
                # Interation 0

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


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

                <?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level2/version4" level="2" version="4">
  <model id="id_x32j">
    <listOfUnitDefinitions>
      <unitDefinition id="id_9i9e">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_mosr">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_7k9j">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_dy3g" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_wjsw" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_y7ht" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_wh74" compartment="id_dy3g" initialConcentration="0.33"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

                Format your response according to the instructions in the system message.
                
## Thoughts
The goal is to discover the missing reactions in the provided SBML model. The initial model contains three species (`id_wjsw`, `id_y7ht`, `id_wh74`) but no reactions. The initial concentrations are 0, 0, and 0.33 respectively.

My first step is to observe the system's behavior under default conditions. This will show if the species concentrations change over time, indicating the presence of unmodeled reactions.

## 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_wjsw  id_y7ht  id_wh74
0         0        0 3.30e-01
...
2.00e-01  1.58e-01 1.57e-01 4.19e-01
...
4.00e-01  2.74e-01 2.70e-01 4.98e-01
...
6.00e-01  3.70e-01 3.59e-01 5.69e-01
...
8.00e-01  4.52e-01 4.30e-01 6.33e-01
...
1.00e+00  5.24e-01 4.87e-01 6.90e-01
...
1.20e+00  5.88e-01 5.29e-01 7.39e-01
...
1.40e+00  6.44e-01 5.60e-01 7.79e-01
...
1.60e+00  6.95e-01 5.80e-01 8.10e-01
...
1.80e+00  7.40e-01 5.93e-01 8.32e-01
...
2.00e+00  7.83e-01 6.02e-01 8.43e-01
...
2.20e+00  8.22e-01 6.08e-01 8.46e-01
...
2.40e+00  8.59e-01 6.14e-01 8.39e-01
...
2.60e+00  8.94e-01 6.22e-01 8.24e-01
...
2.80e+00  9.25e-01 6.34e-01 8.01e-01
...
3.00e+00  9.54e-01 6.52e-01 7.71e-01
...
3.20e+00  9.79e-01 6.75e-01 7.37e-01
...
3.40e+00  9.98e-01 7.03e-01 6.99e-01
...
3.60e+00  1.01e+00 7.37e-01 6.58e-01
...
3.80e+00  1.02e+00 7.75e-01 6.19e-01
...
4.00e+00  1.02e+00 8.15e-01 5.81e-01
...
4.20e+00  1.00e+00 8.57e-01 5.48e-01
...
4.40e+00  9.81e-01 9.00e-01 5.22e-01
...
4.60e+00  9.49e-01 9.42e-01 5.04e-01
...
4.80e+00  9.07e-01 9.83e-01 4.98e-01
...
5.00e+00  8.57e-01 1.02e+00 5.03e-01
...
5.20e+00  7.99e-01 1.06e+00 5.21e-01
...
5.40e+00  7.37e-01 1.10e+00 5.50e-01
...
5.60e+00  6.71e-01 1.13e+00 5.90e-01
...
5.80e+00  6.03e-01 1.15e+00 6.36e-01
...
6.00e+00  5.36e-01 1.17e+00 6.87e-01
...
6.20e+00  4.72e-01 1.18e+00 7.40e-01
...
6.40e+00  4.13e-01 1.18e+00 7.93e-01
...
6.60e+00  3.63e-01 1.17e+00 8.45e-01
...
6.80e+00  3.22e-01 1.14e+00 8.95e-01
...
7.00e+00  2.92e-01 1.10e+00 9.44e-01
...
7.20e+00  2.76e-01 1.06e+00 9.91e-01
...
7.40e+00  2.74e-01 9.97e-01 1.04e+00
...
7.60e+00  2.87e-01 9.31e-01 1.08e+00
...
7.80e+00  3.14e-01 8.57e-01 1.12e+00
...
8.00e+00  3.55e-01 7.79e-01 1.16e+00
...
8.20e+00  4.07e-01 6.97e-01 1.20e+00
...
8.40e+00  4.67e-01 6.14e-01 1.24e+00
...
8.60e+00  5.30e-01 5.31e-01 1.27e+00
...
8.80e+00  5.94e-01 4.51e-01 1.30e+00
...
9.00e+00  6.57e-01 3.77e-01 1.32e+00
...
9.20e+00  7.17e-01 3.10e-01 1.33e+00
...
9.40e+00  7.74e-01 2.52e-01 1.33e+00
...
9.60e+00  8.28e-01 2.06e-01 1.31e+00
...
1.00e+01  9.30e-01 1.48e-01 1.25e+00

## Reminder

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



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

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


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



# Iteration 1
## Thoughts
The observation experiment clearly shows dynamic changes in all species concentrations, indicating missing reactions. `id_wh74` starts at a non-zero concentration and fluctuates, while `id_wjsw` and `id_y7ht` start at zero and increase. This suggests that `id_wh74` might be a source or involved in reactions that produce `id_wjsw` and `id_y7ht`. The complex dynamics of all species suggest multiple reactions and potentially feedback loops.

To get a better understanding of the relationships between the species, I will plot the time series data. This will help visualize the changes and identify potential correlations or dependencies.

## Action

### Code
```python
import pandas as pd
import matplotlib.pyplot as plt
import io

# Access the experiment data
exp_data = experiment_history['iteration_0']

# Plot the time series data
plt.figure(figsize=(10, 6))
plt.plot(exp_data['Time'], exp_data['id_wjsw'], label='id_wjsw')
plt.plot(exp_data['Time'], exp_data['id_y7ht'], label='id_y7ht')
plt.plot(exp_data['Time'], exp_data['id_wh74'], label='id_wh74')
plt.xlabel('Time')
plt.ylabel('Concentration')
plt.title('Species Concentration over Time (Observation)')
plt.legend()
plt.grid(True)

# Save the plot to a string buffer
buf = io.BytesIO()
plt.savefig(buf, format='png')
buf.seek(0)

# To display the plot, you would typically encode it or save it to a file.
# For this environment, I will just indicate that the plot was generated.
print("Plot generated for species concentrations over time.")

# I will also print the data again to refresh my view of the numbers
print(exp_data.head())
print(exp_data.tail())
```
# Observation

## Code Stderror
 Unauthorized modules matplotlib detected. Only these modules are allowed: numpy, pandas, libsbml, math, scipy, jax, sklearn, io, traceback.

## 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. ()

### 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
My previous attempt to plot the data failed because `matplotlib` is not an allowed library. I need to rely on numerical analysis of the data.

Looking at the observation data (`experiment_history['iteration_0']`):
- `id_wjsw` and `id_y7ht` start at 0 and increase.
- `id_wh74` starts at 0.33, increases initially, peaks, and then decreases.

This pattern suggests that `id_wh74` is likely involved in the production of `id_wjsw` and `id_y7ht`. The initial increase in `id_wh74` is puzzling unless there's also a production mechanism for `id_wh74` or the initial state is not a steady state and the system is moving towards one. However, given the task is to find missing reactions, it's more likely `id_wh74` is consumed and produced in different reactions, or its consumption/production rates change over time.

The subsequent decrease in `id_wh74` and the complex dynamics of `id_wjsw` and `id_y7ht` (e.g., `id_wjsw` peaks and then decreases while `id_y7ht` continues to increase) suggest multiple reactions are at play.

Hypotheses:
1. `id_wh74` is converted into `id_wjsw` and `id_y7ht`.
2. There might be a reaction converting `id_wjsw` to `id_y7ht`.
3. There might be a reaction producing `id_wh74` or consuming `id_wjsw` or `id_y7ht`.

To test the first hypothesis (that `id_wh74` is a source for the others), I will perturb the system by increasing the initial concentration of `id_wh74`. If increasing `id_wh74` leads to faster or higher production of `id_wjsw` and `id_y7ht`, it supports this hypothesis.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_wh74": 0.66
    }
}
```
# Observation

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

Total size: 1001 rows × 4 columns. 

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

Time   id_wjsw  id_y7ht  id_wh74
0         0        0 6.60e-01
...
2.00e-01  1.58e-01 1.35e-01 7.21e-01
...
4.00e-01  2.74e-01 2.22e-01 7.78e-01
...
6.00e-01  3.71e-01 2.80e-01 8.31e-01
...
8.00e-01  4.54e-01 3.17e-01 8.81e-01
...
1.00e+00  5.29e-01 3.37e-01 9.25e-01
...
1.20e+00  5.98e-01 3.45e-01 9.62e-01
...
1.40e+00  6.61e-01 3.44e-01 9.91e-01
...
1.60e+00  7.21e-01 3.37e-01 1.01e+00
...
1.80e+00  7.77e-01 3.28e-01 1.02e+00
...
2.00e+00  8.31e-01 3.21e-01 1.01e+00
...
2.20e+00  8.82e-01 3.17e-01 9.95e-01
...
2.40e+00  9.31e-01 3.19e-01 9.66e-01
...
2.60e+00  9.78e-01 3.29e-01 9.25e-01
...
2.80e+00  1.02e+00 3.48e-01 8.75e-01
...
3.00e+00  1.07e+00 3.78e-01 8.16e-01
...
3.20e+00  1.11e+00 4.19e-01 7.51e-01
...
3.40e+00  1.15e+00 4.68e-01 6.81e-01
...
3.60e+00  1.18e+00 5.23e-01 6.08e-01
...
3.80e+00  1.21e+00 5.82e-01 5.35e-01
...
4.00e+00  1.24e+00 6.41e-01 4.63e-01
...
4.20e+00  1.25e+00 7.00e-01 3.96e-01
...
4.40e+00  1.25e+00 7.57e-01 3.35e-01
...
4.60e+00  1.25e+00 8.12e-01 2.83e-01
...
4.80e+00  1.23e+00 8.65e-01 2.41e-01
...
5.00e+00  1.20e+00 9.15e-01 2.10e-01
...
5.20e+00  1.15e+00 9.63e-01 1.92e-01
...
5.40e+00  1.10e+00 1.01e+00 1.86e-01
...
5.60e+00  1.03e+00 1.05e+00 1.93e-01
...
5.80e+00  9.62e-01 1.10e+00 2.13e-01
...
6.00e+00  8.83e-01 1.14e+00 2.47e-01
...
6.20e+00  8.00e-01 1.18e+00 2.93e-01
...
6.40e+00  7.14e-01 1.22e+00 3.49e-01
...
6.60e+00  6.27e-01 1.26e+00 4.13e-01
...
6.80e+00  5.41e-01 1.29e+00 4.81e-01
...
7.00e+00  4.57e-01 1.32e+00 5.48e-01
...
7.20e+00  3.79e-01 1.35e+00 6.14e-01
...
7.40e+00  3.08e-01 1.36e+00 6.77e-01
...
7.60e+00  2.47e-01 1.37e+00 7.36e-01
...
7.80e+00  1.97e-01 1.36e+00 7.92e-01
...
8.00e+00  1.59e-01 1.35e+00 8.46e-01
...
8.20e+00  1.32e-01 1.32e+00 8.97e-01
...
8.40e+00  1.17e-01 1.27e+00 9.46e-01
...
8.60e+00  1.12e-01 1.22e+00 9.93e-01
...
8.80e+00  1.16e-01 1.16e+00 1.04e+00
...
9.00e+00  1.31e-01 1.08e+00 1.08e+00
...
9.20e+00  1.56e-01 1.00e+00 1.13e+00
...
9.40e+00  1.92e-01 9.19e-01 1.17e+00
...
9.60e+00  2.41e-01 8.29e-01 1.21e+00
...
1.00e+01  3.68e-01 6.45e-01 1.28e+00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. ()

### 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
Comparing the results of `iteration_0` (initial `id_wh74` = 0.33) and `iteration_2` (initial `id_wh74` = 0.66):
- In `iteration_0`, `id_wjsw` peaks around 4.0, and `id_y7ht` peaks around 6.4.
- In `iteration_2`, `id_wjsw` peaks around 4.2, and `id_y7ht` peaks around 7.4.
- The peak concentrations for both `id_wjsw` and `id_y7ht` are higher in `iteration_2`.
- `id_wh74` still increases initially in `iteration_2`, peaks later and at a higher concentration than in `iteration_0`, and then decreases.

This confirms that `id_wh74` is involved in the production of `id_wjsw` and `id_y7ht`. The initial increase in `id_wh74` in both experiments is still curious. It suggests either a production reaction for `id_wh74` or a more complex regulatory mechanism.

Let's consider simple reaction schemes first.
Possible reactions:
1. `id_wh74` -> `id_wjsw` (Rate law: k1 * id_wh74)
2. `id_wh74` -> `id_y7ht` (Rate law: k2 * id_wh74)
3. `id_wh74` -> `id_wjsw` + `id_y7ht` (Rate law: k3 * id_wh74)

The data shows that `id_wjsw` and `id_y7ht` dynamics are different. `id_wjsw` peaks and declines, while `id_y7ht` continues to rise for longer. This suggests they are not simply produced together from `id_wh74` with fixed stoichiometry. It's more likely they are produced independently or involved in subsequent reactions.

The decline of `id_wjsw` after its peak suggests it is being consumed or converted into something else. Given the increase in `id_y7ht` continues after `id_wjsw` declines, a reaction like `id_wjsw` -> `id_y7ht` is plausible.

Let's propose a model with the following reactions:
R1: `id_wh74` -> `id_wjsw` (Rate law: k1 * id_wh74)
R2: `id_wh74` -> `id_y7ht` (Rate law: k2 * id_wh74)
R3: `id_wjsw` -> `id_y7ht` (Rate law: k3 * id_wjsw)

This model explains the production of `id_wjsw` and `id_y7ht` from `id_wh74` and the conversion of `id_wjsw` to `id_y7ht`. It doesn't explain the initial increase in `id_wh74`. Perhaps there's an external source for `id_wh74` or a reaction that produces it from an unlisted species (though the task says no new species). Or maybe the initial increase is due to the relative rates of production/consumption at the start.

Let's try to implement this model and see how well it fits the data. I'll start with simple mass action kinetics and guess some initial parameter values.

I will add three reactions to the initial SBML model:
1. `id_wh74` -> `id_wjsw`
2. `id_wh74` -> `id_y7ht`
3. `id_wjsw` -> `id_y7ht`

I'll use placeholder rate constants (e.g., 0.1 for now) and refine them later if the structure seems correct.

## Action

### Code
```python
import libsbml

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

# Add parameters (rate constants)
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(0.1) # Placeholder value
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(0.1) # Placeholder value
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(0.1) # Placeholder value
p3.setConstant(True)


# Create Reaction 1: id_wh74 -> id_wjsw
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1_r1 = reaction1.createReactant()
reactant1_r1.setSpecies("id_wh74")
reactant1_r1.setStoichiometry(1.0)

product1_r1 = reaction1.createProduct()
product1_r1.setSpecies("id_wjsw")
product1_r1.setStoichiometry(1.0)

kinetic_law1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_wh74")
kinetic_law1.setMath(math_ast1)

# Create Reaction 2: id_wh74 -> id_y7ht
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant1_r2 = reaction2.createReactant()
reactant1_r2.setSpecies("id_wh74")
reactant1_r2.setStoichiometry(1.0)

product1_r2 = reaction2.createProduct()
product1_r2.setSpecies("id_y7ht")
product1_r2.setStoichiometry(1.0)

kinetic_law2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k2 * id_wh74")
kinetic_law2.setMath(math_ast2)

# Create Reaction 3: id_wjsw -> id_y7ht
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)
reaction3.setFast(False)

reactant1_r3 = reaction3.createReactant()
reactant1_r3.setSpecies("id_wjsw")
reactant1_r3.setStoichiometry(1.0)

product1_r3 = reaction3.createProduct()
product1_r3.setSpecies("id_y7ht")
product1_r3.setStoichiometry(1.0)

kinetic_law3 = reaction3.createKineticLaw()
math_ast3 = libsbml.parseL3Formula("k3 * id_wjsw")
kinetic_law3.setMath(math_ast3)


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

# Store the updated SBML for simulation
shared_variables.add("model_v1_sbml", updated_sbml)

print("Model v1 created and stored in shared_variables.")
print(updated_sbml)
```
# Observation

## Code Stdout
Model v1 created and stored in shared_variables.
<?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level2/version4" level="2" version="4">
  <model id="id_x32j">
    <listOfUnitDefinitions>
      <unitDefinition id="id_9i9e">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_mosr">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_7k9j">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_dy3g" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_wjsw" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_y7ht" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_wh74" compartment="id_dy3g" initialConcentration="0.33"/>
    </listOfSpecies>
    <listOfParameters>
      <parameter id="k1" value="0.1" constant="true"/>
      <parameter id="k2" value="0.1" constant="true"/>
      <parameter id="k3" value="0.1" constant="true"/>
    </listOfParameters>
    <listOfReactions>
      <reaction id="reaction1" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k1 </ci>
              <ci> id_wh74 </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction2" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k2 </ci>
              <ci> id_wh74 </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction3" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k3 </ci>
              <ci> id_wjsw </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
    </listOfReactions>
  </model>
</sbml>


## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml)

### 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
I have created a candidate model (`model_v1_sbml`) with three reactions:
1. `id_wh74` -> `id_wjsw` (rate k1 * id_wh74)
2. `id_wh74` -> `id_y7ht` (rate k2 * id_wh74)
3. `id_wjsw` -> `id_y7ht` (rate k3 * id_wjsw)

Now I need to simulate this model and compare the results to the experimental data from `iteration_0` (default initial concentrations). The initial parameter values (k1=0.1, k2=0.1, k3=0.1) are just placeholders. I expect the simulation results with these values will not perfectly match the experimental data, but they should give me an idea if the model structure is plausible.

After simulating, I will compare the simulated time courses with the observed time courses from `iteration_0`. I will look at the general shape of the curves, peak times, and relative concentrations.

## Action

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

# Retrieve the stored model
model_sbml = shared_variables.access("model_v1_sbml")

# Simulate the model with default initial concentrations (matching iteration_0)
# The initial concentrations are already set in the model_v1_sbml to 0, 0, 0.33
sim_data = simulate(model_sbml)

# Access the experimental data from iteration_0
exp_data = experiment_history['iteration_0']

# Print head and tail of both dataframes for comparison
print("Simulated Data (Model v1):")
print(sim_data.head())
print(sim_data.tail())

print("\nExperimental Data (Iteration 0):")
print(exp_data.head())
print(exp_data.tail())

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

# Calculate SSE for each species
sse_wjsw = ((merged_data['id_wjsw_exp'] - merged_data['id_wjsw_sim'])**2).sum()
sse_y7ht = ((merged_data['id_y7ht_exp'] - merged_data['id_y7ht_sim'])**2).sum()
sse_wh74 = ((merged_data['id_wh74_exp'] - merged_data['id_wh74_sim'])**2).sum()

print(f"\nSum of Squared Errors (SSE) for k1=0.1, k2=0.1, k3=0.1:")
print(f"SSE id_wjsw: {sse_wjsw}")
print(f"SSE id_y7ht: {sse_y7ht}")
print(f"SSE id_wh74: {sse_wh74}")

```
# Observation

## Code Stdout
Simulated Data (Model v1):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.000330  0.000330  0.329341  0.01
2  0.000658  0.000659  0.328683  0.02
3  0.000986  0.000989  0.328026  0.03
4  0.001312  0.001317  0.327371  0.04
       id_wjsw   id_y7ht   id_wh74   Time
996   0.076867  0.208113  0.045019   9.96
997   0.076835  0.208235  0.044929   9.97
998   0.076804  0.208357  0.044840   9.98
999   0.076772  0.208478  0.044750   9.99
1000  0.076739  0.208600  0.044661  10.00

Experimental Data (Iteration 0):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009839  0.009799  0.334744  0.01
2  0.019374  0.019293  0.339453  0.02
3  0.028634  0.028509  0.344127  0.03
4  0.037639  0.037468  0.348768  0.04
       id_wjsw   id_y7ht   id_wh74   Time
996   0.919942  0.151630  1.260720   9.96
997   0.922398  0.150677  1.258656   9.97
998   0.924849  0.149752  1.256562   9.98
999   0.927295  0.148857  1.254439   9.99
1000  0.929736  0.147990  1.252287  10.00

Sum of Squared Errors (SSE) for k1=0.1, k2=0.1, k3=0.1:
SSE id_wjsw: 406.8167530528104
SSE id_y7ht: 444.14479059351436
SSE id_wh74: 591.345773557158

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml)

### 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 simulation results with the initial placeholder parameters (k1=0.1, k2=0.1, k3=0.1) show that the model structure `id_wh74` -> `id_wjsw`, `id_wh74` -> `id_y7ht`, and `id_wjsw` -> `id_y7ht` does not capture the experimental data well. The simulated concentrations are much lower than the experimental ones, and the dynamics are different (e.g., `id_wh74` decreases monotonically in the simulation, but increases initially in the experiment). The high SSE values confirm the poor fit.

The initial increase in `id_wh74` in the experimental data is a key feature not explained by the current model. This strongly suggests there is a reaction that *produces* `id_wh74`. Since we are not allowed to add new species, this production must come from an existing species or be a zero-order production (constant rate). A zero-order production of `id_wh74` would cause it to increase linearly if there were no consumption, which is not what we see. It's more likely that `id_wh74` is produced from one of the other species, or there's a reversible reaction.

Let's reconsider the species dynamics:
- `id_wh74` starts at 0.33, increases, peaks, then decreases.
- `id_wjsw` starts at 0, increases, peaks, then decreases.
- `id_y7ht` starts at 0, increases, and seems to level off or decrease very slowly at the end.

The fact that `id_wjsw` peaks and then decreases, while `id_y7ht` continues to increase or stays high, still supports the idea of `id_wjsw` being converted to `id_y7ht`.

The initial increase in `id_wh74` could be explained by a reaction like `id_y7ht` -> `id_wh74` or `id_wjsw` -> `id_wh74`, or even a reversible reaction involving `id_wh74`. Given that `id_y7ht` continues to increase for a long time, it's less likely to be the primary source of `id_wh74` production that causes the *initial* increase in `id_wh74` when `id_y7ht` is low. `id_wjsw` is also low initially.

What if there's a reversible reaction between `id_wh74` and `id_wjsw`?
R1: `id_wh74` <=> `id_wjsw`
R2: `id_wh74` -> `id_y7ht`
R3: `id_wjsw` -> `id_y7ht`

Or maybe:
R1: `id_wh74` <=> `id_wjsw`
R2: `id_wh74` <=> `id_y7ht`
R3: `id_wjsw` <=> `id_y7ht`

Let's try a model with a reversible reaction between `id_wh74` and `id_wjsw`, and a reaction from `id_wh74` to `id_y7ht`, and `id_wjsw` to `id_y7ht`.

Model v2 reactions:
R1: `id_wh74` <=> `id_wjsw` (Rate law: k1f * id_wh74 - k1r * id_wjsw)
R2: `id_wh74` -> `id_y7ht` (Rate law: k2 * id_wh74)
R3: `id_wjsw` -> `id_y7ht` (Rate law: k3 * id_wjsw)

This model structure might explain the initial increase in `id_wh74` if the reverse rate of R1 (production of `id_wh74` from `id_wjsw`) is significant, although `id_wjsw` is initially zero. This doesn't quite fit.

Let's reconsider the initial increase in `id_wh74`. If `id_wh74` is consumed by reactions R1 and R2, for it to increase, there must be a production term. Since no new species are allowed, this production must come from `id_wjsw` or `id_y7ht`.
If `id_wjsw` -> `id_wh74` (reverse of R1) and `id_y7ht` -> `id_wh74` (reverse of R2), this could explain the increase.

Let's try a model with reversible reactions between all pairs:
R1: `id_wh74` <=> `id_wjsw` (Rate: k1f * id_wh74 - k1r * id_wjsw)
R2: `id_wh74` <=> `id_y7ht` (Rate: k2f * id_wh74 - k2r * id_y7ht)
R3: `id_wjsw` <=> `id_y7ht` (Rate: k3f * id_wjsw - k3r * id_y7ht)

This seems overly complex. Let's look at the initial rates from `iteration_0`.
At Time = 0:
`id_wjsw` = 0, `id_y7ht` = 0, `id_wh74` = 0.33
Change from Time 0 to 0.01:
`id_wjsw` increases by ~0.0098
`id_y7ht` increases by ~0.0098
`id_wh74` increases by ~0.0047

Initial rates:
d(id_wjsw)/dt ≈ 0.0098 / 0.01 = 0.98
d(id_y7ht)/dt ≈ 0.0098 / 0.01 = 0.98
d(id_wh74)/dt ≈ 0.0047 / 0.01 = 0.47

At t=0, only `id_wh74` is non-zero.
If we have reactions:
`id_wh74` -> `id_wjsw` (rate k1 * id_wh74)
`id_wh74` -> `id_y7ht` (rate k2 * id_wh74)
`id_wjsw` -> `id_y7ht` (rate k3 * id_wjsw)
`id_wjsw` -> `id_wh74` (rate k4 * id_wjsw)
`id_y7ht` -> `id_wh74` (rate k5 * id_y7ht)
`id_y7ht` -> `id_wjsw` (rate k6 * id_y7ht)

At t=0, `id_wjsw` and `id_y7ht` are 0.
d(id_wjsw)/dt = k1 * id_wh74 - k3 * id_wjsw + k6 * id_y7ht - k4 * id_wjsw = k1 * 0.33 ≈ 0.98 => k1 ≈ 0.98 / 0.33 ≈ 2.97
d(id_y7ht)/dt = k2 * id_wh74 + k3 * id_wjsw + k5 * id_wh74 - k6 * id_y7ht = k2 * 0.33 ≈ 0.98 => k2 ≈ 0.98 / 0.33 ≈ 2.97
d(id_wh74)/dt = -k1 * id_wh74 - k2 * id_wh74 + k4 * id_wjsw + k5 * id_y7ht = -(k1 + k2) * 0.33 ≈ 0.47
-(2.97 + 2.97) * 0.33 = -5.94 * 0.33 ≈ -1.96. This is negative, but the observed rate is positive (0.47).

This simple mass action model with only forward reactions from `id_wh74` cannot explain the initial increase in `id_wh74`.

The initial increase in `id_wh74` *must* come from a reaction where `id_wh74` is a product, and the reactant(s) are present at t=0. The only species present at t=0 is `id_wh74` itself (at 0.33). This is impossible unless there's an external input (not allowed) or a reaction like `id_wh74` -> `id_wh74` + X (which doesn't change `id_wh74` concentration unless X is consumed/produced elsewhere) or a reaction like A -> `id_wh74` where A is a boundary species (not allowed to add).

Let's re-examine the SBML. Are there any boundary species or constant species defined? No, all three species are normal species with initial concentrations.

Could the initial increase in `id_wh74` be an artifact of the simulation or measurement? Or is there a reaction type I'm not considering?

What if the rate laws are not simple mass action? For example, autocatalysis?
`id_wh74` + `id_wh74` -> ... ? No, this would consume `id_wh74`.

Could there be a reaction that produces `id_wh74` from `id_wjsw` or `id_y7ht`, and the initial rate calculation is misleading due to the discrete time points? Let's look at the very first time point (0.01).
`id_wjsw` = 0.009839, `id_y7ht` = 0.009799, `id_wh74` = 0.334744.
All three concentrations have increased from their initial values (0, 0, 0.33).

This means:
- `id_wjsw` is produced.
- `id_y7ht` is produced.
- `id_wh74` is produced.

Since `id_wjsw` and `id_y7ht` start at 0, their production must come from `id_wh74`.
R1: `id_wh74` -> `id_wjsw`
R2: `id_wh74` -> `id_y7ht`

For `id_wh74` to be produced, it must come from `id_wjsw` or `id_y7ht` (or itself, which is autocatalysis).
R4: `id_wjsw` -> `id_wh74`
R5: `id_y7ht` -> `id_wh74`

Also, `id_wjsw` peaks and declines, suggesting consumption, likely converting to `id_y7ht`.
R3: `id_wjsw` -> `id_y7ht`

So, a potential set of reactions is:
R1: `id_wh74` -> `id_wjsw`
R2: `id_wh74` -> `id_y7ht`
R3: `id_wjsw` -> `id_y7ht`
R4: `id_wjsw` -> `id_wh74`
R5: `id_y7ht` -> `id_wh74`

Let's consider the net rates at t=0.
d(id_wjsw)/dt = Rate(R1) - Rate(R3) - Rate(R4)
d(id_y7ht)/dt = Rate(R2) + Rate(R3) - Rate(R5)
d(id_wh74)/dt = -Rate(R1) - Rate(R2) + Rate(R4) + Rate(R5)

At t=0, `id_wjsw`=0, `id_y7ht`=0, `id_wh74`=0.33.
Assuming mass action kinetics:
Rate(R1) = k1 * id_wh74
Rate(R2) = k2 * id_wh74
Rate(R3) = k3 * id_wjsw
Rate(R4) = k4 * id_wjsw
Rate(R5) = k5 * id_y7ht

At t=0:
d(id_wjsw)/dt = k1 * 0.33 - k3 * 0 - k4 * 0 = k1 * 0.33 ≈ 0.98 => k1 ≈ 2.97
d(id_y7ht)/dt = k2 * 0.33 + k3 * 0 - k5 * 0 = k2 * 0.33 ≈ 0.98 => k2 ≈ 2.97
d(id_wh74)/dt = -k1 * 0.33 - k2 * 0.33 + k4 * 0 + k5 * 0 = -(k1 + k2) * 0.33 ≈ -(2.97 + 2.97) * 0.33 ≈ -1.96.

This still gives a negative initial rate for `id_wh74`, contradicting the observation.

There must be a reaction producing `id_wh74` whose rate is non-zero at t=0. The only species non-zero at t=0 is `id_wh74`. This points towards an autocatalytic production of `id_wh74` or a reaction involving `id_wh74` that produces more `id_wh74`.

Let's consider:
R_prod_wh74: `id_wh74` -> 2 `id_wh74` (Net production of 1 `id_wh74`. Rate: k_prod * id_wh74)
This is equivalent to a zero-order production if the rate is constant, or first-order if the rate is proportional to `id_wh74`. If it's first order, d(id_wh74)/dt would have a positive term k_prod * id_wh74.

Let's try a model with:
R1: `id_wh74` -> `id_wjsw` (rate k1 * id_wh74)
R2: `id_wh74` -> `id_y7ht` (rate k2 * id_wh74)
R3: `id_wjsw` -> `id_y7ht` (rate k3 * id_wjsw)
R4: Production of `id_wh74` (rate k4 * id_wh74) - This is like `id_wh74` -> 2 `id_wh74`

Model v3 reactions:
R1: `id_wh74` -> `id_wjsw` (rate k1 * id_wh74)
R2: `id_wh74` -> `id_y7ht` (rate k2 * id_wh74)
R3: `id_wjsw` -> `id_y7ht` (rate k3 * id_wjsw)
R4: Production of `id_wh74` (rate k4 * id_wh74) - This is a bit unusual to model directly. A better way is to have a reaction with `id_wh74` as a product and a rate law that depends on `id_wh74`. E.g., `null` -> `id_wh74` with rate k4 * id_wh74. But `null` isn't a species.

Let's model R4 as `id_wh74` -> 2 `id_wh74`.
R1: `id_wh74` -> `id_wjsw` (rate k1 * id_wh74)
R2: `id_wh74` -> `id_y7ht` (rate k2 * id_wh74)
R3: `id_wjsw` -> `id_y7ht` (rate k3 * id_wjsw)
R4: `id_wh74` -> 2 `id_wh74` (rate k4 * id_wh74)

Net change for `id_wh74`: -k1*id_wh74 - k2*id_wh74 + k4*id_wh74 = (k4 - k1 - k2) * id_wh74.
For `id_wh74` to increase initially, we need k4 > k1 + k2.

Let's try implementing this Model v3. I'll use placeholder parameters again.

## Action

### Code
```python
import libsbml

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

# Add parameters (rate constants)
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(0.5) # Placeholder value
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(0.5) # Placeholder value
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(0.5) # Placeholder value
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(2.0) # Placeholder value (needs to be > k1+k2 for initial increase)
p4.setConstant(True)


# Create Reaction 1: id_wh74 -> id_wjsw
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1_r1 = reaction1.createReactant()
reactant1_r1.setSpecies("id_wh74")
reactant1_r1.setStoichiometry(1.0)

product1_r1 = reaction1.createProduct()
product1_r1.setSpecies("id_wjsw")
product1_r1.setStoichiometry(1.0)

kinetic_law1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_wh74")
kinetic_law1.setMath(math_ast1)

# Create Reaction 2: id_wh74 -> id_y7ht
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant1_r2 = reaction2.createReactant()
reactant1_r2.setSpecies("id_wh74")
reactant1_r2.setStoichiometry(1.0)

product1_r2 = reaction2.createProduct()
product1_r2.setSpecies("id_y7ht")
product1_r2.setStoichiometry(1.0)

kinetic_law2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k2 * id_wh74")
kinetic_law2.setMath(math_ast2)

# Create Reaction 3: id_wjsw -> id_y7ht
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)
reaction3.setFast(False)

reactant1_r3 = reaction3.createReactant()
reactant1_r3.setSpecies("id_wjsw")
reactant1_r3.setStoichiometry(1.0)

product1_r3 = reaction3.createProduct()
product1_r3.setSpecies("id_y7ht")
product1_r3.setStoichiometry(1.0)

kinetic_law3 = reaction3.createKineticLaw()
math_ast3 = libsbml.parseL3Formula("k3 * id_wjsw")
kinetic_law3.setMath(math_ast3)

# Create Reaction 4: id_wh74 -> 2 id_wh74 (Net production of id_wh74)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)
reaction4.setFast(False)

# Reactant: id_wh74
reactant1_r4 = reaction4.createReactant()
reactant1_r4.setSpecies("id_wh74")
reactant1_r4.setStoichiometry(1.0)

# Product: id_wh74 with stoichiometry 2
product1_r4 = reaction4.createProduct()
product1_r4.setSpecies("id_wh74")
product1_r4.setStoichiometry(2.0)

kinetic_law4 = reaction4.createKineticLaw()
math_ast4 = libsbml.parseL3Formula("k4 * id_wh74")
kinetic_law4.setMath(math_ast4)


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

# Store the updated SBML for simulation
shared_variables.add("model_v3_sbml", updated_sbml)

print("Model v3 created and stored in shared_variables.")
print(updated_sbml)
```
# Observation

## Code Stdout
Model v3 created and stored in shared_variables.
<?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level2/version4" level="2" version="4">
  <model id="id_x32j">
    <listOfUnitDefinitions>
      <unitDefinition id="id_9i9e">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_mosr">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_7k9j">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_dy3g" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_wjsw" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_y7ht" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_wh74" compartment="id_dy3g" initialConcentration="0.33"/>
    </listOfSpecies>
    <listOfParameters>
      <parameter id="k1" value="0.5" constant="true"/>
      <parameter id="k2" value="0.5" constant="true"/>
      <parameter id="k3" value="0.5" constant="true"/>
      <parameter id="k4" value="2" constant="true"/>
    </listOfParameters>
    <listOfReactions>
      <reaction id="reaction1" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k1 </ci>
              <ci> id_wh74 </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction2" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k2 </ci>
              <ci> id_wh74 </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction3" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k3 </ci>
              <ci> id_wjsw </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction4" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_wh74" stoichiometry="2"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k4 </ci>
              <ci> id_wh74 </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
    </listOfReactions>
  </model>
</sbml>


## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml)

### 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
I have created Model v3, which includes an autocatalytic-like production of `id_wh74` (`id_wh74` -> 2 `id_wh74`) in addition to the previous reactions. This structure aims to explain the initial increase in `id_wh74`.

Now I will simulate Model v3 with the default initial concentrations (matching `iteration_0`) and compare the results to the experimental data. I'm using placeholder parameters (k1=0.5, k2=0.5, k3=0.5, k4=2.0). I chose k4 > k1 + k2 to ensure an initial increase in `id_wh74`.

## Action

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

# Retrieve the stored model
model_sbml = shared_variables.access("model_v3_sbml")

# Simulate the model with default initial concentrations (matching iteration_0)
# The initial concentrations are already set in the model_v3_sbml to 0, 0, 0.33
sim_data = simulate(model_sbml)

# Access the experimental data from iteration_0
exp_data = experiment_history['iteration_0']

# Print head and tail of both dataframes for comparison
print("Simulated Data (Model v3):")
print(sim_data.head())
print(sim_data.tail())

print("\nExperimental Data (Iteration 0):")
print(exp_data.head())
print(exp_data.tail())

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

sse_wjsw = ((merged_data['id_wjsw_exp'] - merged_data['id_wjsw_sim'])**2).sum()
sse_y7ht = ((merged_data['id_y7ht_exp'] - merged_data['id_y7ht_sim'])**2).sum()
sse_wh74 = ((merged_data['id_wh74_exp'] - merged_data['id_wh74_sim'])**2).sum()

print(f"\nSum of Squared Errors (SSE) for Model v3 (k1=0.5, k2=0.5, k3=0.5, k4=2.0):")
print(f"SSE id_wjsw: {sse_wjsw}")
print(f"SSE id_y7ht: {sse_y7ht}")
print(f"SSE id_wh74: {sse_wh74}")
```
# Observation

## Code Stdout
Simulated Data (Model v3):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.001654  0.001662  0.333317  0.01
2  0.003317  0.003350  0.336666  0.02
3  0.004988  0.005062  0.340050  0.03
4  0.006667  0.006800  0.343468  0.04
          id_wjsw      id_y7ht      id_wh74   Time
996   2327.999973  4655.672213  6984.002186   9.96
997   2351.396904  4702.466065  7054.192970   9.97
998   2375.028980  4749.730205  7125.089184   9.98
999   2398.898560  4797.469353  7196.697913   9.99
1000  2423.008029  4845.688281  7269.026310  10.00

Experimental Data (Iteration 0):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009839  0.009799  0.334744  0.01
2  0.019374  0.019293  0.339453  0.02
3  0.028634  0.028509  0.344127  0.03
4  0.037639  0.037468  0.348768  0.04
       id_wjsw   id_y7ht   id_wh74   Time
996   0.919942  0.151630  1.260720   9.96
997   0.922398  0.150677  1.258656   9.97
998   0.924849  0.149752  1.256562   9.98
999   0.927295  0.148857  1.254439   9.99
1000  0.929736  0.147990  1.252287  10.00

Sum of Squared Errors (SSE) for Model v3 (k1=0.5, k2=0.5, k3=0.5, k4=2.0):
SSE id_wjsw: 296154423.9775315
SSE id_y7ht: 1185263088.8469665
SSE id_wh74: 2666611195.2171183

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml)

### 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
Model v3 with the current placeholder parameters (k1=0.5, k2=0.5, k3=0.5, k4=2.0) results in species concentrations that grow exponentially and reach extremely high values, completely diverging from the experimental data. The SSE values are enormous.

This indicates that while the autocatalytic-like production of `id_wh74` (`id_wh74` -> 2 `id_wh74`) might explain the initial *increase* in `id_wh74`, the chosen rate constant (k4=2.0) is far too high, leading to unstable growth. Also, the overall dynamics are not captured. The experimental data shows peaks and declines, suggesting consumption or conversion reactions are significant.

The model structure `id_wh74` -> `id_wjsw`, `id_wh74` -> `id_y7ht`, `id_wjsw` -> `id_y7ht`, and `id_wh74` -> 2 `id_wh74` seems plausible for explaining the initial increase and the general flow from `id_wh74` to `id_wjsw` and `id_y7ht`, and from `id_wjsw` to `id_y7ht`. However, the parameters need to be significantly different.

The initial rates from `iteration_0` were approximately:
d(id_wjsw)/dt ≈ 0.98
d(id_y7ht)/dt ≈ 0.98
d(id_wh74)/dt ≈ 0.47

At t=0, `id_wjsw`=0, `id_y7ht`=0, `id_wh74`=0.33.
Model v3 rates at t=0:
d(id_wjsw)/dt = k1 * id_wh74 = k1 * 0.33
d(id_y7ht)/dt = k2 * id_wh74 = k2 * 0.33
d(id_wh74)/dt = (k4 - k1 - k2) * id_wh74 = (k4 - k1 - k2) * 0.33

Matching initial rates:
k1 * 0.33 ≈ 0.98 => k1 ≈ 2.97
k2 * 0.33 ≈ 0.98 => k2 ≈ 2.97
(k4 - k1 - k2) * 0.33 ≈ 0.47
(k4 - 2.97 - 2.97) * 0.33 ≈ 0.47
(k4 - 5.94) * 0.33 ≈ 0.47
k4 - 5.94 ≈ 0.47 / 0.33 ≈ 1.42
k4 ≈ 1.42 + 5.94 ≈ 7.36

These initial rate calculations suggest parameters around k1 ≈ 2.97, k2 ≈ 2.97, k4 ≈ 7.36. The value of k3 affects the dynamics later when `id_wjsw` is non-zero.

Let's update the parameters in Model v3 based on these initial rate estimates and simulate again. I'll keep k3 as a placeholder for now, maybe slightly higher than the production rates from `id_wh74` to cause the decline in `id_wjsw`. Let's try k3 = 3.0.

Updated parameters for Model v3:
k1 = 2.97
k2 = 2.97
k3 = 3.0
k4 = 7.36

I will modify the SBML string for Model v3 with these new parameters and simulate.

## Action

### Code
```python
import libsbml

# Retrieve the stored model SBML string
model_sbml = shared_variables.access("model_v3_sbml")

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

# Update parameter values
model.getParameter("k1").setValue(2.97)
model.getParameter("k2").setValue(2.97)
model.getParameter("k3").setValue(3.0)
model.getParameter("k4").setValue(7.36)

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

# Store the updated SBML
shared_variables.add("model_v3_tuned_sbml", updated_sbml)

# Simulate the model with updated parameters
sim_data = simulate(updated_sbml)

# Access the experimental data from iteration_0
exp_data = experiment_history['iteration_0']

# Print head and tail of both dataframes for comparison
print("Simulated Data (Model v3, Tuned Parameters):")
print(sim_data.head())
print(sim_data.tail())

print("\nExperimental Data (Iteration 0):")
print(exp_data.head())
print(exp_data.tail())

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

sse_wjsw = ((merged_data['id_wjsw_exp'] - merged_data['id_wjsw_sim'])**2).sum()
sse_y7ht = ((merged_data['id_y7ht_exp'] - merged_data['id_y7ht_sim'])**2).sum()
sse_wh74 = ((merged_data['id_wh74_exp'] - merged_data['id_wh74_sim'])**2).sum()

print(f"\nSum of Squared Errors (SSE) for Model v3 (k1=2.97, k2=2.97, k3=3.0, k4=7.36):")
print(f"SSE id_wjsw: {sse_wjsw}")
print(f"SSE id_y7ht: {sse_y7ht}")
print(f"SSE id_wh74: {sse_wh74}")
```
# Observation

## Code Stderror
 name 'pd' is not defined

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml, model_v3_tuned_sbml)

### 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
I made a mistake in the previous code block by not importing `pandas`. I need to import `pandas` to use `pd.merge`.

I will re-run the simulation and comparison with the tuned parameters for Model v3, making sure to import `pandas`.

The tuned parameters are based on initial rate estimates:
k1 = 2.97 (`id_wh74` -> `id_wjsw`)
k2 = 2.97 (`id_wh74` -> `id_y7ht`)
k3 = 3.0 (`id_wjsw` -> `id_y7ht`)
k4 = 7.36 (`id_wh74` -> 2 `id_wh74`)

I expect this simulation to show a better fit than the previous one, especially in the early phase, but the fit might still be poor over the entire time course as these parameters were only estimated from the initial rates.

## Action

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

# Retrieve the stored model SBML string
model_sbml = shared_variables.access("model_v3_tuned_sbml")

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

# Simulate the model with updated parameters
sim_data = simulate(model_sbml) # Use the stored tuned model

# Access the experimental data from iteration_0
exp_data = experiment_history['iteration_0']

# Print head and tail of both dataframes for comparison
print("Simulated Data (Model v3, Tuned Parameters):")
print(sim_data.head())
print(sim_data.tail())

print("\nExperimental Data (Iteration 0):")
print(exp_data.head())
print(exp_data.tail())

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

sse_wjsw = ((merged_data['id_wjsw_exp'] - merged_data['id_wjsw_sim'])**2).sum()
sse_y7ht = ((merged_data['id_y7ht_exp'] - merged_data['id_y7ht_sim'])**2).sum()
sse_wh74 = ((merged_data['id_wh74_exp'] - merged_data['id_wh74_sim'])**2).sum()

print(f"\nSum of Squared Errors (SSE) for Model v3 (k1=2.97, k2=2.97, k3=3.0, k4=7.36):")
print(f"SSE id_wjsw: {sse_wjsw}")
print(f"SSE id_y7ht: {sse_y7ht}")
print(f"SSE id_wh74: {sse_wh74}")
```
# Observation

## Code Stdout
Simulated Data (Model v3, Tuned Parameters):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009725  0.010017  0.334719  0.01
2  0.019301  0.020465  0.339506  0.02
3  0.028735  0.031341  0.344362  0.03
4  0.038034  0.042644  0.349287  0.04
            id_wjsw       id_y7ht        id_wh74   Time
996   307733.325756  1.608014e+06  457973.501631   9.96
997   312134.320969  1.631010e+06  464523.130870   9.97
998   316598.253073  1.654336e+06  471166.423765   9.98
999   321126.023860  1.677995e+06  477904.722378   9.99
1000  325718.556220  1.701993e+06  484739.400166  10.00

Experimental Data (Iteration 0):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009839  0.009799  0.334744  0.01
2  0.019374  0.019293  0.339453  0.02
3  0.028634  0.028509  0.344127  0.03
4  0.037639  0.037468  0.348768  0.04
       id_wjsw   id_y7ht   id_wh74   Time
996   0.919942  0.151630  1.260720   9.96
997   0.922398  0.150677  1.258656   9.97
998   0.924849  0.149752  1.256562   9.98
999   0.927295  0.148857  1.254439   9.99
1000  0.929736  0.147990  1.252287  10.00

Sum of Squared Errors (SSE) for Model v3 (k1=2.97, k2=2.97, k3=3.0, k4=7.36):
SSE id_wjsw: 3788908601464.554
SSE id_y7ht: 103454049939658.4
SSE id_wh74: 8391607904176.105

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml, model_v3_tuned_sbml)

### 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 simulation results with the tuned parameters for Model v3 are even worse than before, leading to extremely rapid exponential growth and massive SSE values. This indicates that the model structure, particularly the autocatalytic production of `id_wh74` (`id_wh74` -> 2 `id_wh74`) with a simple mass action rate law, is likely incorrect or incomplete. While it can produce an initial increase in `id_wh74`, it doesn't capture the subsequent decrease and the overall system stability observed in the experiment.

The experimental data shows the system eventually reaches a dynamic equilibrium or limit cycle, not unbounded growth. This suggests there are consumption mechanisms or regulatory processes that become significant at higher concentrations.

Let's revisit the initial increase in `id_wh74`. It's possible the production of `id_wh74` is not simply proportional to `id_wh74` concentration, or it depends on other species in a non-linear way, or there's a different reaction producing it.

Could the initial increase in `id_wh74` be due to a reversible reaction where the reverse rate is initially higher than the forward rate?
Example: `id_wjsw` <=> `id_wh74` (Rate: kf * id_wjsw - kr * id_wh74)
At t=0, `id_wjsw`=0, `id_wh74`=0.33. Rate = -kr * 0.33. This would *decrease* `id_wh74`.

Example: `id_y7ht` <=> `id_wh74` (Rate: kf * id_y7ht - kr * id_wh74)
At t=0, `id_y7ht`=0, `id_wh74`=0.33. Rate = -kr * 0.33. This would *decrease* `id_wh74`.

Example: `id_wh74` <=> `id_wjsw` + `id_y7ht` (Rate: kf * id_wh74 - kr * id_wjsw * id_y7ht)
At t=0, `id_wjsw`=0, `id_y7ht`=0, `id_wh74`=0.33. Rate = kf * 0.33 - kr * 0 * 0 = kf * 0.33. This would *increase* `id_wh74` and produce `id_wjsw` and `id_y7ht`. This looks promising for the initial phase.

Let's propose Model v4:
R1: `id_wh74` <=> `id_wjsw` + `id_y7ht` (Rate: k1f * id_wh74 - k1r * id_wjsw * id_y7ht)
R2: `id_wjsw` -> `id_y7ht` (Rate: k2 * id_wjsw) - This explains the decline in `id_wjsw` and continued increase in `id_y7ht`.

Let's check the initial rates for Model v4 at t=0 (`id_wjsw`=0, `id_y7ht`=0, `id_wh74`=0.33):
d(id_wh74)/dt = -Rate(R1) = -(k1f * id_wh74 - k1r * id_wjsw * id_y7ht) = -(k1f * 0.33 - k1r * 0 * 0) = -k1f * 0.33
d(id_wjsw)/dt = Rate(R1) - Rate(R2) = (k1f * id_wh74 - k1r * id_wjsw * id_y7ht) - k2 * id_wjsw = (k1f * 0.33 - k1r * 0 * 0) - k2 * 0 = k1f * 0.33
d(id_y7ht)/dt = Rate(R1) + Rate(R2) = (k1f * id_wh74 - k1r * id_wjsw * id_y7ht) + k2 * id_wjsw = (k1f * 0.33 - k1r * 0 * 0) + k2 * 0 = k1f * 0.33

This model predicts that at t=0, `id_wjsw` and `id_y7ht` increase, and `id_wh74` *decreases*. This contradicts the observed initial increase in `id_wh74`.

My hypothesis about the initial increase in `id_wh74` being a key feature to model seems correct, but the simple mass-action reactions I've tried so far don't explain it without leading to unstable behavior or contradicting initial rates.

Could there be a reaction that produces `id_wh74` from *nothing* (a boundary species or a constant flux)? The task says "You do not need to add new species." This implies I should only use the existing three species.

Let's reconsider the initial increase in `id_wh74`. It's small initially (0.33 to 0.334744 in 0.01s). Perhaps the production rate of `id_wh74` is initially higher than its consumption rate, and the production depends on one of the species that is initially non-zero (`id_wh74`).

What if the production of `id_wh74` is zero-order (constant rate)?
R_prod_wh74: -> `id_wh74` (Rate: k_prod)
R1: `id_wh74` -> `id_wjsw` (rate k1 * id_wh74)
R2: `id_wh74` -> `id_y7ht` (rate k2 * id_wh74)
R3: `id_wjsw` -> `id_y7ht` (rate k3 * id_wjsw)

Model v5 reactions:
R1: `id_wh74` -> `id_wjsw` (rate k1 * id_wh74)
R2: `id_wh74` -> `id_y7ht` (rate k2 * id_wh74)
R3: `id_wjsw` -> `id_y7ht` (rate k3 * id_wjsw)
R4: -> `id_wh74` (rate k4) - Zero-order production

Initial rates at t=0 (`id_wjsw`=0, `id_y7ht`=0, `id_wh74`=0.33):
d(id_wjsw)/dt = k1 * 0.33 ≈ 0.98 => k1 ≈ 2.97
d(id_y7ht)/dt = k2 * 0.33 ≈ 0.98 => k2 ≈ 2.97
d(id_wh74)/dt = -k1 * 0.33 - k2 * 0.33 + k4 ≈ 0.47
-(2.97 * 0.33) - (2.97 * 0.33) + k4 ≈ 0.47
-0.98 - 0.98 + k4 ≈ 0.47
-1.96 + k4 ≈ 0.47
k4 ≈ 0.47 + 1.96 ≈ 2.43

This model structure with these initial rate estimates seems more plausible for the initial phase. Let's implement Model v5 and simulate.

## Action

### Code
```python
import libsbml

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

# Add parameters (rate constants)
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(2.97) # Estimated from initial rates
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(2.97) # Estimated from initial rates
p2.setConstant(True)

p3 = model.createParameter()
p3.setId("k3")
p3.setValue(3.0) # Placeholder, needs tuning
p3.setConstant(True)

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(2.43) # Estimated from initial rates
p4.setConstant(True)


# Create Reaction 1: id_wh74 -> id_wjsw
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1_r1 = reaction1.createReactant()
reactant1_r1.setSpecies("id_wh74")
reactant1_r1.setStoichiometry(1.0)

product1_r1 = reaction1.createProduct()
product1_r1.setSpecies("id_wjsw")
product1_r1.setStoichiometry(1.0)

kinetic_law1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_wh74")
kinetic_law1.setMath(math_ast1)

# Create Reaction 2: id_wh74 -> id_y7ht
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant1_r2 = reaction2.createReactant()
reactant1_r2.setSpecies("id_wh74")
reactant1_r2.setStoichiometry(1.0)

product1_r2 = reaction2.createProduct()
product1_r2.setSpecies("id_y7ht")
product1_r2.setStoichiometry(1.0)

kinetic_law2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k2 * id_wh74")
kinetic_law2.setMath(math_ast2)

# Create Reaction 3: id_wjsw -> id_y7ht
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)
reaction3.setFast(False)

reactant1_r3 = reaction3.createReactant()
reactant1_r3.setSpecies("id_wjsw")
reactant1_r3.setStoichiometry(1.0)

product1_r3 = reaction3.createProduct()
product1_r3.setSpecies("id_y7ht")
product1_r3.setStoichiometry(1.0)

kinetic_law3 = reaction3.createKineticLaw()
math_ast3 = libsbml.parseL3Formula("k3 * id_wjsw")
kinetic_law3.setMath(math_ast3)

# Create Reaction 4: -> id_wh74 (Zero-order production)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)
reaction4.setFast(False)

# No reactants for zero-order production

product1_r4 = reaction4.createProduct()
product1_r4.setSpecies("id_wh74")
product1_r4.setStoichiometry(1.0)

kinetic_law4 = reaction4.createKineticLaw()
math_ast4 = libsbml.parseL3Formula("k4") # Rate is just the constant k4
kinetic_law4.setMath(math_ast4)


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

# Store the updated SBML for simulation
shared_variables.add("model_v5_sbml", updated_sbml)

print("Model v5 created and stored in shared_variables.")
print(updated_sbml)
```
# Observation

## Code Stdout
Model v5 created and stored in shared_variables.
<?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level2/version4" level="2" version="4">
  <model id="id_x32j">
    <listOfUnitDefinitions>
      <unitDefinition id="id_9i9e">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_mosr">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_7k9j">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_dy3g" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_wjsw" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_y7ht" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_wh74" compartment="id_dy3g" initialConcentration="0.33"/>
    </listOfSpecies>
    <listOfParameters>
      <parameter id="k1" value="2.97" constant="true"/>
      <parameter id="k2" value="2.97" constant="true"/>
      <parameter id="k3" value="3" constant="true"/>
      <parameter id="k4" value="2.43" constant="true"/>
    </listOfParameters>
    <listOfReactions>
      <reaction id="reaction1" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k1 </ci>
              <ci> id_wh74 </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction2" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k2 </ci>
              <ci> id_wh74 </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction3" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k3 </ci>
              <ci> id_wjsw </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction4" reversible="false" fast="false">
        <listOfProducts>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <ci> k4 </ci>
          </math>
        </kineticLaw>
      </reaction>
    </listOfReactions>
  </model>
</sbml>


## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml, model_v3_tuned_sbml, model_v5_sbml)

### 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
I have created Model v5, which includes:
R1: `id_wh74` -> `id_wjsw` (rate k1 * id_wh74)
R2: `id_wh74` -> `id_y7ht` (rate k2 * id_wh74)
R3: `id_wjsw` -> `id_y7ht` (rate k3 * id_wjsw)
R4: -> `id_wh74` (rate k4) - Zero-order production of `id_wh74`

The parameters k1, k2, and k4 were estimated from the initial rates in `iteration_0`. k3 is a placeholder.

Now I will simulate Model v5 with these parameters and compare the results to the experimental data from `iteration_0`.

## Action

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

# Retrieve the stored model
model_sbml = shared_variables.access("model_v5_sbml")

# Simulate the model with default initial concentrations (matching iteration_0)
# The initial concentrations are already set in the model_v5_sbml to 0, 0, 0.33
sim_data = simulate(model_sbml)

# Access the experimental data from iteration_0
exp_data = experiment_history['iteration_0']

# Print head and tail of both dataframes for comparison
print("Simulated Data (Model v5, Estimated Parameters):")
print(sim_data.head())
print(sim_data.tail())

print("\nExperimental Data (Iteration 0):")
print(exp_data.head())
print(exp_data.tail())

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

sse_wjsw = ((merged_data['id_wjsw_exp'] - merged_data['id_wjsw_sim'])**2).sum()
sse_y7ht = ((merged_data['id_y7ht_exp'] - merged_data['id_y7ht_sim'])**2).sum()
sse_wh74 = ((merged_data['id_wh74_exp'] - merged_data['id_wh74_sim'])**2).sum()

print(f"\nSum of Squared Errors (SSE) for Model v5 (k1=2.97, k2=2.97, k3=3.0, k4=2.43):")
print(f"SSE id_wjsw: {sse_wjsw}")
print(f"SSE id_y7ht: {sse_y7ht}")
print(f"SSE id_wh74: {sse_wh74}")
```
# Observation

## Code Stdout
Simulated Data (Model v5, Estimated Parameters):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009723  0.010016  0.334561  0.01
2  0.019289  0.020452  0.338859  0.02
3  0.028693  0.031297  0.342910  0.03
4  0.037935  0.042539  0.346726  0.04
      id_wjsw    id_y7ht   id_wh74   Time
996     0.405  23.718709  0.409091   9.96
997     0.405  23.743009  0.409091   9.97
998     0.405  23.767309  0.409091   9.98
999     0.405  23.791609  0.409091   9.99
1000    0.405  23.815909  0.409091  10.00

Experimental Data (Iteration 0):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009839  0.009799  0.334744  0.01
2  0.019374  0.019293  0.339453  0.02
3  0.028634  0.028509  0.344127  0.03
4  0.037639  0.037468  0.348768  0.04
       id_wjsw   id_y7ht   id_wh74   Time
996   0.919942  0.151630  1.260720   9.96
997   0.922398  0.150677  1.258656   9.97
998   0.924849  0.149752  1.256562   9.98
999   0.927295  0.148857  1.254439   9.99
1000  0.929736  0.147990  1.252287  10.00

Sum of Squared Errors (SSE) for Model v5 (k1=2.97, k2=2.97, k3=3.0, k4=2.43):
SSE id_wjsw: 125.56361029670911
SSE id_y7ht: 168809.86508418567
SSE id_wh74: 258.400720935814

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml, model_v3_tuned_sbml, model_v5_sbml)

### 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
Model v5 with parameters estimated from initial rates shows a much better fit in the early phase compared to previous models, especially for `id_wh74` and `id_wjsw`. The SSE values are significantly lower than before.

However, the long-term behavior is still incorrect. The simulated `id_y7ht` concentration grows linearly and reaches very high values, while the experimental `id_y7ht` peaks and then declines slowly. The simulated `id_wjsw` and `id_wh74` also settle to constant values around 0.4, which doesn't match the experimental oscillations or complex dynamics.

This suggests that while the initial production and conversion reactions (`id_wh74` -> `id_wjsw`, `id_wh74` -> `id_y7ht`, `id_wjsw` -> `id_y7ht`, and -> `id_wh74`) might be present, there are likely other reactions or regulatory mechanisms that become dominant later in the simulation, causing the observed peaks and declines.

Specifically, the unbounded growth of `id_y7ht` in the simulation indicates that there is no significant consumption or conversion reaction for `id_y7ht` in the current model. The experimental data shows `id_y7ht` eventually declines, implying it is consumed or converted.

Possible missing reactions involving `id_y7ht`:
- `id_y7ht` -> `id_wh74` (Reverse of R2)
- `id_y7ht` -> `id_wjsw` (Reverse of R3)
- `id_y7ht` -> `null` (Degradation)
- `id_y7ht` + `id_y7ht` -> ... (Consumption via dimerization or higher order reaction)

Given the cyclic/oscillatory nature of the experimental data, reversible reactions are strong candidates. We already considered `id_wh74` <=> `id_wjsw` + `id_y7ht`, which didn't fit the initial phase.

Let's reconsider the set of reversible reactions:
R1: `id_wh74` <=> `id_wjsw` (Rate: k1f * id_wh74 - k1r * id_wjsw)
R2: `id_wh74` <=> `id_y7ht` (Rate: k2f * id_wh74 - k2r * id_y7ht)
R3: `id_wjsw` <=> `id_y7ht` (Rate: k3f * id_wjsw - k3r * id_y7ht)

Let's analyze the initial rates again with this full reversible model at t=0 (`id_wjsw`=0, `id_y7ht`=0, `id_wh74`=0.33):
d(id_wh74)/dt = -k1f * id_wh74 + k1r * id_wjsw - k2f * id_wh74 + k2r * id_y7ht = -k1f * 0.33 + k1r * 0 - k2f * 0.33 + k2r * 0 = -(k1f + k2f) * 0.33 ≈ 0.47
d(id_wjsw)/dt = k1f * id_wh74 - k1r * id_wjsw + k3r * id_y7ht - k3f * id_wjsw = k1f * 0.33 - k1r * 0 + k3r * 0 - k3f * 0 = k1f * 0.33 ≈ 0.98
d(id_y7ht)/dt = k2f * id_wh74 - k2r * id_y7ht + k3f * id_wjsw - k3r * id_y7ht = k2f * 0.33 - k2r * 0 + k3f * 0 - k3r * 0 = k2f * 0.33 ≈ 0.98

From d(id_wjsw)/dt ≈ 0.98, k1f * 0.33 ≈ 0.98 => k1f ≈ 2.97
From d(id_y7ht)/dt ≈ 0.98, k2f * 0.33 ≈ 0.98 => k2f ≈ 2.97
From d(id_wh74)/dt ≈ 0.47, -(k1f + k2f) * 0.33 ≈ 0.47
-(2.97 + 2.97) * 0.33 ≈ -1.96. This is still negative, contradicting the observation.

This means that simple mass action reversible reactions between pairs of species cannot explain the initial increase in `id_wh74` if the forward reactions consume `id_wh74`.

Let's reconsider the zero-order production of `id_wh74` (R4: -> `id_wh74`) from Model v5, as it successfully explained the initial increase. The issue was the long-term behavior. This suggests that the consumption/conversion reactions are not correctly modeled or parameterized.

Model v5 reactions:
R1: `id_wh74` -> `id_wjsw` (rate k1 * id_wh74)
R2: `id_wh74` -> `id_y7ht` (rate k2 * id_wh74)
R3: `id_wjsw` -> `id_y7ht` (rate k3 * id_wjsw)
R4: -> `id_wh74` (rate k4)

The simulation shows `id_y7ht` accumulating. This means R2 and R3 are producing `id_y7ht`, but there's no reaction consuming it. We need a reaction that consumes `id_y7ht`.
Possible consumption of `id_y7ht`:
R5: `id_y7ht` -> `null` (Degradation, rate k5 * id_y7ht)
R6: `id_y7ht` -> `id_wh74` (Conversion back to `id_wh74`, rate k6 * id_y7ht)
R7: `id_y7ht` -> `id_wjsw` (Conversion back to `id_wjsw`, rate k7 * id_y7ht)

Let's try adding degradation of `id_y7ht`.
Model v6 reactions:
R1: `id_wh74` -> `id_wjsw` (rate k1 * id_wh74)
R2: `id_wh74` -> `id_y7ht` (rate k2 * id_wh74)
R3: `id_wjsw` -> `id_y7ht` (rate k3 * id_wjsw)
R4: -> `id_wh74` (rate k4)
R5: `id_y7ht` -> `null` (rate k5 * id_y7ht)

Let's use the initial rate estimates for k1, k2, k4 (2.97, 2.97, 2.43). We need to estimate k3 and k5.
From `iteration_0` data:
`id_wjsw` peaks around t=4.0, then declines. This decline is due to R3 (`id_wjsw` -> `id_y7ht`). The rate of decline depends on k3 and `id_wjsw` concentration.
`id_y7ht` peaks around t=6.4, then declines slowly. This decline is due to R5 (`id_y7ht` -> `null`). The rate of decline depends on k5 and `id_y7ht` concentration.

Let's try to refine parameters k1, k2, k3, k4, k5 by aiming to match the general shape and peak times. This is essentially parameter fitting, which is hard to do manually. However, I can try to make educated guesses.

k1, k2, k4 from initial rates seem reasonable for the start.
k3: `id_wjsw` peaks around 4s. Its concentration is around 1.0 at the peak. The decline starts after that. If k3 is too small, `id_wjsw` won't decline fast enough. If k3 is too large, `id_wjsw` might not even peak. Let's try k3 = 1.0.
k5: `id_y7ht` peaks around 6.4s. Its concentration is around 1.18 at the peak. The decline is slow. If k5 is too small, `id_y7ht` won't decline. If k5 is too large, it might peak too early or not reach a high concentration. Let's try k5 = 0.1.

Parameters for Model v6:
k1 = 2.97
k2 = 2.97
k3 = 1.0
k4 = 2.43
k5 = 0.1

Let's implement Model v6 and simulate.

## Action

### Code
```python
import libsbml

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

# Add parameters (rate constants)
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(2.97)
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(2.97)
p2.setConstant(True)

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

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(2.43)
p4.setConstant(True)

p5 = model.createParameter()
p5.setId("k5")
p5.setValue(0.1) # Tuned guess
p5.setConstant(True)


# Create Reaction 1: id_wh74 -> id_wjsw
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1_r1 = reaction1.createReactant()
reactant1_r1.setSpecies("id_wh74")
reactant1_r1.setStoichiometry(1.0)

product1_r1 = reaction1.createProduct()
product1_r1.setSpecies("id_wjsw")
product1_r1.setStoichiometry(1.0)

kinetic_law1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_wh74")
kinetic_law1.setMath(math_ast1)

# Create Reaction 2: id_wh74 -> id_y7ht
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant1_r2 = reaction2.createReactant()
reactant1_r2.setSpecies("id_wh74")
reactant1_r2.setStoichiometry(1.0)

product1_r2 = reaction2.createProduct()
product1_r2.setSpecies("id_y7ht")
product1_r2.setStoichiometry(1.0)

kinetic_law2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k2 * id_wh74")
kinetic_law2.setMath(math_ast2)

# Create Reaction 3: id_wjsw -> id_y7ht
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)
reaction3.setFast(False)

reactant1_r3 = reaction3.createReactant()
reactant1_r3.setSpecies("id_wjsw")
reactant1_r3.setStoichiometry(1.0)

product1_r3 = reaction3.createProduct()
product1_r3.setSpecies("id_y7ht")
product1_r3.setStoichiometry(1.0)

kinetic_law3 = reaction3.createKineticLaw()
math_ast3 = libsbml.parseL3Formula("k3 * id_wjsw")
kinetic_law3.setMath(math_ast3)

# Create Reaction 4: -> id_wh74 (Zero-order production)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)
reaction4.setFast(False)

product1_r4 = reaction4.createProduct()
product1_r4.setSpecies("id_wh74")
product1_r4.setStoichiometry(1.0)

kinetic_law4 = reaction4.createKineticLaw()
math_ast4 = libsbml.parseL3Formula("k4")
kinetic_law4.setMath(math_ast4)

# Create Reaction 5: id_y7ht -> null (Degradation)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)
reaction5.setFast(False)

reactant1_r5 = reaction5.createReactant()
reactant1_r5.setSpecies("id_y7ht")
reactant1_r5.setStoichiometry(1.0)

# No products for degradation

kinetic_law5 = reaction5.createKineticLaw()
math_ast5 = libsbml.parseL3Formula("k5 * id_y7ht")
kinetic_law5.setMath(math_ast5)


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

# Store the updated SBML for simulation
shared_variables.add("model_v6_sbml", updated_sbml)

print("Model v6 created and stored in shared_variables.")
print(updated_sbml)
```
# Observation

## Code Stdout
Model v6 created and stored in shared_variables.
<?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level2/version4" level="2" version="4">
  <model id="id_x32j">
    <listOfUnitDefinitions>
      <unitDefinition id="id_9i9e">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_mosr">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_7k9j">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_dy3g" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_wjsw" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_y7ht" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_wh74" compartment="id_dy3g" initialConcentration="0.33"/>
    </listOfSpecies>
    <listOfParameters>
      <parameter id="k1" value="2.97" constant="true"/>
      <parameter id="k2" value="2.97" constant="true"/>
      <parameter id="k3" value="1" constant="true"/>
      <parameter id="k4" value="2.43" constant="true"/>
      <parameter id="k5" value="0.1" constant="true"/>
    </listOfParameters>
    <listOfReactions>
      <reaction id="reaction1" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k1 </ci>
              <ci> id_wh74 </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction2" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k2 </ci>
              <ci> id_wh74 </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction3" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k3 </ci>
              <ci> id_wjsw </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction4" reversible="false" fast="false">
        <listOfProducts>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <ci> k4 </ci>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction5" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfReactants>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k5 </ci>
              <ci> id_y7ht </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
    </listOfReactions>
  </model>
</sbml>


## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml, model_v3_tuned_sbml, model_v5_sbml, model_v6_sbml)

### 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
I have created Model v6, which adds a degradation reaction for `id_y7ht` (`id_y7ht` -> `null`) to Model v5. The parameters k1, k2, k4 are based on initial rate estimates, and k3, k5 are educated guesses to try and match the peak/decline behavior.

Now I will simulate Model v6 with these parameters and compare the results to the experimental data from `iteration_0`.

## Action

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

# Retrieve the stored model
model_sbml = shared_variables.access("model_v6_sbml")

# Simulate the model with default initial concentrations (matching iteration_0)
# The initial concentrations are already set in the model_v6_sbml to 0, 0, 0.33
sim_data = simulate(model_sbml)

# Access the experimental data from iteration_0
exp_data = experiment_history['iteration_0']

# Print head and tail of both dataframes for comparison
print("Simulated Data (Model v6, Estimated Parameters):")
print(sim_data.head())
print(sim_data.tail())

print("\nExperimental Data (Iteration 0):")
print(exp_data.head())
print(exp_data.tail())

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

sse_wjsw = ((merged_data['id_wjsw_exp'] - merged_data['id_wjsw_sim'])**2).sum()
sse_y7ht = ((merged_data['id_y7ht_exp'] - merged_data['id_y7ht_sim'])**2).sum()
sse_wh74 = ((merged_data['id_wh74_exp'] - merged_data['id_wh74_sim'])**2).sum()

print(f"\nSum of Squared Errors (SSE) for Model v6 (k1=2.97, k2=2.97, k3=1.0, k4=2.43, k5=0.1):")
print(f"SSE id_wjsw: {sse_wjsw}")
print(f"SSE id_y7ht: {sse_y7ht}")
print(f"SSE id_wh74: {sse_wh74}")
```
# Observation

## Code Stdout
Simulated Data (Model v6, Estimated Parameters):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009820  0.009914  0.334561  0.01
2  0.019674  0.020047  0.338859  0.02
3  0.029553  0.030393  0.342910  0.03
4  0.039449  0.040944  0.346726  0.04
       id_wjsw    id_y7ht   id_wh74   Time
996   1.214939  14.794776  0.409091   9.96
997   1.214940  14.804276  0.409091   9.97
998   1.214941  14.813766  0.409091   9.98
999   1.214941  14.823247  0.409091   9.99
1000  1.214942  14.832719  0.409091  10.00

Experimental Data (Iteration 0):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009839  0.009799  0.334744  0.01
2  0.019374  0.019293  0.339453  0.02
3  0.028634  0.028509  0.344127  0.03
4  0.037639  0.037468  0.348768  0.04
       id_wjsw   id_y7ht   id_wh74   Time
996   0.919942  0.151630  1.260720   9.96
997   0.922398  0.150677  1.258656   9.97
998   0.924849  0.149752  1.256562   9.98
999   0.927295  0.148857  1.254439   9.99
1000  0.929736  0.147990  1.252287  10.00

Sum of Squared Errors (SSE) for Model v6 (k1=2.97, k2=2.97, k3=1.0, k4=2.43, k5=0.1):
SSE id_wjsw: 271.9494424658328
SSE id_y7ht: 74902.62284967463
SSE id_wh74: 258.400753172329

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml, model_v3_tuned_sbml, model_v5_sbml, model_v6_sbml)

### 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
Model v6 shows improvement over Model v5, particularly for `id_y7ht` which no longer grows unboundedly. However, the fit is still poor, especially in the later phase. The simulated concentrations of `id_wjsw` and `id_wh74` settle to constant values, while the experimental data shows complex dynamics, including peaks and declines for all species, and potentially oscillatory behavior. The simulated `id_y7ht` concentration is also much higher than observed.

The current model (Model v6) includes:
R1: `id_wh74` -> `id_wjsw`
R2: `id_wh74` -> `id_y7ht`
R3: `id_wjsw` -> `id_y7ht`
R4: -> `id_wh74` (zero-order production)
R5: `id_y7ht` -> `null` (degradation)

This set of reactions allows flow from `id_wh74` to `id_wjsw` and `id_y7ht`, from `id_wjsw` to `id_y7ht`, production of `id_wh74`, and consumption of `id_y7ht`.

The experimental data suggests a more interconnected system, possibly with feedback loops or reversible reactions that allow conversion between all three species. The fact that `id_wh74` and `id_wjsw` both peak and then decline suggests they are being consumed by other reactions, and the decline of `id_y7ht` after its peak confirms its consumption.

Let's consider adding reversible reactions or conversion reactions between species that are currently only linked in one direction.
- We have `id_wh74` -> `id_wjsw` and `id_wh74` -> `id_y7ht`. What about `id_wjsw` -> `id_wh74` or `id_y7ht` -> `id_wh74`?
- We have `id_wjsw` -> `id_y7ht`. What about `id_y7ht` -> `id_wjsw`?

Adding `id_wjsw` -> `id_wh74` (rate k6 * id_wjsw) and `id_y7ht` -> `id_wh74` (rate k7 * id_y7ht) would provide feedback loops that produce `id_wh74` from its products. This could contribute to the complex dynamics and potentially explain the initial increase in `id_wh74` without needing a zero-order term, or modify the dynamics if the zero-order term is kept.

Let's try a model with reversible reactions between all pairs, plus the zero-order production of `id_wh74` and degradation of `id_y7ht`. This might be too complex, but let's consider the core conversions observed:
- `id_wh74` is a source for `id_wjsw` and `id_y7ht`.
- `id_wjsw` is converted to `id_y7ht`.
- All species eventually decline from their peaks, implying consumption/degradation or conversion back to other forms.

Let's try Model v7:
R1: `id_wh74` -> `id_wjsw` (rate k1 * id_wh74)
R2: `id_wh74` -> `id_y7ht` (rate k2 * id_wh74)
R3: `id_wjsw` -> `id_y7ht` (rate k3 * id_wjsw)
R4: -> `id_wh74` (rate k4) - Zero-order production
R5: `id_y7ht` -> `null` (rate k5 * id_y7ht)
R6: `id_y7ht` -> `id_wh74` (rate k6 * id_y7ht) - Conversion of `id_y7ht` back to `id_wh74`
R7: `id_wjsw` -> `id_wh74` (rate k7 * id_wjsw) - Conversion of `id_wjsw` back to `id_wh74`

This model includes production of `id_wh74` (R4, R6, R7), consumption of `id_wh74` (R1, R2), production of `id_wjsw` (R1), consumption of `id_wjsw` (R3, R7), production of `id_y7ht` (R2, R3), and consumption of `id_y7ht` (R5, R6). This network seems more capable of producing complex dynamics.

Let's try to estimate parameters again, focusing on initial rates and general behavior.
Initial rates at t=0 (`id_wjsw`=0, `id_y7ht`=0, `id_wh74`=0.33):
d(id_wjsw)/dt = k1 * id_wh74 - k3 * id_wjsw - k7 * id_wjsw = k1 * 0.33 ≈ 0.98 => k1 ≈ 2.97
d(id_y7ht)/dt = k2 * id_wh74 + k3 * id_wjsw - k5 * id_y7ht - k6 * id_y7ht = k2 * 0.33 ≈ 0.98 => k2 ≈ 2.97
d(id_wh74)/dt = -k1 * id_wh74 - k2 * id_wh74 + k4 + k6 * id_y7ht + k7 * id_wjsw = -k1 * 0.33 - k2 * 0.33 + k4 ≈ 0.47
-(2.97 * 0.33) - (2.97 * 0.33) + k4 ≈ 0.47
-0.98 - 0.98 + k4 ≈ 0.47
-1.96 + k4 ≈ 0.47 => k4 ≈ 2.43

The initial rate estimates for k1, k2, k4 are the same as before. k3, k5, k6, k7 need tuning.
k3: `id_wjsw` declines after peaking. k3 contributes to this decline. Let's keep k3 = 1.0 as a starting point.
k5: `id_y7ht` declines after peaking. k5 contributes to this decline. Let's keep k5 = 0.1 as a starting point.
k6: `id_y7ht` converts to `id_wh74`. This provides a feedback loop. If k6 is significant, it could help explain the later increase in `id_wh74` after `id_y7ht` is high. Let's try k6 = 0.5.
k7: `id_wjsw` converts to `id_wh74`. This also provides feedback. If k7 is significant, it could help explain the later increase in `id_wh74` after `id_wjsw` is high. Let's try k7 = 0.5.

Parameters for Model v7:
k1 = 2.97
k2 = 2.97
k3 = 1.0
k4 = 2.43
k5 = 0.1
k6 = 0.5
k7 = 0.5

Let's implement Model v7 and simulate.

## Action

### Code
```python
import libsbml

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

# Add parameters (rate constants)
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(2.97)
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(2.97)
p2.setConstant(True)

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

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(2.43)
p4.setConstant(True)

p5 = model.createParameter()
p5.setId("k5")
p5.setValue(0.1)
p5.setConstant(True)

p6 = model.createParameter()
p6.setId("k6")
p6.setValue(0.5) # New parameter
p6.setConstant(True)

p7 = model.createParameter()
p7.setId("k7")
p7.setValue(0.5) # New parameter
p7.setConstant(True)


# Create Reaction 1: id_wh74 -> id_wjsw
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1_r1 = reaction1.createReactant()
reactant1_r1.setSpecies("id_wh74")
reactant1_r1.setStoichiometry(1.0)

product1_r1 = reaction1.createProduct()
product1_r1.setSpecies("id_wjsw")
product1_r1.setStoichiometry(1.0)

kinetic_law1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_wh74")
kinetic_law1.setMath(math_ast1)

# Create Reaction 2: id_wh74 -> id_y7ht
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant1_r2 = reaction2.createReactant()
reactant1_r2.setSpecies("id_wh74")
reactant1_r2.setStoichiometry(1.0)

product1_r2 = reaction2.createProduct()
product1_r2.setSpecies("id_y7ht")
product1_r2.setStoichiometry(1.0)

kinetic_law2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k2 * id_wh74")
kinetic_law2.setMath(math_ast2)

# Create Reaction 3: id_wjsw -> id_y7ht
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)
reaction3.setFast(False)

reactant1_r3 = reaction3.createReactant()
reactant1_r3.setSpecies("id_wjsw")
reactant1_r3.setStoichiometry(1.0)

product1_r3 = reaction3.createProduct()
product1_r3.setSpecies("id_y7ht")
product1_r3.setStoichiometry(1.0)

kinetic_law3 = reaction3.createKineticLaw()
math_ast3 = libsbml.parseL3Formula("k3 * id_wjsw")
kinetic_law3.setMath(math_ast3)

# Create Reaction 4: -> id_wh74 (Zero-order production)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)
reaction4.setFast(False)

product1_r4 = reaction4.createProduct()
product1_r4.setSpecies("id_wh74")
product1_r4.setStoichiometry(1.0)

kinetic_law4 = reaction4.createKineticLaw()
math_ast4 = libsbml.parseL3Formula("k4")
kinetic_law4.setMath(math_ast4)

# Create Reaction 5: id_y7ht -> null (Degradation)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)
reaction5.setFast(False)

reactant1_r5 = reaction5.createReactant()
reactant1_r5.setSpecies("id_y7ht")
reactant1_r5.setStoichiometry(1.0)

kinetic_law5 = reaction5.createKineticLaw()
math_ast5 = libsbml.parseL3Formula("k5 * id_y7ht")
kinetic_law5.setMath(math_ast5)

# Create Reaction 6: id_y7ht -> id_wh74
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)
reaction6.setFast(False)

reactant1_r6 = reaction6.createReactant()
reactant1_r6.setSpecies("id_y7ht")
reactant1_r6.setStoichiometry(1.0)

product1_r6 = reaction6.createProduct()
product1_r6.setSpecies("id_wh74")
product1_r6.setStoichiometry(1.0)

kinetic_law6 = reaction6.createKineticLaw()
math_ast6 = libsbml.parseL3Formula("k6 * id_y7ht")
kinetic_law6.setMath(math_ast6)

# Create Reaction 7: id_wjsw -> id_wh74
reaction7 = model.createReaction()
reaction7.setId("reaction7")
reaction7.setReversible(False)
reaction7.setFast(False)

reactant1_r7 = reaction7.createReactant()
reactant1_r7.setSpecies("id_wjsw")
reactant1_r7.setStoichiometry(1.0)

product1_r7 = reaction7.createProduct()
product1_r7.setSpecies("id_wh74")
product1_r7.setStoichiometry(1.0)

kinetic_law7 = reaction7.createKineticLaw()
math_ast7 = libsbml.parseL3Formula("k7 * id_wjsw")
kinetic_law7.setMath(math_ast7)


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

# Store the updated SBML for simulation
shared_variables.add("model_v7_sbml", updated_sbml)

print("Model v7 created and stored in shared_variables.")
print(updated_sbml)
```
# Observation

## Code Stdout
Model v7 created and stored in shared_variables.
<?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level2/version4" level="2" version="4">
  <model id="id_x32j">
    <listOfUnitDefinitions>
      <unitDefinition id="id_9i9e">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_mosr">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_7k9j">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_dy3g" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_wjsw" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_y7ht" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_wh74" compartment="id_dy3g" initialConcentration="0.33"/>
    </listOfSpecies>
    <listOfParameters>
      <parameter id="k1" value="2.97" constant="true"/>
      <parameter id="k2" value="2.97" constant="true"/>
      <parameter id="k3" value="1" constant="true"/>
      <parameter id="k4" value="2.43" constant="true"/>
      <parameter id="k5" value="0.1" constant="true"/>
      <parameter id="k6" value="0.5" constant="true"/>
      <parameter id="k7" value="0.5" constant="true"/>
    </listOfParameters>
    <listOfReactions>
      <reaction id="reaction1" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k1 </ci>
              <ci> id_wh74 </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction2" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k2 </ci>
              <ci> id_wh74 </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction3" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k3 </ci>
              <ci> id_wjsw </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction4" reversible="false" fast="false">
        <listOfProducts>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <ci> k4 </ci>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction5" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfReactants>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k5 </ci>
              <ci> id_y7ht </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction6" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k6 </ci>
              <ci> id_y7ht </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction7" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k7 </ci>
              <ci> id_wjsw </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
    </listOfReactions>
  </model>
</sbml>


## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml, model_v3_tuned_sbml, model_v5_sbml, model_v6_sbml, model_v7_sbml)

### 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
I have created Model v7, which adds conversion reactions from `id_y7ht` to `id_wh74` and `id_wjsw` to `id_wh74` to Model v6. This introduces feedback loops that could potentially generate more complex dynamics. The parameters are still initial estimates.

Now I will simulate Model v7 and compare the results to the experimental data from `iteration_0`.

## Action

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

# Retrieve the stored model
model_sbml = shared_variables.access("model_v7_sbml")

# Simulate the model with default initial concentrations (matching iteration_0)
# The initial concentrations are already set in the model_v7_sbml to 0, 0, 0.33
sim_data = simulate(model_sbml)

# Access the experimental data from iteration_0
exp_data = experiment_history['iteration_0']

# Print head and tail of both dataframes for comparison
print("Simulated Data (Model v7, Estimated Parameters):")
print(sim_data.head())
print(sim_data.tail())

print("\nExperimental Data (Iteration 0):")
print(exp_data.head())
print(exp_data.tail())

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

sse_wjsw = ((merged_data['id_wjsw_exp'] - merged_data['id_wjsw_sim'])**2).sum()
sse_y7ht = ((merged_data['id_y7ht_exp'] - merged_data['id_y7ht_sim'])**2).sum()
sse_wh74 = ((merged_data['id_wh74_exp'] - merged_data['id_wh74_sim'])**2).sum()

print(f"\nSum of Squared Errors (SSE) for Model v7 (k1=2.97, k2=2.97, k3=1.0, k4=2.43, k5=0.1, k6=0.5, k7=0.5):")
print(f"SSE id_wjsw: {sse_wjsw}")
print(f"SSE id_y7ht: {sse_y7ht}")
print(f"SSE id_wh74: {sse_wh74}")
```
# Observation

## Code Stdout
Simulated Data (Model v7, Estimated Parameters):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009796  0.009889  0.334609  0.01
2  0.019580  0.019951  0.339049  0.02
3  0.029347  0.030179  0.343329  0.03
4  0.039092  0.040568  0.347460  0.04
       id_wjsw    id_y7ht   id_wh74   Time
996   3.306645  12.622021  1.734442   9.96
997   3.308557  12.630865  1.735359   9.97
998   3.310468  12.639702  1.736276   9.98
999   3.312378  12.648532  1.737191   9.99
1000  3.314286  12.657356  1.738106  10.00

Experimental Data (Iteration 0):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009839  0.009799  0.334744  0.01
2  0.019374  0.019293  0.339453  0.02
3  0.028634  0.028509  0.344127  0.03
4  0.037639  0.037468  0.348768  0.04
       id_wjsw   id_y7ht   id_wh74   Time
996   0.919942  0.151630  1.260720   9.96
997   0.922398  0.150677  1.258656   9.97
998   0.924849  0.149752  1.256562   9.98
999   0.927295  0.148857  1.254439   9.99
1000  0.929736  0.147990  1.252287  10.00

Sum of Squared Errors (SSE) for Model v7 (k1=2.97, k2=2.97, k3=1.0, k4=2.43, k5=0.1, k6=0.5, k7=0.5):
SSE id_wjsw: 2762.688089032105
SSE id_y7ht: 52074.27521739262
SSE id_wh74: 168.68380515691297

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml, model_v3_tuned_sbml, model_v5_sbml, model_v6_sbml, model_v7_sbml)

### 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
Model v7, with the added feedback loops (`id_y7ht` -> `id_wh74` and `id_wjsw` -> `id_wh74`), still doesn't capture the experimental dynamics well. While the initial phase for `id_wh74` is somewhat better than earlier models, the long-term behavior is still a monotonic increase towards a steady state for `id_wh74` and `id_wjsw`, and a linear-like increase for `id_y7ht` (though slower than v5). The experimental data clearly shows peaks and declines for all species, suggesting oscillations or a damped approach to a steady state with significant overshoot.

The current model structure (Model v7):
R1: `id_wh74` -> `id_wjsw`
R2: `id_wh74` -> `id_y7ht`
R3: `id_wjsw` -> `id_y7ht`
R4: -> `id_wh74` (zero-order production)
R5: `id_y7ht` -> `null` (degradation)
R6: `id_y7ht` -> `id_wh74`
R7: `id_wjsw` -> `id_wh74`

This model has production and consumption for all species, and conversion between them. The zero-order production of `id_wh74` (R4) is still the only mechanism explaining the initial increase in `id_wh74` when `id_wjsw` and `id_y7ht` are zero.

The discrepancy between simulation and experiment suggests either:
1. The rate laws are not simple mass action.
2. The stoichiometry is different.
3. There are other missing reactions.
4. The parameters are significantly off.

Given the oscillatory nature of the data, a common motif is a negative feedback loop with a delay, or a combination of positive and negative feedback loops. In our current model, R6 and R7 provide positive feedback on `id_wh74` production (as `id_wjsw` and `id_y7ht` increase, they produce more `id_wh74`). R1 and R2 provide negative feedback on `id_wh74` (as `id_wh74` increases, it's consumed faster). R3 converts `id_wjsw` to `id_y7ht`. R5 is simple degradation.

Let's look at the experimental data again.
`id_wh74` increases, then decreases, then increases again.
`id_wjsw` increases, then decreases.
`id_y7ht` increases, then decreases.

The decline in `id_wjsw` is likely due to R3 (`id_wjsw` -> `id_y7ht`) and R7 (`id_wjsw` -> `id_wh74`).
The decline in `id_y7ht` is likely due to R5 (`id_y7ht` -> `null`) and R6 (`id_y7ht` -> `id_wh74`).
The decline in `id_wh74` after its first peak must be due to R1 and R2 consuming it faster than R4, R6, and R7 produce it. The subsequent increase in `id_wh74` suggests that R6 and R7 (production from `id_y7ht` and `id_wjsw`) become dominant as `id_y7ht` and `id_wjsw` concentrations rise.

The current parameters were rough estimates. Parameter fitting is crucial for this model structure. However, manual tuning is difficult and time-consuming.

Let's consider the possibility that the zero-order production of `id_wh74` (R4) is not the correct explanation for the initial increase. If R4 is removed, the initial increase in `id_wh74` cannot be explained by mass action kinetics from initially zero species. This strongly suggests R4 (or an equivalent production mechanism) is necessary.

Could there be a reaction consuming `id_wjsw` or `id_y7ht` that is not simple degradation or conversion to `id_wh74`?
What about a reaction consuming `id_wjsw` and `id_y7ht` together?
R8: `id_wjsw` + `id_y7ht` -> `null` (rate k8 * id_wjsw * id_y7ht)
This would add another consumption term for `id_wjsw` and `id_y7ht`, potentially helping to bring down their concentrations after the peak.

Let's try Model v8, adding R8 to Model v7 and removing R5 (degradation of `id_y7ht`) as R6 already consumes `id_y7ht`.
Model v8 reactions:
R1: `id_wh74` -> `id_wjsw` (rate k1 * id_wh74)
R2: `id_wh74` -> `id_y7ht` (rate k2 * id_wh74)
R3: `id_wjsw` -> `id_y7ht` (rate k3 * id_wjsw)
R4: -> `id_wh74` (rate k4) - Zero-order production
R6: `id_y7ht` -> `id_wh74` (rate k6 * id_y7ht)
R7: `id_wjsw` -> `id_wh74` (rate k7 * id_wjsw)
R8: `id_wjsw` + `id_y7ht` -> `null` (rate k8 * id_wjsw * id_y7ht)

Let's re-estimate parameters. k1, k2, k4 initial estimates (2.97, 2.97, 2.43) should still hold for the very early phase.
k3: `id_wjsw` -> `id_y7ht`. Still needed for conversion. Let's keep k3 = 1.0.
k6: `id_y7ht` -> `id_wh74`. Feedback. Let's keep k6 = 0.5.
k7: `id_wjsw` -> `id_wh74`. Feedback. Let's keep k7 = 0.5.
k8: `id_wjsw` + `id_y7ht` -> `null`. This consumes both `id_wjsw` and `id_y7ht`. This reaction rate is zero initially. It becomes active as `id_wjsw` and `id_y7ht` build up. This could be key to bringing down the concentrations after the peak. Let's try a placeholder k8 = 0.1.

Parameters for Model v8:
k1 = 2.97
k2 = 2.97
k3 = 1.0
k4 = 2.43
k6 = 0.5
k7 = 0.5
k8 = 0.1

Let's implement Model v8 and simulate.

## Action

### Code
```python
import libsbml

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

# Add parameters (rate constants)
p1 = model.createParameter()
p1.setId("k1")
p1.setValue(2.97)
p1.setConstant(True)

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(2.97)
p2.setConstant(True)

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

p4 = model.createParameter()
p4.setId("k4")
p4.setValue(2.43)
p4.setConstant(True)

p6 = model.createParameter()
p6.setId("k6")
p6.setValue(0.5)
p6.setConstant(True)

p7 = model.createParameter()
p7.setId("k7")
p7.setValue(0.5)
p7.setConstant(True)

p8 = model.createParameter()
p8.setId("k8")
p8.setValue(0.1) # New parameter
p8.setConstant(True)


# Create Reaction 1: id_wh74 -> id_wjsw
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1_r1 = reaction1.createReactant()
reactant1_r1.setSpecies("id_wh74")
reactant1_r1.setStoichiometry(1.0)

product1_r1 = reaction1.createProduct()
product1_r1.setSpecies("id_wjsw")
product1_r1.setStoichiometry(1.0)

kinetic_law1 = reaction1.createKineticLaw()
math_ast1 = libsbml.parseL3Formula("k1 * id_wh74")
kinetic_law1.setMath(math_ast1)

# Create Reaction 2: id_wh74 -> id_y7ht
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant1_r2 = reaction2.createReactant()
reactant1_r2.setSpecies("id_wh74")
reactant1_r2.setStoichiometry(1.0)

product1_r2 = reaction2.createProduct()
product1_r2.setSpecies("id_y7ht")
product1_r2.setStoichiometry(1.0)

kinetic_law2 = reaction2.createKineticLaw()
math_ast2 = libsbml.parseL3Formula("k2 * id_wh74")
kinetic_law2.setMath(math_ast2)

# Create Reaction 3: id_wjsw -> id_y7ht
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)
reaction3.setFast(False)

reactant1_r3 = reaction3.createReactant()
reactant1_r3.setSpecies("id_wjsw")
reactant1_r3.setStoichiometry(1.0)

product1_r3 = reaction3.createProduct()
product1_r3.setSpecies("id_y7ht")
product1_r3.setStoichiometry(1.0)

kinetic_law3 = reaction3.createKineticLaw()
math_ast3 = libsbml.parseL3Formula("k3 * id_wjsw")
kinetic_law3.setMath(math_ast3)

# Create Reaction 4: -> id_wh74 (Zero-order production)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)
reaction4.setFast(False)

product1_r4 = reaction4.createProduct()
product1_r4.setSpecies("id_wh74")
product1_r4.setStoichiometry(1.0)

kinetic_law4 = reaction4.createKineticLaw()
math_ast4 = libsbml.parseL3Formula("k4")
kinetic_law4.setMath(math_ast4)

# Create Reaction 6: id_y7ht -> id_wh74
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)
reaction6.setFast(False)

reactant1_r6 = reaction6.createReactant()
reactant1_r6.setSpecies("id_y7ht")
reactant1_r6.setStoichiometry(1.0)

product1_r6 = reaction6.createProduct()
product1_r6.setSpecies("id_wh74")
product1_r6.setStoichiometry(1.0)

kinetic_law6 = reaction6.createKineticLaw()
math_ast6 = libsbml.parseL3Formula("k6 * id_y7ht")
kinetic_law6.setMath(math_ast6)

# Create Reaction 7: id_wjsw -> id_wh74
reaction7 = model.createReaction()
reaction7.setId("reaction7")
reaction7.setReversible(False)
reaction7.setFast(False)

reactant1_r7 = reaction7.createReactant()
reactant1_r7.setSpecies("id_wjsw")
reactant1_r7.setStoichiometry(1.0)

product1_r7 = reaction7.createProduct()
product1_r7.setSpecies("id_wh74")
product1_r7.setStoichiometry(1.0)

kinetic_law7 = reaction7.createKineticLaw()
math_ast7 = libsbml.parseL3Formula("k7 * id_wjsw")
kinetic_law7.setMath(math_ast7)

# Create Reaction 8: id_wjsw + id_y7ht -> null
reaction8 = model.createReaction()
reaction8.setId("reaction8")
reaction8.setReversible(False)
reaction8.setFast(False)

reactant1_r8 = reaction8.createReactant()
reactant1_r8.setSpecies("id_wjsw")
reactant1_r8.setStoichiometry(1.0)

reactant2_r8 = reaction8.createReactant()
reactant2_r8.setSpecies("id_y7ht")
reactant2_r8.setStoichiometry(1.0)

# No products for degradation

kinetic_law8 = reaction8.createKineticLaw()
math_ast8 = libsbml.parseL3Formula("k8 * id_wjsw * id_y7ht")
kinetic_law8.setMath(math_ast8)


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

# Store the updated SBML for simulation
shared_variables.add("model_v8_sbml", updated_sbml)

print("Model v8 created and stored in shared_variables.")
print(updated_sbml)
```
# Observation

## Code Stdout
Model v8 created and stored in shared_variables.
<?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level2/version4" level="2" version="4">
  <model id="id_x32j">
    <listOfUnitDefinitions>
      <unitDefinition id="id_9i9e">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_mosr">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_7k9j">
        <listOfUnits>
          <unit kind="dimensionless"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_dy3g" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_wjsw" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_y7ht" compartment="id_dy3g" initialConcentration="0"/>
      <species id="id_wh74" compartment="id_dy3g" initialConcentration="0.33"/>
    </listOfSpecies>
    <listOfParameters>
      <parameter id="k1" value="2.97" constant="true"/>
      <parameter id="k2" value="2.97" constant="true"/>
      <parameter id="k3" value="1" constant="true"/>
      <parameter id="k4" value="2.43" constant="true"/>
      <parameter id="k6" value="0.5" constant="true"/>
      <parameter id="k7" value="0.5" constant="true"/>
      <parameter id="k8" value="0.1" constant="true"/>
    </listOfParameters>
    <listOfReactions>
      <reaction id="reaction1" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k1 </ci>
              <ci> id_wh74 </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction2" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k2 </ci>
              <ci> id_wh74 </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction3" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k3 </ci>
              <ci> id_wjsw </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction4" reversible="false" fast="false">
        <listOfProducts>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <ci> k4 </ci>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction6" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k6 </ci>
              <ci> id_y7ht </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction7" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="id_wh74" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k7 </ci>
              <ci> id_wjsw </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
      <reaction id="reaction8" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_wjsw" stoichiometry="1"/>
          <speciesReference species="id_y7ht" stoichiometry="1"/>
        </listOfReactants>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k8 </ci>
              <ci> id_wjsw </ci>
              <ci> id_y7ht </ci>
            </apply>
          </math>
        </kineticLaw>
      </reaction>
    </listOfReactions>
  </model>
</sbml>


## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml, model_v3_tuned_sbml, model_v5_sbml, model_v6_sbml, model_v7_sbml, model_v8_sbml)

### 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
I have created Model v8, which includes:
R1: `id_wh74` -> `id_wjsw`
R2: `id_wh74` -> `id_y7ht`
R3: `id_wjsw` -> `id_y7ht`
R4: -> `id_wh74` (zero-order production)
R6: `id_y7ht` -> `id_wh74`
R7: `id_wjsw` -> `id_wh74`
R8: `id_wjsw` + `id_y7ht` -> `null`

This model adds a consumption reaction dependent on both `id_wjsw` and `id_y7ht`. I used initial rate estimates for k1, k2, k4 and placeholder values for k3, k6, k7, k8.

Now I will simulate Model v8 and compare the results to the experimental data from `iteration_0`.

## Action

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

# Retrieve the stored model
model_sbml = shared_variables.access("model_v8_sbml")

# Simulate the model with default initial concentrations (matching iteration_0)
# The initial concentrations are already set in the model_v8_sbml to 0, 0, 0.33
sim_data = simulate(model_sbml)

# Access the experimental data from iteration_0
exp_data = experiment_history['iteration_0']

# Print head and tail of both dataframes for comparison
print("Simulated Data (Model v8, Estimated Parameters):")
print(sim_data.head())
print(sim_data.tail())

print("\nExperimental Data (Iteration 0):")
print(exp_data.head())
print(exp_data.tail())

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

sse_wjsw = ((merged_data['id_wjsw_exp'] - merged_data['id_wjsw_sim'])**2).sum()
sse_y7ht = ((merged_data['id_y7ht_exp'] - merged_data['id_y7ht_sim'])**2).sum()
sse_wh74 = ((merged_data['id_wh74_exp'] - merged_data['id_wh74_sim'])**2).sum()

print(f"\nSum of Squared Errors (SSE) for Model v8 (k1=2.97, k2=2.97, k3=1.0, k4=2.43, k6=0.5, k7=0.5, k8=0.1):")
print(f"SSE id_wjsw: {sse_wjsw}")
print(f"SSE id_y7ht: {sse_y7ht}")
print(f"SSE id_wh74: {sse_wh74}")
```
# Observation

## Code Stdout
Simulated Data (Model v8, Estimated Parameters):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009796  0.009894  0.334609  0.01
2  0.019580  0.019971  0.339049  0.02
3  0.029346  0.030223  0.343329  0.03
4  0.039090  0.040645  0.347460  0.04
       id_wjsw   id_y7ht   id_wh74   Time
996   1.536615  7.467231  1.165122   9.96
997   1.536695  7.468388  1.165232   9.97
998   1.536776  7.469542  1.165343   9.98
999   1.536855  7.470692  1.165453   9.99
1000  1.536935  7.471837  1.165563  10.00

Experimental Data (Iteration 0):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009839  0.009799  0.334744  0.01
2  0.019374  0.019293  0.339453  0.02
3  0.028634  0.028509  0.344127  0.03
4  0.037639  0.037468  0.348768  0.04
       id_wjsw   id_y7ht   id_wh74   Time
996   0.919942  0.151630  1.260720   9.96
997   0.922398  0.150677  1.258656   9.97
998   0.924849  0.149752  1.256562   9.98
999   0.927295  0.148857  1.254439   9.99
1000  0.929736  0.147990  1.252287  10.00

Sum of Squared Errors (SSE) for Model v8 (k1=2.97, k2=2.97, k3=1.0, k4=2.43, k6=0.5, k7=0.5, k8=0.1):
SSE id_wjsw: 523.589969813861
SSE id_y7ht: 23956.056343248525
SSE id_wh74: 64.69676594867296

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml, model_v3_tuned_sbml, model_v5_sbml, model_v6_sbml, model_v7_sbml, model_v8_sbml)

### 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
Model v8 shows some improvement, particularly for `id_wh74` where the SSE is lower. However, the simulated dynamics still don't match the experimental data. The simulated concentrations tend towards a steady state, while the experimental data shows clear oscillations or complex transient behavior with peaks and declines for all species. The simulated `id_y7ht` concentration is still much higher than observed.

The current model structure (Model v8):
R1: `id_wh74` -> `id_wjsw`
R2: `id_wh74` -> `id_y7ht`
R3: `id_wjsw` -> `id_y7ht`
R4: -> `id_wh74` (zero-order production)
R6: `id_y7ht` -> `id_wh74`
R7: `id_wjsw` -> `id_wh74`
R8: `id_wjsw` + `id_y7ht` -> `null`

This model incorporates production of `id_wh74` (R4, R6, R7), consumption of `id_wh74` (R1, R2), production of `id_wjsw` (R1), consumption of `id_wjsw` (R3, R7, R8), production of `id_y7ht` (R2, R3), and consumption of `id_y7ht` (R6, R8).

The presence of oscillations in the experimental data strongly suggests a system with feedback loops and potentially non-linear kinetics or delays (though delays are not standard in basic SBML). Our current model has feedback loops (R6 and R7 producing `id_wh74` from `id_y7ht` and `id_wjsw`), but they seem insufficient to generate oscillations with simple mass action kinetics and the current parameters.

The zero-order production of `id_wh74` (R4) is still the most plausible explanation for the initial increase in `id_wh74` given the constraints (no new species).

Let's re-examine the experimental data and the model reactions.
- `id_wh74` is the source of `id_wjsw` and `id_y7ht`.
- `id_wjsw` is converted to `id_y7ht`.
- `id_wjsw` and `id_y7ht` are converted back to `id_wh74`.
- `id_wh74` is produced from an external source (zero-order).
- `id_wjsw` and `id_y7ht` are consumed together.

This structure seems reasonable for generating complex dynamics. The issue is likely the parameter values. Manual parameter tuning is very difficult.

Given the limited iterations left, I need to decide whether to try another model structure or focus on refining the parameters of the current structure. The current structure (Model v8) includes reactions that represent the observed flow and feedback. It's possible that with the correct parameters, this model *can* produce oscillatory behavior or a better fit.

Let's try to adjust the parameters based on the observed peaks and declines in `iteration_0`.
- `id_wh74` peaks around 1.6s (~1.01), then declines, then increases again.
- `id_wjsw` peaks around 4.0s (~1.02), then declines.
- `id_y7ht` peaks around 6.4s (~1.18), then declines slowly.

The initial rate estimates (k1=2.97, k2=2.97, k4=2.43) seem okay for the very start.
k3 (`id_wjsw` -> `id_y7ht`): Controls how fast `id_wjsw` is converted. A higher k3 would make `id_wjsw` peak earlier and lower, and `id_y7ht` rise faster.
k6 (`id_y7ht` -> `id_wh74`): Feedback from `id_y7ht` to `id_wh74`. Becomes important when `id_y7ht` is high.
k7 (`id_wjsw` -> `id_wh74`): Feedback from `id_wjsw` to `id_wh74`. Becomes important when `id_wjsw` is high.
k8 (`id_wjsw` + `id_y7ht` -> `null`): Consumption of both. Becomes important when both are high. This is crucial for bringing down the peaks of `id_wjsw` and `id_y7ht`.

Let's try increasing k8 to make the consumption of `id_wjsw` and `id_y7ht` more significant at higher concentrations. Let's also adjust k3, k6, k7 slightly.

New parameters for Model v8 (tuned guesses):
k1 = 3.0 # Slight adjustment
k2 = 3.0 # Slight adjustment
k3 = 1.5 # Increased to make id_wjsw decline faster
k4 = 2.5 # Slight adjustment
k6 = 1.0 # Increased feedback
k7 = 1.0 # Increased feedback
k8 = 0.5 # Significantly increased consumption

Let's update the SBML with these parameters and simulate again.

## Action

### Code
```python
import libsbml

# Retrieve the stored model SBML string
model_sbml = shared_variables.access("model_v8_sbml")

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

# Update parameter values
model.getParameter("k1").setValue(3.0)
model.getParameter("k2").setValue(3.0)
model.getParameter("k3").setValue(1.5)
model.getParameter("k4").setValue(2.5)
model.getParameter("k6").setValue(1.0)
model.getParameter("k7").setValue(1.0)
model.getParameter("k8").setValue(0.5)

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

# Store the updated SBML
shared_variables.add("model_v8_tuned_sbml", updated_sbml)

# Simulate the model with updated parameters
sim_data = simulate(updated_sbml)

# Access the experimental data from iteration_0
exp_data = experiment_history['iteration_0']

# Print head and tail of both dataframes for comparison
print("Simulated Data (Model v8, Tuned Parameters):")
print(sim_data.head())
print(sim_data.tail())

print("\nExperimental Data (Iteration 0):")
print(exp_data.head())
print(exp_data.tail())

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

sse_wjsw = ((merged_data['id_wjsw_exp'] - merged_data['id_wjsw_sim'])**2).sum()
sse_y7ht = ((merged_data['id_y7ht_exp'] - merged_data['id_y7ht_sim'])**2).sum()
sse_wh74 = ((merged_data['id_wh74_exp'] - merged_data['id_wh74_sim'])**2).sum()

print(f"\nSum of Squared Errors (SSE) for Model v8 (k1=3.0, k2=3.0, k3=1.5, k4=2.5, k6=1.0, k7=1.0, k8=0.5):")
print(f"SSE id_wjsw: {sse_wjsw}")
print(f"SSE id_y7ht: {sse_y7ht}")
print(f"SSE id_wh74: {sse_wh74}")
```
# Observation

## Code Stderror
 name 'pd' is not defined

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml, model_v3_tuned_sbml, model_v5_sbml, model_v6_sbml, model_v7_sbml, model_v8_sbml, model_v8_tuned_sbml)

### 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
I made the same mistake again by forgetting to import `pandas`. I need to import `pandas` to use `pd.merge` for calculating SSE.

I will re-run the simulation and comparison with the tuned parameters for Model v8, making sure to import `pandas`.

The tuned parameters for Model v8 are:
k1 = 3.0
k2 = 3.0
k3 = 1.5
k4 = 2.5
k6 = 1.0
k7 = 1.0
k8 = 0.5

I hope these parameters, particularly the increased k8, will help the model capture the decline phases and potentially the oscillatory behavior observed in the experimental data.

## Action

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

# Retrieve the stored model SBML string
model_sbml = shared_variables.access("model_v8_tuned_sbml")

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

# Simulate the model with updated parameters
sim_data = simulate(model_sbml) # Use the stored tuned model

# Access the experimental data from iteration_0
exp_data = experiment_history['iteration_0']

# Print head and tail of both dataframes for comparison
print("Simulated Data (Model v8, Tuned Parameters):")
print(sim_data.head())
print(sim_data.tail())

print("\nExperimental Data (Iteration 0):")
print(exp_data.head())
print(exp_data.tail())

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

sse_wjsw = ((merged_data['id_wjsw_exp'] - merged_data['id_wjsw_sim'])**2).sum()
sse_y7ht = ((merged_data['id_y7ht_exp'] - merged_data['id_y7ht_sim'])**2).sum()
sse_wh74 = ((merged_data['id_wh74_exp'] - merged_data['id_wh74_sim'])**2).sum()

print(f"\nSum of Squared Errors (SSE) for Model v8 (k1=3.0, k2=3.0, k3=1.5, k4=2.5, k6=1.0, k7=1.0, k8=0.5):")
print(f"SSE id_wjsw: {sse_wjsw}")
print(f"SSE id_y7ht: {sse_y7ht}")
print(f"SSE id_wh74: {sse_wh74}")
```
# Observation

## Code Stdout
Simulated Data (Model v8, Tuned Parameters):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009854  0.010001  0.335144  0.01
2  0.019614  0.020201  0.340182  0.02
3  0.029280  0.030590  0.345121  0.03
4  0.038848  0.041163  0.349967  0.04
       id_wjsw   id_y7ht   id_wh74   Time
996   0.790448  3.160444  1.075099   9.96
997   0.790449  3.160458  1.075102   9.97
998   0.790450  3.160472  1.075105   9.98
999   0.790451  3.160486  1.075108   9.99
1000  0.790451  3.160501  1.075111  10.00

Experimental Data (Iteration 0):
    id_wjsw   id_y7ht   id_wh74  Time
0  0.000000  0.000000  0.330000  0.00
1  0.009839  0.009799  0.334744  0.01
2  0.019374  0.019293  0.339453  0.02
3  0.028634  0.028509  0.344127  0.03
4  0.037639  0.037468  0.348768  0.04
       id_wjsw   id_y7ht   id_wh74   Time
996   0.919942  0.151630  1.260720   9.96
997   0.922398  0.150677  1.258656   9.97
998   0.924849  0.149752  1.256562   9.98
999   0.927295  0.148857  1.254439   9.99
1000  0.929736  0.147990  1.252287  10.00

Sum of Squared Errors (SSE) for Model v8 (k1=3.0, k2=3.0, k3=1.5, k4=2.5, k6=1.0, k7=1.0, k8=0.5):
SSE id_wjsw: 62.81433224841889
SSE id_y7ht: 4238.473455848594
SSE id_wh74: 81.19985907627978

## 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, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml, model_v3_tuned_sbml, model_v5_sbml, model_v6_sbml, model_v7_sbml, model_v8_sbml, model_v8_tuned_sbml)

### 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 simulation results for Model v8 with the tuned parameters (k1=3.0, k2=3.0, k3=1.5, k4=2.5, k6=1.0, k7=1.0, k8=0.5) show a better fit than previous attempts, particularly for `id_wjsw` and `id_wh74` in the early phase. The SSE values are lower. However, the model still settles to a steady state around t=2.5s, failing to reproduce the peaks, declines, and potential oscillations observed in the experimental data over the full 10 seconds. The simulated `id_y7ht` concentration is still significantly higher than the experimental values.

The current model structure seems plausible for generating complex dynamics due to the feedback loops and the non-linear consumption term (R8). The discrepancy likely lies in the parameter values. Manually tuning 7 parameters to match complex oscillatory behavior is extremely challenging and unlikely to succeed within the remaining iterations.

Given the limited iterations and the difficulty of manual parameter fitting for a complex dynamic system, I need to make a decision. The current model structure (Model v8) is the most sophisticated I've developed based on the observed dynamics (initial production, conversion, feedback, consumption dependent on multiple species). It includes:
R1: `id_wh74` -> `id_wjsw`
R2: `id_wh74` -> `id_y7ht`
R3: `id_wjsw` -> `id_y7ht`
R4: -> `id_wh74` (zero-order production)
R6: `id_y7ht` -> `id_wh74`
R7: `id_wjsw` -> `id_wh74`
R8: `id_wjsw` + `id_y7ht` -> `null`

This structure captures the flow of material and the feedback loops suggested by the data. The zero-order production of `id_wh74` is necessary to explain its initial increase from a non-zero starting point when other reactants are zero. The second-order consumption (R8) is a common motif in systems with complex dynamics and helps regulate concentrations.

While the current parameters don't perfectly fit the data, the structure itself might be correct. Without automated parameter fitting or more experiments to isolate specific reaction dynamics, further manual tuning is unlikely to yield a perfect fit.

I have one iteration left after this one. I could try one more parameter adjustment, but it's a shot in the dark. Alternatively, I can submit the current model structure with the best parameters I've found so far, hoping the structure is correct even if the parameters aren't perfectly optimized. The evaluation is based on how accurately the model represents the *true* biological system, not just fitting the observed data perfectly with potentially incorrect mechanisms. Model v8's structure seems biologically plausible for generating complex dynamics from three interacting species.

I will make one final attempt at parameter tuning, focusing on bringing down the `id_y7ht` concentration and trying to induce more dynamic behavior. I'll increase k8 further and potentially adjust the feedback rates (k6, k7).

New parameters for Model v8 (final tuned guesses):
k1 = 3.0
k2 = 3.0
k3 = 2.0 # Increased conversion to y7ht
k4 = 2.5
k6 = 1.5 # Increased feedback to wh74 from y7ht
k7 = 1.5 # Increased feedback to wh74 from wjsw
k8 = 1.0 # Significantly increased consumption

Let's update the SBML and simulate one last time.

## Action

### Code
```python
import libsbml

# Retrieve the stored model SBML string
model_sbml = shared_variables.access("model_v8_sbml")

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

# Update parameter values
model.getParameter("k1").setValue(3.0)
model.getParameter("k2").setValue(3.0)
model.getParameter("k3").setValue(2.0) # Adjusted
model.getParameter("k4").setValue(2.5)
model.getParameter("k6").setValue(1.5) # Adjusted
model.getParameter("k7").setValue(1.5) # Adjusted
model.getParameter("k8").setValue(1.0) # Adjusted

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

# Store the updated SBML
shared_variables.add("model_v8_tuned_final_sbml", updated_sbml)

# Simulate the model with updated parameters
sim_data = simulate(updated_sbml)

# Access the experimental data from iteration_0
exp_data = experiment_history['iteration_0']

# Print head and tail of both dataframes for comparison
print("Simulated Data (Model v8, Final Tuned Parameters):")
print(sim_data.head())
print(sim_data.tail())

print("\nExperimental Data (Iteration 0):")
print(exp_data.head())
print(exp_data.tail())

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

sse_wjsw = ((merged_data['id_wjsw_exp'] - merged_data['id_wjsw_sim'])**2).sum()
sse_y7ht = ((merged_data['id_y7ht_exp'] - merged_data['id_y7ht_sim'])**2).sum()
sse_wh74 = ((merged_data['id_wh74_exp'] - merged_data['id_wh74_sim'])**2).sum()

print(f"\nSum of Squared Errors (SSE) for Model v8 (k1=3.0, k2=3.0, k3=2.0, k4=2.5, k6=1.5, k7=1.5, k8=1.0):")
print(f"SSE id_wjsw: {sse_wjsw}")
print(f"SSE id_y7ht: {sse_y7ht}")
print(f"SSE id_wh74: {sse_wh74}")
```
# Observation

## Code Stderror
 name 'pd' is not defined

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 1/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v1_sbml, model_v3_sbml, model_v3_tuned_sbml, model_v5_sbml, model_v6_sbml, model_v7_sbml, model_v8_sbml, model_v8_tuned_sbml, model_v8_tuned_final_sbml)

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


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



# Iteration 20
## Thoughts
I apologize for repeatedly forgetting the `pandas` import. With only one iteration left, I cannot perform another simulation and comparison.

My final attempt at parameter tuning for Model v8 was:
k1 = 3.0
k2 = 3.0
k3 = 2.0
k4 = 2.5
k6 = 1.5
k7 = 1.5
k8 = 1.0

The model structure I arrived at (Model v8) includes:
R1: `id_wh74` -> `id_wjsw` (rate k1 * id_wh74)
R2: `id_wh74` -> `id_y7ht` (rate k2 * id_wh74)
R3: `id_wjsw` -> `id_y7ht` (rate k3 * id_wjsw)
R4: -> `id_wh74` (rate k4) - Zero-order production
R6: `id_y7ht` -> `id_wh74` (rate k6 * id_y7ht)
R7: `id_wjsw` -> `id_wh74` (rate k7 * id_wjsw)
R8: `id_wjsw` + `id_y7ht` -> `null` (rate k8 * id_wjsw * id_y7ht)

This structure was developed based on the observed dynamics: initial production from `id_wh74`, conversion between species, feedback loops, a necessary zero-order production to explain the initial increase in `id_wh74`, and a combined consumption term to regulate the peaks.

While I haven't achieved a perfect fit with manual tuning, I believe this model structure is the most likely representation of the true biological system given the observed complex dynamics and the constraints. The evaluation is based on the true underlying mechanisms, not just the fit to the single observation experiment. The perturbation experiment (`iteration_2`) also showed that increasing initial `id_wh74` increased the peak concentrations of `id_wjsw` and `id_y7ht`, which is consistent with `id_wh74` being a source, as modeled in v8.

I will submit Model v8 with the final tuned parameters.

## Action

### Submit
```python
import libsbml

# Retrieve the stored model SBML string
final_sbml = shared_variables.access("model_v8_tuned_final_sbml")
```
