
                # 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_wyxd">
    <listOfUnitDefinitions>
      <unitDefinition id="id_g6d6">
        <listOfUnits>
          <unit kind="litre" exponent="1" scale="-3" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_6gyg">
        <listOfUnits>
          <unit kind="item" exponent="1" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_a6c1" spatialDimensions="3" size="1" constant="true"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_ri7q" compartment="id_a6c1" initialConcentration="100" boundaryCondition="false" constant="false"/>
      <species id="id_nzce" compartment="id_a6c1" initialConcentration="10" boundaryCondition="false" constant="false"/>
      <species id="id_jz57" compartment="id_a6c1" initialConcentration="75" boundaryCondition="false" constant="false"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

                Format your response according to the instructions in the system message.
                
## Thoughts
I'm investigating a biological system with three species: id_ri7q, id_nzce, and id_jz57. The SBML model provided is incomplete - it defines the species but doesn't include any reactions between them. My goal is to discover the missing reactions.

First, I need to observe the default behavior of the system to understand how these species interact over time. Let me run an observation experiment to collect time-series data for all three species.

## 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: 10001 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_ri7q  id_nzce  id_jz57
0  1.00e+02 1.00e+01 7.50e+01
...
2.49e+01  1.59e+02 1.39e+01 5.56e+01
...
4.97e+01  2.04e+02 1.87e+01 4.96e+01
...
7.46e+01  2.40e+02 2.26e+01 4.64e+01
...
9.95e+01  2.68e+02 2.57e+01 4.45e+01
...
1.24e+02  2.89e+02 2.81e+01 4.34e+01
...
1.49e+02  3.06e+02 2.99e+01 4.26e+01
...
1.74e+02  3.19e+02 3.14e+01 4.21e+01
...
1.99e+02  3.30e+02 3.26e+01 4.17e+01
...
2.24e+02  3.38e+02 3.34e+01 4.15e+01
...
2.49e+02  3.44e+02 3.41e+01 4.13e+01
...
2.74e+02  3.49e+02 3.47e+01 4.11e+01
...
2.98e+02  3.52e+02 3.51e+01 4.10e+01
...
3.23e+02  3.55e+02 3.54e+01 4.09e+01
...
3.48e+02  3.58e+02 3.57e+01 4.09e+01
...
3.73e+02  3.60e+02 3.59e+01 4.08e+01
...
3.98e+02  3.61e+02 3.60e+01 4.08e+01
...
4.23e+02  3.62e+02 3.62e+01 4.08e+01
...
4.48e+02  3.63e+02 3.63e+01 4.07e+01
...
4.72e+02  3.64e+02 3.63e+01 4.07e+01
...
4.97e+02  3.64e+02 3.64e+01 4.07e+01
...
5.22e+02  3.64e+02 3.64e+01 4.07e+01
...
5.47e+02  3.65e+02 3.65e+01 4.07e+01
...
5.72e+02  3.65e+02 3.65e+01 4.07e+01
...
5.97e+02  3.65e+02 3.65e+01 4.07e+01
...
6.22e+02  3.65e+02 3.65e+01 4.07e+01
...
6.47e+02  3.65e+02 3.65e+01 4.07e+01
...
6.71e+02  3.66e+02 3.66e+01 4.07e+01
...
6.96e+02  3.66e+02 3.66e+01 4.07e+01
...
7.21e+02  3.66e+02 3.66e+01 4.07e+01
...
7.46e+02  3.66e+02 3.66e+01 4.07e+01
...
7.71e+02  3.66e+02 3.66e+01 4.07e+01
...
7.96e+02  3.66e+02 3.66e+01 4.07e+01
...
8.21e+02  3.66e+02 3.66e+01 4.07e+01
...
8.45e+02  3.66e+02 3.66e+01 4.07e+01
...
8.70e+02  3.66e+02 3.66e+01 4.07e+01
...
8.95e+02  3.66e+02 3.66e+01 4.07e+01
...
9.20e+02  3.66e+02 3.66e+01 4.07e+01
...
9.45e+02  3.66e+02 3.66e+01 4.07e+01
...
9.70e+02  3.66e+02 3.66e+01 4.07e+01
...
9.95e+02  3.66e+02 3.66e+01 4.07e+01
...
1.02e+03  3.66e+02 3.66e+01 4.07e+01
...
1.04e+03  3.66e+02 3.66e+01 4.07e+01
...
1.07e+03  3.66e+02 3.66e+01 4.07e+01
...
1.09e+03  3.66e+02 3.66e+01 4.07e+01
...
1.12e+03  3.66e+02 3.66e+01 4.07e+01
...
1.14e+03  3.66e+02 3.66e+01 4.07e+01
...
1.17e+03  3.66e+02 3.66e+01 4.07e+01
...
1.19e+03  3.66e+02 3.66e+01 4.07e+01
...
1.22e+03  3.66e+02 3.66e+01 4.07e+01

## Reminder

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



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

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


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



# Iteration 1
## Thoughts
Looking at the observation data, I can see some interesting patterns:

1. id_ri7q: Starts at 100 and increases to around 366, eventually reaching a steady state.
2. id_nzce: Starts at 10 and increases to around 36.6, also reaching a steady state.
3. id_jz57: Starts at 75 and decreases to around 40.7, reaching a steady state.

The data suggests several possible reactions:
- id_jz57 might be converted to id_ri7q and id_nzce (since id_jz57 decreases while the others increase)
- The ratio of increase in id_ri7q to id_nzce appears to be approximately 10:1
- The system reaches equilibrium, suggesting some form of feedback or conservation

Let me analyze the data more carefully to understand the relationships between these species and formulate hypotheses about the underlying reactions.

## Action

### Code
```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

# Get the full data
data = experiment_history["iteration_0"]

# Calculate changes in concentrations
data['delta_ri7q'] = data['id_ri7q'].diff()
data['delta_nzce'] = data['id_nzce'].diff()
data['delta_jz57'] = data['id_jz57'].diff()

# Drop the first row which has NaN due to diff()
data = data.dropna()

# Calculate ratios of changes
data['ratio_ri7q_nzce'] = data['delta_ri7q'] / data['delta_nzce']
data['ratio_ri7q_jz57'] = data['delta_ri7q'] / (-data['delta_jz57'])
data['ratio_nzce_jz57'] = data['delta_nzce'] / (-data['delta_jz57'])

# Print summary statistics
print("Initial concentrations:")
print(f"id_ri7q: {data['id_ri7q'].iloc[0]}")
print(f"id_nzce: {data['id_nzce'].iloc[0]}")
print(f"id_jz57: {data['id_jz57'].iloc[0]}")

print("\nFinal concentrations:")
print(f"id_ri7q: {data['id_ri7q'].iloc[-1]}")
print(f"id_nzce: {data['id_nzce'].iloc[-1]}")
print(f"id_jz57: {data['id_jz57'].iloc[-1]}")

print("\nTotal changes:")
print(f"id_ri7q: {data['id_ri7q'].iloc[-1] - data['id_ri7q'].iloc[0]}")
print(f"id_nzce: {data['id_nzce'].iloc[-1] - data['id_nzce'].iloc[0]}")
print(f"id_jz57: {data['id_jz57'].iloc[-1] - data['id_jz57'].iloc[0]}")

# Calculate average ratios (excluding outliers)
# Filter out extreme values that might occur when denominators are close to zero
reasonable_ratios = data[(data['delta_nzce'].abs() > 1e-6) & (data['delta_jz57'].abs() > 1e-6)]
avg_ratio_ri7q_nzce = reasonable_ratios['ratio_ri7q_nzce'].median()
avg_ratio_ri7q_jz57 = reasonable_ratios['ratio_ri7q_jz57'].median()
avg_ratio_nzce_jz57 = reasonable_ratios['ratio_nzce_jz57'].median()

print("\nMedian ratios of changes:")
print(f"id_ri7q / id_nzce: {avg_ratio_ri7q_nzce}")
print(f"id_ri7q / -id_jz57: {avg_ratio_ri7q_jz57}")
print(f"id_nzce / -id_jz57: {avg_ratio_nzce_jz57}")

# Check conservation of mass
data['total_mass'] = data['id_ri7q'] + data['id_nzce'] + data['id_jz57']
print("\nTotal mass (sum of all species):")
print(f"Initial: {data['total_mass'].iloc[0]}")
print(f"Final: {data['total_mass'].iloc[-1]}")
print(f"Change: {data['total_mass'].iloc[-1] - data['total_mass'].iloc[0]}")

# Let's also look at the early dynamics to understand reaction rates
early_data = data.iloc[:100]  # First 100 data points
print("\nEarly dynamics (first 100 points):")
print(f"Average rate of change for id_ri7q: {early_data['delta_ri7q'].mean()}")
print(f"Average rate of change for id_nzce: {early_data['delta_nzce'].mean()}")
print(f"Average rate of change for id_jz57: {early_data['delta_jz57'].mean()}")

# Store the data for future use
shared_variables.add("observation_data", data)
```
# 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
I apologize for trying to use matplotlib, which is not allowed. Let me rewrite the code without it and focus on analyzing the data to understand the relationships between the species.

## Action

### Code
```python
import numpy as np
import pandas as pd
from scipy.optimize import curve_fit

# Get the full data
data = experiment_history["iteration_0"]

# Calculate changes in concentrations
data['delta_ri7q'] = data['id_ri7q'].diff()
data['delta_nzce'] = data['id_nzce'].diff()
data['delta_jz57'] = data['id_jz57'].diff()

# Drop the first row which has NaN due to diff()
data = data.dropna()

# Calculate ratios of changes
data['ratio_ri7q_nzce'] = data['delta_ri7q'] / data['delta_nzce']
data['ratio_ri7q_jz57'] = data['delta_ri7q'] / (-data['delta_jz57'])
data['ratio_nzce_jz57'] = data['delta_nzce'] / (-data['delta_jz57'])

# Print summary statistics
print("Initial concentrations:")
print(f"id_ri7q: {data['id_ri7q'].iloc[0]}")
print(f"id_nzce: {data['id_nzce'].iloc[0]}")
print(f"id_jz57: {data['id_jz57'].iloc[0]}")

print("\nFinal concentrations:")
print(f"id_ri7q: {data['id_ri7q'].iloc[-1]}")
print(f"id_nzce: {data['id_nzce'].iloc[-1]}")
print(f"id_jz57: {data['id_jz57'].iloc[-1]}")

print("\nTotal changes:")
print(f"id_ri7q: {data['id_ri7q'].iloc[-1] - data['id_ri7q'].iloc[0]}")
print(f"id_nzce: {data['id_nzce'].iloc[-1] - data['id_nzce'].iloc[0]}")
print(f"id_jz57: {data['id_jz57'].iloc[-1] - data['id_jz57'].iloc[0]}")

# Calculate average ratios (excluding outliers)
# Filter out extreme values that might occur when denominators are close to zero
reasonable_ratios = data[(data['delta_nzce'].abs() > 1e-6) & (data['delta_jz57'].abs() > 1e-6)]
avg_ratio_ri7q_nzce = reasonable_ratios['ratio_ri7q_nzce'].median()
avg_ratio_ri7q_jz57 = reasonable_ratios['ratio_ri7q_jz57'].median()
avg_ratio_nzce_jz57 = reasonable_ratios['ratio_nzce_jz57'].median()

print("\nMedian ratios of changes:")
print(f"id_ri7q / id_nzce: {avg_ratio_ri7q_nzce}")
print(f"id_ri7q / -id_jz57: {avg_ratio_ri7q_jz57}")
print(f"id_nzce / -id_jz57: {avg_ratio_nzce_jz57}")

# Check conservation of mass
data['total_mass'] = data['id_ri7q'] + data['id_nzce'] + data['id_jz57']
print("\nTotal mass (sum of all species):")
print(f"Initial: {data['total_mass'].iloc[0]}")
print(f"Final: {data['total_mass'].iloc[-1]}")
print(f"Change: {data['total_mass'].iloc[-1] - data['total_mass'].iloc[0]}")

# Let's also look at the early dynamics to understand reaction rates
early_data = data.iloc[:100]  # First 100 data points
print("\nEarly dynamics (first 100 points):")
print(f"Average rate of change for id_ri7q: {early_data['delta_ri7q'].mean()}")
print(f"Average rate of change for id_nzce: {early_data['delta_nzce'].mean()}")
print(f"Average rate of change for id_jz57: {early_data['delta_jz57'].mean()}")

# Let's also check if the rates of change are proportional to the concentrations
# This would suggest mass action kinetics
print("\nCorrelation between species concentrations and rates:")
print(f"Correlation between id_jz57 and delta_ri7q: {data['id_jz57'].corr(data['delta_ri7q'])}")
print(f"Correlation between id_jz57 and delta_nzce: {data['id_jz57'].corr(data['delta_nzce'])}")
print(f"Correlation between id_ri7q and delta_jz57: {data['id_ri7q'].corr(data['delta_jz57'])}")
print(f"Correlation between id_nzce and delta_jz57: {data['id_nzce'].corr(data['delta_jz57'])}")

# Store the data for future use
shared_variables.add("observation_data", data)
```
# Observation

## Code Stdout
Initial concentrations:
id_ri7q: 100.3991261420058
id_nzce: 10.000252292834395
id_jz57: 74.74289644263285

Final concentrations:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937

Total changes:
id_ri7q: 265.51232330870835
id_nzce: 26.590879100195068
id_jz57: -34.085899422563486

Median ratios of changes:
id_ri7q / id_nzce: 8.99989224093057
id_ri7q / -id_jz57: 37.61461159548882
id_nzce / -id_jz57: 4.179349568859056

Total mass (sum of all species):
Initial: 185.14227487747303
Final: 443.15957786381296
Change: 258.0173029863399

Early dynamics (first 100 points):
Average rate of change for id_ri7q: 0.32300906926006634
Average rate of change for id_nzce: 0.014262346914854777
Average rate of change for id_jz57: -0.13772411725162337

Correlation between species concentrations and rates:
Correlation between id_jz57 and delta_ri7q: 0.9442302950455328
Correlation between id_jz57 and delta_nzce: 0.7875054875909222
Correlation between id_ri7q and delta_jz57: 0.7521314734981873
Correlation between id_nzce and delta_jz57: 0.7344267102320734

## Reminder

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



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

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


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



# Iteration 3
## Thoughts
The analysis reveals several important insights about the system:

1. **Total Mass Change**: The total mass (sum of all species) increases from 185.14 to 443.16, an increase of 258.02. This suggests there's a source of mass in the system - possibly a boundary species or a constant influx.

2. **Stoichiometric Ratios**:
   - The ratio of change between id_ri7q and id_nzce is approximately 9:1
   - The ratio of change between id_ri7q and -id_jz57 is approximately 37.6:1
   - The ratio of change between id_nzce and -id_jz57 is approximately 4.18:1

3. **Correlation Analysis**:
   - Strong positive correlation (0.944) between id_jz57 concentration and the rate of change of id_ri7q
   - Moderate positive correlation (0.788) between id_jz57 concentration and the rate of change of id_nzce
   - Moderate positive correlation (0.752) between id_ri7q concentration and the rate of change of id_jz57
   - Moderate positive correlation (0.734) between id_nzce concentration and the rate of change of id_jz57

Based on these observations, I can formulate some hypotheses about the reactions:

1. There appears to be a reaction where id_jz57 is converted to id_ri7q and id_nzce, with stoichiometry suggesting approximately 1 molecule of id_jz57 produces 9 molecules of id_ri7q and 1 molecule of id_nzce.

2. The strong correlation between id_jz57 concentration and the rates of change of id_ri7q and id_nzce suggests that the rate of this reaction is proportional to id_jz57 concentration (first-order kinetics).

3. The total mass increase suggests there's an additional source of mass - possibly a constant influx or a boundary species not included in the model.

Let me run another experiment with different initial concentrations to test these hypotheses. I'll increase the initial concentration of id_jz57 to see if the reaction rates and final equilibrium values change as expected.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration", 
    "meta_data": {
        "id_jz57": 150
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_3
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_3]

Total size: 10001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_3] for the full data

Time   id_ri7q  id_nzce  id_jz57
0  1.00e+02 1.00e+01 1.50e+02
...
2.49e+01  1.76e+02 1.52e+01 6.10e+01
...
4.97e+01  2.20e+02 2.03e+01 4.94e+01
...
7.46e+01  2.53e+02 2.40e+01 4.57e+01
...
9.95e+01  2.78e+02 2.68e+01 4.40e+01
...
1.24e+02  2.97e+02 2.90e+01 4.30e+01
...
1.49e+02  3.13e+02 3.07e+01 4.24e+01
...
1.74e+02  3.24e+02 3.20e+01 4.19e+01
...
1.99e+02  3.33e+02 3.30e+01 4.16e+01
...
2.24e+02  3.41e+02 3.38e+01 4.14e+01
...
2.49e+02  3.46e+02 3.44e+01 4.12e+01
...
2.74e+02  3.51e+02 3.49e+01 4.11e+01
...
2.98e+02  3.54e+02 3.53e+01 4.10e+01
...
3.23e+02  3.57e+02 3.56e+01 4.09e+01
...
3.48e+02  3.59e+02 3.58e+01 4.09e+01
...
3.73e+02  3.60e+02 3.60e+01 4.08e+01
...
3.98e+02  3.61e+02 3.61e+01 4.08e+01
...
4.23e+02  3.62e+02 3.62e+01 4.07e+01
...
4.48e+02  3.63e+02 3.63e+01 4.07e+01
...
4.72e+02  3.64e+02 3.64e+01 4.07e+01
...
4.97e+02  3.64e+02 3.64e+01 4.07e+01
...
5.22e+02  3.65e+02 3.64e+01 4.07e+01
...
5.47e+02  3.65e+02 3.65e+01 4.07e+01
...
5.72e+02  3.65e+02 3.65e+01 4.07e+01
...
5.97e+02  3.65e+02 3.65e+01 4.07e+01
...
6.22e+02  3.65e+02 3.65e+01 4.07e+01
...
6.47e+02  3.66e+02 3.66e+01 4.07e+01
...
6.71e+02  3.66e+02 3.66e+01 4.07e+01
...
6.96e+02  3.66e+02 3.66e+01 4.07e+01
...
7.21e+02  3.66e+02 3.66e+01 4.07e+01
...
7.46e+02  3.66e+02 3.66e+01 4.07e+01
...
7.71e+02  3.66e+02 3.66e+01 4.07e+01
...
7.96e+02  3.66e+02 3.66e+01 4.07e+01
...
8.21e+02  3.66e+02 3.66e+01 4.07e+01
...
8.45e+02  3.66e+02 3.66e+01 4.07e+01
...
8.70e+02  3.66e+02 3.66e+01 4.07e+01
...
8.95e+02  3.66e+02 3.66e+01 4.07e+01
...
9.20e+02  3.66e+02 3.66e+01 4.07e+01
...
9.45e+02  3.66e+02 3.66e+01 4.07e+01
...
9.70e+02  3.66e+02 3.66e+01 4.07e+01
...
9.95e+02  3.66e+02 3.66e+01 4.07e+01
...
1.02e+03  3.66e+02 3.66e+01 4.07e+01
...
1.04e+03  3.66e+02 3.66e+01 4.07e+01
...
1.07e+03  3.66e+02 3.66e+01 4.07e+01
...
1.09e+03  3.66e+02 3.66e+01 4.07e+01
...
1.12e+03  3.66e+02 3.66e+01 4.07e+01
...
1.14e+03  3.66e+02 3.66e+01 4.07e+01
...
1.17e+03  3.66e+02 3.66e+01 4.07e+01
...
1.19e+03  3.66e+02 3.66e+01 4.07e+01
...
1.22e+03  3.66e+02 3.66e+01 4.07e+01

## 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_3)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data)

### 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
Interesting! I doubled the initial concentration of id_jz57 from 75 to 150, and I observe:

1. The system still reaches the same steady state values for all three species (approximately 366 for id_ri7q, 36.6 for id_nzce, and 40.7 for id_jz57).

2. The dynamics are faster initially (as expected with higher id_jz57 concentration), but the final equilibrium is the same.

This suggests that the system has a fixed equilibrium point that is independent of the initial conditions, which is characteristic of systems with feedback mechanisms or conservation laws.

Let me analyze this new experiment data and compare it with the previous one to gain more insights.

## Action

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

# Get both datasets
data1 = experiment_history["iteration_0"]
data2 = experiment_history["iteration_3"]

# Print initial and final values for both experiments
print("Experiment 1 (Default):")
print(f"Initial - id_ri7q: {data1['id_ri7q'].iloc[0]}, id_nzce: {data1['id_nzce'].iloc[0]}, id_jz57: {data1['id_jz57'].iloc[0]}")
print(f"Final - id_ri7q: {data1['id_ri7q'].iloc[-1]}, id_nzce: {data1['id_nzce'].iloc[-1]}, id_jz57: {data1['id_jz57'].iloc[-1]}")

print("\nExperiment 2 (Higher id_jz57):")
print(f"Initial - id_ri7q: {data2['id_ri7q'].iloc[0]}, id_nzce: {data2['id_nzce'].iloc[0]}, id_jz57: {data2['id_jz57'].iloc[0]}")
print(f"Final - id_ri7q: {data2['id_ri7q'].iloc[-1]}, id_nzce: {data2['id_nzce'].iloc[-1]}, id_jz57: {data2['id_jz57'].iloc[-1]}")

# Calculate total mass for both experiments
data1['total_mass'] = data1['id_ri7q'] + data1['id_nzce'] + data1['id_jz57']
data2['total_mass'] = data2['id_ri7q'] + data2['id_nzce'] + data2['id_jz57']

print("\nTotal Mass:")
print(f"Experiment 1 - Initial: {data1['total_mass'].iloc[0]}, Final: {data1['total_mass'].iloc[-1]}")
print(f"Experiment 2 - Initial: {data2['total_mass'].iloc[0]}, Final: {data2['total_mass'].iloc[-1]}")

# Calculate early rates of change for both experiments
data1['delta_ri7q'] = data1['id_ri7q'].diff()
data1['delta_nzce'] = data1['id_nzce'].diff()
data1['delta_jz57'] = data1['id_jz57'].diff()

data2['delta_ri7q'] = data2['id_ri7q'].diff()
data2['delta_nzce'] = data2['id_nzce'].diff()
data2['delta_jz57'] = data2['id_jz57'].diff()

# Drop the first row which has NaN due to diff()
data1 = data1.dropna()
data2 = data2.dropna()

# Look at early dynamics (first 100 points)
early_data1 = data1.iloc[:100]
early_data2 = data2.iloc[:100]

print("\nEarly Dynamics (first 100 points):")
print("Experiment 1:")
print(f"Average rate of change for id_ri7q: {early_data1['delta_ri7q'].mean()}")
print(f"Average rate of change for id_nzce: {early_data1['delta_nzce'].mean()}")
print(f"Average rate of change for id_jz57: {early_data1['delta_jz57'].mean()}")

print("\nExperiment 2:")
print(f"Average rate of change for id_ri7q: {early_data2['delta_ri7q'].mean()}")
print(f"Average rate of change for id_nzce: {early_data2['delta_nzce'].mean()}")
print(f"Average rate of change for id_jz57: {early_data2['delta_jz57'].mean()}")

# Calculate the ratio of rates between experiments
print("\nRatio of rates (Experiment 2 / Experiment 1):")
print(f"id_ri7q: {early_data2['delta_ri7q'].mean() / early_data1['delta_ri7q'].mean()}")
print(f"id_nzce: {early_data2['delta_nzce'].mean() / early_data1['delta_nzce'].mean()}")
print(f"id_jz57: {early_data2['delta_jz57'].mean() / early_data1['delta_jz57'].mean()}")

# Let's check if the rates are proportional to id_jz57 concentration
# If they are, the ratio of rates should be close to the ratio of initial id_jz57 concentrations
initial_jz57_ratio = data2['id_jz57'].iloc[0] / data1['id_jz57'].iloc[0]
print(f"\nRatio of initial id_jz57 concentrations: {initial_jz57_ratio}")

# Let's also check if there's a relationship between the total mass and the equilibrium values
print("\nRelationship between total mass and equilibrium values:")
print(f"Experiment 1 - Final total mass: {data1['total_mass'].iloc[-1]}")
print(f"Experiment 1 - Final id_ri7q: {data1['id_ri7q'].iloc[-1]}")
print(f"Experiment 1 - Final id_nzce: {data1['id_nzce'].iloc[-1]}")
print(f"Experiment 1 - Final id_jz57: {data1['id_jz57'].iloc[-1]}")

print(f"\nExperiment 2 - Final total mass: {data2['total_mass'].iloc[-1]}")
print(f"Experiment 2 - Final id_ri7q: {data2['id_ri7q'].iloc[-1]}")
print(f"Experiment 2 - Final id_nzce: {data2['id_nzce'].iloc[-1]}")
print(f"Experiment 2 - Final id_jz57: {data2['id_jz57'].iloc[-1]}")

# Let's check if the ratio of id_ri7q to id_nzce at equilibrium is constant
print("\nRatio of id_ri7q to id_nzce at equilibrium:")
print(f"Experiment 1: {data1['id_ri7q'].iloc[-1] / data1['id_nzce'].iloc[-1]}")
print(f"Experiment 2: {data2['id_ri7q'].iloc[-1] / data2['id_nzce'].iloc[-1]}")

# Store the data for future use
shared_variables.add("experiment1_data", data1)
shared_variables.add("experiment2_data", data2)
```
# Observation

## Code Stdout
Experiment 1 (Default):
Initial - id_ri7q: 100.0, id_nzce: 10.0, id_jz57: 75.0
Final - id_ri7q: 365.91144945071414, id_nzce: 36.591131393029464, id_jz57: 40.65699702006937

Experiment 2 (Higher id_jz57):
Initial - id_ri7q: 100.0, id_nzce: 10.0, id_jz57: 150.0
Final - id_ri7q: 365.91142217362705, id_nzce: 36.591128040397756, id_jz57: 40.656999290276026

Total Mass:
Experiment 1 - Initial: 185.0, Final: 443.15957786381296
Experiment 2 - Initial: 260.0, Final: 443.1595495043008

Early Dynamics (first 100 points):
Experiment 1:
Average rate of change for id_ri7q: 0.32300906926006634
Average rate of change for id_nzce: 0.014262346914854777
Average rate of change for id_jz57: -0.13772411725162337

Experiment 2:
Average rate of change for id_ri7q: 0.4460152336027107
Average rate of change for id_nzce: 0.02021294984108854
Average rate of change for id_jz57: -0.6972225089870651

Ratio of rates (Experiment 2 / Experiment 1):
id_ri7q: 1.3808133456575105
id_nzce: 1.4172246658813201
id_jz57: 5.062457635602285

Ratio of initial id_jz57 concentrations: 1.987376059631339

Relationship between total mass and equilibrium values:
Experiment 1 - Final total mass: 443.15957786381296
Experiment 1 - Final id_ri7q: 365.91144945071414
Experiment 1 - Final id_nzce: 36.591131393029464
Experiment 1 - Final id_jz57: 40.65699702006937

Experiment 2 - Final total mass: 443.1595495043008
Experiment 2 - Final id_ri7q: 365.91142217362705
Experiment 2 - Final id_nzce: 36.591128040397756
Experiment 2 - Final id_jz57: 40.656999290276026

Ratio of id_ri7q to id_nzce at equilibrium:
Experiment 1: 10.000003703641138
Experiment 2: 10.000003874426865

## 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_3)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data)

### 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 analysis of both experiments reveals several key insights:

1. **Identical Equilibrium Points**: Both experiments reach the same equilibrium values despite different initial conditions:
   - id_ri7q: ~365.91
   - id_nzce: ~36.59
   - id_jz57: ~40.66

2. **Total Mass at Equilibrium**: Both experiments reach the same final total mass (~443.16) despite starting with different total masses (185 vs 260). This confirms there's a source of mass in the system.

3. **Ratio at Equilibrium**: The ratio of id_ri7q to id_nzce at equilibrium is exactly 10:1 in both experiments.

4. **Rate Dependence on id_jz57**: The ratio of initial rates between experiments doesn't match the ratio of initial id_jz57 concentrations (which is ~2). The rates for id_ri7q and id_nzce increased by ~1.4 times, while the rate for id_jz57 increased by ~5 times. This suggests the kinetics are more complex than simple first-order with respect to id_jz57.

Based on these observations, I can formulate a more refined hypothesis about the system:

1. There appears to be a reaction where id_jz57 is converted to id_ri7q and id_nzce with a stoichiometric ratio of 10:1.

2. The system has a fixed equilibrium point regardless of initial conditions, suggesting a reversible reaction or a feedback mechanism.

3. The total mass increases to a fixed value, suggesting there's a constant source or a boundary species not included in the model.

Let me try another experiment with different initial concentrations of id_ri7q and id_nzce to see if that affects the equilibrium point or the dynamics.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration", 
    "meta_data": {
        "id_ri7q": 200,
        "id_nzce": 20
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_5
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_5]

Total size: 10001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_5] for the full data

Time   id_ri7q  id_nzce  id_jz57
0  2.00e+02 2.00e+01 7.50e+01
...
2.49e+01  2.49e+02 2.34e+01 4.84e+01
...
4.97e+01  2.76e+02 2.65e+01 4.45e+01
...
7.46e+01  2.96e+02 2.88e+01 4.31e+01
...
9.95e+01  3.12e+02 3.05e+01 4.24e+01
...
1.24e+02  3.24e+02 3.19e+01 4.20e+01
...
1.49e+02  3.33e+02 3.29e+01 4.16e+01
...
1.74e+02  3.40e+02 3.37e+01 4.14e+01
...
1.99e+02  3.46e+02 3.44e+01 4.12e+01
...
2.24e+02  3.50e+02 3.49e+01 4.11e+01
...
2.49e+02  3.54e+02 3.52e+01 4.10e+01
...
2.74e+02  3.56e+02 3.55e+01 4.09e+01
...
2.98e+02  3.58e+02 3.58e+01 4.09e+01
...
3.23e+02  3.60e+02 3.59e+01 4.08e+01
...
3.48e+02  3.61e+02 3.61e+01 4.08e+01
...
3.73e+02  3.62e+02 3.62e+01 4.07e+01
...
3.98e+02  3.63e+02 3.63e+01 4.07e+01
...
4.23e+02  3.64e+02 3.64e+01 4.07e+01
...
4.48e+02  3.64e+02 3.64e+01 4.07e+01
...
4.72e+02  3.65e+02 3.64e+01 4.07e+01
...
4.97e+02  3.65e+02 3.65e+01 4.07e+01
...
5.22e+02  3.65e+02 3.65e+01 4.07e+01
...
5.47e+02  3.65e+02 3.65e+01 4.07e+01
...
5.72e+02  3.65e+02 3.65e+01 4.07e+01
...
5.97e+02  3.66e+02 3.65e+01 4.07e+01
...
6.22e+02  3.66e+02 3.66e+01 4.07e+01
...
6.47e+02  3.66e+02 3.66e+01 4.07e+01
...
6.71e+02  3.66e+02 3.66e+01 4.07e+01
...
6.96e+02  3.66e+02 3.66e+01 4.07e+01
...
7.21e+02  3.66e+02 3.66e+01 4.07e+01
...
7.46e+02  3.66e+02 3.66e+01 4.07e+01
...
7.71e+02  3.66e+02 3.66e+01 4.07e+01
...
7.96e+02  3.66e+02 3.66e+01 4.07e+01
...
8.21e+02  3.66e+02 3.66e+01 4.07e+01
...
8.45e+02  3.66e+02 3.66e+01 4.07e+01
...
8.70e+02  3.66e+02 3.66e+01 4.07e+01
...
8.95e+02  3.66e+02 3.66e+01 4.07e+01
...
9.20e+02  3.66e+02 3.66e+01 4.07e+01
...
9.45e+02  3.66e+02 3.66e+01 4.07e+01
...
9.70e+02  3.66e+02 3.66e+01 4.07e+01
...
9.95e+02  3.66e+02 3.66e+01 4.07e+01
...
1.02e+03  3.66e+02 3.66e+01 4.07e+01
...
1.04e+03  3.66e+02 3.66e+01 4.07e+01
...
1.07e+03  3.66e+02 3.66e+01 4.07e+01
...
1.09e+03  3.66e+02 3.66e+01 4.07e+01
...
1.12e+03  3.66e+02 3.66e+01 4.07e+01
...
1.14e+03  3.66e+02 3.66e+01 4.07e+01
...
1.17e+03  3.66e+02 3.66e+01 4.07e+01
...
1.19e+03  3.66e+02 3.66e+01 4.07e+01
...
1.22e+03  3.66e+02 3.66e+01 4.07e+01

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data)

### 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
This third experiment provides additional valuable insights:

1. **Same Equilibrium Point**: Even with doubled initial concentrations of id_ri7q and id_nzce, the system still reaches the same equilibrium values (~366 for id_ri7q, ~36.6 for id_nzce, and ~40.7 for id_jz57).

2. **Approach to Equilibrium**: In this case, id_ri7q and id_nzce started above their equilibrium values and decreased, while id_jz57 started above its equilibrium value and also decreased. This suggests a complex set of reactions with multiple directions.

Let me analyze all three experiments together to better understand the system dynamics and formulate a more complete hypothesis.

## Action

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

# Get all three datasets
data1 = experiment_history["iteration_0"]  # Default
data2 = experiment_history["iteration_3"]  # Higher id_jz57
data3 = experiment_history["iteration_5"]  # Higher id_ri7q and id_nzce

# Print initial and final values for all experiments
print("Experiment 1 (Default):")
print(f"Initial - id_ri7q: {data1['id_ri7q'].iloc[0]}, id_nzce: {data1['id_nzce'].iloc[0]}, id_jz57: {data1['id_jz57'].iloc[0]}")
print(f"Final - id_ri7q: {data1['id_ri7q'].iloc[-1]}, id_nzce: {data1['id_nzce'].iloc[-1]}, id_jz57: {data1['id_jz57'].iloc[-1]}")

print("\nExperiment 2 (Higher id_jz57):")
print(f"Initial - id_ri7q: {data2['id_ri7q'].iloc[0]}, id_nzce: {data2['id_nzce'].iloc[0]}, id_jz57: {data2['id_jz57'].iloc[0]}")
print(f"Final - id_ri7q: {data2['id_ri7q'].iloc[-1]}, id_nzce: {data2['id_nzce'].iloc[-1]}, id_jz57: {data2['id_jz57'].iloc[-1]}")

print("\nExperiment 3 (Higher id_ri7q and id_nzce):")
print(f"Initial - id_ri7q: {data3['id_ri7q'].iloc[0]}, id_nzce: {data3['id_nzce'].iloc[0]}, id_jz57: {data3['id_jz57'].iloc[0]}")
print(f"Final - id_ri7q: {data3['id_ri7q'].iloc[-1]}, id_nzce: {data3['id_nzce'].iloc[-1]}, id_jz57: {data3['id_jz57'].iloc[-1]}")

# Calculate total mass for all experiments
data1['total_mass'] = data1['id_ri7q'] + data1['id_nzce'] + data1['id_jz57']
data2['total_mass'] = data2['id_ri7q'] + data2['id_nzce'] + data2['id_jz57']
data3['total_mass'] = data3['id_ri7q'] + data3['id_nzce'] + data3['id_jz57']

print("\nTotal Mass:")
print(f"Experiment 1 - Initial: {data1['total_mass'].iloc[0]}, Final: {data1['total_mass'].iloc[-1]}")
print(f"Experiment 2 - Initial: {data2['total_mass'].iloc[0]}, Final: {data2['total_mass'].iloc[-1]}")
print(f"Experiment 3 - Initial: {data3['total_mass'].iloc[0]}, Final: {data3['total_mass'].iloc[-1]}")

# Calculate rates of change for all experiments
data1['delta_ri7q'] = data1['id_ri7q'].diff()
data1['delta_nzce'] = data1['id_nzce'].diff()
data1['delta_jz57'] = data1['id_jz57'].diff()

data2['delta_ri7q'] = data2['id_ri7q'].diff()
data2['delta_nzce'] = data2['id_nzce'].diff()
data2['delta_jz57'] = data2['id_jz57'].diff()

data3['delta_ri7q'] = data3['id_ri7q'].diff()
data3['delta_nzce'] = data3['id_nzce'].diff()
data3['delta_jz57'] = data3['id_jz57'].diff()

# Drop the first row which has NaN due to diff()
data1 = data1.dropna()
data2 = data2.dropna()
data3 = data3.dropna()

# Look at early dynamics (first 100 points)
early_data1 = data1.iloc[:100]
early_data2 = data2.iloc[:100]
early_data3 = data3.iloc[:100]

print("\nEarly Dynamics (first 100 points):")
print("Experiment 1:")
print(f"Average rate of change for id_ri7q: {early_data1['delta_ri7q'].mean()}")
print(f"Average rate of change for id_nzce: {early_data1['delta_nzce'].mean()}")
print(f"Average rate of change for id_jz57: {early_data1['delta_jz57'].mean()}")

print("\nExperiment 2:")
print(f"Average rate of change for id_ri7q: {early_data2['delta_ri7q'].mean()}")
print(f"Average rate of change for id_nzce: {early_data2['delta_nzce'].mean()}")
print(f"Average rate of change for id_jz57: {early_data2['delta_jz57'].mean()}")

print("\nExperiment 3:")
print(f"Average rate of change for id_ri7q: {early_data3['delta_ri7q'].mean()}")
print(f"Average rate of change for id_nzce: {early_data3['delta_nzce'].mean()}")
print(f"Average rate of change for id_jz57: {early_data3['delta_jz57'].mean()}")

# Check if the ratio of id_ri7q to id_nzce at equilibrium is constant
print("\nRatio of id_ri7q to id_nzce at equilibrium:")
print(f"Experiment 1: {data1['id_ri7q'].iloc[-1] / data1['id_nzce'].iloc[-1]}")
print(f"Experiment 2: {data2['id_ri7q'].iloc[-1] / data2['id_nzce'].iloc[-1]}")
print(f"Experiment 3: {data3['id_ri7q'].iloc[-1] / data3['id_nzce'].iloc[-1]}")

# Let's try to understand the relationship between the species
# Let's check if there's a conservation law involving all three species
# If there is, then a linear combination of the species should be constant
# Let's try to find such a combination

# First, let's check if there's a simple conservation law like a*ri7q + b*nzce + c*jz57 = constant
# We know that at equilibrium, the total mass is constant at around 443
# Let's see if we can find a relationship between the equilibrium values

print("\nEquilibrium values:")
print(f"id_ri7q: {data1['id_ri7q'].iloc[-1]}")
print(f"id_nzce: {data1['id_nzce'].iloc[-1]}")
print(f"id_jz57: {data1['id_jz57'].iloc[-1]}")

# Let's also check if there's a relationship between the changes in the species
# If there is a stoichiometric relationship, then the changes should be proportional
print("\nRelationship between changes in species:")
print("Experiment 1:")
print(f"delta_ri7q / delta_nzce: {early_data1['delta_ri7q'].sum() / early_data1['delta_nzce'].sum()}")
print(f"delta_ri7q / -delta_jz57: {early_data1['delta_ri7q'].sum() / (-early_data1['delta_jz57'].sum())}")
print(f"delta_nzce / -delta_jz57: {early_data1['delta_nzce'].sum() / (-early_data1['delta_jz57'].sum())}")

print("\nExperiment 2:")
print(f"delta_ri7q / delta_nzce: {early_data2['delta_ri7q'].sum() / early_data2['delta_nzce'].sum()}")
print(f"delta_ri7q / -delta_jz57: {early_data2['delta_ri7q'].sum() / (-early_data2['delta_jz57'].sum())}")
print(f"delta_nzce / -delta_jz57: {early_data2['delta_nzce'].sum() / (-early_data2['delta_jz57'].sum())}")

print("\nExperiment 3:")
print(f"delta_ri7q / delta_nzce: {early_data3['delta_ri7q'].sum() / early_data3['delta_nzce'].sum()}")
print(f"delta_ri7q / -delta_jz57: {early_data3['delta_ri7q'].sum() / (-early_data3['delta_jz57'].sum())}")
print(f"delta_nzce / -delta_jz57: {early_data3['delta_nzce'].sum() / (-early_data3['delta_jz57'].sum())}")

# Let's also check if there's a relationship between the initial conditions and the amount of mass added to the system
print("\nMass added to the system:")
print(f"Experiment 1: {data1['total_mass'].iloc[-1] - data1['total_mass'].iloc[0]}")
print(f"Experiment 2: {data2['total_mass'].iloc[-1] - data2['total_mass'].iloc[0]}")
print(f"Experiment 3: {data3['total_mass'].iloc[-1] - data3['total_mass'].iloc[0]}")

# Store the data for future use
shared_variables.add("experiment3_data", data3)
```
# Observation

## Code Stdout
Experiment 1 (Default):
Initial - id_ri7q: 100.0, id_nzce: 10.0, id_jz57: 75.0
Final - id_ri7q: 365.91144945071414, id_nzce: 36.591131393029464, id_jz57: 40.65699702006937

Experiment 2 (Higher id_jz57):
Initial - id_ri7q: 100.0, id_nzce: 10.0, id_jz57: 150.0
Final - id_ri7q: 365.91142217362705, id_nzce: 36.591128040397756, id_jz57: 40.656999290276026

Experiment 3 (Higher id_ri7q and id_nzce):
Initial - id_ri7q: 200.0, id_nzce: 20.0, id_jz57: 75.0
Final - id_ri7q: 365.9112688205561, id_nzce: 36.59111178115032, id_jz57: 40.6570003730284

Total Mass:
Experiment 1 - Initial: 185.0, Final: 443.15957786381296
Experiment 2 - Initial: 260.0, Final: 443.1595495043008
Experiment 3 - Initial: 295.0, Final: 443.15938097473474

Early Dynamics (first 100 points):
Experiment 1:
Average rate of change for id_ri7q: 0.32300906926006634
Average rate of change for id_nzce: 0.014262346914854777
Average rate of change for id_jz57: -0.13772411725162337

Experiment 2:
Average rate of change for id_ri7q: 0.4460152336027107
Average rate of change for id_nzce: 0.02021294984108854
Average rate of change for id_jz57: -0.6972225089870651

Experiment 3:
Average rate of change for id_ri7q: 0.29586209063654934
Average rate of change for id_nzce: 0.01355107237785468
Average rate of change for id_jz57: -0.20419761948747897

Ratio of id_ri7q to id_nzce at equilibrium:
Experiment 1: 10.000003703641138
Experiment 2: 10.000003874426865
Experiment 3: 10.000004126932623

Equilibrium values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937

Relationship between changes in species:
Experiment 1:
delta_ri7q / delta_nzce: 22.647680019873874
delta_ri7q / -delta_jz57: 2.3453341049187886
delta_nzce / -delta_jz57: 0.10355736670867402

Experiment 2:
delta_ri7q / delta_nzce: 22.065816078762463
delta_ri7q / -delta_jz57: 0.6397028607849854
delta_nzce / -delta_jz57: 0.028990673107289963

Experiment 3:
delta_ri7q / delta_nzce: 21.8331127151273
delta_ri7q / -delta_jz57: 1.448900782384934
delta_nzce / -delta_jz57: 0.06636253846576114

Mass added to the system:
Experiment 1: 258.0173029863399
Experiment 2: 184.0101547760995
Experiment 3: 148.13838190170185

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data)

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


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



# Iteration 7
## Thoughts
The analysis of all three experiments provides crucial insights:

1. **Identical Equilibrium Point**: All three experiments reach the same equilibrium values regardless of initial conditions:
   - id_ri7q: ~365.91
   - id_nzce: ~36.59
   - id_jz57: ~40.66

2. **Constant Ratio at Equilibrium**: The ratio of id_ri7q to id_nzce at equilibrium is exactly 10:1 in all experiments.

3. **Total Mass at Equilibrium**: All experiments reach the same final total mass (~443.16) despite starting with different total masses.

4. **Mass Added to System**: The amount of mass added to the system varies between experiments:
   - Experiment 1: 258.02
   - Experiment 2: 184.01
   - Experiment 3: 148.14
   This suggests the system has a fixed carrying capacity or equilibrium point.

5. **Stoichiometric Relationships**: The ratios between changes in species vary between experiments, but within each experiment:
   - delta_ri7q / delta_nzce is approximately 22 (not 10 as at equilibrium)
   - The ratios involving id_jz57 vary significantly between experiments

Based on these observations, I'm formulating a more refined hypothesis:

1. There appears to be a constant influx of mass into the system, possibly through a zero-order reaction (constant production).

2. The system reaches an equilibrium where the production and degradation rates balance.

3. The fixed ratio of id_ri7q to id_nzce at equilibrium (10:1) suggests they are produced or degraded together with this stoichiometry.

4. The varying ratios of changes suggest multiple reactions with different kinetics.

Let me try to formulate a model with these reactions and test it. I'll start by creating a simple model with:
- A constant production of id_ri7q and id_nzce (with 10:1 ratio)
- Conversion between id_jz57 and the other species
- Degradation reactions to balance the system

## Action

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

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

# Add reactions to the model
# 1. Constant production of id_ri7q
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_ri7q")
product1.setStoichiometry(10.0)
product1.setConstant(True)

# Add kinetic law (constant rate)
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(1.0)  # Initial guess
kinetic_law1.setMath(libsbml.parseL3Formula("k1"))

# 2. Constant production of id_nzce
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_nzce")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law (constant rate)
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(1.0)  # Same rate as reaction1
kinetic_law2.setMath(libsbml.parseL3Formula("k2"))

# 3. Degradation of id_ri7q
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_ri7q")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.01)  # Initial guess
kinetic_law3.setMath(libsbml.parseL3Formula("k3 * id_ri7q"))

# 4. Degradation of id_nzce
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_nzce")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.01)  # Initial guess
kinetic_law4.setMath(libsbml.parseL3Formula("k4 * id_nzce"))

# 5. Conversion of id_jz57 to id_ri7q and id_nzce
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactant
reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_jz57")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

# Add products
product5a = reaction5.createProduct()
product5a.setSpecies("id_ri7q")
product5a.setStoichiometry(10.0)
product5a.setConstant(True)

product5b = reaction5.createProduct()
product5b.setSpecies("id_nzce")
product5b.setStoichiometry(1.0)
product5b.setConstant(True)

# Add kinetic law (mass action)
kinetic_law5 = reaction5.createKineticLaw()
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.01)  # Initial guess
kinetic_law5.setMath(libsbml.parseL3Formula("k5 * id_jz57"))

# 6. Conversion of id_ri7q and id_nzce to id_jz57 (reverse of reaction 5)
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

# Add reactants
reactant6a = reaction6.createReactant()
reactant6a.setSpecies("id_ri7q")
reactant6a.setStoichiometry(10.0)
reactant6a.setConstant(True)

reactant6b = reaction6.createReactant()
reactant6b.setSpecies("id_nzce")
reactant6b.setStoichiometry(1.0)
reactant6b.setConstant(True)

# Add product
product6 = reaction6.createProduct()
product6.setSpecies("id_jz57")
product6.setStoichiometry(1.0)
product6.setConstant(True)

# Add kinetic law (mass action)
kinetic_law6 = reaction6.createKineticLaw()
parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.0001)  # Initial guess, smaller than k5
kinetic_law6.setMath(libsbml.parseL3Formula("k6 * id_ri7q * id_nzce"))

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

# Test the model with simulation
print("Testing the model with simulation...")
try:
    result = simulate(updated_sbml)
    
    # Print the first few rows
    print("First few rows of simulation:")
    print(result.head())
    
    # Print the last few rows
    print("\nLast few rows of simulation:")
    print(result.tail())
    
    # Calculate final values
    final_ri7q = result['id_ri7q'].iloc[-1]
    final_nzce = result['id_nzce'].iloc[-1]
    final_jz57 = result['id_jz57'].iloc[-1]
    
    print(f"\nFinal values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    
    # Store the model for future use
    shared_variables.add("first_model", updated_sbml)
    
except Exception as e:
    print(f"Error in simulation: {e}")
```
# Observation

## Code Stdout
Testing the model with simulation...
First few rows of simulation:
      id_ri7q    id_nzce    id_jz57    Time
0  100.000000  10.000000  75.000000  0.0000
1  101.885385  10.188538  74.921053  0.1219
2  103.762950  10.376295  74.842662  0.2438
3  105.632542  10.563254  74.764840  0.3657
4  107.494105  10.749410  74.687594  0.4876

Last few rows of simulation:
          id_ri7q    id_nzce     id_jz57       Time
9996   736.432648  73.643265  517.558760  1218.5124
9997   736.451953  73.645195  517.588958  1218.6343
9998   736.471256  73.647126  517.619153  1218.7562
9999   736.490556  73.649056  517.649346  1218.8781
10000  736.509855  73.650986  517.679537  1219.0000

Final values from simulation:
id_ri7q: 736.5098551933146
id_nzce: 73.65098551932695
id_jz57: 517.6795365836497
Ratio id_ri7q/id_nzce: 10.000000000000613

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data, first_model)

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


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



# Iteration 8
## Thoughts
The simulation of my first model shows that it maintains the 10:1 ratio between id_ri7q and id_nzce, which is consistent with the experimental data. However, there are significant discrepancies:

1. The final values are much higher than observed in the experiments:
   - Simulated: id_ri7q ≈ 736.5, id_nzce ≈ 73.7, id_jz57 ≈ 517.7
   - Experimental: id_ri7q ≈ 365.9, id_nzce ≈ 36.6, id_jz57 ≈ 40.7

2. The id_jz57 value is particularly off - in the simulation it increases from 75 to 517.7, whereas in the experiments it decreases from 75 to around 40.7.

These discrepancies suggest my model needs significant refinement. Let me adjust the reactions and parameters to better match the experimental data:

1. The constant production rates need to be balanced with degradation rates to achieve the observed equilibrium values.
2. The conversion between id_jz57 and the other species needs adjustment to match the observed dynamics.
3. I need to ensure id_jz57 decreases rather than increases.

Let me create a revised model with adjusted reactions and parameters.

## Action

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

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

# Clear any existing reactions (start fresh)
for i in range(model.getNumReactions()-1, -1, -1):
    model.removeReaction(i)

# Add reactions to the model
# 1. Constant production of id_ri7q and id_nzce (with 10:1 ratio)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add products
product1a = reaction1.createProduct()
product1a.setSpecies("id_ri7q")
product1a.setStoichiometry(10.0)
product1a.setConstant(True)

product1b = reaction1.createProduct()
product1b.setSpecies("id_nzce")
product1b.setStoichiometry(1.0)
product1b.setConstant(True)

# Add kinetic law (constant rate)
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.5)  # Adjusted value
kinetic_law1.setMath(libsbml.parseL3Formula("k1"))

# 2. Degradation of id_ri7q
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_ri7q")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.001)  # Adjusted value
kinetic_law2.setMath(libsbml.parseL3Formula("k2 * id_ri7q"))

# 3. Degradation of id_nzce
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_nzce")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.001)  # Same as k2 to maintain 10:1 ratio
kinetic_law3.setMath(libsbml.parseL3Formula("k3 * id_nzce"))

# 4. Conversion of id_jz57 to id_ri7q and id_nzce
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_jz57")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add products
product4a = reaction4.createProduct()
product4a.setSpecies("id_ri7q")
product4a.setStoichiometry(10.0)
product4a.setConstant(True)

product4b = reaction4.createProduct()
product4b.setSpecies("id_nzce")
product4b.setStoichiometry(1.0)
product4b.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.01)  # Adjusted value
kinetic_law4.setMath(libsbml.parseL3Formula("k4 * id_jz57"))

# 5. Conversion of id_ri7q and id_nzce to id_jz57 (reverse of reaction 4)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactants
reactant5a = reaction5.createReactant()
reactant5a.setSpecies("id_ri7q")
reactant5a.setStoichiometry(10.0)
reactant5a.setConstant(True)

reactant5b = reaction5.createReactant()
reactant5b.setSpecies("id_nzce")
reactant5b.setStoichiometry(1.0)
reactant5b.setConstant(True)

# Add product
product5 = reaction5.createProduct()
product5.setSpecies("id_jz57")
product5.setStoichiometry(1.0)
product5.setConstant(True)

# Add kinetic law (mass action)
kinetic_law5 = reaction5.createKineticLaw()
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.0000001)  # Much smaller than k4
kinetic_law5.setMath(libsbml.parseL3Formula("k5 * id_ri7q * id_nzce"))

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

# Test the model with simulation
print("Testing the revised model with simulation...")
try:
    result = simulate(updated_sbml)
    
    # Print the first few rows
    print("First few rows of simulation:")
    print(result.head())
    
    # Print the last few rows
    print("\nLast few rows of simulation:")
    print(result.tail())
    
    # Calculate final values
    final_ri7q = result['id_ri7q'].iloc[-1]
    final_nzce = result['id_nzce'].iloc[-1]
    final_jz57 = result['id_jz57'].iloc[-1]
    
    print(f"\nFinal values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    print(f"Total mass: {final_ri7q + final_nzce + final_jz57}")
    
    # Compare with experimental data
    exp_final_ri7q = experiment_history["iteration_0"]['id_ri7q'].iloc[-1]
    exp_final_nzce = experiment_history["iteration_0"]['id_nzce'].iloc[-1]
    exp_final_jz57 = experiment_history["iteration_0"]['id_jz57'].iloc[-1]
    
    print(f"\nExperimental final values:")
    print(f"id_ri7q: {exp_final_ri7q}")
    print(f"id_nzce: {exp_final_nzce}")
    print(f"id_jz57: {exp_final_jz57}")
    print(f"Total mass: {exp_final_ri7q + exp_final_nzce + exp_final_jz57}")
    
    # Store the model for future use
    shared_variables.add("second_model", updated_sbml)
    
except Exception as e:
    print(f"Error in simulation: {e}")
```
# Observation

## Code Stdout
Testing the revised model with simulation...
First few rows of simulation:
      id_ri7q    id_nzce    id_jz57    Time
0  100.000000  10.000000  75.000000  0.0000
1  101.510685  10.151068  74.908652  0.1219
2  103.020157  10.302016  74.817408  0.2438
3  104.528341  10.452834  74.726274  0.3657
4  106.035229  10.603523  74.635252  0.4876

Last few rows of simulation:
           id_ri7q     id_nzce    id_jz57       Time
9996   3721.913855  372.191385  12.916041  1218.5124
9997   3722.058228  372.205823  12.917183  1218.6343
9998   3722.202584  372.220258  12.918325  1218.7562
9999   3722.346923  372.234692  12.919466  1218.8781
10000  3722.491246  372.249125  12.920608  1219.0000

Final values from simulation:
id_ri7q: 3722.4912460615833
id_nzce: 372.2491246061439
id_jz57: 12.920607672925836
Ratio id_ri7q/id_nzce: 10.000000000000389
Total mass: 4107.660978340653

Experimental final values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937
Total mass: 443.15957786381296

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data, first_model, second_model)

### 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
My second model still has significant discrepancies compared to the experimental data:

1. The final values are much higher than observed:
   - Simulated: id_ri7q ≈ 3722.5, id_nzce ≈ 372.2, id_jz57 ≈ 12.9
   - Experimental: id_ri7q ≈ 365.9, id_nzce ≈ 36.6, id_jz57 ≈ 40.7

2. The total mass at equilibrium is also much higher (4107.7 vs 443.2).

3. While the id_jz57 value now decreases (which matches the experimental trend), it decreases too much.

I need to further refine the model to better match the experimental data. The key issues to address:

1. The constant production rate is too high, leading to excessive accumulation.
2. The degradation rates need adjustment to achieve the correct equilibrium values.
3. The conversion rates between species need fine-tuning.

Let me create a third model with more carefully calibrated parameters.

## Action

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

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

# Clear any existing reactions (start fresh)
for i in range(model.getNumReactions()-1, -1, -1):
    model.removeReaction(i)

# Add reactions to the model
# 1. Constant production of id_ri7q and id_nzce (with 10:1 ratio)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add products
product1a = reaction1.createProduct()
product1a.setSpecies("id_ri7q")
product1a.setStoichiometry(10.0)
product1a.setConstant(True)

product1b = reaction1.createProduct()
product1b.setSpecies("id_nzce")
product1b.setStoichiometry(1.0)
product1b.setConstant(True)

# Add kinetic law (constant rate)
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Reduced value
kinetic_law1.setMath(libsbml.parseL3Formula("k1"))

# 2. Degradation of id_ri7q
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_ri7q")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.0001)  # Adjusted value
kinetic_law2.setMath(libsbml.parseL3Formula("k2 * id_ri7q"))

# 3. Degradation of id_nzce
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_nzce")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.0001)  # Same as k2 to maintain 10:1 ratio
kinetic_law3.setMath(libsbml.parseL3Formula("k3 * id_nzce"))

# 4. Conversion of id_jz57 to id_ri7q and id_nzce
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_jz57")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add products
product4a = reaction4.createProduct()
product4a.setSpecies("id_ri7q")
product4a.setStoichiometry(10.0)
product4a.setConstant(True)

product4b = reaction4.createProduct()
product4b.setSpecies("id_nzce")
product4b.setStoichiometry(1.0)
product4b.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.002)  # Adjusted value
kinetic_law4.setMath(libsbml.parseL3Formula("k4 * id_jz57"))

# 5. Conversion of id_ri7q and id_nzce to id_jz57 (reverse of reaction 4)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactants
reactant5a = reaction5.createReactant()
reactant5a.setSpecies("id_ri7q")
reactant5a.setStoichiometry(10.0)
reactant5a.setConstant(True)

reactant5b = reaction5.createReactant()
reactant5b.setSpecies("id_nzce")
reactant5b.setStoichiometry(1.0)
reactant5b.setConstant(True)

# Add product
product5 = reaction5.createProduct()
product5.setSpecies("id_jz57")
product5.setStoichiometry(1.0)
product5.setConstant(True)

# Add kinetic law (mass action)
kinetic_law5 = reaction5.createKineticLaw()
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.0000001)  # Adjusted value
kinetic_law5.setMath(libsbml.parseL3Formula("k5 * id_ri7q * id_nzce"))

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

# Test the model with simulation
print("Testing the third model with simulation...")
try:
    result = simulate(updated_sbml)
    
    # Print the first few rows
    print("First few rows of simulation:")
    print(result.head())
    
    # Print the last few rows
    print("\nLast few rows of simulation:")
    print(result.tail())
    
    # Calculate final values
    final_ri7q = result['id_ri7q'].iloc[-1]
    final_nzce = result['id_nzce'].iloc[-1]
    final_jz57 = result['id_jz57'].iloc[-1]
    
    print(f"\nFinal values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    print(f"Total mass: {final_ri7q + final_nzce + final_jz57}")
    
    # Compare with experimental data
    exp_final_ri7q = experiment_history["iteration_0"]['id_ri7q'].iloc[-1]
    exp_final_nzce = experiment_history["iteration_0"]['id_nzce'].iloc[-1]
    exp_final_jz57 = experiment_history["iteration_0"]['id_jz57'].iloc[-1]
    
    print(f"\nExperimental final values:")
    print(f"id_ri7q: {exp_final_ri7q}")
    print(f"id_nzce: {exp_final_nzce}")
    print(f"id_jz57: {exp_final_jz57}")
    print(f"Total mass: {exp_final_ri7q + exp_final_nzce + exp_final_jz57}")
    
    # Store the model for future use
    shared_variables.add("third_model", updated_sbml)
    
except Exception as e:
    print(f"Error in simulation: {e}")
```
# Observation

## Code Stdout
Testing the third model with simulation...
First few rows of simulation:
      id_ri7q    id_nzce    id_jz57    Time
0  100.000000  10.000000  75.000000  0.0000
1  100.242400  10.024240  74.981733  0.1219
2  100.484750  10.048475  74.963470  0.2438
3  100.727069  10.072707  74.945211  0.3657
4  100.969351  10.096935  74.926954  0.4876

Last few rows of simulation:
           id_ri7q     id_nzce    id_jz57       Time
9996   1245.351591  124.535159  11.439780  1218.5124
9997   1245.406343  124.540634  11.438881  1218.6343
9998   1245.461090  124.546109  11.437983  1218.7562
9999   1245.515833  124.551583  11.437086  1218.8781
10000  1245.570572  124.557057  11.436189  1219.0000

Final values from simulation:
id_ri7q: 1245.5705715203796
id_nzce: 124.55705715203638
id_jz57: 11.436188770918593
Ratio id_ri7q/id_nzce: 10.000000000000128
Total mass: 1381.5638174433345

Experimental final values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937
Total mass: 443.15957786381296

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data, first_model, second_model, third_model)

### 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
My third model is getting closer but still has significant discrepancies:

1. The final values are still off:
   - Simulated: id_ri7q ≈ 1245.6, id_nzce ≈ 124.6, id_jz57 ≈ 11.4
   - Experimental: id_ri7q ≈ 365.9, id_nzce ≈ 36.6, id_jz57 ≈ 40.7

2. The total mass at equilibrium is still too high (1381.6 vs 443.2).

3. The id_jz57 value is still too low compared to the experimental data.

I need to further refine the model. Let me try a different approach. Instead of having separate constant production reactions for id_ri7q and id_nzce, I'll try a model where:

1. There's a constant production of id_jz57 (to replenish what's consumed)
2. id_jz57 is converted to id_ri7q and id_nzce
3. id_ri7q and id_nzce degrade at appropriate rates

This might better capture the dynamics observed in the experiments.

## Action

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

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

# Clear any existing reactions (start fresh)
for i in range(model.getNumReactions()-1, -1, -1):
    model.removeReaction(i)

# Add reactions to the model
# 1. Constant production of id_jz57
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_jz57")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (constant rate)
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.4)  # Adjusted value
kinetic_law1.setMath(libsbml.parseL3Formula("k1"))

# 2. Conversion of id_jz57 to id_ri7q and id_nzce
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_jz57")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product2a = reaction2.createProduct()
product2a.setSpecies("id_ri7q")
product2a.setStoichiometry(10.0)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_nzce")
product2b.setStoichiometry(1.0)
product2b.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.01)  # Adjusted value
kinetic_law2.setMath(libsbml.parseL3Formula("k2 * id_jz57"))

# 3. Degradation of id_ri7q
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_ri7q")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.001)  # Adjusted value
kinetic_law3.setMath(libsbml.parseL3Formula("k3 * id_ri7q"))

# 4. Degradation of id_nzce
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_nzce")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.001)  # Same as k3 to maintain 10:1 ratio
kinetic_law4.setMath(libsbml.parseL3Formula("k4 * id_nzce"))

# 5. Degradation of id_jz57
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactant
reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_jz57")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

# Add kinetic law (mass action)
kinetic_law5 = reaction5.createKineticLaw()
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.0001)  # Adjusted value
kinetic_law5.setMath(libsbml.parseL3Formula("k5 * id_jz57"))

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

# Test the model with simulation
print("Testing the fourth model with simulation...")
try:
    result = simulate(updated_sbml)
    
    # Print the first few rows
    print("First few rows of simulation:")
    print(result.head())
    
    # Print the last few rows
    print("\nLast few rows of simulation:")
    print(result.tail())
    
    # Calculate final values
    final_ri7q = result['id_ri7q'].iloc[-1]
    final_nzce = result['id_nzce'].iloc[-1]
    final_jz57 = result['id_jz57'].iloc[-1]
    
    print(f"\nFinal values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    print(f"Total mass: {final_ri7q + final_nzce + final_jz57}")
    
    # Compare with experimental data
    exp_final_ri7q = experiment_history["iteration_0"]['id_ri7q'].iloc[-1]
    exp_final_nzce = experiment_history["iteration_0"]['id_nzce'].iloc[-1]
    exp_final_jz57 = experiment_history["iteration_0"]['id_jz57'].iloc[-1]
    
    print(f"\nExperimental final values:")
    print(f"id_ri7q: {exp_final_ri7q}")
    print(f"id_nzce: {exp_final_nzce}")
    print(f"id_jz57: {exp_final_jz57}")
    print(f"Total mass: {exp_final_ri7q + exp_final_nzce + exp_final_jz57}")
    
    # Store the model for future use
    shared_variables.add("fourth_model", updated_sbml)
    
except Exception as e:
    print(f"Error in simulation: {e}")
```
# Observation

## Code Stdout
Testing the fourth model with simulation...
First few rows of simulation:
      id_ri7q    id_nzce    id_jz57    Time
0  100.000000  10.000000  75.000000  0.0000
1  100.901654  10.090165  74.956455  0.1219
2  101.802728  10.180273  74.912958  0.2438
3  102.703181  10.270318  74.869513  0.3657
4  103.602999  10.360300  74.826121  0.4876

Last few rows of simulation:
           id_ri7q     id_nzce    id_jz57       Time
9996   2933.997906  293.399791  39.604136  1218.5124
9997   2934.123018  293.412302  39.604136  1218.6343
9998   2934.248116  293.424812  39.604136  1218.7562
9999   2934.373197  293.437320  39.604136  1218.8781
10000  2934.498264  293.449826  39.604136  1219.0000

Final values from simulation:
id_ri7q: 2934.4982639865952
id_nzce: 293.4498263986624
id_jz57: 39.604135615187005
Ratio id_ri7q/id_nzce: 9.9999999999999
Total mass: 3267.5522260004445

Experimental final values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937
Total mass: 443.15957786381296

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data, first_model, second_model, third_model, fourth_model)

### 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
My fourth model is getting closer in some aspects but still has significant discrepancies:

1. The id_jz57 value (39.6) is now very close to the experimental value (40.7), which is a significant improvement.

2. The ratio of id_ri7q to id_nzce is maintained at 10:1, which matches the experimental data.

3. However, the absolute values of id_ri7q and id_nzce are still much higher than the experimental values, and consequently, the total mass is still too high (3267.6 vs 443.2).

I need to further refine the model to get the correct equilibrium values for all species. Let me try adjusting the parameters to achieve this. Specifically, I need to:

1. Reduce the production rate of id_jz57 or increase the degradation rates of id_ri7q and id_nzce to achieve the correct equilibrium values.

2. Maintain the correct ratio between species.

Let me create a fifth model with adjusted parameters.

## Action

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

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

# Clear any existing reactions (start fresh)
for i in range(model.getNumReactions()-1, -1, -1):
    model.removeReaction(i)

# Add reactions to the model
# 1. Constant production of id_jz57
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_jz57")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (constant rate)
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Reduced value
kinetic_law1.setMath(libsbml.parseL3Formula("k1"))

# 2. Conversion of id_jz57 to id_ri7q and id_nzce
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_jz57")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product2a = reaction2.createProduct()
product2a.setSpecies("id_ri7q")
product2a.setStoichiometry(10.0)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_nzce")
product2b.setStoichiometry(1.0)
product2b.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.01)  # Same value
kinetic_law2.setMath(libsbml.parseL3Formula("k2 * id_jz57"))

# 3. Degradation of id_ri7q
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_ri7q")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.008)  # Increased value
kinetic_law3.setMath(libsbml.parseL3Formula("k3 * id_ri7q"))

# 4. Degradation of id_nzce
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_nzce")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.008)  # Same as k3 to maintain 10:1 ratio
kinetic_law4.setMath(libsbml.parseL3Formula("k4 * id_nzce"))

# 5. Degradation of id_jz57
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactant
reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_jz57")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

# Add kinetic law (mass action)
kinetic_law5 = reaction5.createKineticLaw()
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.0001)  # Same value
kinetic_law5.setMath(libsbml.parseL3Formula("k5 * id_jz57"))

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

# Test the model with simulation
print("Testing the fifth model with simulation...")
try:
    result = simulate(updated_sbml)
    
    # Print the first few rows
    print("First few rows of simulation:")
    print(result.head())
    
    # Print the last few rows
    print("\nLast few rows of simulation:")
    print(result.tail())
    
    # Calculate final values
    final_ri7q = result['id_ri7q'].iloc[-1]
    final_nzce = result['id_nzce'].iloc[-1]
    final_jz57 = result['id_jz57'].iloc[-1]
    
    print(f"\nFinal values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    print(f"Total mass: {final_ri7q + final_nzce + final_jz57}")
    
    # Compare with experimental data
    exp_final_ri7q = experiment_history["iteration_0"]['id_ri7q'].iloc[-1]
    exp_final_nzce = experiment_history["iteration_0"]['id_nzce'].iloc[-1]
    exp_final_jz57 = experiment_history["iteration_0"]['id_jz57'].iloc[-1]
    
    print(f"\nExperimental final values:")
    print(f"id_ri7q: {exp_final_ri7q}")
    print(f"id_nzce: {exp_final_nzce}")
    print(f"id_jz57: {exp_final_jz57}")
    print(f"Total mass: {exp_final_ri7q + exp_final_nzce + exp_final_jz57}")
    
    # Calculate percentage errors
    pct_error_ri7q = 100 * abs(final_ri7q - exp_final_ri7q) / exp_final_ri7q
    pct_error_nzce = 100 * abs(final_nzce - exp_final_nzce) / exp_final_nzce
    pct_error_jz57 = 100 * abs(final_jz57 - exp_final_jz57) / exp_final_jz57
    pct_error_total = 100 * abs((final_ri7q + final_nzce + final_jz57) - (exp_final_ri7q + exp_final_nzce + exp_final_jz57)) / (exp_final_ri7q + exp_final_nzce + exp_final_jz57)
    
    print(f"\nPercentage errors:")
    print(f"id_ri7q: {pct_error_ri7q:.2f}%")
    print(f"id_nzce: {pct_error_nzce:.2f}%")
    print(f"id_jz57: {pct_error_jz57:.2f}%")
    print(f"Total mass: {pct_error_total:.2f}%")
    
    # Store the model for future use
    shared_variables.add("fifth_model", updated_sbml)
    
except Exception as e:
    print(f"Error in simulation: {e}")
```
# Observation

## Code Stdout
Testing the fifth model with simulation...
First few rows of simulation:
      id_ri7q    id_nzce    id_jz57    Time
0  100.000000  10.000000  75.000000  0.0000
1  100.815699  10.081570  74.913815  0.1219
2  101.629651  10.162965  74.827730  0.2438
3  102.441768  10.244177  74.741751  0.3657
4  103.252050  10.325205  74.655878  0.4876

Last few rows of simulation:
         id_ri7q   id_nzce   id_jz57       Time
9996   62.063230  6.206323  4.950813  1218.5124
9997   62.063056  6.206306  4.950812  1218.6343
9998   62.062883  6.206288  4.950812  1218.7562
9999   62.062710  6.206271  4.950811  1218.8781
10000  62.062537  6.206254  4.950811  1219.0000

Final values from simulation:
id_ri7q: 62.06253685422288
id_nzce: 6.2062536854223165
id_jz57: 4.950810948089906
Ratio id_ri7q/id_nzce: 9.999999999999954
Total mass: 73.2196014877351

Experimental final values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937
Total mass: 443.15957786381296

Percentage errors:
id_ri7q: 83.04%
id_nzce: 83.04%
id_jz57: 87.82%
Total mass: 83.48%

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data, first_model, second_model, third_model, fourth_model, fifth_model)

### 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
My fifth model has swung too far in the opposite direction - now the values are much lower than the experimental data:

1. Simulated: id_ri7q ≈ 62.1, id_nzce ≈ 6.2, id_jz57 ≈ 5.0
2. Experimental: id_ri7q ≈ 365.9, id_nzce ≈ 36.6, id_jz57 ≈ 40.7

The percentage errors are very high (>80% for all species). However, the model still maintains the correct 10:1 ratio between id_ri7q and id_nzce.

I need to find a better balance in the parameters. Let me try a more systematic approach. At equilibrium, the rates of production and degradation should balance for each species. Let me calculate the parameters that would give the correct equilibrium values.

For a system at equilibrium:
- Production rate of id_jz57 = Degradation rate of id_jz57 + Conversion rate to id_ri7q and id_nzce
- Production rate of id_ri7q (from id_jz57) = Degradation rate of id_ri7q
- Production rate of id_nzce (from id_jz57) = Degradation rate of id_nzce

Let me create a sixth model with parameters calculated to achieve the correct equilibrium values.

## Action

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

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

# Clear any existing reactions (start fresh)
for i in range(model.getNumReactions()-1, -1, -1):
    model.removeReaction(i)

# Get the target equilibrium values from experimental data
exp_final_ri7q = experiment_history["iteration_0"]['id_ri7q'].iloc[-1]
exp_final_nzce = experiment_history["iteration_0"]['id_nzce'].iloc[-1]
exp_final_jz57 = experiment_history["iteration_0"]['id_jz57'].iloc[-1]

print(f"Target equilibrium values:")
print(f"id_ri7q: {exp_final_ri7q}")
print(f"id_nzce: {exp_final_nzce}")
print(f"id_jz57: {exp_final_jz57}")

# Calculate parameters to achieve these equilibrium values
# Let's set some parameters and calculate the others

# Set degradation rates
k3 = 0.001  # Degradation rate of id_ri7q
k4 = 0.001  # Degradation rate of id_nzce (same as k3 to maintain 10:1 ratio)
k5 = 0.001  # Degradation rate of id_jz57

# At equilibrium:
# k2 * exp_final_jz57 = k3 * exp_final_ri7q / 10 (since 10 id_ri7q are produced per id_jz57)
# So k2 = k3 * exp_final_ri7q / (10 * exp_final_jz57)
k2 = k3 * exp_final_ri7q / (10 * exp_final_jz57)

# At equilibrium:
# k1 = k5 * exp_final_jz57 + k2 * exp_final_jz57
# So k1 = exp_final_jz57 * (k5 + k2)
k1 = exp_final_jz57 * (k5 + k2)

print(f"\nCalculated parameters:")
print(f"k1 (production rate of id_jz57): {k1}")
print(f"k2 (conversion rate of id_jz57 to id_ri7q and id_nzce): {k2}")
print(f"k3 (degradation rate of id_ri7q): {k3}")
print(f"k4 (degradation rate of id_nzce): {k4}")
print(f"k5 (degradation rate of id_jz57): {k5}")

# Add reactions to the model
# 1. Constant production of id_jz57
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_jz57")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (constant rate)
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(k1)
kinetic_law1.setMath(libsbml.parseL3Formula("k1"))

# 2. Conversion of id_jz57 to id_ri7q and id_nzce
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_jz57")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product2a = reaction2.createProduct()
product2a.setSpecies("id_ri7q")
product2a.setStoichiometry(10.0)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_nzce")
product2b.setStoichiometry(1.0)
product2b.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(k2)
kinetic_law2.setMath(libsbml.parseL3Formula("k2 * id_jz57"))

# 3. Degradation of id_ri7q
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_ri7q")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(k3)
kinetic_law3.setMath(libsbml.parseL3Formula("k3 * id_ri7q"))

# 4. Degradation of id_nzce
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_nzce")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(k4)
kinetic_law4.setMath(libsbml.parseL3Formula("k4 * id_nzce"))

# 5. Degradation of id_jz57
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactant
reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_jz57")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

# Add kinetic law (mass action)
kinetic_law5 = reaction5.createKineticLaw()
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(k5)
kinetic_law5.setMath(libsbml.parseL3Formula("k5 * id_jz57"))

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

# Test the model with simulation
print("\nTesting the sixth model with simulation...")
try:
    result = simulate(updated_sbml)
    
    # Print the first few rows
    print("First few rows of simulation:")
    print(result.head())
    
    # Print the last few rows
    print("\nLast few rows of simulation:")
    print(result.tail())
    
    # Calculate final values
    final_ri7q = result['id_ri7q'].iloc[-1]
    final_nzce = result['id_nzce'].iloc[-1]
    final_jz57 = result['id_jz57'].iloc[-1]
    
    print(f"\nFinal values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    print(f"Total mass: {final_ri7q + final_nzce + final_jz57}")
    
    # Compare with experimental data
    print(f"\nExperimental final values:")
    print(f"id_ri7q: {exp_final_ri7q}")
    print(f"id_nzce: {exp_final_nzce}")
    print(f"id_jz57: {exp_final_jz57}")
    print(f"Total mass: {exp_final_ri7q + exp_final_nzce + exp_final_jz57}")
    
    # Calculate percentage errors
    pct_error_ri7q = 100 * abs(final_ri7q - exp_final_ri7q) / exp_final_ri7q
    pct_error_nzce = 100 * abs(final_nzce - exp_final_nzce) / exp_final_nzce
    pct_error_jz57 = 100 * abs(final_jz57 - exp_final_jz57) / exp_final_jz57
    pct_error_total = 100 * abs((final_ri7q + final_nzce + final_jz57) - (exp_final_ri7q + exp_final_nzce + exp_final_jz57)) / (exp_final_ri7q + exp_final_nzce + exp_final_jz57)
    
    print(f"\nPercentage errors:")
    print(f"id_ri7q: {pct_error_ri7q:.2f}%")
    print(f"id_nzce: {pct_error_nzce:.2f}%")
    print(f"id_jz57: {pct_error_jz57:.2f}%")
    print(f"Total mass: {pct_error_total:.2f}%")
    
    # Store the model for future use
    shared_variables.add("sixth_model", updated_sbml)
    
    # Now let's test this model with the other initial conditions
    print("\nTesting the model with different initial conditions...")
    
    # Test with higher id_jz57 (iteration_3)
    exp_data = experiment_history["iteration_3"]
    initial_ri7q = exp_data['id_ri7q'].iloc[0]
    initial_nzce = exp_data['id_nzce'].iloc[0]
    initial_jz57 = exp_data['id_jz57'].iloc[0]
    
    print(f"\nInitial conditions from iteration_3:")
    print(f"id_ri7q: {initial_ri7q}, id_nzce: {initial_nzce}, id_jz57: {initial_jz57}")
    
except Exception as e:
    print(f"Error in simulation: {e}")
```
# Observation

## Code Stdout
Target equilibrium values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937

Calculated parameters:
k1 (production rate of id_jz57): 0.07724814196514078
k2 (conversion rate of id_jz57 to id_ri7q and id_nzce): 0.0008999962522320342
k3 (degradation rate of id_ri7q): 0.001
k4 (degradation rate of id_nzce): 0.001
k5 (degradation rate of id_jz57): 0.001

Testing the sixth model with simulation...
First few rows of simulation:
      id_ri7q    id_nzce    id_jz57    Time
0  100.000000  10.000000  75.000000  0.0000
1  100.070071  10.007007  74.992048  0.1219
2  100.140124  10.014012  74.984098  0.2438
3  100.210166  10.021017  74.976149  0.3657
4  100.280194  10.028019  74.968202  0.4876

Last few rows of simulation:
          id_ri7q    id_nzce    id_jz57       Time
9996   354.918212  35.491821  44.048309  1218.5124
9997   354.923272  35.492327  44.047524  1218.6343
9998   354.928331  35.492833  44.046738  1218.7562
9999   354.933388  35.493339  44.045953  1218.8781
10000  354.938443  35.493844  44.045169  1219.0000

Final values from simulation:
id_ri7q: 354.9384432385736
id_nzce: 35.49384432385732
id_jz57: 44.04516860746928
Ratio id_ri7q/id_nzce: 10.000000000000012
Total mass: 434.4774561699002

Experimental final values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937
Total mass: 443.15957786381296

Percentage errors:
id_ri7q: 3.00%
id_nzce: 3.00%
id_jz57: 8.33%
Total mass: 1.96%

Testing the model with different initial conditions...

Initial conditions from iteration_3:
id_ri7q: 100.0, id_nzce: 10.0, id_jz57: 150.0

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data, first_model, second_model, third_model, fourth_model, fifth_model, sixth_model)

### 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
Great progress! My sixth model is much closer to the experimental data:

1. The percentage errors are now quite low:
   - id_ri7q: 3.00%
   - id_nzce: 3.00%
   - id_jz57: 8.33%
   - Total mass: 1.96%

2. The ratio of id_ri7q to id_nzce is maintained at exactly 10:1.

3. The total mass is very close to the experimental value.

This systematic approach of calculating parameters based on the equilibrium conditions has worked well. Now I need to test this model with different initial conditions to see if it correctly predicts the dynamics observed in the other experiments.

Let me simulate the model with the initial conditions from the other experiments and compare the results.

## Action

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

# Get the sixth model
updated_sbml = shared_variables.access("sixth_model")

# Test with higher id_jz57 (iteration_3)
print("Testing with higher id_jz57 (iteration_3)...")
try:
    # Modify the initial concentrations in the model
    sbml_doc = libsbml.readSBMLFromString(updated_sbml)
    model = sbml_doc.getModel()
    
    # Set initial concentrations from iteration_3
    exp_data3 = experiment_history["iteration_3"]
    initial_ri7q = exp_data3['id_ri7q'].iloc[0]
    initial_nzce = exp_data3['id_nzce'].iloc[0]
    initial_jz57 = exp_data3['id_jz57'].iloc[0]
    
    model.getSpecies("id_ri7q").setInitialConcentration(initial_ri7q)
    model.getSpecies("id_nzce").setInitialConcentration(initial_nzce)
    model.getSpecies("id_jz57").setInitialConcentration(initial_jz57)
    
    # Write the updated SBML
    writer = libsbml.SBMLWriter()
    modified_sbml = writer.writeSBMLToString(sbml_doc)
    
    # Simulate
    result3 = simulate(modified_sbml)
    
    # Print the first few rows
    print("First few rows of simulation:")
    print(result3.head())
    
    # Print the last few rows
    print("\nLast few rows of simulation:")
    print(result3.tail())
    
    # Calculate final values
    final_ri7q = result3['id_ri7q'].iloc[-1]
    final_nzce = result3['id_nzce'].iloc[-1]
    final_jz57 = result3['id_jz57'].iloc[-1]
    
    print(f"\nFinal values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    print(f"Total mass: {final_ri7q + final_nzce + final_jz57}")
    
    # Compare with experimental data
    exp_final_ri7q = exp_data3['id_ri7q'].iloc[-1]
    exp_final_nzce = exp_data3['id_nzce'].iloc[-1]
    exp_final_jz57 = exp_data3['id_jz57'].iloc[-1]
    
    print(f"\nExperimental final values:")
    print(f"id_ri7q: {exp_final_ri7q}")
    print(f"id_nzce: {exp_final_nzce}")
    print(f"id_jz57: {exp_final_jz57}")
    print(f"Total mass: {exp_final_ri7q + exp_final_nzce + exp_final_jz57}")
    
    # Calculate percentage errors
    pct_error_ri7q = 100 * abs(final_ri7q - exp_final_ri7q) / exp_final_ri7q
    pct_error_nzce = 100 * abs(final_nzce - exp_final_nzce) / exp_final_nzce
    pct_error_jz57 = 100 * abs(final_jz57 - exp_final_jz57) / exp_final_jz57
    pct_error_total = 100 * abs((final_ri7q + final_nzce + final_jz57) - (exp_final_ri7q + exp_final_nzce + exp_final_jz57)) / (exp_final_ri7q + exp_final_nzce + exp_final_jz57)
    
    print(f"\nPercentage errors:")
    print(f"id_ri7q: {pct_error_ri7q:.2f}%")
    print(f"id_nzce: {pct_error_nzce:.2f}%")
    print(f"id_jz57: {pct_error_jz57:.2f}%")
    print(f"Total mass: {pct_error_total:.2f}%")
    
    # Test with higher id_ri7q and id_nzce (iteration_5)
    print("\nTesting with higher id_ri7q and id_nzce (iteration_5)...")
    
    # Modify the initial concentrations in the model
    sbml_doc = libsbml.readSBMLFromString(updated_sbml)
    model = sbml_doc.getModel()
    
    # Set initial concentrations from iteration_5
    exp_data5 = experiment_history["iteration_5"]
    initial_ri7q = exp_data5['id_ri7q'].iloc[0]
    initial_nzce = exp_data5['id_nzce'].iloc[0]
    initial_jz57 = exp_data5['id_jz57'].iloc[0]
    
    model.getSpecies("id_ri7q").setInitialConcentration(initial_ri7q)
    model.getSpecies("id_nzce").setInitialConcentration(initial_nzce)
    model.getSpecies("id_jz57").setInitialConcentration(initial_jz57)
    
    # Write the updated SBML
    writer = libsbml.SBMLWriter()
    modified_sbml = writer.writeSBMLToString(sbml_doc)
    
    # Simulate
    result5 = simulate(modified_sbml)
    
    # Print the first few rows
    print("First few rows of simulation:")
    print(result5.head())
    
    # Print the last few rows
    print("\nLast few rows of simulation:")
    print(result5.tail())
    
    # Calculate final values
    final_ri7q = result5['id_ri7q'].iloc[-1]
    final_nzce = result5['id_nzce'].iloc[-1]
    final_jz57 = result5['id_jz57'].iloc[-1]
    
    print(f"\nFinal values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    print(f"Total mass: {final_ri7q + final_nzce + final_jz57}")
    
    # Compare with experimental data
    exp_final_ri7q = exp_data5['id_ri7q'].iloc[-1]
    exp_final_nzce = exp_data5['id_nzce'].iloc[-1]
    exp_final_jz57 = exp_data5['id_jz57'].iloc[-1]
    
    print(f"\nExperimental final values:")
    print(f"id_ri7q: {exp_final_ri7q}")
    print(f"id_nzce: {exp_final_nzce}")
    print(f"id_jz57: {exp_final_jz57}")
    print(f"Total mass: {exp_final_ri7q + exp_final_nzce + exp_final_jz57}")
    
    # Calculate percentage errors
    pct_error_ri7q = 100 * abs(final_ri7q - exp_final_ri7q) / exp_final_ri7q
    pct_error_nzce = 100 * abs(final_nzce - exp_final_nzce) / exp_final_nzce
    pct_error_jz57 = 100 * abs(final_jz57 - exp_final_jz57) / exp_final_jz57
    pct_error_total = 100 * abs((final_ri7q + final_nzce + final_jz57) - (exp_final_ri7q + exp_final_nzce + exp_final_jz57)) / (exp_final_ri7q + exp_final_nzce + exp_final_jz57)
    
    print(f"\nPercentage errors:")
    print(f"id_ri7q: {pct_error_ri7q:.2f}%")
    print(f"id_nzce: {pct_error_nzce:.2f}%")
    print(f"id_jz57: {pct_error_jz57:.2f}%")
    print(f"Total mass: {pct_error_total:.2f}%")
    
except Exception as e:
    print(f"Error in simulation: {e}")
```
# Observation

## Code Stdout
Testing with higher id_jz57 (iteration_3)...
First few rows of simulation:
      id_ri7q    id_nzce     id_jz57    Time
0  100.000000  10.000000  150.000000  0.0000
1  100.152317  10.015232  149.974682  0.1219
2  100.304587  10.030459  149.949371  0.2438
3  100.456825  10.045683  149.924063  0.3657
4  100.609029  10.060903  149.898760  0.4876

Last few rows of simulation:
          id_ri7q    id_nzce    id_jz57       Time
9996   502.607300  50.260730  51.454625  1218.5124
9997   502.602480  50.260248  51.452125  1218.6343
9998   502.597659  50.259766  51.449625  1218.7562
9999   502.592835  50.259284  51.447126  1218.8781
10000  502.588009  50.258801  51.444627  1219.0000

Final values from simulation:
id_ri7q: 502.5880094258409
id_nzce: 50.25880094257592
id_jz57: 51.44462722860194
Ratio id_ri7q/id_nzce: 10.000000000001625
Total mass: 604.2914375970187

Experimental final values:
id_ri7q: 365.91142217362705
id_nzce: 36.591128040397756
id_jz57: 40.656999290276026
Total mass: 443.1595495043008

Percentage errors:
id_ri7q: 37.35%
id_nzce: 37.35%
id_jz57: 26.53%
Total mass: 36.36%

Testing with higher id_ri7q and id_nzce (iteration_5)...
First few rows of simulation:
      id_ri7q    id_nzce    id_jz57    Time
0  200.000000  20.000000  75.000000  0.0000
1  200.057883  20.005788  74.992048  0.1219
2  200.115749  20.011575  74.984098  0.2438
3  200.173605  20.017361  74.976149  0.3657
4  200.231449  20.023145  74.968202  0.4876

Last few rows of simulation:
          id_ri7q    id_nzce    id_jz57       Time
9996   384.485323  38.448532  44.048291  1218.5124
9997   384.486779  38.448678  44.047506  1218.6343
9998   384.488234  38.448823  44.046720  1218.7562
9999   384.489688  38.448969  44.045935  1218.8781
10000  384.491141  38.449114  44.045151  1219.0000

Final values from simulation:
id_ri7q: 384.49114061007964
id_nzce: 38.449114061008224
id_jz57: 44.04515061670154
Ratio id_ri7q/id_nzce: 9.999999999999932
Total mass: 466.98540528778943

Experimental final values:
id_ri7q: 365.9112688205561
id_nzce: 36.59111178115032
id_jz57: 40.6570003730284
Total mass: 443.15938097473474

Percentage errors:
id_ri7q: 5.08%
id_nzce: 5.08%
id_jz57: 8.33%
Total mass: 5.38%

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data, first_model, second_model, third_model, fourth_model, fifth_model, sixth_model)

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


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



# Iteration 14
## Thoughts
The model performs well for the default initial conditions (iteration_0) and reasonably well for the higher id_ri7q and id_nzce conditions (iteration_5), but it has larger errors for the higher id_jz57 conditions (iteration_3):

1. For iteration_0 (default):
   - Percentage errors: id_ri7q: 3.00%, id_nzce: 3.00%, id_jz57: 8.33%, total mass: 1.96%

2. For iteration_5 (higher id_ri7q and id_nzce):
   - Percentage errors: id_ri7q: 5.08%, id_nzce: 5.08%, id_jz57: 8.33%, total mass: 5.38%

3. For iteration_3 (higher id_jz57):
   - Percentage errors: id_ri7q: 37.35%, id_nzce: 37.35%, id_jz57: 26.53%, total mass: 36.36%

The model maintains the correct 10:1 ratio between id_ri7q and id_nzce in all cases, but the absolute values are significantly off for the higher id_jz57 case. This suggests that our model is missing some mechanism that limits the total mass in the system when starting with higher id_jz57.

Let me refine the model to better capture this behavior. One possibility is that there's a feedback mechanism where high concentrations of id_ri7q and id_nzce inhibit the conversion of id_jz57, or where high concentrations of id_jz57 enhance its own degradation.

Let me try a model with feedback inhibition:

## Action

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

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

# Clear any existing reactions (start fresh)
for i in range(model.getNumReactions()-1, -1, -1):
    model.removeReaction(i)

# Get the target equilibrium values from experimental data
exp_final_ri7q = experiment_history["iteration_0"]['id_ri7q'].iloc[-1]
exp_final_nzce = experiment_history["iteration_0"]['id_nzce'].iloc[-1]
exp_final_jz57 = experiment_history["iteration_0"]['id_jz57'].iloc[-1]

print(f"Target equilibrium values:")
print(f"id_ri7q: {exp_final_ri7q}")
print(f"id_nzce: {exp_final_nzce}")
print(f"id_jz57: {exp_final_jz57}")

# Add reactions to the model
# 1. Constant production of id_jz57
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_jz57")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (constant rate)
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.08)  # Adjusted value
kinetic_law1.setMath(libsbml.parseL3Formula("k1"))

# 2. Conversion of id_jz57 to id_ri7q and id_nzce with feedback inhibition
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_jz57")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product2a = reaction2.createProduct()
product2a.setSpecies("id_ri7q")
product2a.setStoichiometry(10.0)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_nzce")
product2b.setStoichiometry(1.0)
product2b.setConstant(True)

# Add kinetic law with feedback inhibition
kinetic_law2 = reaction2.createKineticLaw()
parameter2a = kinetic_law2.createParameter()
parameter2a.setId("k2")
parameter2a.setValue(0.001)  # Base rate
parameter2b = kinetic_law2.createParameter()
parameter2b.setId("Ki")
parameter2b.setValue(400)  # Inhibition constant
kinetic_law2.setMath(libsbml.parseL3Formula("k2 * id_jz57 / (1 + id_ri7q / Ki)"))

# 3. Degradation of id_ri7q
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_ri7q")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.001)  # Adjusted value
kinetic_law3.setMath(libsbml.parseL3Formula("k3 * id_ri7q"))

# 4. Degradation of id_nzce
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_nzce")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.001)  # Same as k3 to maintain 10:1 ratio
kinetic_law4.setMath(libsbml.parseL3Formula("k4 * id_nzce"))

# 5. Degradation of id_jz57
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactant
reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_jz57")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

# Add kinetic law (mass action)
kinetic_law5 = reaction5.createKineticLaw()
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.001)  # Adjusted value
kinetic_law5.setMath(libsbml.parseL3Formula("k5 * id_jz57"))

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

# Test the model with simulation for all three initial conditions
print("\nTesting the feedback inhibition model...")

# Function to test the model with given initial conditions
def test_model_with_initial_conditions(sbml_string, initial_ri7q, initial_nzce, initial_jz57, exp_data, experiment_name):
    print(f"\nTesting with {experiment_name}...")
    
    # Modify the initial concentrations in the model
    sbml_doc = libsbml.readSBMLFromString(sbml_string)
    model = sbml_doc.getModel()
    
    model.getSpecies("id_ri7q").setInitialConcentration(initial_ri7q)
    model.getSpecies("id_nzce").setInitialConcentration(initial_nzce)
    model.getSpecies("id_jz57").setInitialConcentration(initial_jz57)
    
    # Write the updated SBML
    writer = libsbml.SBMLWriter()
    modified_sbml = writer.writeSBMLToString(sbml_doc)
    
    # Simulate
    result = simulate(modified_sbml)
    
    # Calculate final values
    final_ri7q = result['id_ri7q'].iloc[-1]
    final_nzce = result['id_nzce'].iloc[-1]
    final_jz57 = result['id_jz57'].iloc[-1]
    
    print(f"Final values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    print(f"Total mass: {final_ri7q + final_nzce + final_jz57}")
    
    # Compare with experimental data
    exp_final_ri7q = exp_data['id_ri7q'].iloc[-1]
    exp_final_nzce = exp_data['id_nzce'].iloc[-1]
    exp_final_jz57 = exp_data['id_jz57'].iloc[-1]
    
    print(f"Experimental final values:")
    print(f"id_ri7q: {exp_final_ri7q}")
    print(f"id_nzce: {exp_final_nzce}")
    print(f"id_jz57: {exp_final_jz57}")
    print(f"Total mass: {exp_final_ri7q + exp_final_nzce + exp_final_jz57}")
    
    # Calculate percentage errors
    pct_error_ri7q = 100 * abs(final_ri7q - exp_final_ri7q) / exp_final_ri7q
    pct_error_nzce = 100 * abs(final_nzce - exp_final_nzce) / exp_final_nzce
    pct_error_jz57 = 100 * abs(final_jz57 - exp_final_jz57) / exp_final_jz57
    pct_error_total = 100 * abs((final_ri7q + final_nzce + final_jz57) - (exp_final_ri7q + exp_final_nzce + exp_final_jz57)) / (exp_final_ri7q + exp_final_nzce + exp_final_jz57)
    
    print(f"Percentage errors:")
    print(f"id_ri7q: {pct_error_ri7q:.2f}%")
    print(f"id_nzce: {pct_error_nzce:.2f}%")
    print(f"id_jz57: {pct_error_jz57:.2f}%")
    print(f"Total mass: {pct_error_total:.2f}%")
    
    return result

try:
    # Test with default initial conditions (iteration_0)
    exp_data0 = experiment_history["iteration_0"]
    initial_ri7q = exp_data0['id_ri7q'].iloc[0]
    initial_nzce = exp_data0['id_nzce'].iloc[0]
    initial_jz57 = exp_data0['id_jz57'].iloc[0]
    
    result0 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data0, "default initial conditions (iteration_0)")
    
    # Test with higher id_jz57 (iteration_3)
    exp_data3 = experiment_history["iteration_3"]
    initial_ri7q = exp_data3['id_ri7q'].iloc[0]
    initial_nzce = exp_data3['id_nzce'].iloc[0]
    initial_jz57 = exp_data3['id_jz57'].iloc[0]
    
    result3 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data3, "higher id_jz57 (iteration_3)")
    
    # Test with higher id_ri7q and id_nzce (iteration_5)
    exp_data5 = experiment_history["iteration_5"]
    initial_ri7q = exp_data5['id_ri7q'].iloc[0]
    initial_nzce = exp_data5['id_nzce'].iloc[0]
    initial_jz57 = exp_data5['id_jz57'].iloc[0]
    
    result5 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data5, "higher id_ri7q and id_nzce (iteration_5)")
    
    # Store the model for future use
    shared_variables.add("feedback_inhibition_model", updated_sbml)
    
except Exception as e:
    print(f"Error in simulation: {e}")
```
# Observation

## Code Stdout
Target equilibrium values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937

Testing the feedback inhibition model...

Testing with default initial conditions (iteration_0)...
Final values from simulation:
id_ri7q: 284.280987207864
id_nzce: 28.428098720786583
id_jz57: 53.049529023597195
Ratio id_ri7q/id_nzce: 9.999999999999934
Total mass: 365.75861495224774
Experimental final values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937
Total mass: 443.15957786381296
Percentage errors:
id_ri7q: 22.31%
id_nzce: 22.31%
id_jz57: 30.48%
Total mass: 17.47%

Testing with higher id_jz57 (iteration_3)...
Final values from simulation:
id_ri7q: 370.1647558657897
id_nzce: 37.01647558657848
id_jz57: 66.62556930450641
Ratio id_ri7q/id_nzce: 10.000000000000131
Total mass: 473.80680075687457
Experimental final values:
id_ri7q: 365.91142217362705
id_nzce: 36.591128040397756
id_jz57: 40.656999290276026
Total mass: 443.1595495043008
Percentage errors:
id_ri7q: 1.16%
id_nzce: 1.16%
id_jz57: 63.87%
Total mass: 6.92%

Testing with higher id_ri7q and id_nzce (iteration_5)...
Final values from simulation:
id_ri7q: 303.2092881799565
id_nzce: 30.320928817995643
id_jz57: 54.11195090184607
Ratio id_ri7q/id_nzce: 10.000000000000002
Total mass: 387.6421678997982
Experimental final values:
id_ri7q: 365.9112688205561
id_nzce: 36.59111178115032
id_jz57: 40.6570003730284
Total mass: 443.15938097473474
Percentage errors:
id_ri7q: 17.14%
id_nzce: 17.14%
id_jz57: 33.09%
Total mass: 12.53%

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data, first_model, second_model, third_model, fourth_model, fifth_model, sixth_model, feedback_inhibition_model)

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


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



# Iteration 15
## Thoughts
The feedback inhibition model shows mixed results:

1. For iteration_0 (default):
   - Percentage errors: id_ri7q: 22.31%, id_nzce: 22.31%, id_jz57: 30.48%, total mass: 17.47%

2. For iteration_3 (higher id_jz57):
   - Percentage errors: id_ri7q: 1.16%, id_nzce: 1.16%, id_jz57: 63.87%, total mass: 6.92%

3. For iteration_5 (higher id_ri7q and id_nzce):
   - Percentage errors: id_ri7q: 17.14%, id_nzce: 17.14%, id_jz57: 33.09%, total mass: 12.53%

Interestingly, the model performs best for iteration_3 in terms of id_ri7q and id_nzce, but poorly for id_jz57. The feedback inhibition mechanism helps limit the total mass in the system, but the distribution between species is not quite right.

Let me try a different approach. Instead of feedback inhibition, let me try a model with:

1. A constant production of id_jz57
2. Conversion of id_jz57 to id_ri7q and id_nzce with mass action kinetics
3. Degradation of all species with mass action kinetics
4. A conservation relationship that limits the total mass in the system

I'll implement this by adding a reaction that converts id_ri7q and id_nzce back to id_jz57 with appropriate stoichiometry.

## Action

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

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

# Clear any existing reactions (start fresh)
for i in range(model.getNumReactions()-1, -1, -1):
    model.removeReaction(i)

# Get the target equilibrium values from experimental data
exp_final_ri7q = experiment_history["iteration_0"]['id_ri7q'].iloc[-1]
exp_final_nzce = experiment_history["iteration_0"]['id_nzce'].iloc[-1]
exp_final_jz57 = experiment_history["iteration_0"]['id_jz57'].iloc[-1]

print(f"Target equilibrium values:")
print(f"id_ri7q: {exp_final_ri7q}")
print(f"id_nzce: {exp_final_nzce}")
print(f"id_jz57: {exp_final_jz57}")

# Calculate parameters to achieve these equilibrium values
# Let's set some parameters and calculate the others

# Set degradation rates
k3 = 0.001  # Degradation rate of id_ri7q
k4 = 0.001  # Degradation rate of id_nzce (same as k3 to maintain 10:1 ratio)
k5 = 0.001  # Degradation rate of id_jz57

# At equilibrium:
# k2 * exp_final_jz57 = k3 * exp_final_ri7q / 10 (since 10 id_ri7q are produced per id_jz57)
# So k2 = k3 * exp_final_ri7q / (10 * exp_final_jz57)
k2 = k3 * exp_final_ri7q / (10 * exp_final_jz57)

# At equilibrium:
# k1 = k5 * exp_final_jz57 + k2 * exp_final_jz57 - k6 * exp_final_ri7q * exp_final_nzce / 10
# Let's set k6 to a small value
k6 = 0.0000001  # Rate of conversion of id_ri7q and id_nzce back to id_jz57
k1 = k5 * exp_final_jz57 + k2 * exp_final_jz57 - k6 * exp_final_ri7q * exp_final_nzce / 10

print(f"\nCalculated parameters:")
print(f"k1 (production rate of id_jz57): {k1}")
print(f"k2 (conversion rate of id_jz57 to id_ri7q and id_nzce): {k2}")
print(f"k3 (degradation rate of id_ri7q): {k3}")
print(f"k4 (degradation rate of id_nzce): {k4}")
print(f"k5 (degradation rate of id_jz57): {k5}")
print(f"k6 (conversion rate of id_ri7q and id_nzce back to id_jz57): {k6}")

# Add reactions to the model
# 1. Constant production of id_jz57
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_jz57")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (constant rate)
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(k1)
kinetic_law1.setMath(libsbml.parseL3Formula("k1"))

# 2. Conversion of id_jz57 to id_ri7q and id_nzce
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_jz57")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product2a = reaction2.createProduct()
product2a.setSpecies("id_ri7q")
product2a.setStoichiometry(10.0)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_nzce")
product2b.setStoichiometry(1.0)
product2b.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(k2)
kinetic_law2.setMath(libsbml.parseL3Formula("k2 * id_jz57"))

# 3. Degradation of id_ri7q
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_ri7q")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(k3)
kinetic_law3.setMath(libsbml.parseL3Formula("k3 * id_ri7q"))

# 4. Degradation of id_nzce
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_nzce")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(k4)
kinetic_law4.setMath(libsbml.parseL3Formula("k4 * id_nzce"))

# 5. Degradation of id_jz57
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactant
reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_jz57")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

# Add kinetic law (mass action)
kinetic_law5 = reaction5.createKineticLaw()
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(k5)
kinetic_law5.setMath(libsbml.parseL3Formula("k5 * id_jz57"))

# 6. Conversion of id_ri7q and id_nzce back to id_jz57
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

# Add reactants
reactant6a = reaction6.createReactant()
reactant6a.setSpecies("id_ri7q")
reactant6a.setStoichiometry(10.0)
reactant6a.setConstant(True)

reactant6b = reaction6.createReactant()
reactant6b.setSpecies("id_nzce")
reactant6b.setStoichiometry(1.0)
reactant6b.setConstant(True)

# Add product
product6 = reaction6.createProduct()
product6.setSpecies("id_jz57")
product6.setStoichiometry(1.0)
product6.setConstant(True)

# Add kinetic law (mass action)
kinetic_law6 = reaction6.createKineticLaw()
parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(k6)
kinetic_law6.setMath(libsbml.parseL3Formula("k6 * id_ri7q * id_nzce"))

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

# Test the model with simulation for all three initial conditions
print("\nTesting the conservation model...")

# Function to test the model with given initial conditions
def test_model_with_initial_conditions(sbml_string, initial_ri7q, initial_nzce, initial_jz57, exp_data, experiment_name):
    print(f"\nTesting with {experiment_name}...")
    
    # Modify the initial concentrations in the model
    sbml_doc = libsbml.readSBMLFromString(sbml_string)
    model = sbml_doc.getModel()
    
    model.getSpecies("id_ri7q").setInitialConcentration(initial_ri7q)
    model.getSpecies("id_nzce").setInitialConcentration(initial_nzce)
    model.getSpecies("id_jz57").setInitialConcentration(initial_jz57)
    
    # Write the updated SBML
    writer = libsbml.SBMLWriter()
    modified_sbml = writer.writeSBMLToString(sbml_doc)
    
    # Simulate
    result = simulate(modified_sbml)
    
    # Calculate final values
    final_ri7q = result['id_ri7q'].iloc[-1]
    final_nzce = result['id_nzce'].iloc[-1]
    final_jz57 = result['id_jz57'].iloc[-1]
    
    print(f"Final values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    print(f"Total mass: {final_ri7q + final_nzce + final_jz57}")
    
    # Compare with experimental data
    exp_final_ri7q = exp_data['id_ri7q'].iloc[-1]
    exp_final_nzce = exp_data['id_nzce'].iloc[-1]
    exp_final_jz57 = exp_data['id_jz57'].iloc[-1]
    
    print(f"Experimental final values:")
    print(f"id_ri7q: {exp_final_ri7q}")
    print(f"id_nzce: {exp_final_nzce}")
    print(f"id_jz57: {exp_final_jz57}")
    print(f"Total mass: {exp_final_ri7q + exp_final_nzce + exp_final_jz57}")
    
    # Calculate percentage errors
    pct_error_ri7q = 100 * abs(final_ri7q - exp_final_ri7q) / exp_final_ri7q
    pct_error_nzce = 100 * abs(final_nzce - exp_final_nzce) / exp_final_nzce
    pct_error_jz57 = 100 * abs(final_jz57 - exp_final_jz57) / exp_final_jz57
    pct_error_total = 100 * abs((final_ri7q + final_nzce + final_jz57) - (exp_final_ri7q + exp_final_nzce + exp_final_jz57)) / (exp_final_ri7q + exp_final_nzce + exp_final_jz57)
    
    print(f"Percentage errors:")
    print(f"id_ri7q: {pct_error_ri7q:.2f}%")
    print(f"id_nzce: {pct_error_nzce:.2f}%")
    print(f"id_jz57: {pct_error_jz57:.2f}%")
    print(f"Total mass: {pct_error_total:.2f}%")
    
    return result

try:
    # Test with default initial conditions (iteration_0)
    exp_data0 = experiment_history["iteration_0"]
    initial_ri7q = exp_data0['id_ri7q'].iloc[0]
    initial_nzce = exp_data0['id_nzce'].iloc[0]
    initial_jz57 = exp_data0['id_jz57'].iloc[0]
    
    result0 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data0, "default initial conditions (iteration_0)")
    
    # Test with higher id_jz57 (iteration_3)
    exp_data3 = experiment_history["iteration_3"]
    initial_ri7q = exp_data3['id_ri7q'].iloc[0]
    initial_nzce = exp_data3['id_nzce'].iloc[0]
    initial_jz57 = exp_data3['id_jz57'].iloc[0]
    
    result3 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data3, "higher id_jz57 (iteration_3)")
    
    # Test with higher id_ri7q and id_nzce (iteration_5)
    exp_data5 = experiment_history["iteration_5"]
    initial_ri7q = exp_data5['id_ri7q'].iloc[0]
    initial_nzce = exp_data5['id_nzce'].iloc[0]
    initial_jz57 = exp_data5['id_jz57'].iloc[0]
    
    result5 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data5, "higher id_ri7q and id_nzce (iteration_5)")
    
    # Store the model for future use
    shared_variables.add("conservation_model", updated_sbml)
    
except Exception as e:
    print(f"Error in simulation: {e}")
```
# Observation

## Code Stdout
Target equilibrium values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937

Calculated parameters:
k1 (production rate of id_jz57): 0.07711425082589014
k2 (conversion rate of id_jz57 to id_ri7q and id_nzce): 0.0008999962522320342
k3 (degradation rate of id_ri7q): 0.001
k4 (degradation rate of id_nzce): 0.001
k5 (degradation rate of id_jz57): 0.001
k6 (conversion rate of id_ri7q and id_nzce back to id_jz57): 1e-07

Testing the conservation model...

Testing with default initial conditions (iteration_0)...
Final values from simulation:
id_ri7q: 349.9151106151007
id_nzce: 34.99151106150653
id_jz57: 44.453178496183355
Ratio id_ri7q/id_nzce: 10.00000000000101
Total mass: 429.35980017279053
Experimental final values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937
Total mass: 443.15957786381296
Percentage errors:
id_ri7q: 4.37%
id_nzce: 4.37%
id_jz57: 9.34%
Total mass: 3.11%

Testing with higher id_jz57 (iteration_3)...
Final values from simulation:
id_ri7q: 491.88245993681704
id_nzce: 49.18824599368886
id_jz57: 52.42084102913855
Ratio id_ri7q/id_nzce: 9.999999999998545
Total mass: 593.4915469596444
Experimental final values:
id_ri7q: 365.91142217362705
id_nzce: 36.591128040397756
id_jz57: 40.656999290276026
Total mass: 443.1595495043008
Percentage errors:
id_ri7q: 34.43%
id_nzce: 34.43%
id_jz57: 28.93%
Total mass: 33.92%

Testing with higher id_ri7q and id_nzce (iteration_5)...
Final values from simulation:
id_ri7q: 378.1121105160466
id_nzce: 37.8112110516047
id_jz57: 44.58873321832199
Ratio id_ri7q/id_nzce: 9.99999999999999
Total mass: 460.51205478597325
Experimental final values:
id_ri7q: 365.9112688205561
id_nzce: 36.59111178115032
id_jz57: 40.6570003730284
Total mass: 443.15938097473474
Percentage errors:
id_ri7q: 3.33%
id_nzce: 3.33%
id_jz57: 9.67%
Total mass: 3.92%

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data, first_model, second_model, third_model, fourth_model, fifth_model, sixth_model, feedback_inhibition_model, conservation_model)

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


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



# Iteration 16
## Thoughts
The conservation model shows promising results for two of the three experiments:

1. For iteration_0 (default):
   - Percentage errors: id_ri7q: 4.37%, id_nzce: 4.37%, id_jz57: 9.34%, total mass: 3.11%

2. For iteration_5 (higher id_ri7q and id_nzce):
   - Percentage errors: id_ri7q: 3.33%, id_nzce: 3.33%, id_jz57: 9.67%, total mass: 3.92%

3. For iteration_3 (higher id_jz57):
   - Percentage errors: id_ri7q: 34.43%, id_nzce: 34.43%, id_jz57: 28.93%, total mass: 33.92%

The model performs well for the default conditions and for higher id_ri7q and id_nzce, but still struggles with higher id_jz57. This suggests that there might be additional mechanisms at play when id_jz57 is high.

Let me try one more approach. I'll modify the conservation model to include a mechanism that limits the total mass in the system when id_jz57 is high. One possibility is to make the degradation rate of id_jz57 dependent on its concentration - higher concentrations lead to faster degradation.

## Action

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

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

# Clear any existing reactions (start fresh)
for i in range(model.getNumReactions()-1, -1, -1):
    model.removeReaction(i)

# Get the target equilibrium values from experimental data
exp_final_ri7q = experiment_history["iteration_0"]['id_ri7q'].iloc[-1]
exp_final_nzce = experiment_history["iteration_0"]['id_nzce'].iloc[-1]
exp_final_jz57 = experiment_history["iteration_0"]['id_jz57'].iloc[-1]

print(f"Target equilibrium values:")
print(f"id_ri7q: {exp_final_ri7q}")
print(f"id_nzce: {exp_final_nzce}")
print(f"id_jz57: {exp_final_jz57}")

# Add reactions to the model
# 1. Constant production of id_jz57
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_jz57")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (constant rate)
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.077)  # Adjusted value
kinetic_law1.setMath(libsbml.parseL3Formula("k1"))

# 2. Conversion of id_jz57 to id_ri7q and id_nzce
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_jz57")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product2a = reaction2.createProduct()
product2a.setSpecies("id_ri7q")
product2a.setStoichiometry(10.0)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_nzce")
product2b.setStoichiometry(1.0)
product2b.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.0009)  # Adjusted value
kinetic_law2.setMath(libsbml.parseL3Formula("k2 * id_jz57"))

# 3. Degradation of id_ri7q
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_ri7q")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.001)  # Adjusted value
kinetic_law3.setMath(libsbml.parseL3Formula("k3 * id_ri7q"))

# 4. Degradation of id_nzce
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_nzce")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.001)  # Same as k3 to maintain 10:1 ratio
kinetic_law4.setMath(libsbml.parseL3Formula("k4 * id_nzce"))

# 5. Degradation of id_jz57 with concentration-dependent rate
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactant
reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_jz57")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

# Add kinetic law (concentration-dependent)
kinetic_law5 = reaction5.createKineticLaw()
parameter5a = kinetic_law5.createParameter()
parameter5a.setId("k5a")
parameter5a.setValue(0.001)  # Base degradation rate
parameter5b = kinetic_law5.createParameter()
parameter5b.setId("k5b")
parameter5b.setValue(0.00001)  # Additional rate per unit concentration
kinetic_law5.setMath(libsbml.parseL3Formula("(k5a + k5b * id_jz57) * id_jz57"))

# 6. Conversion of id_ri7q and id_nzce back to id_jz57
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

# Add reactants
reactant6a = reaction6.createReactant()
reactant6a.setSpecies("id_ri7q")
reactant6a.setStoichiometry(10.0)
reactant6a.setConstant(True)

reactant6b = reaction6.createReactant()
reactant6b.setSpecies("id_nzce")
reactant6b.setStoichiometry(1.0)
reactant6b.setConstant(True)

# Add product
product6 = reaction6.createProduct()
product6.setSpecies("id_jz57")
product6.setStoichiometry(1.0)
product6.setConstant(True)

# Add kinetic law (mass action)
kinetic_law6 = reaction6.createKineticLaw()
parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.0000001)  # Small value
kinetic_law6.setMath(libsbml.parseL3Formula("k6 * id_ri7q * id_nzce"))

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

# Test the model with simulation for all three initial conditions
print("\nTesting the enhanced conservation model...")

# Function to test the model with given initial conditions
def test_model_with_initial_conditions(sbml_string, initial_ri7q, initial_nzce, initial_jz57, exp_data, experiment_name):
    print(f"\nTesting with {experiment_name}...")
    
    # Modify the initial concentrations in the model
    sbml_doc = libsbml.readSBMLFromString(sbml_string)
    model = sbml_doc.getModel()
    
    model.getSpecies("id_ri7q").setInitialConcentration(initial_ri7q)
    model.getSpecies("id_nzce").setInitialConcentration(initial_nzce)
    model.getSpecies("id_jz57").setInitialConcentration(initial_jz57)
    
    # Write the updated SBML
    writer = libsbml.SBMLWriter()
    modified_sbml = writer.writeSBMLToString(sbml_doc)
    
    # Simulate
    result = simulate(modified_sbml)
    
    # Calculate final values
    final_ri7q = result['id_ri7q'].iloc[-1]
    final_nzce = result['id_nzce'].iloc[-1]
    final_jz57 = result['id_jz57'].iloc[-1]
    
    print(f"Final values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    print(f"Total mass: {final_ri7q + final_nzce + final_jz57}")
    
    # Compare with experimental data
    exp_final_ri7q = exp_data['id_ri7q'].iloc[-1]
    exp_final_nzce = exp_data['id_nzce'].iloc[-1]
    exp_final_jz57 = exp_data['id_jz57'].iloc[-1]
    
    print(f"Experimental final values:")
    print(f"id_ri7q: {exp_final_ri7q}")
    print(f"id_nzce: {exp_final_nzce}")
    print(f"id_jz57: {exp_final_jz57}")
    print(f"Total mass: {exp_final_ri7q + exp_final_nzce + exp_final_jz57}")
    
    # Calculate percentage errors
    pct_error_ri7q = 100 * abs(final_ri7q - exp_final_ri7q) / exp_final_ri7q
    pct_error_nzce = 100 * abs(final_nzce - exp_final_nzce) / exp_final_nzce
    pct_error_jz57 = 100 * abs(final_jz57 - exp_final_jz57) / exp_final_jz57
    pct_error_total = 100 * abs((final_ri7q + final_nzce + final_jz57) - (exp_final_ri7q + exp_final_nzce + exp_final_jz57)) / (exp_final_ri7q + exp_final_nzce + exp_final_jz57)
    
    print(f"Percentage errors:")
    print(f"id_ri7q: {pct_error_ri7q:.2f}%")
    print(f"id_nzce: {pct_error_nzce:.2f}%")
    print(f"id_jz57: {pct_error_jz57:.2f}%")
    print(f"Total mass: {pct_error_total:.2f}%")
    
    return result

try:
    # Test with default initial conditions (iteration_0)
    exp_data0 = experiment_history["iteration_0"]
    initial_ri7q = exp_data0['id_ri7q'].iloc[0]
    initial_nzce = exp_data0['id_nzce'].iloc[0]
    initial_jz57 = exp_data0['id_jz57'].iloc[0]
    
    result0 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data0, "default initial conditions (iteration_0)")
    
    # Test with higher id_jz57 (iteration_3)
    exp_data3 = experiment_history["iteration_3"]
    initial_ri7q = exp_data3['id_ri7q'].iloc[0]
    initial_nzce = exp_data3['id_nzce'].iloc[0]
    initial_jz57 = exp_data3['id_jz57'].iloc[0]
    
    result3 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data3, "higher id_jz57 (iteration_3)")
    
    # Test with higher id_ri7q and id_nzce (iteration_5)
    exp_data5 = experiment_history["iteration_5"]
    initial_ri7q = exp_data5['id_ri7q'].iloc[0]
    initial_nzce = exp_data5['id_nzce'].iloc[0]
    initial_jz57 = exp_data5['id_jz57'].iloc[0]
    
    result5 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data5, "higher id_ri7q and id_nzce (iteration_5)")
    
    # Store the model for future use
    shared_variables.add("enhanced_conservation_model", updated_sbml)
    
except Exception as e:
    print(f"Error in simulation: {e}")
```
# Observation

## Code Stdout
Target equilibrium values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937

Testing the enhanced conservation model...

Testing with default initial conditions (iteration_0)...
Final values from simulation:
id_ri7q: 297.0735954005922
id_nzce: 29.70735954005906
id_jz57: 36.120171583316036
Ratio id_ri7q/id_nzce: 10.000000000000053
Total mass: 362.90112652396726
Experimental final values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937
Total mass: 443.15957786381296
Percentage errors:
id_ri7q: 18.81%
id_nzce: 18.81%
id_jz57: 11.16%
Total mass: 18.11%

Testing with higher id_jz57 (iteration_3)...
Final values from simulation:
id_ri7q: 374.3399061664151
id_nzce: 37.4339906166425
id_jz57: 38.27523800568217
Ratio id_ri7q/id_nzce: 9.999999999999737
Total mass: 450.0491347887398
Experimental final values:
id_ri7q: 365.91142217362705
id_nzce: 36.591128040397756
id_jz57: 40.656999290276026
Total mass: 443.1595495043008
Percentage errors:
id_ri7q: 2.30%
id_nzce: 2.30%
id_jz57: 5.86%
Total mass: 1.55%

Testing with higher id_ri7q and id_nzce (iteration_5)...
Final values from simulation:
id_ri7q: 325.25397280863984
id_nzce: 32.52539728086402
id_jz57: 36.2069892216392
Ratio id_ri7q/id_nzce: 9.99999999999999
Total mass: 393.9863593111431
Experimental final values:
id_ri7q: 365.9112688205561
id_nzce: 36.59111178115032
id_jz57: 40.6570003730284
Total mass: 443.15938097473474
Percentage errors:
id_ri7q: 11.11%
id_nzce: 11.11%
id_jz57: 10.95%
Total mass: 11.10%

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data, first_model, second_model, third_model, fourth_model, fifth_model, sixth_model, feedback_inhibition_model, conservation_model, enhanced_conservation_model)

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


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



# Iteration 17
## Thoughts
The enhanced conservation model with concentration-dependent degradation of id_jz57 shows interesting results:

1. For iteration_0 (default):
   - Percentage errors: id_ri7q: 18.81%, id_nzce: 18.81%, id_jz57: 11.16%, total mass: 18.11%

2. For iteration_3 (higher id_jz57):
   - Percentage errors: id_ri7q: 2.30%, id_nzce: 2.30%, id_jz57: 5.86%, total mass: 1.55%

3. For iteration_5 (higher id_ri7q and id_nzce):
   - Percentage errors: id_ri7q: 11.11%, id_nzce: 11.11%, id_jz57: 10.95%, total mass: 11.10%

Interestingly, this model performs best for the higher id_jz57 case (iteration_3), which was the most challenging case for previous models. However, it performs worse for the default case (iteration_0) and the higher id_ri7q and id_nzce case (iteration_5).

This suggests that different mechanisms might be dominant under different conditions. Let me try to combine the best aspects of the previous models to create a final model that performs well across all conditions.

Based on all the models I've tested, I believe the true system has:
1. A constant production of id_jz57
2. Conversion of id_jz57 to id_ri7q and id_nzce with a 10:1 ratio
3. Degradation of all species
4. Some form of feedback or regulation that maintains the total mass at a specific level

Let me create a final model that incorporates these features.

## Action

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

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

# Clear any existing reactions (start fresh)
for i in range(model.getNumReactions()-1, -1, -1):
    model.removeReaction(i)

# Get the target equilibrium values from experimental data
exp_final_ri7q = experiment_history["iteration_0"]['id_ri7q'].iloc[-1]
exp_final_nzce = experiment_history["iteration_0"]['id_nzce'].iloc[-1]
exp_final_jz57 = experiment_history["iteration_0"]['id_jz57'].iloc[-1]

print(f"Target equilibrium values:")
print(f"id_ri7q: {exp_final_ri7q}")
print(f"id_nzce: {exp_final_nzce}")
print(f"id_jz57: {exp_final_jz57}")

# Add reactions to the model
# 1. Constant production of id_jz57
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_jz57")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (constant rate)
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.077)  # Adjusted value
kinetic_law1.setMath(libsbml.parseL3Formula("k1"))

# 2. Conversion of id_jz57 to id_ri7q and id_nzce with feedback regulation
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_jz57")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product2a = reaction2.createProduct()
product2a.setSpecies("id_ri7q")
product2a.setStoichiometry(10.0)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_nzce")
product2b.setStoichiometry(1.0)
product2b.setConstant(True)

# Add kinetic law with feedback regulation
kinetic_law2 = reaction2.createKineticLaw()
parameter2a = kinetic_law2.createParameter()
parameter2a.setId("k2")
parameter2a.setValue(0.0009)  # Base rate
parameter2b = kinetic_law2.createParameter()
parameter2b.setId("Ki")
parameter2b.setValue(500)  # Inhibition constant
kinetic_law2.setMath(libsbml.parseL3Formula("k2 * id_jz57 / (1 + (id_ri7q + id_nzce) / Ki)"))

# 3. Degradation of id_ri7q
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_ri7q")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.001)  # Adjusted value
kinetic_law3.setMath(libsbml.parseL3Formula("k3 * id_ri7q"))

# 4. Degradation of id_nzce
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_nzce")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.001)  # Same as k3 to maintain 10:1 ratio
kinetic_law4.setMath(libsbml.parseL3Formula("k4 * id_nzce"))

# 5. Degradation of id_jz57 with concentration-dependent rate
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactant
reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_jz57")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

# Add kinetic law (concentration-dependent)
kinetic_law5 = reaction5.createKineticLaw()
parameter5a = kinetic_law5.createParameter()
parameter5a.setId("k5a")
parameter5a.setValue(0.001)  # Base degradation rate
parameter5b = kinetic_law5.createParameter()
parameter5b.setId("k5b")
parameter5b.setValue(0.000005)  # Additional rate per unit concentration
kinetic_law5.setMath(libsbml.parseL3Formula("(k5a + k5b * id_jz57) * id_jz57"))

# 6. Conversion of id_ri7q and id_nzce back to id_jz57
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

# Add reactants
reactant6a = reaction6.createReactant()
reactant6a.setSpecies("id_ri7q")
reactant6a.setStoichiometry(10.0)
reactant6a.setConstant(True)

reactant6b = reaction6.createReactant()
reactant6b.setSpecies("id_nzce")
reactant6b.setStoichiometry(1.0)
reactant6b.setConstant(True)

# Add product
product6 = reaction6.createProduct()
product6.setSpecies("id_jz57")
product6.setStoichiometry(1.0)
product6.setConstant(True)

# Add kinetic law (mass action)
kinetic_law6 = reaction6.createKineticLaw()
parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.0000001)  # Small value
kinetic_law6.setMath(libsbml.parseL3Formula("k6 * id_ri7q * id_nzce"))

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

# Test the model with simulation for all three initial conditions
print("\nTesting the final model...")

# Function to test the model with given initial conditions
def test_model_with_initial_conditions(sbml_string, initial_ri7q, initial_nzce, initial_jz57, exp_data, experiment_name):
    print(f"\nTesting with {experiment_name}...")
    
    # Modify the initial concentrations in the model
    sbml_doc = libsbml.readSBMLFromString(sbml_string)
    model = sbml_doc.getModel()
    
    model.getSpecies("id_ri7q").setInitialConcentration(initial_ri7q)
    model.getSpecies("id_nzce").setInitialConcentration(initial_nzce)
    model.getSpecies("id_jz57").setInitialConcentration(initial_jz57)
    
    # Write the updated SBML
    writer = libsbml.SBMLWriter()
    modified_sbml = writer.writeSBMLToString(sbml_doc)
    
    # Simulate
    result = simulate(modified_sbml)
    
    # Calculate final values
    final_ri7q = result['id_ri7q'].iloc[-1]
    final_nzce = result['id_nzce'].iloc[-1]
    final_jz57 = result['id_jz57'].iloc[-1]
    
    print(f"Final values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    print(f"Total mass: {final_ri7q + final_nzce + final_jz57}")
    
    # Compare with experimental data
    exp_final_ri7q = exp_data['id_ri7q'].iloc[-1]
    exp_final_nzce = exp_data['id_nzce'].iloc[-1]
    exp_final_jz57 = exp_data['id_jz57'].iloc[-1]
    
    print(f"Experimental final values:")
    print(f"id_ri7q: {exp_final_ri7q}")
    print(f"id_nzce: {exp_final_nzce}")
    print(f"id_jz57: {exp_final_jz57}")
    print(f"Total mass: {exp_final_ri7q + exp_final_nzce + exp_final_jz57}")
    
    # Calculate percentage errors
    pct_error_ri7q = 100 * abs(final_ri7q - exp_final_ri7q) / exp_final_ri7q
    pct_error_nzce = 100 * abs(final_nzce - exp_final_nzce) / exp_final_nzce
    pct_error_jz57 = 100 * abs(final_jz57 - exp_final_jz57) / exp_final_jz57
    pct_error_total = 100 * abs((final_ri7q + final_nzce + final_jz57) - (exp_final_ri7q + exp_final_nzce + exp_final_jz57)) / (exp_final_ri7q + exp_final_nzce + exp_final_jz57)
    
    print(f"Percentage errors:")
    print(f"id_ri7q: {pct_error_ri7q:.2f}%")
    print(f"id_nzce: {pct_error_nzce:.2f}%")
    print(f"id_jz57: {pct_error_jz57:.2f}%")
    print(f"Total mass: {pct_error_total:.2f}%")
    
    return result

try:
    # Test with default initial conditions (iteration_0)
    exp_data0 = experiment_history["iteration_0"]
    initial_ri7q = exp_data0['id_ri7q'].iloc[0]
    initial_nzce = exp_data0['id_nzce'].iloc[0]
    initial_jz57 = exp_data0['id_jz57'].iloc[0]
    
    result0 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data0, "default initial conditions (iteration_0)")
    
    # Test with higher id_jz57 (iteration_3)
    exp_data3 = experiment_history["iteration_3"]
    initial_ri7q = exp_data3['id_ri7q'].iloc[0]
    initial_nzce = exp_data3['id_nzce'].iloc[0]
    initial_jz57 = exp_data3['id_jz57'].iloc[0]
    
    result3 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data3, "higher id_jz57 (iteration_3)")
    
    # Test with higher id_ri7q and id_nzce (iteration_5)
    exp_data5 = experiment_history["iteration_5"]
    initial_ri7q = exp_data5['id_ri7q'].iloc[0]
    initial_nzce = exp_data5['id_nzce'].iloc[0]
    initial_jz57 = exp_data5['id_jz57'].iloc[0]
    
    result5 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data5, "higher id_ri7q and id_nzce (iteration_5)")
    
    # Store the model for future use
    shared_variables.add("final_model", updated_sbml)
    
except Exception as e:
    print(f"Error in simulation: {e}")
```
# Observation

## Code Stdout
Target equilibrium values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937

Testing the final model...

Testing with default initial conditions (iteration_0)...
Final values from simulation:
id_ri7q: 246.70823695065664
id_nzce: 24.670823695065536
id_jz57: 45.27831181708831
Ratio id_ri7q/id_nzce: 10.000000000000052
Total mass: 316.6573724628105
Experimental final values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937
Total mass: 443.15957786381296
Percentage errors:
id_ri7q: 32.58%
id_nzce: 32.58%
id_jz57: 11.37%
Total mass: 28.55%

Testing with higher id_jz57 (iteration_3)...
Final values from simulation:
id_ri7q: 304.22448580526554
id_nzce: 30.422448580526567
id_jz57: 51.62362178944985
Ratio id_ri7q/id_nzce: 9.999999999999996
Total mass: 386.27055617524195
Experimental final values:
id_ri7q: 365.91142217362705
id_nzce: 36.591128040397756
id_jz57: 40.656999290276026
Total mass: 443.1595495043008
Percentage errors:
id_ri7q: 16.86%
id_nzce: 16.86%
id_jz57: 26.97%
Total mass: 12.84%

Testing with higher id_ri7q and id_nzce (iteration_5)...
Final values from simulation:
id_ri7q: 265.4909365002121
id_nzce: 26.549093650021447
id_jz57: 46.00640097909586
Ratio id_ri7q/id_nzce: 9.999999999999911
Total mass: 338.04643112932945
Experimental final values:
id_ri7q: 365.9112688205561
id_nzce: 36.59111178115032
id_jz57: 40.6570003730284
Total mass: 443.15938097473474
Percentage errors:
id_ri7q: 27.44%
id_nzce: 27.44%
id_jz57: 13.16%
Total mass: 23.72%

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data, first_model, second_model, third_model, fourth_model, fifth_model, sixth_model, feedback_inhibition_model, conservation_model, enhanced_conservation_model, final_model)

### 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
After several iterations of model development and testing, I've found that the sixth model (stored as `sixth_model`) performs the best overall across the three experimental conditions:

1. For iteration_0 (default):
   - Percentage errors: id_ri7q: 3.00%, id_nzce: 3.00%, id_jz57: 8.33%, total mass: 1.96%

2. For iteration_3 (higher id_jz57):
   - Percentage errors: id_ri7q: 34.43%, id_nzce: 34.43%, id_jz57: 28.93%, total mass: 33.92%

3. For iteration_5 (higher id_ri7q and id_nzce):
   - Percentage errors: id_ri7q: 3.33%, id_nzce: 3.33%, id_jz57: 9.67%, total mass: 3.92%

While this model doesn't perform perfectly for the higher id_jz57 case, it performs very well for the other two cases. Let me retrieve this model and make some final adjustments to improve its performance for the higher id_jz57 case.

## Action

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

# Retrieve the sixth model
sixth_model = shared_variables.access("sixth_model")

# Parse the model
sbml_doc = libsbml.readSBMLFromString(sixth_model)
model = sbml_doc.getModel()

# Print the reactions in the model
print("Reactions in the sixth model:")
for i in range(model.getNumReactions()):
    reaction = model.getReaction(i)
    print(f"Reaction {i+1}: {reaction.getId()}")
    
    # Print reactants
    print("  Reactants:")
    for j in range(reaction.getNumReactants()):
        reactant = reaction.getReactant(j)
        print(f"    {reactant.getSpecies()} (stoichiometry: {reactant.getStoichiometry()})")
    
    # Print products
    print("  Products:")
    for j in range(reaction.getNumProducts()):
        product = reaction.getProduct(j)
        print(f"    {product.getSpecies()} (stoichiometry: {product.getStoichiometry()})")
    
    # Print kinetic law
    kinetic_law = reaction.getKineticLaw()
    if kinetic_law:
        formula = kinetic_law.getFormula()
        print(f"  Kinetic law: {formula}")
        
        # Print parameters
        for j in range(kinetic_law.getNumParameters()):
            parameter = kinetic_law.getParameter(j)
            print(f"    Parameter {parameter.getId()}: {parameter.getValue()}")

# Modify the model to improve performance for higher id_jz57
# Let's adjust the parameters to better handle the higher id_jz57 case

# Find the reaction for constant production of id_jz57 (reaction1)
reaction1 = model.getReaction("reaction1")
kinetic_law1 = reaction1.getKineticLaw()
parameter1 = kinetic_law1.getParameter("k1")
parameter1.setValue(0.075)  # Slightly adjusted value

# Find the reaction for conversion of id_jz57 to id_ri7q and id_nzce (reaction2)
reaction2 = model.getReaction("reaction2")
kinetic_law2 = reaction2.getKineticLaw()
parameter2 = kinetic_law2.getParameter("k2")
parameter2.setValue(0.00085)  # Slightly adjusted value

# Find the reaction for degradation of id_jz57 (reaction5)
reaction5 = model.getReaction("reaction5")
kinetic_law5 = reaction5.getKineticLaw()
parameter5 = kinetic_law5.getParameter("k5")
parameter5.setValue(0.0012)  # Slightly increased value

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

# Test the model with simulation for all three initial conditions
print("\nTesting the adjusted sixth model...")

# Function to test the model with given initial conditions
def test_model_with_initial_conditions(sbml_string, initial_ri7q, initial_nzce, initial_jz57, exp_data, experiment_name):
    print(f"\nTesting with {experiment_name}...")
    
    # Modify the initial concentrations in the model
    sbml_doc = libsbml.readSBMLFromString(sbml_string)
    model = sbml_doc.getModel()
    
    model.getSpecies("id_ri7q").setInitialConcentration(initial_ri7q)
    model.getSpecies("id_nzce").setInitialConcentration(initial_nzce)
    model.getSpecies("id_jz57").setInitialConcentration(initial_jz57)
    
    # Write the updated SBML
    writer = libsbml.SBMLWriter()
    modified_sbml = writer.writeSBMLToString(sbml_doc)
    
    # Simulate
    result = simulate(modified_sbml)
    
    # Calculate final values
    final_ri7q = result['id_ri7q'].iloc[-1]
    final_nzce = result['id_nzce'].iloc[-1]
    final_jz57 = result['id_jz57'].iloc[-1]
    
    print(f"Final values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    print(f"Total mass: {final_ri7q + final_nzce + final_jz57}")
    
    # Compare with experimental data
    exp_final_ri7q = exp_data['id_ri7q'].iloc[-1]
    exp_final_nzce = exp_data['id_nzce'].iloc[-1]
    exp_final_jz57 = exp_data['id_jz57'].iloc[-1]
    
    print(f"Experimental final values:")
    print(f"id_ri7q: {exp_final_ri7q}")
    print(f"id_nzce: {exp_final_nzce}")
    print(f"id_jz57: {exp_final_jz57}")
    print(f"Total mass: {exp_final_ri7q + exp_final_nzce + exp_final_jz57}")
    
    # Calculate percentage errors
    pct_error_ri7q = 100 * abs(final_ri7q - exp_final_ri7q) / exp_final_ri7q
    pct_error_nzce = 100 * abs(final_nzce - exp_final_nzce) / exp_final_nzce
    pct_error_jz57 = 100 * abs(final_jz57 - exp_final_jz57) / exp_final_jz57
    pct_error_total = 100 * abs((final_ri7q + final_nzce + final_jz57) - (exp_final_ri7q + exp_final_nzce + exp_final_jz57)) / (exp_final_ri7q + exp_final_nzce + exp_final_jz57)
    
    print(f"Percentage errors:")
    print(f"id_ri7q: {pct_error_ri7q:.2f}%")
    print(f"id_nzce: {pct_error_nzce:.2f}%")
    print(f"id_jz57: {pct_error_jz57:.2f}%")
    print(f"Total mass: {pct_error_total:.2f}%")
    
    return result

try:
    # Test with default initial conditions (iteration_0)
    exp_data0 = experiment_history["iteration_0"]
    initial_ri7q = exp_data0['id_ri7q'].iloc[0]
    initial_nzce = exp_data0['id_nzce'].iloc[0]
    initial_jz57 = exp_data0['id_jz57'].iloc[0]
    
    result0 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data0, "default initial conditions (iteration_0)")
    
    # Test with higher id_jz57 (iteration_3)
    exp_data3 = experiment_history["iteration_3"]
    initial_ri7q = exp_data3['id_ri7q'].iloc[0]
    initial_nzce = exp_data3['id_nzce'].iloc[0]
    initial_jz57 = exp_data3['id_jz57'].iloc[0]
    
    result3 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data3, "higher id_jz57 (iteration_3)")
    
    # Test with higher id_ri7q and id_nzce (iteration_5)
    exp_data5 = experiment_history["iteration_5"]
    initial_ri7q = exp_data5['id_ri7q'].iloc[0]
    initial_nzce = exp_data5['id_nzce'].iloc[0]
    initial_jz57 = exp_data5['id_jz57'].iloc[0]
    
    result5 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data5, "higher id_ri7q and id_nzce (iteration_5)")
    
    # Store the model for future use
    shared_variables.add("adjusted_sixth_model", updated_sbml)
    
except Exception as e:
    print(f"Error in simulation: {e}")
```
# Observation

## Code Stdout
Reactions in the sixth model:
Reaction 1: reaction1
  Reactants:
  Products:
    id_jz57 (stoichiometry: 1.0)
  Kinetic law: k1
    Parameter k1: 0.0772481419651408
Reaction 2: reaction2
  Reactants:
    id_jz57 (stoichiometry: 1.0)
  Products:
    id_ri7q (stoichiometry: 10.0)
    id_nzce (stoichiometry: 1.0)
  Kinetic law: k2 * id_jz57
    Parameter k2: 0.000899996252232034
Reaction 3: reaction3
  Reactants:
    id_ri7q (stoichiometry: 1.0)
  Products:
  Kinetic law: k3 * id_ri7q
    Parameter k3: 0.001
Reaction 4: reaction4
  Reactants:
    id_nzce (stoichiometry: 1.0)
  Products:
  Kinetic law: k4 * id_nzce
    Parameter k4: 0.001
Reaction 5: reaction5
  Reactants:
    id_jz57 (stoichiometry: 1.0)
  Products:
  Kinetic law: k5 * id_jz57
    Parameter k5: 0.001

Testing the adjusted sixth model...

Testing with default initial conditions (iteration_0)...
Final values from simulation:
id_ri7q: 314.9747112360786
id_nzce: 31.497471123607497
id_jz57: 39.741968357866526
Ratio id_ri7q/id_nzce: 10.000000000000115
Total mass: 386.2141507175526
Experimental final values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937
Total mass: 443.15957786381296
Percentage errors:
id_ri7q: 13.92%
id_nzce: 13.92%
id_jz57: 2.25%
Total mass: 12.85%

Testing with higher id_jz57 (iteration_3)...
Final values from simulation:
id_ri7q: 444.51126041538095
id_nzce: 44.45112604153688
id_jz57: 45.90481038345371
Ratio id_ri7q/id_nzce: 10.000000000000274
Total mass: 534.8671968403715
Experimental final values:
id_ri7q: 365.91142217362705
id_nzce: 36.591128040397756
id_jz57: 40.656999290276026
Total mass: 443.1595495043008
Percentage errors:
id_ri7q: 21.48%
id_nzce: 21.48%
id_jz57: 12.91%
Total mass: 20.69%

Testing with higher id_ri7q and id_nzce (iteration_5)...
Final values from simulation:
id_ri7q: 344.5275149214631
id_nzce: 34.452751492146795
id_jz57: 39.74193521802748
Ratio id_ri7q/id_nzce: 9.999999999999858
Total mass: 418.72220163163735
Experimental final values:
id_ri7q: 365.9112688205561
id_nzce: 36.59111178115032
id_jz57: 40.6570003730284
Total mass: 443.15938097473474
Percentage errors:
id_ri7q: 5.84%
id_nzce: 5.84%
id_jz57: 2.25%
Total mass: 5.51%

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data, first_model, second_model, third_model, fourth_model, fifth_model, sixth_model, feedback_inhibition_model, conservation_model, enhanced_conservation_model, final_model, adjusted_sixth_model)

### 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 adjusted sixth model shows improved performance for some cases but still has significant errors for others:

1. For iteration_0 (default):
   - Percentage errors: id_ri7q: 13.92%, id_nzce: 13.92%, id_jz57: 2.25%, total mass: 12.85%

2. For iteration_3 (higher id_jz57):
   - Percentage errors: id_ri7q: 21.48%, id_nzce: 21.48%, id_jz57: 12.91%, total mass: 20.69%

3. For iteration_5 (higher id_ri7q and id_nzce):
   - Percentage errors: id_ri7q: 5.84%, id_nzce: 5.84%, id_jz57: 2.25%, total mass: 5.51%

The model performs best for iteration_5 (higher id_ri7q and id_nzce) and has improved accuracy for id_jz57 across all conditions. However, the total mass is still off, especially for iteration_0 and iteration_3.

Let me make one final attempt to improve the model by further adjusting the parameters to better match the experimental data across all conditions.

## Action

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

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

# Clear any existing reactions (start fresh)
for i in range(model.getNumReactions()-1, -1, -1):
    model.removeReaction(i)

# Get the target equilibrium values from experimental data
exp_final_ri7q = experiment_history["iteration_0"]['id_ri7q'].iloc[-1]
exp_final_nzce = experiment_history["iteration_0"]['id_nzce'].iloc[-1]
exp_final_jz57 = experiment_history["iteration_0"]['id_jz57'].iloc[-1]

print(f"Target equilibrium values:")
print(f"id_ri7q: {exp_final_ri7q}")
print(f"id_nzce: {exp_final_nzce}")
print(f"id_jz57: {exp_final_jz57}")

# Add reactions to the model
# 1. Constant production of id_jz57
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_jz57")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (constant rate)
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.085)  # Adjusted value
kinetic_law1.setMath(libsbml.parseL3Formula("k1"))

# 2. Conversion of id_jz57 to id_ri7q and id_nzce
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_jz57")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product2a = reaction2.createProduct()
product2a.setSpecies("id_ri7q")
product2a.setStoichiometry(10.0)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_nzce")
product2b.setStoichiometry(1.0)
product2b.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.0009)  # Adjusted value
kinetic_law2.setMath(libsbml.parseL3Formula("k2 * id_jz57"))

# 3. Degradation of id_ri7q
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_ri7q")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.001)  # Adjusted value
kinetic_law3.setMath(libsbml.parseL3Formula("k3 * id_ri7q"))

# 4. Degradation of id_nzce
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_nzce")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.001)  # Same as k3 to maintain 10:1 ratio
kinetic_law4.setMath(libsbml.parseL3Formula("k4 * id_nzce"))

# 5. Degradation of id_jz57
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactant
reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_jz57")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

# Add kinetic law (mass action with concentration-dependent term)
kinetic_law5 = reaction5.createKineticLaw()
parameter5a = kinetic_law5.createParameter()
parameter5a.setId("k5a")
parameter5a.setValue(0.001)  # Base degradation rate
parameter5b = kinetic_law5.createParameter()
parameter5b.setId("k5b")
parameter5b.setValue(0.000005)  # Additional rate per unit concentration
kinetic_law5.setMath(libsbml.parseL3Formula("(k5a + k5b * id_jz57) * id_jz57"))

# 6. Conversion of id_ri7q and id_nzce back to id_jz57
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

# Add reactants
reactant6a = reaction6.createReactant()
reactant6a.setSpecies("id_ri7q")
reactant6a.setStoichiometry(10.0)
reactant6a.setConstant(True)

reactant6b = reaction6.createReactant()
reactant6b.setSpecies("id_nzce")
reactant6b.setStoichiometry(1.0)
reactant6b.setConstant(True)

# Add product
product6 = reaction6.createProduct()
product6.setSpecies("id_jz57")
product6.setStoichiometry(1.0)
product6.setConstant(True)

# Add kinetic law (mass action)
kinetic_law6 = reaction6.createKineticLaw()
parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.0000001)  # Small value
kinetic_law6.setMath(libsbml.parseL3Formula("k6 * id_ri7q * id_nzce"))

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

# Test the model with simulation for all three initial conditions
print("\nTesting the final optimized model...")

# Function to test the model with given initial conditions
def test_model_with_initial_conditions(sbml_string, initial_ri7q, initial_nzce, initial_jz57, exp_data, experiment_name):
    print(f"\nTesting with {experiment_name}...")
    
    # Modify the initial concentrations in the model
    sbml_doc = libsbml.readSBMLFromString(sbml_string)
    model = sbml_doc.getModel()
    
    model.getSpecies("id_ri7q").setInitialConcentration(initial_ri7q)
    model.getSpecies("id_nzce").setInitialConcentration(initial_nzce)
    model.getSpecies("id_jz57").setInitialConcentration(initial_jz57)
    
    # Write the updated SBML
    writer = libsbml.SBMLWriter()
    modified_sbml = writer.writeSBMLToString(sbml_doc)
    
    # Simulate
    result = simulate(modified_sbml)
    
    # Calculate final values
    final_ri7q = result['id_ri7q'].iloc[-1]
    final_nzce = result['id_nzce'].iloc[-1]
    final_jz57 = result['id_jz57'].iloc[-1]
    
    print(f"Final values from simulation:")
    print(f"id_ri7q: {final_ri7q}")
    print(f"id_nzce: {final_nzce}")
    print(f"id_jz57: {final_jz57}")
    print(f"Ratio id_ri7q/id_nzce: {final_ri7q/final_nzce}")
    print(f"Total mass: {final_ri7q + final_nzce + final_jz57}")
    
    # Compare with experimental data
    exp_final_ri7q = exp_data['id_ri7q'].iloc[-1]
    exp_final_nzce = exp_data['id_nzce'].iloc[-1]
    exp_final_jz57 = exp_data['id_jz57'].iloc[-1]
    
    print(f"Experimental final values:")
    print(f"id_ri7q: {exp_final_ri7q}")
    print(f"id_nzce: {exp_final_nzce}")
    print(f"id_jz57: {exp_final_jz57}")
    print(f"Total mass: {exp_final_ri7q + exp_final_nzce + exp_final_jz57}")
    
    # Calculate percentage errors
    pct_error_ri7q = 100 * abs(final_ri7q - exp_final_ri7q) / exp_final_ri7q
    pct_error_nzce = 100 * abs(final_nzce - exp_final_nzce) / exp_final_nzce
    pct_error_jz57 = 100 * abs(final_jz57 - exp_final_jz57) / exp_final_jz57
    pct_error_total = 100 * abs((final_ri7q + final_nzce + final_jz57) - (exp_final_ri7q + exp_final_nzce + exp_final_jz57)) / (exp_final_ri7q + exp_final_nzce + exp_final_jz57)
    
    print(f"Percentage errors:")
    print(f"id_ri7q: {pct_error_ri7q:.2f}%")
    print(f"id_nzce: {pct_error_nzce:.2f}%")
    print(f"id_jz57: {pct_error_jz57:.2f}%")
    print(f"Total mass: {pct_error_total:.2f}%")
    
    return result

try:
    # Test with default initial conditions (iteration_0)
    exp_data0 = experiment_history["iteration_0"]
    initial_ri7q = exp_data0['id_ri7q'].iloc[0]
    initial_nzce = exp_data0['id_nzce'].iloc[0]
    initial_jz57 = exp_data0['id_jz57'].iloc[0]
    
    result0 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data0, "default initial conditions (iteration_0)")
    
    # Test with higher id_jz57 (iteration_3)
    exp_data3 = experiment_history["iteration_3"]
    initial_ri7q = exp_data3['id_ri7q'].iloc[0]
    initial_nzce = exp_data3['id_nzce'].iloc[0]
    initial_jz57 = exp_data3['id_jz57'].iloc[0]
    
    result3 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data3, "higher id_jz57 (iteration_3)")
    
    # Test with higher id_ri7q and id_nzce (iteration_5)
    exp_data5 = experiment_history["iteration_5"]
    initial_ri7q = exp_data5['id_ri7q'].iloc[0]
    initial_nzce = exp_data5['id_nzce'].iloc[0]
    initial_jz57 = exp_data5['id_jz57'].iloc[0]
    
    result5 = test_model_with_initial_conditions(updated_sbml, initial_ri7q, initial_nzce, initial_jz57, exp_data5, "higher id_ri7q and id_nzce (iteration_5)")
    
    # Store the model for future use
    shared_variables.add("optimized_model", updated_sbml)
    
except Exception as e:
    print(f"Error in simulation: {e}")
```
# Observation

## Code Stdout
Target equilibrium values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937

Testing the final optimized model...

Testing with default initial conditions (iteration_0)...
Final values from simulation:
id_ri7q: 335.29303334417745
id_nzce: 33.52930333441801
id_jz57: 42.76103440894878
Ratio id_ri7q/id_nzce: 9.99999999999992
Total mass: 411.5833710875442
Experimental final values:
id_ri7q: 365.91144945071414
id_nzce: 36.591131393029464
id_jz57: 40.65699702006937
Total mass: 443.15957786381296
Percentage errors:
id_ri7q: 8.37%
id_nzce: 8.37%
id_jz57: 5.18%
Total mass: 7.13%

Testing with higher id_jz57 (iteration_3)...
Final values from simulation:
id_ri7q: 434.9511892586065
id_nzce: 43.49511892586277
id_jz57: 46.534008051114505
Ratio id_ri7q/id_nzce: 9.999999999999513
Total mass: 524.9803162355838
Experimental final values:
id_ri7q: 365.91142217362705
id_nzce: 36.591128040397756
id_jz57: 40.656999290276026
Total mass: 443.1595495043008
Percentage errors:
id_ri7q: 18.87%
id_nzce: 18.87%
id_jz57: 14.46%
Total mass: 18.46%

Testing with higher id_ri7q and id_nzce (iteration_5)...
Final values from simulation:
id_ri7q: 363.4314623096361
id_nzce: 36.343146230963434
id_jz57: 42.86838817640008
Ratio id_ri7q/id_nzce: 10.00000000000005
Total mass: 442.6429967169996
Experimental final values:
id_ri7q: 365.9112688205561
id_nzce: 36.59111178115032
id_jz57: 40.6570003730284
Total mass: 443.15938097473474
Percentage errors:
id_ri7q: 0.68%
id_nzce: 0.68%
id_jz57: 5.44%
Total mass: 0.12%

## 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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, experiment1_data, experiment2_data, experiment3_data, first_model, second_model, third_model, fourth_model, fifth_model, sixth_model, feedback_inhibition_model, conservation_model, enhanced_conservation_model, final_model, adjusted_sixth_model, optimized_model)

### 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
The final optimized model shows promising results:

1. For iteration_0 (default):
   - Percentage errors: id_ri7q: 8.37%, id_nzce: 8.37%, id_jz57: 5.18%, total mass: 7.13%

2. For iteration_3 (higher id_jz57):
   - Percentage errors: id_ri7q: 18.87%, id_nzce: 18.87%, id_jz57: 14.46%, total mass: 18.46%

3. For iteration_5 (higher id_ri7q and id_nzce):
   - Percentage errors: id_ri7q: 0.68%, id_nzce: 0.68%, id_jz57: 5.44%, total mass: 0.12%

The model performs exceptionally well for iteration_5, with very low errors across all species and total mass. It also performs reasonably well for iteration_0, with single-digit percentage errors. The performance for iteration_3 is still not ideal, but it's better than many of our previous models.

After multiple iterations of model development and testing, I believe this optimized model captures the essential mechanisms of the biological system:

1. There is a constant production of id_jz57 (reaction1)
2. id_jz57 is converted to id_ri7q and id_nzce with a 10:1 stoichiometric ratio (reaction2)
3. All species undergo degradation (reactions 3, 4, and 5)
4. id_jz57 has a concentration-dependent degradation rate, which helps regulate the system when id_jz57 levels are high
5. There is a small reverse reaction converting id_ri7q and id_nzce back to id_jz57 (reaction6)

This model maintains the correct 10:1 ratio between id_ri7q and id_nzce across all conditions and achieves reasonable accuracy for the equilibrium values of all species.

Let me submit this optimized model as my final answer.

## Action

### Submit
```python
import libsbml

# Retrieve the optimized model
optimized_model = shared_variables.access("optimized_model")

# This is our final model
final_sbml = optimized_model
```
