
                # 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_8hn8">
    <listOfUnitDefinitions>
      <unitDefinition id="id_cm39">
        <listOfUnits>
          <unit kind="litre" exponent="1" scale="-3" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_g8kt">
        <listOfUnits>
          <unit kind="mole" exponent="1" scale="-3" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_6msh" spatialDimensions="3" size="1" constant="true"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_j5qx" compartment="id_6msh" initialConcentration="0.2" boundaryCondition="false" constant="false"/>
      <species id="id_o483" compartment="id_6msh" initialConcentration="0.1" boundaryCondition="false" constant="false"/>
      <species id="id_lti5" compartment="id_6msh" initialConcentration="0.55" 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_j5qx, id_o483, and id_lti5. The SBML model 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. This will give me baseline data to start forming hypotheses about the underlying reactions.

## Action

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

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

Total size: 2797 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_j5qx  id_o483  id_lti5
0  2.00e-01 1.00e-01 5.50e-01
...
6.12e+00  1.91e-01 3.81e-02 8.69e-01
...
1.22e+01  1.83e-01 1.49e-02 9.60e-01
...
1.83e+01  1.75e-01 6.53e-03 9.83e-01
...
2.45e+01  1.67e-01 3.26e-03 9.92e-01
...
3.06e+01  1.60e-01 1.87e-03 9.95e-01
...
3.67e+01  1.53e-01 1.22e-03 9.97e-01
...
4.28e+01  1.46e-01 9.04e-04 9.98e-01
...
4.89e+01  1.40e-01 7.58e-04 9.98e-01
...
5.50e+01  1.33e-01 7.15e-04 9.99e-01
...
6.12e+01  1.27e-01 7.53e-04 9.99e-01
...
6.73e+01  1.22e-01 8.84e-04 9.98e-01
...
7.34e+01  1.16e-01 1.15e-03 9.98e-01
...
7.95e+01  1.11e-01 1.65e-03 9.97e-01
...
8.56e+01  1.06e-01 2.60e-03 9.96e-01
...
9.17e+01  1.02e-01 4.48e-03 9.94e-01
...
9.79e+01  9.71e-02 8.40e-03 9.90e-01
...
1.04e+02  9.28e-02 1.71e-02 9.83e-01
...
1.10e+02  8.87e-02 3.74e-02 9.73e-01
...
1.16e+02  8.49e-02 8.57e-02 9.62e-01
...
1.22e+02  8.17e-02 1.93e-01 9.53e-01
...
1.28e+02  7.99e-02 3.65e-01 9.48e-01
...
1.35e+02  8.00e-02 5.13e-01 9.45e-01
...
1.41e+02  8.13e-02 5.76e-01 9.45e-01
...
1.47e+02  8.30e-02 5.90e-01 9.44e-01
...
1.53e+02  8.48e-02 5.88e-01 9.44e-01
...
1.59e+02  8.65e-02 5.80e-01 9.44e-01
...
1.65e+02  8.82e-02 5.72e-01 9.44e-01
...
1.71e+02  8.99e-02 5.63e-01 9.44e-01
...
1.77e+02  9.14e-02 5.54e-01 9.44e-01
...
1.83e+02  9.28e-02 5.46e-01 9.44e-01
...
1.90e+02  9.42e-02 5.38e-01 9.44e-01
...
1.96e+02  9.55e-02 5.30e-01 9.45e-01
...
2.02e+02  9.67e-02 5.23e-01 9.45e-01
...
2.08e+02  9.78e-02 5.16e-01 9.45e-01
...
2.14e+02  9.88e-02 5.09e-01 9.45e-01
...
2.20e+02  9.97e-02 5.03e-01 9.45e-01
...
2.26e+02  1.01e-01 4.97e-01 9.45e-01
...
2.32e+02  1.01e-01 4.92e-01 9.45e-01
...
2.39e+02  1.02e-01 4.87e-01 9.45e-01
...
2.45e+02  1.03e-01 4.82e-01 9.45e-01
...
2.51e+02  1.03e-01 4.78e-01 9.45e-01
...
2.57e+02  1.04e-01 4.74e-01 9.45e-01
...
2.63e+02  1.04e-01 4.70e-01 9.45e-01
...
2.69e+02  1.05e-01 4.67e-01 9.45e-01
...
2.75e+02  1.05e-01 4.64e-01 9.45e-01
...
2.81e+02  1.06e-01 4.61e-01 9.45e-01
...
2.87e+02  1.06e-01 4.59e-01 9.45e-01
...
2.94e+02  1.06e-01 4.56e-01 9.45e-01
...
3.00e+02  1.06e-01 4.54e-01 9.45e-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
Let me analyze the time-series data from the observation experiment to understand the dynamics of the three species.

Looking at the data:
1. id_j5qx starts at 0.2 and gradually decreases to around 0.106 by the end of the simulation.
2. id_o483 starts at 0.1, initially decreases to a very low value (around 0.0007), then increases dramatically to about 0.58, and finally settles around 0.454.
3. id_lti5 starts at 0.55, increases to nearly 1.0, then decreases slightly and stabilizes around 0.945.

This oscillatory behavior, especially in id_o483, suggests a complex system with feedback loops. Let me visualize and analyze this data more carefully to understand the relationships between these species.

## Action

### Code
```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.integrate import odeint
import libsbml

# Load the data
data = experiment_history["iteration_0"]

# Plot the time series data
plt.figure(figsize=(12, 6))
plt.plot(data['Time'], data['id_j5qx'], label='id_j5qx')
plt.plot(data['Time'], data['id_o483'], label='id_o483')
plt.plot(data['Time'], data['id_lti5'], label='id_lti5')
plt.xlabel('Time')
plt.ylabel('Concentration')
plt.legend()
plt.title('Species Concentrations Over Time')
plt.grid(True)

# Calculate rates of change
data_diff = data.copy()
for species in ['id_j5qx', 'id_o483', 'id_lti5']:
    data_diff[f'd{species}/dt'] = np.gradient(data[species], data['Time'])

# Store the data for future use
shared_variables.add('data', data)
shared_variables.add('data_diff', data_diff)

# Print summary statistics
print("Initial concentrations:")
print(data.iloc[0][['id_j5qx', 'id_o483', 'id_lti5']])
print("\nFinal concentrations:")
print(data.iloc[-1][['id_j5qx', 'id_o483', 'id_lti5']])

# Analyze the relationship between species
print("\nCorrelation matrix:")
correlation = data[['id_j5qx', 'id_o483', 'id_lti5']].corr()
print(correlation)

# Look at the rate of change at different points
print("\nRate of change at key points:")
key_indices = [0, 100, 500, 1000, 2000, -1]  # Start, early, middle, late, end
for idx in key_indices:
    print(f"Time {data.iloc[idx]['Time']:.2f}:")
    print(data_diff.iloc[idx][[f'd{species}/dt' for species in ['id_j5qx', 'id_o483', 'id_lti5']]])

# Let's examine the SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

print("\nSBML Model Information:")
print(f"Number of species: {model.getNumSpecies()}")
print(f"Number of reactions: {model.getNumReactions()}")
print(f"Number of parameters: {model.getNumParameters()}")

# Print species details
print("\nSpecies details:")
for i in range(model.getNumSpecies()):
    species = model.getSpecies(i)
    print(f"Species {i+1}: {species.getId()}, Initial concentration: {species.getInitialConcentration()}")
```
# 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 revise my code to analyze the data without visualization, focusing on numerical analysis instead.

## Action

### Code
```python
import numpy as np
import pandas as pd
import libsbml
from scipy.integrate import odeint

# Load the data
data = experiment_history["iteration_0"]

# Calculate rates of change
data_diff = data.copy()
for species in ['id_j5qx', 'id_o483', 'id_lti5']:
    data_diff[f'd{species}/dt'] = np.gradient(data[species], data['Time'])

# Store the data for future use
shared_variables.add('data', data)
shared_variables.add('data_diff', data_diff)

# Print summary statistics
print("Initial concentrations:")
print(data.iloc[0][['id_j5qx', 'id_o483', 'id_lti5']])
print("\nFinal concentrations:")
print(data.iloc[-1][['id_j5qx', 'id_o483', 'id_lti5']])

# Analyze the relationship between species
print("\nCorrelation matrix:")
correlation = data[['id_j5qx', 'id_o483', 'id_lti5']].corr()
print(correlation)

# Look at the rate of change at different points
print("\nRate of change at key points:")
key_times = [0, 20, 50, 100, 150, 200, 250, 300]  # Different time points
for time in key_times:
    # Find the closest time point in the data
    idx = (data['Time'] - time).abs().idxmin()
    print(f"\nTime {data.iloc[idx]['Time']:.2f}:")
    print(f"Concentrations: {data.iloc[idx][['id_j5qx', 'id_o483', 'id_lti5']].to_dict()}")
    print(f"Rates of change: {data_diff.iloc[idx][[f'd{species}/dt' for species in ['id_j5qx', 'id_o483', 'id_lti5']]].to_dict()}")

# Let's examine the SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

print("\nSBML Model Information:")
print(f"Number of species: {model.getNumSpecies()}")
print(f"Number of reactions: {model.getNumReactions()}")
print(f"Number of parameters: {model.getNumParameters()}")

# Print species details
print("\nSpecies details:")
for i in range(model.getNumSpecies()):
    species = model.getSpecies(i)
    print(f"Species {i+1}: {species.getId()}, Initial concentration: {species.getInitialConcentration()}")

# Let's try to identify patterns in the data that might suggest reaction mechanisms
# First, let's look at times when species are increasing/decreasing
print("\nAnalyzing patterns in species behavior:")
for species in ['id_j5qx', 'id_o483', 'id_lti5']:
    increasing = data_diff[data_diff[f'd{species}/dt'] > 0.001]
    decreasing = data_diff[data_diff[f'd{species}/dt'] < -0.001]
    stable = data_diff[(data_diff[f'd{species}/dt'] >= -0.001) & (data_diff[f'd{species}/dt'] <= 0.001)]
    
    print(f"\n{species}:")
    print(f"  Increasing: {len(increasing)} time points")
    print(f"  Decreasing: {len(decreasing)} time points")
    print(f"  Stable: {len(stable)} time points")
    
    if len(increasing) > 0:
        print(f"  When increasing, average concentrations:")
        print(f"    {species}: {increasing[species].mean():.4f}")
        print(f"    Other species: {increasing.drop([species, 'Time'] + [f'd{s}/dt' for s in ['id_j5qx', 'id_o483', 'id_lti5']]).mean().to_dict()}")
    
    if len(decreasing) > 0:
        print(f"  When decreasing, average concentrations:")
        print(f"    {species}: {decreasing[species].mean():.4f}")
        print(f"    Other species: {decreasing.drop([species, 'Time'] + [f'd{s}/dt' for s in ['id_j5qx', 'id_o483', 'id_lti5']]).mean().to_dict()}")
```
# Observation

## Code Stderror
 "['id_j5qx', 'Time', 'did_j5qx/dt', 'did_o483/dt', 'did_lti5/dt'] not found in axis"

## 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. (data, data_diff)

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


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



# Iteration 3
## Thoughts
I encountered an error in my previous code when trying to analyze patterns. Let me fix that and continue with a more focused analysis of the data to understand the reaction mechanisms.

## Action

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

# Load the data
data = experiment_history["iteration_0"]

# Calculate rates of change
data_diff = data.copy()
for species in ['id_j5qx', 'id_o483', 'id_lti5']:
    data_diff[f'd{species}/dt'] = np.gradient(data[species], data['Time'])

# Store the data for future use
shared_variables.add('data', data)
shared_variables.add('data_diff', data_diff)

# Print summary statistics
print("Initial concentrations:")
print(data.iloc[0][['id_j5qx', 'id_o483', 'id_lti5']])
print("\nFinal concentrations:")
print(data.iloc[-1][['id_j5qx', 'id_o483', 'id_lti5']])

# Analyze the relationship between species
print("\nCorrelation matrix:")
correlation = data[['id_j5qx', 'id_o483', 'id_lti5']].corr()
print(correlation)

# Look at the rate of change at different points
print("\nRate of change at key points:")
key_times = [0, 20, 50, 100, 150, 200, 250, 300]  # Different time points
for time in key_times:
    # Find the closest time point in the data
    idx = (data['Time'] - time).abs().idxmin()
    print(f"\nTime {data.iloc[idx]['Time']:.2f}:")
    print(f"Concentrations: {dict(data.iloc[idx][['id_j5qx', 'id_o483', 'id_lti5']])}")
    print(f"Rates of change: {dict(data_diff.iloc[idx][[f'd{species}/dt' for species in ['id_j5qx', 'id_o483', 'id_lti5']]])}")

# Let's examine the SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

print("\nSBML Model Information:")
print(f"Number of species: {model.getNumSpecies()}")
print(f"Number of reactions: {model.getNumReactions()}")
print(f"Number of parameters: {model.getNumParameters()}")

# Print species details
print("\nSpecies details:")
for i in range(model.getNumSpecies()):
    species = model.getSpecies(i)
    print(f"Species {i+1}: {species.getId()}, Initial concentration: {species.getInitialConcentration()}")

# Let's try to identify patterns in the data that might suggest reaction mechanisms
# First, let's look at times when species are increasing/decreasing
print("\nAnalyzing patterns in species behavior:")
for species in ['id_j5qx', 'id_o483', 'id_lti5']:
    rate_col = f'd{species}/dt'
    increasing = data_diff[data_diff[rate_col] > 0.001]
    decreasing = data_diff[data_diff[rate_col] < -0.001]
    stable = data_diff[(data_diff[rate_col] >= -0.001) & (data_diff[rate_col] <= 0.001)]
    
    print(f"\n{species}:")
    print(f"  Increasing: {len(increasing)} time points")
    print(f"  Decreasing: {len(decreasing)} time points")
    print(f"  Stable: {len(stable)} time points")
    
    if len(increasing) > 0:
        print(f"  When increasing, average concentrations:")
        for other_species in ['id_j5qx', 'id_o483', 'id_lti5']:
            print(f"    {other_species}: {increasing[other_species].mean():.4f}")
    
    if len(decreasing) > 0:
        print(f"  When decreasing, average concentrations:")
        for other_species in ['id_j5qx', 'id_o483', 'id_lti5']:
            print(f"    {other_species}: {decreasing[other_species].mean():.4f}")

# Let's try to identify potential reaction mechanisms
print("\nPotential reaction mechanisms analysis:")

# Check for conservation of mass
print("Conservation of mass check:")
total_mass = data['id_j5qx'] + data['id_o483'] + data['id_lti5']
print(f"Total mass at start: {total_mass.iloc[0]:.4f}")
print(f"Total mass at end: {total_mass.iloc[-1]:.4f}")
print(f"Min total mass: {total_mass.min():.4f}")
print(f"Max total mass: {total_mass.max():.4f}")
print(f"Std dev of total mass: {total_mass.std():.4f}")

# Let's look at specific time periods to understand the dynamics better
# First period: Early dynamics (0-50)
early = data[data['Time'] <= 50]
print("\nEarly dynamics (0-50):")
print(f"id_j5qx: start={early['id_j5qx'].iloc[0]:.4f}, end={early['id_j5qx'].iloc[-1]:.4f}, change={early['id_j5qx'].iloc[-1]-early['id_j5qx'].iloc[0]:.4f}")
print(f"id_o483: start={early['id_o483'].iloc[0]:.4f}, end={early['id_o483'].iloc[-1]:.4f}, change={early['id_o483'].iloc[-1]-early['id_o483'].iloc[0]:.4f}")
print(f"id_lti5: start={early['id_lti5'].iloc[0]:.4f}, end={early['id_lti5'].iloc[-1]:.4f}, change={early['id_lti5'].iloc[-1]-early['id_lti5'].iloc[0]:.4f}")

# Middle period: Transition (50-150)
middle = data[(data['Time'] > 50) & (data['Time'] <= 150)]
print("\nMiddle dynamics (50-150):")
print(f"id_j5qx: start={middle['id_j5qx'].iloc[0]:.4f}, end={middle['id_j5qx'].iloc[-1]:.4f}, change={middle['id_j5qx'].iloc[-1]-middle['id_j5qx'].iloc[0]:.4f}")
print(f"id_o483: start={middle['id_o483'].iloc[0]:.4f}, end={middle['id_o483'].iloc[-1]:.4f}, change={middle['id_o483'].iloc[-1]-middle['id_o483'].iloc[0]:.4f}")
print(f"id_lti5: start={middle['id_lti5'].iloc[0]:.4f}, end={middle['id_lti5'].iloc[-1]:.4f}, change={middle['id_lti5'].iloc[-1]-middle['id_lti5'].iloc[0]:.4f}")

# Late period: Stabilization (150-300)
late = data[data['Time'] > 150]
print("\nLate dynamics (150-300):")
print(f"id_j5qx: start={late['id_j5qx'].iloc[0]:.4f}, end={late['id_j5qx'].iloc[-1]:.4f}, change={late['id_j5qx'].iloc[-1]-late['id_j5qx'].iloc[0]:.4f}")
print(f"id_o483: start={late['id_o483'].iloc[0]:.4f}, end={late['id_o483'].iloc[-1]:.4f}, change={late['id_o483'].iloc[-1]-late['id_o483'].iloc[0]:.4f}")
print(f"id_lti5: start={late['id_lti5'].iloc[0]:.4f}, end={late['id_lti5'].iloc[-1]:.4f}, change={late['id_lti5'].iloc[-1]-late['id_lti5'].iloc[0]:.4f}")
```
# Observation

## Code Stdout
Initial concentrations:
id_j5qx    0.20
id_o483    0.10
id_lti5    0.55
Name: 0, dtype: float64

Final concentrations:
id_j5qx    0.106380
id_o483    0.454252
id_lti5    0.945029
Name: 2796, dtype: float64

Correlation matrix:
          id_j5qx   id_o483   id_lti5
id_j5qx  1.000000 -0.623452 -0.102815
id_o483 -0.623452  1.000000 -0.369348
id_lti5 -0.102815 -0.369348  1.000000

Rate of change at key points:

Time 0.00:
Concentrations: {'id_j5qx': np.float64(0.2), 'id_o483': np.float64(0.1), 'id_lti5': np.float64(0.55)}
Rates of change: {'did_j5qx/dt': np.float64(-0.0013517975085165512), 'did_o483/dt': np.float64(-0.015060081473692647), 'did_lti5/dt': np.float64(0.07349402029742373)}

Time 19.96:
Concentrations: {'id_j5qx': np.float64(0.1728676524704099), 'id_o483': np.float64(0.005366102827408193), 'id_lti5': np.float64(0.9862203221969593)}
Rates of change: {'did_j5qx/dt': np.float64(-0.0012800071611649422), 'did_o483/dt': np.float64(-0.000636808097305451), 'did_lti5/dt': np.float64(0.0016382897980138367)}

Time 50.00:
Concentrations: {'id_j5qx': np.float64(0.1383997608443529), 'id_o483': np.float64(0.0007441279187323424), 'id_lti5': np.float64(0.9984879425647437)}
Rates of change: {'did_j5qx/dt': np.float64(-0.0010242937601888658), 'did_o483/dt': np.float64(-1.1731340735133752e-05), 'did_lti5/dt': np.float64(3.917612489967581e-05)}

Time 100.00:
Concentrations: {'id_j5qx': np.float64(0.09558702295257934), 'id_o483': np.float64(0.010686463409769002), 'id_lti5': np.float64(0.9879538733270186)}
Rates of change: {'did_j5qx/dt': np.float64(-0.0007076763890609961), 'did_o483/dt': np.float64(0.001221252451133678), 'did_lti5/dt': np.float64(-0.001027205012487542)}

Time 150.00:
Concentrations: {'id_j5qx': np.float64(0.08394054104588128), 'id_o483': np.float64(0.59009586905074), 'id_lti5': np.float64(0.9442460205463491)}
Rates of change: {'did_j5qx/dt': np.float64(0.00029298782311176774), 'did_o483/dt': np.float64(-0.0005233839941243268), 'did_lti5/dt': np.float64(-5.876239345781187e-06)}

Time 200.00:
Concentrations: {'id_j5qx': np.float64(0.0963090227343733), 'id_o483': np.float64(0.5248010922863413), 'id_lti5': np.float64(0.9445445606246266)}
Rates of change: {'did_j5qx/dt': np.float64(0.0001911532025527518), 'did_o483/dt': np.float64(-0.0011929144261051405), 'did_lti5/dt': np.float64(7.022144236756844e-06)}

Time 250.00:
Concentrations: {'id_j5qx': np.float64(0.10326772171653346), 'id_o483': np.float64(0.47810379845843237), 'id_lti5': np.float64(0.9448479466534634)}
Rates of change: {'did_j5qx/dt': np.float64(9.34793662708544e-05), 'did_o483/dt': np.float64(-0.0006812938174367567), 'did_lti5/dt': np.float64(4.8914579400261005e-06)}

Time 300.00:
Concentrations: {'id_j5qx': np.float64(0.1063796660150398), 'id_o483': np.float64(0.45425159661360287), 'id_lti5': np.float64(0.9450292302587112)}
Rates of change: {'did_j5qx/dt': np.float64(3.778405704404723e-05), 'did_o483/dt': np.float64(-0.00030635204982056014), 'did_lti5/dt': np.float64(2.4672544758173692e-06)}

SBML Model Information:
Number of species: 3
Number of reactions: 0
Number of parameters: 0

Species details:
Species 1: id_j5qx, Initial concentration: 0.2
Species 2: id_o483, Initial concentration: 0.1
Species 3: id_lti5, Initial concentration: 0.55

Analyzing patterns in species behavior:

id_j5qx:
  Increasing: 0 time points
  Decreasing: 497 time points
  Stable: 2300 time points
  When decreasing, average concentrations:
    id_j5qx: 0.1656
    id_o483: 0.0127
    id_lti5: 0.9544

id_o483:
  Increasing: 439 time points
  Decreasing: 769 time points
  Stable: 1589 time points
  When increasing, average concentrations:
    id_j5qx: 0.0848
    id_o483: 0.2554
    id_lti5: 0.9596
  When decreasing, average concentrations:
    id_j5qx: 0.1127
    id_o483: 0.4389
    id_lti5: 0.9288

id_lti5:
  Increasing: 219 time points
  Decreasing: 228 time points
  Stable: 2350 time points
  When increasing, average concentrations:
    id_j5qx: 0.1840
    id_o483: 0.0271
    id_lti5: 0.9009
  When decreasing, average concentrations:
    id_j5qx: 0.0878
    id_o483: 0.0722
    id_lti5: 0.9699

Potential reaction mechanisms analysis:
Conservation of mass check:
Total mass at start: 0.8500
Total mass at end: 1.5057
Min total mass: 0.8500
Max total mass: 1.6184
Std dev of total mass: 0.2135

Early dynamics (0-50):
id_j5qx: start=0.2000, end=0.1384, change=-0.0616
id_o483: start=0.1000, end=0.0007, change=-0.0993
id_lti5: start=0.5500, end=0.9985, change=0.4485

Middle dynamics (50-150):
id_j5qx: start=0.1383, end=0.0839, change=-0.0543
id_o483: start=0.0007, end=0.5901, change=0.5894
id_lti5: start=0.9985, end=0.9442, change=-0.0542

Late dynamics (150-300):
id_j5qx: start=0.0840, end=0.1064, change=0.0224
id_o483: start=0.5900, end=0.4543, change=-0.1358
id_lti5: start=0.9442, end=0.9450, change=0.0008

## Reminder

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



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

### 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
Based on the analysis of the time-series data, I can make several observations about the system dynamics:

1. **Conservation of mass**: The total mass in the system increases from 0.85 to about 1.51, suggesting that there might be some production or inflow of species.

2. **Early dynamics (0-50)**:
   - id_j5qx decreases (-0.0616)
   - id_o483 decreases significantly (-0.0993)
   - id_lti5 increases significantly (+0.4485)
   - This suggests a reaction where both id_j5qx and id_o483 are converted to id_lti5, but the increase in id_lti5 is greater than the combined decrease of the other two.

3. **Middle dynamics (50-150)**:
   - id_j5qx continues to decrease (-0.0543)
   - id_o483 increases dramatically (+0.5894)
   - id_lti5 decreases slightly (-0.0542)
   - This suggests a reaction where id_j5qx and id_lti5 are converted to id_o483, but the increase in id_o483 is much greater than the combined decrease of the other two.

4. **Late dynamics (150-300)**:
   - id_j5qx increases slightly (+0.0224)
   - id_o483 decreases (-0.1358)
   - id_lti5 remains almost stable (+0.0008)
   - This suggests a reaction where id_o483 is converted to id_j5qx, but the decrease in id_o483 is greater than the increase in id_j5qx.

5. **Correlation matrix**:
   - Negative correlation between id_j5qx and id_o483 (-0.623)
   - Negative correlation between id_o483 and id_lti5 (-0.369)
   - Slight negative correlation between id_j5qx and id_lti5 (-0.103)

Based on these observations, I can hypothesize the following reactions:

1. id_j5qx + id_o483 → id_lti5 (dominant in early phase)
2. id_lti5 → id_o483 (dominant in middle phase)
3. id_o483 → id_j5qx (dominant in late phase)

Additionally, there might be some production or autocatalytic reactions to explain the increase in total mass.

Let me now try to formulate a more complete model and test it with a simulation. I'll start by implementing these reactions in the SBML model.

## Action

### Code
```python
import libsbml
import numpy as np
import pandas as pd
from scipy.integrate import odeint

# Load the original SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

# Add reactions to the model
# Reaction 1: id_j5qx + id_o483 → id_lti5
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactants
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

reactant2 = reaction1.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.5)  # Initial guess for rate constant
math_ast1 = libsbml.parseL3Formula(f"k1 * id_j5qx * id_o483")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_lti5 → id_o483 (with amplification)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant3 = reaction2.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_o483")
product2.setStoichiometry(2.0)  # Amplification factor
product2.setConstant(True)

# Add kinetic law
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.05)  # Initial guess for rate constant
math_ast2 = libsbml.parseL3Formula(f"k2 * id_lti5")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_o483 → id_j5qx
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant4 = reaction3.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add product
product3 = reaction3.createProduct()
product3.setSpecies("id_j5qx")
product3.setStoichiometry(1.0)
product3.setConstant(True)

# Add kinetic law
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.01)  # Initial guess for rate constant
math_ast3 = libsbml.parseL3Formula(f"k3 * id_o483")
kinetic_law3.setMath(math_ast3)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(document)

# Store the updated SBML model
shared_variables.add('updated_sbml', updated_sbml)

# Simulate the updated model
simulation_result = simulate(updated_sbml)

# Compare the simulation with the experimental data
print("Comparing simulation with experimental data:")
# Get the experimental data at specific time points
exp_data = experiment_history["iteration_0"]
time_points = [0, 50, 100, 150, 200, 250, 300]
for time in time_points:
    # Find the closest time point in the experimental data
    exp_idx = (exp_data['Time'] - time).abs().idxmin()
    exp_time = exp_data.iloc[exp_idx]['Time']
    
    # Find the closest time point in the simulation data
    sim_idx = (simulation_result['Time'] - time).abs().idxmin()
    sim_time = simulation_result.iloc[sim_idx]['Time']
    
    print(f"\nTime ~{time}:")
    print(f"Experimental (t={exp_time:.2f}):")
    print(f"  id_j5qx: {exp_data.iloc[exp_idx]['id_j5qx']:.4f}")
    print(f"  id_o483: {exp_data.iloc[exp_idx]['id_o483']:.4f}")
    print(f"  id_lti5: {exp_data.iloc[exp_idx]['id_lti5']:.4f}")
    
    print(f"Simulation (t={sim_time:.2f}):")
    print(f"  id_j5qx: {simulation_result.iloc[sim_idx]['id_j5qx']:.4f}")
    print(f"  id_o483: {simulation_result.iloc[sim_idx]['id_o483']:.4f}")
    print(f"  id_lti5: {simulation_result.iloc[sim_idx]['id_lti5']:.4f}")

# Let's try a different experiment to further validate our model
# Let's change the initial concentrations and see how the system behaves
print("\nLet's try a different experiment to further validate our model")
```
# Observation

## Code Stdout
Comparing simulation with experimental data:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500
Simulation (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1384
  id_o483: 0.0007
  id_lti5: 0.9985
Simulation (t=50.00):
  id_j5qx: 0.0200
  id_o483: 0.9463
  id_lti5: 0.2169

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.0956
  id_o483: 0.0107
  id_lti5: 0.9880
Simulation (t=100.00):
  id_j5qx: 0.0200
  id_o483: 0.9845
  id_lti5: 0.1977

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0839
  id_o483: 0.5901
  id_lti5: 0.9442
Simulation (t=150.00):
  id_j5qx: 0.0200
  id_o483: 0.9857
  id_lti5: 0.1972

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0963
  id_o483: 0.5248
  id_lti5: 0.9445
Simulation (t=200.00):
  id_j5qx: 0.0200
  id_o483: 0.9857
  id_lti5: 0.1971

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.4781
  id_lti5: 0.9448
Simulation (t=250.00):
  id_j5qx: 0.0200
  id_o483: 0.9857
  id_lti5: 0.1971

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1064
  id_o483: 0.4543
  id_lti5: 0.9450
Simulation (t=300.00):
  id_j5qx: 0.0200
  id_o483: 0.9857
  id_lti5: 0.1971

Let's try a different experiment to further validate our model

## Reminder

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



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

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


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



# Iteration 5
## Thoughts
My initial model doesn't match the experimental data well. The simulation shows:
1. id_j5qx decreases too quickly and reaches a much lower steady state
2. id_o483 increases too much and doesn't show the oscillatory behavior
3. id_lti5 doesn't increase enough and stays at a much lower level

I need to revise my hypothesis about the reaction mechanisms. Let me try a different approach:

1. The total mass increases in the system, suggesting production of species.
2. id_lti5 increases significantly in the early phase, while id_j5qx and id_o483 decrease.
3. id_o483 shows oscillatory behavior, first decreasing then increasing dramatically.

Let me try a different set of reactions:

1. id_j5qx → id_lti5 (conversion)
2. id_o483 → id_lti5 (conversion)
3. id_lti5 → id_o483 (feedback, activated at higher id_lti5 concentrations)
4. id_o483 → id_j5qx (recycling)

Let me also try a different experiment to gather more data about the system's behavior under different initial conditions. I'll change the initial concentrations to see how the system responds.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration", 
    "meta_data": {
        "id_j5qx": 0.3,
        "id_o483": 0.2,
        "id_lti5": 0.4
    }
}
```
# 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: 2797 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_j5qx  id_o483  id_lti5
0  3.00e-01 2.00e-01 4.00e-01
...
6.12e+00  2.88e-01 1.48e-02 8.05e-01
...
1.22e+01  2.75e-01 1.00e-03 9.64e-01
...
1.83e+01  2.63e-01 8.14e-05 9.95e-01
...
2.45e+01  2.51e-01 8.18e-06 9.99e-01
...
3.06e+01  2.40e-01 1.01e-06 1.00e+00
...
3.67e+01  2.29e-01 1.54e-07 1.00e+00
...
4.28e+01  2.19e-01 2.83e-08 1.00e+00
...
4.89e+01  2.09e-01 6.26e-09 1.00e+00
...
5.50e+01  2.00e-01 1.65e-09 1.00e+00
...
6.12e+01  1.91e-01 5.16e-10 1.00e+00
...
6.73e+01  1.83e-01 1.90e-10 1.00e+00
...
7.34e+01  1.75e-01 8.11e-11 1.00e+00
...
7.95e+01  1.67e-01 4.02e-11 1.00e+00
...
8.56e+01  1.60e-01 2.29e-11 1.00e+00
...
9.17e+01  1.53e-01 1.50e-11 1.00e+00
...
9.79e+01  1.46e-01 1.12e-11 1.00e+00
...
1.04e+02  1.39e-01 9.24e-12 1.00e+00
...
1.10e+02  1.33e-01 8.14e-12 1.00e+00
...
1.16e+02  1.27e-01 8.61e-12 1.00e+00
...
1.22e+02  1.22e-01 1.02e-11 1.00e+00
...
1.28e+02  1.16e-01 1.34e-11 1.00e+00
...
1.35e+02  1.11e-01 1.92e-11 1.00e+00
...
1.41e+02  1.06e-01 3.04e-11 1.00e+00
...
1.47e+02  1.02e-01 5.27e-11 1.00e+00
...
1.53e+02  9.71e-02 9.93e-11 1.00e+00
...
1.59e+02  9.28e-02 2.03e-10 1.00e+00
...
1.65e+02  8.87e-02 4.48e-10 1.00e+00
...
1.71e+02  8.47e-02 1.06e-09 1.00e+00
...
1.77e+02  8.10e-02 2.71e-09 1.00e+00
...
1.83e+02  7.74e-02 7.40e-09 1.00e+00
...
1.90e+02  7.40e-02 2.16e-08 1.00e+00
...
1.96e+02  7.07e-02 6.68e-08 1.00e+00
...
2.02e+02  6.76e-02 2.20e-07 1.00e+00
...
2.08e+02  6.46e-02 7.64e-07 1.00e+00
...
2.14e+02  6.17e-02 2.81e-06 1.00e+00
...
2.20e+02  5.90e-02 1.09e-05 1.00e+00
...
2.26e+02  5.64e-02 4.42e-05 1.00e+00
...
2.32e+02  5.39e-02 1.89e-04 1.00e+00
...
2.39e+02  5.15e-02 8.42e-04 9.99e-01
...
2.45e+02  4.92e-02 3.92e-03 9.96e-01
...
2.51e+02  4.70e-02 1.88e-02 9.86e-01
...
2.57e+02  4.50e-02 8.96e-02 9.66e-01
...
2.63e+02  4.36e-02 3.36e-01 9.51e-01
...
2.69e+02  4.40e-02 6.44e-01 9.45e-01
...
2.75e+02  4.57e-02 7.44e-01 9.44e-01
...
2.81e+02  4.77e-02 7.54e-01 9.44e-01
...
2.87e+02  4.99e-02 7.49e-01 9.44e-01
...
2.94e+02  5.21e-02 7.40e-01 9.44e-01
...
3.00e+02  5.44e-02 7.31e-01 9.44e-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_5)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml)

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


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



# Iteration 6
## Thoughts
The second experiment with different initial concentrations provides valuable insights:

1. With higher initial id_j5qx (0.3) and id_o483 (0.2), and lower id_lti5 (0.4):
   - id_j5qx decreases steadily throughout the experiment
   - id_o483 initially decreases rapidly to near-zero values (around 10^-11)
   - id_lti5 increases rapidly to nearly 1.0 and stays there for a long time
   - Around t=240, id_o483 suddenly increases dramatically from ~10^-11 to ~0.73
   - When id_o483 increases, id_lti5 decreases slightly from 1.0 to ~0.944

This behavior suggests:
1. Both id_j5qx and id_o483 are converted to id_lti5 in the early phase
2. There's a threshold effect: when id_lti5 reaches a high concentration and/or id_j5qx drops below a threshold, id_o483 starts to be produced
3. The system eventually reaches a similar steady state regardless of initial conditions

Let me revise my model with these insights. I'll try the following reactions:

1. id_j5qx → id_lti5 (conversion)
2. id_o483 → id_lti5 (conversion)
3. id_lti5 → id_o483 (feedback, activated at higher id_lti5 concentrations)
4. id_o483 → id_j5qx (recycling)
5. id_lti5 + id_j5qx → id_lti5 + id_o483 (catalytic production of id_o483)

Let me implement this model and test it against both experiments.

## Action

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

# Load the original SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

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

# Add reactions to the model
# Reaction 1: id_j5qx → id_lti5 (conversion)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactant
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Rate constant
math_ast1 = libsbml.parseL3Formula("k1 * id_j5qx")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_o483 → id_lti5 (conversion)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_lti5")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.5)  # Rate constant
math_ast2 = libsbml.parseL3Formula("k2 * id_o483")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_lti5 → id_o483 (feedback, activated at higher id_lti5 concentrations)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add product
product3 = reaction3.createProduct()
product3.setSpecies("id_o483")
product3.setStoichiometry(2.0)  # Amplification
product3.setConstant(True)

# Add kinetic law with Hill function for threshold effect
kinetic_law3 = reaction3.createKineticLaw()
parameter3a = kinetic_law3.createParameter()
parameter3a.setId("k3")
parameter3a.setValue(0.001)  # Rate constant

parameter3b = kinetic_law3.createParameter()
parameter3b.setId("threshold")
parameter3b.setValue(0.9)  # Threshold for activation

parameter3c = kinetic_law3.createParameter()
parameter3c.setId("n")
parameter3c.setValue(10)  # Hill coefficient for steepness

# Hill function: k3 * (id_lti5^n) / (threshold^n + id_lti5^n)
math_ast3 = libsbml.parseL3Formula("k3 * (id_lti5^n) / (threshold^n + id_lti5^n)")
kinetic_law3.setMath(math_ast3)

# Reaction 4: id_o483 → id_j5qx (recycling)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add product
product4 = reaction4.createProduct()
product4.setSpecies("id_j5qx")
product4.setStoichiometry(1.0)
product4.setConstant(True)

# Add kinetic law
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.01)  # Rate constant
math_ast4 = libsbml.parseL3Formula("k4 * id_o483")
kinetic_law4.setMath(math_ast4)

# Reaction 5: id_lti5 + id_j5qx → id_lti5 + id_o483 (catalytic production of id_o483)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactants
reactant5a = reaction5.createReactant()
reactant5a.setSpecies("id_lti5")
reactant5a.setStoichiometry(1.0)
reactant5a.setConstant(True)

reactant5b = reaction5.createReactant()
reactant5b.setSpecies("id_j5qx")
reactant5b.setStoichiometry(1.0)
reactant5b.setConstant(True)

# Add products
product5a = reaction5.createProduct()
product5a.setSpecies("id_lti5")
product5a.setStoichiometry(1.0)
product5a.setConstant(True)

product5b = reaction5.createProduct()
product5b.setSpecies("id_o483")
product5b.setStoichiometry(1.0)
product5b.setConstant(True)

# Add kinetic law with threshold effect
kinetic_law5 = reaction5.createKineticLaw()
parameter5a = kinetic_law5.createParameter()
parameter5a.setId("k5")
parameter5a.setValue(0.01)  # Rate constant

parameter5b = kinetic_law5.createParameter()
parameter5b.setId("threshold2")
parameter5b.setValue(0.9)  # Threshold for activation

parameter5c = kinetic_law5.createParameter()
parameter5c.setId("n2")
parameter5c.setValue(10)  # Hill coefficient for steepness

# Hill function with both species: k5 * id_j5qx * (id_lti5^n2) / (threshold2^n2 + id_lti5^n2)
math_ast5 = libsbml.parseL3Formula("k5 * id_j5qx * (id_lti5^n2) / (threshold2^n2 + id_lti5^n2)")
kinetic_law5.setMath(math_ast5)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(document)

# Store the updated SBML model
shared_variables.add('updated_sbml_v2', updated_sbml)

# Simulate the updated model with original initial conditions
print("Simulating with original initial conditions:")
simulation_result1 = simulate(updated_sbml)

# Compare with experimental data at key time points
exp_data1 = experiment_history["iteration_0"]
time_points = [0, 50, 100, 150, 200, 250, 300]

for time in time_points:
    # Find the closest time point in the experimental data
    exp_idx = (exp_data1['Time'] - time).abs().idxmin()
    exp_time = exp_data1.iloc[exp_idx]['Time']
    
    # Find the closest time point in the simulation data
    sim_idx = (simulation_result1['Time'] - time).abs().idxmin()
    sim_time = simulation_result1.iloc[sim_idx]['Time']
    
    print(f"\nTime ~{time}:")
    print(f"Experimental (t={exp_time:.2f}):")
    print(f"  id_j5qx: {exp_data1.iloc[exp_idx]['id_j5qx']:.4f}")
    print(f"  id_o483: {exp_data1.iloc[exp_idx]['id_o483']:.4f}")
    print(f"  id_lti5: {exp_data1.iloc[exp_idx]['id_lti5']:.4f}")
    
    print(f"Simulation (t={sim_time:.2f}):")
    print(f"  id_j5qx: {simulation_result1.iloc[sim_idx]['id_j5qx']:.4f}")
    print(f"  id_o483: {simulation_result1.iloc[sim_idx]['id_o483']:.4f}")
    print(f"  id_lti5: {simulation_result1.iloc[sim_idx]['id_lti5']:.4f}")

# Now simulate with the second set of initial conditions
print("\nSimulating with second set of initial conditions:")
# Create a new SBML document with different initial conditions
document2 = libsbml.readSBMLFromString(updated_sbml)
model2 = document2.getModel()

# Set new initial conditions
model2.getSpecies("id_j5qx").setInitialConcentration(0.3)
model2.getSpecies("id_o483").setInitialConcentration(0.2)
model2.getSpecies("id_lti5").setInitialConcentration(0.4)

# Write the updated SBML model to a string
updated_sbml2 = writer.writeSBMLToString(document2)

# Simulate with new initial conditions
simulation_result2 = simulate(updated_sbml2)

# Compare with experimental data at key time points
exp_data2 = experiment_history["iteration_5"]

for time in time_points:
    # Find the closest time point in the experimental data
    exp_idx = (exp_data2['Time'] - time).abs().idxmin()
    exp_time = exp_data2.iloc[exp_idx]['Time']
    
    # Find the closest time point in the simulation data
    sim_idx = (simulation_result2['Time'] - time).abs().idxmin()
    sim_time = simulation_result2.iloc[sim_idx]['Time']
    
    print(f"\nTime ~{time}:")
    print(f"Experimental (t={exp_time:.2f}):")
    print(f"  id_j5qx: {exp_data2.iloc[exp_idx]['id_j5qx']:.4f}")
    print(f"  id_o483: {exp_data2.iloc[exp_idx]['id_o483']:.4f}")
    print(f"  id_lti5: {exp_data2.iloc[exp_idx]['id_lti5']:.4f}")
    
    print(f"Simulation (t={sim_time:.2f}):")
    print(f"  id_j5qx: {simulation_result2.iloc[sim_idx]['id_j5qx']:.4f}")
    print(f"  id_o483: {simulation_result2.iloc[sim_idx]['id_o483']:.4f}")
    print(f"  id_lti5: {simulation_result2.iloc[sim_idx]['id_lti5']:.4f}")
```
# Observation

## Code Stdout
Simulating with original initial conditions:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500
Simulation (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1384
  id_o483: 0.0007
  id_lti5: 0.9985
Simulation (t=50.00):
  id_j5qx: 0.0152
  id_o483: 0.0014
  id_lti5: 0.8439

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.0956
  id_o483: 0.0107
  id_lti5: 0.9880
Simulation (t=100.00):
  id_j5qx: 0.0013
  id_o483: 0.0017
  id_lti5: 0.8773

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0839
  id_o483: 0.5901
  id_lti5: 0.9442
Simulation (t=150.00):
  id_j5qx: 0.0004
  id_o483: 0.0020
  id_lti5: 0.9014

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0963
  id_o483: 0.5248
  id_lti5: 0.9445
Simulation (t=200.00):
  id_j5qx: 0.0004
  id_o483: 0.0023
  id_lti5: 0.9281

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.4781
  id_lti5: 0.9448
Simulation (t=250.00):
  id_j5qx: 0.0004
  id_o483: 0.0026
  id_lti5: 0.9585

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1064
  id_o483: 0.4543
  id_lti5: 0.9450
Simulation (t=300.00):
  id_j5qx: 0.0005
  id_o483: 0.0028
  id_lti5: 0.9926

Simulating with second set of initial conditions:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000
Simulation (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.2078
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=50.00):
  id_j5qx: 0.0223
  id_o483: 0.0020
  id_lti5: 0.8885

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1436
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=100.00):
  id_j5qx: 0.0018
  id_o483: 0.0023
  id_lti5: 0.9358

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0992
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=150.00):
  id_j5qx: 0.0005
  id_o483: 0.0026
  id_lti5: 0.9686

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0685
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=200.00):
  id_j5qx: 0.0005
  id_o483: 0.0029
  id_lti5: 1.0040

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.0473
  id_o483: 0.0155
  id_lti5: 0.9876
Simulation (t=250.00):
  id_j5qx: 0.0005
  id_o483: 0.0032
  id_lti5: 1.0428

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.0544
  id_o483: 0.7310
  id_lti5: 0.9437
Simulation (t=300.00):
  id_j5qx: 0.0006
  id_o483: 0.0034
  id_lti5: 1.0846

## 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_5)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2)

### 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
My second model still doesn't match the experimental data well. The key issues are:

1. In the simulation, id_j5qx decreases too much and doesn't recover
2. id_o483 doesn't show the dramatic increase seen in the experiments
3. The threshold effect for id_o483 production isn't triggering properly

Let me try a different approach. Looking at both experiments:

1. In both cases, id_lti5 increases to a high level (~0.95-1.0)
2. id_o483 initially decreases, then dramatically increases later
3. id_j5qx decreases initially, then slightly recovers

The key insight might be that there's a delayed activation of id_o483 production when id_lti5 reaches a high level. Let me try a different experiment with a higher initial concentration of id_lti5 to see if that triggers the id_o483 production more quickly.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration", 
    "meta_data": {
        "id_j5qx": 0.1,
        "id_o483": 0.05,
        "id_lti5": 0.8
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_7
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_7]

Total size: 2797 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_7] for the full data

Time   id_j5qx  id_o483  id_lti5
0  1.00e-01 5.00e-02 8.00e-01
...
6.12e+00  9.58e-02 9.72e-02 9.32e-01
...
1.22e+01  9.22e-02 1.84e-01 9.49e-01
...
1.83e+01  8.99e-02 3.16e-01 9.48e-01
...
2.45e+01  8.92e-02 4.42e-01 9.46e-01
...
3.06e+01  8.97e-02 5.14e-01 9.45e-01
...
3.67e+01  9.09e-02 5.39e-01 9.45e-01
...
4.28e+01  9.22e-02 5.43e-01 9.44e-01
...
4.89e+01  9.36e-02 5.39e-01 9.44e-01
...
5.50e+01  9.49e-02 5.33e-01 9.45e-01
...
6.12e+01  9.61e-02 5.26e-01 9.45e-01
...
6.73e+01  9.72e-02 5.19e-01 9.45e-01
...
7.34e+01  9.83e-02 5.12e-01 9.45e-01
...
7.95e+01  9.93e-02 5.06e-01 9.45e-01
...
8.56e+01  1.00e-01 5.00e-01 9.45e-01
...
9.17e+01  1.01e-01 4.94e-01 9.45e-01
...
9.79e+01  1.02e-01 4.89e-01 9.45e-01
...
1.04e+02  1.02e-01 4.84e-01 9.45e-01
...
1.10e+02  1.03e-01 4.80e-01 9.45e-01
...
1.16e+02  1.04e-01 4.76e-01 9.45e-01
...
1.22e+02  1.04e-01 4.72e-01 9.45e-01
...
1.28e+02  1.05e-01 4.68e-01 9.45e-01
...
1.35e+02  1.05e-01 4.65e-01 9.45e-01
...
1.41e+02  1.05e-01 4.62e-01 9.45e-01
...
1.47e+02  1.06e-01 4.60e-01 9.45e-01
...
1.53e+02  1.06e-01 4.57e-01 9.45e-01
...
1.59e+02  1.06e-01 4.55e-01 9.45e-01
...
1.65e+02  1.06e-01 4.53e-01 9.45e-01
...
1.71e+02  1.07e-01 4.52e-01 9.45e-01
...
1.77e+02  1.07e-01 4.50e-01 9.45e-01
...
1.83e+02  1.07e-01 4.49e-01 9.45e-01
...
1.90e+02  1.07e-01 4.48e-01 9.45e-01
...
1.96e+02  1.07e-01 4.47e-01 9.45e-01
...
2.02e+02  1.07e-01 4.46e-01 9.45e-01
...
2.08e+02  1.08e-01 4.45e-01 9.45e-01
...
2.14e+02  1.08e-01 4.44e-01 9.45e-01
...
2.20e+02  1.08e-01 4.43e-01 9.45e-01
...
2.26e+02  1.08e-01 4.43e-01 9.45e-01
...
2.32e+02  1.08e-01 4.42e-01 9.45e-01
...
2.39e+02  1.08e-01 4.42e-01 9.45e-01
...
2.45e+02  1.08e-01 4.42e-01 9.45e-01
...
2.51e+02  1.08e-01 4.41e-01 9.45e-01
...
2.57e+02  1.08e-01 4.41e-01 9.45e-01
...
2.63e+02  1.08e-01 4.41e-01 9.45e-01
...
2.69e+02  1.08e-01 4.40e-01 9.45e-01
...
2.75e+02  1.08e-01 4.40e-01 9.45e-01
...
2.81e+02  1.08e-01 4.40e-01 9.45e-01
...
2.87e+02  1.08e-01 4.40e-01 9.45e-01
...
2.94e+02  1.08e-01 4.40e-01 9.45e-01
...
3.00e+02  1.08e-01 4.40e-01 9.45e-01

## 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_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2)

### 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
This third experiment with higher initial id_lti5 (0.8) provides crucial insights:

1. With higher initial id_lti5, id_o483 immediately starts increasing (from 0.05 to ~0.54) without the long delay seen in the other experiments.
2. id_j5qx initially decreases slightly, then recovers and stabilizes around 0.108.
3. id_lti5 increases from 0.8 to ~0.945 and stabilizes.
4. The system reaches a similar steady state as the other experiments (~0.108 for id_j5qx, ~0.44 for id_o483, ~0.945 for id_lti5).

This confirms that id_lti5 catalyzes the production of id_o483, and there's a threshold effect. When id_lti5 is already high (as in this experiment), id_o483 production starts immediately. When id_lti5 is lower (as in the previous experiments), id_o483 production is delayed until id_lti5 reaches a threshold.

Let me revise my model with these insights:

1. id_j5qx → id_lti5 (conversion)
2. id_o483 → id_lti5 (conversion)
3. id_lti5 → id_lti5 + id_o483 (catalytic production of id_o483, activated at higher id_lti5 concentrations)
4. id_o483 → id_j5qx (recycling)

Let me implement this model and test it against all three experiments.

## Action

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

# Load the original SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

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

# Add reactions to the model
# Reaction 1: id_j5qx → id_lti5 (conversion)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactant
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Rate constant
math_ast1 = libsbml.parseL3Formula("k1 * id_j5qx")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_o483 → id_lti5 (conversion)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_lti5")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.5)  # Rate constant
math_ast2 = libsbml.parseL3Formula("k2 * id_o483")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_lti5 → id_lti5 + id_o483 (catalytic production of id_o483)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add products
product3a = reaction3.createProduct()
product3a.setSpecies("id_lti5")
product3a.setStoichiometry(1.0)
product3a.setConstant(True)

product3b = reaction3.createProduct()
product3b.setSpecies("id_o483")
product3b.setStoichiometry(1.0)
product3b.setConstant(True)

# Add kinetic law with Hill function for threshold effect
kinetic_law3 = reaction3.createKineticLaw()
parameter3a = kinetic_law3.createParameter()
parameter3a.setId("k3")
parameter3a.setValue(0.1)  # Rate constant

parameter3b = kinetic_law3.createParameter()
parameter3b.setId("threshold")
parameter3b.setValue(0.9)  # Threshold for activation

parameter3c = kinetic_law3.createParameter()
parameter3c.setId("n")
parameter3c.setValue(10)  # Hill coefficient for steepness

# Hill function: k3 * id_lti5 * (id_lti5^n) / (threshold^n + id_lti5^n)
math_ast3 = libsbml.parseL3Formula("k3 * id_lti5 * (id_lti5^n) / (threshold^n + id_lti5^n)")
kinetic_law3.setMath(math_ast3)

# Reaction 4: id_o483 → id_j5qx (recycling)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add product
product4 = reaction4.createProduct()
product4.setSpecies("id_j5qx")
product4.setStoichiometry(1.0)
product4.setConstant(True)

# Add kinetic law
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.02)  # Rate constant
math_ast4 = libsbml.parseL3Formula("k4 * id_o483")
kinetic_law4.setMath(math_ast4)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(document)

# Store the updated SBML model
shared_variables.add('updated_sbml_v3', updated_sbml)

# Function to compare simulation with experimental data
def compare_simulation_with_experiment(simulation_result, exp_data, experiment_name):
    print(f"\nComparing simulation with {experiment_name}:")
    time_points = [0, 50, 100, 150, 200, 250, 300]
    
    for time in time_points:
        # Find the closest time point in the experimental data
        exp_idx = (exp_data['Time'] - time).abs().idxmin()
        exp_time = exp_data.iloc[exp_idx]['Time']
        
        # Find the closest time point in the simulation data
        sim_idx = (simulation_result['Time'] - time).abs().idxmin()
        sim_time = simulation_result.iloc[sim_idx]['Time']
        
        print(f"\nTime ~{time}:")
        print(f"Experimental (t={exp_time:.2f}):")
        print(f"  id_j5qx: {exp_data.iloc[exp_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {exp_data.iloc[exp_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {exp_data.iloc[exp_idx]['id_lti5']:.4f}")
        
        print(f"Simulation (t={sim_time:.2f}):")
        print(f"  id_j5qx: {simulation_result.iloc[sim_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {simulation_result.iloc[sim_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {simulation_result.iloc[sim_idx]['id_lti5']:.4f}")

# Simulate with original initial conditions (Experiment 1)
print("Simulating with original initial conditions (Experiment 1):")
simulation_result1 = simulate(updated_sbml)
compare_simulation_with_experiment(simulation_result1, experiment_history["iteration_0"], "Experiment 1")

# Simulate with second set of initial conditions (Experiment 2)
print("\nSimulating with second set of initial conditions (Experiment 2):")
document2 = libsbml.readSBMLFromString(updated_sbml)
model2 = document2.getModel()
model2.getSpecies("id_j5qx").setInitialConcentration(0.3)
model2.getSpecies("id_o483").setInitialConcentration(0.2)
model2.getSpecies("id_lti5").setInitialConcentration(0.4)
updated_sbml2 = writer.writeSBMLToString(document2)
simulation_result2 = simulate(updated_sbml2)
compare_simulation_with_experiment(simulation_result2, experiment_history["iteration_5"], "Experiment 2")

# Simulate with third set of initial conditions (Experiment 3)
print("\nSimulating with third set of initial conditions (Experiment 3):")
document3 = libsbml.readSBMLFromString(updated_sbml)
model3 = document3.getModel()
model3.getSpecies("id_j5qx").setInitialConcentration(0.1)
model3.getSpecies("id_o483").setInitialConcentration(0.05)
model3.getSpecies("id_lti5").setInitialConcentration(0.8)
updated_sbml3 = writer.writeSBMLToString(document3)
simulation_result3 = simulate(updated_sbml3)
compare_simulation_with_experiment(simulation_result3, experiment_history["iteration_7"], "Experiment 3")
```
# Observation

## Code Stdout
Simulating with original initial conditions (Experiment 1):

Comparing simulation with Experiment 1:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500
Simulation (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1384
  id_o483: 0.0007
  id_lti5: 0.9985
Simulation (t=50.00):
  id_j5qx: 0.3314
  id_o483: 2.1381
  id_lti5: 12.9157

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.0956
  id_o483: 0.0107
  id_lti5: 0.9880
Simulation (t=100.00):
  id_j5qx: 21.3037
  id_o483: 142.7444
  id_lti5: 862.1973

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0839
  id_o483: 0.5901
  id_lti5: 0.9442
Simulation (t=150.00):
  id_j5qx: 1421.6622
  id_o483: 9526.1885
  id_lti5: 57539.5887

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0963
  id_o483: 0.5248
  id_lti5: 0.9445
Simulation (t=200.00):
  id_j5qx: 94875.9898
  id_o483: 635739.3646
  id_lti5: 3839959.8846

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.4781
  id_lti5: 0.9448
Simulation (t=250.00):
  id_j5qx: 6331640.5582
  id_o483: 42426678.8076
  id_lti5: 256263421.3626

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1064
  id_o483: 0.4543
  id_lti5: 0.9450
Simulation (t=300.00):
  id_j5qx: 422548130.5593
  id_o483: 2831385270.7253
  id_lti5: 17101986228.1013

Simulating with second set of initial conditions (Experiment 2):

Comparing simulation with Experiment 2:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000
Simulation (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.2078
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=50.00):
  id_j5qx: 0.3107
  id_o483: 1.9465
  id_lti5: 11.7590

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1436
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=100.00):
  id_j5qx: 19.4012
  id_o483: 129.9918
  id_lti5: 785.1699

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0992
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=150.00):
  id_j5qx: 1294.6517
  id_o483: 8675.1240
  id_lti5: 52399.0335

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0685
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=200.00):
  id_j5qx: 86399.7043
  id_o483: 578941.9768
  id_lti5: 3496895.2538

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.0473
  id_o483: 0.0155
  id_lti5: 0.9876
Simulation (t=250.00):
  id_j5qx: 5765959.7565
  id_o483: 38636198.6844
  id_lti5: 233368360.2294

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.0544
  id_o483: 0.7310
  id_lti5: 0.9437
Simulation (t=300.00):
  id_j5qx: 384796362.4909
  id_o483: 2578420478.4985
  id_lti5: 15574041431.0484

Simulating with third set of initial conditions (Experiment 3):

Comparing simulation with Experiment 3:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.0938
  id_o483: 0.5383
  id_lti5: 0.9445
Simulation (t=50.00):
  id_j5qx: 0.9772
  id_o483: 6.5101
  id_lti5: 39.3226

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1020
  id_o483: 0.4873
  id_lti5: 0.9448
Simulation (t=100.00):
  id_j5qx: 64.8423
  id_o483: 434.4885
  id_lti5: 2624.3749

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1059
  id_o483: 0.4585
  id_lti5: 0.9450
Simulation (t=150.00):
  id_j5qx: 4327.3192
  id_o483: 28996.2418
  id_lti5: 175141.5934

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1074
  id_o483: 0.4460
  id_lti5: 0.9451
Simulation (t=200.00):
  id_j5qx: 288790.1213
  id_o483: 1935107.5930
  id_lti5: 11688336.3587

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1079
  id_o483: 0.4413
  id_lti5: 0.9451
Simulation (t=250.00):
  id_j5qx: 19272840.9219
  id_o483: 129142301.1128
  id_lti5: 780038618.5279

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 1286201877.5709
  id_o483: 8618504705.0444
  id_lti5: 52057044407.3604

## 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_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2, updated_sbml_v3)

### 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 model is showing exponential growth, which is clearly incorrect. The issue is likely with the catalytic production of id_o483 by id_lti5 (reaction 3), which is creating a positive feedback loop that's causing the system to grow without bounds.

Looking at the experimental data again:
1. All three experiments reach a similar steady state (~0.106-0.108 for id_j5qx, ~0.44 for id_o483, ~0.945 for id_lti5)
2. The total mass in the system increases but eventually stabilizes
3. There must be some mechanism that limits the growth of the species

Let me revise my model with these insights:

1. I need to add a limiting factor to prevent unbounded growth
2. The reactions should balance to reach the observed steady state
3. I should use mass action kinetics with appropriate rate constants

Let me try a simpler model first:

1. id_j5qx → id_lti5 (conversion)
2. id_o483 → id_lti5 (conversion)
3. id_lti5 → id_o483 (conversion, with a rate that depends on id_lti5 concentration)
4. id_o483 → id_j5qx (recycling)

Let me implement this model with carefully chosen rate constants.

## Action

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

# Load the original SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

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

# Add reactions to the model
# Reaction 1: id_j5qx → id_lti5 (conversion)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactant
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Rate constant
math_ast1 = libsbml.parseL3Formula("k1 * id_j5qx")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_o483 → id_lti5 (conversion)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_lti5")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.5)  # Rate constant
math_ast2 = libsbml.parseL3Formula("k2 * id_o483")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_lti5 → id_o483 (conversion with saturation)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add product
product3 = reaction3.createProduct()
product3.setSpecies("id_o483")
product3.setStoichiometry(1.0)
product3.setConstant(True)

# Add kinetic law with saturation (Michaelis-Menten kinetics)
kinetic_law3 = reaction3.createKineticLaw()
parameter3a = kinetic_law3.createParameter()
parameter3a.setId("vmax")
parameter3a.setValue(0.1)  # Maximum rate

parameter3b = kinetic_law3.createParameter()
parameter3b.setId("km")
parameter3b.setValue(0.5)  # Michaelis constant

# Michaelis-Menten kinetics: vmax * id_lti5 / (km + id_lti5)
math_ast3 = libsbml.parseL3Formula("vmax * id_lti5 / (km + id_lti5)")
kinetic_law3.setMath(math_ast3)

# Reaction 4: id_o483 → id_j5qx (recycling)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add product
product4 = reaction4.createProduct()
product4.setSpecies("id_j5qx")
product4.setStoichiometry(1.0)
product4.setConstant(True)

# Add kinetic law
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.02)  # Rate constant
math_ast4 = libsbml.parseL3Formula("k4 * id_o483")
kinetic_law4.setMath(math_ast4)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(document)

# Store the updated SBML model
shared_variables.add('updated_sbml_v4', updated_sbml)

# Function to compare simulation with experimental data
def compare_simulation_with_experiment(simulation_result, exp_data, experiment_name):
    print(f"\nComparing simulation with {experiment_name}:")
    time_points = [0, 50, 100, 150, 200, 250, 300]
    
    for time in time_points:
        # Find the closest time point in the experimental data
        exp_idx = (exp_data['Time'] - time).abs().idxmin()
        exp_time = exp_data.iloc[exp_idx]['Time']
        
        # Find the closest time point in the simulation data
        sim_idx = (simulation_result['Time'] - time).abs().idxmin()
        sim_time = simulation_result.iloc[sim_idx]['Time']
        
        print(f"\nTime ~{time}:")
        print(f"Experimental (t={exp_time:.2f}):")
        print(f"  id_j5qx: {exp_data.iloc[exp_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {exp_data.iloc[exp_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {exp_data.iloc[exp_idx]['id_lti5']:.4f}")
        
        print(f"Simulation (t={sim_time:.2f}):")
        print(f"  id_j5qx: {simulation_result.iloc[sim_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {simulation_result.iloc[sim_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {simulation_result.iloc[sim_idx]['id_lti5']:.4f}")

# Simulate with original initial conditions (Experiment 1)
print("Simulating with original initial conditions (Experiment 1):")
simulation_result1 = simulate(updated_sbml)
compare_simulation_with_experiment(simulation_result1, experiment_history["iteration_0"], "Experiment 1")

# Simulate with second set of initial conditions (Experiment 2)
print("\nSimulating with second set of initial conditions (Experiment 2):")
document2 = libsbml.readSBMLFromString(updated_sbml)
model2 = document2.getModel()
model2.getSpecies("id_j5qx").setInitialConcentration(0.3)
model2.getSpecies("id_o483").setInitialConcentration(0.2)
model2.getSpecies("id_lti5").setInitialConcentration(0.4)
updated_sbml2 = writer.writeSBMLToString(document2)
simulation_result2 = simulate(updated_sbml2)
compare_simulation_with_experiment(simulation_result2, experiment_history["iteration_5"], "Experiment 2")

# Simulate with third set of initial conditions (Experiment 3)
print("\nSimulating with third set of initial conditions (Experiment 3):")
document3 = libsbml.readSBMLFromString(updated_sbml)
model3 = document3.getModel()
model3.getSpecies("id_j5qx").setInitialConcentration(0.1)
model3.getSpecies("id_o483").setInitialConcentration(0.05)
model3.getSpecies("id_lti5").setInitialConcentration(0.8)
updated_sbml3 = writer.writeSBMLToString(document3)
simulation_result3 = simulate(updated_sbml3)
compare_simulation_with_experiment(simulation_result3, experiment_history["iteration_7"], "Experiment 3")
```
# Observation

## Code Stdout
Simulating with original initial conditions (Experiment 1):

Comparing simulation with Experiment 1:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500
Simulation (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1384
  id_o483: 0.0007
  id_lti5: 0.9985
Simulation (t=50.00):
  id_j5qx: 0.0566
  id_o483: 0.1109
  id_lti5: 0.6825

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.0956
  id_o483: 0.0107
  id_lti5: 0.9880
Simulation (t=100.00):
  id_j5qx: 0.0456
  id_o483: 0.1117
  id_lti5: 0.6927

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0839
  id_o483: 0.5901
  id_lti5: 0.9442
Simulation (t=150.00):
  id_j5qx: 0.0448
  id_o483: 0.1117
  id_lti5: 0.6935

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0963
  id_o483: 0.5248
  id_lti5: 0.9445
Simulation (t=200.00):
  id_j5qx: 0.0447
  id_o483: 0.1117
  id_lti5: 0.6935

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.4781
  id_lti5: 0.9448
Simulation (t=250.00):
  id_j5qx: 0.0447
  id_o483: 0.1117
  id_lti5: 0.6936

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1064
  id_o483: 0.4543
  id_lti5: 0.9450
Simulation (t=300.00):
  id_j5qx: 0.0447
  id_o483: 0.1117
  id_lti5: 0.6936

Simulating with second set of initial conditions (Experiment 2):

Comparing simulation with Experiment 2:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000
Simulation (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.2078
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=50.00):
  id_j5qx: 0.0656
  id_o483: 0.1134
  id_lti5: 0.7209

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1436
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=100.00):
  id_j5qx: 0.0474
  id_o483: 0.1146
  id_lti5: 0.7380

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0992
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=150.00):
  id_j5qx: 0.0460
  id_o483: 0.1147
  id_lti5: 0.7393

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0685
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=200.00):
  id_j5qx: 0.0459
  id_o483: 0.1147
  id_lti5: 0.7394

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.0473
  id_o483: 0.0155
  id_lti5: 0.9876
Simulation (t=250.00):
  id_j5qx: 0.0459
  id_o483: 0.1147
  id_lti5: 0.7394

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.0544
  id_o483: 0.7310
  id_lti5: 0.9437
Simulation (t=300.00):
  id_j5qx: 0.0459
  id_o483: 0.1147
  id_lti5: 0.7394

Simulating with third set of initial conditions (Experiment 3):

Comparing simulation with Experiment 3:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.0938
  id_o483: 0.5383
  id_lti5: 0.9445
Simulation (t=50.00):
  id_j5qx: 0.0509
  id_o483: 0.1173
  id_lti5: 0.7818

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1020
  id_o483: 0.4873
  id_lti5: 0.9448
Simulation (t=100.00):
  id_j5qx: 0.0473
  id_o483: 0.1175
  id_lti5: 0.7852

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1059
  id_o483: 0.4585
  id_lti5: 0.9450
Simulation (t=150.00):
  id_j5qx: 0.0470
  id_o483: 0.1175
  id_lti5: 0.7855

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1074
  id_o483: 0.4460
  id_lti5: 0.9451
Simulation (t=200.00):
  id_j5qx: 0.0470
  id_o483: 0.1175
  id_lti5: 0.7855

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1079
  id_o483: 0.4413
  id_lti5: 0.9451
Simulation (t=250.00):
  id_j5qx: 0.0470
  id_o483: 0.1175
  id_lti5: 0.7855

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 0.0470
  id_o483: 0.1175
  id_lti5: 0.7855

## 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_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4)

### 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 model is now stable (no exponential growth), but it still doesn't match the experimental data well. The key issues are:

1. In the simulation, id_lti5 only reaches ~0.7-0.8, while in the experiments it reaches ~0.95-1.0
2. id_o483 doesn't show the dramatic increase seen in the experiments
3. id_j5qx decreases too much and doesn't recover

Let me try a different approach. Looking at the experimental data again:

1. In all experiments, id_lti5 increases to a high level (~0.95-1.0)
2. id_o483 shows a complex behavior: initially decreases, then dramatically increases
3. id_j5qx decreases initially, then slightly recovers

Let me try a more complex model with the following reactions:

1. id_j5qx → id_lti5 (conversion)
2. id_o483 → id_lti5 (conversion)
3. id_lti5 → id_o483 (conversion, activated at higher id_lti5 concentrations)
4. id_o483 → id_j5qx (recycling)
5. id_lti5 → id_lti5 + id_o483 (autocatalytic production of id_o483)

Let me also try a different experiment with a higher initial concentration of id_o483 to see how the system responds.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration", 
    "meta_data": {
        "id_j5qx": 0.1,
        "id_o483": 0.5,
        "id_lti5": 0.3
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_10
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_10]

Total size: 2797 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_10] for the full data

Time   id_j5qx  id_o483  id_lti5
0  1.00e-01 5.00e-01 3.00e-01
...
6.12e+00  1.01e-01 5.33e-01 7.17e-01
...
1.22e+01  1.02e-01 5.11e-01 9.02e-01
...
1.83e+01  1.03e-01 4.91e-01 9.38e-01
...
2.45e+01  1.04e-01 4.79e-01 9.44e-01
...
3.06e+01  1.05e-01 4.72e-01 9.45e-01
...
3.67e+01  1.05e-01 4.67e-01 9.45e-01
...
4.28e+01  1.05e-01 4.63e-01 9.45e-01
...
4.89e+01  1.06e-01 4.60e-01 9.45e-01
...
5.50e+01  1.06e-01 4.57e-01 9.45e-01
...
6.12e+01  1.06e-01 4.55e-01 9.45e-01
...
6.73e+01  1.06e-01 4.53e-01 9.45e-01
...
7.34e+01  1.07e-01 4.52e-01 9.45e-01
...
7.95e+01  1.07e-01 4.50e-01 9.45e-01
...
8.56e+01  1.07e-01 4.49e-01 9.45e-01
...
9.17e+01  1.07e-01 4.48e-01 9.45e-01
...
9.79e+01  1.07e-01 4.47e-01 9.45e-01
...
1.04e+02  1.07e-01 4.46e-01 9.45e-01
...
1.10e+02  1.08e-01 4.45e-01 9.45e-01
...
1.16e+02  1.08e-01 4.44e-01 9.45e-01
...
1.22e+02  1.08e-01 4.43e-01 9.45e-01
...
1.28e+02  1.08e-01 4.43e-01 9.45e-01
...
1.35e+02  1.08e-01 4.42e-01 9.45e-01
...
1.41e+02  1.08e-01 4.42e-01 9.45e-01
...
1.47e+02  1.08e-01 4.42e-01 9.45e-01
...
1.53e+02  1.08e-01 4.41e-01 9.45e-01
...
1.59e+02  1.08e-01 4.41e-01 9.45e-01
...
1.65e+02  1.08e-01 4.41e-01 9.45e-01
...
1.71e+02  1.08e-01 4.40e-01 9.45e-01
...
1.77e+02  1.08e-01 4.40e-01 9.45e-01
...
1.83e+02  1.08e-01 4.40e-01 9.45e-01
...
1.90e+02  1.08e-01 4.40e-01 9.45e-01
...
1.96e+02  1.08e-01 4.40e-01 9.45e-01
...
2.02e+02  1.08e-01 4.40e-01 9.45e-01
...
2.08e+02  1.08e-01 4.40e-01 9.45e-01
...
2.14e+02  1.08e-01 4.39e-01 9.45e-01
...
2.20e+02  1.08e-01 4.39e-01 9.45e-01
...
2.26e+02  1.08e-01 4.39e-01 9.45e-01
...
2.32e+02  1.08e-01 4.39e-01 9.45e-01
...
2.39e+02  1.08e-01 4.39e-01 9.45e-01
...
2.45e+02  1.08e-01 4.39e-01 9.45e-01
...
2.51e+02  1.08e-01 4.39e-01 9.45e-01
...
2.57e+02  1.08e-01 4.39e-01 9.45e-01
...
2.63e+02  1.08e-01 4.39e-01 9.45e-01
...
2.69e+02  1.08e-01 4.39e-01 9.45e-01
...
2.75e+02  1.08e-01 4.39e-01 9.45e-01
...
2.81e+02  1.08e-01 4.39e-01 9.45e-01
...
2.87e+02  1.08e-01 4.39e-01 9.45e-01
...
2.94e+02  1.08e-01 4.39e-01 9.45e-01
...
3.00e+02  1.08e-01 4.39e-01 9.45e-01

## 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_5, iteration_7, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4)

### 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
This fourth experiment with higher initial id_o483 (0.5) provides additional insights:

1. With higher initial id_o483, the system quickly reaches a steady state similar to the other experiments.
2. id_lti5 increases from 0.3 to ~0.945 and stabilizes.
3. id_o483 increases slightly from 0.5 to ~0.53, then decreases to ~0.439 and stabilizes.
4. id_j5qx increases slightly from 0.1 to ~0.108 and stabilizes.

This confirms that the system has a stable steady state that it reaches regardless of initial conditions. The steady state values are approximately:
- id_j5qx: ~0.108
- id_o483: ~0.44
- id_lti5: ~0.945

Let me analyze the total mass in each experiment to understand the conservation properties:

## Action

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

# Analyze the steady state and mass conservation in all experiments
experiments = ["iteration_0", "iteration_5", "iteration_7", "iteration_10"]
experiment_names = ["Exp1 (default)", "Exp2 (high j5qx, o483)", "Exp3 (high lti5)", "Exp4 (high o483)"]

print("Initial conditions:")
for i, exp_id in enumerate(experiments):
    exp_data = experiment_history[exp_id]
    initial = exp_data.iloc[0]
    print(f"{experiment_names[i]}: id_j5qx={initial['id_j5qx']:.2f}, id_o483={initial['id_o483']:.2f}, id_lti5={initial['id_lti5']:.2f}, Total={initial['id_j5qx'] + initial['id_o483'] + initial['id_lti5']:.2f}")

print("\nFinal steady state:")
for i, exp_id in enumerate(experiments):
    exp_data = experiment_history[exp_id]
    final = exp_data.iloc[-1]
    print(f"{experiment_names[i]}: id_j5qx={final['id_j5qx']:.4f}, id_o483={final['id_o483']:.4f}, id_lti5={final['id_lti5']:.4f}, Total={final['id_j5qx'] + final['id_o483'] + final['id_lti5']:.4f}")

# Calculate total mass over time for each experiment
print("\nTotal mass analysis:")
for i, exp_id in enumerate(experiments):
    exp_data = experiment_history[exp_id]
    exp_data['total_mass'] = exp_data['id_j5qx'] + exp_data['id_o483'] + exp_data['id_lti5']
    
    print(f"\n{experiment_names[i]}:")
    print(f"Initial total mass: {exp_data['total_mass'].iloc[0]:.4f}")
    print(f"Final total mass: {exp_data['total_mass'].iloc[-1]:.4f}")
    print(f"Change in total mass: {exp_data['total_mass'].iloc[-1] - exp_data['total_mass'].iloc[0]:.4f}")
    print(f"Min total mass: {exp_data['total_mass'].min():.4f}")
    print(f"Max total mass: {exp_data['total_mass'].max():.4f}")
    
    # Find when total mass stabilizes (within 1% of final value)
    final_mass = exp_data['total_mass'].iloc[-1]
    stabilization_idx = (abs(exp_data['total_mass'] - final_mass) / final_mass < 0.01).idxmax()
    stabilization_time = exp_data['Time'].iloc[stabilization_idx]
    print(f"Total mass stabilizes around t={stabilization_time:.2f}")

# Let's look at the rates of change at key time points for each experiment
print("\nRates of change at key time points:")
for i, exp_id in enumerate(experiments):
    exp_data = experiment_history[exp_id]
    data_diff = exp_data.copy()
    for species in ['id_j5qx', 'id_o483', 'id_lti5']:
        data_diff[f'd{species}/dt'] = np.gradient(exp_data[species], exp_data['Time'])
    
    print(f"\n{experiment_names[i]}:")
    # Look at early, middle, and late phases
    time_points = [10, 50, 100, 200, 300]
    for time in time_points:
        idx = (exp_data['Time'] - time).abs().idxmin()
        actual_time = exp_data['Time'].iloc[idx]
        print(f"\nTime ~{time} (t={actual_time:.2f}):")
        print(f"Concentrations: id_j5qx={exp_data['id_j5qx'].iloc[idx]:.4f}, id_o483={exp_data['id_o483'].iloc[idx]:.4f}, id_lti5={exp_data['id_lti5'].iloc[idx]:.4f}")
        print(f"Rates: d(id_j5qx)/dt={data_diff['did_j5qx/dt'].iloc[idx]:.6f}, d(id_o483)/dt={data_diff['did_o483/dt'].iloc[idx]:.6f}, d(id_lti5)/dt={data_diff['did_lti5/dt'].iloc[idx]:.6f}")

# Based on the analysis, let's create a new model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

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

# Reaction 1: id_j5qx → id_lti5 (conversion)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Rate constant
math_ast1 = libsbml.parseL3Formula("k1 * id_j5qx")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_o483 → id_lti5 (conversion)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

product2 = reaction2.createProduct()
product2.setSpecies("id_lti5")
product2.setStoichiometry(1.0)
product2.setConstant(True)

kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.5)  # Rate constant
math_ast2 = libsbml.parseL3Formula("k2 * id_o483")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_lti5 → id_o483 (conversion with threshold)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

product3 = reaction3.createProduct()
product3.setSpecies("id_o483")
product3.setStoichiometry(2.0)  # Amplification
product3.setConstant(True)

kinetic_law3 = reaction3.createKineticLaw()
parameter3a = kinetic_law3.createParameter()
parameter3a.setId("k3")
parameter3a.setValue(0.1)  # Rate constant

parameter3b = kinetic_law3.createParameter()
parameter3b.setId("threshold")
parameter3b.setValue(0.9)  # Threshold for activation

parameter3c = kinetic_law3.createParameter()
parameter3c.setId("n")
parameter3c.setValue(8)  # Hill coefficient for steepness

# Hill function: k3 * id_lti5 * (id_lti5^n) / (threshold^n + id_lti5^n)
math_ast3 = libsbml.parseL3Formula("k3 * id_lti5 * (id_lti5^n) / (threshold^n + id_lti5^n)")
kinetic_law3.setMath(math_ast3)

# Reaction 4: id_o483 → id_j5qx (recycling)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

product4 = reaction4.createProduct()
product4.setSpecies("id_j5qx")
product4.setStoichiometry(1.0)
product4.setConstant(True)

kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.02)  # Rate constant
math_ast4 = libsbml.parseL3Formula("k4 * id_o483")
kinetic_law4.setMath(math_ast4)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(document)
shared_variables.add('updated_sbml_v5', updated_sbml)

# Test the model with the original initial conditions
print("\nTesting the new model with original initial conditions:")
simulation_result = simulate(updated_sbml)

# Compare with experimental data at key time points
exp_data = experiment_history["iteration_0"]
time_points = [0, 50, 100, 150, 200, 250, 300]

for time in time_points:
    # Find the closest time point in the experimental data
    exp_idx = (exp_data['Time'] - time).abs().idxmin()
    exp_time = exp_data.iloc[exp_idx]['Time']
    
    # Find the closest time point in the simulation data
    sim_idx = (simulation_result['Time'] - time).abs().idxmin()
    sim_time = simulation_result.iloc[sim_idx]['Time']
    
    print(f"\nTime ~{time}:")
    print(f"Experimental (t={exp_time:.2f}):")
    print(f"  id_j5qx: {exp_data.iloc[exp_idx]['id_j5qx']:.4f}")
    print(f"  id_o483: {exp_data.iloc[exp_idx]['id_o483']:.4f}")
    print(f"  id_lti5: {exp_data.iloc[exp_idx]['id_lti5']:.4f}")
    
    print(f"Simulation (t={sim_time:.2f}):")
    print(f"  id_j5qx: {simulation_result.iloc[sim_idx]['id_j5qx']:.4f}")
    print(f"  id_o483: {simulation_result.iloc[sim_idx]['id_o483']:.4f}")
    print(f"  id_lti5: {simulation_result.iloc[sim_idx]['id_lti5']:.4f}")
```
# Observation

## Code Stdout
Initial conditions:
Exp1 (default): id_j5qx=0.20, id_o483=0.10, id_lti5=0.55, Total=0.85
Exp2 (high j5qx, o483): id_j5qx=0.30, id_o483=0.20, id_lti5=0.40, Total=0.90
Exp3 (high lti5): id_j5qx=0.10, id_o483=0.05, id_lti5=0.80, Total=0.95
Exp4 (high o483): id_j5qx=0.10, id_o483=0.50, id_lti5=0.30, Total=0.90

Final steady state:
Exp1 (default): id_j5qx=0.1064, id_o483=0.4543, id_lti5=0.9450, Total=1.5057
Exp2 (high j5qx, o483): id_j5qx=0.0544, id_o483=0.7310, id_lti5=0.9437, Total=1.7290
Exp3 (high lti5): id_j5qx=0.1081, id_o483=0.4397, id_lti5=0.9452, Total=1.4929
Exp4 (high o483): id_j5qx=0.1082, id_o483=0.4389, id_lti5=0.9452, Total=1.4923

Total mass analysis:

Exp1 (default):
Initial total mass: 0.8500
Final total mass: 1.5057
Change in total mass: 0.6557
Min total mass: 0.8500
Max total mass: 1.6184
Total mass stabilizes around t=132.19

Exp2 (high j5qx, o483):
Initial total mass: 0.9000
Final total mass: 1.7290
Change in total mass: 0.8290
Min total mass: 0.8994
Max total mass: 1.7457
Total mass stabilizes around t=272.75

Exp3 (high lti5):
Initial total mass: 0.9500
Final total mass: 1.4929
Change in total mass: 0.5429
Min total mass: 0.9500
Max total mass: 1.5799
Total mass stabilizes around t=24.57

Exp4 (high o483):
Initial total mass: 0.9000
Final total mass: 1.4923
Change in total mass: 0.5923
Min total mass: 0.9000
Max total mass: 1.5329
Total mass stabilizes around t=9.66

Rates of change at key time points:

Exp1 (default):

Time ~10 (t=9.98):
Concentrations: id_j5qx=0.1861, id_o483=0.0209, id_lti5=0.9404
Rates: d(id_j5qx)/dt=-0.001375, d(id_o483)/dt=-0.003172, d(id_lti5)/dt=0.011125

Time ~50 (t=50.00):
Concentrations: id_j5qx=0.1384, id_o483=0.0007, id_lti5=0.9985
Rates: d(id_j5qx)/dt=-0.001024, d(id_o483)/dt=-0.000012, d(id_lti5)/dt=0.000039

Time ~100 (t=100.00):
Concentrations: id_j5qx=0.0956, id_o483=0.0107, id_lti5=0.9880
Rates: d(id_j5qx)/dt=-0.000708, d(id_o483)/dt=0.001221, d(id_lti5)/dt=-0.001027

Time ~200 (t=200.00):
Concentrations: id_j5qx=0.0963, id_o483=0.5248, id_lti5=0.9445
Rates: d(id_j5qx)/dt=0.000191, d(id_o483)/dt=-0.001193, d(id_lti5)/dt=0.000007

Time ~300 (t=300.00):
Concentrations: id_j5qx=0.1064, id_o483=0.4543, id_lti5=0.9450
Rates: d(id_j5qx)/dt=0.000038, d(id_o483)/dt=-0.000306, d(id_lti5)/dt=0.000002

Exp2 (high j5qx, o483):

Time ~10 (t=9.98):
Concentrations: id_j5qx=0.2795, id_o483=0.0027, id_lti5=0.9302
Rates: d(id_j5qx)/dt=-0.002069, d(id_o483)/dt=-0.001165, d(id_lti5)/dt=0.020028

Time ~50 (t=50.00):
Concentrations: id_j5qx=0.2078, id_o483=0.0000, id_lti5=1.0000
Rates: d(id_j5qx)/dt=-0.001538, d(id_o483)/dt=-0.000000, d(id_lti5)/dt=0.000000

Time ~100 (t=100.00):
Concentrations: id_j5qx=0.1436, id_o483=0.0000, id_lti5=1.0000
Rates: d(id_j5qx)/dt=-0.001062, d(id_o483)/dt=-0.000000, d(id_lti5)/dt=0.000000

Time ~200 (t=200.00):
Concentrations: id_j5qx=0.0685, id_o483=0.0000, id_lti5=1.0000
Rates: d(id_j5qx)/dt=-0.000507, d(id_o483)/dt=0.000000, d(id_lti5)/dt=-0.000000

Time ~300 (t=300.00):
Concentrations: id_j5qx=0.0544, id_o483=0.7310, id_lti5=0.9437
Rates: d(id_j5qx)/dt=0.000364, d(id_o483)/dt=-0.001487, d(id_lti5)/dt=0.000004

Exp3 (high lti5):

Time ~10 (t=9.98):
Concentrations: id_j5qx=0.0934, id_o483=0.1464, id_lti5=0.9465
Rates: d(id_j5qx)/dt=-0.000569, d(id_o483)/dt=0.015258, d(id_lti5)/dt=0.001546

Time ~50 (t=50.00):
Concentrations: id_j5qx=0.0938, id_o483=0.5383, id_lti5=0.9445
Rates: d(id_j5qx)/dt=0.000215, d(id_o483)/dt=-0.000973, d(id_lti5)/dt=0.000003

Time ~100 (t=100.00):
Concentrations: id_j5qx=0.1020, id_o483=0.4873, id_lti5=0.9448
Rates: d(id_j5qx)/dt=0.000114, d(id_o483)/dt=-0.000802, d(id_lti5)/dt=0.000006

Time ~200 (t=200.00):
Concentrations: id_j5qx=0.1074, id_o483=0.4460, id_lti5=0.9451
Rates: d(id_j5qx)/dt=0.000018, d(id_o483)/dt=-0.000150, d(id_lti5)/dt=0.000001

Time ~300 (t=300.00):
Concentrations: id_j5qx=0.1081, id_o483=0.4397, id_lti5=0.9452
Rates: d(id_j5qx)/dt=0.000002, d(id_o483)/dt=-0.000018, d(id_lti5)/dt=0.000000

Exp4 (high o483):

Time ~10 (t=9.98):
Concentrations: id_j5qx=0.1020, id_o483=0.5203, id_lti5=0.8625
Rates: d(id_j5qx)/dt=0.000192, d(id_o483)/dt=-0.004083, d(id_lti5)/dt=0.023421

Time ~50 (t=50.00):
Concentrations: id_j5qx=0.1058, id_o483=0.4595, id_lti5=0.9450
Rates: d(id_j5qx)/dt=0.000050, d(id_o483)/dt=-0.000434, d(id_lti5)/dt=0.000004

Time ~100 (t=100.00):
Concentrations: id_j5qx=0.1073, id_o483=0.4462, id_lti5=0.9451
Rates: d(id_j5qx)/dt=0.000018, d(id_o483)/dt=-0.000155, d(id_lti5)/dt=0.000001

Time ~200 (t=200.00):
Concentrations: id_j5qx=0.1081, id_o483=0.4397, id_lti5=0.9452
Rates: d(id_j5qx)/dt=0.000002, d(id_o483)/dt=-0.000019, d(id_lti5)/dt=0.000000

Time ~300 (t=300.00):
Concentrations: id_j5qx=0.1082, id_o483=0.4389, id_lti5=0.9452
Rates: d(id_j5qx)/dt=0.000000, d(id_o483)/dt=-0.000002, d(id_lti5)/dt=0.000000

Testing the new model with original initial conditions:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500
Simulation (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1384
  id_o483: 0.0007
  id_lti5: 0.9985
Simulation (t=50.00):
  id_j5qx: 0.4010
  id_o483: 2.3947
  id_lti5: 7.0859

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.0956
  id_o483: 0.0107
  id_lti5: 0.9880
Simulation (t=100.00):
  id_j5qx: 14.2316
  id_o483: 86.6405
  id_lti5: 256.3530

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0839
  id_o483: 0.5901
  id_lti5: 0.9442
Simulation (t=150.00):
  id_j5qx: 514.6837
  id_o483: 3133.4561
  id_lti5: 9271.3077

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0963
  id_o483: 0.5248
  id_lti5: 0.9445
Simulation (t=200.00):
  id_j5qx: 18614.1278
  id_o483: 113325.0595
  id_lti5: 335307.5555

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.4781
  id_lti5: 0.9448
Simulation (t=250.00):
  id_j5qx: 673201.4374
  id_o483: 4098531.7038
  id_lti5: 12126785.1337

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1064
  id_o483: 0.4543
  id_lti5: 0.9450
Simulation (t=300.00):
  id_j5qx: 24347107.7124
  id_o483: 148228133.9747
  id_lti5: 438579194.0647

## 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_5, iteration_7, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5)

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


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



# Iteration 12
## Thoughts
The analysis of all four experiments provides valuable insights:

1. **Steady State**: All experiments reach a similar steady state regardless of initial conditions:
   - id_j5qx: ~0.106-0.108
   - id_o483: ~0.44-0.73 (varies more than the others)
   - id_lti5: ~0.945

2. **Total Mass**: The total mass increases in all experiments but stabilizes at different values:
   - Exp1: 0.85 → 1.51 (+0.66)
   - Exp2: 0.90 → 1.73 (+0.83)
   - Exp3: 0.95 → 1.49 (+0.54)
   - Exp4: 0.90 → 1.49 (+0.59)

3. **Dynamics**:
   - In Exp1 and Exp2, id_o483 initially decreases to near zero, then increases dramatically
   - In Exp3 and Exp4 (with higher initial id_lti5 or id_o483), id_o483 shows a more direct path to steady state

My latest model is still showing exponential growth, which is incorrect. The issue is likely with the amplification in reaction 3 (id_lti5 → 2 id_o483), which is creating a positive feedback loop.

Let me revise my approach. Since the total mass increases but stabilizes, there must be a production reaction that slows down as the system approaches steady state. Let me try a different model:

1. id_j5qx → id_lti5 (conversion)
2. id_o483 → id_lti5 (conversion)
3. id_lti5 → id_o483 (conversion with saturation)
4. id_o483 → id_j5qx (recycling)
5. ∅ → id_lti5 (production with negative feedback)

Let me implement this model with carefully chosen rate constants.

## Action

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

# Load the original SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

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

# Reaction 1: id_j5qx → id_lti5 (conversion)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactant
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Rate constant
math_ast1 = libsbml.parseL3Formula("k1 * id_j5qx")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_o483 → id_lti5 (conversion)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_lti5")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.5)  # Rate constant
math_ast2 = libsbml.parseL3Formula("k2 * id_o483")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_lti5 → id_o483 (conversion with saturation)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add product
product3 = reaction3.createProduct()
product3.setSpecies("id_o483")
product3.setStoichiometry(1.0)
product3.setConstant(True)

# Add kinetic law with saturation (Michaelis-Menten kinetics)
kinetic_law3 = reaction3.createKineticLaw()
parameter3a = kinetic_law3.createParameter()
parameter3a.setId("vmax")
parameter3a.setValue(0.1)  # Maximum rate

parameter3b = kinetic_law3.createParameter()
parameter3b.setId("km")
parameter3b.setValue(0.5)  # Michaelis constant

parameter3c = kinetic_law3.createParameter()
parameter3c.setId("n")
parameter3c.setValue(4)  # Hill coefficient for steepness

# Hill kinetics: vmax * (id_lti5^n) / (km^n + id_lti5^n)
math_ast3 = libsbml.parseL3Formula("vmax * (id_lti5^n) / (km^n + id_lti5^n)")
kinetic_law3.setMath(math_ast3)

# Reaction 4: id_o483 → id_j5qx (recycling)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add product
product4 = reaction4.createProduct()
product4.setSpecies("id_j5qx")
product4.setStoichiometry(1.0)
product4.setConstant(True)

# Add kinetic law
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.02)  # Rate constant
math_ast4 = libsbml.parseL3Formula("k4 * id_o483")
kinetic_law4.setMath(math_ast4)

# Reaction 5: ∅ → id_lti5 (production with negative feedback)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# No reactants (empty set)

# Add product
product5 = reaction5.createProduct()
product5.setSpecies("id_lti5")
product5.setStoichiometry(1.0)
product5.setConstant(True)

# Add kinetic law with negative feedback
kinetic_law5 = reaction5.createKineticLaw()
parameter5a = kinetic_law5.createParameter()
parameter5a.setId("k5")
parameter5a.setValue(0.1)  # Base production rate

parameter5b = kinetic_law5.createParameter()
parameter5b.setId("k_inhib")
parameter5b.setValue(1.0)  # Inhibition constant

# Negative feedback: k5 * (1 / (1 + id_lti5/k_inhib))
math_ast5 = libsbml.parseL3Formula("k5 * (1 / (1 + id_lti5/k_inhib))")
kinetic_law5.setMath(math_ast5)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(document)

# Store the updated SBML model
shared_variables.add('updated_sbml_v6', updated_sbml)

# Function to compare simulation with experimental data
def compare_simulation_with_experiment(simulation_result, exp_data, experiment_name):
    print(f"\nComparing simulation with {experiment_name}:")
    time_points = [0, 50, 100, 150, 200, 250, 300]
    
    for time in time_points:
        # Find the closest time point in the experimental data
        exp_idx = (exp_data['Time'] - time).abs().idxmin()
        exp_time = exp_data.iloc[exp_idx]['Time']
        
        # Find the closest time point in the simulation data
        sim_idx = (simulation_result['Time'] - time).abs().idxmin()
        sim_time = simulation_result.iloc[sim_idx]['Time']
        
        print(f"\nTime ~{time}:")
        print(f"Experimental (t={exp_time:.2f}):")
        print(f"  id_j5qx: {exp_data.iloc[exp_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {exp_data.iloc[exp_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {exp_data.iloc[exp_idx]['id_lti5']:.4f}")
        
        print(f"Simulation (t={sim_time:.2f}):")
        print(f"  id_j5qx: {simulation_result.iloc[sim_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {simulation_result.iloc[sim_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {simulation_result.iloc[sim_idx]['id_lti5']:.4f}")

# Simulate with original initial conditions (Experiment 1)
print("Simulating with original initial conditions (Experiment 1):")
simulation_result1 = simulate(updated_sbml)
compare_simulation_with_experiment(simulation_result1, experiment_history["iteration_0"], "Experiment 1")

# Simulate with second set of initial conditions (Experiment 2)
print("\nSimulating with second set of initial conditions (Experiment 2):")
document2 = libsbml.readSBMLFromString(updated_sbml)
model2 = document2.getModel()
model2.getSpecies("id_j5qx").setInitialConcentration(0.3)
model2.getSpecies("id_o483").setInitialConcentration(0.2)
model2.getSpecies("id_lti5").setInitialConcentration(0.4)
updated_sbml2 = writer.writeSBMLToString(document2)
simulation_result2 = simulate(updated_sbml2)
compare_simulation_with_experiment(simulation_result2, experiment_history["iteration_5"], "Experiment 2")

# Simulate with third set of initial conditions (Experiment 3)
print("\nSimulating with third set of initial conditions (Experiment 3):")
document3 = libsbml.readSBMLFromString(updated_sbml)
model3 = document3.getModel()
model3.getSpecies("id_j5qx").setInitialConcentration(0.1)
model3.getSpecies("id_o483").setInitialConcentration(0.05)
model3.getSpecies("id_lti5").setInitialConcentration(0.8)
updated_sbml3 = writer.writeSBMLToString(document3)
simulation_result3 = simulate(updated_sbml3)
compare_simulation_with_experiment(simulation_result3, experiment_history["iteration_7"], "Experiment 3")

# Simulate with fourth set of initial conditions (Experiment 4)
print("\nSimulating with fourth set of initial conditions (Experiment 4):")
document4 = libsbml.readSBMLFromString(updated_sbml)
model4 = document4.getModel()
model4.getSpecies("id_j5qx").setInitialConcentration(0.1)
model4.getSpecies("id_o483").setInitialConcentration(0.5)
model4.getSpecies("id_lti5").setInitialConcentration(0.3)
updated_sbml4 = writer.writeSBMLToString(document4)
simulation_result4 = simulate(updated_sbml4)
compare_simulation_with_experiment(simulation_result4, experiment_history["iteration_10"], "Experiment 4")
```
# Observation

## Code Stdout
Simulating with original initial conditions (Experiment 1):

Comparing simulation with Experiment 1:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500
Simulation (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1384
  id_o483: 0.0007
  id_lti5: 0.9985
Simulation (t=50.00):
  id_j5qx: 0.0857
  id_o483: 0.1920
  id_lti5: 2.5457

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.0956
  id_o483: 0.0107
  id_lti5: 0.9880
Simulation (t=100.00):
  id_j5qx: 0.0776
  id_o483: 0.1922
  id_lti5: 3.7575

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0839
  id_o483: 0.5901
  id_lti5: 0.9442
Simulation (t=150.00):
  id_j5qx: 0.0770
  id_o483: 0.1923
  id_lti5: 4.7131

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0963
  id_o483: 0.5248
  id_lti5: 0.9445
Simulation (t=200.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 5.5300

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.4781
  id_lti5: 0.9448
Simulation (t=250.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 6.2554

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1064
  id_o483: 0.4543
  id_lti5: 0.9450
Simulation (t=300.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 6.9146

Simulating with second set of initial conditions (Experiment 2):

Comparing simulation with Experiment 2:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000
Simulation (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.2078
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=50.00):
  id_j5qx: 0.0941
  id_o483: 0.1920
  id_lti5: 2.5862

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1436
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=100.00):
  id_j5qx: 0.0783
  id_o483: 0.1922
  id_lti5: 3.7943

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0992
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=150.00):
  id_j5qx: 0.0770
  id_o483: 0.1923
  id_lti5: 4.7444

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0685
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=200.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 5.5574

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.0473
  id_o483: 0.0155
  id_lti5: 0.9876
Simulation (t=250.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 6.2800

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.0544
  id_o483: 0.7310
  id_lti5: 0.9437
Simulation (t=300.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 6.9372

Simulating with third set of initial conditions (Experiment 3):

Comparing simulation with Experiment 3:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.0938
  id_o483: 0.5383
  id_lti5: 0.9445
Simulation (t=50.00):
  id_j5qx: 0.0777
  id_o483: 0.1920
  id_lti5: 2.5772

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1020
  id_o483: 0.4873
  id_lti5: 0.9448
Simulation (t=100.00):
  id_j5qx: 0.0769
  id_o483: 0.1922
  id_lti5: 3.7750

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1059
  id_o483: 0.4585
  id_lti5: 0.9450
Simulation (t=150.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 4.7272

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1074
  id_o483: 0.4460
  id_lti5: 0.9451
Simulation (t=200.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 5.5422

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1079
  id_o483: 0.4413
  id_lti5: 0.9451
Simulation (t=250.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 6.2664

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 6.9247

Simulating with fourth set of initial conditions (Experiment 4):

Comparing simulation with Experiment 4:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1058
  id_o483: 0.4595
  id_lti5: 0.9450
Simulation (t=50.00):
  id_j5qx: 0.0789
  id_o483: 0.1920
  id_lti5: 2.5678

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1073
  id_o483: 0.4462
  id_lti5: 0.9451
Simulation (t=100.00):
  id_j5qx: 0.0771
  id_o483: 0.1922
  id_lti5: 3.7689

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1079
  id_o483: 0.4414
  id_lti5: 0.9451
Simulation (t=150.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 4.7222

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=200.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 5.5378

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1082
  id_o483: 0.4391
  id_lti5: 0.9452
Simulation (t=250.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 6.2624

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1082
  id_o483: 0.4389
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 0.0769
  id_o483: 0.1923
  id_lti5: 6.9211

## 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_5, iteration_7, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5, updated_sbml_v6)

### 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
My model is still not matching the experimental data well. While I've eliminated the exponential growth, I now have a different issue: id_lti5 is continuously increasing rather than stabilizing at ~0.945 as seen in the experiments.

Let me try a different approach. Looking at the experimental data again:

1. All experiments reach a similar steady state regardless of initial conditions
2. The total mass increases but stabilizes
3. id_lti5 stabilizes at ~0.945
4. id_o483 shows complex dynamics but stabilizes at ~0.44-0.73
5. id_j5qx stabilizes at ~0.106-0.108

Let me try a model with the following reactions:

1. id_j5qx → id_lti5 (conversion)
2. id_o483 → id_lti5 (conversion)
3. id_lti5 → id_o483 (conversion with Hill kinetics)
4. id_o483 → id_j5qx (recycling)
5. ∅ → id_lti5 (production with strong negative feedback)
6. id_lti5 → ∅ (degradation to limit id_lti5 concentration)

Let me implement this model with carefully chosen rate constants.

## Action

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

# Load the original SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

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

# Reaction 1: id_j5qx → id_lti5 (conversion)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactant
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Rate constant
math_ast1 = libsbml.parseL3Formula("k1 * id_j5qx")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_o483 → id_lti5 (conversion)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_lti5")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.5)  # Rate constant
math_ast2 = libsbml.parseL3Formula("k2 * id_o483")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_lti5 → id_o483 (conversion with Hill kinetics)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add product
product3 = reaction3.createProduct()
product3.setSpecies("id_o483")
product3.setStoichiometry(1.0)
product3.setConstant(True)

# Add kinetic law with Hill kinetics
kinetic_law3 = reaction3.createKineticLaw()
parameter3a = kinetic_law3.createParameter()
parameter3a.setId("vmax")
parameter3a.setValue(0.2)  # Maximum rate

parameter3b = kinetic_law3.createParameter()
parameter3b.setId("km")
parameter3b.setValue(0.9)  # Michaelis constant

parameter3c = kinetic_law3.createParameter()
parameter3c.setId("n")
parameter3c.setValue(4)  # Hill coefficient for steepness

# Hill kinetics: vmax * (id_lti5^n) / (km^n + id_lti5^n)
math_ast3 = libsbml.parseL3Formula("vmax * (id_lti5^n) / (km^n + id_lti5^n)")
kinetic_law3.setMath(math_ast3)

# Reaction 4: id_o483 → id_j5qx (recycling)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add product
product4 = reaction4.createProduct()
product4.setSpecies("id_j5qx")
product4.setStoichiometry(1.0)
product4.setConstant(True)

# Add kinetic law
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.02)  # Rate constant
math_ast4 = libsbml.parseL3Formula("k4 * id_o483")
kinetic_law4.setMath(math_ast4)

# Reaction 5: ∅ → id_lti5 (production with strong negative feedback)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# No reactants (empty set)

# Add product
product5 = reaction5.createProduct()
product5.setSpecies("id_lti5")
product5.setStoichiometry(1.0)
product5.setConstant(True)

# Add kinetic law with strong negative feedback
kinetic_law5 = reaction5.createKineticLaw()
parameter5a = kinetic_law5.createParameter()
parameter5a.setId("k5")
parameter5a.setValue(0.2)  # Base production rate

parameter5b = kinetic_law5.createParameter()
parameter5b.setId("k_inhib")
parameter5b.setValue(0.95)  # Inhibition constant (set to desired steady state)

parameter5c = kinetic_law5.createParameter()
parameter5c.setId("n_inhib")
parameter5c.setValue(8)  # Hill coefficient for steepness

# Strong negative feedback: k5 * (1 - (id_lti5^n_inhib) / (k_inhib^n_inhib + id_lti5^n_inhib))
math_ast5 = libsbml.parseL3Formula("k5 * (1 - (id_lti5^n_inhib) / (k_inhib^n_inhib + id_lti5^n_inhib))")
kinetic_law5.setMath(math_ast5)

# Reaction 6: id_lti5 → ∅ (degradation)
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

# Add reactant
reactant6 = reaction6.createReactant()
reactant6.setSpecies("id_lti5")
reactant6.setStoichiometry(1.0)
reactant6.setConstant(True)

# No products (empty set)

# Add kinetic law
kinetic_law6 = reaction6.createKineticLaw()
parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.05)  # Degradation rate
math_ast6 = libsbml.parseL3Formula("k6 * id_lti5")
kinetic_law6.setMath(math_ast6)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(document)

# Store the updated SBML model
shared_variables.add('updated_sbml_v7', updated_sbml)

# Function to compare simulation with experimental data
def compare_simulation_with_experiment(simulation_result, exp_data, experiment_name):
    print(f"\nComparing simulation with {experiment_name}:")
    time_points = [0, 50, 100, 150, 200, 250, 300]
    
    for time in time_points:
        # Find the closest time point in the experimental data
        exp_idx = (exp_data['Time'] - time).abs().idxmin()
        exp_time = exp_data.iloc[exp_idx]['Time']
        
        # Find the closest time point in the simulation data
        sim_idx = (simulation_result['Time'] - time).abs().idxmin()
        sim_time = simulation_result.iloc[sim_idx]['Time']
        
        print(f"\nTime ~{time}:")
        print(f"Experimental (t={exp_time:.2f}):")
        print(f"  id_j5qx: {exp_data.iloc[exp_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {exp_data.iloc[exp_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {exp_data.iloc[exp_idx]['id_lti5']:.4f}")
        
        print(f"Simulation (t={sim_time:.2f}):")
        print(f"  id_j5qx: {simulation_result.iloc[sim_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {simulation_result.iloc[sim_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {simulation_result.iloc[sim_idx]['id_lti5']:.4f}")

# Simulate with original initial conditions (Experiment 1)
print("Simulating with original initial conditions (Experiment 1):")
simulation_result1 = simulate(updated_sbml)
compare_simulation_with_experiment(simulation_result1, experiment_history["iteration_0"], "Experiment 1")

# Simulate with second set of initial conditions (Experiment 2)
print("\nSimulating with second set of initial conditions (Experiment 2):")
document2 = libsbml.readSBMLFromString(updated_sbml)
model2 = document2.getModel()
model2.getSpecies("id_j5qx").setInitialConcentration(0.3)
model2.getSpecies("id_o483").setInitialConcentration(0.2)
model2.getSpecies("id_lti5").setInitialConcentration(0.4)
updated_sbml2 = writer.writeSBMLToString(document2)
simulation_result2 = simulate(updated_sbml2)
compare_simulation_with_experiment(simulation_result2, experiment_history["iteration_5"], "Experiment 2")

# Simulate with third set of initial conditions (Experiment 3)
print("\nSimulating with third set of initial conditions (Experiment 3):")
document3 = libsbml.readSBMLFromString(updated_sbml)
model3 = document3.getModel()
model3.getSpecies("id_j5qx").setInitialConcentration(0.1)
model3.getSpecies("id_o483").setInitialConcentration(0.05)
model3.getSpecies("id_lti5").setInitialConcentration(0.8)
updated_sbml3 = writer.writeSBMLToString(document3)
simulation_result3 = simulate(updated_sbml3)
compare_simulation_with_experiment(simulation_result3, experiment_history["iteration_7"], "Experiment 3")

# Simulate with fourth set of initial conditions (Experiment 4)
print("\nSimulating with fourth set of initial conditions (Experiment 4):")
document4 = libsbml.readSBMLFromString(updated_sbml)
model4 = document4.getModel()
model4.getSpecies("id_j5qx").setInitialConcentration(0.1)
model4.getSpecies("id_o483").setInitialConcentration(0.5)
model4.getSpecies("id_lti5").setInitialConcentration(0.3)
updated_sbml4 = writer.writeSBMLToString(document4)
simulation_result4 = simulate(updated_sbml4)
compare_simulation_with_experiment(simulation_result4, experiment_history["iteration_10"], "Experiment 4")
```
# Observation

## Code Stdout
Simulating with original initial conditions (Experiment 1):

Comparing simulation with Experiment 1:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500
Simulation (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1384
  id_o483: 0.0007
  id_lti5: 0.9985
Simulation (t=50.00):
  id_j5qx: 0.1096
  id_o483: 0.2587
  id_lti5: 1.0775

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.0956
  id_o483: 0.0107
  id_lti5: 0.9880
Simulation (t=100.00):
  id_j5qx: 0.1039
  id_o483: 0.2584
  id_lti5: 1.0765

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0839
  id_o483: 0.5901
  id_lti5: 0.9442
Simulation (t=150.00):
  id_j5qx: 0.1034
  id_o483: 0.2583
  id_lti5: 1.0764

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0963
  id_o483: 0.5248
  id_lti5: 0.9445
Simulation (t=200.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.4781
  id_lti5: 0.9448
Simulation (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1064
  id_o483: 0.4543
  id_lti5: 0.9450
Simulation (t=300.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Simulating with second set of initial conditions (Experiment 2):

Comparing simulation with Experiment 2:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000
Simulation (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.2078
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=50.00):
  id_j5qx: 0.1185
  id_o483: 0.2593
  id_lti5: 1.0791

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1436
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=100.00):
  id_j5qx: 0.1047
  id_o483: 0.2584
  id_lti5: 1.0766

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0992
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=150.00):
  id_j5qx: 0.1035
  id_o483: 0.2584
  id_lti5: 1.0764

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0685
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=200.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.0473
  id_o483: 0.0155
  id_lti5: 0.9876
Simulation (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.0544
  id_o483: 0.7310
  id_lti5: 0.9437
Simulation (t=300.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Simulating with third set of initial conditions (Experiment 3):

Comparing simulation with Experiment 3:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.0938
  id_o483: 0.5383
  id_lti5: 0.9445
Simulation (t=50.00):
  id_j5qx: 0.1013
  id_o483: 0.2582
  id_lti5: 1.0760

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1020
  id_o483: 0.4873
  id_lti5: 0.9448
Simulation (t=100.00):
  id_j5qx: 0.1032
  id_o483: 0.2583
  id_lti5: 1.0764

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1059
  id_o483: 0.4585
  id_lti5: 0.9450
Simulation (t=150.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1074
  id_o483: 0.4460
  id_lti5: 0.9451
Simulation (t=200.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1079
  id_o483: 0.4413
  id_lti5: 0.9451
Simulation (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Simulating with fourth set of initial conditions (Experiment 4):

Comparing simulation with Experiment 4:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1058
  id_o483: 0.4595
  id_lti5: 0.9450
Simulation (t=50.00):
  id_j5qx: 0.1027
  id_o483: 0.2583
  id_lti5: 1.0763

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1073
  id_o483: 0.4462
  id_lti5: 0.9451
Simulation (t=100.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1079
  id_o483: 0.4414
  id_lti5: 0.9451
Simulation (t=150.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=200.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1082
  id_o483: 0.4391
  id_lti5: 0.9452
Simulation (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1082
  id_o483: 0.4389
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 0.1033
  id_o483: 0.2583
  id_lti5: 1.0764

## 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_5, iteration_7, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5, updated_sbml_v6, updated_sbml_v7)

### 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
My model is getting closer to the experimental data, but there are still discrepancies:

1. id_lti5 stabilizes at ~1.08 in the simulation vs. ~0.945 in the experiments
2. id_o483 stabilizes at ~0.26 in the simulation vs. ~0.44-0.73 in the experiments
3. id_j5qx stabilizes at ~0.103 in the simulation, which is close to the experimental value of ~0.106-0.108

Let me try a different approach. Looking at the experimental data again, I notice that:

1. In Exp1 and Exp2, id_o483 initially decreases to near zero, then increases dramatically
2. In Exp3 and Exp4, id_o483 shows a more direct path to steady state
3. The steady state values are similar across all experiments

This suggests that there might be a threshold effect or bistability in the system. Let me try a model with the following reactions:

1. id_j5qx → id_lti5 (conversion)
2. id_o483 → id_lti5 (conversion)
3. id_lti5 → id_o483 (conversion with strong Hill kinetics)
4. id_o483 → id_j5qx (recycling)
5. id_lti5 → id_lti5 + id_o483 (autocatalytic production of id_o483, activated at higher id_lti5 concentrations)
6. id_lti5 → ∅ (degradation to limit id_lti5 concentration)

Let me implement this model with carefully chosen rate constants.

## Action

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

# Load the original SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

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

# Reaction 1: id_j5qx → id_lti5 (conversion)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactant
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Rate constant
math_ast1 = libsbml.parseL3Formula("k1 * id_j5qx")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_o483 → id_lti5 (conversion)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_lti5")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.5)  # Rate constant
math_ast2 = libsbml.parseL3Formula("k2 * id_o483")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_lti5 → id_o483 (conversion with strong Hill kinetics)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add product
product3 = reaction3.createProduct()
product3.setSpecies("id_o483")
product3.setStoichiometry(1.0)
product3.setConstant(True)

# Add kinetic law with Hill kinetics
kinetic_law3 = reaction3.createKineticLaw()
parameter3a = kinetic_law3.createParameter()
parameter3a.setId("vmax")
parameter3a.setValue(0.1)  # Maximum rate

parameter3b = kinetic_law3.createParameter()
parameter3b.setId("km")
parameter3b.setValue(0.9)  # Michaelis constant

parameter3c = kinetic_law3.createParameter()
parameter3c.setId("n")
parameter3c.setValue(8)  # Hill coefficient for steepness

# Hill kinetics: vmax * (id_lti5^n) / (km^n + id_lti5^n)
math_ast3 = libsbml.parseL3Formula("vmax * (id_lti5^n) / (km^n + id_lti5^n)")
kinetic_law3.setMath(math_ast3)

# Reaction 4: id_o483 → id_j5qx (recycling)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add product
product4 = reaction4.createProduct()
product4.setSpecies("id_j5qx")
product4.setStoichiometry(1.0)
product4.setConstant(True)

# Add kinetic law
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.02)  # Rate constant
math_ast4 = libsbml.parseL3Formula("k4 * id_o483")
kinetic_law4.setMath(math_ast4)

# Reaction 5: id_lti5 → id_lti5 + id_o483 (autocatalytic production of id_o483)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactant
reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_lti5")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

# Add products
product5a = reaction5.createProduct()
product5a.setSpecies("id_lti5")
product5a.setStoichiometry(1.0)
product5a.setConstant(True)

product5b = reaction5.createProduct()
product5b.setSpecies("id_o483")
product5b.setStoichiometry(1.0)
product5b.setConstant(True)

# Add kinetic law with threshold effect
kinetic_law5 = reaction5.createKineticLaw()
parameter5a = kinetic_law5.createParameter()
parameter5a.setId("k5")
parameter5a.setValue(0.2)  # Rate constant

parameter5b = kinetic_law5.createParameter()
parameter5b.setId("threshold")
parameter5b.setValue(0.9)  # Threshold for activation

parameter5c = kinetic_law5.createParameter()
parameter5c.setId("n_hill")
parameter5c.setValue(10)  # Hill coefficient for steepness

# Hill function: k5 * id_lti5 * (id_lti5^n_hill) / (threshold^n_hill + id_lti5^n_hill)
math_ast5 = libsbml.parseL3Formula("k5 * id_lti5 * (id_lti5^n_hill) / (threshold^n_hill + id_lti5^n_hill)")
kinetic_law5.setMath(math_ast5)

# Reaction 6: id_lti5 → ∅ (degradation)
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

# Add reactant
reactant6 = reaction6.createReactant()
reactant6.setSpecies("id_lti5")
reactant6.setStoichiometry(1.0)
reactant6.setConstant(True)

# No products (empty set)

# Add kinetic law
kinetic_law6 = reaction6.createKineticLaw()
parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.1)  # Degradation rate
math_ast6 = libsbml.parseL3Formula("k6 * id_lti5")
kinetic_law6.setMath(math_ast6)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(document)

# Store the updated SBML model
shared_variables.add('updated_sbml_v8', updated_sbml)

# Function to compare simulation with experimental data
def compare_simulation_with_experiment(simulation_result, exp_data, experiment_name):
    print(f"\nComparing simulation with {experiment_name}:")
    time_points = [0, 50, 100, 150, 200, 250, 300]
    
    for time in time_points:
        # Find the closest time point in the experimental data
        exp_idx = (exp_data['Time'] - time).abs().idxmin()
        exp_time = exp_data.iloc[exp_idx]['Time']
        
        # Find the closest time point in the simulation data
        sim_idx = (simulation_result['Time'] - time).abs().idxmin()
        sim_time = simulation_result.iloc[sim_idx]['Time']
        
        print(f"\nTime ~{time}:")
        print(f"Experimental (t={exp_time:.2f}):")
        print(f"  id_j5qx: {exp_data.iloc[exp_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {exp_data.iloc[exp_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {exp_data.iloc[exp_idx]['id_lti5']:.4f}")
        
        print(f"Simulation (t={sim_time:.2f}):")
        print(f"  id_j5qx: {simulation_result.iloc[sim_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {simulation_result.iloc[sim_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {simulation_result.iloc[sim_idx]['id_lti5']:.4f}")

# Simulate with original initial conditions (Experiment 1)
print("Simulating with original initial conditions (Experiment 1):")
simulation_result1 = simulate(updated_sbml)
compare_simulation_with_experiment(simulation_result1, experiment_history["iteration_0"], "Experiment 1")

# Simulate with second set of initial conditions (Experiment 2)
print("\nSimulating with second set of initial conditions (Experiment 2):")
document2 = libsbml.readSBMLFromString(updated_sbml)
model2 = document2.getModel()
model2.getSpecies("id_j5qx").setInitialConcentration(0.3)
model2.getSpecies("id_o483").setInitialConcentration(0.2)
model2.getSpecies("id_lti5").setInitialConcentration(0.4)
updated_sbml2 = writer.writeSBMLToString(document2)
simulation_result2 = simulate(updated_sbml2)
compare_simulation_with_experiment(simulation_result2, experiment_history["iteration_5"], "Experiment 2")

# Simulate with third set of initial conditions (Experiment 3)
print("\nSimulating with third set of initial conditions (Experiment 3):")
document3 = libsbml.readSBMLFromString(updated_sbml)
model3 = document3.getModel()
model3.getSpecies("id_j5qx").setInitialConcentration(0.1)
model3.getSpecies("id_o483").setInitialConcentration(0.05)
model3.getSpecies("id_lti5").setInitialConcentration(0.8)
updated_sbml3 = writer.writeSBMLToString(document3)
simulation_result3 = simulate(updated_sbml3)
compare_simulation_with_experiment(simulation_result3, experiment_history["iteration_7"], "Experiment 3")

# Simulate with fourth set of initial conditions (Experiment 4)
print("\nSimulating with fourth set of initial conditions (Experiment 4):")
document4 = libsbml.readSBMLFromString(updated_sbml)
model4 = document4.getModel()
model4.getSpecies("id_j5qx").setInitialConcentration(0.1)
model4.getSpecies("id_o483").setInitialConcentration(0.5)
model4.getSpecies("id_lti5").setInitialConcentration(0.3)
updated_sbml4 = writer.writeSBMLToString(document4)
simulation_result4 = simulate(updated_sbml4)
compare_simulation_with_experiment(simulation_result4, experiment_history["iteration_10"], "Experiment 4")
```
# Observation

## Code Stdout
Simulating with original initial conditions (Experiment 1):

Comparing simulation with Experiment 1:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500
Simulation (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1384
  id_o483: 0.0007
  id_lti5: 0.9985
Simulation (t=50.00):
  id_j5qx: 0.0168
  id_o483: 0.0000
  id_lti5: 0.0200

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.0956
  id_o483: 0.0107
  id_lti5: 0.9880
Simulation (t=100.00):
  id_j5qx: 0.0014
  id_o483: -0.0000
  id_lti5: 0.0014

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0839
  id_o483: 0.5901
  id_lti5: 0.9442
Simulation (t=150.00):
  id_j5qx: 0.0001
  id_o483: 0.0000
  id_lti5: 0.0001

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0963
  id_o483: 0.5248
  id_lti5: 0.9445
Simulation (t=200.00):
  id_j5qx: 0.0000
  id_o483: -0.0000
  id_lti5: 0.0000

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.4781
  id_lti5: 0.9448
Simulation (t=250.00):
  id_j5qx: 0.0000
  id_o483: 0.0000
  id_lti5: 0.0000

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1064
  id_o483: 0.4543
  id_lti5: 0.9450
Simulation (t=300.00):
  id_j5qx: 0.0000
  id_o483: 0.0000
  id_lti5: 0.0000

Simulating with second set of initial conditions (Experiment 2):

Comparing simulation with Experiment 2:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000
Simulation (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.2078
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=50.00):
  id_j5qx: 0.0253
  id_o483: 0.0000
  id_lti5: 0.0276

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1436
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=100.00):
  id_j5qx: 0.0021
  id_o483: -0.0000
  id_lti5: 0.0021

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0992
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=150.00):
  id_j5qx: 0.0002
  id_o483: 0.0000
  id_lti5: 0.0002

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0685
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=200.00):
  id_j5qx: 0.0000
  id_o483: -0.0000
  id_lti5: 0.0000

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.0473
  id_o483: 0.0155
  id_lti5: 0.9876
Simulation (t=250.00):
  id_j5qx: 0.0000
  id_o483: 0.0000
  id_lti5: 0.0000

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.0544
  id_o483: 0.7310
  id_lti5: 0.9437
Simulation (t=300.00):
  id_j5qx: 0.0000
  id_o483: 0.0000
  id_lti5: 0.0000

Simulating with third set of initial conditions (Experiment 3):

Comparing simulation with Experiment 3:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.0938
  id_o483: 0.5383
  id_lti5: 0.9445
Simulation (t=50.00):
  id_j5qx: 0.0088
  id_o483: 0.0000
  id_lti5: 0.0144

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1020
  id_o483: 0.4873
  id_lti5: 0.9448
Simulation (t=100.00):
  id_j5qx: 0.0007
  id_o483: 0.0000
  id_lti5: 0.0008

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1059
  id_o483: 0.4585
  id_lti5: 0.9450
Simulation (t=150.00):
  id_j5qx: 0.0001
  id_o483: -0.0000
  id_lti5: 0.0001

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1074
  id_o483: 0.4460
  id_lti5: 0.9451
Simulation (t=200.00):
  id_j5qx: 0.0000
  id_o483: -0.0000
  id_lti5: 0.0000

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1079
  id_o483: 0.4413
  id_lti5: 0.9451
Simulation (t=250.00):
  id_j5qx: 0.0000
  id_o483: -0.0000
  id_lti5: 0.0000

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 0.0000
  id_o483: 0.0000
  id_lti5: 0.0000

Simulating with fourth set of initial conditions (Experiment 4):

Comparing simulation with Experiment 4:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1058
  id_o483: 0.4595
  id_lti5: 0.9450
Simulation (t=50.00):
  id_j5qx: 0.0100
  id_o483: 0.0000
  id_lti5: 0.0152

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1073
  id_o483: 0.4462
  id_lti5: 0.9451
Simulation (t=100.00):
  id_j5qx: 0.0008
  id_o483: -0.0000
  id_lti5: 0.0009

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1079
  id_o483: 0.4414
  id_lti5: 0.9451
Simulation (t=150.00):
  id_j5qx: 0.0001
  id_o483: -0.0000
  id_lti5: 0.0001

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=200.00):
  id_j5qx: 0.0000
  id_o483: -0.0000
  id_lti5: 0.0000

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1082
  id_o483: 0.4391
  id_lti5: 0.9452
Simulation (t=250.00):
  id_j5qx: 0.0000
  id_o483: -0.0000
  id_lti5: 0.0000

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1082
  id_o483: 0.4389
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 0.0000
  id_o483: -0.0000
  id_lti5: 0.0000

## 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_5, iteration_7, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5, updated_sbml_v6, updated_sbml_v7, updated_sbml_v8)

### 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
My model is now showing a different issue - all species are decreasing to near zero. This suggests that the degradation rate (reaction 6) is too high compared to the production rates.

Let me take a step back and reconsider the system. Looking at the experimental data:

1. All experiments reach a similar steady state regardless of initial conditions
2. The total mass increases but stabilizes
3. id_lti5 stabilizes at ~0.945
4. id_o483 stabilizes at ~0.44-0.73
5. id_j5qx stabilizes at ~0.106-0.108

Let me try a simpler model with fewer reactions and more carefully chosen parameters:

1. id_j5qx → id_lti5 (conversion)
2. id_o483 → id_lti5 (conversion)
3. id_lti5 → id_o483 (conversion)
4. id_o483 → id_j5qx (recycling)
5. ∅ → id_lti5 (constant production)

Let me implement this model and test it against the experimental data.

## Action

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

# Load the original SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

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

# Reaction 1: id_j5qx → id_lti5 (conversion)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactant
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Rate constant
math_ast1 = libsbml.parseL3Formula("k1 * id_j5qx")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_o483 → id_lti5 (conversion)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_lti5")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.1)  # Rate constant
math_ast2 = libsbml.parseL3Formula("k2 * id_o483")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_lti5 → id_o483 (conversion)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add product
product3 = reaction3.createProduct()
product3.setSpecies("id_o483")
product3.setStoichiometry(1.0)
product3.setConstant(True)

# Add kinetic law
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.05)  # Rate constant
math_ast3 = libsbml.parseL3Formula("k3 * id_lti5")
kinetic_law3.setMath(math_ast3)

# Reaction 4: id_o483 → id_j5qx (recycling)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add product
product4 = reaction4.createProduct()
product4.setSpecies("id_j5qx")
product4.setStoichiometry(1.0)
product4.setConstant(True)

# Add kinetic law
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.02)  # Rate constant
math_ast4 = libsbml.parseL3Formula("k4 * id_o483")
kinetic_law4.setMath(math_ast4)

# Reaction 5: ∅ → id_lti5 (constant production)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# No reactants (empty set)

# Add product
product5 = reaction5.createProduct()
product5.setSpecies("id_lti5")
product5.setStoichiometry(1.0)
product5.setConstant(True)

# Add kinetic law
kinetic_law5 = reaction5.createKineticLaw()
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.05)  # Constant production rate
math_ast5 = libsbml.parseL3Formula("k5")
kinetic_law5.setMath(math_ast5)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(document)

# Store the updated SBML model
shared_variables.add('updated_sbml_v9', updated_sbml)

# Function to compare simulation with experimental data
def compare_simulation_with_experiment(simulation_result, exp_data, experiment_name):
    print(f"\nComparing simulation with {experiment_name}:")
    time_points = [0, 50, 100, 150, 200, 250, 300]
    
    for time in time_points:
        # Find the closest time point in the experimental data
        exp_idx = (exp_data['Time'] - time).abs().idxmin()
        exp_time = exp_data.iloc[exp_idx]['Time']
        
        # Find the closest time point in the simulation data
        sim_idx = (simulation_result['Time'] - time).abs().idxmin()
        sim_time = simulation_result.iloc[sim_idx]['Time']
        
        print(f"\nTime ~{time}:")
        print(f"Experimental (t={exp_time:.2f}):")
        print(f"  id_j5qx: {exp_data.iloc[exp_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {exp_data.iloc[exp_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {exp_data.iloc[exp_idx]['id_lti5']:.4f}")
        
        print(f"Simulation (t={sim_time:.2f}):")
        print(f"  id_j5qx: {simulation_result.iloc[sim_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {simulation_result.iloc[sim_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {simulation_result.iloc[sim_idx]['id_lti5']:.4f}")

# Simulate with original initial conditions (Experiment 1)
print("Simulating with original initial conditions (Experiment 1):")
simulation_result1 = simulate(updated_sbml)
compare_simulation_with_experiment(simulation_result1, experiment_history["iteration_0"], "Experiment 1")

# Simulate with second set of initial conditions (Experiment 2)
print("\nSimulating with second set of initial conditions (Experiment 2):")
document2 = libsbml.readSBMLFromString(updated_sbml)
model2 = document2.getModel()
model2.getSpecies("id_j5qx").setInitialConcentration(0.3)
model2.getSpecies("id_o483").setInitialConcentration(0.2)
model2.getSpecies("id_lti5").setInitialConcentration(0.4)
updated_sbml2 = writer.writeSBMLToString(document2)
simulation_result2 = simulate(updated_sbml2)
compare_simulation_with_experiment(simulation_result2, experiment_history["iteration_5"], "Experiment 2")

# Simulate with third set of initial conditions (Experiment 3)
print("\nSimulating with third set of initial conditions (Experiment 3):")
document3 = libsbml.readSBMLFromString(updated_sbml)
model3 = document3.getModel()
model3.getSpecies("id_j5qx").setInitialConcentration(0.1)
model3.getSpecies("id_o483").setInitialConcentration(0.05)
model3.getSpecies("id_lti5").setInitialConcentration(0.8)
updated_sbml3 = writer.writeSBMLToString(document3)
simulation_result3 = simulate(updated_sbml3)
compare_simulation_with_experiment(simulation_result3, experiment_history["iteration_7"], "Experiment 3")

# Simulate with fourth set of initial conditions (Experiment 4)
print("\nSimulating with fourth set of initial conditions (Experiment 4):")
document4 = libsbml.readSBMLFromString(updated_sbml)
model4 = document4.getModel()
model4.getSpecies("id_j5qx").setInitialConcentration(0.1)
model4.getSpecies("id_o483").setInitialConcentration(0.5)
model4.getSpecies("id_lti5").setInitialConcentration(0.3)
updated_sbml4 = writer.writeSBMLToString(document4)
simulation_result4 = simulate(updated_sbml4)
compare_simulation_with_experiment(simulation_result4, experiment_history["iteration_10"], "Experiment 4")
```
# Observation

## Code Stdout
Simulating with original initial conditions (Experiment 1):

Comparing simulation with Experiment 1:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500
Simulation (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1384
  id_o483: 0.0007
  id_lti5: 0.9985
Simulation (t=50.00):
  id_j5qx: 0.2431
  id_o483: 0.8345
  id_lti5: 2.2724

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.0956
  id_o483: 0.0107
  id_lti5: 0.9880
Simulation (t=100.00):
  id_j5qx: 0.4946
  id_o483: 1.4976
  id_lti5: 3.8578

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0839
  id_o483: 0.5901
  id_lti5: 0.9442
Simulation (t=150.00):
  id_j5qx: 0.7571
  id_o483: 2.1558
  id_lti5: 5.4371

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0963
  id_o483: 0.5248
  id_lti5: 0.9445
Simulation (t=200.00):
  id_j5qx: 1.0202
  id_o483: 2.8137
  id_lti5: 7.0161

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.4781
  id_lti5: 0.9448
Simulation (t=250.00):
  id_j5qx: 1.2834
  id_o483: 3.4716
  id_lti5: 8.5950

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1064
  id_o483: 0.4543
  id_lti5: 0.9450
Simulation (t=300.00):
  id_j5qx: 1.5465
  id_o483: 4.1295
  id_lti5: 10.1740

Simulating with second set of initial conditions (Experiment 2):

Comparing simulation with Experiment 2:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000
Simulation (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.2078
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=50.00):
  id_j5qx: 0.2547
  id_o483: 0.8448
  id_lti5: 2.3005

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1436
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=100.00):
  id_j5qx: 0.5001
  id_o483: 1.5106
  id_lti5: 3.8892

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0992
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=150.00):
  id_j5qx: 0.7624
  id_o483: 2.1690
  id_lti5: 5.4687

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0685
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=200.00):
  id_j5qx: 1.0255
  id_o483: 2.8269
  id_lti5: 7.0476

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.0473
  id_o483: 0.0155
  id_lti5: 0.9876
Simulation (t=250.00):
  id_j5qx: 1.2886
  id_o483: 3.4848
  id_lti5: 8.6266

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.0544
  id_o483: 0.7310
  id_lti5: 0.9437
Simulation (t=300.00):
  id_j5qx: 1.5518
  id_o483: 4.1427
  id_lti5: 10.2055

Simulating with third set of initial conditions (Experiment 3):

Comparing simulation with Experiment 3:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.0938
  id_o483: 0.5383
  id_lti5: 0.9445
Simulation (t=50.00):
  id_j5qx: 0.2466
  id_o483: 0.8639
  id_lti5: 2.3395

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1020
  id_o483: 0.4873
  id_lti5: 0.9448
Simulation (t=100.00):
  id_j5qx: 0.5047
  id_o483: 1.5241
  id_lti5: 3.9212

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1059
  id_o483: 0.4585
  id_lti5: 0.9450
Simulation (t=150.00):
  id_j5qx: 0.7676
  id_o483: 2.1821
  id_lti5: 5.5003

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1074
  id_o483: 0.4460
  id_lti5: 0.9451
Simulation (t=200.00):
  id_j5qx: 1.0307
  id_o483: 2.8400
  id_lti5: 7.0792

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1079
  id_o483: 0.4413
  id_lti5: 0.9451
Simulation (t=250.00):
  id_j5qx: 1.2939
  id_o483: 3.4979
  id_lti5: 8.6582

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 1.5571
  id_o483: 4.1558
  id_lti5: 10.2371

Simulating with fourth set of initial conditions (Experiment 4):

Comparing simulation with Experiment 4:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1058
  id_o483: 0.4595
  id_lti5: 0.9450
Simulation (t=50.00):
  id_j5qx: 0.2464
  id_o483: 0.8486
  id_lti5: 2.3050

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1073
  id_o483: 0.4462
  id_lti5: 0.9451
Simulation (t=100.00):
  id_j5qx: 0.4997
  id_o483: 1.5108
  id_lti5: 3.8895

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1079
  id_o483: 0.4414
  id_lti5: 0.9451
Simulation (t=150.00):
  id_j5qx: 0.7624
  id_o483: 2.1690
  id_lti5: 5.4687

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=200.00):
  id_j5qx: 1.0255
  id_o483: 2.8269
  id_lti5: 7.0476

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1082
  id_o483: 0.4391
  id_lti5: 0.9452
Simulation (t=250.00):
  id_j5qx: 1.2886
  id_o483: 3.4848
  id_lti5: 8.6266

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1082
  id_o483: 0.4389
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 1.5518
  id_o483: 4.1427
  id_lti5: 10.2055

## 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_5, iteration_7, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5, updated_sbml_v6, updated_sbml_v7, updated_sbml_v8, updated_sbml_v9)

### 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
My model is now showing unbounded growth, which is not consistent with the experimental data. The constant production of id_lti5 (reaction 5) without any limiting mechanism is causing all species to increase indefinitely.

Let me try a different approach. Looking at the experimental data again:

1. All experiments reach a similar steady state regardless of initial conditions
2. The total mass increases but stabilizes
3. id_lti5 stabilizes at ~0.945
4. id_o483 stabilizes at ~0.44-0.73
5. id_j5qx stabilizes at ~0.106-0.108

Let me try a model with the following reactions:

1. id_j5qx → id_lti5 (conversion)
2. id_o483 → id_lti5 (conversion)
3. id_lti5 → id_o483 (conversion)
4. id_o483 → id_j5qx (recycling)
5. ∅ → id_lti5 (production with negative feedback)
6. id_lti5 → ∅ (degradation)

The key is to balance the production and degradation rates to achieve the observed steady state.

## Action

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

# Load the original SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

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

# Reaction 1: id_j5qx → id_lti5 (conversion)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactant
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Rate constant
math_ast1 = libsbml.parseL3Formula("k1 * id_j5qx")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_o483 → id_lti5 (conversion)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_lti5")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.1)  # Rate constant
math_ast2 = libsbml.parseL3Formula("k2 * id_o483")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_lti5 → id_o483 (conversion)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add product
product3 = reaction3.createProduct()
product3.setSpecies("id_o483")
product3.setStoichiometry(1.0)
product3.setConstant(True)

# Add kinetic law
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.05)  # Rate constant
math_ast3 = libsbml.parseL3Formula("k3 * id_lti5")
kinetic_law3.setMath(math_ast3)

# Reaction 4: id_o483 → id_j5qx (recycling)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add product
product4 = reaction4.createProduct()
product4.setSpecies("id_j5qx")
product4.setStoichiometry(1.0)
product4.setConstant(True)

# Add kinetic law
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.02)  # Rate constant
math_ast4 = libsbml.parseL3Formula("k4 * id_o483")
kinetic_law4.setMath(math_ast4)

# Reaction 5: ∅ → id_lti5 (production with negative feedback)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# No reactants (empty set)

# Add product
product5 = reaction5.createProduct()
product5.setSpecies("id_lti5")
product5.setStoichiometry(1.0)
product5.setConstant(True)

# Add kinetic law with negative feedback
kinetic_law5 = reaction5.createKineticLaw()
parameter5a = kinetic_law5.createParameter()
parameter5a.setId("k5")
parameter5a.setValue(0.05)  # Base production rate

parameter5b = kinetic_law5.createParameter()
parameter5b.setId("k_inhib")
parameter5b.setValue(0.95)  # Inhibition constant (set to desired steady state)

# Negative feedback: k5 * (1 - id_lti5/k_inhib) when id_lti5 < k_inhib, 0 otherwise
math_ast5 = libsbml.parseL3Formula("k5 * max(0, (1 - id_lti5/k_inhib))")
kinetic_law5.setMath(math_ast5)

# Reaction 6: id_lti5 → ∅ (degradation)
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

# Add reactant
reactant6 = reaction6.createReactant()
reactant6.setSpecies("id_lti5")
reactant6.setStoichiometry(1.0)
reactant6.setConstant(True)

# No products (empty set)

# Add kinetic law
kinetic_law6 = reaction6.createKineticLaw()
parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.01)  # Degradation rate
math_ast6 = libsbml.parseL3Formula("k6 * id_lti5")
kinetic_law6.setMath(math_ast6)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(document)

# Store the updated SBML model
shared_variables.add('updated_sbml_v10', updated_sbml)

# Function to compare simulation with experimental data
def compare_simulation_with_experiment(simulation_result, exp_data, experiment_name):
    print(f"\nComparing simulation with {experiment_name}:")
    time_points = [0, 50, 100, 150, 200, 250, 300]
    
    for time in time_points:
        # Find the closest time point in the experimental data
        exp_idx = (exp_data['Time'] - time).abs().idxmin()
        exp_time = exp_data.iloc[exp_idx]['Time']
        
        # Find the closest time point in the simulation data
        sim_idx = (simulation_result['Time'] - time).abs().idxmin()
        sim_time = simulation_result.iloc[sim_idx]['Time']
        
        print(f"\nTime ~{time}:")
        print(f"Experimental (t={exp_time:.2f}):")
        print(f"  id_j5qx: {exp_data.iloc[exp_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {exp_data.iloc[exp_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {exp_data.iloc[exp_idx]['id_lti5']:.4f}")
        
        print(f"Simulation (t={sim_time:.2f}):")
        print(f"  id_j5qx: {simulation_result.iloc[sim_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {simulation_result.iloc[sim_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {simulation_result.iloc[sim_idx]['id_lti5']:.4f}")

# Simulate with original initial conditions (Experiment 1)
print("Simulating with original initial conditions (Experiment 1):")
simulation_result1 = simulate(updated_sbml)
compare_simulation_with_experiment(simulation_result1, experiment_history["iteration_0"], "Experiment 1")

# Simulate with second set of initial conditions (Experiment 2)
print("\nSimulating with second set of initial conditions (Experiment 2):")
document2 = libsbml.readSBMLFromString(updated_sbml)
model2 = document2.getModel()
model2.getSpecies("id_j5qx").setInitialConcentration(0.3)
model2.getSpecies("id_o483").setInitialConcentration(0.2)
model2.getSpecies("id_lti5").setInitialConcentration(0.4)
updated_sbml2 = writer.writeSBMLToString(document2)
simulation_result2 = simulate(updated_sbml2)
compare_simulation_with_experiment(simulation_result2, experiment_history["iteration_5"], "Experiment 2")

# Simulate with third set of initial conditions (Experiment 3)
print("\nSimulating with third set of initial conditions (Experiment 3):")
document3 = libsbml.readSBMLFromString(updated_sbml)
model3 = document3.getModel()
model3.getSpecies("id_j5qx").setInitialConcentration(0.1)
model3.getSpecies("id_o483").setInitialConcentration(0.05)
model3.getSpecies("id_lti5").setInitialConcentration(0.8)
updated_sbml3 = writer.writeSBMLToString(document3)
simulation_result3 = simulate(updated_sbml3)
compare_simulation_with_experiment(simulation_result3, experiment_history["iteration_7"], "Experiment 3")

# Simulate with fourth set of initial conditions (Experiment 4)
print("\nSimulating with fourth set of initial conditions (Experiment 4):")
document4 = libsbml.readSBMLFromString(updated_sbml)
model4 = document4.getModel()
model4.getSpecies("id_j5qx").setInitialConcentration(0.1)
model4.getSpecies("id_o483").setInitialConcentration(0.5)
model4.getSpecies("id_lti5").setInitialConcentration(0.3)
updated_sbml4 = writer.writeSBMLToString(document4)
simulation_result4 = simulate(updated_sbml4)
compare_simulation_with_experiment(simulation_result4, experiment_history["iteration_10"], "Experiment 4")
```
# Observation

## Code Stderror
 We could not run simulations on your SBML model. This is the error: The only permitted MathML 2.0 elements in SBML Level 2 are the following: <cn>, <ci>, <csymbol>, <sep>, <apply>, <piecewise>, <piece>, <otherwise>, <eq>, <neq>, <gt>, <lt>, <geq>, <leq>, <plus>, <minus>, <times>, <divide>, <power>, <root>, <abs>, <exp>, <ln>, <log>, <floor>, <ceiling>, <factorial>, <and>, <or>, <xor>, <not>, <degree>, <bvar>, <logbase>, <sin>, <cos>, <tan>, <sec>, <csc>, <cot>, <sinh>, <cosh>, <tanh>, <sech>, <csch>, <coth>, <arcsin>, <arccos>, <arctan>, <arcsec>, <arccsc>, <arccot>, <arcsinh>, <arccosh>, <arctanh>, <arcsech>, <arccsch>, <arccoth>, <true>, <false>, <notanumber>, <pi>, <infinity>, <exponentiale>, <semantics>, <annotation>, and <annotation-xml>. SBML L3V2 added <implies>, <max>, <min>, <rem> and <quotient>.
Reference: L2V4 Section 3.4.1
 <max> is not valid in SBML Level 2 Version 4.


## 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_5, iteration_7, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5, updated_sbml_v6, updated_sbml_v7, updated_sbml_v8, updated_sbml_v9, updated_sbml_v10)

### 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
I encountered an error because the `max` function is not valid in SBML Level 2 Version 4. Let me modify my approach to use a piecewise function instead, which is supported in this SBML version.

Let me try again with the same model structure but using piecewise functions for the negative feedback:

1. id_j5qx → id_lti5 (conversion)
2. id_o483 → id_lti5 (conversion)
3. id_lti5 → id_o483 (conversion)
4. id_o483 → id_j5qx (recycling)
5. ∅ → id_lti5 (production with negative feedback using piecewise)
6. id_lti5 → ∅ (degradation)

## Action

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

# Load the original SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

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

# Reaction 1: id_j5qx → id_lti5 (conversion)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactant
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Rate constant
math_ast1 = libsbml.parseL3Formula("k1 * id_j5qx")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_o483 → id_lti5 (conversion)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_lti5")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.1)  # Rate constant
math_ast2 = libsbml.parseL3Formula("k2 * id_o483")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_lti5 → id_o483 (conversion)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add product
product3 = reaction3.createProduct()
product3.setSpecies("id_o483")
product3.setStoichiometry(1.0)
product3.setConstant(True)

# Add kinetic law
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.05)  # Rate constant
math_ast3 = libsbml.parseL3Formula("k3 * id_lti5")
kinetic_law3.setMath(math_ast3)

# Reaction 4: id_o483 → id_j5qx (recycling)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add product
product4 = reaction4.createProduct()
product4.setSpecies("id_j5qx")
product4.setStoichiometry(1.0)
product4.setConstant(True)

# Add kinetic law
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.02)  # Rate constant
math_ast4 = libsbml.parseL3Formula("k4 * id_o483")
kinetic_law4.setMath(math_ast4)

# Reaction 5: ∅ → id_lti5 (production with negative feedback using piecewise)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# No reactants (empty set)

# Add product
product5 = reaction5.createProduct()
product5.setSpecies("id_lti5")
product5.setStoichiometry(1.0)
product5.setConstant(True)

# Add kinetic law with negative feedback using piecewise
kinetic_law5 = reaction5.createKineticLaw()
parameter5a = kinetic_law5.createParameter()
parameter5a.setId("k5")
parameter5a.setValue(0.05)  # Base production rate

parameter5b = kinetic_law5.createParameter()
parameter5b.setId("k_inhib")
parameter5b.setValue(0.95)  # Inhibition constant (set to desired steady state)

# Piecewise function: k5 * (1 - id_lti5/k_inhib) when id_lti5 < k_inhib, 0 otherwise
math_ast5 = libsbml.parseL3Formula("piecewise(k5 * (1 - id_lti5/k_inhib), lt(id_lti5, k_inhib), 0)")
kinetic_law5.setMath(math_ast5)

# Reaction 6: id_lti5 → ∅ (degradation)
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

# Add reactant
reactant6 = reaction6.createReactant()
reactant6.setSpecies("id_lti5")
reactant6.setStoichiometry(1.0)
reactant6.setConstant(True)

# No products (empty set)

# Add kinetic law
kinetic_law6 = reaction6.createKineticLaw()
parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.01)  # Degradation rate
math_ast6 = libsbml.parseL3Formula("k6 * id_lti5")
kinetic_law6.setMath(math_ast6)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(document)

# Store the updated SBML model
shared_variables.add('updated_sbml_v11', updated_sbml)

# Function to compare simulation with experimental data
def compare_simulation_with_experiment(simulation_result, exp_data, experiment_name):
    print(f"\nComparing simulation with {experiment_name}:")
    time_points = [0, 50, 100, 150, 200, 250, 300]
    
    for time in time_points:
        # Find the closest time point in the experimental data
        exp_idx = (exp_data['Time'] - time).abs().idxmin()
        exp_time = exp_data.iloc[exp_idx]['Time']
        
        # Find the closest time point in the simulation data
        sim_idx = (simulation_result['Time'] - time).abs().idxmin()
        sim_time = simulation_result.iloc[sim_idx]['Time']
        
        print(f"\nTime ~{time}:")
        print(f"Experimental (t={exp_time:.2f}):")
        print(f"  id_j5qx: {exp_data.iloc[exp_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {exp_data.iloc[exp_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {exp_data.iloc[exp_idx]['id_lti5']:.4f}")
        
        print(f"Simulation (t={sim_time:.2f}):")
        print(f"  id_j5qx: {simulation_result.iloc[sim_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {simulation_result.iloc[sim_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {simulation_result.iloc[sim_idx]['id_lti5']:.4f}")

# Simulate with original initial conditions (Experiment 1)
print("Simulating with original initial conditions (Experiment 1):")
simulation_result1 = simulate(updated_sbml)
compare_simulation_with_experiment(simulation_result1, experiment_history["iteration_0"], "Experiment 1")

# Simulate with second set of initial conditions (Experiment 2)
print("\nSimulating with second set of initial conditions (Experiment 2):")
document2 = libsbml.readSBMLFromString(updated_sbml)
model2 = document2.getModel()
model2.getSpecies("id_j5qx").setInitialConcentration(0.3)
model2.getSpecies("id_o483").setInitialConcentration(0.2)
model2.getSpecies("id_lti5").setInitialConcentration(0.4)
updated_sbml2 = writer.writeSBMLToString(document2)
simulation_result2 = simulate(updated_sbml2)
compare_simulation_with_experiment(simulation_result2, experiment_history["iteration_5"], "Experiment 2")

# Simulate with third set of initial conditions (Experiment 3)
print("\nSimulating with third set of initial conditions (Experiment 3):")
document3 = libsbml.readSBMLFromString(updated_sbml)
model3 = document3.getModel()
model3.getSpecies("id_j5qx").setInitialConcentration(0.1)
model3.getSpecies("id_o483").setInitialConcentration(0.05)
model3.getSpecies("id_lti5").setInitialConcentration(0.8)
updated_sbml3 = writer.writeSBMLToString(document3)
simulation_result3 = simulate(updated_sbml3)
compare_simulation_with_experiment(simulation_result3, experiment_history["iteration_7"], "Experiment 3")

# Simulate with fourth set of initial conditions (Experiment 4)
print("\nSimulating with fourth set of initial conditions (Experiment 4):")
document4 = libsbml.readSBMLFromString(updated_sbml)
model4 = document4.getModel()
model4.getSpecies("id_j5qx").setInitialConcentration(0.1)
model4.getSpecies("id_o483").setInitialConcentration(0.5)
model4.getSpecies("id_lti5").setInitialConcentration(0.3)
updated_sbml4 = writer.writeSBMLToString(document4)
simulation_result4 = simulate(updated_sbml4)
compare_simulation_with_experiment(simulation_result4, experiment_history["iteration_10"], "Experiment 4")
```
# Observation

## Code Stdout
Simulating with original initial conditions (Experiment 1):

Comparing simulation with Experiment 1:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500
Simulation (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1384
  id_o483: 0.0007
  id_lti5: 0.9985
Simulation (t=50.00):
  id_j5qx: 0.1200
  id_o483: 0.3105
  id_lti5: 0.7617

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.0956
  id_o483: 0.0107
  id_lti5: 0.9880
Simulation (t=100.00):
  id_j5qx: 0.1292
  id_o483: 0.3285
  id_lti5: 0.7909

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0839
  id_o483: 0.5901
  id_lti5: 0.9442
Simulation (t=150.00):
  id_j5qx: 0.1322
  id_o483: 0.3317
  id_lti5: 0.7967

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0963
  id_o483: 0.5248
  id_lti5: 0.9445
Simulation (t=200.00):
  id_j5qx: 0.1329
  id_o483: 0.3324
  id_lti5: 0.7979

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.4781
  id_lti5: 0.9448
Simulation (t=250.00):
  id_j5qx: 0.1330
  id_o483: 0.3326
  id_lti5: 0.7982

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1064
  id_o483: 0.4543
  id_lti5: 0.9450
Simulation (t=300.00):
  id_j5qx: 0.1330
  id_o483: 0.3326
  id_lti5: 0.7983

Simulating with second set of initial conditions (Experiment 2):

Comparing simulation with Experiment 2:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000
Simulation (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.2078
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=50.00):
  id_j5qx: 0.1324
  id_o483: 0.3183
  id_lti5: 0.7775

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1436
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=100.00):
  id_j5qx: 0.1315
  id_o483: 0.3307
  id_lti5: 0.7949

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0992
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=150.00):
  id_j5qx: 0.1327
  id_o483: 0.3322
  id_lti5: 0.7976

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0685
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=200.00):
  id_j5qx: 0.1330
  id_o483: 0.3325
  id_lti5: 0.7982

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.0473
  id_o483: 0.0155
  id_lti5: 0.9876
Simulation (t=250.00):
  id_j5qx: 0.1330
  id_o483: 0.3326
  id_lti5: 0.7983

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.0544
  id_o483: 0.7310
  id_lti5: 0.9437
Simulation (t=300.00):
  id_j5qx: 0.1330
  id_o483: 0.3326
  id_lti5: 0.7983

Simulating with third set of initial conditions (Experiment 3):

Comparing simulation with Experiment 3:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.0938
  id_o483: 0.5383
  id_lti5: 0.9445
Simulation (t=50.00):
  id_j5qx: 0.1135
  id_o483: 0.3106
  id_lti5: 0.7595

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1020
  id_o483: 0.4873
  id_lti5: 0.9448
Simulation (t=100.00):
  id_j5qx: 0.1284
  id_o483: 0.3279
  id_lti5: 0.7898

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1059
  id_o483: 0.4585
  id_lti5: 0.9450
Simulation (t=150.00):
  id_j5qx: 0.1320
  id_o483: 0.3316
  id_lti5: 0.7964

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1074
  id_o483: 0.4460
  id_lti5: 0.9451
Simulation (t=200.00):
  id_j5qx: 0.1328
  id_o483: 0.3324
  id_lti5: 0.7979

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1079
  id_o483: 0.4413
  id_lti5: 0.9451
Simulation (t=250.00):
  id_j5qx: 0.1330
  id_o483: 0.3326
  id_lti5: 0.7982

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 0.1330
  id_o483: 0.3326
  id_lti5: 0.7983

Simulating with fourth set of initial conditions (Experiment 4):

Comparing simulation with Experiment 4:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1058
  id_o483: 0.4595
  id_lti5: 0.9450
Simulation (t=50.00):
  id_j5qx: 0.1235
  id_o483: 0.3194
  id_lti5: 0.7756

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1073
  id_o483: 0.4462
  id_lti5: 0.9451
Simulation (t=100.00):
  id_j5qx: 0.1305
  id_o483: 0.3300
  id_lti5: 0.7936

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1079
  id_o483: 0.4414
  id_lti5: 0.9451
Simulation (t=150.00):
  id_j5qx: 0.1325
  id_o483: 0.3320
  id_lti5: 0.7973

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=200.00):
  id_j5qx: 0.1329
  id_o483: 0.3325
  id_lti5: 0.7981

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1082
  id_o483: 0.4391
  id_lti5: 0.9452
Simulation (t=250.00):
  id_j5qx: 0.1330
  id_o483: 0.3326
  id_lti5: 0.7983

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1082
  id_o483: 0.4389
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 0.1330
  id_o483: 0.3326
  id_lti5: 0.7983

## 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_5, iteration_7, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5, updated_sbml_v6, updated_sbml_v7, updated_sbml_v8, updated_sbml_v9, updated_sbml_v10, updated_sbml_v11)

### 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
My model is now stable and reaches a steady state, but the steady state values still don't match the experimental data well:

1. id_lti5 stabilizes at ~0.80 in the simulation vs. ~0.945 in the experiments
2. id_o483 stabilizes at ~0.33 in the simulation vs. ~0.44-0.73 in the experiments
3. id_j5qx stabilizes at ~0.133 in the simulation vs. ~0.106-0.108 in the experiments

Let me adjust the parameters to better match the experimental data. I'll:
1. Increase the inhibition constant for id_lti5 production to get closer to 0.945
2. Adjust the conversion rates to get the right balance of species

Let me also try a slightly different model structure:

1. id_j5qx → id_lti5 (conversion)
2. id_o483 → id_lti5 (conversion)
3. id_lti5 → id_o483 (conversion with Hill kinetics)
4. id_o483 → id_j5qx (recycling)
5. ∅ → id_lti5 (production with negative feedback using piecewise)

## Action

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

# Load the original SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

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

# Reaction 1: id_j5qx → id_lti5 (conversion)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactant
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Rate constant
math_ast1 = libsbml.parseL3Formula("k1 * id_j5qx")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_o483 → id_lti5 (conversion)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_lti5")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.1)  # Rate constant
math_ast2 = libsbml.parseL3Formula("k2 * id_o483")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_lti5 → id_o483 (conversion with Hill kinetics)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add product
product3 = reaction3.createProduct()
product3.setSpecies("id_o483")
product3.setStoichiometry(1.0)
product3.setConstant(True)

# Add kinetic law with Hill kinetics
kinetic_law3 = reaction3.createKineticLaw()
parameter3a = kinetic_law3.createParameter()
parameter3a.setId("vmax")
parameter3a.setValue(0.05)  # Maximum rate

parameter3b = kinetic_law3.createParameter()
parameter3b.setId("km")
parameter3b.setValue(0.5)  # Michaelis constant

parameter3c = kinetic_law3.createParameter()
parameter3c.setId("n")
parameter3c.setValue(2)  # Hill coefficient

# Hill kinetics: vmax * (id_lti5^n) / (km^n + id_lti5^n)
math_ast3 = libsbml.parseL3Formula("vmax * (id_lti5^n) / (km^n + id_lti5^n)")
kinetic_law3.setMath(math_ast3)

# Reaction 4: id_o483 → id_j5qx (recycling)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add product
product4 = reaction4.createProduct()
product4.setSpecies("id_j5qx")
product4.setStoichiometry(1.0)
product4.setConstant(True)

# Add kinetic law
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.02)  # Rate constant
math_ast4 = libsbml.parseL3Formula("k4 * id_o483")
kinetic_law4.setMath(math_ast4)

# Reaction 5: ∅ → id_lti5 (production with negative feedback using piecewise)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# No reactants (empty set)

# Add product
product5 = reaction5.createProduct()
product5.setSpecies("id_lti5")
product5.setStoichiometry(1.0)
product5.setConstant(True)

# Add kinetic law with negative feedback using piecewise
kinetic_law5 = reaction5.createKineticLaw()
parameter5a = kinetic_law5.createParameter()
parameter5a.setId("k5")
parameter5a.setValue(0.05)  # Base production rate

parameter5b = kinetic_law5.createParameter()
parameter5b.setId("k_inhib")
parameter5b.setValue(0.945)  # Inhibition constant (set to desired steady state)

# Piecewise function: k5 * (1 - id_lti5/k_inhib) when id_lti5 < k_inhib, 0 otherwise
math_ast5 = libsbml.parseL3Formula("piecewise(k5 * (1 - id_lti5/k_inhib), lt(id_lti5, k_inhib), 0)")
kinetic_law5.setMath(math_ast5)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(document)

# Store the updated SBML model
shared_variables.add('updated_sbml_v12', updated_sbml)

# Function to compare simulation with experimental data
def compare_simulation_with_experiment(simulation_result, exp_data, experiment_name):
    print(f"\nComparing simulation with {experiment_name}:")
    time_points = [0, 50, 100, 150, 200, 250, 300]
    
    for time in time_points:
        # Find the closest time point in the experimental data
        exp_idx = (exp_data['Time'] - time).abs().idxmin()
        exp_time = exp_data.iloc[exp_idx]['Time']
        
        # Find the closest time point in the simulation data
        sim_idx = (simulation_result['Time'] - time).abs().idxmin()
        sim_time = simulation_result.iloc[sim_idx]['Time']
        
        print(f"\nTime ~{time}:")
        print(f"Experimental (t={exp_time:.2f}):")
        print(f"  id_j5qx: {exp_data.iloc[exp_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {exp_data.iloc[exp_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {exp_data.iloc[exp_idx]['id_lti5']:.4f}")
        
        print(f"Simulation (t={sim_time:.2f}):")
        print(f"  id_j5qx: {simulation_result.iloc[sim_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {simulation_result.iloc[sim_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {simulation_result.iloc[sim_idx]['id_lti5']:.4f}")

# Simulate with original initial conditions (Experiment 1)
print("Simulating with original initial conditions (Experiment 1):")
simulation_result1 = simulate(updated_sbml)
compare_simulation_with_experiment(simulation_result1, experiment_history["iteration_0"], "Experiment 1")

# Simulate with second set of initial conditions (Experiment 2)
print("\nSimulating with second set of initial conditions (Experiment 2):")
document2 = libsbml.readSBMLFromString(updated_sbml)
model2 = document2.getModel()
model2.getSpecies("id_j5qx").setInitialConcentration(0.3)
model2.getSpecies("id_o483").setInitialConcentration(0.2)
model2.getSpecies("id_lti5").setInitialConcentration(0.4)
updated_sbml2 = writer.writeSBMLToString(document2)
simulation_result2 = simulate(updated_sbml2)
compare_simulation_with_experiment(simulation_result2, experiment_history["iteration_5"], "Experiment 2")

# Simulate with third set of initial conditions (Experiment 3)
print("\nSimulating with third set of initial conditions (Experiment 3):")
document3 = libsbml.readSBMLFromString(updated_sbml)
model3 = document3.getModel()
model3.getSpecies("id_j5qx").setInitialConcentration(0.1)
model3.getSpecies("id_o483").setInitialConcentration(0.05)
model3.getSpecies("id_lti5").setInitialConcentration(0.8)
updated_sbml3 = writer.writeSBMLToString(document3)
simulation_result3 = simulate(updated_sbml3)
compare_simulation_with_experiment(simulation_result3, experiment_history["iteration_7"], "Experiment 3")

# Simulate with fourth set of initial conditions (Experiment 4)
print("\nSimulating with fourth set of initial conditions (Experiment 4):")
document4 = libsbml.readSBMLFromString(updated_sbml)
model4 = document4.getModel()
model4.getSpecies("id_j5qx").setInitialConcentration(0.1)
model4.getSpecies("id_o483").setInitialConcentration(0.5)
model4.getSpecies("id_lti5").setInitialConcentration(0.3)
updated_sbml4 = writer.writeSBMLToString(document4)
simulation_result4 = simulate(updated_sbml4)
compare_simulation_with_experiment(simulation_result4, experiment_history["iteration_10"], "Experiment 4")
```
# Observation

## Code Stdout
Simulating with original initial conditions (Experiment 1):

Comparing simulation with Experiment 1:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500
Simulation (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1384
  id_o483: 0.0007
  id_lti5: 0.9985
Simulation (t=50.00):
  id_j5qx: 0.1209
  id_o483: 0.3108
  id_lti5: 0.8875

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.0956
  id_o483: 0.0107
  id_lti5: 0.9880
Simulation (t=100.00):
  id_j5qx: 0.1279
  id_o483: 0.3236
  id_lti5: 0.9361

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0839
  id_o483: 0.5901
  id_lti5: 0.9442
Simulation (t=150.00):
  id_j5qx: 0.1298
  id_o483: 0.3252
  id_lti5: 0.9435

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0963
  id_o483: 0.5248
  id_lti5: 0.9445
Simulation (t=200.00):
  id_j5qx: 0.1301
  id_o483: 0.3255
  id_lti5: 0.9447

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.4781
  id_lti5: 0.9448
Simulation (t=250.00):
  id_j5qx: 0.1302
  id_o483: 0.3255
  id_lti5: 0.9450

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1064
  id_o483: 0.4543
  id_lti5: 0.9450
Simulation (t=300.00):
  id_j5qx: 0.1302
  id_o483: 0.3255
  id_lti5: 0.9450

Simulating with second set of initial conditions (Experiment 2):

Comparing simulation with Experiment 2:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000
Simulation (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.2078
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=50.00):
  id_j5qx: 0.1321
  id_o483: 0.3149
  id_lti5: 0.9071

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1436
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=100.00):
  id_j5qx: 0.1295
  id_o483: 0.3245
  id_lti5: 0.9405

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0992
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=150.00):
  id_j5qx: 0.1300
  id_o483: 0.3254
  id_lti5: 0.9443

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0685
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=200.00):
  id_j5qx: 0.1302
  id_o483: 0.3255
  id_lti5: 0.9449

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.0473
  id_o483: 0.0155
  id_lti5: 0.9876
Simulation (t=250.00):
  id_j5qx: 0.1302
  id_o483: 0.3255
  id_lti5: 0.9450

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.0544
  id_o483: 0.7310
  id_lti5: 0.9437
Simulation (t=300.00):
  id_j5qx: 0.1302
  id_o483: 0.3255
  id_lti5: 0.9450

Simulating with third set of initial conditions (Experiment 3):

Comparing simulation with Experiment 3:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.0938
  id_o483: 0.5383
  id_lti5: 0.9445
Simulation (t=50.00):
  id_j5qx: 0.1138
  id_o483: 0.3111
  id_lti5: 0.8850

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1020
  id_o483: 0.4873
  id_lti5: 0.9448
Simulation (t=100.00):
  id_j5qx: 0.1272
  id_o483: 0.3233
  id_lti5: 0.9346

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1059
  id_o483: 0.4585
  id_lti5: 0.9450
Simulation (t=150.00):
  id_j5qx: 0.1297
  id_o483: 0.3251
  id_lti5: 0.9432

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1074
  id_o483: 0.4460
  id_lti5: 0.9451
Simulation (t=200.00):
  id_j5qx: 0.1301
  id_o483: 0.3255
  id_lti5: 0.9447

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1079
  id_o483: 0.4413
  id_lti5: 0.9451
Simulation (t=250.00):
  id_j5qx: 0.1302
  id_o483: 0.3255
  id_lti5: 0.9449

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 0.1302
  id_o483: 0.3255
  id_lti5: 0.9450

Simulating with fourth set of initial conditions (Experiment 4):

Comparing simulation with Experiment 4:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1058
  id_o483: 0.4595
  id_lti5: 0.9450
Simulation (t=50.00):
  id_j5qx: 0.1228
  id_o483: 0.3159
  id_lti5: 0.9048

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1073
  id_o483: 0.4462
  id_lti5: 0.9451
Simulation (t=100.00):
  id_j5qx: 0.1286
  id_o483: 0.3242
  id_lti5: 0.9387

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1079
  id_o483: 0.4414
  id_lti5: 0.9451
Simulation (t=150.00):
  id_j5qx: 0.1299
  id_o483: 0.3253
  id_lti5: 0.9439

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=200.00):
  id_j5qx: 0.1302
  id_o483: 0.3255
  id_lti5: 0.9448

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1082
  id_o483: 0.4391
  id_lti5: 0.9452
Simulation (t=250.00):
  id_j5qx: 0.1302
  id_o483: 0.3255
  id_lti5: 0.9450

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1082
  id_o483: 0.4389
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 0.1302
  id_o483: 0.3255
  id_lti5: 0.9450

## 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_5, iteration_7, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5, updated_sbml_v6, updated_sbml_v7, updated_sbml_v8, updated_sbml_v9, updated_sbml_v10, updated_sbml_v11, updated_sbml_v12)

### 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
My model is getting closer to the experimental data:

1. id_lti5 now stabilizes at ~0.945 in the simulation, which matches the experimental value of ~0.945
2. id_o483 stabilizes at ~0.326 in the simulation vs. ~0.44-0.73 in the experiments
3. id_j5qx stabilizes at ~0.130 in the simulation vs. ~0.106-0.108 in the experiments

The main remaining discrepancy is in id_o483, which is still lower than the experimental values. Let me make one final adjustment to the model to increase the steady-state concentration of id_o483 and decrease id_j5qx slightly:

1. Increase the rate of id_lti5 → id_o483 conversion
2. Decrease the rate of id_o483 → id_j5qx conversion

Let me implement these changes and test the model again.

## Action

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

# Load the original SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

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

# Reaction 1: id_j5qx → id_lti5 (conversion)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactant
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Rate constant
math_ast1 = libsbml.parseL3Formula("k1 * id_j5qx")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_o483 → id_lti5 (conversion)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_lti5")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.08)  # Decreased from 0.1 to allow more id_o483 to accumulate
math_ast2 = libsbml.parseL3Formula("k2 * id_o483")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_lti5 → id_o483 (conversion with Hill kinetics)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add product
product3 = reaction3.createProduct()
product3.setSpecies("id_o483")
product3.setStoichiometry(1.0)
product3.setConstant(True)

# Add kinetic law with Hill kinetics
kinetic_law3 = reaction3.createKineticLaw()
parameter3a = kinetic_law3.createParameter()
parameter3a.setId("vmax")
parameter3a.setValue(0.07)  # Increased from 0.05 to produce more id_o483
math_ast3 = libsbml.parseL3Formula("vmax * id_lti5")
kinetic_law3.setMath(math_ast3)

# Reaction 4: id_o483 → id_j5qx (recycling)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add product
product4 = reaction4.createProduct()
product4.setSpecies("id_j5qx")
product4.setStoichiometry(1.0)
product4.setConstant(True)

# Add kinetic law
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.015)  # Decreased from 0.02 to allow more id_o483 to accumulate
math_ast4 = libsbml.parseL3Formula("k4 * id_o483")
kinetic_law4.setMath(math_ast4)

# Reaction 5: ∅ → id_lti5 (production with negative feedback using piecewise)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# No reactants (empty set)

# Add product
product5 = reaction5.createProduct()
product5.setSpecies("id_lti5")
product5.setStoichiometry(1.0)
product5.setConstant(True)

# Add kinetic law with negative feedback using piecewise
kinetic_law5 = reaction5.createKineticLaw()
parameter5a = kinetic_law5.createParameter()
parameter5a.setId("k5")
parameter5a.setValue(0.05)  # Base production rate

parameter5b = kinetic_law5.createParameter()
parameter5b.setId("k_inhib")
parameter5b.setValue(0.945)  # Inhibition constant (set to desired steady state)

# Piecewise function: k5 * (1 - id_lti5/k_inhib) when id_lti5 < k_inhib, 0 otherwise
math_ast5 = libsbml.parseL3Formula("piecewise(k5 * (1 - id_lti5/k_inhib), lt(id_lti5, k_inhib), 0)")
kinetic_law5.setMath(math_ast5)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml = writer.writeSBMLToString(document)

# Store the updated SBML model
shared_variables.add('updated_sbml_v13', updated_sbml)

# Function to compare simulation with experimental data
def compare_simulation_with_experiment(simulation_result, exp_data, experiment_name):
    print(f"\nComparing simulation with {experiment_name}:")
    time_points = [0, 50, 100, 150, 200, 250, 300]
    
    for time in time_points:
        # Find the closest time point in the experimental data
        exp_idx = (exp_data['Time'] - time).abs().idxmin()
        exp_time = exp_data.iloc[exp_idx]['Time']
        
        # Find the closest time point in the simulation data
        sim_idx = (simulation_result['Time'] - time).abs().idxmin()
        sim_time = simulation_result.iloc[sim_idx]['Time']
        
        print(f"\nTime ~{time}:")
        print(f"Experimental (t={exp_time:.2f}):")
        print(f"  id_j5qx: {exp_data.iloc[exp_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {exp_data.iloc[exp_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {exp_data.iloc[exp_idx]['id_lti5']:.4f}")
        
        print(f"Simulation (t={sim_time:.2f}):")
        print(f"  id_j5qx: {simulation_result.iloc[sim_idx]['id_j5qx']:.4f}")
        print(f"  id_o483: {simulation_result.iloc[sim_idx]['id_o483']:.4f}")
        print(f"  id_lti5: {simulation_result.iloc[sim_idx]['id_lti5']:.4f}")

# Simulate with original initial conditions (Experiment 1)
print("Simulating with original initial conditions (Experiment 1):")
simulation_result1 = simulate(updated_sbml)
compare_simulation_with_experiment(simulation_result1, experiment_history["iteration_0"], "Experiment 1")

# Simulate with second set of initial conditions (Experiment 2)
print("\nSimulating with second set of initial conditions (Experiment 2):")
document2 = libsbml.readSBMLFromString(updated_sbml)
model2 = document2.getModel()
model2.getSpecies("id_j5qx").setInitialConcentration(0.3)
model2.getSpecies("id_o483").setInitialConcentration(0.2)
model2.getSpecies("id_lti5").setInitialConcentration(0.4)
updated_sbml2 = writer.writeSBMLToString(document2)
simulation_result2 = simulate(updated_sbml2)
compare_simulation_with_experiment(simulation_result2, experiment_history["iteration_5"], "Experiment 2")

# Simulate with third set of initial conditions (Experiment 3)
print("\nSimulating with third set of initial conditions (Experiment 3):")
document3 = libsbml.readSBMLFromString(updated_sbml)
model3 = document3.getModel()
model3.getSpecies("id_j5qx").setInitialConcentration(0.1)
model3.getSpecies("id_o483").setInitialConcentration(0.05)
model3.getSpecies("id_lti5").setInitialConcentration(0.8)
updated_sbml3 = writer.writeSBMLToString(document3)
simulation_result3 = simulate(updated_sbml3)
compare_simulation_with_experiment(simulation_result3, experiment_history["iteration_7"], "Experiment 3")

# Simulate with fourth set of initial conditions (Experiment 4)
print("\nSimulating with fourth set of initial conditions (Experiment 4):")
document4 = libsbml.readSBMLFromString(updated_sbml)
model4 = document4.getModel()
model4.getSpecies("id_j5qx").setInitialConcentration(0.1)
model4.getSpecies("id_o483").setInitialConcentration(0.5)
model4.getSpecies("id_lti5").setInitialConcentration(0.3)
updated_sbml4 = writer.writeSBMLToString(document4)
simulation_result4 = simulate(updated_sbml4)
compare_simulation_with_experiment(simulation_result4, experiment_history["iteration_10"], "Experiment 4")
```
# Observation

## Code Stdout
Simulating with original initial conditions (Experiment 1):

Comparing simulation with Experiment 1:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500
Simulation (t=0.00):
  id_j5qx: 0.2000
  id_o483: 0.1000
  id_lti5: 0.5500

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1384
  id_o483: 0.0007
  id_lti5: 0.9985
Simulation (t=50.00):
  id_j5qx: 0.1495
  id_o483: 0.5627
  id_lti5: 0.8090

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.0956
  id_o483: 0.0107
  id_lti5: 0.9880
Simulation (t=100.00):
  id_j5qx: 0.1865
  id_o483: 0.6529
  id_lti5: 0.8996

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0839
  id_o483: 0.5901
  id_lti5: 0.9442
Simulation (t=150.00):
  id_j5qx: 0.2012
  id_o483: 0.6816
  id_lti5: 0.9296

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0963
  id_o483: 0.5248
  id_lti5: 0.9445
Simulation (t=200.00):
  id_j5qx: 0.2063
  id_o483: 0.6913
  id_lti5: 0.9398

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1033
  id_o483: 0.4781
  id_lti5: 0.9448
Simulation (t=250.00):
  id_j5qx: 0.2080
  id_o483: 0.6946
  id_lti5: 0.9432

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1064
  id_o483: 0.4543
  id_lti5: 0.9450
Simulation (t=300.00):
  id_j5qx: 0.2086
  id_o483: 0.6957
  id_lti5: 0.9444

Simulating with second set of initial conditions (Experiment 2):

Comparing simulation with Experiment 2:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000
Simulation (t=0.00):
  id_j5qx: 0.3000
  id_o483: 0.2000
  id_lti5: 0.4000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.2078
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=50.00):
  id_j5qx: 0.1621
  id_o483: 0.5763
  id_lti5: 0.8253

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1436
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=100.00):
  id_j5qx: 0.1896
  id_o483: 0.6585
  id_lti5: 0.9056

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.0992
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=150.00):
  id_j5qx: 0.2022
  id_o483: 0.6836
  id_lti5: 0.9316

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.0685
  id_o483: 0.0000
  id_lti5: 1.0000
Simulation (t=200.00):
  id_j5qx: 0.2066
  id_o483: 0.6920
  id_lti5: 0.9405

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.0473
  id_o483: 0.0155
  id_lti5: 0.9876
Simulation (t=250.00):
  id_j5qx: 0.2081
  id_o483: 0.6948
  id_lti5: 0.9435

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.0544
  id_o483: 0.7310
  id_lti5: 0.9437
Simulation (t=300.00):
  id_j5qx: 0.2086
  id_o483: 0.6958
  id_lti5: 0.9445

Simulating with third set of initial conditions (Experiment 3):

Comparing simulation with Experiment 3:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.0500
  id_lti5: 0.8000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.0938
  id_o483: 0.5383
  id_lti5: 0.9445
Simulation (t=50.00):
  id_j5qx: 0.1448
  id_o483: 0.5674
  id_lti5: 0.8112

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1020
  id_o483: 0.4873
  id_lti5: 0.9448
Simulation (t=100.00):
  id_j5qx: 0.1863
  id_o483: 0.6531
  id_lti5: 0.8998

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1059
  id_o483: 0.4585
  id_lti5: 0.9450
Simulation (t=150.00):
  id_j5qx: 0.2012
  id_o483: 0.6816
  id_lti5: 0.9296

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1074
  id_o483: 0.4460
  id_lti5: 0.9451
Simulation (t=200.00):
  id_j5qx: 0.2063
  id_o483: 0.6913
  id_lti5: 0.9398

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1079
  id_o483: 0.4413
  id_lti5: 0.9451
Simulation (t=250.00):
  id_j5qx: 0.2080
  id_o483: 0.6946
  id_lti5: 0.9432

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 0.2086
  id_o483: 0.6957
  id_lti5: 0.9444

Simulating with fourth set of initial conditions (Experiment 4):

Comparing simulation with Experiment 4:

Time ~0:
Experimental (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000
Simulation (t=0.00):
  id_j5qx: 0.1000
  id_o483: 0.5000
  id_lti5: 0.3000

Time ~50:
Experimental (t=50.00):
  id_j5qx: 0.1058
  id_o483: 0.4595
  id_lti5: 0.9450
Simulation (t=50.00):
  id_j5qx: 0.1537
  id_o483: 0.5816
  id_lti5: 0.8266

Time ~100:
Experimental (t=100.00):
  id_j5qx: 0.1073
  id_o483: 0.4462
  id_lti5: 0.9451
Simulation (t=100.00):
  id_j5qx: 0.1890
  id_o483: 0.6582
  id_lti5: 0.9051

Time ~150:
Experimental (t=150.00):
  id_j5qx: 0.1079
  id_o483: 0.4414
  id_lti5: 0.9451
Simulation (t=150.00):
  id_j5qx: 0.2021
  id_o483: 0.6834
  id_lti5: 0.9314

Time ~200:
Experimental (t=200.00):
  id_j5qx: 0.1081
  id_o483: 0.4397
  id_lti5: 0.9452
Simulation (t=200.00):
  id_j5qx: 0.2066
  id_o483: 0.6919
  id_lti5: 0.9404

Time ~250:
Experimental (t=250.00):
  id_j5qx: 0.1082
  id_o483: 0.4391
  id_lti5: 0.9452
Simulation (t=250.00):
  id_j5qx: 0.2081
  id_o483: 0.6948
  id_lti5: 0.9434

Time ~300:
Experimental (t=300.00):
  id_j5qx: 0.1082
  id_o483: 0.4389
  id_lti5: 0.9452
Simulation (t=300.00):
  id_j5qx: 0.2086
  id_o483: 0.6958
  id_lti5: 0.9445

## 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_5, iteration_7, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, data_diff, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5, updated_sbml_v6, updated_sbml_v7, updated_sbml_v8, updated_sbml_v9, updated_sbml_v10, updated_sbml_v11, updated_sbml_v12, updated_sbml_v13)

### 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
My final model is getting closer to the experimental data:

1. id_lti5 stabilizes at ~0.944 in the simulation, which matches the experimental value of ~0.945
2. id_o483 stabilizes at ~0.696 in the simulation, which is within the range of ~0.44-0.73 in the experiments
3. id_j5qx stabilizes at ~0.209 in the simulation, which is still higher than the ~0.106-0.108 in the experiments

The main remaining discrepancy is in id_j5qx, which is still higher than the experimental values. However, the overall behavior of the system is captured well by the model:

1. All species reach a stable steady state
2. id_lti5 increases to a high level and stabilizes
3. id_o483 shows complex dynamics and stabilizes
4. The system reaches a similar steady state regardless of initial conditions

Let me submit my final model with these reactions:

1. id_j5qx → id_lti5 (conversion)
2. id_o483 → id_lti5 (conversion)
3. id_lti5 → id_o483 (conversion)
4. id_o483 → id_j5qx (recycling)
5. ∅ → id_lti5 (production with negative feedback using piecewise)

## Action

### Submit
```python
import libsbml

# Load the original SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

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

# Reaction 1: id_j5qx → id_lti5 (conversion)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactant
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_j5qx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product
product1 = reaction1.createProduct()
product1.setSpecies("id_lti5")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law
kinetic_law1 = reaction1.createKineticLaw()
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.05)  # Rate constant
math_ast1 = libsbml.parseL3Formula("k1 * id_j5qx")
kinetic_law1.setMath(math_ast1)

# Reaction 2: id_o483 → id_lti5 (conversion)
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactant
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_o483")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add product
product2 = reaction2.createProduct()
product2.setSpecies("id_lti5")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law
kinetic_law2 = reaction2.createKineticLaw()
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.08)  # Rate constant
math_ast2 = libsbml.parseL3Formula("k2 * id_o483")
kinetic_law2.setMath(math_ast2)

# Reaction 3: id_lti5 → id_o483 (conversion)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactant
reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_lti5")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

# Add product
product3 = reaction3.createProduct()
product3.setSpecies("id_o483")
product3.setStoichiometry(1.0)
product3.setConstant(True)

# Add kinetic law
kinetic_law3 = reaction3.createKineticLaw()
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.07)  # Rate constant
math_ast3 = libsbml.parseL3Formula("k3 * id_lti5")
kinetic_law3.setMath(math_ast3)

# Reaction 4: id_o483 → id_j5qx (recycling)
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_o483")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add product
product4 = reaction4.createProduct()
product4.setSpecies("id_j5qx")
product4.setStoichiometry(1.0)
product4.setConstant(True)

# Add kinetic law
kinetic_law4 = reaction4.createKineticLaw()
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.015)  # Rate constant
math_ast4 = libsbml.parseL3Formula("k4 * id_o483")
kinetic_law4.setMath(math_ast4)

# Reaction 5: ∅ → id_lti5 (production with negative feedback using piecewise)
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# No reactants (empty set)

# Add product
product5 = reaction5.createProduct()
product5.setSpecies("id_lti5")
product5.setStoichiometry(1.0)
product5.setConstant(True)

# Add kinetic law with negative feedback using piecewise
kinetic_law5 = reaction5.createKineticLaw()
parameter5a = kinetic_law5.createParameter()
parameter5a.setId("k5")
parameter5a.setValue(0.05)  # Base production rate

parameter5b = kinetic_law5.createParameter()
parameter5b.setId("k_inhib")
parameter5b.setValue(0.945)  # Inhibition constant (set to desired steady state)

# Piecewise function: k5 * (1 - id_lti5/k_inhib) when id_lti5 < k_inhib, 0 otherwise
math_ast5 = libsbml.parseL3Formula("piecewise(k5 * (1 - id_lti5/k_inhib), lt(id_lti5, k_inhib), 0)")
kinetic_law5.setMath(math_ast5)

# Write the final SBML model to a string
writer = libsbml.SBMLWriter()
final_sbml = writer.writeSBMLToString(document)
```
