
                # 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/level3/version1/core" xmlns:layout="http://www.sbml.org/sbml/level3/version1/layout/version1" xmlns:render="http://www.sbml.org/sbml/level3/version1/render/version1" level="3" version="1" layout:required="false" render:required="false">
  <model id="id_1noa" substanceUnits="id_3ywo" timeUnits="id_d77q" volumeUnits="id_68qd" areaUnits="id_jg67" lengthUnits="id_zrq5" extentUnits="id_3ywo">
    <listOfUnitDefinitions>
      <unitDefinition id="id_zrq5">
        <listOfUnits>
          <unit kind="metre" exponent="1" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_jg67">
        <listOfUnits>
          <unit kind="metre" exponent="2" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_68qd">
        <listOfUnits>
          <unit kind="litre" exponent="1" scale="-3" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_d77q">
        <listOfUnits>
          <unit kind="second" exponent="1" scale="0" multiplier="86400"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_3ywo">
        <listOfUnits>
          <unit kind="item" exponent="1" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_87kj" spatialDimensions="3" size="1" units="id_68qd" constant="true"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_8n7o" compartment="id_87kj" initialConcentration="11080778" substanceUnits="id_3ywo" hasOnlySubstanceUnits="false" boundaryCondition="false" constant="false"/>
      <species id="id_caoz" compartment="id_87kj" initialConcentration="193" substanceUnits="id_3ywo" hasOnlySubstanceUnits="false" boundaryCondition="false" constant="false"/>
      <species id="id_ty7g" compartment="id_87kj" initialConcentration="2" substanceUnits="id_3ywo" hasOnlySubstanceUnits="false" boundaryCondition="false" constant="false"/>
      <species id="id_250q" compartment="id_87kj" initialConcentration="11081000" substanceUnits="id_3ywo" hasOnlySubstanceUnits="false" boundaryCondition="true" constant="true"/>
      <species id="id_1wsx" compartment="id_87kj" initialConcentration="27" substanceUnits="id_3ywo" hasOnlySubstanceUnits="false" 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 where I need to discover the missing reactions. Let me first understand what I have in the SBML model:

1. There are 5 species in the model:
   - id_8n7o: Initial concentration 11080778, not a boundary condition
   - id_caoz: Initial concentration 193, not a boundary condition
   - id_ty7g: Initial concentration 2, not a boundary condition
   - id_250q: Initial concentration 11081000, boundary condition (constant)
   - id_1wsx: Initial concentration 27, not a boundary condition

2. There are no reactions defined yet, which is what I need to discover.

To start understanding this system, I should first observe the default behavior without any perturbations. This will give me baseline data about how these species interact over time.

## 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: 184 rows × 6 columns. 

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

Time   id_8n7o  id_caoz  id_ty7g  id_1wsx  id_250q
0  1.11e+07 1.93e+02 2.00e+00 2.70e+01 1.11e+07
...
3.00e+00  1.11e+07 4.46e+02 1.31e+01 1.41e+02 1.11e+07
...
6.00e+00  1.11e+07 1.11e+03 4.99e+01 4.09e+02 1.11e+07
...
9.00e+00  1.11e+07 2.81e+03 1.50e+02 1.08e+03 1.11e+07
...
1.20e+01  1.11e+07 7.18e+03 4.08e+02 2.78e+03 1.11e+07
...
1.50e+01  1.11e+07 1.83e+04 1.07e+03 7.11e+03 1.11e+07
...
1.80e+01  1.10e+07 4.66e+04 2.77e+03 1.81e+04 1.11e+07
...
2.10e+01  1.09e+07 1.18e+05 7.09e+03 4.61e+04 1.11e+07
...
2.40e+01  1.07e+07 2.92e+05 1.80e+04 1.16e+05 1.11e+07
...
2.70e+01  1.01e+07 6.94e+05 4.52e+04 2.85e+05 1.11e+07
...
3.00e+01  8.81e+06 1.50e+06 1.10e+05 6.64e+05 1.11e+07
...
3.30e+01  6.75e+06 2.69e+06 2.53e+05 1.39e+06 1.11e+07
...
3.60e+01  4.34e+06 3.73e+06 5.29e+05 2.48e+06 1.11e+07
...
3.90e+01  2.42e+06 4.00e+06 9.74e+05 3.69e+06 1.11e+07
...
4.20e+01  1.27e+06 3.55e+06 1.58e+06 4.69e+06 1.11e+07
...
4.50e+01  6.71e+05 2.81e+06 2.31e+06 5.30e+06 1.11e+07
...
4.80e+01  3.71e+05 2.08e+06 3.09e+06 5.54e+06 1.11e+07
...
5.10e+01  2.18e+05 1.49e+06 3.89e+06 5.49e+06 1.11e+07
...
5.40e+01  1.36e+05 1.04e+06 4.66e+06 5.24e+06 1.11e+07
...
5.70e+01  8.99e+04 7.23e+05 5.39e+06 4.88e+06 1.11e+07
...
6.00e+01  6.25e+04 4.97e+05 6.06e+06 4.46e+06 1.11e+07
...
6.30e+01  4.56e+04 3.40e+05 6.67e+06 4.02e+06 1.11e+07
...
6.60e+01  3.46e+04 2.32e+05 7.22e+06 3.59e+06 1.11e+07
...
6.90e+01  2.73e+04 1.59e+05 7.71e+06 3.19e+06 1.11e+07
...
7.20e+01  2.22e+04 1.08e+05 8.14e+06 2.81e+06 1.11e+07
...
7.50e+01  1.85e+04 7.42e+04 8.52e+06 2.47e+06 1.11e+07
...
7.80e+01  1.58e+04 5.09e+04 8.85e+06 2.16e+06 1.11e+07
...
8.10e+01  1.38e+04 3.51e+04 9.14e+06 1.89e+06 1.11e+07
...
8.40e+01  1.23e+04 2.43e+04 9.40e+06 1.65e+06 1.11e+07
...
8.70e+01  1.11e+04 1.69e+04 9.62e+06 1.43e+06 1.11e+07
...
9.00e+01  1.02e+04 1.19e+04 9.81e+06 1.25e+06 1.11e+07
...
9.30e+01  9.42e+03 8.41e+03 9.98e+06 1.08e+06 1.11e+07
...
9.60e+01  8.81e+03 6.02e+03 1.01e+07 9.41e+05 1.11e+07
...
9.90e+01  8.32e+03 4.35e+03 1.03e+07 8.17e+05 1.11e+07
...
1.02e+02  7.92e+03 3.19e+03 1.04e+07 7.09e+05 1.11e+07
...
1.05e+02  7.58e+03 2.37e+03 1.05e+07 6.15e+05 1.11e+07
...
1.08e+02  7.30e+03 1.78e+03 1.05e+07 5.33e+05 1.11e+07
...
1.11e+02  7.07e+03 1.36e+03 1.06e+07 4.62e+05 1.11e+07
...
1.14e+02  6.87e+03 1.05e+03 1.07e+07 4.01e+05 1.11e+07
...
1.17e+02  6.71e+03 8.25e+02 1.07e+07 3.47e+05 1.11e+07
...
1.20e+02  6.57e+03 6.56e+02 1.08e+07 3.01e+05 1.11e+07
...
1.23e+02  6.45e+03 5.28e+02 1.08e+07 2.61e+05 1.11e+07
...
1.26e+02  6.35e+03 4.29e+02 1.08e+07 2.26e+05 1.11e+07
...
1.29e+02  6.26e+03 3.52e+02 1.09e+07 1.96e+05 1.11e+07
...
1.32e+02  6.19e+03 2.91e+02 1.09e+07 1.70e+05 1.11e+07
...
1.35e+02  6.12e+03 2.43e+02 1.09e+07 1.47e+05 1.11e+07
...
1.38e+02  6.07e+03 2.04e+02 1.09e+07 1.27e+05 1.11e+07
...
1.41e+02  6.02e+03 1.72e+02 1.10e+07 1.10e+05 1.11e+07
...
1.44e+02  5.98e+03 1.46e+02 1.10e+07 9.57e+04 1.11e+07
...
1.83e+02  5.77e+03 2.03e+01 1.11e+07 1.48e+04 1.11e+07

## 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
Now I have some data from observing the system without any perturbations. Let me analyze this data to understand the dynamics of the species and try to infer the missing reactions.

Looking at the time series data:
1. `id_250q` remains constant at ~11.1e+07 (as expected since it's a boundary species)
2. `id_8n7o` starts high (~11.1e+07) and decreases over time
3. `id_caoz` starts low (193), increases to a peak (~4.0e+06 around t=39), then decreases
4. `id_ty7g` starts very low (2) and continuously increases to ~1.1e+07
5. `id_1wsx` starts low (27), increases to a peak (~5.54e+06 around t=48), then decreases

Let me write some code to visualize and analyze this data to better 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

# Get the data from the experiment
data = experiment_history["iteration_0"]

# Print the first few rows to confirm we have the data
print("First few rows of data:")
print(data.head())

# Print the last few rows
print("\nLast few rows of data:")
print(data.tail())

# Calculate the sum of all non-boundary species at each time point
data['sum_non_boundary'] = data['id_8n7o'] + data['id_caoz'] + data['id_ty7g'] + data['id_1wsx']
print("\nSum of non-boundary species (first few rows):")
print(data[['Time', 'sum_non_boundary']].head())
print("\nSum of non-boundary species (last few rows):")
print(data[['Time', 'sum_non_boundary']].tail())

# Check if the total amount of non-boundary species is conserved
print("\nIs the sum of non-boundary species approximately constant?")
print(f"Min: {data['sum_non_boundary'].min()}, Max: {data['sum_non_boundary'].max()}")
print(f"Mean: {data['sum_non_boundary'].mean()}, Std: {data['sum_non_boundary'].std()}")

# Calculate the rate of change for each species
# We'll use simple finite differences
data['d_id_8n7o'] = np.gradient(data['id_8n7o'], data['Time'])
data['d_id_caoz'] = np.gradient(data['id_caoz'], data['Time'])
data['d_id_ty7g'] = np.gradient(data['id_ty7g'], data['Time'])
data['d_id_1wsx'] = np.gradient(data['id_1wsx'], data['Time'])

# Print the rate of change at a few time points
print("\nRate of change at selected time points:")
selected_times = [0, 30, 60, 90, 120, 150, 180]
for t in selected_times:
    idx = data[data['Time'] >= t].index[0]
    print(f"Time {data.loc[idx, 'Time']:.1f}:")
    print(f"  d_id_8n7o: {data.loc[idx, 'd_id_8n7o']:.2e}")
    print(f"  d_id_caoz: {data.loc[idx, 'd_id_caoz']:.2e}")
    print(f"  d_id_ty7g: {data.loc[idx, 'd_id_ty7g']:.2e}")
    print(f"  d_id_1wsx: {data.loc[idx, 'd_id_1wsx']:.2e}")

# Let's look for relationships between species concentrations and rates
# For example, is the rate of change of id_8n7o proportional to id_8n7o?
print("\nCorrelation between species concentrations and their rates of change:")
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    corr = np.corrcoef(data[species], data[f'd_{species}'])[0, 1]
    print(f"{species} concentration vs. rate: {corr:.4f}")

# Let's also check if there are correlations between different species
print("\nCorrelation matrix between species:")
corr_matrix = data[['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']].corr()
print(corr_matrix)

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

# Parse the SBML model to understand the structure
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

print("\nModel information:")
print(f"Number of species: {model.getNumSpecies()}")
print(f"Number of reactions: {model.getNumReactions()}")
print(f"Number of compartments: {model.getNumCompartments()}")

# Print species information
print("\nSpecies information:")
for i in range(model.getNumSpecies()):
    species = model.getSpecies(i)
    print(f"Species {i+1}: {species.getId()}")
    print(f"  Initial concentration: {species.getInitialConcentration()}")
    print(f"  Boundary condition: {species.getBoundaryCondition()}")
    print(f"  Constant: {species.getConstant()}")
```
# 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 in the allowed libraries. Let me revise my code to only use the allowed libraries for analysis.

I'll focus on analyzing the data to understand the relationships between species and infer the possible reactions. I'll look at:
1. Conservation of mass (sum of non-boundary species)
2. Rates of change for each species
3. Correlations between species concentrations and their rates of change
4. Correlations between different species

This should help me identify potential reaction mechanisms.

## Action

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

# Get the data from the experiment
data = experiment_history["iteration_0"]

# Print the first few rows to confirm we have the data
print("First few rows of data:")
print(data.head())

# Print the last few rows
print("\nLast few rows of data:")
print(data.tail())

# Calculate the sum of all non-boundary species at each time point
data['sum_non_boundary'] = data['id_8n7o'] + data['id_caoz'] + data['id_ty7g'] + data['id_1wsx']
print("\nSum of non-boundary species (first few rows):")
print(data[['Time', 'sum_non_boundary']].head())
print("\nSum of non-boundary species (last few rows):")
print(data[['Time', 'sum_non_boundary']].tail())

# Check if the total amount of non-boundary species is conserved
print("\nIs the sum of non-boundary species approximately constant?")
print(f"Min: {data['sum_non_boundary'].min()}, Max: {data['sum_non_boundary'].max()}")
print(f"Mean: {data['sum_non_boundary'].mean()}, Std: {data['sum_non_boundary'].std()}")

# Calculate the rate of change for each species
# We'll use simple finite differences
data['d_id_8n7o'] = np.gradient(data['id_8n7o'], data['Time'])
data['d_id_caoz'] = np.gradient(data['id_caoz'], data['Time'])
data['d_id_ty7g'] = np.gradient(data['id_ty7g'], data['Time'])
data['d_id_1wsx'] = np.gradient(data['id_1wsx'], data['Time'])

# Print the rate of change at a few time points
print("\nRate of change at selected time points:")
selected_times = [0, 30, 60, 90, 120, 150, 180]
for t in selected_times:
    idx = data[data['Time'] >= t].index[0]
    print(f"Time {data.loc[idx, 'Time']:.1f}:")
    print(f"  d_id_8n7o: {data.loc[idx, 'd_id_8n7o']:.2e}")
    print(f"  d_id_caoz: {data.loc[idx, 'd_id_caoz']:.2e}")
    print(f"  d_id_ty7g: {data.loc[idx, 'd_id_ty7g']:.2e}")
    print(f"  d_id_1wsx: {data.loc[idx, 'd_id_1wsx']:.2e}")

# Let's look for relationships between species concentrations and rates
# For example, is the rate of change of id_8n7o proportional to id_8n7o?
print("\nCorrelation between species concentrations and their rates of change:")
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    corr = np.corrcoef(data[species], data[f'd_{species}'])[0, 1]
    print(f"{species} concentration vs. rate: {corr:.4f}")

# Let's also check if there are correlations between different species
print("\nCorrelation matrix between species:")
corr_matrix = data[['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']].corr()
print(corr_matrix)

# Let's check for potential relationships between rates and products of species
# This might indicate mass action kinetics
print("\nChecking for mass action kinetics relationships:")

# Check if d_id_8n7o is proportional to id_8n7o (first-order decay)
corr_8n7o_decay = np.corrcoef(data['id_8n7o'], -data['d_id_8n7o'])[0, 1]
print(f"Correlation between id_8n7o and -d_id_8n7o: {corr_8n7o_decay:.4f}")

# Check if d_id_8n7o is proportional to id_8n7o * id_caoz (second-order reaction)
data['id_8n7o_x_id_caoz'] = data['id_8n7o'] * data['id_caoz']
corr_8n7o_caoz = np.corrcoef(data['id_8n7o_x_id_caoz'], -data['d_id_8n7o'])[0, 1]
print(f"Correlation between id_8n7o*id_caoz and -d_id_8n7o: {corr_8n7o_caoz:.4f}")

# Check if d_id_8n7o is proportional to id_8n7o * id_ty7g (second-order reaction)
data['id_8n7o_x_id_ty7g'] = data['id_8n7o'] * data['id_ty7g']
corr_8n7o_ty7g = np.corrcoef(data['id_8n7o_x_id_ty7g'], -data['d_id_8n7o'])[0, 1]
print(f"Correlation between id_8n7o*id_ty7g and -d_id_8n7o: {corr_8n7o_ty7g:.4f}")

# Check if d_id_8n7o is proportional to id_8n7o * id_1wsx (second-order reaction)
data['id_8n7o_x_id_1wsx'] = data['id_8n7o'] * data['id_1wsx']
corr_8n7o_1wsx = np.corrcoef(data['id_8n7o_x_id_1wsx'], -data['d_id_8n7o'])[0, 1]
print(f"Correlation between id_8n7o*id_1wsx and -d_id_8n7o: {corr_8n7o_1wsx:.4f}")

# Check if the rates of change sum to zero (conservation of mass)
data['sum_rates'] = data['d_id_8n7o'] + data['d_id_caoz'] + data['d_id_ty7g'] + data['d_id_1wsx']
print("\nSum of rates of change (should be close to zero if mass is conserved):")
print(f"Mean: {data['sum_rates'].mean()}, Std: {data['sum_rates'].std()}")

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

# Parse the SBML model to understand the structure
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

print("\nModel information:")
print(f"Number of species: {model.getNumSpecies()}")
print(f"Number of reactions: {model.getNumReactions()}")
print(f"Number of compartments: {model.getNumCompartments()}")

# Print species information
print("\nSpecies information:")
for i in range(model.getNumSpecies()):
    species = model.getSpecies(i)
    print(f"Species {i+1}: {species.getId()}")
    print(f"  Initial concentration: {species.getInitialConcentration()}")
    print(f"  Boundary condition: {species.getBoundaryCondition()}")
    print(f"  Constant: {species.getConstant()}")
```
# Observation

## Code Stdout
First few rows of data:
        id_8n7o     id_caoz    id_ty7g     id_1wsx     id_250q  Time
0  1.108078e+07  193.000000   2.000000   27.000000  11081000.0   0.0
1  1.108069e+07  251.326651   3.962829   55.910131  11081000.0   1.0
2  1.108057e+07  332.752133   7.497062   92.949434  11081000.0   2.0
3  1.108040e+07  445.548519  13.068573  141.434861  11081000.0   3.0
4  1.108017e+07  601.055871  21.329173  205.859118  11081000.0   4.0

Last few rows of data:
         id_8n7o    id_caoz       id_ty7g       id_1wsx     id_250q   Time
179  5775.566112  24.667175  1.105724e+07  17957.293008  11081000.0  179.0
180  5773.368567  23.494121  1.105808e+07  17118.994295  11081000.0  180.0
181  5771.274391  22.377909  1.105889e+07  16319.826728  11081000.0  181.0
182  5769.278690  21.315683  1.105965e+07  15557.964628  11081000.0  182.0
183  5767.376799  20.304735  1.106038e+07  14831.666104  11081000.0  183.0

Sum of non-boundary species (first few rows):
   Time  sum_non_boundary
0   0.0        11081000.0
1   1.0        11081000.0
2   2.0        11081000.0
3   3.0        11081000.0
4   4.0        11081000.0

Sum of non-boundary species (last few rows):
      Time  sum_non_boundary
179  179.0        11081000.0
180  180.0        11081000.0
181  181.0        11081000.0
182  182.0        11081000.0
183  183.0        11081000.0

Is the sum of non-boundary species approximately constant?
Min: 11080999.999999993, Max: 11081000.000000015
Mean: 11081000.000000006, Std: 5.93668868885888e-09

Rate of change at selected time points:
Time 0.0:
  d_id_8n7o: -8.92e+01
  d_id_caoz: 5.83e+01
  d_id_ty7g: 1.96e+00
  d_id_1wsx: 2.89e+01
Time 30.0:
  d_id_8n7o: -5.55e+05
  d_id_caoz: 3.44e+05
  d_id_ty7g: 3.22e+04
  d_id_1wsx: 1.79e+05
Time 60.0:
  d_id_8n7o: -7.09e+03
  d_id_caoz: -6.27e+04
  d_id_ty7g: 2.14e+05
  d_id_1wsx: -1.44e+05
Time 90.0:
  d_id_8n7o: -2.79e+02
  d_id_caoz: -1.39e+03
  d_id_ty7g: 5.99e+04
  d_id_1wsx: -5.82e+04
Time 120.0:
  d_id_8n7o: -4.30e+01
  d_id_caoz: -4.90e+01
  d_id_ty7g: 1.45e+04
  d_id_1wsx: -1.44e+04
Time 150.0:
  d_id_8n7o: -9.23e+00
  d_id_caoz: -5.56e+00
  d_id_ty7g: 3.45e+03
  d_id_1wsx: -3.43e+03
Time 180.0:
  d_id_8n7o: -2.15e+00
  d_id_caoz: -1.14e+00
  d_id_ty7g: 8.22e+02
  d_id_1wsx: -8.19e+02

Correlation between species concentrations and their rates of change:
id_8n7o concentration vs. rate: -0.2986
id_caoz concentration vs. rate: 0.0000
id_ty7g concentration vs. rate: -0.2856
id_1wsx concentration vs. rate: -0.0005

Correlation matrix between species:
          id_8n7o   id_caoz   id_ty7g   id_1wsx
id_8n7o  1.000000  0.085982 -0.840314 -0.254504
id_caoz  0.085982  1.000000 -0.532408  0.606129
id_ty7g -0.840314 -0.532408  1.000000 -0.285426
id_1wsx -0.254504  0.606129 -0.285426  1.000000

Checking for mass action kinetics relationships:
Correlation between id_8n7o and -d_id_8n7o: 0.2986
Correlation between id_8n7o*id_caoz and -d_id_8n7o: 0.9946
Correlation between id_8n7o*id_ty7g and -d_id_8n7o: 0.8292
Correlation between id_8n7o*id_1wsx and -d_id_8n7o: 0.9702

Sum of rates of change (should be close to zero if mass is conserved):
Mean: -1.495449175120919e-11, Std: 7.957675001083867e-10

Model information:
Number of species: 5
Number of reactions: 0
Number of compartments: 1

Species information:
Species 1: id_8n7o
  Initial concentration: 11080778.0
  Boundary condition: False
  Constant: False
Species 2: id_caoz
  Initial concentration: 193.0
  Boundary condition: False
  Constant: False
Species 3: id_ty7g
  Initial concentration: 2.0
  Boundary condition: False
  Constant: False
Species 4: id_250q
  Initial concentration: 11081000.0
  Boundary condition: True
  Constant: True
Species 5: id_1wsx
  Initial concentration: 27.0
  Boundary condition: False
  Constant: False

## 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)

### 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
Based on the analysis of the data, I've made several important observations:

1. **Conservation of Mass**: The sum of all non-boundary species remains constant at 11,081,000, which is exactly equal to the initial concentration of the boundary species `id_250q`. This suggests that the total mass in the system is conserved.

2. **Correlations between rates and species products**:
   - There's a very strong correlation (0.9946) between `id_8n7o * id_caoz` and the negative rate of change of `id_8n7o`. This strongly suggests a second-order reaction where `id_8n7o` and `id_caoz` interact.
   - There's also a strong correlation (0.9702) between `id_8n7o * id_1wsx` and the negative rate of change of `id_8n7o`.
   - The correlation between `id_8n7o * id_ty7g` and the negative rate of change of `id_8n7o` is also significant (0.8292).

3. **Species Behavior**:
   - `id_8n7o` starts high and decreases
   - `id_caoz` increases then decreases
   - `id_ty7g` continuously increases
   - `id_1wsx` increases then decreases

4. **Sum of Rates**: The sum of all rates of change is very close to zero, confirming mass conservation.

Based on these observations, I'm starting to form a hypothesis about the reaction network. It appears that:

1. `id_8n7o` is being consumed in reactions with `id_caoz` and possibly with `id_1wsx`
2. `id_ty7g` is being produced and accumulates over time
3. `id_1wsx` is both produced and consumed

Let me now try to formulate specific reaction hypotheses and test them. I'll start by looking at the rates of change of all species and see if I can identify patterns that suggest specific reactions.

## Action

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

# Access the data we stored previously
data = shared_variables.access('data')

# Let's look at the rates of change more carefully
print("Checking for relationships between rates of change:")

# Check if d_id_caoz is proportional to id_8n7o * id_caoz
corr_caoz_prod = np.corrcoef(data['id_8n7o_x_id_caoz'], data['d_id_caoz'])[0, 1]
print(f"Correlation between id_8n7o*id_caoz and d_id_caoz: {corr_caoz_prod:.4f}")

# Check if d_id_ty7g is proportional to id_8n7o * id_caoz
corr_ty7g_prod = np.corrcoef(data['id_8n7o_x_id_caoz'], data['d_id_ty7g'])[0, 1]
print(f"Correlation between id_8n7o*id_caoz and d_id_ty7g: {corr_ty7g_prod:.4f}")

# Check if d_id_1wsx is proportional to id_8n7o * id_caoz
corr_1wsx_prod = np.corrcoef(data['id_8n7o_x_id_caoz'], data['d_id_1wsx'])[0, 1]
print(f"Correlation between id_8n7o*id_caoz and d_id_1wsx: {corr_1wsx_prod:.4f}")

# Let's check the stoichiometric relationships
# If id_8n7o + id_caoz -> id_ty7g + id_1wsx, then:
# 1. The rate of decrease of id_8n7o should equal the rate of decrease of id_caoz
# 2. The rate of increase of id_ty7g should equal the rate of increase of id_1wsx
# 3. The sum of rates should be zero

# Calculate the ratio of rates at each time point
data['ratio_8n7o_caoz'] = -data['d_id_8n7o'] / -data['d_id_caoz']
data['ratio_ty7g_1wsx'] = data['d_id_ty7g'] / data['d_id_1wsx']

# Filter out points where denominators are close to zero to avoid division by zero
valid_ratio_8n7o_caoz = data[abs(data['d_id_caoz']) > 1e-10]['ratio_8n7o_caoz']
valid_ratio_ty7g_1wsx = data[abs(data['d_id_1wsx']) > 1e-10]['ratio_ty7g_1wsx']

print("\nStoichiometric ratios:")
print(f"Ratio of -d_id_8n7o / -d_id_caoz (mean): {valid_ratio_8n7o_caoz.mean()}")
print(f"Ratio of d_id_ty7g / d_id_1wsx (mean): {valid_ratio_ty7g_1wsx.mean()}")

# Let's check if there's a second reaction involving id_1wsx
# For example, id_8n7o + id_1wsx -> id_ty7g
corr_8n7o_1wsx_ty7g = np.corrcoef(data['id_8n7o_x_id_1wsx'], data['d_id_ty7g'])[0, 1]
print(f"\nCorrelation between id_8n7o*id_1wsx and d_id_ty7g: {corr_8n7o_1wsx_ty7g:.4f}")

# Let's also check if there's a reaction id_caoz + id_1wsx -> id_ty7g
data['id_caoz_x_id_1wsx'] = data['id_caoz'] * data['id_1wsx']
corr_caoz_1wsx_ty7g = np.corrcoef(data['id_caoz_x_id_1wsx'], data['d_id_ty7g'])[0, 1]
print(f"Correlation between id_caoz*id_1wsx and d_id_ty7g: {corr_caoz_1wsx_ty7g:.4f}")

# Let's check if there's a reaction id_8n7o + id_ty7g -> id_caoz + id_1wsx
data['id_8n7o_x_id_ty7g'] = data['id_8n7o'] * data['id_ty7g']
corr_8n7o_ty7g_caoz = np.corrcoef(data['id_8n7o_x_id_ty7g'], data['d_id_caoz'])[0, 1]
print(f"Correlation between id_8n7o*id_ty7g and d_id_caoz: {corr_8n7o_ty7g_caoz:.4f}")

# Let's check if there's a reaction id_caoz + id_ty7g -> id_8n7o + id_1wsx
data['id_caoz_x_id_ty7g'] = data['id_caoz'] * data['id_ty7g']
corr_caoz_ty7g_8n7o = np.corrcoef(data['id_caoz_x_id_ty7g'], data['d_id_8n7o'])[0, 1]
print(f"Correlation between id_caoz*id_ty7g and d_id_8n7o: {corr_caoz_ty7g_8n7o:.4f}")

# Let's check if there's a reaction id_1wsx + id_ty7g -> id_8n7o + id_caoz
data['id_1wsx_x_id_ty7g'] = data['id_1wsx'] * data['id_ty7g']
corr_1wsx_ty7g_8n7o = np.corrcoef(data['id_1wsx_x_id_ty7g'], data['d_id_8n7o'])[0, 1]
print(f"Correlation between id_1wsx*id_ty7g and d_id_8n7o: {corr_1wsx_ty7g_8n7o:.4f}")

# Let's check the ratio of rates for potential reactions
print("\nChecking ratios of rates for potential reactions:")

# For reaction id_8n7o + id_caoz -> id_ty7g + id_1wsx
# The rates should satisfy: -d_id_8n7o = -d_id_caoz = d_id_ty7g = d_id_1wsx
print("For reaction id_8n7o + id_caoz -> id_ty7g + id_1wsx:")
data['ratio_8n7o_caoz_1'] = -data['d_id_8n7o'] / -data['d_id_caoz']
data['ratio_8n7o_ty7g_1'] = -data['d_id_8n7o'] / data['d_id_ty7g']
data['ratio_8n7o_1wsx_1'] = -data['d_id_8n7o'] / data['d_id_1wsx']

valid_data_1 = data[(abs(data['d_id_caoz']) > 1e-10) & 
                    (abs(data['d_id_ty7g']) > 1e-10) & 
                    (abs(data['d_id_1wsx']) > 1e-10)]

print(f"Ratio -d_id_8n7o / -d_id_caoz (mean): {valid_data_1['ratio_8n7o_caoz_1'].mean()}")
print(f"Ratio -d_id_8n7o / d_id_ty7g (mean): {valid_data_1['ratio_8n7o_ty7g_1'].mean()}")
print(f"Ratio -d_id_8n7o / d_id_1wsx (mean): {valid_data_1['ratio_8n7o_1wsx_1'].mean()}")

# For reaction id_8n7o + id_1wsx -> 2 id_ty7g
# The rates should satisfy: -d_id_8n7o = -d_id_1wsx = 0.5 * d_id_ty7g
print("\nFor reaction id_8n7o + id_1wsx -> 2 id_ty7g:")
data['ratio_8n7o_1wsx_2'] = -data['d_id_8n7o'] / -data['d_id_1wsx']
data['ratio_8n7o_ty7g_2'] = -data['d_id_8n7o'] / (0.5 * data['d_id_ty7g'])

valid_data_2 = data[(abs(data['d_id_1wsx']) > 1e-10) & 
                    (abs(data['d_id_ty7g']) > 1e-10)]

print(f"Ratio -d_id_8n7o / -d_id_1wsx (mean): {valid_data_2['ratio_8n7o_1wsx_2'].mean()}")
print(f"Ratio -d_id_8n7o / (0.5 * d_id_ty7g) (mean): {valid_data_2['ratio_8n7o_ty7g_2'].mean()}")

# Let's try to formulate a hypothesis for the reaction network
print("\nHypothesis for the reaction network:")
print("Based on the correlations and rate ratios, I'm considering these reactions:")
print("1. id_8n7o + id_caoz -> id_ty7g + id_1wsx")
print("2. id_8n7o + id_1wsx -> 2 id_ty7g")

# Let's test this hypothesis by simulating the system with these reactions
# and comparing with the observed data
print("\nLet's create a model with these reactions and test it.")

# Create a new SBML model with the hypothesized reactions
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

# Add the first reaction: id_8n7o + id_caoz -> id_ty7g + id_1wsx
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactants
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_8n7o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

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

# Add products
product1 = reaction1.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

product2 = reaction1.createProduct()
product2.setSpecies("id_1wsx")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law (mass action)
kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1 * id_8n7o * id_caoz")

# Add parameter k1
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(1.0)  # We'll adjust this later if needed

# Add the second reaction: id_8n7o + id_1wsx -> 2 id_ty7g
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactants
reactant1 = reaction2.createReactant()
reactant1.setSpecies("id_8n7o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_1wsx")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product1 = reaction2.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(2.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_8n7o * id_1wsx")

# Add parameter k2
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(1.0)  # We'll adjust this later if needed

# 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)

print("\nCreated SBML model with two reactions:")
print("1. id_8n7o + id_caoz -> id_ty7g + id_1wsx (k1 * id_8n7o * id_caoz)")
print("2. id_8n7o + id_1wsx -> 2 id_ty7g (k2 * id_8n7o * id_1wsx)")

# Let's simulate this model and compare with the observed data
print("\nNow let's simulate this model and compare with the observed data.")
```
# Observation

## Code Stdout
Checking for relationships between rates of change:
Correlation between id_8n7o*id_caoz and d_id_caoz: 0.6701
Correlation between id_8n7o*id_caoz and d_id_ty7g: 0.1390
Correlation between id_8n7o*id_caoz and d_id_1wsx: 0.8267

Stoichiometric ratios:
Ratio of -d_id_8n7o / -d_id_caoz (mean): 0.33258841647796794
Ratio of d_id_ty7g / d_id_1wsx (mean): -1.0542152278726027

Correlation between id_8n7o*id_1wsx and d_id_ty7g: 0.3377
Correlation between id_caoz*id_1wsx and d_id_ty7g: 0.7304
Correlation between id_8n7o*id_ty7g and d_id_caoz: 0.0460
Correlation between id_caoz*id_ty7g and d_id_8n7o: -0.2418
Correlation between id_1wsx*id_ty7g and d_id_8n7o: 0.1687

Checking ratios of rates for potential reactions:
For reaction id_8n7o + id_caoz -> id_ty7g + id_1wsx:
Ratio -d_id_8n7o / -d_id_caoz (mean): 0.33258841647796794
Ratio -d_id_8n7o / d_id_ty7g (mean): 4.697220094555521
Ratio -d_id_8n7o / d_id_1wsx (mean): 0.672335718627807

For reaction id_8n7o + id_1wsx -> 2 id_ty7g:
Ratio -d_id_8n7o / -d_id_1wsx (mean): -0.672335718627807
Ratio -d_id_8n7o / (0.5 * d_id_ty7g) (mean): 9.394440189111043

Hypothesis for the reaction network:
Based on the correlations and rate ratios, I'm considering these reactions:
1. id_8n7o + id_caoz -> id_ty7g + id_1wsx
2. id_8n7o + id_1wsx -> 2 id_ty7g

Let's create a model with these reactions and test it.

Created SBML model with two reactions:
1. id_8n7o + id_caoz -> id_ty7g + id_1wsx (k1 * id_8n7o * id_caoz)
2. id_8n7o + id_1wsx -> 2 id_ty7g (k2 * id_8n7o * id_1wsx)

Now let's simulate this model and compare with the observed data.

## 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, 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 4
## Thoughts
I've created a model with two reactions based on my analysis:
1. `id_8n7o + id_caoz -> id_ty7g + id_1wsx` (with rate law k1 * id_8n7o * id_caoz)
2. `id_8n7o + id_1wsx -> 2 id_ty7g` (with rate law k2 * id_8n7o * id_1wsx)

Now I need to:
1. Simulate this model to see if it matches the observed data
2. Adjust the rate constants (k1 and k2) if needed
3. Verify if these reactions fully explain the observed behavior

Let me simulate the model and compare it with the experimental data.

## Action

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

# Access the updated SBML model and experimental data
updated_sbml = shared_variables.access('updated_sbml')
data = shared_variables.access('data')
exp_data = experiment_history["iteration_0"]

# Let's simulate the model using scipy's ODE solver
def model_ode(t, y, k1, k2):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    r1 = k1 * y[0] * y[1]
    
    # Reaction 2: id_8n7o + id_1wsx -> 2 id_ty7g
    r2 = k2 * y[0] * y[3]
    
    # ODEs
    dy_dt = [
        -r1 - r2,       # d[id_8n7o]/dt
        -r1,            # d[id_caoz]/dt
        r1 + 2*r2,      # d[id_ty7g]/dt
        r1 - r2         # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Initial conditions from the SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

y0 = []
for species_id in ["id_8n7o", "id_caoz", "id_ty7g", "id_1wsx"]:
    species = model.getSpecies(species_id)
    y0.append(species.getInitialConcentration())

print("Initial conditions:")
print(f"id_8n7o: {y0[0]}")
print(f"id_caoz: {y0[1]}")
print(f"id_ty7g: {y0[2]}")
print(f"id_1wsx: {y0[3]}")

# Time points for simulation
t_span = (0, 183)  # Match the experimental data time range
t_eval = exp_data['Time'].values

# Let's try different values for k1 and k2 to find a good fit
# We'll use a simple grid search
k1_values = [1e-8, 1e-7, 1e-6, 1e-5]
k2_values = [1e-8, 1e-7, 1e-6, 1e-5]

best_k1 = None
best_k2 = None
best_error = float('inf')
best_sim_data = None

for k1 in k1_values:
    for k2 in k2_values:
        # Solve the ODE system
        sol = solve_ivp(
            lambda t, y: model_ode(t, y, k1, k2),
            t_span,
            y0,
            method='LSODA',
            t_eval=t_eval
        )
        
        # Calculate error (mean squared error)
        sim_data = pd.DataFrame({
            'Time': sol.t,
            'id_8n7o': sol.y[0],
            'id_caoz': sol.y[1],
            'id_ty7g': sol.y[2],
            'id_1wsx': sol.y[3]
        })
        
        error = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            # Normalize by the maximum value to give equal weight to each species
            max_val = max(max(exp_data[species]), max(sim_data[species]))
            if max_val > 0:
                error += np.mean(((exp_data[species] - sim_data[species]) / max_val) ** 2)
        
        if error < best_error:
            best_error = error
            best_k1 = k1
            best_k2 = k2
            best_sim_data = sim_data

print(f"\nBest parameters: k1 = {best_k1}, k2 = {best_k2}")
print(f"Best error: {best_error}")

# Compare the best simulation with experimental data
print("\nComparison of simulation vs. experimental data at selected time points:")
selected_times = [0, 30, 60, 90, 120, 150, 180]
for t in selected_times:
    idx = np.argmin(np.abs(best_sim_data['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = best_sim_data.loc[idx, species]
        exp_val = exp_data[exp_data['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Update the SBML model with the best parameters
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(updated_sbml)
model = document.getModel()

# Update k1
reaction1 = model.getReaction("reaction1")
kinetic_law1 = reaction1.getKineticLaw()
parameter1 = kinetic_law1.getParameter("k1")
parameter1.setValue(best_k1)

# Update k2
reaction2 = model.getReaction("reaction2")
kinetic_law2 = reaction2.getKineticLaw()
parameter2 = kinetic_law2.getParameter("k2")
parameter2.setValue(best_k2)

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

# Store the final SBML model
shared_variables.add('final_sbml', final_sbml)

print("\nUpdated SBML model with optimized parameters:")
print(f"Reaction 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx (k1 = {best_k1})")
print(f"Reaction 2: id_8n7o + id_1wsx -> 2 id_ty7g (k2 = {best_k2})")

# Let's also check if there might be a third reaction we're missing
# For example, let's check if there's evidence for a reaction involving id_caoz and id_1wsx
print("\nChecking for additional reactions:")
residuals = {}
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    residuals[species] = exp_data[species] - best_sim_data[species]
    print(f"Mean absolute residual for {species}: {np.mean(np.abs(residuals[species]))}")

# Let's check if there's a correlation between the residuals and potential missing reactions
data['id_caoz_x_id_1wsx'] = exp_data['id_caoz'] * exp_data['id_1wsx']
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    corr = np.corrcoef(data['id_caoz_x_id_1wsx'], residuals[species])[0, 1]
    print(f"Correlation between id_caoz*id_1wsx and {species} residual: {corr:.4f}")

# Let's also check if there's evidence for a third reaction: id_caoz + id_1wsx -> id_ty7g
print("\nChecking for reaction: id_caoz + id_1wsx -> id_ty7g")
corr = np.corrcoef(exp_data['id_caoz'] * exp_data['id_1wsx'], residuals['id_ty7g'])[0, 1]
print(f"Correlation between id_caoz*id_1wsx and id_ty7g residual: {corr:.4f}")

# Let's also check if there's evidence for a third reaction: id_caoz + id_ty7g -> id_1wsx
print("\nChecking for reaction: id_caoz + id_ty7g -> id_1wsx")
corr = np.corrcoef(exp_data['id_caoz'] * exp_data['id_ty7g'], residuals['id_1wsx'])[0, 1]
print(f"Correlation between id_caoz*id_ty7g and id_1wsx residual: {corr:.4f}")
```
# Observation

## Code Stdout
Initial conditions:
id_8n7o: 11080778.0
id_caoz: 193.0
id_ty7g: 2.0
id_1wsx: 27.0

Best parameters: k1 = 1e-08, k2 = 1e-08
Best error: 1.5959425893287982

Comparison of simulation vs. experimental data at selected time points:

Time 0:
  id_8n7o: Sim = 1.11e+07, Exp = 1.11e+07, Rel Error = 0.00%
  id_caoz: Sim = 1.93e+02, Exp = 1.93e+02, Rel Error = 0.00%
  id_ty7g: Sim = 2.00e+00, Exp = 2.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 2.70e+01, Exp = 2.70e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 1.11e+07, Exp = 8.81e+06, Rel Error = 25.77%
  id_caoz: Sim = 6.95e+00, Exp = 1.50e+06, Rel Error = 100.00%
  id_ty7g: Sim = 5.66e+02, Exp = 1.10e+05, Rel Error = 99.49%
  id_1wsx: Sim = 2.41e+01, Exp = 6.64e+05, Rel Error = 100.00%

Time 60:
  id_8n7o: Sim = 1.11e+07, Exp = 6.25e+04, Rel Error = 17615.09%
  id_caoz: Sim = 2.50e-01, Exp = 4.97e+05, Rel Error = 100.00%
  id_ty7g: Sim = 6.31e+02, Exp = 6.06e+06, Rel Error = 99.99%
  id_1wsx: Sim = 1.70e+00, Exp = 4.46e+06, Rel Error = 100.00%

Time 90:
  id_8n7o: Sim = 1.11e+07, Exp = 1.02e+04, Rel Error = 108879.32%
  id_caoz: Sim = 9.03e-03, Exp = 1.19e+04, Rel Error = 100.00%
  id_ty7g: Sim = 6.35e+02, Exp = 9.81e+06, Rel Error = 99.99%
  id_1wsx: Sim = 9.10e-02, Exp = 1.25e+06, Rel Error = 100.00%

Time 120:
  id_8n7o: Sim = 1.11e+07, Exp = 6.57e+03, Rel Error = 168582.88%
  id_caoz: Sim = 3.26e-04, Exp = 6.56e+02, Rel Error = 100.00%
  id_ty7g: Sim = 6.35e+02, Exp = 1.08e+07, Rel Error = 99.99%
  id_1wsx: Sim = 4.36e-03, Exp = 3.01e+05, Rel Error = 100.00%

Time 150:
  id_8n7o: Sim = 1.11e+07, Exp = 5.92e+03, Rel Error = 187113.14%
  id_caoz: Sim = 1.18e-05, Exp = 1.06e+02, Rel Error = 100.00%
  id_ty7g: Sim = 6.35e+02, Exp = 1.10e+07, Rel Error = 99.99%
  id_1wsx: Sim = 1.96e-04, Exp = 7.18e+04, Rel Error = 100.00%

Time 180:
  id_8n7o: Sim = 1.11e+07, Exp = 5.77e+03, Rel Error = 191822.01%
  id_caoz: Sim = 4.33e-07, Exp = 2.35e+01, Rel Error = 100.00%
  id_ty7g: Sim = 6.35e+02, Exp = 1.11e+07, Rel Error = 99.99%
  id_1wsx: Sim = 8.58e-06, Exp = 1.71e+04, Rel Error = 100.00%

Updated SBML model with optimized parameters:
Reaction 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx (k1 = 1e-08)
Reaction 2: id_8n7o + id_1wsx -> 2 id_ty7g (k2 = 1e-08)

Checking for additional reactions:
Mean absolute residual for id_8n7o: 8945757.657870201
Mean absolute residual for id_caoz: 429927.71430764056
Mean absolute residual for id_ty7g: 7263503.740144676
Mean absolute residual for id_1wsx: 1252336.5694297112
Correlation between id_caoz*id_1wsx and id_8n7o residual: -0.0535
Correlation between id_caoz*id_1wsx and id_caoz residual: 0.9183
Correlation between id_caoz*id_1wsx and id_ty7g residual: -0.4344
Correlation between id_caoz*id_1wsx and id_1wsx residual: 0.7307

Checking for reaction: id_caoz + id_1wsx -> id_ty7g
Correlation between id_caoz*id_1wsx and id_ty7g residual: -0.4344

Checking for reaction: id_caoz + id_ty7g -> id_1wsx
Correlation between id_caoz*id_ty7g and id_1wsx residual: 0.9208

## 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, updated_sbml, final_sbml)

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


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



# Iteration 5
## Thoughts
The simulation results show that our current model with just two reactions doesn't match the experimental data well. The relative errors are very high, especially as time progresses. This suggests that our model is missing important reactions or has incorrect rate constants.

Key observations from the simulation:
1. The simulated `id_8n7o` barely decreases, while the experimental data shows a significant decrease.
2. The simulated `id_caoz` decreases too quickly, while the experimental data shows it first increases then decreases.
3. The simulated `id_ty7g` barely increases, while the experimental data shows a significant increase.
4. The simulated `id_1wsx` decreases too quickly, while the experimental data shows it first increases then decreases.

The correlation analysis of residuals suggests:
1. Strong correlation (0.9183) between `id_caoz*id_1wsx` and `id_caoz` residual
2. Strong correlation (0.9208) between `id_caoz*id_ty7g` and `id_1wsx` residual

This suggests we might need to add more reactions to our model. Let's revise our hypothesis and try a different set of reactions:

1. `id_8n7o + id_caoz -> id_ty7g + id_1wsx` (keep this)
2. `id_8n7o + id_1wsx -> 2 id_ty7g` (keep this)
3. `id_caoz + id_ty7g -> id_1wsx` (add this based on correlation)

Let's also try a wider range of rate constants to see if we can get a better fit.

## Action

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

# Access the experimental data
exp_data = experiment_history["iteration_0"]

# Let's create a new model with three reactions
def model_ode(t, y, k1, k2, k3):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    r1 = k1 * y[0] * y[1]
    
    # Reaction 2: id_8n7o + id_1wsx -> 2 id_ty7g
    r2 = k2 * y[0] * y[3]
    
    # Reaction 3: id_caoz + id_ty7g -> id_1wsx
    r3 = k3 * y[1] * y[2]
    
    # ODEs
    dy_dt = [
        -r1 - r2,           # d[id_8n7o]/dt
        -r1 - r3,           # d[id_caoz]/dt
        r1 + 2*r2 - r3,     # d[id_ty7g]/dt
        r1 - r2 + r3        # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Initial conditions from the SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

y0 = []
for species_id in ["id_8n7o", "id_caoz", "id_ty7g", "id_1wsx"]:
    species = model.getSpecies(species_id)
    y0.append(species.getInitialConcentration())

print("Initial conditions:")
print(f"id_8n7o: {y0[0]}")
print(f"id_caoz: {y0[1]}")
print(f"id_ty7g: {y0[2]}")
print(f"id_1wsx: {y0[3]}")

# Time points for simulation
t_span = (0, 183)  # Match the experimental data time range
t_eval = exp_data['Time'].values

# Let's try different values for k1, k2, and k3 to find a good fit
# We'll use a wider range for the grid search
k1_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]
k2_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]
k3_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]

best_k1 = None
best_k2 = None
best_k3 = None
best_error = float('inf')
best_sim_data = None

# We'll do a coarse grid search first
for k1 in k1_values:
    for k2 in k2_values:
        for k3 in k3_values:
            # Solve the ODE system
            try:
                sol = solve_ivp(
                    lambda t, y: model_ode(t, y, k1, k2, k3),
                    t_span,
                    y0,
                    method='LSODA',
                    t_eval=t_eval
                )
                
                # Calculate error (mean squared error)
                sim_data = pd.DataFrame({
                    'Time': sol.t,
                    'id_8n7o': sol.y[0],
                    'id_caoz': sol.y[1],
                    'id_ty7g': sol.y[2],
                    'id_1wsx': sol.y[3]
                })
                
                error = 0
                for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
                    # Normalize by the maximum value to give equal weight to each species
                    max_val = max(max(exp_data[species]), max(sim_data[species]))
                    if max_val > 0:
                        error += np.mean(((exp_data[species] - sim_data[species]) / max_val) ** 2)
                
                if error < best_error:
                    best_error = error
                    best_k1 = k1
                    best_k2 = k2
                    best_k3 = k3
                    best_sim_data = sim_data
            except:
                # Skip if the solver fails
                continue

print(f"\nBest parameters: k1 = {best_k1}, k2 = {best_k2}, k3 = {best_k3}")
print(f"Best error: {best_error}")

# Compare the best simulation with experimental data
print("\nComparison of simulation vs. experimental data at selected time points:")
selected_times = [0, 30, 60, 90, 120, 150, 180]
for t in selected_times:
    idx = np.argmin(np.abs(best_sim_data['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = best_sim_data.loc[idx, species]
        exp_val = exp_data[exp_data['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Let's try a different set of reactions
print("\nLet's try a different set of reactions:")
print("1. id_8n7o + id_caoz -> id_ty7g + id_1wsx")
print("2. id_8n7o + id_1wsx -> 2 id_ty7g")
print("3. id_250q + id_caoz -> id_8n7o + id_1wsx")

def model_ode2(t, y, k1, k2, k3):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    # id_250q is constant at 11081000
    
    # Reaction 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    r1 = k1 * y[0] * y[1]
    
    # Reaction 2: id_8n7o + id_1wsx -> 2 id_ty7g
    r2 = k2 * y[0] * y[3]
    
    # Reaction 3: id_250q + id_caoz -> id_8n7o + id_1wsx
    r3 = k3 * 11081000 * y[1]
    
    # ODEs
    dy_dt = [
        -r1 - r2 + r3,      # d[id_8n7o]/dt
        -r1 - r3,           # d[id_caoz]/dt
        r1 + 2*r2,          # d[id_ty7g]/dt
        r1 - r2 + r3        # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Let's try different values for k1, k2, and k3 to find a good fit
k1_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]
k2_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]
k3_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]

best_k1_2 = None
best_k2_2 = None
best_k3_2 = None
best_error_2 = float('inf')
best_sim_data_2 = None

# We'll do a coarse grid search
for k1 in k1_values:
    for k2 in k2_values:
        for k3 in k3_values:
            # Solve the ODE system
            try:
                sol = solve_ivp(
                    lambda t, y: model_ode2(t, y, k1, k2, k3),
                    t_span,
                    y0,
                    method='LSODA',
                    t_eval=t_eval
                )
                
                # Calculate error (mean squared error)
                sim_data = pd.DataFrame({
                    'Time': sol.t,
                    'id_8n7o': sol.y[0],
                    'id_caoz': sol.y[1],
                    'id_ty7g': sol.y[2],
                    'id_1wsx': sol.y[3]
                })
                
                error = 0
                for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
                    # Normalize by the maximum value to give equal weight to each species
                    max_val = max(max(exp_data[species]), max(sim_data[species]))
                    if max_val > 0:
                        error += np.mean(((exp_data[species] - sim_data[species]) / max_val) ** 2)
                
                if error < best_error_2:
                    best_error_2 = error
                    best_k1_2 = k1
                    best_k2_2 = k2
                    best_k3_2 = k3
                    best_sim_data_2 = sim_data
            except:
                # Skip if the solver fails
                continue

print(f"\nBest parameters for second model: k1 = {best_k1_2}, k2 = {best_k2_2}, k3 = {best_k3_2}")
print(f"Best error for second model: {best_error_2}")

# Compare the best simulation with experimental data
if best_sim_data_2 is not None:
    print("\nComparison of second model simulation vs. experimental data at selected time points:")
    for t in selected_times:
        idx = np.argmin(np.abs(best_sim_data_2['Time'] - t))
        print(f"\nTime {t}:")
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            sim_val = best_sim_data_2.loc[idx, species]
            exp_val = exp_data[exp_data['Time'] == t][species].values[0]
            rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
            print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Let's try a third set of reactions
print("\nLet's try a third set of reactions:")
print("1. id_8n7o + id_caoz -> id_ty7g + id_1wsx")
print("2. id_8n7o + id_1wsx -> 2 id_ty7g")
print("3. id_250q -> id_8n7o")
print("4. id_caoz + id_ty7g -> id_1wsx")

def model_ode3(t, y, k1, k2, k3, k4):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    # id_250q is constant at 11081000
    
    # Reaction 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    r1 = k1 * y[0] * y[1]
    
    # Reaction 2: id_8n7o + id_1wsx -> 2 id_ty7g
    r2 = k2 * y[0] * y[3]
    
    # Reaction 3: id_250q -> id_8n7o
    r3 = k3 * 11081000
    
    # Reaction 4: id_caoz + id_ty7g -> id_1wsx
    r4 = k4 * y[1] * y[2]
    
    # ODEs
    dy_dt = [
        -r1 - r2 + r3,      # d[id_8n7o]/dt
        -r1 - r4,           # d[id_caoz]/dt
        r1 + 2*r2 - r4,     # d[id_ty7g]/dt
        r1 - r2 + r4        # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Let's try different values for k1, k2, k3, and k4 to find a good fit
k1_values = [1e-10, 1e-9, 1e-8, 1e-7]
k2_values = [1e-10, 1e-9, 1e-8, 1e-7]
k3_values = [1e-10, 1e-9, 1e-8, 1e-7]
k4_values = [1e-10, 1e-9, 1e-8, 1e-7]

best_k1_3 = None
best_k2_3 = None
best_k3_3 = None
best_k4_3 = None
best_error_3 = float('inf')
best_sim_data_3 = None

# We'll do a coarse grid search
for k1 in k1_values:
    for k2 in k2_values:
        for k3 in k3_values:
            for k4 in k4_values:
                # Solve the ODE system
                try:
                    sol = solve_ivp(
                        lambda t, y: model_ode3(t, y, k1, k2, k3, k4),
                        t_span,
                        y0,
                        method='LSODA',
                        t_eval=t_eval
                    )
                    
                    # Calculate error (mean squared error)
                    sim_data = pd.DataFrame({
                        'Time': sol.t,
                        'id_8n7o': sol.y[0],
                        'id_caoz': sol.y[1],
                        'id_ty7g': sol.y[2],
                        'id_1wsx': sol.y[3]
                    })
                    
                    error = 0
                    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
                        # Normalize by the maximum value to give equal weight to each species
                        max_val = max(max(exp_data[species]), max(sim_data[species]))
                        if max_val > 0:
                            error += np.mean(((exp_data[species] - sim_data[species]) / max_val) ** 2)
                    
                    if error < best_error_3:
                        best_error_3 = error
                        best_k1_3 = k1
                        best_k2_3 = k2
                        best_k3_3 = k3
                        best_k4_3 = k4
                        best_sim_data_3 = sim_data
                except:
                    # Skip if the solver fails
                    continue

print(f"\nBest parameters for third model: k1 = {best_k1_3}, k2 = {best_k2_3}, k3 = {best_k3_3}, k4 = {best_k4_3}")
print(f"Best error for third model: {best_error_3}")

# Compare the best simulation with experimental data
if best_sim_data_3 is not None:
    print("\nComparison of third model simulation vs. experimental data at selected time points:")
    for t in selected_times:
        idx = np.argmin(np.abs(best_sim_data_3['Time'] - t))
        print(f"\nTime {t}:")
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            sim_val = best_sim_data_3.loc[idx, species]
            exp_val = exp_data[exp_data['Time'] == t][species].values[0]
            rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
            print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Compare the errors of all three models
print("\nComparison of all three models:")
print(f"Model 1 error: {best_error}")
print(f"Model 2 error: {best_error_2}")
print(f"Model 3 error: {best_error_3}")

# Choose the best model
if best_error <= min(best_error_2, best_error_3):
    print("\nModel 1 is the best fit.")
    best_model = 1
    best_params = (best_k1, best_k2, best_k3)
elif best_error_2 <= min(best_error, best_error_3):
    print("\nModel 2 is the best fit.")
    best_model = 2
    best_params = (best_k1_2, best_k2_2, best_k3_2)
else:
    print("\nModel 3 is the best fit.")
    best_model = 3
    best_params = (best_k1_3, best_k2_3, best_k3_3, best_k4_3)

# Create the final SBML model with the best reactions and parameters
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

if best_model == 1:
    # Add the first reaction: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    reaction1 = model.createReaction()
    reaction1.setId("reaction1")
    reaction1.setReversible(False)

    # Add reactants
    reactant1 = reaction1.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

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

    # Add products
    product1 = reaction1.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    product2 = reaction1.createProduct()
    product2.setSpecies("id_1wsx")
    product2.setStoichiometry(1.0)
    product2.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law1 = reaction1.createKineticLaw()
    kinetic_law1.setFormula("k1 * id_8n7o * id_caoz")

    # Add parameter k1
    parameter1 = kinetic_law1.createParameter()
    parameter1.setId("k1")
    parameter1.setValue(best_params[0])

    # Add the second reaction: id_8n7o + id_1wsx -> 2 id_ty7g
    reaction2 = model.createReaction()
    reaction2.setId("reaction2")
    reaction2.setReversible(False)

    # Add reactants
    reactant1 = reaction2.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    reactant2 = reaction2.createReactant()
    reactant2.setSpecies("id_1wsx")
    reactant2.setStoichiometry(1.0)
    reactant2.setConstant(True)

    # Add products
    product1 = reaction2.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(2.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law2 = reaction2.createKineticLaw()
    kinetic_law2.setFormula("k2 * id_8n7o * id_1wsx")

    # Add parameter k2
    parameter2 = kinetic_law2.createParameter()
    parameter2.setId("k2")
    parameter2.setValue(best_params[1])

    # Add the third reaction: id_caoz + id_ty7g -> id_1wsx
    reaction3 = model.createReaction()
    reaction3.setId("reaction3")
    reaction3.setReversible(False)

    # Add reactants
    reactant1 = reaction3.createReactant()
    reactant1.setSpecies("id_caoz")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    reactant2 = reaction3.createReactant()
    reactant2.setSpecies("id_ty7g")
    reactant2.setStoichiometry(1.0)
    reactant2.setConstant(True)

    # Add products
    product1 = reaction3.createProduct()
    product1.setSpecies("id_1wsx")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law3 = reaction3.createKineticLaw()
    kinetic_law3.setFormula("k3 * id_caoz * id_ty7g")

    # Add parameter k3
    parameter3 = kinetic_law3.createParameter()
    parameter3.setId("k3")
    parameter3.setValue(best_params[2])

elif best_model == 2:
    # Add the first reaction: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    reaction1 = model.createReaction()
    reaction1.setId("reaction1")
    reaction1.setReversible(False)

    # Add reactants
    reactant1 = reaction1.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

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

    # Add products
    product1 = reaction1.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    product2 = reaction1.createProduct()
    product2.setSpecies("id_1wsx")
    product2.setStoichiometry(1.0)
    product2.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law1 = reaction1.createKineticLaw()
    kinetic_law1.setFormula("k1 * id_8n7o * id_caoz")

    # Add parameter k1
    parameter1 = kinetic_law1.createParameter()
    parameter1.setId("k1")
    parameter1.setValue(best_params[0])

    # Add the second reaction: id_8n7o + id_1wsx -> 2 id_ty7g
    reaction2 = model.createReaction()
    reaction2.setId("reaction2")
    reaction2.setReversible(False)

    # Add reactants
    reactant1 = reaction2.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    reactant2 = reaction2.createReactant()
    reactant2.setSpecies("id_1wsx")
    reactant2.setStoichiometry(1.0)
    reactant2.setConstant(True)

    # Add products
    product1 = reaction2.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(2.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law2 = reaction2.createKineticLaw()
    kinetic_law2.setFormula("k2 * id_8n7o * id_1wsx")

    # Add parameter k2
    parameter2 = kinetic_law2.createParameter()
    parameter2.setId("k2")
    parameter2.setValue(best_params[1])

    # Add the third reaction: id_250q + id_caoz -> id_8n7o + id_1wsx
    reaction3 = model.createReaction()
    reaction3.setId("reaction3")
    reaction3.setReversible(False)

    # Add reactants
    reactant1 = reaction3.createReactant()
    reactant1.setSpecies("id_250q")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    reactant2 = reaction3.createReactant()
    reactant2.setSpecies("id_caoz")
    reactant2.setStoichiometry(1.0)
    reactant2.setConstant(True)

    # Add products
    product1 = reaction3.createProduct()
    product1.setSpecies("id_8n7o")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    product2 = reaction3.createProduct()
    product2.setSpecies("id_1wsx")
    product2.setStoichiometry(1.0)
    product2.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law3 = reaction3.createKineticLaw()
    kinetic_law3.setFormula("k3 * id_250q * id_caoz")

    # Add parameter k3
    parameter3 = kinetic_law3.createParameter()
    parameter3.setId("k3")
    parameter3.setValue(best_params[2])

else:  # best_model == 3
    # Add the first reaction: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    reaction1 = model.createReaction()
    reaction1.setId("reaction1")
    reaction1.setReversible(False)

    # Add reactants
    reactant1 = reaction1.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

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

    # Add products
    product1 = reaction1.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    product2 = reaction1.createProduct()
    product2.setSpecies("id_1wsx")
    product2.setStoichiometry(1.0)
    product2.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law1 = reaction1.createKineticLaw()
    kinetic_law1.setFormula("k1 * id_8n7o * id_caoz")

    # Add parameter k1
    parameter1 = kinetic_law1.createParameter()
    parameter1.setId("k1")
    parameter1.setValue(best_params[0])

    # Add the second reaction: id_8n7o + id_1wsx -> 2 id_ty7g
    reaction2 = model.createReaction()
    reaction2.setId("reaction2")
    reaction2.setReversible(False)

    # Add reactants
    reactant1 = reaction2.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    reactant2 = reaction2.createReactant()
    reactant2.setSpecies("id_1wsx")
    reactant2.setStoichiometry(1.0)
    reactant2.setConstant(True)

    # Add products
    product1 = reaction2.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(2.0)
    product1.setConstant(True)

    # Add kinetic law
# Observation

## Parsing error
Your response must include either a Python code block or a JSON experiment block.
# Iteration 6
## Thoughts
I apologize for the error in my previous response. It seems the code was too long and got cut off. Let me continue with a more focused approach. I'll test the three different models I proposed:

1. Model 1:
   - id_8n7o + id_caoz -> id_ty7g + id_1wsx
   - id_8n7o + id_1wsx -> 2 id_ty7g
   - id_caoz + id_ty7g -> id_1wsx

2. Model 2:
   - id_8n7o + id_caoz -> id_ty7g + id_1wsx
   - id_8n7o + id_1wsx -> 2 id_ty7g
   - id_250q + id_caoz -> id_8n7o + id_1wsx

3. Model 3:
   - id_8n7o + id_caoz -> id_ty7g + id_1wsx
   - id_8n7o + id_1wsx -> 2 id_ty7g
   - id_250q -> id_8n7o
   - id_caoz + id_ty7g -> id_1wsx

I'll test each model separately to keep the code manageable.

## Action

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

# Access the experimental data
exp_data = experiment_history["iteration_0"]

# Initial conditions from the SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

y0 = []
for species_id in ["id_8n7o", "id_caoz", "id_ty7g", "id_1wsx"]:
    species = model.getSpecies(species_id)
    y0.append(species.getInitialConcentration())

print("Initial conditions:")
print(f"id_8n7o: {y0[0]}")
print(f"id_caoz: {y0[1]}")
print(f"id_ty7g: {y0[2]}")
print(f"id_1wsx: {y0[3]}")

# Time points for simulation
t_span = (0, 183)  # Match the experimental data time range
t_eval = exp_data['Time'].values

# Model 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx, id_8n7o + id_1wsx -> 2 id_ty7g, id_caoz + id_ty7g -> id_1wsx
def model_ode1(t, y, k1, k2, k3):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    r1 = k1 * y[0] * y[1]
    
    # Reaction 2: id_8n7o + id_1wsx -> 2 id_ty7g
    r2 = k2 * y[0] * y[3]
    
    # Reaction 3: id_caoz + id_ty7g -> id_1wsx
    r3 = k3 * y[1] * y[2]
    
    # ODEs
    dy_dt = [
        -r1 - r2,           # d[id_8n7o]/dt
        -r1 - r3,           # d[id_caoz]/dt
        r1 + 2*r2 - r3,     # d[id_ty7g]/dt
        r1 - r2 + r3        # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Model 2: id_8n7o + id_caoz -> id_ty7g + id_1wsx, id_8n7o + id_1wsx -> 2 id_ty7g, id_250q + id_caoz -> id_8n7o + id_1wsx
def model_ode2(t, y, k1, k2, k3):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    # id_250q is constant at 11081000
    
    # Reaction 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    r1 = k1 * y[0] * y[1]
    
    # Reaction 2: id_8n7o + id_1wsx -> 2 id_ty7g
    r2 = k2 * y[0] * y[3]
    
    # Reaction 3: id_250q + id_caoz -> id_8n7o + id_1wsx
    r3 = k3 * 11081000 * y[1]
    
    # ODEs
    dy_dt = [
        -r1 - r2 + r3,      # d[id_8n7o]/dt
        -r1 - r3,           # d[id_caoz]/dt
        r1 + 2*r2,          # d[id_ty7g]/dt
        r1 - r2 + r3        # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Model 3: id_8n7o + id_caoz -> id_ty7g + id_1wsx, id_8n7o + id_1wsx -> 2 id_ty7g, id_250q -> id_8n7o, id_caoz + id_ty7g -> id_1wsx
def model_ode3(t, y, k1, k2, k3, k4):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    # id_250q is constant at 11081000
    
    # Reaction 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    r1 = k1 * y[0] * y[1]
    
    # Reaction 2: id_8n7o + id_1wsx -> 2 id_ty7g
    r2 = k2 * y[0] * y[3]
    
    # Reaction 3: id_250q -> id_8n7o
    r3 = k3 * 11081000
    
    # Reaction 4: id_caoz + id_ty7g -> id_1wsx
    r4 = k4 * y[1] * y[2]
    
    # ODEs
    dy_dt = [
        -r1 - r2 + r3,      # d[id_8n7o]/dt
        -r1 - r4,           # d[id_caoz]/dt
        r1 + 2*r2 - r4,     # d[id_ty7g]/dt
        r1 - r2 + r4        # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Let's test Model 2 first
print("\nTesting Model 2:")
print("1. id_8n7o + id_caoz -> id_ty7g + id_1wsx")
print("2. id_8n7o + id_1wsx -> 2 id_ty7g")
print("3. id_250q + id_caoz -> id_8n7o + id_1wsx")

# Let's try different values for k1, k2, and k3 to find a good fit
k1_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]
k2_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]
k3_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]

best_k1_2 = None
best_k2_2 = None
best_k3_2 = None
best_error_2 = float('inf')
best_sim_data_2 = None

# We'll do a coarse grid search
for k1 in k1_values:
    for k2 in k2_values:
        for k3 in k3_values:
            # Solve the ODE system
            try:
                sol = solve_ivp(
                    lambda t, y: model_ode2(t, y, k1, k2, k3),
                    t_span,
                    y0,
                    method='LSODA',
                    t_eval=t_eval
                )
                
                # Calculate error (mean squared error)
                sim_data = pd.DataFrame({
                    'Time': sol.t,
                    'id_8n7o': sol.y[0],
                    'id_caoz': sol.y[1],
                    'id_ty7g': sol.y[2],
                    'id_1wsx': sol.y[3]
                })
                
                error = 0
                for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
                    # Normalize by the maximum value to give equal weight to each species
                    max_val = max(max(exp_data[species]), max(sim_data[species]))
                    if max_val > 0:
                        error += np.mean(((exp_data[species] - sim_data[species]) / max_val) ** 2)
                
                if error < best_error_2:
                    best_error_2 = error
                    best_k1_2 = k1
                    best_k2_2 = k2
                    best_k3_2 = k3
                    best_sim_data_2 = sim_data
            except:
                # Skip if the solver fails
                continue

print(f"\nBest parameters for Model 2: k1 = {best_k1_2}, k2 = {best_k2_2}, k3 = {best_k3_2}")
print(f"Best error for Model 2: {best_error_2}")

# Compare the best simulation with experimental data
if best_sim_data_2 is not None:
    print("\nComparison of Model 2 simulation vs. experimental data at selected time points:")
    selected_times = [0, 30, 60, 90, 120, 150, 180]
    for t in selected_times:
        idx = np.argmin(np.abs(best_sim_data_2['Time'] - t))
        print(f"\nTime {t}:")
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            sim_val = best_sim_data_2.loc[idx, species]
            exp_val = exp_data[exp_data['Time'] == t][species].values[0]
            rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
            print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Create the final SBML model with Model 2 reactions and parameters
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

# Add the first reaction: id_8n7o + id_caoz -> id_ty7g + id_1wsx
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactants
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_8n7o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

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

# Add products
product1 = reaction1.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

product2 = reaction1.createProduct()
product2.setSpecies("id_1wsx")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law (mass action)
kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1 * id_8n7o * id_caoz")

# Add parameter k1
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(best_k1_2)

# Add the second reaction: id_8n7o + id_1wsx -> 2 id_ty7g
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactants
reactant1 = reaction2.createReactant()
reactant1.setSpecies("id_8n7o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_1wsx")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product1 = reaction2.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(2.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_8n7o * id_1wsx")

# Add parameter k2
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(best_k2_2)

# Add the third reaction: id_250q + id_caoz -> id_8n7o + id_1wsx
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactants
reactant1 = reaction3.createReactant()
reactant1.setSpecies("id_250q")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

reactant2 = reaction3.createReactant()
reactant2.setSpecies("id_caoz")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product1 = reaction3.createProduct()
product1.setSpecies("id_8n7o")
product1.setStoichiometry(1.0)
product1.setConstant(True)

product2 = reaction3.createProduct()
product2.setSpecies("id_1wsx")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_250q * id_caoz")

# Add parameter k3
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(best_k3_2)

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

# Store the final SBML model
shared_variables.add('model2_sbml', final_sbml)

print("\nCreated SBML model with Model 2 reactions:")
print(f"1. id_8n7o + id_caoz -> id_ty7g + id_1wsx (k1 = {best_k1_2})")
print(f"2. id_8n7o + id_1wsx -> 2 id_ty7g (k2 = {best_k2_2})")
print(f"3. id_250q + id_caoz -> id_8n7o + id_1wsx (k3 = {best_k3_2})")
```
# Observation

## Code Stdout
Initial conditions:
id_8n7o: 11080778.0
id_caoz: 193.0
id_ty7g: 2.0
id_1wsx: 27.0

Testing Model 2:
1. id_8n7o + id_caoz -> id_ty7g + id_1wsx
2. id_8n7o + id_1wsx -> 2 id_ty7g
3. id_250q + id_caoz -> id_8n7o + id_1wsx

Best parameters for Model 2: k1 = 1e-06, k2 = 1e-08, k3 = 1e-10
Best error for Model 2: 1.5959426633657634

Comparison of Model 2 simulation vs. experimental data at selected time points:

Time 0:
  id_8n7o: Sim = 1.11e+07, Exp = 1.11e+07, Rel Error = 0.00%
  id_caoz: Sim = 1.93e+02, Exp = 1.93e+02, Rel Error = 0.00%
  id_ty7g: Sim = 2.00e+00, Exp = 2.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 2.70e+01, Exp = 2.70e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 1.11e+07, Exp = 8.81e+06, Rel Error = 25.77%
  id_caoz: Sim = -1.64e-11, Exp = 1.50e+06, Rel Error = 100.00%
  id_ty7g: Sim = 6.19e+02, Exp = 1.10e+05, Rel Error = 99.44%
  id_1wsx: Sim = 8.01e+00, Exp = 6.64e+05, Rel Error = 100.00%

Time 60:
  id_8n7o: Sim = 1.11e+07, Exp = 6.25e+04, Rel Error = 17615.09%
  id_caoz: Sim = 4.81e-11, Exp = 4.97e+05, Rel Error = 100.00%
  id_ty7g: Sim = 6.34e+02, Exp = 6.06e+06, Rel Error = 99.99%
  id_1wsx: Sim = 2.88e-01, Exp = 4.46e+06, Rel Error = 100.00%

Time 90:
  id_8n7o: Sim = 1.11e+07, Exp = 1.02e+04, Rel Error = 108879.32%
  id_caoz: Sim = -9.16e-10, Exp = 1.19e+04, Rel Error = 100.00%
  id_ty7g: Sim = 6.35e+02, Exp = 9.81e+06, Rel Error = 99.99%
  id_1wsx: Sim = 1.04e-02, Exp = 1.25e+06, Rel Error = 100.00%

Time 120:
  id_8n7o: Sim = 1.11e+07, Exp = 6.57e+03, Rel Error = 168582.88%
  id_caoz: Sim = -6.00e-10, Exp = 6.56e+02, Rel Error = 100.00%
  id_ty7g: Sim = 6.35e+02, Exp = 1.08e+07, Rel Error = 99.99%
  id_1wsx: Sim = 3.71e-04, Exp = 3.01e+05, Rel Error = 100.00%

Time 150:
  id_8n7o: Sim = 1.11e+07, Exp = 5.92e+03, Rel Error = 187113.14%
  id_caoz: Sim = -3.58e-09, Exp = 1.06e+02, Rel Error = 100.00%
  id_ty7g: Sim = 6.35e+02, Exp = 1.10e+07, Rel Error = 99.99%
  id_1wsx: Sim = 1.27e-05, Exp = 7.18e+04, Rel Error = 100.00%

Time 180:
  id_8n7o: Sim = 1.11e+07, Exp = 5.77e+03, Rel Error = 191822.01%
  id_caoz: Sim = 1.66e-12, Exp = 2.35e+01, Rel Error = 100.00%
  id_ty7g: Sim = 6.35e+02, Exp = 1.11e+07, Rel Error = 99.99%
  id_1wsx: Sim = 3.15e-07, Exp = 1.71e+04, Rel Error = 100.00%

Created SBML model with Model 2 reactions:
1. id_8n7o + id_caoz -> id_ty7g + id_1wsx (k1 = 1e-06)
2. id_8n7o + id_1wsx -> 2 id_ty7g (k2 = 1e-08)
3. id_250q + id_caoz -> id_8n7o + id_1wsx (k3 = 1e-10)

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml)

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


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



# Iteration 7
## Thoughts
The results from Model 2 are still not satisfactory. The simulation doesn't match the experimental data well, with very high relative errors for most species at most time points. Let me try Model 3, which includes a direct production of `id_8n7o` from the boundary species `id_250q` and a reaction between `id_caoz` and `id_ty7g` to produce `id_1wsx`.

I'll also try a different approach to parameter optimization. Instead of a grid search, I'll try to use a more targeted approach based on the observed dynamics.

## Action

### Code
```python
import numpy as np
import pandas as pd
import libsbml
from scipy.integrate import solve_ivp
from scipy.optimize import minimize

# Access the experimental data
exp_data = experiment_history["iteration_0"]

# Initial conditions from the SBML model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

y0 = []
for species_id in ["id_8n7o", "id_caoz", "id_ty7g", "id_1wsx"]:
    species = model.getSpecies(species_id)
    y0.append(species.getInitialConcentration())

print("Initial conditions:")
print(f"id_8n7o: {y0[0]}")
print(f"id_caoz: {y0[1]}")
print(f"id_ty7g: {y0[2]}")
print(f"id_1wsx: {y0[3]}")

# Time points for simulation
t_span = (0, 183)  # Match the experimental data time range
t_eval = exp_data['Time'].values

# Model 3: id_8n7o + id_caoz -> id_ty7g + id_1wsx, id_8n7o + id_1wsx -> 2 id_ty7g, id_250q -> id_8n7o, id_caoz + id_ty7g -> id_1wsx
def model_ode3(t, y, k1, k2, k3, k4):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    # id_250q is constant at 11081000
    
    # Reaction 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    r1 = k1 * y[0] * y[1]
    
    # Reaction 2: id_8n7o + id_1wsx -> 2 id_ty7g
    r2 = k2 * y[0] * y[3]
    
    # Reaction 3: id_250q -> id_8n7o
    r3 = k3 * 11081000
    
    # Reaction 4: id_caoz + id_ty7g -> id_1wsx
    r4 = k4 * y[1] * y[2]
    
    # ODEs
    dy_dt = [
        -r1 - r2 + r3,      # d[id_8n7o]/dt
        -r1 - r4,           # d[id_caoz]/dt
        r1 + 2*r2 - r4,     # d[id_ty7g]/dt
        r1 - r2 + r4        # d[id_1wsx]/dt
    ]
    
    return dy_dt

print("\nTesting Model 3:")
print("1. id_8n7o + id_caoz -> id_ty7g + id_1wsx")
print("2. id_8n7o + id_1wsx -> 2 id_ty7g")
print("3. id_250q -> id_8n7o")
print("4. id_caoz + id_ty7g -> id_1wsx")

# Let's try different values for k1, k2, k3, and k4 to find a good fit
k1_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]
k2_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]
k3_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]
k4_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]

best_k1_3 = None
best_k2_3 = None
best_k3_3 = None
best_k4_3 = None
best_error_3 = float('inf')
best_sim_data_3 = None

# We'll do a coarse grid search
for k1 in k1_values:
    for k2 in k2_values:
        for k3 in k3_values:
            for k4 in k4_values:
                # Solve the ODE system
                try:
                    sol = solve_ivp(
                        lambda t, y: model_ode3(t, y, k1, k2, k3, k4),
                        t_span,
                        y0,
                        method='LSODA',
                        t_eval=t_eval
                    )
                    
                    # Calculate error (mean squared error)
                    sim_data = pd.DataFrame({
                        'Time': sol.t,
                        'id_8n7o': sol.y[0],
                        'id_caoz': sol.y[1],
                        'id_ty7g': sol.y[2],
                        'id_1wsx': sol.y[3]
                    })
                    
                    error = 0
                    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
                        # Normalize by the maximum value to give equal weight to each species
                        max_val = max(max(exp_data[species]), max(sim_data[species]))
                        if max_val > 0:
                            error += np.mean(((exp_data[species] - sim_data[species]) / max_val) ** 2)
                    
                    if error < best_error_3:
                        best_error_3 = error
                        best_k1_3 = k1
                        best_k2_3 = k2
                        best_k3_3 = k3
                        best_k4_3 = k4
                        best_sim_data_3 = sim_data
                except:
                    # Skip if the solver fails
                    continue

print(f"\nBest parameters for Model 3: k1 = {best_k1_3}, k2 = {best_k2_3}, k3 = {best_k3_3}, k4 = {best_k4_3}")
print(f"Best error for Model 3: {best_error_3}")

# Compare the best simulation with experimental data
if best_sim_data_3 is not None:
    print("\nComparison of Model 3 simulation vs. experimental data at selected time points:")
    selected_times = [0, 30, 60, 90, 120, 150, 180]
    for t in selected_times:
        idx = np.argmin(np.abs(best_sim_data_3['Time'] - t))
        print(f"\nTime {t}:")
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            sim_val = best_sim_data_3.loc[idx, species]
            exp_val = exp_data[exp_data['Time'] == t][species].values[0]
            rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
            print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Let's try a different model based on the observed dynamics
print("\nTrying a new model based on observed dynamics:")
print("1. id_8n7o -> id_caoz + id_ty7g")
print("2. id_caoz + id_8n7o -> id_1wsx + id_ty7g")
print("3. id_1wsx + id_8n7o -> 2 id_ty7g")

def model_ode4(t, y, k1, k2, k3):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o -> id_caoz + id_ty7g
    r1 = k1 * y[0]
    
    # Reaction 2: id_caoz + id_8n7o -> id_1wsx + id_ty7g
    r2 = k2 * y[1] * y[0]
    
    # Reaction 3: id_1wsx + id_8n7o -> 2 id_ty7g
    r3 = k3 * y[3] * y[0]
    
    # ODEs
    dy_dt = [
        -r1 - r2 - r3,      # d[id_8n7o]/dt
        r1 - r2,            # d[id_caoz]/dt
        r1 + r2 + 2*r3,     # d[id_ty7g]/dt
        r2 - r3             # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Let's try different values for k1, k2, and k3 to find a good fit
k1_values = [1e-6, 1e-5, 1e-4, 1e-3, 1e-2]
k2_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]
k3_values = [1e-10, 1e-9, 1e-8, 1e-7, 1e-6]

best_k1_4 = None
best_k2_4 = None
best_k3_4 = None
best_error_4 = float('inf')
best_sim_data_4 = None

# We'll do a coarse grid search
for k1 in k1_values:
    for k2 in k2_values:
        for k3 in k3_values:
            # Solve the ODE system
            try:
                sol = solve_ivp(
                    lambda t, y: model_ode4(t, y, k1, k2, k3),
                    t_span,
                    y0,
                    method='LSODA',
                    t_eval=t_eval
                )
                
                # Calculate error (mean squared error)
                sim_data = pd.DataFrame({
                    'Time': sol.t,
                    'id_8n7o': sol.y[0],
                    'id_caoz': sol.y[1],
                    'id_ty7g': sol.y[2],
                    'id_1wsx': sol.y[3]
                })
                
                error = 0
                for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
                    # Normalize by the maximum value to give equal weight to each species
                    max_val = max(max(exp_data[species]), max(sim_data[species]))
                    if max_val > 0:
                        error += np.mean(((exp_data[species] - sim_data[species]) / max_val) ** 2)
                
                if error < best_error_4:
                    best_error_4 = error
                    best_k1_4 = k1
                    best_k2_4 = k2
                    best_k3_4 = k3
                    best_sim_data_4 = sim_data
            except:
                # Skip if the solver fails
                continue

print(f"\nBest parameters for Model 4: k1 = {best_k1_4}, k2 = {best_k2_4}, k3 = {best_k3_4}")
print(f"Best error for Model 4: {best_error_4}")

# Compare the best simulation with experimental data
if best_sim_data_4 is not None:
    print("\nComparison of Model 4 simulation vs. experimental data at selected time points:")
    selected_times = [0, 30, 60, 90, 120, 150, 180]
    for t in selected_times:
        idx = np.argmin(np.abs(best_sim_data_4['Time'] - t))
        print(f"\nTime {t}:")
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            sim_val = best_sim_data_4.loc[idx, species]
            exp_val = exp_data[exp_data['Time'] == t][species].values[0]
            rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
            print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Compare the errors of all models
print("\nComparison of all models:")
model2_error = 1.5959426633657634  # From previous run
print(f"Model 2 error: {model2_error}")
print(f"Model 3 error: {best_error_3}")
print(f"Model 4 error: {best_error_4}")

# Choose the best model
if model2_error <= min(best_error_3, best_error_4):
    print("\nModel 2 is the best fit.")
    best_model = 2
elif best_error_3 <= min(model2_error, best_error_4):
    print("\nModel 3 is the best fit.")
    best_model = 3
else:
    print("\nModel 4 is the best fit.")
    best_model = 4

# Create the final SBML model with the best model's reactions and parameters
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

if best_model == 4:
    # Add the first reaction: id_8n7o -> id_caoz + id_ty7g
    reaction1 = model.createReaction()
    reaction1.setId("reaction1")
    reaction1.setReversible(False)

    # Add reactants
    reactant1 = reaction1.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction1.createProduct()
    product1.setSpecies("id_caoz")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    product2 = reaction1.createProduct()
    product2.setSpecies("id_ty7g")
    product2.setStoichiometry(1.0)
    product2.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law1 = reaction1.createKineticLaw()
    kinetic_law1.setFormula("k1 * id_8n7o")

    # Add parameter k1
    parameter1 = kinetic_law1.createParameter()
    parameter1.setId("k1")
    parameter1.setValue(best_k1_4)

    # Add the second reaction: id_caoz + id_8n7o -> id_1wsx + id_ty7g
    reaction2 = model.createReaction()
    reaction2.setId("reaction2")
    reaction2.setReversible(False)

    # Add reactants
    reactant1 = reaction2.createReactant()
    reactant1.setSpecies("id_caoz")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    reactant2 = reaction2.createReactant()
    reactant2.setSpecies("id_8n7o")
    reactant2.setStoichiometry(1.0)
    reactant2.setConstant(True)

    # Add products
    product1 = reaction2.createProduct()
    product1.setSpecies("id_1wsx")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    product2 = reaction2.createProduct()
    product2.setSpecies("id_ty7g")
    product2.setStoichiometry(1.0)
    product2.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law2 = reaction2.createKineticLaw()
    kinetic_law2.setFormula("k2 * id_caoz * id_8n7o")

    # Add parameter k2
    parameter2 = kinetic_law2.createParameter()
    parameter2.setId("k2")
    parameter2.setValue(best_k2_4)

    # Add the third reaction: id_1wsx + id_8n7o -> 2 id_ty7g
    reaction3 = model.createReaction()
    reaction3.setId("reaction3")
    reaction3.setReversible(False)

    # Add reactants
    reactant1 = reaction3.createReactant()
    reactant1.setSpecies("id_1wsx")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    reactant2 = reaction3.createReactant()
    reactant2.setSpecies("id_8n7o")
    reactant2.setStoichiometry(1.0)
    reactant2.setConstant(True)

    # Add products
    product1 = reaction3.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(2.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law3 = reaction3.createKineticLaw()
    kinetic_law3.setFormula("k3 * id_1wsx * id_8n7o")

    # Add parameter k3
    parameter3 = kinetic_law3.createParameter()
    parameter3.setId("k3")
    parameter3.setValue(best_k3_4)

    print("\nCreated SBML model with Model 4 reactions:")
    print(f"1. id_8n7o -> id_caoz + id_ty7g (k1 = {best_k1_4})")
    print(f"2. id_caoz + id_8n7o -> id_1wsx + id_ty7g (k2 = {best_k2_4})")
    print(f"3. id_1wsx + id_8n7o -> 2 id_ty7g (k3 = {best_k3_4})")

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

# Store the final SBML model
shared_variables.add('final_sbml', final_sbml)
```
# Observation

## Code Stdout
Initial conditions:
id_8n7o: 11080778.0
id_caoz: 193.0
id_ty7g: 2.0
id_1wsx: 27.0

Testing Model 3:
1. id_8n7o + id_caoz -> id_ty7g + id_1wsx
2. id_8n7o + id_1wsx -> 2 id_ty7g
3. id_250q -> id_8n7o
4. id_caoz + id_ty7g -> id_1wsx

Best parameters for Model 3: k1 = 1e-08, k2 = 1e-08, k3 = 1e-06, k4 = 1e-10
Best error for Model 3: 1.5958891814110692

Comparison of Model 3 simulation vs. experimental data at selected time points:

Time 0:
  id_8n7o: Sim = 1.11e+07, Exp = 1.11e+07, Rel Error = 0.00%
  id_caoz: Sim = 1.93e+02, Exp = 1.93e+02, Rel Error = 0.00%
  id_ty7g: Sim = 2.00e+00, Exp = 2.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 2.70e+01, Exp = 2.70e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 1.11e+07, Exp = 8.81e+06, Rel Error = 25.77%
  id_caoz: Sim = 6.95e+00, Exp = 1.50e+06, Rel Error = 100.00%
  id_ty7g: Sim = 5.66e+02, Exp = 1.10e+05, Rel Error = 99.49%
  id_1wsx: Sim = 2.41e+01, Exp = 6.64e+05, Rel Error = 100.00%

Time 60:
  id_8n7o: Sim = 1.11e+07, Exp = 6.25e+04, Rel Error = 17616.16%
  id_caoz: Sim = 2.50e-01, Exp = 4.97e+05, Rel Error = 100.00%
  id_ty7g: Sim = 6.31e+02, Exp = 6.06e+06, Rel Error = 99.99%
  id_1wsx: Sim = 1.70e+00, Exp = 4.46e+06, Rel Error = 100.00%

Time 90:
  id_8n7o: Sim = 1.11e+07, Exp = 1.02e+04, Rel Error = 108889.13%
  id_caoz: Sim = 9.03e-03, Exp = 1.19e+04, Rel Error = 100.00%
  id_ty7g: Sim = 6.35e+02, Exp = 9.81e+06, Rel Error = 99.99%
  id_1wsx: Sim = 9.09e-02, Exp = 1.25e+06, Rel Error = 100.00%

Time 120:
  id_8n7o: Sim = 1.11e+07, Exp = 6.57e+03, Rel Error = 168603.12%
  id_caoz: Sim = 3.26e-04, Exp = 6.56e+02, Rel Error = 100.00%
  id_ty7g: Sim = 6.35e+02, Exp = 1.08e+07, Rel Error = 99.99%
  id_1wsx: Sim = 4.36e-03, Exp = 3.01e+05, Rel Error = 100.00%

Time 150:
  id_8n7o: Sim = 1.11e+07, Exp = 5.92e+03, Rel Error = 187141.23%
  id_caoz: Sim = 1.18e-05, Exp = 1.06e+02, Rel Error = 100.00%
  id_ty7g: Sim = 6.35e+02, Exp = 1.10e+07, Rel Error = 99.99%
  id_1wsx: Sim = 1.96e-04, Exp = 7.18e+04, Rel Error = 100.00%

Time 180:
  id_8n7o: Sim = 1.11e+07, Exp = 5.77e+03, Rel Error = 191856.56%
  id_caoz: Sim = 4.33e-07, Exp = 2.35e+01, Rel Error = 100.00%
  id_ty7g: Sim = 6.35e+02, Exp = 1.11e+07, Rel Error = 99.99%
  id_1wsx: Sim = 8.56e-06, Exp = 1.71e+04, Rel Error = 100.00%

Trying a new model based on observed dynamics:
1. id_8n7o -> id_caoz + id_ty7g
2. id_caoz + id_8n7o -> id_1wsx + id_ty7g
3. id_1wsx + id_8n7o -> 2 id_ty7g

Best parameters for Model 4: k1 = 0.01, k2 = 1e-08, k3 = 1e-08
Best error for Model 4: 0.263823598045391

Comparison of Model 4 simulation vs. experimental data at selected time points:

Time 0:
  id_8n7o: Sim = 1.11e+07, Exp = 1.11e+07, Rel Error = 0.00%
  id_caoz: Sim = 1.93e+02, Exp = 1.93e+02, Rel Error = 0.00%
  id_ty7g: Sim = 2.00e+00, Exp = 2.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 2.70e+01, Exp = 2.70e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 5.93e+06, Exp = 8.81e+06, Rel Error = 32.65%
  id_caoz: Sim = 9.24e+05, Exp = 1.50e+06, Rel Error = 38.28%
  id_ty7g: Sim = 6.07e+06, Exp = 1.10e+05, Rel Error = 5412.30%
  id_1wsx: Sim = 7.28e+05, Exp = 6.64e+05, Rel Error = 9.58%

Time 60:
  id_8n7o: Sim = 2.57e+06, Exp = 6.25e+04, Rel Error = 4006.86%
  id_caoz: Sim = 9.77e+05, Exp = 4.97e+05, Rel Error = 96.53%
  id_ty7g: Sim = 1.04e+07, Exp = 6.06e+06, Rel Error = 72.03%
  id_1wsx: Sim = 8.91e+05, Exp = 4.46e+06, Rel Error = 80.01%

Time 90:
  id_8n7o: Sim = 1.08e+06, Exp = 1.02e+04, Rel Error = 10504.16%
  id_caoz: Sim = 9.86e+05, Exp = 1.19e+04, Rel Error = 8206.47%
  id_ty7g: Sim = 1.24e+07, Exp = 9.81e+06, Rel Error = 26.27%
  id_1wsx: Sim = 9.28e+05, Exp = 1.25e+06, Rel Error = 25.58%

Time 120:
  id_8n7o: Sim = 4.48e+05, Exp = 6.57e+03, Rel Error = 6722.17%
  id_caoz: Sim = 9.89e+05, Exp = 6.56e+02, Rel Error = 150655.06%
  id_ty7g: Sim = 1.32e+07, Exp = 1.08e+07, Rel Error = 22.73%
  id_1wsx: Sim = 9.39e+05, Exp = 3.01e+05, Rel Error = 212.11%

Time 150:
  id_8n7o: Sim = 1.86e+05, Exp = 5.92e+03, Rel Error = 3046.60%
  id_caoz: Sim = 9.90e+05, Exp = 1.06e+02, Rel Error = 937331.41%
  id_ty7g: Sim = 1.36e+07, Exp = 1.10e+07, Rel Error = 23.30%
  id_1wsx: Sim = 9.44e+05, Exp = 7.18e+04, Rel Error = 1213.90%

Time 180:
  id_8n7o: Sim = 7.72e+04, Exp = 5.77e+03, Rel Error = 1237.63%
  id_caoz: Sim = 9.90e+05, Exp = 2.35e+01, Rel Error = 4215026.12%
  id_ty7g: Sim = 1.37e+07, Exp = 1.11e+07, Rel Error = 23.99%
  id_1wsx: Sim = 9.45e+05, Exp = 1.71e+04, Rel Error = 5422.75%

Comparison of all models:
Model 2 error: 1.5959426633657634
Model 3 error: 1.5958891814110692
Model 4 error: 0.263823598045391

Model 4 is the best fit.

Created SBML model with Model 4 reactions:
1. id_8n7o -> id_caoz + id_ty7g (k1 = 0.01)
2. id_caoz + id_8n7o -> id_1wsx + id_ty7g (k2 = 1e-08)
3. id_1wsx + id_8n7o -> 2 id_ty7g (k3 = 1e-08)

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml)

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


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



# Iteration 8
## Thoughts
Model 4 shows a significant improvement over the previous models, with an error of 0.26 compared to ~1.6 for Models 2 and 3. This suggests that the reactions in Model 4 better capture the underlying dynamics of the system:

1. `id_8n7o -> id_caoz + id_ty7g` (k1 = 0.01)
2. `id_caoz + id_8n7o -> id_1wsx + id_ty7g` (k2 = 1e-08)
3. `id_1wsx + id_8n7o -> 2 id_ty7g` (k3 = 1e-08)

However, there are still significant discrepancies between the simulated and experimental data, especially for `id_caoz` at later time points. Let's try to refine this model further by:

1. Testing a slightly different set of reactions
2. Fine-tuning the rate constants
3. Checking if we need additional reactions

Let's also run an experiment with different initial conditions to see if our model can predict the system's behavior under different conditions.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration", 
    "meta_data": {
        "id_8n7o": 5000000,
        "id_caoz": 1000,
        "id_ty7g": 10,
        "id_1wsx": 100
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_8
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_8]

Total size: 184 rows × 6 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_8] for the full data

Time   id_8n7o  id_caoz  id_ty7g  id_1wsx  id_250q
0  5.00e+06 1.00e+03 1.00e+01 1.00e+02 1.11e+07
...
3.00e+00  5.00e+06 1.17e+03 5.36e+01 5.07e+02 1.11e+07
...
6.00e+00  5.00e+06 1.49e+03 1.58e+02 9.57e+02 1.11e+07
...
9.00e+00  5.00e+06 2.01e+03 3.34e+02 1.51e+03 1.11e+07
...
1.20e+01  5.00e+06 2.77e+03 6.01e+02 2.23e+03 1.11e+07
...
1.50e+01  4.99e+06 3.86e+03 9.90e+02 3.22e+03 1.11e+07
...
1.80e+01  4.99e+06 5.43e+03 1.55e+03 4.60e+03 1.11e+07
...
2.10e+01  4.98e+06 7.64e+03 2.34e+03 6.52e+03 1.11e+07
...
2.40e+01  4.98e+06 1.08e+04 3.46e+03 9.23e+03 1.11e+07
...
2.70e+01  4.97e+06 1.51e+04 5.05e+03 1.30e+04 1.11e+07
...
3.00e+01  4.95e+06 2.13e+04 7.29e+03 1.84e+04 1.11e+07
...
3.30e+01  4.93e+06 2.99e+04 1.04e+04 2.59e+04 1.11e+07
...
3.60e+01  4.91e+06 4.19e+04 1.49e+04 3.64e+04 1.11e+07
...
3.90e+01  4.87e+06 5.85e+04 2.11e+04 5.10e+04 1.11e+07
...
4.20e+01  4.82e+06 8.12e+04 2.99e+04 7.14e+04 1.11e+07
...
4.50e+01  4.75e+06 1.12e+05 4.20e+04 9.94e+04 1.11e+07
...
4.80e+01  4.65e+06 1.53e+05 5.90e+04 1.38e+05 1.11e+07
...
5.10e+01  4.52e+06 2.06e+05 8.23e+04 1.89e+05 1.11e+07
...
5.40e+01  4.36e+06 2.73e+05 1.14e+05 2.57e+05 1.11e+07
...
5.70e+01  4.14e+06 3.54e+05 1.57e+05 3.45e+05 1.11e+07
...
6.00e+01  3.88e+06 4.46e+05 2.15e+05 4.56e+05 1.11e+07
...
6.30e+01  3.58e+06 5.44e+05 2.90e+05 5.89e+05 1.11e+07
...
6.60e+01  3.23e+06 6.39e+05 3.85e+05 7.42e+05 1.11e+07
...
6.90e+01  2.87e+06 7.19e+05 5.04e+05 9.09e+05 1.11e+07
...
7.20e+01  2.50e+06 7.73e+05 6.47e+05 1.08e+06 1.11e+07
...
7.50e+01  2.15e+06 7.96e+05 8.15e+05 1.24e+06 1.11e+07
...
7.80e+01  1.82e+06 7.85e+05 1.00e+06 1.39e+06 1.11e+07
...
8.10e+01  1.54e+06 7.46e+05 1.21e+06 1.50e+06 1.11e+07
...
8.40e+01  1.30e+06 6.86e+05 1.44e+06 1.58e+06 1.11e+07
...
8.70e+01  1.10e+06 6.14e+05 1.67e+06 1.62e+06 1.11e+07
...
9.00e+01  9.35e+05 5.36e+05 1.90e+06 1.63e+06 1.11e+07
...
9.30e+01  8.02e+05 4.60e+05 2.13e+06 1.61e+06 1.11e+07
...
9.60e+01  6.94e+05 3.90e+05 2.36e+06 1.56e+06 1.11e+07
...
9.90e+01  6.07e+05 3.26e+05 2.58e+06 1.49e+06 1.11e+07
...
1.02e+02  5.37e+05 2.71e+05 2.79e+06 1.40e+06 1.11e+07
...
1.05e+02  4.80e+05 2.25e+05 2.98e+06 1.31e+06 1.11e+07
...
1.08e+02  4.33e+05 1.85e+05 3.17e+06 1.22e+06 1.11e+07
...
1.11e+02  3.95e+05 1.53e+05 3.33e+06 1.12e+06 1.11e+07
...
1.14e+02  3.64e+05 1.26e+05 3.49e+06 1.02e+06 1.11e+07
...
1.17e+02  3.37e+05 1.04e+05 3.63e+06 9.30e+05 1.11e+07
...
1.20e+02  3.16e+05 8.60e+04 3.76e+06 8.42e+05 1.11e+07
...
1.23e+02  2.97e+05 7.13e+04 3.87e+06 7.60e+05 1.11e+07
...
1.26e+02  2.82e+05 5.94e+04 3.98e+06 6.84e+05 1.11e+07
...
1.29e+02  2.69e+05 4.96e+04 4.07e+06 6.13e+05 1.11e+07
...
1.32e+02  2.58e+05 4.16e+04 4.15e+06 5.49e+05 1.11e+07
...
1.35e+02  2.48e+05 3.50e+04 4.23e+06 4.90e+05 1.11e+07
...
1.38e+02  2.40e+05 2.96e+04 4.29e+06 4.37e+05 1.11e+07
...
1.41e+02  2.33e+05 2.51e+04 4.35e+06 3.89e+05 1.11e+07
...
1.44e+02  2.27e+05 2.14e+04 4.41e+06 3.46e+05 1.11e+07
...
1.83e+02  1.94e+05 3.32e+03 4.73e+06 7.07e+04 1.11e+07

## 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_8)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml)

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


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



# Iteration 9
## Thoughts
Now I have data from two experiments with different initial conditions. Let me analyze the new data and see if it's consistent with our current model or if we need to refine it further.

In the new experiment:
1. `id_8n7o` starts at 5,000,000 (lower than the first experiment) and decreases over time
2. `id_caoz` starts at 1,000 (higher than the first experiment), increases to a peak (~8.0e+05 around t=75), then decreases
3. `id_ty7g` starts at 10 (higher than the first experiment) and continuously increases to ~4.7e+06
4. `id_1wsx` starts at 100 (higher than the first experiment), increases to a peak (~1.6e+06 around t=90), then decreases

This behavior is qualitatively similar to what we observed in the first experiment, which is a good sign. Let me now test our current model (Model 4) against this new data to see how well it performs.

## Action

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

# Access the experimental data
exp_data_1 = experiment_history["iteration_0"]
exp_data_2 = experiment_history["iteration_8"]

# Access the final model from the previous iteration
final_sbml = shared_variables.access('final_sbml')

# Define the Model 4 ODE function
def model_ode4(t, y, k1, k2, k3):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o -> id_caoz + id_ty7g
    r1 = k1 * y[0]
    
    # Reaction 2: id_caoz + id_8n7o -> id_1wsx + id_ty7g
    r2 = k2 * y[1] * y[0]
    
    # Reaction 3: id_1wsx + id_8n7o -> 2 id_ty7g
    r3 = k3 * y[3] * y[0]
    
    # ODEs
    dy_dt = [
        -r1 - r2 - r3,      # d[id_8n7o]/dt
        r1 - r2,            # d[id_caoz]/dt
        r1 + r2 + 2*r3,     # d[id_ty7g]/dt
        r2 - r3             # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Get the best parameters from the previous iteration
best_k1_4 = 0.01
best_k2_4 = 1e-8
best_k3_4 = 1e-8

# Initial conditions for the second experiment
y0_exp2 = [5000000, 1000, 10, 100]

# Time points for simulation
t_span = (0, 183)
t_eval = exp_data_2['Time'].values

# Simulate the model with the best parameters
sol = solve_ivp(
    lambda t, y: model_ode4(t, y, best_k1_4, best_k2_4, best_k3_4),
    t_span,
    y0_exp2,
    method='LSODA',
    t_eval=t_eval
)

# Calculate error (mean squared error)
sim_data = pd.DataFrame({
    'Time': sol.t,
    'id_8n7o': sol.y[0],
    'id_caoz': sol.y[1],
    'id_ty7g': sol.y[2],
    'id_1wsx': sol.y[3]
})

error = 0
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    # Normalize by the maximum value to give equal weight to each species
    max_val = max(max(exp_data_2[species]), max(sim_data[species]))
    if max_val > 0:
        error += np.mean(((exp_data_2[species] - sim_data[species]) / max_val) ** 2)

print(f"Error for Model 4 on the second experiment: {error}")

# Compare the simulation with experimental data
print("\nComparison of Model 4 simulation vs. experimental data at selected time points:")
selected_times = [0, 30, 60, 90, 120, 150, 180]
for t in selected_times:
    idx = np.argmin(np.abs(sim_data['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data.loc[idx, species]
        exp_val = exp_data_2[exp_data_2['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Let's try to refine the model further
print("\nTrying a refined model:")
print("1. id_8n7o -> id_caoz + id_ty7g")
print("2. id_caoz + id_8n7o -> id_1wsx + id_ty7g")
print("3. id_1wsx + id_8n7o -> 2 id_ty7g")
print("4. id_caoz -> id_ty7g (added to better match the decrease in id_caoz)")

def model_ode5(t, y, k1, k2, k3, k4):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o -> id_caoz + id_ty7g
    r1 = k1 * y[0]
    
    # Reaction 2: id_caoz + id_8n7o -> id_1wsx + id_ty7g
    r2 = k2 * y[1] * y[0]
    
    # Reaction 3: id_1wsx + id_8n7o -> 2 id_ty7g
    r3 = k3 * y[3] * y[0]
    
    # Reaction 4: id_caoz -> id_ty7g
    r4 = k4 * y[1]
    
    # ODEs
    dy_dt = [
        -r1 - r2 - r3,      # d[id_8n7o]/dt
        r1 - r2 - r4,       # d[id_caoz]/dt
        r1 + r2 + 2*r3 + r4,# d[id_ty7g]/dt
        r2 - r3             # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Let's optimize the parameters for both experiments simultaneously
def objective_function(params):
    k1, k2, k3, k4 = params
    
    # Simulate for the first experiment
    y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
    t_eval_1 = exp_data_1['Time'].values
    
    try:
        sol1 = solve_ivp(
            lambda t, y: model_ode5(t, y, k1, k2, k3, k4),
            t_span,
            y0_exp1,
            method='LSODA',
            t_eval=t_eval_1
        )
        
        sim_data1 = pd.DataFrame({
            'Time': sol1.t,
            'id_8n7o': sol1.y[0],
            'id_caoz': sol1.y[1],
            'id_ty7g': sol1.y[2],
            'id_1wsx': sol1.y[3]
        })
        
        error1 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_1[species]), max(sim_data1[species]))
            if max_val > 0:
                error1 += np.mean(((exp_data_1[species] - sim_data1[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the second experiment
    y0_exp2 = [5000000, 1000, 10, 100]
    t_eval_2 = exp_data_2['Time'].values
    
    try:
        sol2 = solve_ivp(
            lambda t, y: model_ode5(t, y, k1, k2, k3, k4),
            t_span,
            y0_exp2,
            method='LSODA',
            t_eval=t_eval_2
        )
        
        sim_data2 = pd.DataFrame({
            'Time': sol2.t,
            'id_8n7o': sol2.y[0],
            'id_caoz': sol2.y[1],
            'id_ty7g': sol2.y[2],
            'id_1wsx': sol2.y[3]
        })
        
        error2 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_2[species]), max(sim_data2[species]))
            if max_val > 0:
                error2 += np.mean(((exp_data_2[species] - sim_data2[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Return the total error
    return error1 + error2

# Let's try a few parameter combinations manually
param_sets = [
    [0.01, 1e-8, 1e-8, 0.01],
    [0.01, 1e-8, 1e-8, 0.1],
    [0.01, 1e-7, 1e-8, 0.01],
    [0.01, 1e-8, 1e-7, 0.01],
    [0.005, 1e-8, 1e-8, 0.01],
    [0.02, 1e-8, 1e-8, 0.01]
]

best_params = None
best_error = float('inf')

for params in param_sets:
    error = objective_function(params)
    if error < best_error:
        best_error = error
        best_params = params

print(f"\nBest parameters for Model 5: k1 = {best_params[0]}, k2 = {best_params[1]}, k3 = {best_params[2]}, k4 = {best_params[3]}")
print(f"Best error for Model 5: {best_error}")

# Simulate with the best parameters for both experiments
# First experiment
y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
t_eval_1 = exp_data_1['Time'].values

sol1 = solve_ivp(
    lambda t, y: model_ode5(t, y, *best_params),
    t_span,
    y0_exp1,
    method='LSODA',
    t_eval=t_eval_1
)

sim_data1 = pd.DataFrame({
    'Time': sol1.t,
    'id_8n7o': sol1.y[0],
    'id_caoz': sol1.y[1],
    'id_ty7g': sol1.y[2],
    'id_1wsx': sol1.y[3]
})

# Second experiment
y0_exp2 = [5000000, 1000, 10, 100]
t_eval_2 = exp_data_2['Time'].values

sol2 = solve_ivp(
    lambda t, y: model_ode5(t, y, *best_params),
    t_span,
    y0_exp2,
    method='LSODA',
    t_eval=t_eval_2
)

sim_data2 = pd.DataFrame({
    'Time': sol2.t,
    'id_8n7o': sol2.y[0],
    'id_caoz': sol2.y[1],
    'id_ty7g': sol2.y[2],
    'id_1wsx': sol2.y[3]
})

# Compare the simulation with experimental data for both experiments
print("\nComparison of Model 5 simulation vs. experimental data for the first experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data1['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data1.loc[idx, species]
        exp_val = exp_data_1[exp_data_1['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

print("\nComparison of Model 5 simulation vs. experimental data for the second experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data2['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data2.loc[idx, species]
        exp_val = exp_data_2[exp_data_2['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Create the final SBML model with the refined reactions and parameters
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

# Add the first reaction: id_8n7o -> id_caoz + id_ty7g
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactants
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_8n7o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction1.createProduct()
product1.setSpecies("id_caoz")
product1.setStoichiometry(1.0)
product1.setConstant(True)

product2 = reaction1.createProduct()
product2.setSpecies("id_ty7g")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law (mass action)
kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1 * id_8n7o")

# Add parameter k1
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(best_params[0])

# Add the second reaction: id_caoz + id_8n7o -> id_1wsx + id_ty7g
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactants
reactant1 = reaction2.createReactant()
reactant1.setSpecies("id_caoz")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_8n7o")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product1 = reaction2.createProduct()
product1.setSpecies("id_1wsx")
product1.setStoichiometry(1.0)
product1.setConstant(True)

product2 = reaction2.createProduct()
product2.setSpecies("id_ty7g")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_caoz * id_8n7o")

# Add parameter k2
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(best_params[1])

# Add the third reaction: id_1wsx + id_8n7o -> 2 id_ty7g
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactants
reactant1 = reaction3.createReactant()
reactant1.setSpecies("id_1wsx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

reactant2 = reaction3.createReactant()
reactant2.setSpecies("id_8n7o")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product1 = reaction3.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(2.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_1wsx * id_8n7o")

# Add parameter k3
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(best_params[2])

# Add the fourth reaction: id_caoz -> id_ty7g
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactants
reactant1 = reaction4.createReactant()
reactant1.setSpecies("id_caoz")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction4.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_caoz")

# Add parameter k4
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(best_params[3])

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

# Store the final SBML model
shared_variables.add('final_sbml_refined', final_sbml)

print("\nCreated SBML model with Model 5 reactions:")
print(f"1. id_8n7o -> id_caoz + id_ty7g (k1 = {best_params[0]})")
print(f"2. id_caoz + id_8n7o -> id_1wsx + id_ty7g (k2 = {best_params[1]})")
print(f"3. id_1wsx + id_8n7o -> 2 id_ty7g (k3 = {best_params[2]})")
print(f"4. id_caoz -> id_ty7g (k4 = {best_params[3]})")
```
# Observation

## Code Stdout
Error for Model 4 on the second experiment: 0.8473233019635737

Comparison of Model 4 simulation vs. experimental data at selected time points:

Time 0:
  id_8n7o: Sim = 5.00e+06, Exp = 5.00e+06, Rel Error = 0.00%
  id_caoz: Sim = 1.00e+03, Exp = 1.00e+03, Rel Error = 0.00%
  id_ty7g: Sim = 1.00e+01, Exp = 1.00e+01, Rel Error = 0.00%
  id_1wsx: Sim = 1.00e+02, Exp = 1.00e+02, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 3.09e+06, Exp = 4.95e+06, Rel Error = 37.66%
  id_caoz: Sim = 7.06e+05, Exp = 2.13e+04, Rel Error = 3211.87%
  id_ty7g: Sim = 2.08e+06, Exp = 7.29e+03, Rel Error = 28476.83%
  id_1wsx: Sim = 3.46e+05, Exp = 1.84e+04, Rel Error = 1782.05%

Time 60:
  id_8n7o: Sim = 1.56e+06, Exp = 3.88e+06, Rel Error = 59.72%
  id_caoz: Sim = 8.51e+05, Exp = 4.46e+05, Rel Error = 90.60%
  id_ty7g: Sim = 3.92e+06, Exp = 2.15e+05, Rel Error = 1724.63%
  id_1wsx: Sim = 5.67e+05, Exp = 4.56e+05, Rel Error = 24.35%

Time 90:
  id_8n7o: Sim = 7.41e+05, Exp = 9.35e+05, Rel Error = 20.76%
  id_caoz: Sim = 8.93e+05, Exp = 5.36e+05, Rel Error = 66.46%
  id_ty7g: Sim = 4.95e+06, Exp = 1.90e+06, Rel Error = 160.24%
  id_1wsx: Sim = 6.53e+05, Exp = 1.63e+06, Rel Error = 59.90%

Time 120:
  id_8n7o: Sim = 3.42e+05, Exp = 3.16e+05, Rel Error = 8.40%
  id_caoz: Sim = 9.08e+05, Exp = 8.60e+04, Rel Error = 956.23%
  id_ty7g: Sim = 5.45e+06, Exp = 3.76e+06, Rel Error = 45.03%
  id_1wsx: Sim = 6.89e+05, Exp = 8.42e+05, Rel Error = 18.23%

Time 150:
  id_8n7o: Sim = 1.56e+05, Exp = 2.18e+05, Rel Error = 28.13%
  id_caoz: Sim = 9.14e+05, Exp = 1.57e+04, Rel Error = 5740.44%
  id_ty7g: Sim = 5.68e+06, Exp = 4.50e+06, Rel Error = 26.45%
  id_1wsx: Sim = 7.04e+05, Exp = 2.73e+05, Rel Error = 158.37%

Time 180:
  id_8n7o: Sim = 7.12e+04, Exp = 1.95e+05, Rel Error = 63.45%
  id_caoz: Sim = 9.17e+05, Exp = 3.80e+03, Rel Error = 24067.19%
  id_ty7g: Sim = 5.79e+06, Exp = 4.72e+06, Rel Error = 22.66%
  id_1wsx: Sim = 7.11e+05, Exp = 8.01e+04, Rel Error = 787.68%

Trying a refined model:
1. id_8n7o -> id_caoz + id_ty7g
2. id_caoz + id_8n7o -> id_1wsx + id_ty7g
3. id_1wsx + id_8n7o -> 2 id_ty7g
4. id_caoz -> id_ty7g (added to better match the decrease in id_caoz)

Best parameters for Model 5: k1 = 0.005, k2 = 1e-08, k3 = 1e-08, k4 = 0.01
Best error for Model 5: 0.5966018531647623

Comparison of Model 5 simulation vs. experimental data for the first experiment:

Time 0:
  id_8n7o: Sim = 1.11e+07, Exp = 1.11e+07, Rel Error = 0.00%
  id_caoz: Sim = 1.93e+02, Exp = 1.93e+02, Rel Error = 0.00%
  id_ty7g: Sim = 2.00e+00, Exp = 2.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 2.70e+01, Exp = 2.70e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 8.13e+06, Exp = 8.81e+06, Rel Error = 7.67%
  id_caoz: Sim = 4.32e+05, Exp = 1.50e+06, Rel Error = 71.14%
  id_ty7g: Sim = 3.61e+06, Exp = 1.10e+05, Rel Error = 3174.81%
  id_1wsx: Sim = 3.66e+05, Exp = 6.64e+05, Rel Error = 44.82%

Time 60:
  id_8n7o: Sim = 5.44e+06, Exp = 6.25e+04, Rel Error = 8591.19%
  id_caoz: Sim = 4.31e+05, Exp = 4.97e+05, Rel Error = 13.32%
  id_ty7g: Sim = 7.25e+06, Exp = 6.06e+06, Rel Error = 19.61%
  id_1wsx: Sim = 4.26e+05, Exp = 4.46e+06, Rel Error = 90.45%

Time 90:
  id_8n7o: Sim = 3.63e+06, Exp = 1.02e+04, Rel Error = 35600.51%
  id_caoz: Sim = 4.10e+05, Exp = 1.19e+04, Rel Error = 3350.52%
  id_ty7g: Sim = 9.75e+06, Exp = 9.81e+06, Rel Error = 0.59%
  id_1wsx: Sim = 4.21e+05, Exp = 1.25e+06, Rel Error = 66.23%

Time 120:
  id_8n7o: Sim = 2.45e+06, Exp = 6.57e+03, Rel Error = 37203.47%
  id_caoz: Sim = 3.83e+05, Exp = 6.56e+02, Rel Error = 58260.79%
  id_ty7g: Sim = 1.14e+07, Exp = 1.08e+07, Rel Error = 6.06%
  id_1wsx: Sim = 4.06e+05, Exp = 3.01e+05, Rel Error = 34.85%

Time 150:
  id_8n7o: Sim = 1.68e+06, Exp = 5.92e+03, Rel Error = 28236.86%
  id_caoz: Sim = 3.53e+05, Exp = 1.06e+02, Rel Error = 333827.46%
  id_ty7g: Sim = 1.26e+07, Exp = 1.10e+07, Rel Error = 14.07%
  id_1wsx: Sim = 3.88e+05, Exp = 7.18e+04, Rel Error = 440.52%

Time 180:
  id_8n7o: Sim = 1.16e+06, Exp = 5.77e+03, Rel Error = 20076.52%
  id_caoz: Sim = 3.20e+05, Exp = 2.35e+01, Rel Error = 1362744.49%
  id_ty7g: Sim = 1.33e+07, Exp = 1.11e+07, Rel Error = 20.50%
  id_1wsx: Sim = 3.70e+05, Exp = 1.71e+04, Rel Error = 2063.50%

Comparison of Model 5 simulation vs. experimental data for the second experiment:

Time 0:
  id_8n7o: Sim = 5.00e+06, Exp = 5.00e+06, Rel Error = 0.00%
  id_caoz: Sim = 1.00e+03, Exp = 1.00e+03, Rel Error = 0.00%
  id_ty7g: Sim = 1.00e+01, Exp = 1.00e+01, Rel Error = 0.00%
  id_1wsx: Sim = 1.00e+02, Exp = 1.00e+02, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 3.94e+06, Exp = 4.95e+06, Rel Error = 20.51%
  id_caoz: Sim = 3.29e+05, Exp = 2.13e+04, Rel Error = 1443.72%
  id_ty7g: Sim = 1.23e+06, Exp = 7.29e+03, Rel Error = 16775.24%
  id_1wsx: Sim = 1.80e+05, Exp = 1.84e+04, Rel Error = 878.83%

Time 60:
  id_8n7o: Sim = 2.83e+06, Exp = 3.88e+06, Rel Error = 27.17%
  id_caoz: Sim = 3.68e+05, Exp = 4.46e+05, Rel Error = 17.57%
  id_ty7g: Sim = 2.69e+06, Exp = 2.15e+05, Rel Error = 1152.89%
  id_1wsx: Sim = 2.93e+05, Exp = 4.56e+05, Rel Error = 35.62%

Time 90:
  id_8n7o: Sim = 1.99e+06, Exp = 9.35e+05, Rel Error = 112.43%
  id_caoz: Sim = 3.56e+05, Exp = 5.36e+05, Rel Error = 33.63%
  id_ty7g: Sim = 3.87e+06, Exp = 1.90e+06, Rel Error = 103.52%
  id_1wsx: Sim = 3.29e+05, Exp = 1.63e+06, Rel Error = 79.80%

Time 120:
  id_8n7o: Sim = 1.40e+06, Exp = 3.16e+05, Rel Error = 342.02%
  id_caoz: Sim = 3.31e+05, Exp = 8.60e+04, Rel Error = 284.61%
  id_ty7g: Sim = 4.73e+06, Exp = 3.76e+06, Rel Error = 25.88%
  id_1wsx: Sim = 3.35e+05, Exp = 8.42e+05, Rel Error = 60.27%

Time 150:
  id_8n7o: Sim = 9.89e+05, Exp = 2.18e+05, Rel Error = 354.49%
  id_caoz: Sim = 3.01e+05, Exp = 1.57e+04, Rel Error = 1820.62%
  id_ty7g: Sim = 5.35e+06, Exp = 4.50e+06, Rel Error = 18.97%
  id_1wsx: Sim = 3.29e+05, Exp = 2.73e+05, Rel Error = 20.73%

Time 180:
  id_8n7o: Sim = 7.09e+05, Exp = 1.95e+05, Rel Error = 264.02%
  id_caoz: Sim = 2.69e+05, Exp = 3.80e+03, Rel Error = 6993.51%
  id_ty7g: Sim = 5.80e+06, Exp = 4.72e+06, Rel Error = 22.72%
  id_1wsx: Sim = 3.19e+05, Exp = 8.01e+04, Rel Error = 298.56%

Created SBML model with Model 5 reactions:
1. id_8n7o -> id_caoz + id_ty7g (k1 = 0.005)
2. id_caoz + id_8n7o -> id_1wsx + id_ty7g (k2 = 1e-08)
3. id_1wsx + id_8n7o -> 2 id_ty7g (k3 = 1e-08)
4. id_caoz -> id_ty7g (k4 = 0.01)

## 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_8)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml, final_sbml_refined)

### 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
Model 5 shows some improvement over Model 4, with a combined error of 0.597 compared to 0.847 for Model 4 on the second experiment alone. The addition of the reaction `id_caoz -> id_ty7g` helps to better capture the decrease in `id_caoz` at later time points.

However, there are still significant discrepancies between the simulated and experimental data, particularly:

1. For the first experiment:
   - `id_8n7o` decreases too slowly in the simulation compared to the experimental data
   - `id_ty7g` increases too quickly in the simulation at early time points
   - `id_caoz` doesn't reach as high a peak in the simulation as in the experimental data

2. For the second experiment:
   - Similar issues as the first experiment, but with better agreement for some species

Let me try one more model refinement. Looking at the data more carefully, I notice that:
1. `id_8n7o` decreases rapidly, suggesting it might be consumed in additional reactions
2. `id_ty7g` increases steadily, suggesting it's a product of multiple reactions
3. `id_caoz` and `id_1wsx` both show a rise and fall pattern, suggesting they are both produced and consumed

Let me try a model with the following reactions:
1. `id_8n7o -> id_caoz + id_ty7g` (kept from Model 5)
2. `id_caoz + id_8n7o -> id_1wsx + id_ty7g` (kept from Model 5)
3. `id_1wsx + id_8n7o -> 2 id_ty7g` (kept from Model 5)
4. `id_caoz -> id_ty7g` (kept from Model 5)
5. `id_8n7o -> id_ty7g` (new reaction to accelerate `id_8n7o` consumption and `id_ty7g` production)

Let me also try a different experiment with higher initial concentrations to see if our model can predict the system's behavior under these conditions.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration", 
    "meta_data": {
        "id_8n7o": 15000000,
        "id_caoz": 500,
        "id_ty7g": 5,
        "id_1wsx": 50
    }
}
```
# 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: 184 rows × 6 columns. 

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

Time   id_8n7o  id_caoz  id_ty7g  id_1wsx  id_250q
0  1.50e+07 5.00e+02 5.00e+00 5.00e+01 1.11e+07
...
3.00e+00  1.50e+07 1.71e+03 3.42e+01 4.30e+02 1.11e+07
...
6.00e+00  1.50e+07 6.31e+03 1.72e+02 1.77e+03 1.11e+07
...
9.00e+00  1.50e+07 2.35e+04 7.08e+02 6.73e+03 1.11e+07
...
1.20e+01  1.49e+07 8.76e+04 2.72e+03 2.52e+04 1.11e+07
...
1.50e+01  1.46e+07 3.20e+05 1.02e+04 9.33e+04 1.11e+07
...
1.80e+01  1.35e+07 1.10e+06 3.75e+04 3.34e+05 1.11e+07
...
2.10e+01  1.07e+07 3.09e+06 1.30e+05 1.07e+06 1.11e+07
...
2.40e+01  6.16e+06 5.76e+06 3.90e+05 2.69e+06 1.11e+07
...
2.70e+01  2.58e+06 6.65e+06 9.31e+05 4.84e+06 1.11e+07
...
3.00e+01  9.64e+05 5.64e+06 1.77e+06 6.63e+06 1.11e+07
...
3.30e+01  3.74e+05 4.17e+06 2.80e+06 7.65e+06 1.11e+07
...
3.60e+01  1.59e+05 2.91e+06 3.94e+06 7.99e+06 1.11e+07
...
3.90e+01  7.51e+04 1.98e+06 5.08e+06 7.86e+06 1.11e+07
...
4.20e+01  3.89e+04 1.33e+06 6.19e+06 7.45e+06 1.11e+07
...
4.50e+01  2.19e+04 8.87e+05 7.22e+06 6.87e+06 1.11e+07
...
4.80e+01  1.33e+04 5.90e+05 8.16e+06 6.23e+06 1.11e+07
...
5.10e+01  8.67e+03 3.91e+05 9.01e+06 5.59e+06 1.11e+07
...
5.40e+01  5.97e+03 2.59e+05 9.77e+06 4.96e+06 1.11e+07
...
5.70e+01  4.32e+03 1.72e+05 1.04e+07 4.38e+06 1.11e+07
...
6.00e+01  3.26e+03 1.14e+05 1.10e+07 3.85e+06 1.11e+07
...
6.30e+01  2.56e+03 7.52e+04 1.16e+07 3.37e+06 1.11e+07
...
6.60e+01  2.07e+03 4.98e+04 1.20e+07 2.94e+06 1.11e+07
...
6.90e+01  1.73e+03 3.30e+04 1.24e+07 2.56e+06 1.11e+07
...
7.20e+01  1.47e+03 2.19e+04 1.27e+07 2.23e+06 1.11e+07
...
7.50e+01  1.29e+03 1.45e+04 1.30e+07 1.94e+06 1.11e+07
...
7.80e+01  1.14e+03 9.67e+03 1.33e+07 1.68e+06 1.11e+07
...
8.10e+01  1.03e+03 6.44e+03 1.35e+07 1.46e+06 1.11e+07
...
8.40e+01  9.42e+02 4.30e+03 1.37e+07 1.27e+06 1.11e+07
...
8.70e+01  8.73e+02 2.88e+03 1.39e+07 1.10e+06 1.11e+07
...
9.00e+01  8.16e+02 1.94e+03 1.40e+07 9.51e+05 1.11e+07
...
9.30e+01  7.71e+02 1.31e+03 1.42e+07 8.24e+05 1.11e+07
...
9.60e+01  7.33e+02 8.93e+02 1.43e+07 7.14e+05 1.11e+07
...
9.90e+01  7.02e+02 6.12e+02 1.44e+07 6.18e+05 1.11e+07
...
1.02e+02  6.76e+02 4.23e+02 1.45e+07 5.36e+05 1.11e+07
...
1.05e+02  6.55e+02 2.95e+02 1.45e+07 4.64e+05 1.11e+07
...
1.08e+02  6.36e+02 2.09e+02 1.46e+07 4.02e+05 1.11e+07
...
1.11e+02  6.21e+02 1.50e+02 1.47e+07 3.48e+05 1.11e+07
...
1.14e+02  6.08e+02 1.09e+02 1.47e+07 3.01e+05 1.11e+07
...
1.17e+02  5.97e+02 8.04e+01 1.47e+07 2.61e+05 1.11e+07
...
1.20e+02  5.88e+02 6.05e+01 1.48e+07 2.26e+05 1.11e+07
...
1.23e+02  5.80e+02 4.62e+01 1.48e+07 1.96e+05 1.11e+07
...
1.26e+02  5.73e+02 3.59e+01 1.48e+07 1.70e+05 1.11e+07
...
1.29e+02  5.67e+02 2.83e+01 1.49e+07 1.47e+05 1.11e+07
...
1.32e+02  5.62e+02 2.27e+01 1.49e+07 1.27e+05 1.11e+07
...
1.35e+02  5.58e+02 1.84e+01 1.49e+07 1.10e+05 1.11e+07
...
1.38e+02  5.54e+02 1.51e+01 1.49e+07 9.53e+04 1.11e+07
...
1.41e+02  5.51e+02 1.25e+01 1.49e+07 8.25e+04 1.11e+07
...
1.44e+02  5.48e+02 1.05e+01 1.49e+07 7.15e+04 1.11e+07
...
1.83e+02  5.33e+02 1.39e+00 1.50e+07 1.10e+04 1.11e+07

## 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_8, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml, final_sbml_refined)

### 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
Now I have data from three experiments with different initial conditions. Let me analyze the new data and see if it's consistent with our current model or if we need to refine it further.

In the third experiment:
1. `id_8n7o` starts at 15,000,000 (higher than previous experiments) and decreases over time
2. `id_caoz` starts at 500, increases to a peak (~6.65e+06 around t=27), then decreases
3. `id_ty7g` starts at 5 and continuously increases to ~1.5e+07
4. `id_1wsx` starts at 50, increases to a peak (~7.99e+06 around t=36), then decreases

This behavior is qualitatively similar to what we observed in the previous experiments, which is a good sign. Let me now test our current model (Model 5) against this new data and also try the refined model I proposed.

## Action

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

# Access the experimental data
exp_data_1 = experiment_history["iteration_0"]
exp_data_2 = experiment_history["iteration_8"]
exp_data_3 = experiment_history["iteration_10"]

# Access the final model from the previous iteration
final_sbml_refined = shared_variables.access('final_sbml_refined')

# Define the Model 5 ODE function
def model_ode5(t, y, k1, k2, k3, k4):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o -> id_caoz + id_ty7g
    r1 = k1 * y[0]
    
    # Reaction 2: id_caoz + id_8n7o -> id_1wsx + id_ty7g
    r2 = k2 * y[1] * y[0]
    
    # Reaction 3: id_1wsx + id_8n7o -> 2 id_ty7g
    r3 = k3 * y[3] * y[0]
    
    # Reaction 4: id_caoz -> id_ty7g
    r4 = k4 * y[1]
    
    # ODEs
    dy_dt = [
        -r1 - r2 - r3,      # d[id_8n7o]/dt
        r1 - r2 - r4,       # d[id_caoz]/dt
        r1 + r2 + 2*r3 + r4,# d[id_ty7g]/dt
        r2 - r3             # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Define the Model 6 ODE function (with an additional reaction)
def model_ode6(t, y, k1, k2, k3, k4, k5):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o -> id_caoz + id_ty7g
    r1 = k1 * y[0]
    
    # Reaction 2: id_caoz + id_8n7o -> id_1wsx + id_ty7g
    r2 = k2 * y[1] * y[0]
    
    # Reaction 3: id_1wsx + id_8n7o -> 2 id_ty7g
    r3 = k3 * y[3] * y[0]
    
    # Reaction 4: id_caoz -> id_ty7g
    r4 = k4 * y[1]
    
    # Reaction 5: id_8n7o -> id_ty7g
    r5 = k5 * y[0]
    
    # ODEs
    dy_dt = [
        -r1 - r2 - r3 - r5,      # d[id_8n7o]/dt
        r1 - r2 - r4,            # d[id_caoz]/dt
        r1 + r2 + 2*r3 + r4 + r5,# d[id_ty7g]/dt
        r2 - r3                  # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Get the best parameters from the previous iteration for Model 5
best_params_5 = [0.005, 1e-8, 1e-8, 0.01]

# Initial conditions for the third experiment
y0_exp3 = [15000000, 500, 5, 50]

# Time points for simulation
t_span = (0, 183)
t_eval = exp_data_3['Time'].values

# Simulate Model 5 with the best parameters for the third experiment
sol5 = solve_ivp(
    lambda t, y: model_ode5(t, y, *best_params_5),
    t_span,
    y0_exp3,
    method='LSODA',
    t_eval=t_eval
)

# Calculate error (mean squared error)
sim_data5 = pd.DataFrame({
    'Time': sol5.t,
    'id_8n7o': sol5.y[0],
    'id_caoz': sol5.y[1],
    'id_ty7g': sol5.y[2],
    'id_1wsx': sol5.y[3]
})

error5 = 0
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    # Normalize by the maximum value to give equal weight to each species
    max_val = max(max(exp_data_3[species]), max(sim_data5[species]))
    if max_val > 0:
        error5 += np.mean(((exp_data_3[species] - sim_data5[species]) / max_val) ** 2)

print(f"Error for Model 5 on the third experiment: {error5}")

# Compare the simulation with experimental data
print("\nComparison of Model 5 simulation vs. experimental data at selected time points:")
selected_times = [0, 30, 60, 90, 120, 150, 180]
for t in selected_times:
    idx = np.argmin(np.abs(sim_data5['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data5.loc[idx, species]
        exp_val = exp_data_3[exp_data_3['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Let's optimize the parameters for Model 6 using all three experiments
def objective_function(params):
    k1, k2, k3, k4, k5 = params
    
    # Simulate for the first experiment
    y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
    t_eval_1 = exp_data_1['Time'].values
    
    try:
        sol1 = solve_ivp(
            lambda t, y: model_ode6(t, y, k1, k2, k3, k4, k5),
            t_span,
            y0_exp1,
            method='LSODA',
            t_eval=t_eval_1
        )
        
        sim_data1 = pd.DataFrame({
            'Time': sol1.t,
            'id_8n7o': sol1.y[0],
            'id_caoz': sol1.y[1],
            'id_ty7g': sol1.y[2],
            'id_1wsx': sol1.y[3]
        })
        
        error1 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_1[species]), max(sim_data1[species]))
            if max_val > 0:
                error1 += np.mean(((exp_data_1[species] - sim_data1[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the second experiment
    y0_exp2 = [5000000, 1000, 10, 100]
    t_eval_2 = exp_data_2['Time'].values
    
    try:
        sol2 = solve_ivp(
            lambda t, y: model_ode6(t, y, k1, k2, k3, k4, k5),
            t_span,
            y0_exp2,
            method='LSODA',
            t_eval=t_eval_2
        )
        
        sim_data2 = pd.DataFrame({
            'Time': sol2.t,
            'id_8n7o': sol2.y[0],
            'id_caoz': sol2.y[1],
            'id_ty7g': sol2.y[2],
            'id_1wsx': sol2.y[3]
        })
        
        error2 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_2[species]), max(sim_data2[species]))
            if max_val > 0:
                error2 += np.mean(((exp_data_2[species] - sim_data2[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the third experiment
    y0_exp3 = [15000000, 500, 5, 50]
    t_eval_3 = exp_data_3['Time'].values
    
    try:
        sol3 = solve_ivp(
            lambda t, y: model_ode6(t, y, k1, k2, k3, k4, k5),
            t_span,
            y0_exp3,
            method='LSODA',
            t_eval=t_eval_3
        )
        
        sim_data3 = pd.DataFrame({
            'Time': sol3.t,
            'id_8n7o': sol3.y[0],
            'id_caoz': sol3.y[1],
            'id_ty7g': sol3.y[2],
            'id_1wsx': sol3.y[3]
        })
        
        error3 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_3[species]), max(sim_data3[species]))
            if max_val > 0:
                error3 += np.mean(((exp_data_3[species] - sim_data3[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Return the total error
    return error1 + error2 + error3

# Let's try a few parameter combinations manually
param_sets = [
    [0.005, 1e-8, 1e-8, 0.01, 0.001],
    [0.005, 1e-8, 1e-8, 0.01, 0.01],
    [0.005, 1e-7, 1e-8, 0.01, 0.001],
    [0.005, 1e-8, 1e-7, 0.01, 0.001],
    [0.005, 1e-8, 1e-8, 0.1, 0.001],
    [0.01, 1e-8, 1e-8, 0.01, 0.001],
    [0.001, 1e-8, 1e-8, 0.01, 0.001]
]

best_params = None
best_error = float('inf')

for params in param_sets:
    error = objective_function(params)
    if error < best_error:
        best_error = error
        best_params = params

print(f"\nBest parameters for Model 6: k1 = {best_params[0]}, k2 = {best_params[1]}, k3 = {best_params[2]}, k4 = {best_params[3]}, k5 = {best_params[4]}")
print(f"Best error for Model 6: {best_error}")

# Simulate with the best parameters for all three experiments
# First experiment
y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
t_eval_1 = exp_data_1['Time'].values

sol1 = solve_ivp(
    lambda t, y: model_ode6(t, y, *best_params),
    t_span,
    y0_exp1,
    method='LSODA',
    t_eval=t_eval_1
)

sim_data1 = pd.DataFrame({
    'Time': sol1.t,
    'id_8n7o': sol1.y[0],
    'id_caoz': sol1.y[1],
    'id_ty7g': sol1.y[2],
    'id_1wsx': sol1.y[3]
})

# Second experiment
y0_exp2 = [5000000, 1000, 10, 100]
t_eval_2 = exp_data_2['Time'].values

sol2 = solve_ivp(
    lambda t, y: model_ode6(t, y, *best_params),
    t_span,
    y0_exp2,
    method='LSODA',
    t_eval=t_eval_2
)

sim_data2 = pd.DataFrame({
    'Time': sol2.t,
    'id_8n7o': sol2.y[0],
    'id_caoz': sol2.y[1],
    'id_ty7g': sol2.y[2],
    'id_1wsx': sol2.y[3]
})

# Third experiment
y0_exp3 = [15000000, 500, 5, 50]
t_eval_3 = exp_data_3['Time'].values

sol3 = solve_ivp(
    lambda t, y: model_ode6(t, y, *best_params),
    t_span,
    y0_exp3,
    method='LSODA',
    t_eval=t_eval_3
)

sim_data3 = pd.DataFrame({
    'Time': sol3.t,
    'id_8n7o': sol3.y[0],
    'id_caoz': sol3.y[1],
    'id_ty7g': sol3.y[2],
    'id_1wsx': sol3.y[3]
})

# Compare the simulation with experimental data for all three experiments
print("\nComparison of Model 6 simulation vs. experimental data for the first experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data1['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data1.loc[idx, species]
        exp_val = exp_data_1[exp_data_1['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

print("\nComparison of Model 6 simulation vs. experimental data for the second experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data2['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data2.loc[idx, species]
        exp_val = exp_data_2[exp_data_2['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

print("\nComparison of Model 6 simulation vs. experimental data for the third experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data3['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data3.loc[idx, species]
        exp_val = exp_data_3[exp_data_3['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Create the final SBML model with the refined reactions and parameters
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

# Add the first reaction: id_8n7o -> id_caoz + id_ty7g
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactants
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_8n7o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction1.createProduct()
product1.setSpecies("id_caoz")
product1.setStoichiometry(1.0)
product1.setConstant(True)

product2 = reaction1.createProduct()
product2.setSpecies("id_ty7g")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law (mass action)
kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1 * id_8n7o")

# Add parameter k1
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(best_params[0])

# Add the second reaction: id_caoz + id_8n7o -> id_1wsx + id_ty7g
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactants
reactant1 = reaction2.createReactant()
reactant1.setSpecies("id_caoz")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_8n7o")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product1 = reaction2.createProduct()
product1.setSpecies("id_1wsx")
product1.setStoichiometry(1.0)
product1.setConstant(True)

product2 = reaction2.createProduct()
product2.setSpecies("id_ty7g")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_caoz * id_8n7o")

# Add parameter k2
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(best_params[1])

# Add the third reaction: id_1wsx + id_8n7o -> 2 id_ty7g
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactants
reactant1 = reaction3.createReactant()
reactant1.setSpecies("id_1wsx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

reactant2 = reaction3.createReactant()
reactant2.setSpecies("id_8n7o")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(True)

# Add products
product1 = reaction3.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(2.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_1wsx * id_8n7o")

# Add parameter k3
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(best_params[2])

# Add the fourth reaction: id_caoz -> id_ty7g
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactants
reactant1 = reaction4.createReactant()
reactant1.setSpecies("id_caoz")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction4.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_caoz")

# Add parameter k4
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(best_params[3])

# Add the fifth reaction: id_8n7o -> id_ty7g
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactants
reactant1 = reaction5.createReactant()
reactant1.setSpecies("id_8n7o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction5.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law5 = reaction5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_8n7o")

# Add parameter k5
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(best_params[4])

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

# Store the final SBML model
shared_variables.add('final_sbml_model6', final_sbml)

print("\nCreated SBML model with Model 6 reactions:")
print(f"1. id_8n7o -> id_caoz + id_ty7g (k1 = {best_params[0]})")
print(f"2. id_caoz + id_8n7o -> id_1wsx + id_ty7g (k2 = {best_params[1]})")
print(f"3. id_1wsx + id_8n7o -> 2 id_ty7g (k3 = {best_params[2]})")
print(f"4. id_caoz -> id_ty7g (k4 = {best_params[3]})")
print(f"5. id_8n7o -> id_ty7g (k5 = {best_params[4]})")
```
# Observation

## Code Stdout
Error for Model 5 on the third experiment: 0.2845142304702989

Comparison of Model 5 simulation vs. experimental data at selected time points:

Time 0:
  id_8n7o: Sim = 1.50e+07, Exp = 1.50e+07, Rel Error = 0.00%
  id_caoz: Sim = 5.00e+02, Exp = 5.00e+02, Rel Error = 0.00%
  id_ty7g: Sim = 5.00e+00, Exp = 5.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 5.00e+01, Exp = 5.00e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 1.07e+07, Exp = 9.64e+05, Rel Error = 1009.71%
  id_caoz: Sim = 4.54e+05, Exp = 5.64e+06, Rel Error = 91.96%
  id_ty7g: Sim = 5.37e+06, Exp = 1.77e+06, Rel Error = 204.23%
  id_1wsx: Sim = 4.22e+05, Exp = 6.63e+06, Rel Error = 93.63%

Time 60:
  id_8n7o: Sim = 7.04e+06, Exp = 3.26e+03, Rel Error = 215947.70%
  id_caoz: Sim = 4.45e+05, Exp = 1.14e+05, Rel Error = 291.63%
  id_ty7g: Sim = 1.03e+07, Exp = 1.10e+07, Rel Error = 6.45%
  id_1wsx: Sim = 4.48e+05, Exp = 3.85e+06, Rel Error = 88.36%

Time 90:
  id_8n7o: Sim = 4.66e+06, Exp = 8.16e+02, Rel Error = 570623.35%
  id_caoz: Sim = 4.25e+05, Exp = 1.94e+03, Rel Error = 21793.70%
  id_ty7g: Sim = 1.36e+07, Exp = 1.40e+07, Rel Error = 3.14%
  id_1wsx: Sim = 4.36e+05, Exp = 9.51e+05, Rel Error = 54.17%

Time 120:
  id_8n7o: Sim = 3.12e+06, Exp = 5.88e+02, Rel Error = 530172.37%
  id_caoz: Sim = 4.00e+05, Exp = 6.05e+01, Rel Error = 662011.34%
  id_ty7g: Sim = 1.58e+07, Exp = 1.48e+07, Rel Error = 6.70%
  id_1wsx: Sim = 4.19e+05, Exp = 2.26e+05, Rel Error = 85.43%

Time 150:
  id_8n7o: Sim = 2.11e+06, Exp = 5.44e+02, Rel Error = 388563.16%
  id_caoz: Sim = 3.72e+05, Exp = 7.43e+00, Rel Error = 5000095.96%
  id_ty7g: Sim = 1.72e+07, Exp = 1.49e+07, Rel Error = 15.09%
  id_1wsx: Sim = 4.01e+05, Exp = 5.36e+04, Rel Error = 648.08%

Time 180:
  id_8n7o: Sim = 1.45e+06, Exp = 5.34e+02, Rel Error = 272296.40%
  id_caoz: Sim = 3.40e+05, Exp = 1.61e+00, Rel Error = 21110436.52%
  id_ty7g: Sim = 1.82e+07, Exp = 1.50e+07, Rel Error = 21.27%
  id_1wsx: Sim = 3.82e+05, Exp = 1.27e+04, Rel Error = 2909.36%

Best parameters for Model 6: k1 = 0.005, k2 = 1e-08, k3 = 1e-08, k4 = 0.01, k5 = 0.001
Best error for Model 6: 0.8670575500789958

Comparison of Model 6 simulation vs. experimental data for the first experiment:

Time 0:
  id_8n7o: Sim = 1.11e+07, Exp = 1.11e+07, Rel Error = 0.00%
  id_caoz: Sim = 1.93e+02, Exp = 1.93e+02, Rel Error = 0.00%
  id_ty7g: Sim = 2.00e+00, Exp = 2.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 2.70e+01, Exp = 2.70e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 7.90e+06, Exp = 8.81e+06, Rel Error = 10.33%
  id_caoz: Sim = 4.30e+05, Exp = 1.50e+06, Rel Error = 71.24%
  id_ty7g: Sim = 3.82e+06, Exp = 1.10e+05, Rel Error = 3373.34%
  id_1wsx: Sim = 3.63e+05, Exp = 6.64e+05, Rel Error = 45.30%

Time 60:
  id_8n7o: Sim = 5.13e+06, Exp = 6.25e+04, Rel Error = 8104.40%
  id_caoz: Sim = 4.28e+05, Exp = 4.97e+05, Rel Error = 13.84%
  id_ty7g: Sim = 7.50e+06, Exp = 6.06e+06, Rel Error = 23.70%
  id_1wsx: Sim = 4.23e+05, Exp = 4.46e+06, Rel Error = 90.52%

Time 90:
  id_8n7o: Sim = 3.33e+06, Exp = 1.02e+04, Rel Error = 32667.71%
  id_caoz: Sim = 4.05e+05, Exp = 1.19e+04, Rel Error = 3312.59%
  id_ty7g: Sim = 9.95e+06, Exp = 9.81e+06, Rel Error = 1.43%
  id_1wsx: Sim = 4.18e+05, Exp = 1.25e+06, Rel Error = 66.48%

Time 120:
  id_8n7o: Sim = 2.19e+06, Exp = 6.57e+03, Rel Error = 33217.59%
  id_caoz: Sim = 3.76e+05, Exp = 6.56e+02, Rel Error = 57203.68%
  id_ty7g: Sim = 1.15e+07, Exp = 1.08e+07, Rel Error = 7.19%
  id_1wsx: Sim = 4.02e+05, Exp = 3.01e+05, Rel Error = 33.67%

Time 150:
  id_8n7o: Sim = 1.46e+06, Exp = 5.92e+03, Rel Error = 24552.48%
  id_caoz: Sim = 3.43e+05, Exp = 1.06e+02, Rel Error = 324795.27%
  id_ty7g: Sim = 1.26e+07, Exp = 1.10e+07, Rel Error = 14.49%
  id_1wsx: Sim = 3.84e+05, Exp = 7.18e+04, Rel Error = 435.14%

Time 180:
  id_8n7o: Sim = 9.88e+05, Exp = 5.77e+03, Rel Error = 17010.07%
  id_caoz: Sim = 3.08e+05, Exp = 2.35e+01, Rel Error = 1311527.71%
  id_ty7g: Sim = 1.33e+07, Exp = 1.11e+07, Rel Error = 20.29%
  id_1wsx: Sim = 3.67e+05, Exp = 1.71e+04, Rel Error = 2041.10%

Comparison of Model 6 simulation vs. experimental data for the second experiment:

Time 0:
  id_8n7o: Sim = 5.00e+06, Exp = 5.00e+06, Rel Error = 0.00%
  id_caoz: Sim = 1.00e+03, Exp = 1.00e+03, Rel Error = 0.00%
  id_ty7g: Sim = 1.00e+01, Exp = 1.00e+01, Rel Error = 0.00%
  id_1wsx: Sim = 1.00e+02, Exp = 1.00e+02, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 3.82e+06, Exp = 4.95e+06, Rel Error = 22.81%
  id_caoz: Sim = 3.26e+05, Exp = 2.13e+04, Rel Error = 1431.63%
  id_ty7g: Sim = 1.34e+06, Exp = 7.29e+03, Rel Error = 18282.10%
  id_1wsx: Sim = 1.77e+05, Exp = 1.84e+04, Rel Error = 861.97%

Time 60:
  id_8n7o: Sim = 2.67e+06, Exp = 3.88e+06, Rel Error = 31.19%
  id_caoz: Sim = 3.64e+05, Exp = 4.46e+05, Rel Error = 18.52%
  id_ty7g: Sim = 2.83e+06, Exp = 2.15e+05, Rel Error = 1216.30%
  id_1wsx: Sim = 2.87e+05, Exp = 4.56e+05, Rel Error = 37.00%

Time 90:
  id_8n7o: Sim = 1.83e+06, Exp = 9.35e+05, Rel Error = 95.46%
  id_caoz: Sim = 3.50e+05, Exp = 5.36e+05, Rel Error = 34.74%
  id_ty7g: Sim = 3.99e+06, Exp = 1.90e+06, Rel Error = 109.70%
  id_1wsx: Sim = 3.22e+05, Exp = 1.63e+06, Rel Error = 80.25%

Time 120:
  id_8n7o: Sim = 1.25e+06, Exp = 3.16e+05, Rel Error = 296.43%
  id_caoz: Sim = 3.23e+05, Exp = 8.60e+04, Rel Error = 275.48%
  id_ty7g: Sim = 4.81e+06, Exp = 3.76e+06, Rel Error = 28.06%
  id_1wsx: Sim = 3.27e+05, Exp = 8.42e+05, Rel Error = 61.17%

Time 150:
  id_8n7o: Sim = 8.65e+05, Exp = 2.18e+05, Rel Error = 297.54%
  id_caoz: Sim = 2.91e+05, Exp = 1.57e+04, Rel Error = 1757.80%
  id_ty7g: Sim = 5.39e+06, Exp = 4.50e+06, Rel Error = 19.95%
  id_1wsx: Sim = 3.22e+05, Exp = 2.73e+05, Rel Error = 18.04%

Time 180:
  id_8n7o: Sim = 6.05e+05, Exp = 1.95e+05, Rel Error = 210.66%
  id_caoz: Sim = 2.58e+05, Exp = 3.80e+03, Rel Error = 6688.00%
  id_ty7g: Sim = 5.80e+06, Exp = 4.72e+06, Rel Error = 22.88%
  id_1wsx: Sim = 3.12e+05, Exp = 8.01e+04, Rel Error = 290.10%

Comparison of Model 6 simulation vs. experimental data for the third experiment:

Time 0:
  id_8n7o: Sim = 1.50e+07, Exp = 1.50e+07, Rel Error = 0.00%
  id_caoz: Sim = 5.00e+02, Exp = 5.00e+02, Rel Error = 0.00%
  id_ty7g: Sim = 5.00e+00, Exp = 5.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 5.00e+01, Exp = 5.00e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 1.04e+07, Exp = 9.64e+05, Rel Error = 977.68%
  id_caoz: Sim = 4.53e+05, Exp = 5.64e+06, Rel Error = 91.98%
  id_ty7g: Sim = 5.66e+06, Exp = 1.77e+06, Rel Error = 220.40%
  id_1wsx: Sim = 4.20e+05, Exp = 6.63e+06, Rel Error = 93.67%

Time 60:
  id_8n7o: Sim = 6.65e+06, Exp = 3.26e+03, Rel Error = 203727.88%
  id_caoz: Sim = 4.43e+05, Exp = 1.14e+05, Rel Error = 289.71%
  id_ty7g: Sim = 1.06e+07, Exp = 1.10e+07, Rel Error = 3.54%
  id_1wsx: Sim = 4.46e+05, Exp = 3.85e+06, Rel Error = 88.41%

Time 90:
  id_8n7o: Sim = 4.27e+06, Exp = 8.16e+02, Rel Error = 523262.68%
  id_caoz: Sim = 4.21e+05, Exp = 1.94e+03, Rel Error = 21582.23%
  id_ty7g: Sim = 1.39e+07, Exp = 1.40e+07, Rel Error = 1.35%
  id_1wsx: Sim = 4.33e+05, Exp = 9.51e+05, Rel Error = 54.43%

Time 120:
  id_8n7o: Sim = 2.78e+06, Exp = 5.88e+02, Rel Error = 472986.22%
  id_caoz: Sim = 3.94e+05, Exp = 6.05e+01, Rel Error = 651188.08%
  id_ty7g: Sim = 1.59e+07, Exp = 1.48e+07, Rel Error = 7.72%
  id_1wsx: Sim = 4.16e+05, Exp = 2.26e+05, Rel Error = 83.96%

Time 150:
  id_8n7o: Sim = 1.84e+06, Exp = 5.44e+02, Rel Error = 337434.60%
  id_caoz: Sim = 3.62e+05, Exp = 7.43e+00, Rel Error = 4875144.52%
  id_ty7g: Sim = 1.73e+07, Exp = 1.49e+07, Rel Error = 15.42%
  id_1wsx: Sim = 3.97e+05, Exp = 5.36e+04, Rel Error = 640.67%

Time 180:
  id_8n7o: Sim = 1.23e+06, Exp = 5.34e+02, Rel Error = 230260.14%
  id_caoz: Sim = 3.28e+05, Exp = 1.61e+00, Rel Error = 20357092.77%
  id_ty7g: Sim = 1.81e+07, Exp = 1.50e+07, Rel Error = 21.01%
  id_1wsx: Sim = 3.78e+05, Exp = 1.27e+04, Rel Error = 2876.29%

Created SBML model with Model 6 reactions:
1. id_8n7o -> id_caoz + id_ty7g (k1 = 0.005)
2. id_caoz + id_8n7o -> id_1wsx + id_ty7g (k2 = 1e-08)
3. id_1wsx + id_8n7o -> 2 id_ty7g (k3 = 1e-08)
4. id_caoz -> id_ty7g (k4 = 0.01)
5. id_8n7o -> id_ty7g (k5 = 0.001)

## 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_8, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml, final_sbml_refined, final_sbml_model6)

### 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
Interestingly, Model 5 (without the direct `id_8n7o -> id_ty7g` reaction) performs better on the third experiment than Model 6 (which includes this reaction). The error for Model 5 on the third experiment is 0.285, while the combined error for Model 6 across all three experiments is 0.867.

However, both models still show significant discrepancies between the simulated and experimental data, particularly:

1. `id_8n7o` decreases much more slowly in the simulations than in the experimental data
2. `id_caoz` doesn't reach as high a peak in the simulations as in the experimental data for the third experiment
3. The timing of the peaks for `id_caoz` and `id_1wsx` doesn't match well between simulations and experiments

Let me try a different approach. Instead of adding more reactions, let me revisit the basic reactions and see if I can find a simpler model that better explains the data. I'll focus on the conservation of mass and the observed dynamics.

Looking at the data more carefully:
1. The sum of all species remains constant at 11,081,000
2. `id_8n7o` decreases rapidly
3. `id_ty7g` increases steadily
4. `id_caoz` and `id_1wsx` both show a rise and fall pattern

Let me try a model with the following reactions:
1. `id_8n7o -> id_caoz` (direct conversion)
2. `id_caoz -> id_ty7g` (direct conversion)
3. `id_caoz -> id_1wsx` (direct conversion)
4. `id_1wsx -> id_ty7g` (direct conversion)

This model is simpler and focuses on the sequential conversion of species, which might better capture the observed dynamics.

## Action

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

# Access the experimental data
exp_data_1 = experiment_history["iteration_0"]
exp_data_2 = experiment_history["iteration_8"]
exp_data_3 = experiment_history["iteration_10"]

# Define the Model 7 ODE function (simpler sequential model)
def model_ode7(t, y, k1, k2, k3, k4):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o -> id_caoz
    r1 = k1 * y[0]
    
    # Reaction 2: id_caoz -> id_ty7g
    r2 = k2 * y[1]
    
    # Reaction 3: id_caoz -> id_1wsx
    r3 = k3 * y[1]
    
    # Reaction 4: id_1wsx -> id_ty7g
    r4 = k4 * y[3]
    
    # ODEs
    dy_dt = [
        -r1,            # d[id_8n7o]/dt
        r1 - r2 - r3,   # d[id_caoz]/dt
        r2 + r4,        # d[id_ty7g]/dt
        r3 - r4         # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Let's optimize the parameters for Model 7 using all three experiments
def objective_function(params):
    k1, k2, k3, k4 = params
    
    # Simulate for the first experiment
    y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
    t_eval_1 = exp_data_1['Time'].values
    
    try:
        sol1 = solve_ivp(
            lambda t, y: model_ode7(t, y, k1, k2, k3, k4),
            (0, 183),
            y0_exp1,
            method='LSODA',
            t_eval=t_eval_1
        )
        
        sim_data1 = pd.DataFrame({
            'Time': sol1.t,
            'id_8n7o': sol1.y[0],
            'id_caoz': sol1.y[1],
            'id_ty7g': sol1.y[2],
            'id_1wsx': sol1.y[3]
        })
        
        error1 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_1[species]), max(sim_data1[species]))
            if max_val > 0:
                error1 += np.mean(((exp_data_1[species] - sim_data1[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the second experiment
    y0_exp2 = [5000000, 1000, 10, 100]
    t_eval_2 = exp_data_2['Time'].values
    
    try:
        sol2 = solve_ivp(
            lambda t, y: model_ode7(t, y, k1, k2, k3, k4),
            (0, 183),
            y0_exp2,
            method='LSODA',
            t_eval=t_eval_2
        )
        
        sim_data2 = pd.DataFrame({
            'Time': sol2.t,
            'id_8n7o': sol2.y[0],
            'id_caoz': sol2.y[1],
            'id_ty7g': sol2.y[2],
            'id_1wsx': sol2.y[3]
        })
        
        error2 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_2[species]), max(sim_data2[species]))
            if max_val > 0:
                error2 += np.mean(((exp_data_2[species] - sim_data2[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the third experiment
    y0_exp3 = [15000000, 500, 5, 50]
    t_eval_3 = exp_data_3['Time'].values
    
    try:
        sol3 = solve_ivp(
            lambda t, y: model_ode7(t, y, k1, k2, k3, k4),
            (0, 183),
            y0_exp3,
            method='LSODA',
            t_eval=t_eval_3
        )
        
        sim_data3 = pd.DataFrame({
            'Time': sol3.t,
            'id_8n7o': sol3.y[0],
            'id_caoz': sol3.y[1],
            'id_ty7g': sol3.y[2],
            'id_1wsx': sol3.y[3]
        })
        
        error3 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_3[species]), max(sim_data3[species]))
            if max_val > 0:
                error3 += np.mean(((exp_data_3[species] - sim_data3[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Return the total error
    return error1 + error2 + error3

# Let's try a few parameter combinations manually
param_sets = [
    [0.1, 0.01, 0.1, 0.01],
    [0.1, 0.01, 0.1, 0.1],
    [0.1, 0.1, 0.1, 0.01],
    [0.1, 0.01, 0.01, 0.01],
    [0.05, 0.01, 0.1, 0.01],
    [0.2, 0.01, 0.1, 0.01]
]

best_params = None
best_error = float('inf')

for params in param_sets:
    error = objective_function(params)
    if error < best_error:
        best_error = error
        best_params = params

print(f"Best parameters for Model 7: k1 = {best_params[0]}, k2 = {best_params[1]}, k3 = {best_params[2]}, k4 = {best_params[3]}")
print(f"Best error for Model 7: {best_error}")

# Simulate with the best parameters for all three experiments
# First experiment
y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
t_eval_1 = exp_data_1['Time'].values

sol1 = solve_ivp(
    lambda t, y: model_ode7(t, y, *best_params),
    (0, 183),
    y0_exp1,
    method='LSODA',
    t_eval=t_eval_1
)

sim_data1 = pd.DataFrame({
    'Time': sol1.t,
    'id_8n7o': sol1.y[0],
    'id_caoz': sol1.y[1],
    'id_ty7g': sol1.y[2],
    'id_1wsx': sol1.y[3]
})

# Second experiment
y0_exp2 = [5000000, 1000, 10, 100]
t_eval_2 = exp_data_2['Time'].values

sol2 = solve_ivp(
    lambda t, y: model_ode7(t, y, *best_params),
    (0, 183),
    y0_exp2,
    method='LSODA',
    t_eval=t_eval_2
)

sim_data2 = pd.DataFrame({
    'Time': sol2.t,
    'id_8n7o': sol2.y[0],
    'id_caoz': sol2.y[1],
    'id_ty7g': sol2.y[2],
    'id_1wsx': sol2.y[3]
})

# Third experiment
y0_exp3 = [15000000, 500, 5, 50]
t_eval_3 = exp_data_3['Time'].values

sol3 = solve_ivp(
    lambda t, y: model_ode7(t, y, *best_params),
    (0, 183),
    y0_exp3,
    method='LSODA',
    t_eval=t_eval_3
)

sim_data3 = pd.DataFrame({
    'Time': sol3.t,
    'id_8n7o': sol3.y[0],
    'id_caoz': sol3.y[1],
    'id_ty7g': sol3.y[2],
    'id_1wsx': sol3.y[3]
})

# Compare the simulation with experimental data for all three experiments
selected_times = [0, 30, 60, 90, 120, 150, 180]

print("\nComparison of Model 7 simulation vs. experimental data for the first experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data1['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data1.loc[idx, species]
        exp_val = exp_data_1[exp_data_1['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

print("\nComparison of Model 7 simulation vs. experimental data for the second experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data2['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data2.loc[idx, species]
        exp_val = exp_data_2[exp_data_2['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

print("\nComparison of Model 7 simulation vs. experimental data for the third experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data3['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data3.loc[idx, species]
        exp_val = exp_data_3[exp_data_3['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Create the final SBML model with the refined reactions and parameters
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

# Add the first reaction: id_8n7o -> id_caoz
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactants
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_8n7o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction1.createProduct()
product1.setSpecies("id_caoz")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1 * id_8n7o")

# Add parameter k1
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(best_params[0])

# Add the second reaction: id_caoz -> id_ty7g
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactants
reactant1 = reaction2.createReactant()
reactant1.setSpecies("id_caoz")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction2.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_caoz")

# Add parameter k2
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(best_params[1])

# Add the third reaction: id_caoz -> id_1wsx
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactants
reactant1 = reaction3.createReactant()
reactant1.setSpecies("id_caoz")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction3.createProduct()
product1.setSpecies("id_1wsx")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_caoz")

# Add parameter k3
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(best_params[2])

# Add the fourth reaction: id_1wsx -> id_ty7g
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactants
reactant1 = reaction4.createReactant()
reactant1.setSpecies("id_1wsx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction4.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_1wsx")

# Add parameter k4
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(best_params[3])

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

# Store the final SBML model
shared_variables.add('final_sbml_model7', final_sbml)

print("\nCreated SBML model with Model 7 reactions:")
print(f"1. id_8n7o -> id_caoz (k1 = {best_params[0]})")
print(f"2. id_caoz -> id_ty7g (k2 = {best_params[1]})")
print(f"3. id_caoz -> id_1wsx (k3 = {best_params[2]})")
print(f"4. id_1wsx -> id_ty7g (k4 = {best_params[3]})")

# Let's also try a model with direct conversion from id_8n7o to id_ty7g
def model_ode8(t, y, k1, k2, k3, k4, k5):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o -> id_caoz
    r1 = k1 * y[0]
    
    # Reaction 2: id_caoz -> id_ty7g
    r2 = k2 * y[1]
    
    # Reaction 3: id_caoz -> id_1wsx
    r3 = k3 * y[1]
    
    # Reaction 4: id_1wsx -> id_ty7g
    r4 = k4 * y[3]
    
    # Reaction 5: id_8n7o -> id_ty7g
    r5 = k5 * y[0]
    
    # ODEs
    dy_dt = [
        -r1 - r5,        # d[id_8n7o]/dt
        r1 - r2 - r3,    # d[id_caoz]/dt
        r2 + r4 + r5,    # d[id_ty7g]/dt
        r3 - r4          # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Let's try a few parameter combinations manually for Model 8
param_sets = [
    [0.1, 0.01, 0.1, 0.01, 0.01],
    [0.1, 0.01, 0.1, 0.01, 0.1],
    [0.1, 0.01, 0.1, 0.01, 0.001],
    [0.05, 0.01, 0.1, 0.01, 0.01],
    [0.2, 0.01, 0.1, 0.01, 0.01]
]

best_params8 = None
best_error8 = float('inf')

for params in param_sets:
    # Simulate for the first experiment
    y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
    t_eval_1 = exp_data_1['Time'].values
    
    try:
        sol1 = solve_ivp(
            lambda t, y: model_ode8(t, y, *params),
            (0, 183),
            y0_exp1,
            method='LSODA',
            t_eval=t_eval_1
        )
        
        sim_data1 = pd.DataFrame({
            'Time': sol1.t,
            'id_8n7o': sol1.y[0],
            'id_caoz': sol1.y[1],
            'id_ty7g': sol1.y[2],
            'id_1wsx': sol1.y[3]
        })
        
        error1 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_1[species]), max(sim_data1[species]))
            if max_val > 0:
                error1 += np.mean(((exp_data_1[species] - sim_data1[species]) / max_val) ** 2)
    except:
        continue  # Skip if the solver fails
    
    # Simulate for the second experiment
    y0_exp2 = [5000000, 1000, 10, 100]
    t_eval_2 = exp_data_2['Time'].values
    
    try:
        sol2 = solve_ivp(
            lambda t, y: model_ode8(t, y, *params),
            (0, 183),
            y0_exp2,
            method='LSODA',
            t_eval=t_eval_2
        )
        
        sim_data2 = pd.DataFrame({
            'Time': sol2.t,
            'id_8n7o': sol2.y[0],
            'id_caoz': sol2.y[1],
            'id_ty7g': sol2.y[2],
            'id_1wsx': sol2.y[3]
        })
        
        error2 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_2[species]), max(sim_data2[species]))
            if max_val > 0:
                error2 += np.mean(((exp_data_2[species] - sim_data2[species]) / max_val) ** 2)
    except:
        continue  # Skip if the solver fails
    
    # Simulate for the third experiment
    y0_exp3 = [15000000, 500, 5, 50]
    t_eval_3 = exp_data_3['Time'].values
    
    try:
        sol3 = solve_ivp(
            lambda t, y: model_ode8(t, y, *params),
            (0, 183),
            y0_exp3,
            method='LSODA',
            t_eval=t_eval_3
        )
        
        sim_data3 = pd.DataFrame({
            'Time': sol3.t,
            'id_8n7o': sol3.y[0],
            'id_caoz': sol3.y[1],
            'id_ty7g': sol3.y[2],
            'id_1wsx': sol3.y[3]
        })
        
        error3 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_3[species]), max(sim_data3[species]))
            if max_val > 0:
                error3 += np.mean(((exp_data_3[species] - sim_data3[species]) / max_val) ** 2)
    except:
        continue  # Skip if the solver fails
    
    # Calculate total error
    total_error = error1 + error2 + error3
    
    if total_error < best_error8:
        best_error8 = total_error
        best_params8 = params

if best_params8 is not None:
    print(f"\nBest parameters for Model 8: k1 = {best_params8[0]}, k2 = {best_params8[1]}, k3 = {best_params8[2]}, k4 = {best_params8[3]}, k5 = {best_params8[4]}")
    print(f"Best error for Model 8: {best_error8}")

    # Compare the errors of Model 7 and Model 8
    print("\nComparison of Model 7 and Model 8:")
    print(f"Model 7 error: {best_error}")
    print(f"Model 8 error: {best_error8}")

    if best_error <= best_error8:
        print("\nModel 7 is the better fit.")
        final_model = 7
        final_params = best_params
    else:
        print("\nModel 8 is the better fit.")
        final_model = 8
        final_params = best_params8

    # Create the final SBML model with the best model's reactions and parameters
    if final_model == 8:
        # Add the fifth reaction: id_8n7o -> id_ty7g
        reaction5 = model.createReaction()
        reaction5.setId("reaction5")
        reaction5.setReversible(False)

        # Add reactants
        reactant1 = reaction5.createReactant()
        reactant1.setSpecies("id_8n7o")
        reactant1.setStoichiometry(1.0)
        reactant1.setConstant(True)

        # Add products
        product1 = reaction5.createProduct()
        product1.setSpecies("id_ty7g")
        product1.setStoichiometry(1.0)
        product1.setConstant(True)

        # Add kinetic law (mass action)
        kinetic_law5 = reaction5.createKineticLaw()
        kinetic_law5.setFormula("k5 * id_8n7o")

        # Add parameter k5
        parameter5 = kinetic_law5.createParameter()
        parameter5.setId("k5")
        parameter5.setValue(final_params[4])

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

        # Store the final SBML model
        shared_variables.add('final_sbml_model8', final_sbml)

        print("\nCreated SBML model with Model 8 reactions:")
        print(f"1. id_8n7o -> id_caoz (k1 = {final_params[0]})")
        print(f"2. id_caoz -> id_ty7g (k2 = {final_params[1]})")
        print(f"3. id_caoz -> id_1wsx (k3 = {final_params[2]})")
        print(f"4. id_1wsx -> id_ty7g (k4 = {final_params[3]})")
        print(f"5. id_8n7o -> id_ty7g (k5 = {final_params[4]})")
```
# Observation

## Code Stdout
Best parameters for Model 7: k1 = 0.1, k2 = 0.1, k3 = 0.1, k4 = 0.01
Best error for Model 7: 1.3309402882832346

Comparison of Model 7 simulation vs. experimental data for the first experiment:

Time 0:
  id_8n7o: Sim = 1.11e+07, Exp = 1.11e+07, Rel Error = 0.00%
  id_caoz: Sim = 1.93e+02, Exp = 1.93e+02, Rel Error = 0.00%
  id_ty7g: Sim = 2.00e+00, Exp = 2.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 2.70e+01, Exp = 2.70e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 5.52e+05, Exp = 8.81e+06, Rel Error = 93.74%
  id_caoz: Sim = 5.24e+05, Exp = 1.50e+06, Rel Error = 64.96%
  id_ty7g: Sim = 5.80e+06, Exp = 1.10e+05, Rel Error = 5169.94%
  id_1wsx: Sim = 4.20e+06, Exp = 6.64e+05, Rel Error = 532.85%

Time 60:
  id_8n7o: Sim = 2.75e+04, Exp = 6.25e+04, Rel Error = 56.07%
  id_caoz: Sim = 2.74e+04, Exp = 4.97e+05, Rel Error = 94.50%
  id_ty7g: Sim = 7.50e+06, Exp = 6.06e+06, Rel Error = 23.72%
  id_1wsx: Sim = 3.53e+06, Exp = 4.46e+06, Rel Error = 20.92%

Time 90:
  id_8n7o: Sim = 1.37e+03, Exp = 1.02e+04, Rel Error = 86.53%
  id_caoz: Sim = 1.37e+03, Exp = 1.19e+04, Rel Error = 88.47%
  id_ty7g: Sim = 8.45e+06, Exp = 9.81e+06, Rel Error = 13.93%
  id_1wsx: Sim = 2.63e+06, Exp = 1.25e+06, Rel Error = 111.20%

Time 120:
  id_8n7o: Sim = 6.81e+01, Exp = 6.57e+03, Rel Error = 98.96%
  id_caoz: Sim = 6.81e+01, Exp = 6.56e+02, Rel Error = 89.61%
  id_ty7g: Sim = 9.13e+06, Exp = 1.08e+07, Rel Error = 15.26%
  id_1wsx: Sim = 1.95e+06, Exp = 3.01e+05, Rel Error = 548.41%

Time 150:
  id_8n7o: Sim = 3.40e+00, Exp = 5.92e+03, Rel Error = 99.94%
  id_caoz: Sim = 3.39e+00, Exp = 1.06e+02, Rel Error = 96.79%
  id_ty7g: Sim = 9.64e+06, Exp = 1.10e+07, Rel Error = 12.43%
  id_1wsx: Sim = 1.45e+06, Exp = 7.18e+04, Rel Error = 1913.01%

Time 180:
  id_8n7o: Sim = 1.69e-01, Exp = 5.77e+03, Rel Error = 100.00%
  id_caoz: Sim = 1.69e-01, Exp = 2.35e+01, Rel Error = 99.28%
  id_ty7g: Sim = 1.00e+07, Exp = 1.11e+07, Rel Error = 9.48%
  id_1wsx: Sim = 1.07e+06, Exp = 1.71e+04, Rel Error = 6157.12%

Comparison of Model 7 simulation vs. experimental data for the second experiment:

Time 0:
  id_8n7o: Sim = 5.00e+06, Exp = 5.00e+06, Rel Error = 0.00%
  id_caoz: Sim = 1.00e+03, Exp = 1.00e+03, Rel Error = 0.00%
  id_ty7g: Sim = 1.00e+01, Exp = 1.00e+01, Rel Error = 0.00%
  id_1wsx: Sim = 1.00e+02, Exp = 1.00e+02, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 2.49e+05, Exp = 4.95e+06, Rel Error = 94.97%
  id_caoz: Sim = 2.37e+05, Exp = 2.13e+04, Rel Error = 1010.61%
  id_ty7g: Sim = 2.62e+06, Exp = 7.29e+03, Rel Error = 35827.16%
  id_1wsx: Sim = 1.90e+06, Exp = 1.84e+04, Rel Error = 10222.11%

Time 60:
  id_8n7o: Sim = 1.24e+04, Exp = 3.88e+06, Rel Error = 99.68%
  id_caoz: Sim = 1.24e+04, Exp = 4.46e+05, Rel Error = 97.23%
  id_ty7g: Sim = 3.39e+06, Exp = 2.15e+05, Rel Error = 1475.74%
  id_1wsx: Sim = 1.59e+06, Exp = 4.56e+05, Rel Error = 249.18%

Time 90:
  id_8n7o: Sim = 6.18e+02, Exp = 9.35e+05, Rel Error = 99.93%
  id_caoz: Sim = 6.18e+02, Exp = 5.36e+05, Rel Error = 99.88%
  id_ty7g: Sim = 3.81e+06, Exp = 1.90e+06, Rel Error = 100.54%
  id_1wsx: Sim = 1.19e+06, Exp = 1.63e+06, Rel Error = 27.06%

Time 120:
  id_8n7o: Sim = 3.08e+01, Exp = 3.16e+05, Rel Error = 99.99%
  id_caoz: Sim = 3.08e+01, Exp = 8.60e+04, Rel Error = 99.96%
  id_ty7g: Sim = 4.12e+06, Exp = 3.76e+06, Rel Error = 9.66%
  id_1wsx: Sim = 8.81e+05, Exp = 8.42e+05, Rel Error = 4.56%

Time 150:
  id_8n7o: Sim = 1.53e+00, Exp = 2.18e+05, Rel Error = 100.00%
  id_caoz: Sim = 1.53e+00, Exp = 1.57e+04, Rel Error = 99.99%
  id_ty7g: Sim = 4.35e+06, Exp = 4.50e+06, Rel Error = 3.27%
  id_1wsx: Sim = 6.53e+05, Exp = 2.73e+05, Rel Error = 139.43%

Time 180:
  id_8n7o: Sim = 7.64e-02, Exp = 1.95e+05, Rel Error = 100.00%
  id_caoz: Sim = 7.64e-02, Exp = 3.80e+03, Rel Error = 100.00%
  id_ty7g: Sim = 4.52e+06, Exp = 4.72e+06, Rel Error = 4.34%
  id_1wsx: Sim = 4.83e+05, Exp = 8.01e+04, Rel Error = 503.59%

Comparison of Model 7 simulation vs. experimental data for the third experiment:

Time 0:
  id_8n7o: Sim = 1.50e+07, Exp = 1.50e+07, Rel Error = 0.00%
  id_caoz: Sim = 5.00e+02, Exp = 5.00e+02, Rel Error = 0.00%
  id_ty7g: Sim = 5.00e+00, Exp = 5.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 5.00e+01, Exp = 5.00e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 7.47e+05, Exp = 9.64e+05, Rel Error = 22.53%
  id_caoz: Sim = 7.10e+05, Exp = 5.64e+06, Rel Error = 87.42%
  id_ty7g: Sim = 7.86e+06, Exp = 1.77e+06, Rel Error = 344.95%
  id_1wsx: Sim = 5.69e+06, Exp = 6.63e+06, Rel Error = 14.17%

Time 60:
  id_8n7o: Sim = 3.72e+04, Exp = 3.26e+03, Rel Error = 1040.91%
  id_caoz: Sim = 3.71e+04, Exp = 1.14e+05, Rel Error = 67.38%
  id_ty7g: Sim = 1.02e+07, Exp = 1.10e+07, Rel Error = 8.01%
  id_1wsx: Sim = 4.77e+06, Exp = 3.85e+06, Rel Error = 24.08%

Time 90:
  id_8n7o: Sim = 1.85e+03, Exp = 8.16e+02, Rel Error = 127.04%
  id_caoz: Sim = 1.85e+03, Exp = 1.94e+03, Rel Error = 4.52%
  id_ty7g: Sim = 1.14e+07, Exp = 1.40e+07, Rel Error = 18.61%
  id_1wsx: Sim = 3.56e+06, Exp = 9.51e+05, Rel Error = 274.88%

Time 120:
  id_8n7o: Sim = 9.22e+01, Exp = 5.88e+02, Rel Error = 84.31%
  id_caoz: Sim = 9.22e+01, Exp = 6.05e+01, Rel Error = 52.58%
  id_ty7g: Sim = 1.24e+07, Exp = 1.48e+07, Rel Error = 16.35%
  id_1wsx: Sim = 2.64e+06, Exp = 2.26e+05, Rel Error = 1068.86%

Time 150:
  id_8n7o: Sim = 4.60e+00, Exp = 5.44e+02, Rel Error = 99.15%
  id_caoz: Sim = 4.59e+00, Exp = 7.43e+00, Rel Error = 38.20%
  id_ty7g: Sim = 1.30e+07, Exp = 1.49e+07, Rel Error = 12.73%
  id_1wsx: Sim = 1.96e+06, Exp = 5.36e+04, Rel Error = 3552.16%

Time 180:
  id_8n7o: Sim = 2.29e-01, Exp = 5.34e+02, Rel Error = 99.96%
  id_caoz: Sim = 2.29e-01, Exp = 1.61e+00, Rel Error = 85.80%
  id_ty7g: Sim = 1.36e+07, Exp = 1.50e+07, Rel Error = 9.59%
  id_1wsx: Sim = 1.45e+06, Exp = 1.27e+04, Rel Error = 11313.21%

Created SBML model with Model 7 reactions:
1. id_8n7o -> id_caoz (k1 = 0.1)
2. id_caoz -> id_ty7g (k2 = 0.1)
3. id_caoz -> id_1wsx (k3 = 0.1)
4. id_1wsx -> id_ty7g (k4 = 0.01)

Best parameters for Model 8: k1 = 0.05, k2 = 0.01, k3 = 0.1, k4 = 0.01, k5 = 0.01
Best error for Model 8: 1.4045031734966673

Comparison of Model 7 and Model 8:
Model 7 error: 1.3309402882832346
Model 8 error: 1.4045031734966673

Model 7 is the better fit.

## 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_8, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml, final_sbml_refined, final_sbml_model6, final_sbml_model7)

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


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



# Iteration 13
## Thoughts
Model 7, with its simpler sequential conversion reactions, performs better than Model 8 (which included a direct conversion from `id_8n7o` to `id_ty7g`). However, the overall error is still quite high (1.33), and there are significant discrepancies between the simulated and experimental data.

Looking at the comparison between Model 7 and the experimental data:

1. For the first experiment:
   - `id_8n7o` decreases too quickly in the simulation
   - `id_ty7g` increases too quickly in the simulation at early time points
   - `id_1wsx` increases too much in the simulation

2. For the second experiment:
   - Similar issues as the first experiment

3. For the third experiment:
   - Better agreement for some species, but still significant discrepancies

Let me try one more model refinement. Looking at the data more carefully, I notice that:
1. `id_8n7o` decreases at a rate that suggests it might be consumed in a reaction with another species
2. `id_caoz` shows a rise and fall pattern that suggests it's both produced and consumed
3. `id_1wsx` also shows a rise and fall pattern
4. `id_ty7g` increases steadily, suggesting it's a product of multiple reactions

Let me try a model with the following reactions:
1. `id_8n7o + id_caoz -> id_ty7g + id_1wsx` (second-order reaction)
2. `id_8n7o -> id_caoz` (first-order reaction)
3. `id_1wsx + id_8n7o -> 2 id_ty7g` (second-order reaction)

This model includes both first-order and second-order reactions, which might better capture the observed dynamics.

## Action

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

# Access the experimental data
exp_data_1 = experiment_history["iteration_0"]
exp_data_2 = experiment_history["iteration_8"]
exp_data_3 = experiment_history["iteration_10"]

# Define the Model 9 ODE function (mixed first-order and second-order reactions)
def model_ode9(t, y, k1, k2, k3):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    r1 = k1 * y[0] * y[1]
    
    # Reaction 2: id_8n7o -> id_caoz
    r2 = k2 * y[0]
    
    # Reaction 3: id_1wsx + id_8n7o -> 2 id_ty7g
    r3 = k3 * y[3] * y[0]
    
    # ODEs
    dy_dt = [
        -r1 - r2 - r3,      # d[id_8n7o]/dt
        -r1 + r2,           # d[id_caoz]/dt
        r1 + 2*r3,          # d[id_ty7g]/dt
        r1 - r3             # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Let's optimize the parameters for Model 9 using all three experiments
def objective_function(params):
    k1, k2, k3 = params
    
    # Simulate for the first experiment
    y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
    t_eval_1 = exp_data_1['Time'].values
    
    try:
        sol1 = solve_ivp(
            lambda t, y: model_ode9(t, y, k1, k2, k3),
            (0, 183),
            y0_exp1,
            method='LSODA',
            t_eval=t_eval_1
        )
        
        sim_data1 = pd.DataFrame({
            'Time': sol1.t,
            'id_8n7o': sol1.y[0],
            'id_caoz': sol1.y[1],
            'id_ty7g': sol1.y[2],
            'id_1wsx': sol1.y[3]
        })
        
        error1 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_1[species]), max(sim_data1[species]))
            if max_val > 0:
                error1 += np.mean(((exp_data_1[species] - sim_data1[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the second experiment
    y0_exp2 = [5000000, 1000, 10, 100]
    t_eval_2 = exp_data_2['Time'].values
    
    try:
        sol2 = solve_ivp(
            lambda t, y: model_ode9(t, y, k1, k2, k3),
            (0, 183),
            y0_exp2,
            method='LSODA',
            t_eval=t_eval_2
        )
        
        sim_data2 = pd.DataFrame({
            'Time': sol2.t,
            'id_8n7o': sol2.y[0],
            'id_caoz': sol2.y[1],
            'id_ty7g': sol2.y[2],
            'id_1wsx': sol2.y[3]
        })
        
        error2 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_2[species]), max(sim_data2[species]))
            if max_val > 0:
                error2 += np.mean(((exp_data_2[species] - sim_data2[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the third experiment
    y0_exp3 = [15000000, 500, 5, 50]
    t_eval_3 = exp_data_3['Time'].values
    
    try:
        sol3 = solve_ivp(
            lambda t, y: model_ode9(t, y, k1, k2, k3),
            (0, 183),
            y0_exp3,
            method='LSODA',
            t_eval=t_eval_3
        )
        
        sim_data3 = pd.DataFrame({
            'Time': sol3.t,
            'id_8n7o': sol3.y[0],
            'id_caoz': sol3.y[1],
            'id_ty7g': sol3.y[2],
            'id_1wsx': sol3.y[3]
        })
        
        error3 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_3[species]), max(sim_data3[species]))
            if max_val > 0:
                error3 += np.mean(((exp_data_3[species] - sim_data3[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Return the total error
    return error1 + error2 + error3

# Let's try a few parameter combinations manually
param_sets = [
    [1e-8, 0.05, 1e-8],
    [1e-7, 0.05, 1e-8],
    [1e-8, 0.1, 1e-8],
    [1e-8, 0.05, 1e-7],
    [1e-7, 0.1, 1e-8],
    [1e-8, 0.1, 1e-7],
    [1e-7, 0.1, 1e-7]
]

best_params = None
best_error = float('inf')

for params in param_sets:
    error = objective_function(params)
    if error < best_error:
        best_error = error
        best_params = params

print(f"Best parameters for Model 9: k1 = {best_params[0]}, k2 = {best_params[1]}, k3 = {best_params[2]}")
print(f"Best error for Model 9: {best_error}")

# Simulate with the best parameters for all three experiments
# First experiment
y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
t_eval_1 = exp_data_1['Time'].values

sol1 = solve_ivp(
    lambda t, y: model_ode9(t, y, *best_params),
    (0, 183),
    y0_exp1,
    method='LSODA',
    t_eval=t_eval_1
)

sim_data1 = pd.DataFrame({
    'Time': sol1.t,
    'id_8n7o': sol1.y[0],
    'id_caoz': sol1.y[1],
    'id_ty7g': sol1.y[2],
    'id_1wsx': sol1.y[3]
})

# Second experiment
y0_exp2 = [5000000, 1000, 10, 100]
t_eval_2 = exp_data_2['Time'].values

sol2 = solve_ivp(
    lambda t, y: model_ode9(t, y, *best_params),
    (0, 183),
    y0_exp2,
    method='LSODA',
    t_eval=t_eval_2
)

sim_data2 = pd.DataFrame({
    'Time': sol2.t,
    'id_8n7o': sol2.y[0],
    'id_caoz': sol2.y[1],
    'id_ty7g': sol2.y[2],
    'id_1wsx': sol2.y[3]
})

# Third experiment
y0_exp3 = [15000000, 500, 5, 50]
t_eval_3 = exp_data_3['Time'].values

sol3 = solve_ivp(
    lambda t, y: model_ode9(t, y, *best_params),
    (0, 183),
    y0_exp3,
    method='LSODA',
    t_eval=t_eval_3
)

sim_data3 = pd.DataFrame({
    'Time': sol3.t,
    'id_8n7o': sol3.y[0],
    'id_caoz': sol3.y[1],
    'id_ty7g': sol3.y[2],
    'id_1wsx': sol3.y[3]
})

# Compare the simulation with experimental data for all three experiments
selected_times = [0, 30, 60, 90, 120, 150, 180]

print("\nComparison of Model 9 simulation vs. experimental data for the first experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data1['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data1.loc[idx, species]
        exp_val = exp_data_1[exp_data_1['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

print("\nComparison of Model 9 simulation vs. experimental data for the second experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data2['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data2.loc[idx, species]
        exp_val = exp_data_2[exp_data_2['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

print("\nComparison of Model 9 simulation vs. experimental data for the third experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data3['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data3.loc[idx, species]
        exp_val = exp_data_3[exp_data_3['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Compare the errors of Model 7 and Model 9
print("\nComparison of Model 7 and Model 9:")
print(f"Model 7 error: 1.3309402882832346")
print(f"Model 9 error: {best_error}")

if 1.3309402882832346 <= best_error:
    print("\nModel 7 is the better fit.")
    final_model = 7
    final_params = [0.1, 0.1, 0.1, 0.01]  # From previous run
else:
    print("\nModel 9 is the better fit.")
    final_model = 9
    final_params = best_params

# Create the final SBML model with the best model's reactions and parameters
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

if final_model == 7:
    # Add the first reaction: id_8n7o -> id_caoz
    reaction1 = model.createReaction()
    reaction1.setId("reaction1")
    reaction1.setReversible(False)

    # Add reactants
    reactant1 = reaction1.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction1.createProduct()
    product1.setSpecies("id_caoz")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law1 = reaction1.createKineticLaw()
    kinetic_law1.setFormula("k1 * id_8n7o")

    # Add parameter k1
    parameter1 = kinetic_law1.createParameter()
    parameter1.setId("k1")
    parameter1.setValue(final_params[0])

    # Add the second reaction: id_caoz -> id_ty7g
    reaction2 = model.createReaction()
    reaction2.setId("reaction2")
    reaction2.setReversible(False)

    # Add reactants
    reactant1 = reaction2.createReactant()
    reactant1.setSpecies("id_caoz")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction2.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law2 = reaction2.createKineticLaw()
    kinetic_law2.setFormula("k2 * id_caoz")

    # Add parameter k2
    parameter2 = kinetic_law2.createParameter()
    parameter2.setId("k2")
    parameter2.setValue(final_params[1])

    # Add the third reaction: id_caoz -> id_1wsx
    reaction3 = model.createReaction()
    reaction3.setId("reaction3")
    reaction3.setReversible(False)

    # Add reactants
    reactant1 = reaction3.createReactant()
    reactant1.setSpecies("id_caoz")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction3.createProduct()
    product1.setSpecies("id_1wsx")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law3 = reaction3.createKineticLaw()
    kinetic_law3.setFormula("k3 * id_caoz")

    # Add parameter k3
    parameter3 = kinetic_law3.createParameter()
    parameter3.setId("k3")
    parameter3.setValue(final_params[2])

    # Add the fourth reaction: id_1wsx -> id_ty7g
    reaction4 = model.createReaction()
    reaction4.setId("reaction4")
    reaction4.setReversible(False)

    # Add reactants
    reactant1 = reaction4.createReactant()
    reactant1.setSpecies("id_1wsx")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction4.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law4 = reaction4.createKineticLaw()
    kinetic_law4.setFormula("k4 * id_1wsx")

    # Add parameter k4
    parameter4 = kinetic_law4.createParameter()
    parameter4.setId("k4")
    parameter4.setValue(final_params[3])

    print("\nCreated SBML model with Model 7 reactions:")
    print(f"1. id_8n7o -> id_caoz (k1 = {final_params[0]})")
    print(f"2. id_caoz -> id_ty7g (k2 = {final_params[1]})")
    print(f"3. id_caoz -> id_1wsx (k3 = {final_params[2]})")
    print(f"4. id_1wsx -> id_ty7g (k4 = {final_params[3]})")

else:  # final_model == 9
    # Add the first reaction: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    reaction1 = model.createReaction()
    reaction1.setId("reaction1")
    reaction1.setReversible(False)

    # Add reactants
    reactant1 = reaction1.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

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

    # Add products
    product1 = reaction1.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    product2 = reaction1.createProduct()
    product2.setSpecies("id_1wsx")
    product2.setStoichiometry(1.0)
    product2.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law1 = reaction1.createKineticLaw()
    kinetic_law1.setFormula("k1 * id_8n7o * id_caoz")

    # Add parameter k1
    parameter1 = kinetic_law1.createParameter()
    parameter1.setId("k1")
    parameter1.setValue(final_params[0])

    # Add the second reaction: id_8n7o -> id_caoz
    reaction2 = model.createReaction()
    reaction2.setId("reaction2")
    reaction2.setReversible(False)

    # Add reactants
    reactant1 = reaction2.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction2.createProduct()
    product1.setSpecies("id_caoz")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law2 = reaction2.createKineticLaw()
    kinetic_law2.setFormula("k2 * id_8n7o")

    # Add parameter k2
    parameter2 = kinetic_law2.createParameter()
    parameter2.setId("k2")
    parameter2.setValue(final_params[1])

    # Add the third reaction: id_1wsx + id_8n7o -> 2 id_ty7g
    reaction3 = model.createReaction()
    reaction3.setId("reaction3")
    reaction3.setReversible(False)

    # Add reactants
    reactant1 = reaction3.createReactant()
    reactant1.setSpecies("id_1wsx")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    reactant2 = reaction3.createReactant()
    reactant2.setSpecies("id_8n7o")
    reactant2.setStoichiometry(1.0)
    reactant2.setConstant(True)

    # Add products
    product1 = reaction3.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(2.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law3 = reaction3.createKineticLaw()
    kinetic_law3.setFormula("k3 * id_1wsx * id_8n7o")

    # Add parameter k3
    parameter3 = kinetic_law3.createParameter()
    parameter3.setId("k3")
    parameter3.setValue(final_params[2])

    print("\nCreated SBML model with Model 9 reactions:")
    print(f"1. id_8n7o + id_caoz -> id_ty7g + id_1wsx (k1 = {final_params[0]})")
    print(f"2. id_8n7o -> id_caoz (k2 = {final_params[1]})")
    print(f"3. id_1wsx + id_8n7o -> 2 id_ty7g (k3 = {final_params[2]})")

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

# Store the final SBML model
shared_variables.add('final_sbml_best', final_sbml)
```
# Observation

## Code Stdout
Best parameters for Model 9: k1 = 1e-07, k2 = 0.05, k3 = 1e-08
Best error for Model 9: 1.932395786571636

Comparison of Model 9 simulation vs. experimental data for the first experiment:

Time 0:
  id_8n7o: Sim = 1.11e+07, Exp = 1.11e+07, Rel Error = 0.00%
  id_caoz: Sim = 1.93e+02, Exp = 1.93e+02, Rel Error = 0.00%
  id_ty7g: Sim = 2.00e+00, Exp = 2.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 2.70e+01, Exp = 2.70e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 2.95e+05, Exp = 8.81e+06, Rel Error = 96.65%
  id_caoz: Sim = 5.00e+05, Exp = 1.50e+06, Rel Error = 66.60%
  id_ty7g: Sim = 7.37e+06, Exp = 1.10e+05, Rel Error = 6594.29%
  id_1wsx: Sim = 2.91e+06, Exp = 6.64e+05, Rel Error = 339.03%

Time 60:
  id_8n7o: Sim = 6.08e+03, Exp = 6.25e+04, Rel Error = 90.29%
  id_caoz: Sim = 5.00e+05, Exp = 4.97e+05, Rel Error = 0.55%
  id_ty7g: Sim = 7.61e+06, Exp = 6.06e+06, Rel Error = 25.59%
  id_1wsx: Sim = 2.96e+06, Exp = 4.46e+06, Rel Error = 33.59%

Time 90:
  id_8n7o: Sim = 1.25e+02, Exp = 1.02e+04, Rel Error = 98.77%
  id_caoz: Sim = 5.00e+05, Exp = 1.19e+04, Rel Error = 4110.64%
  id_ty7g: Sim = 7.62e+06, Exp = 9.81e+06, Rel Error = 22.35%
  id_1wsx: Sim = 2.96e+06, Exp = 1.25e+06, Rel Error = 137.57%

Time 120:
  id_8n7o: Sim = 2.56e+00, Exp = 6.57e+03, Rel Error = 99.96%
  id_caoz: Sim = 5.00e+05, Exp = 6.56e+02, Rel Error = 76113.65%
  id_ty7g: Sim = 7.62e+06, Exp = 1.08e+07, Rel Error = 29.27%
  id_1wsx: Sim = 2.96e+06, Exp = 3.01e+05, Rel Error = 884.04%

Time 150:
  id_8n7o: Sim = 5.27e-02, Exp = 5.92e+03, Rel Error = 100.00%
  id_caoz: Sim = 5.00e+05, Exp = 1.06e+02, Rel Error = 473361.31%
  id_ty7g: Sim = 7.62e+06, Exp = 1.10e+07, Rel Error = 30.76%
  id_1wsx: Sim = 2.96e+06, Exp = 7.18e+04, Rel Error = 4023.67%

Time 180:
  id_8n7o: Sim = 1.08e-03, Exp = 5.77e+03, Rel Error = 100.00%
  id_caoz: Sim = 5.00e+05, Exp = 2.35e+01, Rel Error = 2128011.93%
  id_ty7g: Sim = 7.62e+06, Exp = 1.11e+07, Rel Error = 31.10%
  id_1wsx: Sim = 2.96e+06, Exp = 1.71e+04, Rel Error = 17202.13%

Comparison of Model 9 simulation vs. experimental data for the second experiment:

Time 0:
  id_8n7o: Sim = 5.00e+06, Exp = 5.00e+06, Rel Error = 0.00%
  id_caoz: Sim = 1.00e+03, Exp = 1.00e+03, Rel Error = 0.00%
  id_ty7g: Sim = 1.00e+01, Exp = 1.00e+01, Rel Error = 0.00%
  id_1wsx: Sim = 1.00e+02, Exp = 1.00e+02, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 2.01e+05, Exp = 4.95e+06, Rel Error = 95.94%
  id_caoz: Sim = 4.96e+05, Exp = 2.13e+04, Rel Error = 2229.74%
  id_ty7g: Sim = 2.69e+06, Exp = 7.29e+03, Rel Error = 36805.84%
  id_1wsx: Sim = 1.61e+06, Exp = 1.84e+04, Rel Error = 8680.60%

Time 60:
  id_8n7o: Sim = 6.16e+03, Exp = 3.88e+06, Rel Error = 99.84%
  id_caoz: Sim = 4.97e+05, Exp = 4.46e+05, Rel Error = 11.35%
  id_ty7g: Sim = 2.83e+06, Exp = 2.15e+05, Rel Error = 1216.85%
  id_1wsx: Sim = 1.67e+06, Exp = 4.56e+05, Rel Error = 266.24%

Time 90:
  id_8n7o: Sim = 1.88e+02, Exp = 9.35e+05, Rel Error = 99.98%
  id_caoz: Sim = 4.97e+05, Exp = 5.36e+05, Rel Error = 7.33%
  id_ty7g: Sim = 2.83e+06, Exp = 1.90e+06, Rel Error = 49.07%
  id_1wsx: Sim = 1.67e+06, Exp = 1.63e+06, Rel Error = 2.55%

Time 120:
  id_8n7o: Sim = 5.72e+00, Exp = 3.16e+05, Rel Error = 100.00%
  id_caoz: Sim = 4.97e+05, Exp = 8.60e+04, Rel Error = 478.05%
  id_ty7g: Sim = 2.83e+06, Exp = 3.76e+06, Rel Error = 24.59%
  id_1wsx: Sim = 1.67e+06, Exp = 8.42e+05, Rel Error = 98.34%

Time 150:
  id_8n7o: Sim = 1.74e-01, Exp = 2.18e+05, Rel Error = 100.00%
  id_caoz: Sim = 4.97e+05, Exp = 1.57e+04, Rel Error = 3074.14%
  id_ty7g: Sim = 2.83e+06, Exp = 4.50e+06, Rel Error = 36.97%
  id_1wsx: Sim = 1.67e+06, Exp = 2.73e+05, Rel Error = 513.03%

Time 180:
  id_8n7o: Sim = 5.31e-03, Exp = 1.95e+05, Rel Error = 100.00%
  id_caoz: Sim = 4.97e+05, Exp = 3.80e+03, Rel Error = 12995.14%
  id_ty7g: Sim = 2.83e+06, Exp = 4.72e+06, Rel Error = 40.00%
  id_1wsx: Sim = 1.67e+06, Exp = 8.01e+04, Rel Error = 1986.10%

Comparison of Model 9 simulation vs. experimental data for the third experiment:

Time 0:
  id_8n7o: Sim = 1.50e+07, Exp = 1.50e+07, Rel Error = 0.00%
  id_caoz: Sim = 5.00e+02, Exp = 5.00e+02, Rel Error = 0.00%
  id_ty7g: Sim = 5.00e+00, Exp = 5.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 5.00e+01, Exp = 5.00e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 3.38e+05, Exp = 9.64e+05, Rel Error = 64.90%
  id_caoz: Sim = 5.00e+05, Exp = 5.64e+06, Rel Error = 91.14%
  id_ty7g: Sim = 1.07e+07, Exp = 1.77e+06, Rel Error = 507.02%
  id_1wsx: Sim = 3.45e+06, Exp = 6.63e+06, Rel Error = 48.02%

Time 60:
  id_8n7o: Sim = 5.94e+03, Exp = 3.26e+03, Rel Error = 82.28%
  id_caoz: Sim = 5.00e+05, Exp = 1.14e+05, Rel Error = 340.07%
  id_ty7g: Sim = 1.10e+07, Exp = 1.10e+07, Rel Error = 0.23%
  id_1wsx: Sim = 3.48e+06, Exp = 3.85e+06, Rel Error = 9.45%

Time 90:
  id_8n7o: Sim = 1.04e+02, Exp = 8.16e+02, Rel Error = 87.23%
  id_caoz: Sim = 5.00e+05, Exp = 1.94e+03, Rel Error = 25662.80%
  id_ty7g: Sim = 1.10e+07, Exp = 1.40e+07, Rel Error = 21.57%
  id_1wsx: Sim = 3.48e+06, Exp = 9.51e+05, Rel Error = 266.40%

Time 120:
  id_8n7o: Sim = 1.83e+00, Exp = 5.88e+02, Rel Error = 99.69%
  id_caoz: Sim = 5.00e+05, Exp = 6.05e+01, Rel Error = 827021.74%
  id_ty7g: Sim = 1.10e+07, Exp = 1.48e+07, Rel Error = 25.43%
  id_1wsx: Sim = 3.48e+06, Exp = 2.26e+05, Rel Error = 1441.30%

Time 150:
  id_8n7o: Sim = 3.21e-02, Exp = 5.44e+02, Rel Error = 99.99%
  id_caoz: Sim = 5.00e+05, Exp = 7.43e+00, Rel Error = 6725792.62%
  id_ty7g: Sim = 1.10e+07, Exp = 1.49e+07, Rel Error = 26.29%
  id_1wsx: Sim = 3.48e+06, Exp = 5.36e+04, Rel Error = 6400.50%

Time 180:
  id_8n7o: Sim = 5.64e-04, Exp = 5.34e+02, Rel Error = 100.00%
  id_caoz: Sim = 5.00e+05, Exp = 1.61e+00, Rel Error = 31005108.96%
  id_ty7g: Sim = 1.10e+07, Exp = 1.50e+07, Rel Error = 26.49%
  id_1wsx: Sim = 3.48e+06, Exp = 1.27e+04, Rel Error = 27321.55%

Comparison of Model 7 and Model 9:
Model 7 error: 1.3309402882832346
Model 9 error: 1.932395786571636

Model 7 is the better fit.

Created SBML model with Model 7 reactions:
1. id_8n7o -> id_caoz (k1 = 0.1)
2. id_caoz -> id_ty7g (k2 = 0.1)
3. id_caoz -> id_1wsx (k3 = 0.1)
4. id_1wsx -> id_ty7g (k4 = 0.01)

## 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_8, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml, final_sbml_refined, final_sbml_model6, final_sbml_model7, final_sbml_best)

### 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
After testing multiple models, Model 7 with its sequential conversion reactions remains the best fit with an error of 1.33, compared to 1.93 for Model 9. The reactions in Model 7 are:

1. `id_8n7o -> id_caoz` (k1 = 0.1)
2. `id_caoz -> id_ty7g` (k2 = 0.1)
3. `id_caoz -> id_1wsx` (k3 = 0.1)
4. `id_1wsx -> id_ty7g` (k4 = 0.01)

This model captures the general trends in the data, but there are still significant discrepancies between the simulated and experimental data. Let me try one more approach to see if I can improve the fit.

Looking at the data more carefully, I notice that:
1. `id_8n7o` decreases rapidly, which is captured well by the first reaction
2. `id_caoz` shows a rise and fall pattern, which is captured by the first reaction (production) and the second and third reactions (consumption)
3. `id_1wsx` also shows a rise and fall pattern, which is captured by the third reaction (production) and the fourth reaction (consumption)
4. `id_ty7g` increases steadily, which is captured by the second and fourth reactions (production)

However, the timing and magnitude of the peaks for `id_caoz` and `id_1wsx` don't match well between simulations and experiments. Let me try to refine the rate constants further using a more sophisticated optimization approach.

## Action

### Code
```python
import numpy as np
import pandas as pd
import libsbml
from scipy.integrate import solve_ivp
from scipy.optimize import minimize

# Access the experimental data
exp_data_1 = experiment_history["iteration_0"]
exp_data_2 = experiment_history["iteration_8"]
exp_data_3 = experiment_history["iteration_10"]

# Define the Model 7 ODE function (sequential conversion model)
def model_ode7(t, y, k1, k2, k3, k4):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o -> id_caoz
    r1 = k1 * y[0]
    
    # Reaction 2: id_caoz -> id_ty7g
    r2 = k2 * y[1]
    
    # Reaction 3: id_caoz -> id_1wsx
    r3 = k3 * y[1]
    
    # Reaction 4: id_1wsx -> id_ty7g
    r4 = k4 * y[3]
    
    # ODEs
    dy_dt = [
        -r1,            # d[id_8n7o]/dt
        r1 - r2 - r3,   # d[id_caoz]/dt
        r2 + r4,        # d[id_ty7g]/dt
        r3 - r4         # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Define the objective function for optimization
def objective_function(params):
    k1, k2, k3, k4 = 10**params[0], 10**params[1], 10**params[2], 10**params[3]  # Log-scale parameters
    
    # Simulate for the first experiment
    y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
    t_eval_1 = exp_data_1['Time'].values
    
    try:
        sol1 = solve_ivp(
            lambda t, y: model_ode7(t, y, k1, k2, k3, k4),
            (0, 183),
            y0_exp1,
            method='LSODA',
            t_eval=t_eval_1
        )
        
        sim_data1 = pd.DataFrame({
            'Time': sol1.t,
            'id_8n7o': sol1.y[0],
            'id_caoz': sol1.y[1],
            'id_ty7g': sol1.y[2],
            'id_1wsx': sol1.y[3]
        })
        
        error1 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_1[species]), max(sim_data1[species]))
            if max_val > 0:
                error1 += np.mean(((exp_data_1[species] - sim_data1[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the second experiment
    y0_exp2 = [5000000, 1000, 10, 100]
    t_eval_2 = exp_data_2['Time'].values
    
    try:
        sol2 = solve_ivp(
            lambda t, y: model_ode7(t, y, k1, k2, k3, k4),
            (0, 183),
            y0_exp2,
            method='LSODA',
            t_eval=t_eval_2
        )
        
        sim_data2 = pd.DataFrame({
            'Time': sol2.t,
            'id_8n7o': sol2.y[0],
            'id_caoz': sol2.y[1],
            'id_ty7g': sol2.y[2],
            'id_1wsx': sol2.y[3]
        })
        
        error2 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_2[species]), max(sim_data2[species]))
            if max_val > 0:
                error2 += np.mean(((exp_data_2[species] - sim_data2[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the third experiment
    y0_exp3 = [15000000, 500, 5, 50]
    t_eval_3 = exp_data_3['Time'].values
    
    try:
        sol3 = solve_ivp(
            lambda t, y: model_ode7(t, y, k1, k2, k3, k4),
            (0, 183),
            y0_exp3,
            method='LSODA',
            t_eval=t_eval_3
        )
        
        sim_data3 = pd.DataFrame({
            'Time': sol3.t,
            'id_8n7o': sol3.y[0],
            'id_caoz': sol3.y[1],
            'id_ty7g': sol3.y[2],
            'id_1wsx': sol3.y[3]
        })
        
        error3 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_3[species]), max(sim_data3[species]))
            if max_val > 0:
                error3 += np.mean(((exp_data_3[species] - sim_data3[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Return the total error
    return error1 + error2 + error3

# Initial guess for the parameters (log scale)
initial_guess = np.log10([0.1, 0.1, 0.1, 0.01])  # From previous run

# Bounds for the parameters (log scale)
bounds = [(-3, 0), (-3, 0), (-3, 0), (-3, 0)]

# Run the optimization
result = minimize(objective_function, initial_guess, method='L-BFGS-B', bounds=bounds)

# Get the optimized parameters
optimized_params = 10**result.x

print(f"Optimized parameters for Model 7: k1 = {optimized_params[0]:.6f}, k2 = {optimized_params[1]:.6f}, k3 = {optimized_params[2]:.6f}, k4 = {optimized_params[3]:.6f}")
print(f"Optimized error for Model 7: {result.fun}")

# Simulate with the optimized parameters for all three experiments
# First experiment
y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
t_eval_1 = exp_data_1['Time'].values

sol1 = solve_ivp(
    lambda t, y: model_ode7(t, y, *optimized_params),
    (0, 183),
    y0_exp1,
    method='LSODA',
    t_eval=t_eval_1
)

sim_data1 = pd.DataFrame({
    'Time': sol1.t,
    'id_8n7o': sol1.y[0],
    'id_caoz': sol1.y[1],
    'id_ty7g': sol1.y[2],
    'id_1wsx': sol1.y[3]
})

# Second experiment
y0_exp2 = [5000000, 1000, 10, 100]
t_eval_2 = exp_data_2['Time'].values

sol2 = solve_ivp(
    lambda t, y: model_ode7(t, y, *optimized_params),
    (0, 183),
    y0_exp2,
    method='LSODA',
    t_eval=t_eval_2
)

sim_data2 = pd.DataFrame({
    'Time': sol2.t,
    'id_8n7o': sol2.y[0],
    'id_caoz': sol2.y[1],
    'id_ty7g': sol2.y[2],
    'id_1wsx': sol2.y[3]
})

# Third experiment
y0_exp3 = [15000000, 500, 5, 50]
t_eval_3 = exp_data_3['Time'].values

sol3 = solve_ivp(
    lambda t, y: model_ode7(t, y, *optimized_params),
    (0, 183),
    y0_exp3,
    method='LSODA',
    t_eval=t_eval_3
)

sim_data3 = pd.DataFrame({
    'Time': sol3.t,
    'id_8n7o': sol3.y[0],
    'id_caoz': sol3.y[1],
    'id_ty7g': sol3.y[2],
    'id_1wsx': sol3.y[3]
})

# Compare the simulation with experimental data for all three experiments
selected_times = [0, 30, 60, 90, 120, 150, 180]

print("\nComparison of optimized Model 7 simulation vs. experimental data for the first experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data1['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data1.loc[idx, species]
        exp_val = exp_data_1[exp_data_1['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

print("\nComparison of optimized Model 7 simulation vs. experimental data for the second experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data2['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data2.loc[idx, species]
        exp_val = exp_data_2[exp_data_2['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

print("\nComparison of optimized Model 7 simulation vs. experimental data for the third experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data3['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data3.loc[idx, species]
        exp_val = exp_data_3[exp_data_3['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Compare the errors of the original Model 7 and the optimized Model 7
print("\nComparison of original Model 7 and optimized Model 7:")
print(f"Original Model 7 error: 1.3309402882832346")
print(f"Optimized Model 7 error: {result.fun}")

# Create the final SBML model with the optimized parameters
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

# Add the first reaction: id_8n7o -> id_caoz
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactants
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_8n7o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction1.createProduct()
product1.setSpecies("id_caoz")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1 * id_8n7o")

# Add parameter k1
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(optimized_params[0])

# Add the second reaction: id_caoz -> id_ty7g
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactants
reactant1 = reaction2.createReactant()
reactant1.setSpecies("id_caoz")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction2.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_caoz")

# Add parameter k2
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(optimized_params[1])

# Add the third reaction: id_caoz -> id_1wsx
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactants
reactant1 = reaction3.createReactant()
reactant1.setSpecies("id_caoz")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction3.createProduct()
product1.setSpecies("id_1wsx")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_caoz")

# Add parameter k3
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(optimized_params[2])

# Add the fourth reaction: id_1wsx -> id_ty7g
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactants
reactant1 = reaction4.createReactant()
reactant1.setSpecies("id_1wsx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction4.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_1wsx")

# Add parameter k4
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(optimized_params[3])

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

# Store the final SBML model
shared_variables.add('final_sbml_optimized', final_sbml)

print("\nCreated SBML model with optimized Model 7 reactions:")
print(f"1. id_8n7o -> id_caoz (k1 = {optimized_params[0]:.6f})")
print(f"2. id_caoz -> id_ty7g (k2 = {optimized_params[1]:.6f})")
print(f"3. id_caoz -> id_1wsx (k3 = {optimized_params[2]:.6f})")
print(f"4. id_1wsx -> id_ty7g (k4 = {optimized_params[3]:.6f})")
```
# Observation

## Code Stdout
Optimized parameters for Model 7: k1 = 0.019317, k2 = 0.044277, k3 = 0.101668, k4 = 0.029516
Optimized error for Model 7: 0.6904687280474515

Comparison of optimized Model 7 simulation vs. experimental data for the first experiment:

Time 0:
  id_8n7o: Sim = 1.11e+07, Exp = 1.11e+07, Rel Error = 0.00%
  id_caoz: Sim = 1.93e+02, Exp = 1.93e+02, Rel Error = 0.00%
  id_ty7g: Sim = 2.00e+00, Exp = 2.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 2.70e+01, Exp = 2.70e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 6.21e+06, Exp = 8.81e+06, Rel Error = 29.55%
  id_caoz: Sim = 9.26e+05, Exp = 1.50e+06, Rel Error = 38.15%
  id_ty7g: Sim = 2.05e+06, Exp = 1.10e+05, Rel Error = 1762.12%
  id_1wsx: Sim = 1.90e+06, Exp = 6.64e+05, Rel Error = 185.83%

Time 60:
  id_8n7o: Sim = 3.48e+06, Exp = 6.25e+04, Rel Error = 5458.60%
  id_caoz: Sim = 5.30e+05, Exp = 4.97e+05, Rel Error = 6.61%
  id_ty7g: Sim = 4.90e+06, Exp = 6.06e+06, Rel Error = 19.10%
  id_1wsx: Sim = 2.17e+06, Exp = 4.46e+06, Rel Error = 51.34%

Time 90:
  id_8n7o: Sim = 1.95e+06, Exp = 1.02e+04, Rel Error = 19060.02%
  id_caoz: Sim = 2.97e+05, Exp = 1.19e+04, Rel Error = 2403.73%
  id_ty7g: Sim = 7.16e+06, Exp = 9.81e+06, Rel Error = 27.02%
  id_1wsx: Sim = 1.67e+06, Exp = 1.25e+06, Rel Error = 34.34%

Time 120:
  id_8n7o: Sim = 1.09e+06, Exp = 6.57e+03, Rel Error = 16504.67%
  id_caoz: Sim = 1.66e+05, Exp = 6.56e+02, Rel Error = 25263.70%
  id_ty7g: Sim = 8.70e+06, Exp = 1.08e+07, Rel Error = 19.28%
  id_1wsx: Sim = 1.13e+06, Exp = 3.01e+05, Rel Error = 274.89%

Time 150:
  id_8n7o: Sim = 6.11e+05, Exp = 5.92e+03, Rel Error = 10230.61%
  id_caoz: Sim = 9.33e+04, Exp = 1.06e+02, Rel Error = 88209.68%
  id_ty7g: Sim = 9.67e+06, Exp = 1.10e+07, Rel Error = 12.15%
  id_1wsx: Sim = 7.10e+05, Exp = 7.18e+04, Rel Error = 888.78%

Time 180:
  id_8n7o: Sim = 3.43e+05, Exp = 5.77e+03, Rel Error = 5833.40%
  id_caoz: Sim = 5.22e+04, Exp = 2.35e+01, Rel Error = 222094.45%
  id_ty7g: Sim = 1.03e+07, Exp = 1.11e+07, Rel Error = 7.26%
  id_1wsx: Sim = 4.31e+05, Exp = 1.71e+04, Rel Error = 2415.48%

Comparison of optimized Model 7 simulation vs. experimental data for the second experiment:

Time 0:
  id_8n7o: Sim = 5.00e+06, Exp = 5.00e+06, Rel Error = 0.00%
  id_caoz: Sim = 1.00e+03, Exp = 1.00e+03, Rel Error = 0.00%
  id_ty7g: Sim = 1.00e+01, Exp = 1.00e+01, Rel Error = 0.00%
  id_1wsx: Sim = 1.00e+02, Exp = 1.00e+02, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 2.80e+06, Exp = 4.95e+06, Rel Error = 43.46%
  id_caoz: Sim = 4.18e+05, Exp = 2.13e+04, Rel Error = 1860.35%
  id_ty7g: Sim = 9.26e+05, Exp = 7.29e+03, Rel Error = 12600.70%
  id_1wsx: Sim = 8.57e+05, Exp = 1.84e+04, Rel Error = 4562.87%

Time 60:
  id_8n7o: Sim = 1.57e+06, Exp = 3.88e+06, Rel Error = 59.61%
  id_caoz: Sim = 2.39e+05, Exp = 4.46e+05, Rel Error = 46.40%
  id_ty7g: Sim = 2.21e+06, Exp = 2.15e+05, Rel Error = 930.58%
  id_1wsx: Sim = 9.79e+05, Exp = 4.56e+05, Rel Error = 114.86%

Time 90:
  id_8n7o: Sim = 8.79e+05, Exp = 9.35e+05, Rel Error = 5.98%
  id_caoz: Sim = 1.34e+05, Exp = 5.36e+05, Rel Error = 74.98%
  id_ty7g: Sim = 3.23e+06, Exp = 1.90e+06, Rel Error = 70.06%
  id_1wsx: Sim = 7.56e+05, Exp = 1.63e+06, Rel Error = 53.61%

Time 120:
  id_8n7o: Sim = 4.92e+05, Exp = 3.16e+05, Rel Error = 55.94%
  id_caoz: Sim = 7.51e+04, Exp = 8.60e+04, Rel Error = 12.67%
  id_ty7g: Sim = 3.92e+06, Exp = 3.76e+06, Rel Error = 4.46%
  id_1wsx: Sim = 5.09e+05, Exp = 8.42e+05, Rel Error = 39.55%

Time 150:
  id_8n7o: Sim = 2.76e+05, Exp = 2.18e+05, Rel Error = 26.80%
  id_caoz: Sim = 4.21e+04, Exp = 1.57e+04, Rel Error = 168.74%
  id_ty7g: Sim = 4.36e+06, Exp = 4.50e+06, Rel Error = 2.95%
  id_1wsx: Sim = 3.20e+05, Exp = 2.73e+05, Rel Error = 17.57%

Time 180:
  id_8n7o: Sim = 1.55e+05, Exp = 1.95e+05, Rel Error = 20.66%
  id_caoz: Sim = 2.35e+04, Exp = 3.80e+03, Rel Error = 520.50%
  id_ty7g: Sim = 4.63e+06, Exp = 4.72e+06, Rel Error = 1.98%
  id_1wsx: Sim = 1.94e+05, Exp = 8.01e+04, Rel Error = 142.60%

Comparison of optimized Model 7 simulation vs. experimental data for the third experiment:

Time 0:
  id_8n7o: Sim = 1.50e+07, Exp = 1.50e+07, Rel Error = 0.00%
  id_caoz: Sim = 5.00e+02, Exp = 5.00e+02, Rel Error = 0.00%
  id_ty7g: Sim = 5.00e+00, Exp = 5.00e+00, Rel Error = 0.00%
  id_1wsx: Sim = 5.00e+01, Exp = 5.00e+01, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 8.40e+06, Exp = 9.64e+05, Rel Error = 771.27%
  id_caoz: Sim = 1.25e+06, Exp = 5.64e+06, Rel Error = 77.79%
  id_ty7g: Sim = 2.78e+06, Exp = 1.77e+06, Rel Error = 57.23%
  id_1wsx: Sim = 2.57e+06, Exp = 6.63e+06, Rel Error = 61.24%

Time 60:
  id_8n7o: Sim = 4.71e+06, Exp = 3.26e+03, Rel Error = 144257.04%
  id_caoz: Sim = 7.18e+05, Exp = 1.14e+05, Rel Error = 531.59%
  id_ty7g: Sim = 6.64e+06, Exp = 1.10e+07, Rel Error = 39.84%
  id_1wsx: Sim = 2.94e+06, Exp = 3.85e+06, Rel Error = 23.65%

Time 90:
  id_8n7o: Sim = 2.64e+06, Exp = 8.16e+02, Rel Error = 322917.26%
  id_caoz: Sim = 4.02e+05, Exp = 1.94e+03, Rel Error = 20636.78%
  id_ty7g: Sim = 9.69e+06, Exp = 1.40e+07, Rel Error = 30.99%
  id_1wsx: Sim = 2.27e+06, Exp = 9.51e+05, Rel Error = 138.45%

Time 120:
  id_8n7o: Sim = 1.48e+06, Exp = 5.88e+02, Rel Error = 251083.87%
  id_caoz: Sim = 2.25e+05, Exp = 6.05e+01, Rel Error = 372507.90%
  id_ty7g: Sim = 1.18e+07, Exp = 1.48e+07, Rel Error = 20.32%
  id_1wsx: Sim = 1.53e+06, Exp = 2.26e+05, Rel Error = 575.79%

Time 150:
  id_8n7o: Sim = 8.28e+05, Exp = 5.44e+02, Rel Error = 152106.96%
  id_caoz: Sim = 1.26e+05, Exp = 7.43e+00, Rel Error = 1698045.82%
  id_ty7g: Sim = 1.31e+07, Exp = 1.49e+07, Rel Error = 12.45%
  id_1wsx: Sim = 9.61e+05, Exp = 5.36e+04, Rel Error = 1693.86%

Time 180:
  id_8n7o: Sim = 4.64e+05, Exp = 5.34e+02, Rel Error = 86756.10%
  id_caoz: Sim = 7.07e+04, Exp = 1.61e+00, Rel Error = 4381872.68%
  id_ty7g: Sim = 1.39e+07, Exp = 1.50e+07, Rel Error = 7.37%
  id_1wsx: Sim = 5.83e+05, Exp = 1.27e+04, Rel Error = 4488.10%

Comparison of original Model 7 and optimized Model 7:
Original Model 7 error: 1.3309402882832346
Optimized Model 7 error: 0.6904687280474515

Created SBML model with optimized Model 7 reactions:
1. id_8n7o -> id_caoz (k1 = 0.019317)
2. id_caoz -> id_ty7g (k2 = 0.044277)
3. id_caoz -> id_1wsx (k3 = 0.101668)
4. id_1wsx -> id_ty7g (k4 = 0.029516)

## 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_8, iteration_10)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml, final_sbml_refined, final_sbml_model6, final_sbml_model7, final_sbml_best, final_sbml_optimized)

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


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



# Iteration 15
## Thoughts
The optimization has significantly improved the fit of Model 7, reducing the error from 1.33 to 0.69. The optimized rate constants are:

1. `id_8n7o -> id_caoz` (k1 = 0.019317)
2. `id_caoz -> id_ty7g` (k2 = 0.044277)
3. `id_caoz -> id_1wsx` (k3 = 0.101668)
4. `id_1wsx -> id_ty7g` (k4 = 0.029516)

While the fit has improved, there are still some significant discrepancies between the simulated and experimental data, particularly:

1. For the first experiment:
   - `id_8n7o` decreases too slowly in the simulation at later time points
   - `id_ty7g` increases too quickly in the simulation at early time points

2. For the third experiment:
   - `id_8n7o` decreases much too slowly in the simulation
   - `id_caoz` doesn't reach as high a peak in the simulation as in the experimental data

Let me try one more experiment with different initial conditions to further validate our model. I'll set the initial concentration of `id_8n7o` to a very low value and see how the system behaves.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration", 
    "meta_data": {
        "id_8n7o": 100000,
        "id_caoz": 5000,
        "id_ty7g": 100,
        "id_1wsx": 500
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_15
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_15]

Total size: 184 rows × 6 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_15] for the full data

Time   id_8n7o  id_caoz  id_ty7g  id_1wsx  id_250q
0  1.00e+05 5.00e+03 1.00e+02 5.00e+02 1.11e+07
...
3.00e+00  1.00e+05 3.32e+03 2.93e+02 2.03e+03 1.11e+07
...
6.00e+00  9.99e+04 2.22e+03 6.50e+02 2.82e+03 1.11e+07
...
9.00e+00  9.99e+04 1.49e+03 1.08e+03 3.16e+03 1.11e+07
...
1.20e+01  9.98e+04 1.00e+03 1.55e+03 3.21e+03 1.11e+07
...
1.50e+01  9.98e+04 6.83e+02 2.00e+03 3.11e+03 1.11e+07
...
1.80e+01  9.98e+04 4.69e+02 2.44e+03 2.91e+03 1.11e+07
...
2.10e+01  9.98e+04 3.26e+02 2.84e+03 2.67e+03 1.11e+07
...
2.40e+01  9.97e+04 2.30e+02 3.20e+03 2.42e+03 1.11e+07
...
2.70e+01  9.97e+04 1.65e+02 3.54e+03 2.17e+03 1.11e+07
...
3.00e+01  9.97e+04 1.20e+02 3.83e+03 1.94e+03 1.11e+07
...
3.30e+01  9.97e+04 8.94e+01 4.09e+03 1.72e+03 1.11e+07
...
3.60e+01  9.97e+04 6.79e+01 4.33e+03 1.52e+03 1.11e+07
...
3.90e+01  9.97e+04 5.26e+01 4.53e+03 1.34e+03 1.11e+07
...
4.20e+01  9.97e+04 4.15e+01 4.71e+03 1.18e+03 1.11e+07
...
4.50e+01  9.97e+04 3.34e+01 4.87e+03 1.03e+03 1.11e+07
...
4.80e+01  9.97e+04 2.73e+01 5.01e+03 9.06e+02 1.11e+07
...
5.10e+01  9.96e+04 2.26e+01 5.13e+03 7.94e+02 1.11e+07
...
5.40e+01  9.96e+04 1.89e+01 5.24e+03 6.96e+02 1.11e+07
...
5.70e+01  9.96e+04 1.60e+01 5.33e+03 6.09e+02 1.11e+07
...
6.00e+01  9.96e+04 1.36e+01 5.42e+03 5.33e+02 1.11e+07
...
6.30e+01  9.96e+04 1.17e+01 5.49e+03 4.67e+02 1.11e+07
...
6.60e+01  9.96e+04 1.01e+01 5.55e+03 4.08e+02 1.11e+07
...
6.90e+01  9.96e+04 8.69e+00 5.61e+03 3.57e+02 1.11e+07
...
7.20e+01  9.96e+04 7.54e+00 5.65e+03 3.13e+02 1.11e+07
...
7.50e+01  9.96e+04 6.55e+00 5.70e+03 2.73e+02 1.11e+07
...
7.80e+01  9.96e+04 5.70e+00 5.73e+03 2.39e+02 1.11e+07
...
8.10e+01  9.96e+04 4.96e+00 5.77e+03 2.09e+02 1.11e+07
...
8.40e+01  9.96e+04 4.33e+00 5.79e+03 1.83e+02 1.11e+07
...
8.70e+01  9.96e+04 3.77e+00 5.82e+03 1.60e+02 1.11e+07
...
9.00e+01  9.96e+04 3.30e+00 5.84e+03 1.40e+02 1.11e+07
...
9.30e+01  9.96e+04 2.88e+00 5.86e+03 1.22e+02 1.11e+07
...
9.60e+01  9.96e+04 2.51e+00 5.88e+03 1.07e+02 1.11e+07
...
9.90e+01  9.96e+04 2.20e+00 5.89e+03 9.35e+01 1.11e+07
...
1.02e+02  9.96e+04 1.92e+00 5.90e+03 8.18e+01 1.11e+07
...
1.05e+02  9.96e+04 1.68e+00 5.91e+03 7.15e+01 1.11e+07
...
1.08e+02  9.96e+04 1.47e+00 5.92e+03 6.25e+01 1.11e+07
...
1.11e+02  9.96e+04 1.28e+00 5.93e+03 5.47e+01 1.11e+07
...
1.14e+02  9.96e+04 1.12e+00 5.94e+03 4.78e+01 1.11e+07
...
1.17e+02  9.96e+04 9.81e-01 5.95e+03 4.18e+01 1.11e+07
...
1.20e+02  9.96e+04 8.57e-01 5.95e+03 3.66e+01 1.11e+07
...
1.23e+02  9.96e+04 7.50e-01 5.96e+03 3.20e+01 1.11e+07
...
1.26e+02  9.96e+04 6.56e-01 5.96e+03 2.80e+01 1.11e+07
...
1.29e+02  9.96e+04 5.73e-01 5.96e+03 2.45e+01 1.11e+07
...
1.32e+02  9.96e+04 5.01e-01 5.97e+03 2.14e+01 1.11e+07
...
1.35e+02  9.96e+04 4.38e-01 5.97e+03 1.87e+01 1.11e+07
...
1.38e+02  9.96e+04 3.83e-01 5.97e+03 1.64e+01 1.11e+07
...
1.41e+02  9.96e+04 3.35e-01 5.97e+03 1.43e+01 1.11e+07
...
1.44e+02  9.96e+04 2.93e-01 5.98e+03 1.25e+01 1.11e+07
...
1.83e+02  9.96e+04 5.12e-02 5.99e+03 2.19e+00 1.11e+07

## 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_8, iteration_10, iteration_15)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml, final_sbml_refined, final_sbml_model6, final_sbml_model7, final_sbml_best, final_sbml_optimized)

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


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



# Iteration 16
## Thoughts
The new experiment with very low initial concentrations shows some interesting behavior:

1. `id_8n7o` remains almost constant at ~100,000 throughout the experiment
2. `id_caoz` starts at 5,000 and decreases steadily to near zero
3. `id_ty7g` starts at 100 and increases to ~6,000
4. `id_1wsx` starts at 500, increases to ~3,200 at around t=12, then decreases

This behavior is quite different from the previous experiments where `id_8n7o` decreased significantly. Let me test our optimized Model 7 against this new data to see how well it performs.

## Action

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

# Access the experimental data
exp_data_4 = experiment_history["iteration_15"]

# Define the Model 7 ODE function (sequential conversion model)
def model_ode7(t, y, k1, k2, k3, k4):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o -> id_caoz
    r1 = k1 * y[0]
    
    # Reaction 2: id_caoz -> id_ty7g
    r2 = k2 * y[1]
    
    # Reaction 3: id_caoz -> id_1wsx
    r3 = k3 * y[1]
    
    # Reaction 4: id_1wsx -> id_ty7g
    r4 = k4 * y[3]
    
    # ODEs
    dy_dt = [
        -r1,            # d[id_8n7o]/dt
        r1 - r2 - r3,   # d[id_caoz]/dt
        r2 + r4,        # d[id_ty7g]/dt
        r3 - r4         # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Get the optimized parameters from the previous iteration
optimized_params = [0.019317, 0.044277, 0.101668, 0.029516]

# Initial conditions for the fourth experiment
y0_exp4 = [100000, 5000, 100, 500]
t_eval_4 = exp_data_4['Time'].values

# Simulate with the optimized parameters for the fourth experiment
sol4 = solve_ivp(
    lambda t, y: model_ode7(t, y, *optimized_params),
    (0, 183),
    y0_exp4,
    method='LSODA',
    t_eval=t_eval_4
)

sim_data4 = pd.DataFrame({
    'Time': sol4.t,
    'id_8n7o': sol4.y[0],
    'id_caoz': sol4.y[1],
    'id_ty7g': sol4.y[2],
    'id_1wsx': sol4.y[3]
})

# Calculate error (mean squared error)
error4 = 0
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    max_val = max(max(exp_data_4[species]), max(sim_data4[species]))
    if max_val > 0:
        error4 += np.mean(((exp_data_4[species] - sim_data4[species]) / max_val) ** 2)

print(f"Error for optimized Model 7 on the fourth experiment: {error4}")

# Compare the simulation with experimental data
selected_times = [0, 30, 60, 90, 120, 150, 180]
print("\nComparison of optimized Model 7 simulation vs. experimental data for the fourth experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data4['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data4.loc[idx, species]
        exp_val = exp_data_4[exp_data_4['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Let's try a different model that might better explain the behavior in the fourth experiment
# Model 10: id_8n7o + id_caoz -> id_ty7g + id_1wsx, id_caoz -> id_ty7g, id_1wsx -> id_ty7g
def model_ode10(t, y, k1, k2, k3):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    r1 = k1 * y[0] * y[1]
    
    # Reaction 2: id_caoz -> id_ty7g
    r2 = k2 * y[1]
    
    # Reaction 3: id_1wsx -> id_ty7g
    r3 = k3 * y[3]
    
    # ODEs
    dy_dt = [
        -r1,            # d[id_8n7o]/dt
        -r1 - r2,       # d[id_caoz]/dt
        r1 + r2 + r3,   # d[id_ty7g]/dt
        r1 - r3         # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Let's optimize the parameters for Model 10 using all four experiments
def objective_function(params):
    k1, k2, k3 = 10**params[0], 10**params[1], 10**params[2]  # Log-scale parameters
    
    # Simulate for the first experiment
    y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
    t_eval_1 = experiment_history["iteration_0"]['Time'].values
    
    try:
        sol1 = solve_ivp(
            lambda t, y: model_ode10(t, y, k1, k2, k3),
            (0, 183),
            y0_exp1,
            method='LSODA',
            t_eval=t_eval_1
        )
        
        sim_data1 = pd.DataFrame({
            'Time': sol1.t,
            'id_8n7o': sol1.y[0],
            'id_caoz': sol1.y[1],
            'id_ty7g': sol1.y[2],
            'id_1wsx': sol1.y[3]
        })
        
        error1 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(experiment_history["iteration_0"][species]), max(sim_data1[species]))
            if max_val > 0:
                error1 += np.mean(((experiment_history["iteration_0"][species] - sim_data1[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the second experiment
    y0_exp2 = [5000000, 1000, 10, 100]
    t_eval_2 = experiment_history["iteration_8"]['Time'].values
    
    try:
        sol2 = solve_ivp(
            lambda t, y: model_ode10(t, y, k1, k2, k3),
            (0, 183),
            y0_exp2,
            method='LSODA',
            t_eval=t_eval_2
        )
        
        sim_data2 = pd.DataFrame({
            'Time': sol2.t,
            'id_8n7o': sol2.y[0],
            'id_caoz': sol2.y[1],
            'id_ty7g': sol2.y[2],
            'id_1wsx': sol2.y[3]
        })
        
        error2 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(experiment_history["iteration_8"][species]), max(sim_data2[species]))
            if max_val > 0:
                error2 += np.mean(((experiment_history["iteration_8"][species] - sim_data2[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the third experiment
    y0_exp3 = [15000000, 500, 5, 50]
    t_eval_3 = experiment_history["iteration_10"]['Time'].values
    
    try:
        sol3 = solve_ivp(
            lambda t, y: model_ode10(t, y, k1, k2, k3),
            (0, 183),
            y0_exp3,
            method='LSODA',
            t_eval=t_eval_3
        )
        
        sim_data3 = pd.DataFrame({
            'Time': sol3.t,
            'id_8n7o': sol3.y[0],
            'id_caoz': sol3.y[1],
            'id_ty7g': sol3.y[2],
            'id_1wsx': sol3.y[3]
        })
        
        error3 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(experiment_history["iteration_10"][species]), max(sim_data3[species]))
            if max_val > 0:
                error3 += np.mean(((experiment_history["iteration_10"][species] - sim_data3[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the fourth experiment
    y0_exp4 = [100000, 5000, 100, 500]
    t_eval_4 = experiment_history["iteration_15"]['Time'].values
    
    try:
        sol4 = solve_ivp(
            lambda t, y: model_ode10(t, y, k1, k2, k3),
            (0, 183),
            y0_exp4,
            method='LSODA',
            t_eval=t_eval_4
        )
        
        sim_data4 = pd.DataFrame({
            'Time': sol4.t,
            'id_8n7o': sol4.y[0],
            'id_caoz': sol4.y[1],
            'id_ty7g': sol4.y[2],
            'id_1wsx': sol4.y[3]
        })
        
        error4 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(experiment_history["iteration_15"][species]), max(sim_data4[species]))
            if max_val > 0:
                error4 += np.mean(((experiment_history["iteration_15"][species] - sim_data4[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Return the total error
    return error1 + error2 + error3 + error4

# Initial guess for the parameters (log scale)
initial_guess = np.log10([1e-7, 0.1, 0.01])  # Reasonable starting values

# Bounds for the parameters (log scale)
bounds = [(-10, -5), (-2, 0), (-3, -1)]

# Run the optimization
from scipy.optimize import minimize
result = minimize(objective_function, initial_guess, method='L-BFGS-B', bounds=bounds)

# Get the optimized parameters
optimized_params_10 = 10**result.x

print(f"\nOptimized parameters for Model 10: k1 = {optimized_params_10[0]:.10f}, k2 = {optimized_params_10[1]:.6f}, k3 = {optimized_params_10[2]:.6f}")
print(f"Optimized error for Model 10: {result.fun}")

# Simulate with the optimized parameters for all four experiments
# Fourth experiment
y0_exp4 = [100000, 5000, 100, 500]
t_eval_4 = exp_data_4['Time'].values

sol4_10 = solve_ivp(
    lambda t, y: model_ode10(t, y, *optimized_params_10),
    (0, 183),
    y0_exp4,
    method='LSODA',
    t_eval=t_eval_4
)

sim_data4_10 = pd.DataFrame({
    'Time': sol4_10.t,
    'id_8n7o': sol4_10.y[0],
    'id_caoz': sol4_10.y[1],
    'id_ty7g': sol4_10.y[2],
    'id_1wsx': sol4_10.y[3]
})

# Calculate error for Model 10 on the fourth experiment
error4_10 = 0
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    max_val = max(max(exp_data_4[species]), max(sim_data4_10[species]))
    if max_val > 0:
        error4_10 += np.mean(((exp_data_4[species] - sim_data4_10[species]) / max_val) ** 2)

print(f"\nError for optimized Model 10 on the fourth experiment: {error4_10}")

# Compare the simulation with experimental data
print("\nComparison of optimized Model 10 simulation vs. experimental data for the fourth experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data4_10['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data4_10.loc[idx, species]
        exp_val = exp_data_4[exp_data_4['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Compare the errors of Model 7 and Model 10 on the fourth experiment
print("\nComparison of Model 7 and Model 10 on the fourth experiment:")
print(f"Model 7 error: {error4}")
print(f"Model 10 error: {error4_10}")

# Create the final SBML model with the best model's reactions and parameters
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

if error4 <= error4_10:
    print("\nModel 7 is the better fit for the fourth experiment.")
    final_model = 7
    final_params = optimized_params
else:
    print("\nModel 10 is the better fit for the fourth experiment.")
    final_model = 10
    final_params = optimized_params_10

if final_model == 7:
    # Add the first reaction: id_8n7o -> id_caoz
    reaction1 = model.createReaction()
    reaction1.setId("reaction1")
    reaction1.setReversible(False)

    # Add reactants
    reactant1 = reaction1.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction1.createProduct()
    product1.setSpecies("id_caoz")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law1 = reaction1.createKineticLaw()
    kinetic_law1.setFormula("k1 * id_8n7o")

    # Add parameter k1
    parameter1 = kinetic_law1.createParameter()
    parameter1.setId("k1")
    parameter1.setValue(final_params[0])

    # Add the second reaction: id_caoz -> id_ty7g
    reaction2 = model.createReaction()
    reaction2.setId("reaction2")
    reaction2.setReversible(False)

    # Add reactants
    reactant1 = reaction2.createReactant()
    reactant1.setSpecies("id_caoz")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction2.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law2 = reaction2.createKineticLaw()
    kinetic_law2.setFormula("k2 * id_caoz")

    # Add parameter k2
    parameter2 = kinetic_law2.createParameter()
    parameter2.setId("k2")
    parameter2.setValue(final_params[1])

    # Add the third reaction: id_caoz -> id_1wsx
    reaction3 = model.createReaction()
    reaction3.setId("reaction3")
    reaction3.setReversible(False)

    # Add reactants
    reactant1 = reaction3.createReactant()
    reactant1.setSpecies("id_caoz")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction3.createProduct()
    product1.setSpecies("id_1wsx")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law3 = reaction3.createKineticLaw()
    kinetic_law3.setFormula("k3 * id_caoz")

    # Add parameter k3
    parameter3 = kinetic_law3.createParameter()
    parameter3.setId("k3")
    parameter3.setValue(final_params[2])

    # Add the fourth reaction: id_1wsx -> id_ty7g
    reaction4 = model.createReaction()
    reaction4.setId("reaction4")
    reaction4.setReversible(False)

    # Add reactants
    reactant1 = reaction4.createReactant()
    reactant1.setSpecies("id_1wsx")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction4.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law4 = reaction4.createKineticLaw()
    kinetic_law4.setFormula("k4 * id_1wsx")

    # Add parameter k4
    parameter4 = kinetic_law4.createParameter()
    parameter4.setId("k4")
    parameter4.setValue(final_params[3])

    print("\nCreated SBML model with Model 7 reactions:")
    print(f"1. id_8n7o -> id_caoz (k1 = {final_params[0]:.6f})")
    print(f"2. id_caoz -> id_ty7g (k2 = {final_params[1]:.6f})")
    print(f"3. id_caoz -> id_1wsx (k3 = {final_params[2]:.6f})")
    print(f"4. id_1wsx -> id_ty7g (k4 = {final_params[3]:.6f})")

else:  # final_model == 10
    # Add the first reaction: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    reaction1 = model.createReaction()
    reaction1.setId("reaction1")
    reaction1.setReversible(False)

    # Add reactants
    reactant1 = reaction1.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

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

    # Add products
    product1 = reaction1.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    product2 = reaction1.createProduct()
    product2.setSpecies("id_1wsx")
    product2.setStoichiometry(1.0)
    product2.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law1 = reaction1.createKineticLaw()
    kinetic_law1.setFormula("k1 * id_8n7o * id_caoz")

    # Add parameter k1
    parameter1 = kinetic_law1.createParameter()
    parameter1.setId("k1")
    parameter1.setValue(final_params[0])

    # Add the second reaction: id_caoz -> id_ty7g
    reaction2 = model.createReaction()
    reaction2.setId("reaction2")
    reaction2.setReversible(False)

    # Add reactants
    reactant1 = reaction2.createReactant()
    reactant1.setSpecies("id_caoz")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction2.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law2 = reaction2.createKineticLaw()
    kinetic_law2.setFormula("k2 * id_caoz")

    # Add parameter k2
    parameter2 = kinetic_law2.createParameter()
    parameter2.setId("k2")
    parameter2.setValue(final_params[1])

    # Add the third reaction: id_1wsx -> id_ty7g
    reaction3 = model.createReaction()
    reaction3.setId("reaction3")
    reaction3.setReversible(False)

    # Add reactants
    reactant1 = reaction3.createReactant()
    reactant1.setSpecies("id_1wsx")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction3.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law3 = reaction3.createKineticLaw()
    kinetic_law3.setFormula("k3 * id_1wsx")

    # Add parameter k3
    parameter3 = kinetic_law3.createParameter()
    parameter3.setId("k3")
    parameter3.setValue(final_params[2])

    print("\nCreated SBML model with Model 10 reactions:")
    print(f"1. id_8n7o + id_caoz -> id_ty7g + id_1wsx (k1 = {final_params[0]:.10f})")
    print(f"2. id_caoz -> id_ty7g (k2 = {final_params[1]:.6f})")
    print(f"3. id_1wsx -> id_ty7g (k3 = {final_params[2]:.6f})")

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

# Store the final SBML model
shared_variables.add('final_sbml_final', final_sbml)
```
# Observation

## Code Stdout
Error for optimized Model 7 on the fourth experiment: 1.5937661565518517

Comparison of optimized Model 7 simulation vs. experimental data for the fourth experiment:

Time 0:
  id_8n7o: Sim = 1.00e+05, Exp = 1.00e+05, Rel Error = 0.00%
  id_caoz: Sim = 5.00e+03, Exp = 5.00e+03, Rel Error = 0.00%
  id_ty7g: Sim = 1.00e+02, Exp = 1.00e+02, Rel Error = 0.00%
  id_1wsx: Sim = 5.00e+02, Exp = 5.00e+02, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 5.60e+04, Exp = 9.97e+04, Rel Error = 43.82%
  id_caoz: Sim = 8.42e+03, Exp = 1.20e+02, Rel Error = 6904.74%
  id_ty7g: Sim = 2.21e+04, Exp = 3.83e+03, Rel Error = 476.55%
  id_1wsx: Sim = 1.91e+04, Exp = 1.94e+03, Rel Error = 885.08%

Time 60:
  id_8n7o: Sim = 3.14e+04, Exp = 9.96e+04, Rel Error = 68.51%
  id_caoz: Sim = 4.78e+03, Exp = 1.36e+01, Rel Error = 35011.19%
  id_ty7g: Sim = 4.90e+04, Exp = 5.42e+03, Rel Error = 805.32%
  id_1wsx: Sim = 2.04e+04, Exp = 5.33e+02, Rel Error = 3724.94%

Time 90:
  id_8n7o: Sim = 1.76e+04, Exp = 9.96e+04, Rel Error = 82.35%
  id_caoz: Sim = 2.68e+03, Exp = 3.30e+00, Rel Error = 81280.48%
  id_ty7g: Sim = 6.99e+04, Exp = 5.84e+03, Rel Error = 1096.59%
  id_1wsx: Sim = 1.55e+04, Exp = 1.40e+02, Rel Error = 10953.90%

Time 120:
  id_8n7o: Sim = 9.84e+03, Exp = 9.96e+04, Rel Error = 90.12%
  id_caoz: Sim = 1.50e+03, Exp = 8.57e-01, Rel Error = 174922.31%
  id_ty7g: Sim = 8.39e+04, Exp = 5.95e+03, Rel Error = 1310.52%
  id_1wsx: Sim = 1.03e+04, Exp = 3.66e+01, Rel Error = 28130.75%

Time 150:
  id_8n7o: Sim = 5.52e+03, Exp = 9.96e+04, Rel Error = 94.46%
  id_caoz: Sim = 8.41e+02, Exp = 2.24e-01, Rel Error = 375280.22%
  id_ty7g: Sim = 9.28e+04, Exp = 5.98e+03, Rel Error = 1451.47%
  id_1wsx: Sim = 6.47e+03, Exp = 9.56e+00, Rel Error = 67547.85%

Time 180:
  id_8n7o: Sim = 3.09e+03, Exp = 9.96e+04, Rel Error = 96.90%
  id_caoz: Sim = 4.71e+02, Exp = 5.86e-02, Rel Error = 804342.04%
  id_ty7g: Sim = 9.81e+04, Exp = 5.99e+03, Rel Error = 1538.94%
  id_1wsx: Sim = 3.91e+03, Exp = 2.50e+00, Rel Error = 156267.96%

Optimized parameters for Model 10: k1 = 0.0000003152, k2 = 0.073928, k3 = 0.015099
Optimized error for Model 10: 4.618983371813609

Error for optimized Model 10 on the fourth experiment: 0.06572040226433988

Comparison of optimized Model 10 simulation vs. experimental data for the fourth experiment:

Time 0:
  id_8n7o: Sim = 1.00e+05, Exp = 1.00e+05, Rel Error = 0.00%
  id_caoz: Sim = 5.00e+03, Exp = 5.00e+03, Rel Error = 0.00%
  id_ty7g: Sim = 1.00e+02, Exp = 1.00e+02, Rel Error = 0.00%
  id_1wsx: Sim = 5.00e+02, Exp = 5.00e+02, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 9.86e+04, Exp = 9.97e+04, Rel Error = 1.14%
  id_caoz: Sim = 2.13e+02, Exp = 1.20e+02, Rel Error = 77.64%
  id_ty7g: Sim = 5.46e+03, Exp = 3.83e+03, Rel Error = 42.59%
  id_1wsx: Sim = 1.35e+03, Exp = 1.94e+03, Rel Error = 30.43%

Time 60:
  id_8n7o: Sim = 9.85e+04, Exp = 9.96e+04, Rel Error = 1.12%
  id_caoz: Sim = 9.17e+00, Exp = 1.36e+01, Rel Error = 32.71%
  id_ty7g: Sim = 6.17e+03, Exp = 5.42e+03, Rel Error = 14.00%
  id_1wsx: Sim = 9.00e+02, Exp = 5.33e+02, Rel Error = 68.77%

Time 90:
  id_8n7o: Sim = 9.85e+04, Exp = 9.96e+04, Rel Error = 1.11%
  id_caoz: Sim = 3.94e-01, Exp = 3.30e+00, Rel Error = 88.05%
  id_ty7g: Sim = 6.51e+03, Exp = 5.84e+03, Rel Error = 11.51%
  id_1wsx: Sim = 5.74e+02, Exp = 1.40e+02, Rel Error = 310.54%

Time 120:
  id_8n7o: Sim = 9.85e+04, Exp = 9.96e+04, Rel Error = 1.10%
  id_caoz: Sim = 1.69e-02, Exp = 8.57e-01, Rel Error = 98.03%
  id_ty7g: Sim = 6.72e+03, Exp = 5.95e+03, Rel Error = 12.95%
  id_1wsx: Sim = 3.65e+02, Exp = 3.66e+01, Rel Error = 898.34%

Time 150:
  id_8n7o: Sim = 9.85e+04, Exp = 9.96e+04, Rel Error = 1.10%
  id_caoz: Sim = 7.27e-04, Exp = 2.24e-01, Rel Error = 99.68%
  id_ty7g: Sim = 6.85e+03, Exp = 5.98e+03, Rel Error = 14.63%
  id_1wsx: Sim = 2.32e+02, Exp = 9.56e+00, Rel Error = 2327.62%

Time 180:
  id_8n7o: Sim = 9.85e+04, Exp = 9.96e+04, Rel Error = 1.10%
  id_caoz: Sim = 3.13e-05, Exp = 5.86e-02, Rel Error = 99.95%
  id_ty7g: Sim = 6.94e+03, Exp = 5.99e+03, Rel Error = 15.90%
  id_1wsx: Sim = 1.48e+02, Exp = 2.50e+00, Rel Error = 5803.14%

Comparison of Model 7 and Model 10 on the fourth experiment:
Model 7 error: 1.5937661565518517
Model 10 error: 0.06572040226433988

Model 10 is the better fit for the fourth experiment.

Created SBML model with Model 10 reactions:
1. id_8n7o + id_caoz -> id_ty7g + id_1wsx (k1 = 0.0000003152)
2. id_caoz -> id_ty7g (k2 = 0.073928)
3. id_1wsx -> id_ty7g (k3 = 0.015099)

## 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_8, iteration_10, iteration_15)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml, final_sbml_refined, final_sbml_model6, final_sbml_model7, final_sbml_best, final_sbml_optimized, final_sbml_final)

### 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
Interestingly, Model 10 performs much better than Model 7 on the fourth experiment, with an error of 0.066 compared to 1.59. However, when considering all four experiments together, Model 10 has a higher total error (4.62) than Model 7 had on the first three experiments (0.69).

The reactions in Model 10 are:
1. `id_8n7o + id_caoz -> id_ty7g + id_1wsx` (k1 = 0.0000003152)
2. `id_caoz -> id_ty7g` (k2 = 0.073928)
3. `id_1wsx -> id_ty7g` (k3 = 0.015099)

The key difference between Model 7 and Model 10 is that Model 10 includes a second-order reaction between `id_8n7o` and `id_caoz`, while Model 7 has a first-order conversion from `id_8n7o` to `id_caoz`. This second-order reaction seems to better explain the behavior in the fourth experiment, where `id_8n7o` remains almost constant.

Let me try one more model that combines elements of both Model 7 and Model 10, to see if we can get a better fit across all experiments:

Model 11:
1. `id_8n7o -> id_caoz` (from Model 7)
2. `id_8n7o + id_caoz -> id_ty7g + id_1wsx` (from Model 10)
3. `id_caoz -> id_ty7g` (common to both models)
4. `id_1wsx -> id_ty7g` (common to both models)

Let me implement and test this combined model.

## Action

### Code
```python
import numpy as np
import pandas as pd
import libsbml
from scipy.integrate import solve_ivp
from scipy.optimize import minimize

# Access the experimental data
exp_data_1 = experiment_history["iteration_0"]
exp_data_2 = experiment_history["iteration_8"]
exp_data_3 = experiment_history["iteration_10"]
exp_data_4 = experiment_history["iteration_15"]

# Define the Model 11 ODE function (combined model)
def model_ode11(t, y, k1, k2, k3, k4, k5):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o -> id_caoz
    r1 = k1 * y[0]
    
    # Reaction 2: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    r2 = k2 * y[0] * y[1]
    
    # Reaction 3: id_caoz -> id_ty7g
    r3 = k3 * y[1]
    
    # Reaction 4: id_caoz -> id_1wsx
    r4 = k4 * y[1]
    
    # Reaction 5: id_1wsx -> id_ty7g
    r5 = k5 * y[3]
    
    # ODEs
    dy_dt = [
        -r1 - r2,            # d[id_8n7o]/dt
        r1 - r2 - r3 - r4,   # d[id_caoz]/dt
        r2 + r3 + r5,        # d[id_ty7g]/dt
        r2 + r4 - r5         # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Define the objective function for optimization
def objective_function(params):
    k1, k2, k3, k4, k5 = 10**params[0], 10**params[1], 10**params[2], 10**params[3], 10**params[4]  # Log-scale parameters
    
    # Simulate for the first experiment
    y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
    t_eval_1 = exp_data_1['Time'].values
    
    try:
        sol1 = solve_ivp(
            lambda t, y: model_ode11(t, y, k1, k2, k3, k4, k5),
            (0, 183),
            y0_exp1,
            method='LSODA',
            t_eval=t_eval_1
        )
        
        sim_data1 = pd.DataFrame({
            'Time': sol1.t,
            'id_8n7o': sol1.y[0],
            'id_caoz': sol1.y[1],
            'id_ty7g': sol1.y[2],
            'id_1wsx': sol1.y[3]
        })
        
        error1 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_1[species]), max(sim_data1[species]))
            if max_val > 0:
                error1 += np.mean(((exp_data_1[species] - sim_data1[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the second experiment
    y0_exp2 = [5000000, 1000, 10, 100]
    t_eval_2 = exp_data_2['Time'].values
    
    try:
        sol2 = solve_ivp(
            lambda t, y: model_ode11(t, y, k1, k2, k3, k4, k5),
            (0, 183),
            y0_exp2,
            method='LSODA',
            t_eval=t_eval_2
        )
        
        sim_data2 = pd.DataFrame({
            'Time': sol2.t,
            'id_8n7o': sol2.y[0],
            'id_caoz': sol2.y[1],
            'id_ty7g': sol2.y[2],
            'id_1wsx': sol2.y[3]
        })
        
        error2 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_2[species]), max(sim_data2[species]))
            if max_val > 0:
                error2 += np.mean(((exp_data_2[species] - sim_data2[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the third experiment
    y0_exp3 = [15000000, 500, 5, 50]
    t_eval_3 = exp_data_3['Time'].values
    
    try:
        sol3 = solve_ivp(
            lambda t, y: model_ode11(t, y, k1, k2, k3, k4, k5),
            (0, 183),
            y0_exp3,
            method='LSODA',
            t_eval=t_eval_3
        )
        
        sim_data3 = pd.DataFrame({
            'Time': sol3.t,
            'id_8n7o': sol3.y[0],
            'id_caoz': sol3.y[1],
            'id_ty7g': sol3.y[2],
            'id_1wsx': sol3.y[3]
        })
        
        error3 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_3[species]), max(sim_data3[species]))
            if max_val > 0:
                error3 += np.mean(((exp_data_3[species] - sim_data3[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Simulate for the fourth experiment
    y0_exp4 = [100000, 5000, 100, 500]
    t_eval_4 = exp_data_4['Time'].values
    
    try:
        sol4 = solve_ivp(
            lambda t, y: model_ode11(t, y, k1, k2, k3, k4, k5),
            (0, 183),
            y0_exp4,
            method='LSODA',
            t_eval=t_eval_4
        )
        
        sim_data4 = pd.DataFrame({
            'Time': sol4.t,
            'id_8n7o': sol4.y[0],
            'id_caoz': sol4.y[1],
            'id_ty7g': sol4.y[2],
            'id_1wsx': sol4.y[3]
        })
        
        error4 = 0
        for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
            max_val = max(max(exp_data_4[species]), max(sim_data4[species]))
            if max_val > 0:
                error4 += np.mean(((exp_data_4[species] - sim_data4[species]) / max_val) ** 2)
    except:
        return 1e10  # Return a large error if the solver fails
    
    # Return the total error
    return error1 + error2 + error3 + error4

# Initial guess for the parameters (log scale)
initial_guess = np.log10([0.01, 1e-7, 0.05, 0.05, 0.01])  # Reasonable starting values

# Bounds for the parameters (log scale)
bounds = [(-3, -1), (-10, -5), (-2, 0), (-2, 0), (-3, -1)]

# Run the optimization
result = minimize(objective_function, initial_guess, method='L-BFGS-B', bounds=bounds)

# Get the optimized parameters
optimized_params_11 = 10**result.x

print(f"Optimized parameters for Model 11:")
print(f"k1 (id_8n7o -> id_caoz) = {optimized_params_11[0]:.6f}")
print(f"k2 (id_8n7o + id_caoz -> id_ty7g + id_1wsx) = {optimized_params_11[1]:.10f}")
print(f"k3 (id_caoz -> id_ty7g) = {optimized_params_11[2]:.6f}")
print(f"k4 (id_caoz -> id_1wsx) = {optimized_params_11[3]:.6f}")
print(f"k5 (id_1wsx -> id_ty7g) = {optimized_params_11[4]:.6f}")
print(f"Optimized error for Model 11: {result.fun}")

# Simulate with the optimized parameters for all four experiments
# First experiment
y0_exp1 = [11080778.0, 193.0, 2.0, 27.0]
t_eval_1 = exp_data_1['Time'].values

sol1 = solve_ivp(
    lambda t, y: model_ode11(t, y, *optimized_params_11),
    (0, 183),
    y0_exp1,
    method='LSODA',
    t_eval=t_eval_1
)

sim_data1 = pd.DataFrame({
    'Time': sol1.t,
    'id_8n7o': sol1.y[0],
    'id_caoz': sol1.y[1],
    'id_ty7g': sol1.y[2],
    'id_1wsx': sol1.y[3]
})

# Calculate error for Model 11 on the first experiment
error1 = 0
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    max_val = max(max(exp_data_1[species]), max(sim_data1[species]))
    if max_val > 0:
        error1 += np.mean(((exp_data_1[species] - sim_data1[species]) / max_val) ** 2)

# Second experiment
y0_exp2 = [5000000, 1000, 10, 100]
t_eval_2 = exp_data_2['Time'].values

sol2 = solve_ivp(
    lambda t, y: model_ode11(t, y, *optimized_params_11),
    (0, 183),
    y0_exp2,
    method='LSODA',
    t_eval=t_eval_2
)

sim_data2 = pd.DataFrame({
    'Time': sol2.t,
    'id_8n7o': sol2.y[0],
    'id_caoz': sol2.y[1],
    'id_ty7g': sol2.y[2],
    'id_1wsx': sol2.y[3]
})

# Calculate error for Model 11 on the second experiment
error2 = 0
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    max_val = max(max(exp_data_2[species]), max(sim_data2[species]))
    if max_val > 0:
        error2 += np.mean(((exp_data_2[species] - sim_data2[species]) / max_val) ** 2)

# Third experiment
y0_exp3 = [15000000, 500, 5, 50]
t_eval_3 = exp_data_3['Time'].values

sol3 = solve_ivp(
    lambda t, y: model_ode11(t, y, *optimized_params_11),
    (0, 183),
    y0_exp3,
    method='LSODA',
    t_eval=t_eval_3
)

sim_data3 = pd.DataFrame({
    'Time': sol3.t,
    'id_8n7o': sol3.y[0],
    'id_caoz': sol3.y[1],
    'id_ty7g': sol3.y[2],
    'id_1wsx': sol3.y[3]
})

# Calculate error for Model 11 on the third experiment
error3 = 0
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    max_val = max(max(exp_data_3[species]), max(sim_data3[species]))
    if max_val > 0:
        error3 += np.mean(((exp_data_3[species] - sim_data3[species]) / max_val) ** 2)

# Fourth experiment
y0_exp4 = [100000, 5000, 100, 500]
t_eval_4 = exp_data_4['Time'].values

sol4 = solve_ivp(
    lambda t, y: model_ode11(t, y, *optimized_params_11),
    (0, 183),
    y0_exp4,
    method='LSODA',
    t_eval=t_eval_4
)

sim_data4 = pd.DataFrame({
    'Time': sol4.t,
    'id_8n7o': sol4.y[0],
    'id_caoz': sol4.y[1],
    'id_ty7g': sol4.y[2],
    'id_1wsx': sol4.y[3]
})

# Calculate error for Model 11 on the fourth experiment
error4 = 0
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    max_val = max(max(exp_data_4[species]), max(sim_data4[species]))
    if max_val > 0:
        error4 += np.mean(((exp_data_4[species] - sim_data4[species]) / max_val) ** 2)

print("\nErrors for Model 11 on individual experiments:")
print(f"Error on experiment 1: {error1}")
print(f"Error on experiment 2: {error2}")
print(f"Error on experiment 3: {error3}")
print(f"Error on experiment 4: {error4}")

# Compare the simulation with experimental data for all four experiments
selected_times = [0, 30, 60, 90, 120, 150, 180]

print("\nComparison of Model 11 simulation vs. experimental data for the fourth experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(sim_data4['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = sim_data4.loc[idx, species]
        exp_val = exp_data_4[exp_data_4['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Compare the errors of Model 7, Model 10, and Model 11
print("\nComparison of all models:")
print(f"Model 7 error on experiments 1-3: 0.6904687280474515")
print(f"Model 7 error on experiment 4: 1.5937661565518517")
print(f"Model 10 error on all experiments: 4.618983371813609")
print(f"Model 10 error on experiment 4: 0.06572040226433988")
print(f"Model 11 error on all experiments: {result.fun}")
print(f"Model 11 error on experiment 4: {error4}")

# Create the final SBML model with Model 11 reactions and parameters
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

# Add the first reaction: id_8n7o -> id_caoz
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)

# Add reactants
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_8n7o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction1.createProduct()
product1.setSpecies("id_caoz")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1 * id_8n7o")

# Add parameter k1
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(optimized_params_11[0])

# Add the second reaction: id_8n7o + id_caoz -> id_ty7g + id_1wsx
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Add reactants
reactant1 = reaction2.createReactant()
reactant1.setSpecies("id_8n7o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

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

# Add products
product1 = reaction2.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

product2 = reaction2.createProduct()
product2.setSpecies("id_1wsx")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_8n7o * id_caoz")

# Add parameter k2
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(optimized_params_11[1])

# Add the third reaction: id_caoz -> id_ty7g
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactants
reactant1 = reaction3.createReactant()
reactant1.setSpecies("id_caoz")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction3.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_caoz")

# Add parameter k3
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(optimized_params_11[2])

# Add the fourth reaction: id_caoz -> id_1wsx
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactants
reactant1 = reaction4.createReactant()
reactant1.setSpecies("id_caoz")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction4.createProduct()
product1.setSpecies("id_1wsx")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_caoz")

# Add parameter k4
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(optimized_params_11[3])

# Add the fifth reaction: id_1wsx -> id_ty7g
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

# Add reactants
reactant1 = reaction5.createReactant()
reactant1.setSpecies("id_1wsx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction5.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law5 = reaction5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_1wsx")

# Add parameter k5
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(optimized_params_11[4])

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

# Store the final SBML model
shared_variables.add('final_sbml_model11', final_sbml)

print("\nCreated SBML model with Model 11 reactions:")
print(f"1. id_8n7o -> id_caoz (k1 = {optimized_params_11[0]:.6f})")
print(f"2. id_8n7o + id_caoz -> id_ty7g + id_1wsx (k2 = {optimized_params_11[1]:.10f})")
print(f"3. id_caoz -> id_ty7g (k3 = {optimized_params_11[2]:.6f})")
print(f"4. id_caoz -> id_1wsx (k4 = {optimized_params_11[3]:.6f})")
print(f"5. id_1wsx -> id_ty7g (k5 = {optimized_params_11[4]:.6f})")
```
# Observation

## Code Stdout
Optimized parameters for Model 11:
k1 (id_8n7o -> id_caoz) = 0.007462
k2 (id_8n7o + id_caoz -> id_ty7g + id_1wsx) = 0.0000007333
k3 (id_caoz -> id_ty7g) = 1.000000
k4 (id_caoz -> id_1wsx) = 0.010000
k5 (id_1wsx -> id_ty7g) = 0.024900
Optimized error for Model 11: 1.6184124328537768

Errors for Model 11 on individual experiments:
Error on experiment 1: 0.25348076915873524
Error on experiment 2: 0.3564133346924956
Error on experiment 3: 0.27220245551049405
Error on experiment 4: 0.7363158734920519

Comparison of Model 11 simulation vs. experimental data for the fourth experiment:

Time 0:
  id_8n7o: Sim = 1.00e+05, Exp = 1.00e+05, Rel Error = 0.00%
  id_caoz: Sim = 5.00e+03, Exp = 5.00e+03, Rel Error = 0.00%
  id_ty7g: Sim = 1.00e+02, Exp = 1.00e+02, Rel Error = 0.00%
  id_1wsx: Sim = 5.00e+02, Exp = 5.00e+02, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 7.86e+04, Exp = 9.97e+04, Rel Error = 21.14%
  id_caoz: Sim = 5.53e+02, Exp = 1.20e+02, Rel Error = 360.54%
  id_ty7g: Sim = 2.51e+04, Exp = 3.83e+03, Rel Error = 554.10%
  id_1wsx: Sim = 1.36e+03, Exp = 1.94e+03, Rel Error = 29.87%

Time 60:
  id_8n7o: Sim = 6.22e+04, Exp = 9.96e+04, Rel Error = 37.60%
  id_caoz: Sim = 4.43e+02, Exp = 1.36e+01, Rel Error = 3148.39%
  id_ty7g: Sim = 4.17e+04, Exp = 5.42e+03, Rel Error = 670.05%
  id_1wsx: Sim = 1.27e+03, Exp = 5.33e+02, Rel Error = 138.44%

Time 90:
  id_8n7o: Sim = 4.93e+04, Exp = 9.96e+04, Rel Error = 50.54%
  id_caoz: Sim = 3.54e+02, Exp = 3.30e+00, Rel Error = 10642.37%
  id_ty7g: Sim = 5.50e+04, Exp = 5.84e+03, Rel Error = 840.99%
  id_1wsx: Sim = 1.02e+03, Exp = 1.40e+02, Rel Error = 628.16%

Time 120:
  id_8n7o: Sim = 3.91e+04, Exp = 9.96e+04, Rel Error = 60.73%
  id_caoz: Sim = 2.83e+02, Exp = 8.57e-01, Rel Error = 32910.76%
  id_ty7g: Sim = 6.54e+04, Exp = 5.95e+03, Rel Error = 999.67%
  id_1wsx: Sim = 7.60e+02, Exp = 3.66e+01, Rel Error = 1978.45%

Time 150:
  id_8n7o: Sim = 3.11e+04, Exp = 9.96e+04, Rel Error = 68.78%
  id_caoz: Sim = 2.26e+02, Exp = 2.24e-01, Rel Error = 100883.64%
  id_ty7g: Sim = 7.37e+04, Exp = 5.98e+03, Rel Error = 1132.97%
  id_1wsx: Sim = 5.47e+02, Exp = 9.56e+00, Rel Error = 5624.02%

Time 180:
  id_8n7o: Sim = 2.47e+04, Exp = 9.96e+04, Rel Error = 75.15%
  id_caoz: Sim = 1.81e+02, Exp = 5.86e-02, Rel Error = 308720.75%
  id_ty7g: Sim = 8.03e+04, Exp = 5.99e+03, Rel Error = 1240.86%
  id_1wsx: Sim = 3.87e+02, Exp = 2.50e+00, Rel Error = 15383.34%

Comparison of all models:
Model 7 error on experiments 1-3: 0.6904687280474515
Model 7 error on experiment 4: 1.5937661565518517
Model 10 error on all experiments: 4.618983371813609
Model 10 error on experiment 4: 0.06572040226433988
Model 11 error on all experiments: 1.6184124328537768
Model 11 error on experiment 4: 0.7363158734920519

Created SBML model with Model 11 reactions:
1. id_8n7o -> id_caoz (k1 = 0.007462)
2. id_8n7o + id_caoz -> id_ty7g + id_1wsx (k2 = 0.0000007333)
3. id_caoz -> id_ty7g (k3 = 1.000000)
4. id_caoz -> id_1wsx (k4 = 0.010000)
5. id_1wsx -> id_ty7g (k5 = 0.024900)

## 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_8, iteration_10, iteration_15)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml, final_sbml_refined, final_sbml_model6, final_sbml_model7, final_sbml_best, final_sbml_optimized, final_sbml_final, final_sbml_model11)

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


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



# Iteration 18
## Thoughts
After testing multiple models, I now have a better understanding of the biological system. Let me summarize what I've learned:

1. Model 7 (sequential conversion model) performs well on experiments 1-3 with an error of 0.69, but poorly on experiment 4 with an error of 1.59.
2. Model 10 (second-order reaction model) performs very well on experiment 4 with an error of 0.066, but poorly on experiments 1-3, with a total error of 4.62.
3. Model 11 (combined model) performs reasonably well across all experiments with a total error of 1.62, but not as well as Model 7 on experiments 1-3 or Model 10 on experiment 4.

The key reactions that seem to be important are:
1. `id_8n7o -> id_caoz` (first-order conversion)
2. `id_8n7o + id_caoz -> id_ty7g + id_1wsx` (second-order reaction)
3. `id_caoz -> id_ty7g` (first-order conversion)
4. `id_caoz -> id_1wsx` (first-order conversion)
5. `id_1wsx -> id_ty7g` (first-order conversion)

The fact that different models perform better on different experiments suggests that the system might have more complex dynamics than what we've captured so far. Let me try one more experiment with different initial conditions to further validate our models.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration", 
    "meta_data": {
        "id_8n7o": 1000000,
        "id_caoz": 10000,
        "id_ty7g": 1000,
        "id_1wsx": 1000
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_18
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_18]

Total size: 184 rows × 6 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_18] for the full data

Time   id_8n7o  id_caoz  id_ty7g  id_1wsx  id_250q
0  1.00e+06 1.00e+04 1.00e+03 1.00e+03 1.11e+07
...
3.00e+00  9.99e+05 7.40e+03 1.39e+03 4.22e+03 1.11e+07
...
6.00e+00  9.98e+05 5.65e+03 2.16e+03 6.18e+03 1.11e+07
...
9.00e+00  9.97e+05 4.47e+03 3.13e+03 7.31e+03 1.11e+07
...
1.20e+01  9.96e+05 3.66e+03 4.24e+03 7.91e+03 1.11e+07
...
1.50e+01  9.95e+05 3.10e+03 5.40e+03 8.16e+03 1.11e+07
...
1.80e+01  9.95e+05 2.70e+03 6.58e+03 8.19e+03 1.11e+07
...
2.10e+01  9.94e+05 2.40e+03 7.75e+03 8.09e+03 1.11e+07
...
2.40e+01  9.93e+05 2.18e+03 8.90e+03 7.89e+03 1.11e+07
...
2.70e+01  9.92e+05 2.00e+03 1.00e+04 7.65e+03 1.11e+07
...
3.00e+01  9.92e+05 1.86e+03 1.11e+04 7.38e+03 1.11e+07
...
3.30e+01  9.91e+05 1.75e+03 1.21e+04 7.10e+03 1.11e+07
...
3.60e+01  9.90e+05 1.65e+03 1.31e+04 6.81e+03 1.11e+07
...
3.90e+01  9.90e+05 1.56e+03 1.41e+04 6.52e+03 1.11e+07
...
4.20e+01  9.89e+05 1.48e+03 1.50e+04 6.24e+03 1.11e+07
...
4.50e+01  9.89e+05 1.40e+03 1.59e+04 5.96e+03 1.11e+07
...
4.80e+01  9.88e+05 1.33e+03 1.67e+04 5.70e+03 1.11e+07
...
5.10e+01  9.88e+05 1.27e+03 1.75e+04 5.44e+03 1.11e+07
...
5.40e+01  9.87e+05 1.21e+03 1.83e+04 5.20e+03 1.11e+07
...
5.70e+01  9.87e+05 1.15e+03 1.90e+04 4.96e+03 1.11e+07
...
6.00e+01  9.86e+05 1.10e+03 1.97e+04 4.74e+03 1.11e+07
...
6.30e+01  9.86e+05 1.05e+03 2.04e+04 4.52e+03 1.11e+07
...
6.60e+01  9.86e+05 1.00e+03 2.10e+04 4.32e+03 1.11e+07
...
6.90e+01  9.85e+05 9.54e+02 2.17e+04 4.12e+03 1.11e+07
...
7.20e+01  9.85e+05 9.10e+02 2.22e+04 3.93e+03 1.11e+07
...
7.50e+01  9.85e+05 8.67e+02 2.28e+04 3.75e+03 1.11e+07
...
7.80e+01  9.84e+05 8.27e+02 2.33e+04 3.58e+03 1.11e+07
...
8.10e+01  9.84e+05 7.89e+02 2.38e+04 3.42e+03 1.11e+07
...
8.40e+01  9.84e+05 7.53e+02 2.43e+04 3.26e+03 1.11e+07
...
8.70e+01  9.83e+05 7.18e+02 2.48e+04 3.11e+03 1.11e+07
...
9.00e+01  9.83e+05 6.85e+02 2.52e+04 2.97e+03 1.11e+07
...
9.30e+01  9.83e+05 6.53e+02 2.56e+04 2.83e+03 1.11e+07
...
9.60e+01  9.83e+05 6.23e+02 2.60e+04 2.70e+03 1.11e+07
...
9.90e+01  9.82e+05 5.94e+02 2.64e+04 2.58e+03 1.11e+07
...
1.02e+02  9.82e+05 5.66e+02 2.67e+04 2.46e+03 1.11e+07
...
1.05e+02  9.82e+05 5.40e+02 2.71e+04 2.34e+03 1.11e+07
...
1.08e+02  9.82e+05 5.15e+02 2.74e+04 2.24e+03 1.11e+07
...
1.11e+02  9.82e+05 4.91e+02 2.77e+04 2.13e+03 1.11e+07
...
1.14e+02  9.81e+05 4.68e+02 2.80e+04 2.03e+03 1.11e+07
...
1.17e+02  9.81e+05 4.47e+02 2.83e+04 1.94e+03 1.11e+07
...
1.20e+02  9.81e+05 4.26e+02 2.86e+04 1.85e+03 1.11e+07
...
1.23e+02  9.81e+05 4.06e+02 2.89e+04 1.76e+03 1.11e+07
...
1.26e+02  9.81e+05 3.87e+02 2.91e+04 1.68e+03 1.11e+07
...
1.29e+02  9.81e+05 3.69e+02 2.93e+04 1.61e+03 1.11e+07
...
1.32e+02  9.81e+05 3.52e+02 2.96e+04 1.53e+03 1.11e+07
...
1.35e+02  9.80e+05 3.36e+02 2.98e+04 1.46e+03 1.11e+07
...
1.38e+02  9.80e+05 3.20e+02 3.00e+04 1.39e+03 1.11e+07
...
1.41e+02  9.80e+05 3.05e+02 3.02e+04 1.33e+03 1.11e+07
...
1.44e+02  9.80e+05 2.91e+02 3.04e+04 1.27e+03 1.11e+07
...
1.83e+02  9.79e+05 1.57e+02 3.21e+04 6.83e+02 1.11e+07

## 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_8, iteration_10, iteration_15, iteration_18)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml, final_sbml_refined, final_sbml_model6, final_sbml_model7, final_sbml_best, final_sbml_optimized, final_sbml_final, final_sbml_model11)

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


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



# Iteration 19
## Thoughts
The new experiment (iteration_18) shows a different behavior compared to the previous experiments:

1. `id_8n7o` starts at 1,000,000 and decreases very slowly to ~979,000 by the end
2. `id_caoz` starts at 10,000 and decreases steadily to ~157 by the end
3. `id_ty7g` starts at 1,000 and increases steadily to ~32,100 by the end
4. `id_1wsx` starts at 1,000, increases to a peak of ~8,190 at around t=18, then decreases to ~683 by the end

Let me test our models against this new data to see which one performs best.

## Action

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

# Access the experimental data
exp_data_5 = experiment_history["iteration_18"]

# Define the Model 7 ODE function (sequential conversion model)
def model_ode7(t, y, k1, k2, k3, k4):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o -> id_caoz
    r1 = k1 * y[0]
    
    # Reaction 2: id_caoz -> id_ty7g
    r2 = k2 * y[1]
    
    # Reaction 3: id_caoz -> id_1wsx
    r3 = k3 * y[1]
    
    # Reaction 4: id_1wsx -> id_ty7g
    r4 = k4 * y[3]
    
    # ODEs
    dy_dt = [
        -r1,            # d[id_8n7o]/dt
        r1 - r2 - r3,   # d[id_caoz]/dt
        r2 + r4,        # d[id_ty7g]/dt
        r3 - r4         # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Define the Model 10 ODE function (second-order reaction model)
def model_ode10(t, y, k1, k2, k3):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    r1 = k1 * y[0] * y[1]
    
    # Reaction 2: id_caoz -> id_ty7g
    r2 = k2 * y[1]
    
    # Reaction 3: id_1wsx -> id_ty7g
    r3 = k3 * y[3]
    
    # ODEs
    dy_dt = [
        -r1,            # d[id_8n7o]/dt
        -r1 - r2,       # d[id_caoz]/dt
        r1 + r2 + r3,   # d[id_ty7g]/dt
        r1 - r3         # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Define the Model 11 ODE function (combined model)
def model_ode11(t, y, k1, k2, k3, k4, k5):
    # y[0] = id_8n7o
    # y[1] = id_caoz
    # y[2] = id_ty7g
    # y[3] = id_1wsx
    
    # Reaction 1: id_8n7o -> id_caoz
    r1 = k1 * y[0]
    
    # Reaction 2: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    r2 = k2 * y[0] * y[1]
    
    # Reaction 3: id_caoz -> id_ty7g
    r3 = k3 * y[1]
    
    # Reaction 4: id_caoz -> id_1wsx
    r4 = k4 * y[1]
    
    # Reaction 5: id_1wsx -> id_ty7g
    r5 = k5 * y[3]
    
    # ODEs
    dy_dt = [
        -r1 - r2,            # d[id_8n7o]/dt
        r1 - r2 - r3 - r4,   # d[id_caoz]/dt
        r2 + r3 + r5,        # d[id_ty7g]/dt
        r2 + r4 - r5         # d[id_1wsx]/dt
    ]
    
    return dy_dt

# Get the optimized parameters for each model
optimized_params_7 = [0.019317, 0.044277, 0.101668, 0.029516]  # From iteration 14
optimized_params_10 = [0.0000003152, 0.073928, 0.015099]  # From iteration 16
optimized_params_11 = [0.007462, 0.0000007333, 1.000000, 0.010000, 0.024900]  # From iteration 17

# Initial conditions for the fifth experiment
y0_exp5 = [1000000, 10000, 1000, 1000]
t_eval_5 = exp_data_5['Time'].values

# Simulate with the optimized parameters for the fifth experiment
# Model 7
sol7 = solve_ivp(
    lambda t, y: model_ode7(t, y, *optimized_params_7),
    (0, 183),
    y0_exp5,
    method='LSODA',
    t_eval=t_eval_5
)

sim_data7 = pd.DataFrame({
    'Time': sol7.t,
    'id_8n7o': sol7.y[0],
    'id_caoz': sol7.y[1],
    'id_ty7g': sol7.y[2],
    'id_1wsx': sol7.y[3]
})

# Calculate error for Model 7 on the fifth experiment
error7 = 0
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    max_val = max(max(exp_data_5[species]), max(sim_data7[species]))
    if max_val > 0:
        error7 += np.mean(((exp_data_5[species] - sim_data7[species]) / max_val) ** 2)

# Model 10
sol10 = solve_ivp(
    lambda t, y: model_ode10(t, y, *optimized_params_10),
    (0, 183),
    y0_exp5,
    method='LSODA',
    t_eval=t_eval_5
)

sim_data10 = pd.DataFrame({
    'Time': sol10.t,
    'id_8n7o': sol10.y[0],
    'id_caoz': sol10.y[1],
    'id_ty7g': sol10.y[2],
    'id_1wsx': sol10.y[3]
})

# Calculate error for Model 10 on the fifth experiment
error10 = 0
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    max_val = max(max(exp_data_5[species]), max(sim_data10[species]))
    if max_val > 0:
        error10 += np.mean(((exp_data_5[species] - sim_data10[species]) / max_val) ** 2)

# Model 11
sol11 = solve_ivp(
    lambda t, y: model_ode11(t, y, *optimized_params_11),
    (0, 183),
    y0_exp5,
    method='LSODA',
    t_eval=t_eval_5
)

sim_data11 = pd.DataFrame({
    'Time': sol11.t,
    'id_8n7o': sol11.y[0],
    'id_caoz': sol11.y[1],
    'id_ty7g': sol11.y[2],
    'id_1wsx': sol11.y[3]
})

# Calculate error for Model 11 on the fifth experiment
error11 = 0
for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
    max_val = max(max(exp_data_5[species]), max(sim_data11[species]))
    if max_val > 0:
        error11 += np.mean(((exp_data_5[species] - sim_data11[species]) / max_val) ** 2)

print("Errors for each model on the fifth experiment:")
print(f"Model 7 error: {error7}")
print(f"Model 10 error: {error10}")
print(f"Model 11 error: {error11}")

# Compare the simulation with experimental data for the best model
selected_times = [0, 30, 60, 90, 120, 150, 180]

# Find the best model
best_model = min([(error7, 7), (error10, 10), (error11, 11)], key=lambda x: x[0])[1]
print(f"\nBest model for the fifth experiment: Model {best_model}")

if best_model == 7:
    best_sim_data = sim_data7
    best_params = optimized_params_7
elif best_model == 10:
    best_sim_data = sim_data10
    best_params = optimized_params_10
else:  # best_model == 11
    best_sim_data = sim_data11
    best_params = optimized_params_11

print(f"\nComparison of Model {best_model} simulation vs. experimental data for the fifth experiment:")
for t in selected_times:
    idx = np.argmin(np.abs(best_sim_data['Time'] - t))
    print(f"\nTime {t}:")
    for species in ['id_8n7o', 'id_caoz', 'id_ty7g', 'id_1wsx']:
        sim_val = best_sim_data.loc[idx, species]
        exp_val = exp_data_5[exp_data_5['Time'] == t][species].values[0]
        rel_error = abs(sim_val - exp_val) / max(abs(exp_val), 1e-10) * 100
        print(f"  {species}: Sim = {sim_val:.2e}, Exp = {exp_val:.2e}, Rel Error = {rel_error:.2f}%")

# Calculate the total error for each model across all five experiments
# We'll use the previously calculated errors for experiments 1-4
print("\nTotal errors for each model across all five experiments:")
print(f"Model 7: 0.6904687280474515 (exp 1-3) + 1.5937661565518517 (exp 4) + {error7} (exp 5) = {0.6904687280474515 + 1.5937661565518517 + error7}")
print(f"Model 10: 4.618983371813609 (exp 1-4) + {error10} (exp 5) = {4.618983371813609 + error10}")
print(f"Model 11: 1.6184124328537768 (exp 1-4) + {error11} (exp 5) = {1.6184124328537768 + error11}")

# Determine the best overall model
model7_total_error = 0.6904687280474515 + 1.5937661565518517 + error7
model10_total_error = 4.618983371813609 + error10
model11_total_error = 1.6184124328537768 + error11

best_overall_model = min([(model7_total_error, 7), (model10_total_error, 10), (model11_total_error, 11)], key=lambda x: x[0])[1]
print(f"\nBest overall model: Model {best_overall_model}")

# Create the final SBML model with the best overall model's reactions and parameters
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

if best_overall_model == 7:
    # Add the first reaction: id_8n7o -> id_caoz
    reaction1 = model.createReaction()
    reaction1.setId("reaction1")
    reaction1.setReversible(False)

    # Add reactants
    reactant1 = reaction1.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction1.createProduct()
    product1.setSpecies("id_caoz")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law1 = reaction1.createKineticLaw()
    kinetic_law1.setFormula("k1 * id_8n7o")

    # Add parameter k1
    parameter1 = kinetic_law1.createParameter()
    parameter1.setId("k1")
    parameter1.setValue(optimized_params_7[0])

    # Add the second reaction: id_caoz -> id_ty7g
    reaction2 = model.createReaction()
    reaction2.setId("reaction2")
    reaction2.setReversible(False)

    # Add reactants
    reactant1 = reaction2.createReactant()
    reactant1.setSpecies("id_caoz")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction2.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law2 = reaction2.createKineticLaw()
    kinetic_law2.setFormula("k2 * id_caoz")

    # Add parameter k2
    parameter2 = kinetic_law2.createParameter()
    parameter2.setId("k2")
    parameter2.setValue(optimized_params_7[1])

    # Add the third reaction: id_caoz -> id_1wsx
    reaction3 = model.createReaction()
    reaction3.setId("reaction3")
    reaction3.setReversible(False)

    # Add reactants
    reactant1 = reaction3.createReactant()
    reactant1.setSpecies("id_caoz")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction3.createProduct()
    product1.setSpecies("id_1wsx")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law3 = reaction3.createKineticLaw()
    kinetic_law3.setFormula("k3 * id_caoz")

    # Add parameter k3
    parameter3 = kinetic_law3.createParameter()
    parameter3.setId("k3")
    parameter3.setValue(optimized_params_7[2])

    # Add the fourth reaction: id_1wsx -> id_ty7g
    reaction4 = model.createReaction()
    reaction4.setId("reaction4")
    reaction4.setReversible(False)

    # Add reactants
    reactant1 = reaction4.createReactant()
    reactant1.setSpecies("id_1wsx")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction4.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law4 = reaction4.createKineticLaw()
    kinetic_law4.setFormula("k4 * id_1wsx")

    # Add parameter k4
    parameter4 = kinetic_law4.createParameter()
    parameter4.setId("k4")
    parameter4.setValue(optimized_params_7[3])

    print("\nCreated SBML model with Model 7 reactions:")
    print(f"1. id_8n7o -> id_caoz (k1 = {optimized_params_7[0]:.6f})")
    print(f"2. id_caoz -> id_ty7g (k2 = {optimized_params_7[1]:.6f})")
    print(f"3. id_caoz -> id_1wsx (k3 = {optimized_params_7[2]:.6f})")
    print(f"4. id_1wsx -> id_ty7g (k4 = {optimized_params_7[3]:.6f})")

elif best_overall_model == 10:
    # Add the first reaction: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    reaction1 = model.createReaction()
    reaction1.setId("reaction1")
    reaction1.setReversible(False)

    # Add reactants
    reactant1 = reaction1.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

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

    # Add products
    product1 = reaction1.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    product2 = reaction1.createProduct()
    product2.setSpecies("id_1wsx")
    product2.setStoichiometry(1.0)
    product2.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law1 = reaction1.createKineticLaw()
    kinetic_law1.setFormula("k1 * id_8n7o * id_caoz")

    # Add parameter k1
    parameter1 = kinetic_law1.createParameter()
    parameter1.setId("k1")
    parameter1.setValue(optimized_params_10[0])

    # Add the second reaction: id_caoz -> id_ty7g
    reaction2 = model.createReaction()
    reaction2.setId("reaction2")
    reaction2.setReversible(False)

    # Add reactants
    reactant1 = reaction2.createReactant()
    reactant1.setSpecies("id_caoz")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction2.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law2 = reaction2.createKineticLaw()
    kinetic_law2.setFormula("k2 * id_caoz")

    # Add parameter k2
    parameter2 = kinetic_law2.createParameter()
    parameter2.setId("k2")
    parameter2.setValue(optimized_params_10[1])

    # Add the third reaction: id_1wsx -> id_ty7g
    reaction3 = model.createReaction()
    reaction3.setId("reaction3")
    reaction3.setReversible(False)

    # Add reactants
    reactant1 = reaction3.createReactant()
    reactant1.setSpecies("id_1wsx")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction3.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law3 = reaction3.createKineticLaw()
    kinetic_law3.setFormula("k3 * id_1wsx")

    # Add parameter k3
    parameter3 = kinetic_law3.createParameter()
    parameter3.setId("k3")
    parameter3.setValue(optimized_params_10[2])

    print("\nCreated SBML model with Model 10 reactions:")
    print(f"1. id_8n7o + id_caoz -> id_ty7g + id_1wsx (k1 = {optimized_params_10[0]:.10f})")
    print(f"2. id_caoz -> id_ty7g (k2 = {optimized_params_10[1]:.6f})")
    print(f"3. id_1wsx -> id_ty7g (k3 = {optimized_params_10[2]:.6f})")

else:  # best_overall_model == 11
    # Add the first reaction: id_8n7o -> id_caoz
    reaction1 = model.createReaction()
    reaction1.setId("reaction1")
    reaction1.setReversible(False)

    # Add reactants
    reactant1 = reaction1.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction1.createProduct()
    product1.setSpecies("id_caoz")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law1 = reaction1.createKineticLaw()
    kinetic_law1.setFormula("k1 * id_8n7o")

    # Add parameter k1
    parameter1 = kinetic_law1.createParameter()
    parameter1.setId("k1")
    parameter1.setValue(optimized_params_11[0])

    # Add the second reaction: id_8n7o + id_caoz -> id_ty7g + id_1wsx
    reaction2 = model.createReaction()
    reaction2.setId("reaction2")
    reaction2.setReversible(False)

    # Add reactants
    reactant1 = reaction2.createReactant()
    reactant1.setSpecies("id_8n7o")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

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

    # Add products
    product1 = reaction2.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    product2 = reaction2.createProduct()
    product2.setSpecies("id_1wsx")
    product2.setStoichiometry(1.0)
    product2.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law2 = reaction2.createKineticLaw()
    kinetic_law2.setFormula("k2 * id_8n7o * id_caoz")

    # Add parameter k2
    parameter2 = kinetic_law2.createParameter()
    parameter2.setId("k2")
    parameter2.setValue(optimized_params_11[1])

    # Add the third reaction: id_caoz -> id_ty7g
    reaction3 = model.createReaction()
    reaction3.setId("reaction3")
    reaction3.setReversible(False)

    # Add reactants
    reactant1 = reaction3.createReactant()
    reactant1.setSpecies("id_caoz")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction3.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law3 = reaction3.createKineticLaw()
    kinetic_law3.setFormula("k3 * id_caoz")

    # Add parameter k3
    parameter3 = kinetic_law3.createParameter()
    parameter3.setId("k3")
    parameter3.setValue(optimized_params_11[2])

    # Add the fourth reaction: id_caoz -> id_1wsx
    reaction4 = model.createReaction()
    reaction4.setId("reaction4")
    reaction4.setReversible(False)

    # Add reactants
    reactant1 = reaction4.createReactant()
    reactant1.setSpecies("id_caoz")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction4.createProduct()
    product1.setSpecies("id_1wsx")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law4 = reaction4.createKineticLaw()
    kinetic_law4.setFormula("k4 * id_caoz")

    # Add parameter k4
    parameter4 = kinetic_law4.createParameter()
    parameter4.setId("k4")
    parameter4.setValue(optimized_params_11[3])

    # Add the fifth reaction: id_1wsx -> id_ty7g
    reaction5 = model.createReaction()
    reaction5.setId("reaction5")
    reaction5.setReversible(False)

    # Add reactants
    reactant1 = reaction5.createReactant()
    reactant1.setSpecies("id_1wsx")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(True)

    # Add products
    product1 = reaction5.createProduct()
    product1.setSpecies("id_ty7g")
    product1.setStoichiometry(1.0)
    product1.setConstant(True)

    # Add kinetic law (mass action)
    kinetic_law5 = reaction5.createKineticLaw()
    kinetic_law5.setFormula("k5 * id_1wsx")

    # Add parameter k5
    parameter5 = kinetic_law5.createParameter()
    parameter5.setId("k5")
    parameter5.setValue(optimized_params_11[4])

    print("\nCreated SBML model with Model 11 reactions:")
    print(f"1. id_8n7o -> id_caoz (k1 = {optimized_params_11[0]:.6f})")
    print(f"2. id_8n7o + id_caoz -> id_ty7g + id_1wsx (k2 = {optimized_params_11[1]:.10f})")
    print(f"3. id_caoz -> id_ty7g (k3 = {optimized_params_11[2]:.6f})")
    print(f"4. id_caoz -> id_1wsx (k4 = {optimized_params_11[3]:.6f})")
    print(f"5. id_1wsx -> id_ty7g (k5 = {optimized_params_11[4]:.6f})")

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

## Code Stdout
Errors for each model on the fifth experiment:
Model 7 error: 1.6319539135015264
Model 10 error: 0.10134482998448056
Model 11 error: 1.1810576231681167

Best model for the fifth experiment: Model 10

Comparison of Model 10 simulation vs. experimental data for the fifth experiment:

Time 0:
  id_8n7o: Sim = 1.00e+06, Exp = 1.00e+06, Rel Error = 0.00%
  id_caoz: Sim = 1.00e+04, Exp = 1.00e+04, Rel Error = 0.00%
  id_ty7g: Sim = 1.00e+03, Exp = 1.00e+03, Rel Error = 0.00%
  id_1wsx: Sim = 1.00e+03, Exp = 1.00e+03, Rel Error = 0.00%

Time 30:
  id_8n7o: Sim = 9.92e+05, Exp = 9.92e+05, Rel Error = 0.03%
  id_caoz: Sim = 9.18e-02, Exp = 1.86e+03, Rel Error = 100.00%
  id_ty7g: Sim = 1.41e+04, Exp = 1.11e+04, Rel Error = 27.03%
  id_1wsx: Sim = 5.99e+03, Exp = 7.38e+03, Rel Error = 18.85%

Time 60:
  id_8n7o: Sim = 9.92e+05, Exp = 9.86e+05, Rel Error = 0.56%
  id_caoz: Sim = 8.88e-07, Exp = 1.10e+03, Rel Error = 100.00%
  id_ty7g: Sim = 1.63e+04, Exp = 1.97e+04, Rel Error = 17.50%
  id_1wsx: Sim = 3.81e+03, Exp = 4.74e+03, Rel Error = 19.64%

Time 90:
  id_8n7o: Sim = 9.92e+05, Exp = 9.83e+05, Rel Error = 0.89%
  id_caoz: Sim = -6.54e-09, Exp = 6.85e+02, Rel Error = 100.00%
  id_ty7g: Sim = 1.77e+04, Exp = 2.52e+04, Rel Error = 29.83%
  id_1wsx: Sim = 2.42e+03, Exp = 2.97e+03, Rel Error = 18.49%

Time 120:
  id_8n7o: Sim = 9.92e+05, Exp = 9.81e+05, Rel Error = 1.10%
  id_caoz: Sim = 6.86e-09, Exp = 4.26e+02, Rel Error = 100.00%
  id_ty7g: Sim = 1.86e+04, Exp = 2.86e+04, Rel Error = 35.11%
  id_1wsx: Sim = 1.54e+03, Exp = 1.85e+03, Rel Error = 16.87%

Time 150:
  id_8n7o: Sim = 9.92e+05, Exp = 9.80e+05, Rel Error = 1.23%
  id_caoz: Sim = -6.04e-10, Exp = 2.65e+02, Rel Error = 100.00%
  id_ty7g: Sim = 1.91e+04, Exp = 3.07e+04, Rel Error = 37.78%
  id_1wsx: Sim = 9.79e+02, Exp = 1.15e+03, Rel Error = 15.03%

Time 180:
  id_8n7o: Sim = 9.92e+05, Exp = 9.79e+05, Rel Error = 1.31%
  id_caoz: Sim = 1.12e-09, Exp = 1.65e+02, Rel Error = 100.00%
  id_ty7g: Sim = 1.95e+04, Exp = 3.20e+04, Rel Error = 39.23%
  id_1wsx: Sim = 6.23e+02, Exp = 7.16e+02, Rel Error = 13.09%

Total errors for each model across all five experiments:
Model 7: 0.6904687280474515 (exp 1-3) + 1.5937661565518517 (exp 4) + 1.6319539135015264 (exp 5) = 3.91618879810083
Model 10: 4.618983371813609 (exp 1-4) + 0.10134482998448056 (exp 5) = 4.72032820179809
Model 11: 1.6184124328537768 (exp 1-4) + 1.1810576231681167 (exp 5) = 2.7994700560218932

Best overall model: Model 11

Created SBML model with Model 11 reactions:
1. id_8n7o -> id_caoz (k1 = 0.007462)
2. id_8n7o + id_caoz -> id_ty7g + id_1wsx (k2 = 0.0000007333)
3. id_caoz -> id_ty7g (k3 = 1.000000)
4. id_caoz -> id_1wsx (k4 = 0.010000)
5. id_1wsx -> id_ty7g (k5 = 0.024900)

## 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_8, iteration_10, iteration_15, iteration_18)
- `shared_variables`: all variables you have saved from the previous iterations. (data, updated_sbml, final_sbml, model2_sbml, final_sbml_refined, final_sbml_model6, final_sbml_model7, final_sbml_best, final_sbml_optimized, final_sbml_final, final_sbml_model11)

### 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
After testing our models on five different experiments with varying initial conditions, we have a good understanding of the biological system. Let's summarize our findings:

1. Model 7 (sequential conversion model) performs well on experiments 1-3 but poorly on experiments 4-5.
2. Model 10 (second-order reaction model) performs very well on experiments 4-5 but poorly on experiments 1-3.
3. Model 11 (combined model) performs reasonably well across all five experiments and has the lowest total error.

The reactions in Model 11 are:
1. `id_8n7o -> id_caoz` (k1 = 0.007462)
2. `id_8n7o + id_caoz -> id_ty7g + id_1wsx` (k2 = 0.0000007333)
3. `id_caoz -> id_ty7g` (k3 = 1.000000)
4. `id_caoz -> id_1wsx` (k4 = 0.010000)
5. `id_1wsx -> id_ty7g` (k5 = 0.024900)

This model captures the key dynamics of the system:
- `id_8n7o` is converted to `id_caoz` (reaction 1) and also participates in a second-order reaction with `id_caoz` (reaction 2)
- `id_caoz` is converted to both `id_ty7g` (reaction 3) and `id_1wsx` (reaction 4)
- `id_1wsx` is converted to `id_ty7g` (reaction 5)

Let's submit this model as our final answer.

## Action

### Submit
```python
import libsbml

# Access the final SBML model with Model 11 reactions
final_sbml = shared_variables.access('final_sbml_model11')

# Print a summary of the model
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(final_sbml)
model = document.getModel()

print("Final model summary:")
print(f"Number of species: {model.getNumSpecies()}")
print(f"Number of reactions: {model.getNumReactions()}")

print("\nSpecies:")
for i in range(model.getNumSpecies()):
    species = model.getSpecies(i)
    print(f"  {species.getId()}: Initial concentration = {species.getInitialConcentration()}, Boundary condition = {species.getBoundaryCondition()}")

print("\nReactions:")
for i in range(model.getNumReactions()):
    reaction = model.getReaction(i)
    print(f"  {reaction.getId()}: {reaction.getKineticLaw().getFormula()}")
    print("    Reactants:")
    for j in range(reaction.getNumReactants()):
        reactant = reaction.getReactant(j)
        print(f"      {reactant.getSpecies()} (stoichiometry: {reactant.getStoichiometry()})")
    print("    Products:")
    for j in range(reaction.getNumProducts()):
        product = reaction.getProduct(j)
        print(f"      {product.getSpecies()} (stoichiometry: {product.getStoichiometry()})")
    print("    Parameters:")
    for j in range(reaction.getKineticLaw().getNumParameters()):
        parameter = reaction.getKineticLaw().getParameter(j)
        print(f"      {parameter.getId()} = {parameter.getValue()}")

# Submit the final model
final_sbml = shared_variables.access('final_sbml_model11')
```
# Observation


            ## Important Notice 
            You have used up all interactions. Please put your final model as a string variable called `final_sbml` in your code.
            ```python
            final_sbml = ....
            ```

            It is recommended using libsbml to modify `input_sbml_string` rather than write the entire xml on your own.
## Parsing error
ERROR: A <reaction> object must have the required attributes 'id', 'reversible' and 'fast', and may have the optional attributes 'metaid', 'sboTerm', 'name' and 'compartment'. No other attributes from the SBML Level 3 Core namespace are permitted on a Reaction object.
Reference: L3V1 Section 4.11
 The required attribute 'fast' is missing from the <reaction> with the id 'reaction1'.

# Iteration 21
## Thoughts
I need to fix the SBML model to include the required 'fast' attribute for each reaction. Let me create a corrected version of the model.

## Action

### Submit
```python
import libsbml

# Create a new SBML model with Model 11 reactions
reader = libsbml.SBMLReader()
document = libsbml.readSBMLFromString(input_sbml_string)
model = document.getModel()

# Add the first reaction: id_8n7o -> id_caoz
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(False)
reaction1.setFast(False)  # Required in SBML Level 3

# Add reactants
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_8n7o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction1.createProduct()
product1.setSpecies("id_caoz")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1 * id_8n7o")

# Add parameter k1
parameter1 = kinetic_law1.createParameter()
parameter1.setId("k1")
parameter1.setValue(0.007462)

# Add the second reaction: id_8n7o + id_caoz -> id_ty7g + id_1wsx
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)
reaction2.setFast(False)  # Required in SBML Level 3

# Add reactants
reactant1 = reaction2.createReactant()
reactant1.setSpecies("id_8n7o")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

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

# Add products
product1 = reaction2.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

product2 = reaction2.createProduct()
product2.setSpecies("id_1wsx")
product2.setStoichiometry(1.0)
product2.setConstant(True)

# Add kinetic law (mass action)
kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_8n7o * id_caoz")

# Add parameter k2
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.0000007333)

# Add the third reaction: id_caoz -> id_ty7g
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)
reaction3.setFast(False)  # Required in SBML Level 3

# Add reactants
reactant1 = reaction3.createReactant()
reactant1.setSpecies("id_caoz")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction3.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_caoz")

# Add parameter k3
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(1.000000)

# Add the fourth reaction: id_caoz -> id_1wsx
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)
reaction4.setFast(False)  # Required in SBML Level 3

# Add reactants
reactant1 = reaction4.createReactant()
reactant1.setSpecies("id_caoz")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction4.createProduct()
product1.setSpecies("id_1wsx")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_caoz")

# Add parameter k4
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.010000)

# Add the fifth reaction: id_1wsx -> id_ty7g
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)
reaction5.setFast(False)  # Required in SBML Level 3

# Add reactants
reactant1 = reaction5.createReactant()
reactant1.setSpecies("id_1wsx")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add products
product1 = reaction5.createProduct()
product1.setSpecies("id_ty7g")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law (mass action)
kinetic_law5 = reaction5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_1wsx")

# Add parameter k5
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.024900)

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