈ 10.6144
k2 = 1.0 * 32 = 32.0
k3 = 0.9455 * 32 ≈ 30.256
k4 = 1.0 * 32 = 32.0

Let's try these parameters: k1=10.6144, k2=32.0, k3=30.256, k4=32.0.
Ratios: k1/k2 = 10.6144/32 ≈ 0.3317, k3/k4 = 30.256/32 ≈ 0.9455. Ratios match the target equilibrium. The magnitude is chosen to match the initial rate of `id_0e6o`.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(10.6144) # Calculated forward rate constant R1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(32.0) # Calculated reverse rate constant R1
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(30.256) # Calculated forward rate constant R2
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(32.0) # Calculated reverse rate constant R2
p4.setConstant(True)


# Create Reaction 1: id_v92z <=> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z - k2 * id_0e6o")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o <=> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(True)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k3 * id_0e6o - k4 * id_hura")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.6144, k2=32.0, k3=30.256, k4=32.0):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.6144, k2=32.0, k3=30.256, k4=32.0):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.6144, k2=32.0, k3=30.256, k4=32.0): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reversible_reactions_k1_10_6144_k2_32_k3_30_256_k4_32", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.6144, k2=32.0, k3=30.256, k4=32.0):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.112470  0.192346  1.395184  0.01
2  0.138617  0.240183  1.321200  0.02
3  0.166866  0.267499  1.265635  0.03
4  0.192943  0.284813  1.222245  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.6144, k2=32.0, k3=30.256, k4=32.0):
       id_hura   id_0e6o   id_v92z   Time
996   0.324045  0.342723  1.033232   9.96
997   0.324045  0.342723  1.033232   9.97
998   0.324045  0.342723  1.033232   9.98
999   0.324045  0.342723  1.033232   9.99
1000  0.324045  0.342723  1.033232  10.00

Sum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=10.6144, k2=32.0, k3=30.256, k4=32.0): 97.86824350086795

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1, model_with_two_reactions_k1_5_k2_0_5, model_with_two_reactions_reversible_k1_5_k2_0_5_k3_0_1, model_with_two_reversible_reactions_k1_5_k2_0_5_k3_0_5_k4_0_1, model_with_two_reversible_reactions_k1_1_k2_3_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_3_k2_9_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_10_k2_30_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_9_96_k2_30_k3_28_32_k4_30, model_with_two_reversible_reactions_k1_5_k2_15_k3_5_k4_5_3, model_with_two_reversible_reactions_k1_10_k2_30_k3_10_k4_10_6, model_with_two_reversible_reactions_k1_10_6144_k2_32_k3_30_256_k4_32)

### 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 attempt with rate constants calculated to match both equilibrium ratios and the initial rate of `id_0e6o` production resulted in an SSE of 97.87, which is still not the best fit. The simulated initial phase for `id_0e6o` is getting closer, but the tail concentrations are consistently wrong.

The fact that the tail concentrations in the simulation are consistently higher for `id_hura` and `id_0e6o`, and lower for `id_v92z`, compared to the experimental data, suggests that the equilibrium is shifted in the simulation. This points back to the equilibrium ratios k1/k2 and k3/k4.

Let's re-examine the experimental tail data and the calculated ratios:
[id_hura] ≈ 0.1873
[id_0e6o] ≈ 0.1981
[id_v92z] ≈ 0.5972

k1/k2 = [id_0e6o] / [id_v92z] ≈ 0.1981 / 0.5972 ≈ 0.3317
k3/k4 = [id_hura] / [id_0e6o] ≈ 0.1873 / 0.1981 ≈ 0.9455

My calculations for the ratios seem correct based on the provided tail data. If the model structure is correct, then setting the rate constant ratios to these values should result in the correct equilibrium concentrations, regardless of the overall magnitude. The magnitude only affects how quickly the system reaches equilibrium.

The previous best fit had k1=1.0, k2=3.0, k3=1.0, k4=1.06 (SSE 85.86).
Ratios: k1/k2 = 1/3 ≈ 0.333, k3/k4 = 1/1.06 ≈ 0.943. These ratios are very close to the target equilibrium ratios (0.3317 and 0.9455).

Let's try to use the exact equilibrium ratios for k1/k2 and k3/k4 and scale the magnitudes to get a better fit for the dynamics.

Let k2 = 1.0, k1 = 0.3317.
Let k4 = 1.0, k3 = 0.9455.

Let's try scaling these by a factor `s`.
k1 = 0.3317 * s
k2 = 1.0 * s
k3 = 0.9455 * s
k4 = 1.0 * s

We need to find the best scaling factor `s`. Let's try a few values around the previous successful scales (5, 10, 32). Let's try s = 20.
k1 = 0.3317 * 20 = 6.634
k2 = 1.0 * 20 = 20.0
k3 = 0.9455 * 20 = 18.91
k4 = 1.0 * 20 = 20.0

Let's try these parameters: k1=6.634, k2=20.0, k3=18.91, k4=20.0.
Ratios: k1/k2 = 6.634/20 ≈ 0.3317, k3/k4 = 18.91/20 ≈ 0.9455. Ratios match.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(6.634) # Scaled forward rate constant R1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(20.0) # Scaled reverse rate constant R1
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(18.91) # Scaled forward rate constant R2
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(20.0) # Scaled reverse rate constant R2
p4.setConstant(True)


# Create Reaction 1: id_v92z <=> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z - k2 * id_0e6o")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o <=> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(True)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k3 * id_0e6o - k4 * id_hura")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=6.634, k2=20.0, k3=18.91, k4=20.0):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=6.634, k2=20.0, k3=18.91, k4=20.0):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=6.634, k2=20.0, k3=18.91, k4=20.0): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reversible_reactions_k1_6_634_k2_20_k3_18_91_k4_20", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=6.634, k2=20.0, k3=18.91, k4=20.0):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.105173  0.164941  1.429886  0.01
2  0.118367  0.207196  1.374438  0.02
3  0.135093  0.235642  1.329265  0.03
4  0.152849  0.255554  1.291597  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=6.634, k2=20.0, k3=18.91, k4=20.0):
       id_hura   id_0e6o   id_v92z   Time
996   0.324045  0.342723  1.033232   9.96
997   0.324045  0.342723  1.033232   9.97
998   0.324045  0.342723  1.033232   9.98
999   0.324045  0.342723  1.033232   9.99
1000  0.324045  0.342723  1.033232  10.00

Sum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=6.634, k2=20.0, k3=18.91, k4=20.0): 97.20534222397288

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 4/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1, model_with_two_reactions_k1_5_k2_0_5, model_with_two_reactions_reversible_k1_5_k2_0_5_k3_0_1, model_with_two_reversible_reactions_k1_5_k2_0_5_k3_0_5_k4_0_1, model_with_two_reversible_reactions_k1_1_k2_3_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_3_k2_9_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_10_k2_30_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_9_96_k2_30_k3_28_32_k4_30, model_with_two_reversible_reactions_k1_5_k2_15_k3_5_k4_5_3, model_with_two_reversible_reactions_k1_10_k2_30_k3_10_k4_10_6, model_with_two_reversible_reactions_k1_10_6144_k2_32_k3_30_256_k4_32, model_with_two_reversible_reactions_k1_6_634_k2_20_k3_18_91_k4_20)

### 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
Scaling the rate constants by 20 (k1=6.634, k2=20.0, k3=18.91, k4=20.0) resulted in an SSE of 97.21, still not the best. The tail concentrations are consistently wrong, indicating the equilibrium ratios are not being met in the simulation despite setting the rate constant ratios based on the experimental equilibrium.

There might be a subtle issue with how the simulator handles equilibrium or floating-point precision, or perhaps my reading of the equilibrium concentrations from the tail data is not precise enough.

Let's go back to the best performing parameters so far: k1=1.0, k2=3.0, k3=1.0, k4=1.06 (SSE 85.86).
Simulated Tail (k1=1.0, k2=3.0, k3=1.0, k4=1.06):
hura ~ 0.3244
0e6o ~ 0.3439
v92z ~ 1.0317

Experimental Tail:
hura ~ 0.1873
0e6o ~ 0.1981
v92z ~ 0.5972

The simulated equilibrium concentrations are consistently higher than the experimental ones for hura and 0e6o, and higher for v92z.

Let's calculate the ratios from the *simulated* tail concentrations for the best fit:
k1/k2 = [id_0e6o] / [id_v92z] ≈ 0.3439 / 1.0317 ≈ 0.3333
k3/k4 = [id_hura] / [id_0e6o] ≈ 0.3244 / 0.3439 ≈ 0.9434

These ratios (0.3333 and 0.9434) are very close to the rate constant ratios I set (1/3 ≈ 0.3333 and 1/1.06 ≈ 0.9434). This confirms that the simulator reaches the equilibrium predicted by the rate constant ratios.

The problem is that the equilibrium predicted by these ratios (and thus reached by the simulation) does not match the experimental equilibrium. This means my calculation of the target equilibrium ratios from the experimental data might be incorrect, or the experimental data itself doesn't represent a true equilibrium within the observed timeframe, or there's something else affecting the equilibrium that's not in the model.

Given the limited iterations left, and the consistent discrepancy in equilibrium, let's try to adjust the rate constant ratios slightly to force the simulated equilibrium closer to the experimental one.

Target k1/k2 ≈ 0.3317
Target k3/k4 ≈ 0.9455

Let's try to adjust the k1/k2 ratio downwards slightly from 1/3, and k3/k4 upwards slightly from 1/1.06.

Let's try k1/k2 = 0.33 and k3/k4 = 0.95.
Let's use the magnitudes from the previous best fit (k1=1.0, k2=3.0, k3=1.0, k4=1.06) as a starting point for scaling.

Let k2 = 3.0, then k1 = 0.33 * 3.0 = 0.99.
Let k4 = 1.06, then k3 = 0.95 * 1.06 = 1.007.

Let's try these parameters: k1=0.99, k2=3.0, k3=1.007, k4=1.06.
Ratios: k1/k2 = 0.99/3.0 = 0.33, k3/k4 = 1.007/1.06 ≈ 0.95.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(0.99) # Adjusted forward rate constant R1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(3.0) # Adjusted reverse rate constant R1
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(1.007) # Adjusted forward rate constant R2
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(1.06) # Adjusted reverse rate constant R2
p4.setConstant(True)


# Create Reaction 1: id_v92z <=> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z - k2 * id_0e6o")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o <=> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(True)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k3 * id_0e6o - k4 * id_hura")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=0.99, k2=3.0, k3=1.007, k4=1.06):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=0.99, k2=3.0, k3=1.007, k4=1.06):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=0.99, k2=3.0, k3=1.007, k4=1.06): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reversible_reactions_k1_0_99_k2_3_k3_1_007_k4_1_06", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=0.99, k2=3.0, k3=1.007, k4=1.06):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100006  0.111611  1.488383  0.01
2  0.100125  0.122656  1.477219  0.02
3  0.100351  0.133162  1.466486  0.03
4  0.100678  0.143157  1.456166  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=0.99, k2=3.0, k3=1.007, k4=1.06):
       id_hura   id_0e6o   id_v92z   Time
996   0.324268  0.341345  1.034387   9.96
997   0.324268  0.341345  1.034387   9.97
998   0.324269  0.341345  1.034387   9.98
999   0.324269  0.341345  1.034387   9.99
1000  0.324269  0.341345  1.034387  10.00

Sum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=0.99, k2=3.0, k3=1.007, k4=1.06): 86.34507994886171

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 3/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1, model_with_two_reactions_k1_5_k2_0_5, model_with_two_reactions_reversible_k1_5_k2_0_5_k3_0_1, model_with_two_reversible_reactions_k1_5_k2_0_5_k3_0_5_k4_0_1, model_with_two_reversible_reactions_k1_1_k2_3_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_3_k2_9_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_10_k2_30_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_9_96_k2_30_k3_28_32_k4_30, model_with_two_reversible_reactions_k1_5_k2_15_k3_5_k4_5_3, model_with_two_reversible_reactions_k1_10_k2_30_k3_10_k4_10_6, model_with_two_reversible_reactions_k1_10_6144_k2_32_k3_30_256_k4_32, model_with_two_reversible_reactions_k1_6_634_k2_20_k3_18_91_k4_20, model_with_two_reversible_reactions_k1_0_99_k2_3_k3_1_007_k4_1_06)

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


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



# Iteration 18
## Thoughts
Adjusting the ratios slightly (k1=0.99, k2=3.0, k3=1.007, k4=1.06) resulted in an SSE of 86.35, which is very close to the previous best (85.86). The simulated initial phase is still not matching the rapid experimental increase in `id_0e6o`. The tail concentrations are also still off.

The consistent discrepancy in the tail concentrations, despite setting the rate constant ratios based on the experimental equilibrium, is puzzling if the model structure is correct and the experimental data represents a true equilibrium.

Let's consider the possibility that the stoichiometry is not 1:1 for all reactions. However, the initial rapid changes in `id_v92z` and `id_0e6o` being nearly equal and opposite strongly suggest a 1:1 relationship in the primary reaction. The slower change in `id_hura` suggests it might be produced with a different stoichiometry or in a secondary reaction.

Let's assume the model structure with two consecutive reversible reactions (`id_v92z` <=> `id_0e6o` and `id_0e6o` <=> `id_hura`) is correct with 1:1 stoichiometry. The issue must be the rate constants.

Given the difficulty in manually tuning the parameters to fit both the initial dynamics and the equilibrium, and the limited iterations left, I will make one more attempt to adjust the rate constants based on the best fit so far (k1=1.0, k2=3.0, k3=1.0, k4=1.06, SSE 85.86).

The initial `id_0e6o` increase is too slow. This means the net forward rate of the first reaction (k1 * id_v92z - k2 * id_0e6o) is too low initially. We can increase k1 or decrease k2.
The tail concentrations are too high for `id_hura` and `id_0e6o`, and too high for `id_v92z`. This means the equilibrium is shifted too far to the right in both reactions in the simulation. To shift the equilibrium to the left (towards reactants), we need to decrease the k_forward / k_reverse ratio for both reactions.
For R1 (`id_v92z` <=> `id_0e6o`), decrease k1/k2.
For R2 (`id_0e6o` <=> `id_hura`), decrease k3/k4.

This creates a conflict: to speed up the initial `id_0e6o` increase, we need a higher k1/k2 ratio (or higher k1), but to shift the equilibrium left, we need a lower k1/k2 ratio.

Perhaps the initial phase is dominated by the forward reaction of R1, and the reverse reaction of R1 and both directions of R2 become significant later.

Let's try increasing k1 significantly to match the initial burst, and then adjust the other rates to compensate and try to get the equilibrium right.

Let's try k1 = 20.0.
To get the equilibrium ratio k1/k2 ≈ 0.3317, k2 ≈ 20.0 / 0.3317 ≈ 60.3. Let's use 60.0.
k1=20.0, k2=60.0. Ratio = 20/60 = 1/3 ≈ 0.333.

Now for the second reaction. Let's keep the ratio k3/k4 ≈ 0.9455. Let's try scaling the previous k3, k4 (1.0, 1.06) by a factor that makes the dynamics reasonable. If R1 is fast, R2 might be slower. Let's try scaling by 5.
k3 = 1.0 * 5 = 5.0
k4 = 1.06 * 5 = 5.3
k3/k4 = 5/5.3 ≈ 0.943.

Let's try these parameters: k1=20.0, k2=60.0, k3=5.0, k4=5.3.
Ratios: k1/k2 = 20/60 = 1/3 ≈ 0.333, k3/k4 = 5/5.3 ≈ 0.943. These ratios are close to the target equilibrium ratios. The magnitudes are higher for R1 than R2, which fits the initial rapid change in `id_0e6o`.

## Action

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

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(20.0) # Adjusted forward rate constant R1
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(60.0) # Adjusted reverse rate constant R1
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(5.0) # Adjusted forward rate constant R2
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(5.3) # Adjusted reverse rate constant R2
p4.setConstant(True)


# Create Reaction 1: id_v92z <=> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z - k2 * id_0e6o")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o <=> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(True)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k3 * id_0e6o - k4 * id_hura")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


# 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']

# Compare simulation and experiment
print("Experimental Data Head:")
print(exp_data.head())
print("\nSimulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=20.0, k2=60.0, k3=5.0, k4=5.3):")
print(sim_data.head())

print("\nExperimental Data Tail:")
print(exp_data.tail())
print("\nSimulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=20.0, k2=60.0, k3=5.0, k4=5.3):")
print(sim_data.tail())

# Calculate sum of squared errors
merged_data = pd.merge(exp_data, sim_data, on='Time', suffixes=('_exp', '_sim'))

species_ids = ['id_hura', 'id_0e6o', 'id_v92z']
sse = 0
for species_id in species_ids:
    sse += np.sum((merged_data[f'{species_id}_exp'] - merged_data[f'{species_id}_sim'])**2)

print(f"\nSum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=20.0, k2=60.0, k3=5.0, k4=5.3): {sse}")

# Store the updated SBML
shared_variables.add("model_with_two_reversible_reactions_k1_20_k2_60_k3_5_k4_5_3", updated_sbml)
```
# Observation

## Code Stdout
Experimental Data Head:
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.100047  0.229289  1.370336  0.01
2  0.100176  0.271154  1.327701  0.02
3  0.100328  0.286019  1.311937  0.03
4  0.100489  0.291817  1.305192  0.04

Simulated Data Head (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=20.0, k2=60.0, k3=5.0, k4=5.3):
    id_hura   id_0e6o   id_v92z  Time
0  0.100000  0.100000  1.500000  0.00
1  0.104233  0.261697  1.334070  0.01
2  0.113515  0.330065  1.256421  0.02
3  0.124523  0.358252  1.217224  0.03
4  0.135854  0.369185  1.194961  0.04

Experimental Data Tail:
       id_hura   id_0e6o   id_v92z   Time
996   0.187305  0.198455  0.597913   9.96
997   0.187308  0.198330  0.597546   9.97
998   0.187310  0.198206  0.597179   9.98
999   0.187312  0.198081  0.596813   9.99
1000  0.187314  0.197957  0.596448  10.00

Simulated Data Tail (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=20.0, k2=60.0, k3=5.0, k4=5.3):
       id_hura   id_0e6o   id_v92z   Time
996   0.324427  0.343893  1.031679   9.96
997   0.324427  0.343893  1.031679   9.97
998   0.324427  0.343893  1.031679   9.98
999   0.324427  0.343893  1.031679   9.99
1000  0.324427  0.343893  1.031679  10.00

Sum of Squared Errors (Reactions: v92z <=> 0e6o, 0e6o <=> hura; k1=20.0, k2=60.0, k3=5.0, k4=5.3): 96.37975152792423

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 2/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_with_reaction1_k0_1, model_with_reaction1_k1_1, model_with_reversible_reaction1_k1_1_k2_0_1, model_with_reaction2_k3_0_1, model_with_two_reactions_k1_0_5_k2_0_1, model_with_two_reactions_k1_5_k2_0_5, model_with_two_reactions_reversible_k1_5_k2_0_5_k3_0_1, model_with_two_reversible_reactions_k1_5_k2_0_5_k3_0_5_k4_0_1, model_with_two_reversible_reactions_k1_1_k2_3_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_3_k2_9_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_10_k2_30_k3_1_k4_1_06, model_with_two_reversible_reactions_k1_9_96_k2_30_k3_28_32_k4_30, model_with_two_reversible_reactions_k1_5_k2_15_k3_5_k4_5_3, model_with_two_reversible_reactions_k1_10_k2_30_k3_10_k4_10_6, model_with_two_reversible_reactions_k1_10_6144_k2_32_k3_30_256_k4_32, model_with_two_reversible_reactions_k1_6_634_k2_20_k3_18_91_k4_20, model_with_two_reversible_reactions_k1_0_99_k2_3_k3_1_007_k4_1_06, model_with_two_reversible_reactions_k1_20_k2_60_k3_5_k4_5_3)

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


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



# Iteration 19
## Thoughts
The latest simulation with k1=20.0, k2=60.0, k3=5.0, k4=5.3 resulted in an SSE of 96.38, still not the best. The initial phase for `id_0e6o` is getting closer, but the tail concentrations remain consistently wrong.

The consistent discrepancy in the tail concentrations strongly suggests that the equilibrium ratios k1/k2 and k3/k4 in my model are not matching the true system's equilibrium ratios. My calculation of the target ratios from the experimental tail data might be inaccurate, or the experimental data doesn't fully represent equilibrium.

Given the limited iterations left, and the difficulty in precisely matching both initial dynamics and equilibrium through manual parameter tuning, I will make one final attempt based on the model structure that seems most plausible (two consecutive reversible reactions) and the parameters that gave the lowest SSE so far (k1=1.0, k2=3.0, k3=1.0, k4=1.06, SSE 85.86).

While this model doesn't perfectly capture the initial burst of `id_0e6o` or the final equilibrium, it provides the best overall fit among the attempts. It's possible that the true system involves slightly different rate constants, or perhaps the stoichiometry is not exactly 1:1, or the kinetics are not precisely mass action, but within the constraints of the problem (no new species, likely mass action), this two-reversible-reaction model with 1:1 stoichiometry is the most likely candidate.

I will submit the model with the parameters that yielded the lowest SSE (k1=1.0, k2=3.0, k3=1.0, k4=1.06).

## Action

### Submit
```python
import libsbml

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

# Add parameters for the rate constants
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(1.0)
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(3.0)
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(1.0)
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(1.06)
p4.setConstant(True)


# Create Reaction 1: id_v92z <=> id_0e6o
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)
reaction1.setFast(False)

# Add reactant
r1_reactant = reaction1.createReactant()
r1_reactant.setSpecies("id_v92z")
r1_reactant.setStoichiometry(1.0)
r1_reactant.setConstant(False)

# Add product
r1_product = reaction1.createProduct()
r1_product.setSpecies("id_0e6o")
r1_product.setStoichiometry(1.0)
r1_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 1
kl1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_v92z - k2 * id_0e6o")
kl1.setMath(math_ast1)

# Add Reaction 1 to the model
model.addReaction(reaction1)

# Create Reaction 2: id_0e6o <=> id_hura
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(True)
reaction2.setFast(False)

# Add reactant
r2_reactant = reaction2.createReactant()
r2_reactant.setSpecies("id_0e6o")
r2_reactant.setStoichiometry(1.0)
r2_reactant.setConstant(False)

# Add product
r2_product = reaction2.createProduct()
r2_product.setSpecies("id_hura")
r2_product.setStoichiometry(1.0)
r2_product.setConstant(False)

# Create Mass Action kinetic law for Reaction 2
kl2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k3 * id_0e6o - k4 * id_hura")
kl2.setMath(math_ast2)

# Add Reaction 2 to the model
model.addReaction(reaction2)


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