
                # Interation 0

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


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

                <?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level2" level="2" version="1">
  <model id="id_1fz1">
    <listOfUnitDefinitions>
      <unitDefinition id="id_x3bb">
        <listOfUnits>
          <unit kind="mole" scale="-6"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_1ljm">
        <listOfUnits>
          <unit kind="mole" scale="-6"/>
          <unit kind="second" exponent="-1"/>
          <unit kind="litre" exponent="-1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_6d2q">
        <listOfUnits>
          <unit kind="litre"/>
          <unit kind="mole" exponent="-1" scale="-6"/>
          <unit kind="second" exponent="-1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_p0jk">
        <listOfUnits>
          <unit kind="second" exponent="-1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_gukt">
        <listOfUnits>
          <unit kind="mole" scale="-6"/>
          <unit kind="litre" exponent="-1"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_utjg" size="1.2e-11"/>
      <compartment id="id_julz" size="1.8e-11"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_udn6" compartment="id_julz" initialConcentration="0"/>
      <species id="id_ml0z" compartment="id_utjg" initialConcentration="0"/>
      <species id="id_aprv" compartment="id_utjg" initialConcentration="0"/>
      <species id="id_j3mt" compartment="id_utjg" initialConcentration="0"/>
      <species id="id_uqzr" compartment="id_julz" initialConcentration="5"/>
      <species id="id_ageg" compartment="id_utjg" initialConcentration="0.7"/>
      <species id="id_4vc0" compartment="id_utjg" initialConcentration="1.6" boundaryCondition="true"/>
      <species id="id_nh4a" compartment="id_utjg" initialConcentration="0"/>
      <species id="id_hdof" compartment="id_julz" initialConcentration="0"/>
      <species id="id_9e2p" compartment="id_julz" initialConcentration="2"/>
      <species id="id_tod7" compartment="id_julz" initialConcentration="0.7"/>
      <species id="id_r693" compartment="id_utjg" initialConcentration="500" boundaryCondition="true"/>
      <species id="id_o2wu" compartment="id_utjg" initialConcentration="0"/>
    </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. The SBML model provided contains information about the species, compartments, and unit definitions, but no reactions are defined yet. Let's start by understanding what we have:

1. There are 13 species (id_udn6, id_ml0z, id_aprv, id_j3mt, id_uqzr, id_ageg, id_4vc0, id_nh4a, id_hdof, id_9e2p, id_tod7, id_r693, id_o2wu)
2. Two of them (id_4vc0 and id_r693) are boundary conditions, meaning they are not affected by reactions
3. There are 2 compartments (id_utjg and id_julz)
4. Initial concentrations are provided for all species

To understand the system dynamics, I'll first run an observation experiment to see how the species concentrations change over time with the default settings. This will give me a baseline understanding of the system behavior.

## Action

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

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

Total size: 1001 rows × 14 columns. 

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

Time   id_udn6  id_ml0z  id_aprv  id_j3mt  id_uqzr  id_ageg  id_nh4a  id_hdof  id_9e2p  id_tod7  id_o2wu  id_4vc0  id_r693
0         0        0        0        0 5.00e+00 7.00e-01        0        0 2.00e+00 7.00e-01        0 1.60e+00 5.00e+02
...
2.00e-01  1.90e-05 2.41e-02 3.84e-02 2.25e-02 4.92e+00 6.43e-01 3.34e-03 1.28e-07 2.00e+00 7.00e-01 3.00e-02 1.60e+00 5.00e+02
...
4.00e-01  8.66e-05 3.00e-02 5.03e-02 6.91e-02 4.84e+00 5.85e-01 6.61e-03 6.45e-07 2.00e+00 7.00e-01 7.82e-02 1.60e+00 5.00e+02
...
6.00e-01  1.76e-04 3.25e-02 5.86e-02 1.23e-01 4.77e+00 5.34e-01 9.54e-03 1.35e-06 2.00e+00 7.00e-01 1.24e-01 1.60e+00 5.00e+02
...
8.00e-01  2.76e-04 3.43e-02 6.65e-02 1.80e-01 4.69e+00 4.88e-01 1.21e-02 2.13e-06 2.00e+00 7.00e-01 1.65e-01 1.60e+00 5.00e+02
...
1.00e+00  3.81e-04 3.58e-02 7.46e-02 2.41e-01 4.62e+00 4.48e-01 1.44e-02 2.97e-06 2.00e+00 7.00e-01 2.02e-01 1.60e+00 5.00e+02
...
1.20e+00  4.92e-04 3.70e-02 8.29e-02 3.04e-01 4.55e+00 4.13e-01 1.64e-02 3.84e-06 2.00e+00 7.00e-01 2.34e-01 1.60e+00 5.00e+02
...
1.40e+00  6.06e-04 3.81e-02 9.13e-02 3.69e-01 4.48e+00 3.82e-01 1.82e-02 4.75e-06 2.00e+00 7.00e-01 2.62e-01 1.60e+00 5.00e+02
...
1.60e+00  7.24e-04 3.89e-02 9.98e-02 4.35e-01 4.41e+00 3.55e-01 1.97e-02 5.68e-06 2.00e+00 7.00e-01 2.87e-01 1.60e+00 5.00e+02
...
1.80e+00  8.43e-04 3.97e-02 1.08e-01 5.03e-01 4.35e+00 3.31e-01 2.11e-02 6.63e-06 2.00e+00 7.00e-01 3.09e-01 1.60e+00 5.00e+02
...
2.00e+00  9.64e-04 4.03e-02 1.17e-01 5.71e-01 4.28e+00 3.10e-01 2.23e-02 7.59e-06 2.00e+00 7.00e-01 3.28e-01 1.60e+00 5.00e+02
...
2.20e+00  1.09e-03 4.08e-02 1.25e-01 6.39e-01 4.22e+00 2.91e-01 2.33e-02 8.56e-06 2.00e+00 7.00e-01 3.45e-01 1.60e+00 5.00e+02
...
2.40e+00  1.21e-03 4.12e-02 1.33e-01 7.08e-01 4.15e+00 2.75e-01 2.42e-02 9.53e-06 2.00e+00 7.00e-01 3.60e-01 1.60e+00 5.00e+02
...
2.60e+00  1.33e-03 4.16e-02 1.42e-01 7.76e-01 4.09e+00 2.60e-01 2.51e-02 1.05e-05 2.00e+00 7.00e-01 3.73e-01 1.60e+00 5.00e+02
...
2.80e+00  1.45e-03 4.19e-02 1.50e-01 8.44e-01 4.03e+00 2.47e-01 2.58e-02 1.15e-05 2.00e+00 7.00e-01 3.85e-01 1.60e+00 5.00e+02
...
3.00e+00  1.57e-03 4.21e-02 1.57e-01 9.12e-01 3.98e+00 2.35e-01 2.65e-02 1.24e-05 2.00e+00 7.00e-01 3.96e-01 1.60e+00 5.00e+02
...
3.20e+00  1.70e-03 4.23e-02 1.65e-01 9.79e-01 3.92e+00 2.24e-01 2.71e-02 1.34e-05 2.00e+00 7.00e-01 4.06e-01 1.60e+00 5.00e+02
...
3.40e+00  1.81e-03 4.25e-02 1.72e-01 1.05e+00 3.86e+00 2.15e-01 2.76e-02 1.43e-05 2.00e+00 7.00e-01 4.15e-01 1.60e+00 5.00e+02
...
3.60e+00  1.93e-03 4.26e-02 1.80e-01 1.11e+00 3.81e+00 2.06e-01 2.81e-02 1.53e-05 2.00e+00 7.00e-01 4.23e-01 1.60e+00 5.00e+02
...
3.80e+00  2.05e-03 4.27e-02 1.87e-01 1.18e+00 3.76e+00 1.98e-01 2.86e-02 1.62e-05 2.00e+00 7.00e-01 4.30e-01 1.60e+00 5.00e+02
...
4.00e+00  2.16e-03 4.27e-02 1.93e-01 1.24e+00 3.70e+00 1.91e-01 2.90e-02 1.71e-05 2.00e+00 7.00e-01 4.37e-01 1.60e+00 5.00e+02
...
4.20e+00  2.28e-03 4.28e-02 2.00e-01 1.30e+00 3.65e+00 1.85e-01 2.93e-02 1.80e-05 2.00e+00 7.00e-01 4.43e-01 1.60e+00 5.00e+02
...
4.40e+00  2.39e-03 4.28e-02 2.07e-01 1.36e+00 3.60e+00 1.79e-01 2.97e-02 1.89e-05 2.00e+00 7.00e-01 4.49e-01 1.60e+00 5.00e+02
...
4.60e+00  2.50e-03 4.28e-02 2.13e-01 1.42e+00 3.55e+00 1.73e-01 3.00e-02 1.98e-05 2.00e+00 7.00e-01 4.54e-01 1.60e+00 5.00e+02
...
4.80e+00  2.61e-03 4.28e-02 2.19e-01 1.48e+00 3.51e+00 1.68e-01 3.03e-02 2.06e-05 2.00e+00 7.00e-01 4.59e-01 1.60e+00 5.00e+02
...
5.00e+00  2.71e-03 4.27e-02 2.25e-01 1.54e+00 3.46e+00 1.63e-01 3.06e-02 2.15e-05 2.00e+00 7.00e-01 4.64e-01 1.60e+00 5.00e+02
...
5.20e+00  2.82e-03 4.27e-02 2.30e-01 1.60e+00 3.42e+00 1.59e-01 3.08e-02 2.23e-05 2.00e+00 7.00e-01 4.68e-01 1.60e+00 5.00e+02
...
5.40e+00  2.92e-03 4.27e-02 2.36e-01 1.66e+00 3.37e+00 1.55e-01 3.10e-02 2.31e-05 2.00e+00 7.00e-01 4.72e-01 1.60e+00 5.00e+02
...
5.60e+00  3.02e-03 4.26e-02 2.41e-01 1.71e+00 3.33e+00 1.51e-01 3.13e-02 2.39e-05 2.00e+00 7.00e-01 4.75e-01 1.60e+00 5.00e+02
...
5.80e+00  3.12e-03 4.26e-02 2.46e-01 1.77e+00 3.29e+00 1.47e-01 3.15e-02 2.47e-05 2.00e+00 7.00e-01 4.79e-01 1.60e+00 5.00e+02
...
6.00e+00  3.22e-03 4.25e-02 2.51e-01 1.82e+00 3.25e+00 1.44e-01 3.16e-02 2.55e-05 2.00e+00 7.00e-01 4.82e-01 1.60e+00 5.00e+02
...
6.20e+00  3.31e-03 4.24e-02 2.56e-01 1.87e+00 3.21e+00 1.41e-01 3.18e-02 2.62e-05 2.00e+00 7.00e-01 4.85e-01 1.60e+00 5.00e+02
...
6.40e+00  3.40e-03 4.23e-02 2.60e-01 1.92e+00 3.17e+00 1.38e-01 3.20e-02 2.70e-05 2.00e+00 7.00e-01 4.88e-01 1.60e+00 5.00e+02
...
6.60e+00  3.50e-03 4.23e-02 2.65e-01 1.97e+00 3.13e+00 1.35e-01 3.21e-02 2.77e-05 2.00e+00 7.00e-01 4.91e-01 1.60e+00 5.00e+02
...
6.80e+00  3.58e-03 4.22e-02 2.69e-01 2.02e+00 3.09e+00 1.32e-01 3.23e-02 2.84e-05 2.00e+00 7.00e-01 4.93e-01 1.60e+00 5.00e+02
...
7.00e+00  3.67e-03 4.21e-02 2.73e-01 2.07e+00 3.05e+00 1.30e-01 3.24e-02 2.91e-05 2.00e+00 7.00e-01 4.95e-01 1.60e+00 5.00e+02
...
7.20e+00  3.76e-03 4.20e-02 2.77e-01 2.12e+00 3.02e+00 1.28e-01 3.25e-02 2.98e-05 2.00e+00 7.00e-01 4.98e-01 1.60e+00 5.00e+02
...
7.40e+00  3.84e-03 4.19e-02 2.81e-01 2.17e+00 2.98e+00 1.26e-01 3.27e-02 3.05e-05 2.00e+00 7.00e-01 5.00e-01 1.60e+00 5.00e+02
...
7.60e+00  3.93e-03 4.18e-02 2.85e-01 2.21e+00 2.95e+00 1.24e-01 3.28e-02 3.11e-05 2.00e+00 7.00e-01 5.02e-01 1.60e+00 5.00e+02
...
7.80e+00  4.01e-03 4.18e-02 2.88e-01 2.26e+00 2.91e+00 1.22e-01 3.29e-02 3.18e-05 2.00e+00 7.00e-01 5.04e-01 1.60e+00 5.00e+02
...
8.00e+00  4.09e-03 4.17e-02 2.92e-01 2.30e+00 2.88e+00 1.20e-01 3.30e-02 3.24e-05 2.00e+00 7.00e-01 5.06e-01 1.60e+00 5.00e+02
...
8.20e+00  4.16e-03 4.16e-02 2.95e-01 2.34e+00 2.85e+00 1.18e-01 3.31e-02 3.30e-05 2.00e+00 7.00e-01 5.07e-01 1.60e+00 5.00e+02
...
8.40e+00  4.24e-03 4.15e-02 2.98e-01 2.38e+00 2.82e+00 1.16e-01 3.32e-02 3.36e-05 2.00e+00 7.00e-01 5.09e-01 1.60e+00 5.00e+02
...
8.60e+00  4.31e-03 4.14e-02 3.02e-01 2.42e+00 2.79e+00 1.15e-01 3.33e-02 3.42e-05 2.00e+00 7.00e-01 5.11e-01 1.60e+00 5.00e+02
...
8.80e+00  4.39e-03 4.13e-02 3.05e-01 2.46e+00 2.76e+00 1.13e-01 3.34e-02 3.48e-05 2.00e+00 7.00e-01 5.12e-01 1.60e+00 5.00e+02
...
9.00e+00  4.46e-03 4.12e-02 3.08e-01 2.50e+00 2.73e+00 1.12e-01 3.34e-02 3.54e-05 2.00e+00 7.00e-01 5.14e-01 1.60e+00 5.00e+02
...
9.20e+00  4.53e-03 4.11e-02 3.10e-01 2.54e+00 2.70e+00 1.10e-01 3.35e-02 3.59e-05 2.00e+00 7.00e-01 5.15e-01 1.60e+00 5.00e+02
...
9.40e+00  4.60e-03 4.10e-02 3.13e-01 2.58e+00 2.67e+00 1.09e-01 3.36e-02 3.65e-05 2.00e+00 7.00e-01 5.16e-01 1.60e+00 5.00e+02
...
9.60e+00  4.66e-03 4.09e-02 3.16e-01 2.62e+00 2.65e+00 1.08e-01 3.37e-02 3.70e-05 2.00e+00 7.00e-01 5.18e-01 1.60e+00 5.00e+02
...
1.00e+01  4.79e-03 4.08e-02 3.21e-01 2.69e+00 2.59e+00 1.05e-01 3.38e-02 3.80e-05 2.00e+00 7.00e-01 5.20e-01 1.60e+00 5.00e+02

## 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 the observation data from the system with default settings. Let me analyze this data to understand the dynamics and identify potential reactions.

Looking at the time series data:
1. Several species start at 0 concentration and increase over time (id_udn6, id_ml0z, id_aprv, id_j3mt, id_nh4a, id_hdof, id_o2wu)
2. Some species start with non-zero concentrations and decrease (id_uqzr, id_ageg)
3. Some species remain constant (id_9e2p, id_tod7, id_4vc0, id_r693) - the last two are boundary conditions as noted in the model

I need to analyze the data more carefully to identify potential reactions. Let me write some code to visualize and analyze the data.

## Action

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

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

# Print the initial and final concentrations to see the changes
initial = data.iloc[0]
final = data.iloc[-1]
changes = final - initial

print("Initial concentrations:")
print(initial[1:])  # Skip the Time column
print("\nFinal concentrations:")
print(final[1:])  # Skip the Time column
print("\nChanges in concentrations:")
print(changes[1:])  # Skip the Time column

# Check which species are boundary conditions
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()
boundary_species = []
for species in model.getListOfSpecies():
    if species.getBoundaryCondition():
        boundary_species.append(species.getId())
print("\nBoundary species:", boundary_species)

# Check which species are constant (concentration doesn't change)
constant_species = []
for column in data.columns[1:]:  # Skip the Time column
    if np.allclose(data[column], data[column].iloc[0], rtol=1e-5, atol=1e-5):
        constant_species.append(column)
print("Constant species:", constant_species)

# Calculate rates of change for each species
# We'll use the difference between consecutive time points
time_diff = np.diff(data['Time'])
rates = {}
for column in data.columns[1:]:  # Skip the Time column
    if column not in constant_species:
        conc_diff = np.diff(data[column])
        rates[column] = conc_diff / time_diff

# Look for correlations between rates to identify potential reactions
rate_df = pd.DataFrame(rates)
correlation = rate_df.corr()
print("\nCorrelation between rates of change:")
print(correlation)

# Check for conservation relationships
# If species are involved in the same reaction, their sum might be conserved
print("\nChecking for conservation relationships...")
for i, col1 in enumerate(data.columns[1:]):  # Skip the Time column
    for j, col2 in enumerate(data.columns[1:i+1]):  # Check only unique pairs
        if col1 != col2 and col1 not in boundary_species and col2 not in boundary_species:
            # Check if sum is approximately constant
            total = data[col1] + data[col2]
            if np.std(total) < 0.01 * np.mean(total):  # Less than 1% variation
                print(f"Sum of {col1} and {col2} is approximately constant: {np.mean(total):.4f} ± {np.std(total):.4f}")
            
            # Check if difference is approximately constant
            diff = data[col1] - data[col2]
            if np.std(diff) < 0.01 * np.mean(np.abs(diff)):  # Less than 1% variation
                print(f"Difference of {col1} and {col2} is approximately constant: {np.mean(diff):.4f} ± {np.std(diff):.4f}")

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

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

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 19/20



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

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


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



# Iteration 2
## Thoughts
I apologize for trying to use matplotlib, which is not allowed. Let me revise my code to analyze the data without visualization, focusing on numerical analysis to identify potential reactions.

## Action

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

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

# Print the initial and final concentrations to see the changes
initial = data.iloc[0]
final = data.iloc[-1]
changes = final - initial

print("Initial concentrations:")
print(initial[1:])  # Skip the Time column
print("\nFinal concentrations:")
print(final[1:])  # Skip the Time column
print("\nChanges in concentrations:")
print(changes[1:])  # Skip the Time column

# Check which species are boundary conditions
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()
boundary_species = []
for species in model.getListOfSpecies():
    if species.getBoundaryCondition():
        boundary_species.append(species.getId())
print("\nBoundary species:", boundary_species)

# Check which species are constant (concentration doesn't change)
constant_species = []
for column in data.columns[1:]:  # Skip the Time column
    if np.allclose(data[column], data[column].iloc[0], rtol=1e-5, atol=1e-5):
        constant_species.append(column)
print("Constant species:", constant_species)

# Calculate rates of change for each species
# We'll use the difference between consecutive time points
time_diff = np.diff(data['Time'])
rates = {}
for column in data.columns[1:]:  # Skip the Time column
    if column not in constant_species:
        conc_diff = np.diff(data[column])
        rates[column] = conc_diff / time_diff

# Look for correlations between rates to identify potential reactions
rate_df = pd.DataFrame(rates)
correlation = rate_df.corr()
print("\nCorrelation between rates of change:")
print(correlation)

# Check for conservation relationships
# If species are involved in the same reaction, their sum might be conserved
print("\nChecking for conservation relationships...")
for i, col1 in enumerate(data.columns[1:]):  # Skip the Time column
    for j, col2 in enumerate(data.columns[1:i+1]):  # Check only unique pairs
        if col1 != col2 and col1 not in boundary_species and col2 not in boundary_species:
            # Check if sum is approximately constant
            total = data[col1] + data[col2]
            if np.std(total) < 0.01 * np.mean(total):  # Less than 1% variation
                print(f"Sum of {col1} and {col2} is approximately constant: {np.mean(total):.4f} ± {np.std(total):.4f}")
            
            # Check if difference is approximately constant
            diff = data[col1] - data[col2]
            if np.std(diff) < 0.01 * np.mean(np.abs(diff)) and np.mean(np.abs(diff)) > 0.01:  # Less than 1% variation
                print(f"Difference of {col1} and {col2} is approximately constant: {np.mean(diff):.4f} ± {np.std(diff):.4f}")

# Look for stoichiometric relationships
print("\nLooking for stoichiometric relationships...")
for i, col1 in enumerate(data.columns[1:]):  # Skip the Time column
    if col1 not in constant_species and col1 not in boundary_species:
        for j, col2 in enumerate(data.columns[1:]):  # Check all other columns
            if i != j and col2 not in constant_species and col2 not in boundary_species:
                # Calculate the ratio of changes
                change1 = data[col1].iloc[-1] - data[col1].iloc[0]
                change2 = data[col2].iloc[-1] - data[col2].iloc[0]
                if abs(change2) > 1e-10:  # Avoid division by zero
                    ratio = change1 / change2
                    print(f"Ratio of change {col1}/{col2}: {ratio:.4f}")

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

## Code Stdout
Initial concentrations:
id_ml0z      0.0
id_aprv      0.0
id_j3mt      0.0
id_uqzr      5.0
id_ageg      0.7
id_nh4a      0.0
id_hdof      0.0
id_9e2p      2.0
id_tod7      0.7
id_o2wu      0.0
id_4vc0      1.6
id_r693    500.0
Time         0.0
Name: 0, dtype: float64

Final concentrations:
id_ml0z      0.040759
id_aprv      0.320706
id_j3mt      2.688295
id_uqzr      2.592793
id_ageg      0.105439
id_nh4a      0.033802
id_hdof      0.000038
id_9e2p      1.999962
id_tod7      0.700000
id_o2wu      0.520000
id_4vc0      1.600000
id_r693    500.000000
Time        10.000000
Name: 1000, dtype: float64

Changes in concentrations:
id_ml0z     0.040759
id_aprv     0.320706
id_j3mt     2.688295
id_uqzr    -2.407207
id_ageg    -0.594561
id_nh4a     0.033802
id_hdof     0.000038
id_9e2p    -0.000038
id_tod7     0.000000
id_o2wu     0.520000
id_4vc0     0.000000
id_r693     0.000000
Time       10.000000
dtype: float64

Boundary species: ['id_4vc0', 'id_r693']
Constant species: ['id_tod7', 'id_4vc0', 'id_r693']

Correlation between rates of change:
          id_ml0z   id_aprv   id_j3mt   id_uqzr   id_ageg   id_nh4a   id_hdof   id_9e2p   id_o2wu  Time
id_ml0z  1.000000  0.886883 -0.364481 -0.415644 -0.576358  0.584276 -0.499248  0.499248  0.360411   NaN
id_aprv  0.886883  1.000000 -0.091038 -0.576876 -0.572868  0.571606 -0.212454  0.212454  0.390619   NaN
id_j3mt -0.364481 -0.091038  1.000000 -0.577557 -0.160533  0.155004  0.975653 -0.975653  0.291662   NaN
id_uqzr -0.415644 -0.576876 -0.577557  1.000000  0.874425 -0.871194 -0.411020  0.411020 -0.874606   NaN
id_ageg -0.576358 -0.572868 -0.160533  0.874425  1.000000 -0.999727  0.029991 -0.029991 -0.970001   NaN
id_nh4a  0.584276  0.571606  0.155004 -0.871194 -0.999727  1.000000 -0.036677  0.036677  0.967303   NaN
id_hdof -0.499248 -0.212454  0.975653 -0.411020  0.029991 -0.036677  1.000000 -1.000000  0.114341   NaN
id_9e2p  0.499248  0.212454 -0.975653  0.411020 -0.029991  0.036677 -1.000000  1.000000 -0.114341   NaN
id_o2wu  0.360411  0.390619  0.291662 -0.874606 -0.970001  0.967303  0.114341 -0.114341  1.000000   NaN
Time          NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN       NaN   NaN

Checking for conservation relationships...
Sum of id_9e2p and id_ml0z is approximately constant: 2.0402 ± 0.0049
Difference of id_9e2p and id_ml0z is approximately constant: 1.9597 ± 0.0050
Sum of id_9e2p and id_nh4a is approximately constant: 2.0271 ± 0.0080
Difference of id_9e2p and id_nh4a is approximately constant: 1.9728 ± 0.0080
Sum of id_9e2p and id_hdof is approximately constant: 2.0000 ± 0.0000
Difference of id_9e2p and id_hdof is approximately constant: 2.0000 ± 0.0000
Sum of id_tod7 and id_ml0z is approximately constant: 0.7402 ± 0.0050
Difference of id_tod7 and id_ml0z is approximately constant: 0.6598 ± 0.0050
Sum of id_tod7 and id_hdof is approximately constant: 0.7000 ± 0.0000
Difference of id_tod7 and id_hdof is approximately constant: 0.7000 ± 0.0000
Sum of id_tod7 and id_9e2p is approximately constant: 2.7000 ± 0.0000
Difference of id_tod7 and id_9e2p is approximately constant: -1.3000 ± 0.0000

Looking for stoichiometric relationships...
Ratio of change id_ml0z/id_aprv: 0.1271
Ratio of change id_ml0z/id_j3mt: 0.0152
Ratio of change id_ml0z/id_uqzr: -0.0169
Ratio of change id_ml0z/id_ageg: -0.0686
Ratio of change id_ml0z/id_nh4a: 1.2058
Ratio of change id_ml0z/id_hdof: 1071.7189
Ratio of change id_ml0z/id_9e2p: -1071.7189
Ratio of change id_ml0z/id_o2wu: 0.0784
Ratio of change id_ml0z/Time: 0.0041
Ratio of change id_aprv/id_ml0z: 7.8684
Ratio of change id_aprv/id_j3mt: 0.1193
Ratio of change id_aprv/id_uqzr: -0.1332
Ratio of change id_aprv/id_ageg: -0.5394
Ratio of change id_aprv/id_nh4a: 9.4877
Ratio of change id_aprv/id_hdof: 8432.7192
Ratio of change id_aprv/id_9e2p: -8432.7192
Ratio of change id_aprv/id_o2wu: 0.6167
Ratio of change id_aprv/Time: 0.0321
Ratio of change id_j3mt/id_ml0z: 65.9563
Ratio of change id_j3mt/id_aprv: 8.3824
Ratio of change id_j3mt/id_uqzr: -1.1168
Ratio of change id_j3mt/id_ageg: -4.5215
Ratio of change id_j3mt/id_nh4a: 79.5299
Ratio of change id_j3mt/id_hdof: 70686.5893
Ratio of change id_j3mt/id_9e2p: -70686.5893
Ratio of change id_j3mt/id_o2wu: 5.1698
Ratio of change id_j3mt/Time: 0.2688
Ratio of change id_uqzr/id_ml0z: -59.0599
Ratio of change id_uqzr/id_aprv: -7.5060
Ratio of change id_uqzr/id_j3mt: -0.8954
Ratio of change id_uqzr/id_ageg: 4.0487
Ratio of change id_uqzr/id_nh4a: -71.2142
Ratio of change id_uqzr/id_hdof: -63295.6155
Ratio of change id_uqzr/id_9e2p: 63295.6155
Ratio of change id_uqzr/id_o2wu: -4.6292
Ratio of change id_uqzr/Time: -0.2407
Ratio of change id_ageg/id_ml0z: -14.5873
Ratio of change id_ageg/id_aprv: -1.8539
Ratio of change id_ageg/id_j3mt: -0.2212
Ratio of change id_ageg/id_uqzr: 0.2470
Ratio of change id_ageg/id_nh4a: -17.5894
Ratio of change id_ageg/id_hdof: -15633.5157
Ratio of change id_ageg/id_9e2p: 15633.5157
Ratio of change id_ageg/id_o2wu: -1.1434
Ratio of change id_ageg/Time: -0.0595
Ratio of change id_nh4a/id_ml0z: 0.8293
Ratio of change id_nh4a/id_aprv: 0.1054
Ratio of change id_nh4a/id_j3mt: 0.0126
Ratio of change id_nh4a/id_uqzr: -0.0140
Ratio of change id_nh4a/id_ageg: -0.0569
Ratio of change id_nh4a/id_hdof: 888.8056
Ratio of change id_nh4a/id_9e2p: -888.8056
Ratio of change id_nh4a/id_o2wu: 0.0650
Ratio of change id_nh4a/Time: 0.0034
Ratio of change id_hdof/id_ml0z: 0.0009
Ratio of change id_hdof/id_aprv: 0.0001
Ratio of change id_hdof/id_j3mt: 0.0000
Ratio of change id_hdof/id_uqzr: -0.0000
Ratio of change id_hdof/id_ageg: -0.0001
Ratio of change id_hdof/id_nh4a: 0.0011
Ratio of change id_hdof/id_9e2p: -1.0000
Ratio of change id_hdof/id_o2wu: 0.0001
Ratio of change id_hdof/Time: 0.0000
Ratio of change id_9e2p/id_ml0z: -0.0009
Ratio of change id_9e2p/id_aprv: -0.0001
Ratio of change id_9e2p/id_j3mt: -0.0000
Ratio of change id_9e2p/id_uqzr: 0.0000
Ratio of change id_9e2p/id_ageg: 0.0001
Ratio of change id_9e2p/id_nh4a: -0.0011
Ratio of change id_9e2p/id_hdof: -1.0000
Ratio of change id_9e2p/id_o2wu: -0.0001
Ratio of change id_9e2p/Time: -0.0000
Ratio of change id_o2wu/id_ml0z: 12.7580
Ratio of change id_o2wu/id_aprv: 1.6214
Ratio of change id_o2wu/id_j3mt: 0.1934
Ratio of change id_o2wu/id_uqzr: -0.2160
Ratio of change id_o2wu/id_ageg: -0.8746
Ratio of change id_o2wu/id_nh4a: 15.3836
Ratio of change id_o2wu/id_hdof: 13672.9913
Ratio of change id_o2wu/id_9e2p: -13672.9913
Ratio of change id_o2wu/Time: 0.0520
Ratio of change Time/id_ml0z: 245.3462
Ratio of change Time/id_aprv: 31.1812
Ratio of change Time/id_j3mt: 3.7198
Ratio of change Time/id_uqzr: -4.1542
Ratio of change Time/id_ageg: -16.8191
Ratio of change Time/id_nh4a: 295.8376
Ratio of change Time/id_hdof: 262942.1338
Ratio of change Time/id_9e2p: -262942.1338
Ratio of change Time/id_o2wu: 19.2308

## Reminder

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



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

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


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



# Iteration 3
## Thoughts
Based on the analysis of the observation data, I can make several observations about the system:

1. **Boundary species**: id_4vc0 and id_r693 are boundary species, which means they are not affected by reactions.

2. **Constant species**: id_tod7, id_4vc0, and id_r693 remain constant throughout the simulation.

3. **Changing species**:
   - Increasing: id_ml0z, id_aprv, id_j3mt, id_nh4a, id_hdof, id_o2wu
   - Decreasing: id_uqzr, id_ageg
   - Slight decrease: id_9e2p (very small change)

4. **Correlations between rates of change**:
   - Strong negative correlation (-0.999727) between id_ageg and id_nh4a
   - Strong negative correlation (-1.0) between id_hdof and id_9e2p
   - Strong positive correlation (0.975653) between id_j3mt and id_hdof
   - Strong negative correlation (-0.975653) between id_j3mt and id_9e2p
   - Strong negative correlation (-0.970001) between id_ageg and id_o2wu
   - Strong positive correlation (0.967303) between id_nh4a and id_o2wu

5. **Conservation relationships**:
   - The sum of id_9e2p and id_hdof is constant (2.0000 ± 0.0000)
   - The difference of id_9e2p and id_hdof is constant (2.0000 ± 0.0000)
   - This suggests that id_hdof + id_9e2p = constant, which could indicate a conversion reaction between these species.

6. **Stoichiometric relationships**:
   - The ratio of change between id_hdof and id_9e2p is -1.0, suggesting a 1:1 stoichiometry in their reaction.

Based on these observations, I can start formulating hypotheses about the reactions in the system:

1. There seems to be a direct conversion between id_9e2p and id_hdof (with a 1:1 stoichiometry).
2. id_ageg seems to be converted to id_nh4a (strong negative correlation).
3. id_j3mt appears to be related to both id_hdof and id_9e2p.
4. id_o2wu seems to be produced as id_ageg is consumed.

Let me run another experiment to test these hypotheses. I'll change the initial concentration of id_uqzr to see how it affects the system dynamics.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_uqzr": 10.0
    }
}
```
# Observation

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

Total size: 1001 rows × 14 columns. 

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

Time   id_udn6  id_ml0z  id_aprv  id_j3mt  id_uqzr  id_ageg  id_nh4a  id_hdof  id_9e2p  id_tod7  id_o2wu  id_4vc0  id_r693
0         0        0        0        0 1.00e+01 7.00e-01        0        0 2.00e+00 7.00e-01        0 1.60e+00 5.00e+02
...
2.00e-01  3.86e-05 4.67e-02 8.09e-02 4.60e-02 9.84e+00 5.90e-01 6.39e-03 2.59e-07 2.00e+00 7.00e-01 5.69e-02 1.60e+00 5.00e+02
...
4.00e-01  1.81e-04 5.68e-02 1.14e-01 1.45e-01 9.69e+00 4.91e-01 1.21e-02 1.34e-06 2.00e+00 7.00e-01 1.40e-01 1.60e+00 5.00e+02
...
6.00e-01  3.78e-04 6.04e-02 1.41e-01 2.66e-01 9.54e+00 4.12e-01 1.65e-02 2.89e-06 2.00e+00 7.00e-01 2.11e-01 1.60e+00 5.00e+02
...
8.00e-01  6.04e-04 6.24e-02 1.69e-01 3.98e-01 9.39e+00 3.51e-01 2.00e-02 4.67e-06 2.00e+00 7.00e-01 2.67e-01 1.60e+00 5.00e+02
...
1.00e+00  8.48e-04 6.36e-02 1.98e-01 5.38e-01 9.24e+00 3.03e-01 2.27e-02 6.60e-06 2.00e+00 7.00e-01 3.10e-01 1.60e+00 5.00e+02
...
1.20e+00  1.10e-03 6.45e-02 2.27e-01 6.83e-01 9.10e+00 2.66e-01 2.48e-02 8.63e-06 2.00e+00 7.00e-01 3.44e-01 1.60e+00 5.00e+02
...
1.40e+00  1.37e-03 6.50e-02 2.56e-01 8.31e-01 8.97e+00 2.37e-01 2.65e-02 1.07e-05 2.00e+00 7.00e-01 3.72e-01 1.60e+00 5.00e+02
...
1.60e+00  1.63e-03 6.54e-02 2.84e-01 9.81e-01 8.83e+00 2.13e-01 2.79e-02 1.28e-05 2.00e+00 7.00e-01 3.94e-01 1.60e+00 5.00e+02
...
1.80e+00  1.90e-03 6.56e-02 3.12e-01 1.13e+00 8.70e+00 1.94e-01 2.90e-02 1.49e-05 2.00e+00 7.00e-01 4.12e-01 1.60e+00 5.00e+02
...
2.00e+00  2.17e-03 6.56e-02 3.40e-01 1.28e+00 8.57e+00 1.78e-01 2.99e-02 1.71e-05 2.00e+00 7.00e-01 4.27e-01 1.60e+00 5.00e+02
...
2.20e+00  2.43e-03 6.56e-02 3.66e-01 1.43e+00 8.45e+00 1.64e-01 3.06e-02 1.92e-05 2.00e+00 7.00e-01 4.40e-01 1.60e+00 5.00e+02
...
2.40e+00  2.70e-03 6.55e-02 3.92e-01 1.57e+00 8.32e+00 1.53e-01 3.13e-02 2.13e-05 2.00e+00 7.00e-01 4.51e-01 1.60e+00 5.00e+02
...
2.60e+00  2.96e-03 6.54e-02 4.17e-01 1.72e+00 8.20e+00 1.43e-01 3.18e-02 2.33e-05 2.00e+00 7.00e-01 4.60e-01 1.60e+00 5.00e+02
...
2.80e+00  3.21e-03 6.52e-02 4.41e-01 1.86e+00 8.09e+00 1.34e-01 3.23e-02 2.54e-05 2.00e+00 7.00e-01 4.68e-01 1.60e+00 5.00e+02
...
3.00e+00  3.47e-03 6.50e-02 4.64e-01 2.00e+00 7.97e+00 1.27e-01 3.27e-02 2.74e-05 2.00e+00 7.00e-01 4.75e-01 1.60e+00 5.00e+02
...
3.20e+00  3.72e-03 6.47e-02 4.86e-01 2.14e+00 7.86e+00 1.21e-01 3.31e-02 2.94e-05 2.00e+00 7.00e-01 4.82e-01 1.60e+00 5.00e+02
...
3.40e+00  3.96e-03 6.45e-02 5.08e-01 2.27e+00 7.75e+00 1.15e-01 3.34e-02 3.13e-05 2.00e+00 7.00e-01 4.87e-01 1.60e+00 5.00e+02
...
3.60e+00  4.20e-03 6.42e-02 5.28e-01 2.40e+00 7.65e+00 1.10e-01 3.37e-02 3.32e-05 2.00e+00 7.00e-01 4.92e-01 1.60e+00 5.00e+02
...
3.80e+00  4.44e-03 6.39e-02 5.48e-01 2.53e+00 7.54e+00 1.05e-01 3.40e-02 3.51e-05 2.00e+00 7.00e-01 4.97e-01 1.60e+00 5.00e+02
...
4.00e+00  4.67e-03 6.36e-02 5.67e-01 2.66e+00 7.44e+00 1.01e-01 3.42e-02 3.70e-05 2.00e+00 7.00e-01 5.01e-01 1.60e+00 5.00e+02
...
4.20e+00  4.90e-03 6.33e-02 5.85e-01 2.79e+00 7.35e+00 9.72e-02 3.44e-02 3.88e-05 2.00e+00 7.00e-01 5.05e-01 1.60e+00 5.00e+02
...
4.40e+00  5.12e-03 6.30e-02 6.02e-01 2.91e+00 7.25e+00 9.37e-02 3.46e-02 4.06e-05 2.00e+00 7.00e-01 5.09e-01 1.60e+00 5.00e+02
...
4.60e+00  5.34e-03 6.27e-02 6.19e-01 3.03e+00 7.16e+00 9.06e-02 3.48e-02 4.23e-05 2.00e+00 7.00e-01 5.12e-01 1.60e+00 5.00e+02
...
4.80e+00  5.56e-03 6.24e-02 6.35e-01 3.15e+00 7.06e+00 8.78e-02 3.49e-02 4.40e-05 2.00e+00 7.00e-01 5.15e-01 1.60e+00 5.00e+02
...
5.00e+00  5.77e-03 6.20e-02 6.50e-01 3.27e+00 6.97e+00 8.52e-02 3.51e-02 4.57e-05 2.00e+00 7.00e-01 5.18e-01 1.60e+00 5.00e+02
...
5.20e+00  5.98e-03 6.17e-02 6.65e-01 3.38e+00 6.89e+00 8.27e-02 3.52e-02 4.74e-05 2.00e+00 7.00e-01 5.20e-01 1.60e+00 5.00e+02
...
5.40e+00  6.18e-03 6.14e-02 6.79e-01 3.49e+00 6.80e+00 8.05e-02 3.53e-02 4.90e-05 2.00e+00 7.00e-01 5.23e-01 1.60e+00 5.00e+02
...
5.60e+00  6.38e-03 6.11e-02 6.92e-01 3.60e+00 6.72e+00 7.84e-02 3.54e-02 5.06e-05 2.00e+00 7.00e-01 5.25e-01 1.60e+00 5.00e+02
...
5.80e+00  6.58e-03 6.08e-02 7.05e-01 3.71e+00 6.64e+00 7.65e-02 3.56e-02 5.21e-05 2.00e+00 7.00e-01 5.27e-01 1.60e+00 5.00e+02
...
6.00e+00  6.77e-03 6.05e-02 7.17e-01 3.81e+00 6.56e+00 7.47e-02 3.57e-02 5.37e-05 2.00e+00 7.00e-01 5.29e-01 1.60e+00 5.00e+02
...
6.20e+00  6.96e-03 6.02e-02 7.29e-01 3.91e+00 6.48e+00 7.30e-02 3.57e-02 5.51e-05 2.00e+00 7.00e-01 5.31e-01 1.60e+00 5.00e+02
...
6.40e+00  7.14e-03 5.98e-02 7.40e-01 4.01e+00 6.40e+00 7.15e-02 3.58e-02 5.66e-05 2.00e+00 7.00e-01 5.33e-01 1.60e+00 5.00e+02
...
6.60e+00  7.32e-03 5.95e-02 7.51e-01 4.11e+00 6.33e+00 7.00e-02 3.59e-02 5.80e-05 2.00e+00 7.00e-01 5.35e-01 1.60e+00 5.00e+02
...
6.80e+00  7.50e-03 5.92e-02 7.61e-01 4.21e+00 6.26e+00 6.86e-02 3.60e-02 5.95e-05 2.00e+00 7.00e-01 5.36e-01 1.60e+00 5.00e+02
...
7.00e+00  7.67e-03 5.89e-02 7.71e-01 4.30e+00 6.19e+00 6.73e-02 3.61e-02 6.08e-05 2.00e+00 7.00e-01 5.38e-01 1.60e+00 5.00e+02
...
7.20e+00  7.84e-03 5.87e-02 7.81e-01 4.39e+00 6.12e+00 6.61e-02 3.61e-02 6.22e-05 2.00e+00 7.00e-01 5.39e-01 1.60e+00 5.00e+02
...
7.40e+00  8.01e-03 5.84e-02 7.90e-01 4.49e+00 6.05e+00 6.50e-02 3.62e-02 6.35e-05 2.00e+00 7.00e-01 5.40e-01 1.60e+00 5.00e+02
...
7.60e+00  8.17e-03 5.81e-02 7.98e-01 4.57e+00 5.99e+00 6.39e-02 3.63e-02 6.48e-05 2.00e+00 7.00e-01 5.42e-01 1.60e+00 5.00e+02
...
7.80e+00  8.33e-03 5.78e-02 8.07e-01 4.66e+00 5.92e+00 6.29e-02 3.63e-02 6.61e-05 2.00e+00 7.00e-01 5.43e-01 1.60e+00 5.00e+02
...
8.00e+00  8.49e-03 5.75e-02 8.15e-01 4.75e+00 5.86e+00 6.19e-02 3.64e-02 6.73e-05 2.00e+00 7.00e-01 5.44e-01 1.60e+00 5.00e+02
...
8.20e+00  8.64e-03 5.73e-02 8.22e-01 4.83e+00 5.80e+00 6.10e-02 3.64e-02 6.85e-05 2.00e+00 7.00e-01 5.45e-01 1.60e+00 5.00e+02
...
8.40e+00  8.79e-03 5.70e-02 8.29e-01 4.91e+00 5.74e+00 6.01e-02 3.65e-02 6.97e-05 2.00e+00 7.00e-01 5.46e-01 1.60e+00 5.00e+02
...
8.60e+00  8.94e-03 5.67e-02 8.36e-01 4.99e+00 5.68e+00 5.93e-02 3.65e-02 7.09e-05 2.00e+00 7.00e-01 5.48e-01 1.60e+00 5.00e+02
...
8.80e+00  9.08e-03 5.65e-02 8.43e-01 5.07e+00 5.62e+00 5.85e-02 3.65e-02 7.20e-05 2.00e+00 7.00e-01 5.49e-01 1.60e+00 5.00e+02
...
9.00e+00  9.22e-03 5.62e-02 8.49e-01 5.14e+00 5.57e+00 5.77e-02 3.66e-02 7.32e-05 2.00e+00 7.00e-01 5.49e-01 1.60e+00 5.00e+02
...
9.20e+00  9.36e-03 5.60e-02 8.55e-01 5.22e+00 5.51e+00 5.70e-02 3.66e-02 7.42e-05 2.00e+00 7.00e-01 5.50e-01 1.60e+00 5.00e+02
...
9.40e+00  9.49e-03 5.57e-02 8.61e-01 5.29e+00 5.46e+00 5.63e-02 3.67e-02 7.53e-05 2.00e+00 7.00e-01 5.51e-01 1.60e+00 5.00e+02
...
9.60e+00  9.63e-03 5.55e-02 8.67e-01 5.36e+00 5.41e+00 5.57e-02 3.67e-02 7.64e-05 2.00e+00 7.00e-01 5.52e-01 1.60e+00 5.00e+02
...
1.00e+01  9.88e-03 5.50e-02 8.77e-01 5.50e+00 5.31e+00 5.44e-02 3.68e-02 7.84e-05 2.00e+00 7.00e-01 5.54e-01 1.60e+00 5.00e+02

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data)

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


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



# Iteration 4
## Thoughts
Now I have data from two experiments:
1. Default settings (iteration_0)
2. Increased initial concentration of id_uqzr from 5.0 to 10.0 (iteration_3)

Let me compare these two experiments to see how the change in id_uqzr affects the system dynamics. This will help me understand the reactions involving id_uqzr.

## Action

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

# Load the data from both experiments
data_default = experiment_history["iteration_0"]
data_high_uqzr = experiment_history["iteration_3"]

# Compare final concentrations
final_default = data_default.iloc[-1]
final_high_uqzr = data_high_uqzr.iloc[-1]

print("Comparison of final concentrations (t=10):")
comparison = pd.DataFrame({
    'Default': final_default[1:],  # Skip the Time column
    'High_uqzr': final_high_uqzr[1:],  # Skip the Time column
    'Difference': final_high_uqzr[1:] - final_default[1:],  # Skip the Time column
    'Ratio': final_high_uqzr[1:] / final_default[1:]  # Skip the Time column
})
print(comparison)

# Compare the rates of change for key species
print("\nComparing dynamics between experiments:")
for species in ['id_uqzr', 'id_ageg', 'id_nh4a', 'id_j3mt', 'id_o2wu', 'id_aprv', 'id_ml0z', 'id_hdof', 'id_9e2p']:
    # Calculate rate of change at t=1 for both experiments
    rate_default = (data_default[species].iloc[100] - data_default[species].iloc[0]) / 1.0
    rate_high_uqzr = (data_high_uqzr[species].iloc[100] - data_high_uqzr[species].iloc[0]) / 1.0
    
    print(f"{species} rate at t=1: Default={rate_default:.6f}, High_uqzr={rate_high_uqzr:.6f}, Ratio={rate_high_uqzr/rate_default if rate_default != 0 else 'N/A':.2f}")

# Let's look at the relationship between id_uqzr and id_ageg more closely
print("\nRelationship between id_uqzr and id_ageg:")
for t in [1, 2, 5, 10]:
    idx = int(t * 100)  # Assuming 100 data points per time unit
    uqzr_default = data_default['id_uqzr'].iloc[idx]
    ageg_default = data_default['id_ageg'].iloc[idx]
    uqzr_high = data_high_uqzr['id_uqzr'].iloc[idx]
    ageg_high = data_high_uqzr['id_ageg'].iloc[idx]
    
    print(f"t={t}: Default(uqzr={uqzr_default:.4f}, ageg={ageg_default:.4f}), High(uqzr={uqzr_high:.4f}, ageg={ageg_high:.4f})")

# Let's also look at the relationship between id_ageg and id_nh4a
print("\nRelationship between id_ageg and id_nh4a:")
for t in [1, 2, 5, 10]:
    idx = int(t * 100)  # Assuming 100 data points per time unit
    ageg_default = data_default['id_ageg'].iloc[idx]
    nh4a_default = data_default['id_nh4a'].iloc[idx]
    ageg_high = data_high_uqzr['id_ageg'].iloc[idx]
    nh4a_high = data_high_uqzr['id_nh4a'].iloc[idx]
    
    print(f"t={t}: Default(ageg={ageg_default:.4f}, nh4a={nh4a_default:.4f}), High(ageg={ageg_high:.4f}, nh4a={nh4a_high:.4f})")
    print(f"  Sum: Default={ageg_default+nh4a_default:.4f}, High={ageg_high+nh4a_high:.4f}")

# Let's check the relationship between id_j3mt and id_o2wu
print("\nRelationship between id_j3mt and id_o2wu:")
for t in [1, 2, 5, 10]:
    idx = int(t * 100)  # Assuming 100 data points per time unit
    j3mt_default = data_default['id_j3mt'].iloc[idx]
    o2wu_default = data_default['id_o2wu'].iloc[idx]
    j3mt_high = data_high_uqzr['id_j3mt'].iloc[idx]
    o2wu_high = data_high_uqzr['id_o2wu'].iloc[idx]
    
    print(f"t={t}: Default(j3mt={j3mt_default:.4f}, o2wu={o2wu_default:.4f}), High(j3mt={j3mt_high:.4f}, o2wu={o2wu_high:.4f})")
    print(f"  Ratio j3mt/o2wu: Default={j3mt_default/o2wu_default if o2wu_default != 0 else 'N/A':.4f}, High={j3mt_high/o2wu_high if o2wu_high != 0 else 'N/A':.4f}")

# Let's check the relationship between id_9e2p and id_hdof
print("\nRelationship between id_9e2p and id_hdof:")
for t in [1, 2, 5, 10]:
    idx = int(t * 100)  # Assuming 100 data points per time unit
    p9e2p_default = data_default['id_9e2p'].iloc[idx]
    hdof_default = data_default['id_hdof'].iloc[idx]
    p9e2p_high = data_high_uqzr['id_9e2p'].iloc[idx]
    hdof_high = data_high_uqzr['id_hdof'].iloc[idx]
    
    print(f"t={t}: Default(9e2p={p9e2p_default:.4f}, hdof={hdof_default:.6f}), High(9e2p={p9e2p_high:.4f}, hdof={hdof_high:.6f})")
    print(f"  Sum: Default={p9e2p_default+hdof_default:.6f}, High={p9e2p_high+hdof_high:.6f}")

# Let's check the relationship between id_udn6 and other species
if 'id_udn6' in data_default.columns:
    print("\nRelationship involving id_udn6:")
    for t in [1, 2, 5, 10]:
        idx = int(t * 100)  # Assuming 100 data points per time unit
        udn6_default = data_default['id_udn6'].iloc[idx]
        udn6_high = data_high_uqzr['id_udn6'].iloc[idx]
        
        print(f"t={t}: Default(udn6={udn6_default:.6f}), High(udn6={udn6_high:.6f}), Ratio={udn6_high/udn6_default if udn6_default != 0 else 'N/A'}")

# Based on the observations, let's formulate some hypotheses about the reactions
print("\nPotential reactions based on observations:")
print("1. id_9e2p <-> id_hdof (conservation relationship)")
print("2. id_ageg -> id_nh4a (negative correlation)")
print("3. id_uqzr -> id_j3mt (increased id_uqzr leads to increased id_j3mt)")
print("4. id_j3mt -> id_o2wu (positive correlation)")
print("5. id_uqzr + id_ageg -> id_j3mt + id_nh4a (potential combined reaction)")
```
# Observation

## Code Stdout
Comparison of final concentrations (t=10):
            Default   High_uqzr    Difference     Ratio
id_ml0z    0.040759    0.055010  1.425171e-02  1.349660
id_aprv    0.320706    0.876831  5.561246e-01  2.734062
id_j3mt    2.688295    5.501873  2.813578e+00  2.046603
id_uqzr    2.592793    5.307200  2.714407e+00  2.046905
id_ageg    0.105439    0.054443 -5.099585e-02  0.516347
id_nh4a    0.033802    0.036766  2.963699e-03  1.087677
id_hdof    0.000038    0.000078  4.038406e-05  2.061867
id_9e2p    1.999962    1.999922 -4.038406e-05  0.999980
id_tod7    0.700000    0.700000  1.110223e-16  1.000000
id_o2wu    0.520000    0.553780  3.378044e-02  1.064962
id_4vc0    1.600000    1.600000  0.000000e+00  1.000000
id_r693  500.000000  500.000000  0.000000e+00  1.000000
Time      10.000000   10.000000  0.000000e+00  1.000000

Comparing dynamics between experiments:
id_uqzr rate at t=1: Default=-0.378818, High_uqzr=-0.755789, Ratio=2.00
id_ageg rate at t=1: Default=-0.252127, High_uqzr=-0.396545, Ratio=1.57
id_nh4a rate at t=1: Default=0.014413, High_uqzr=0.022726, Ratio=1.58
id_j3mt rate at t=1: Default=0.240898, High_uqzr=0.538078, Ratio=2.23
id_o2wu rate at t=1: Default=0.201922, High_uqzr=0.310185, Ratio=1.54
id_aprv rate at t=1: Default=0.074626, High_uqzr=0.197779, Ratio=2.65
id_ml0z rate at t=1: Default=0.035793, High_uqzr=0.063633, Ratio=1.78
id_hdof rate at t=1: Default=0.000003, High_uqzr=0.000007, Ratio=2.22
id_9e2p rate at t=1: Default=-0.000003, High_uqzr=-0.000007, Ratio=2.22

Relationship between id_uqzr and id_ageg:
t=1: Default(uqzr=4.6212, ageg=0.4479), High(uqzr=9.2442, ageg=0.3035)
t=2: Default(uqzr=4.2805, ageg=0.3096), High(uqzr=8.5705, ageg=0.1775)
t=5: Default(uqzr=3.4613, ageg=0.1631), High(uqzr=6.9742, ageg=0.0852)
t=10: Default(uqzr=2.5928, ageg=0.1054), High(uqzr=5.3072, ageg=0.0544)

Relationship between id_ageg and id_nh4a:
t=1: Default(ageg=0.4479, nh4a=0.0144), High(ageg=0.3035, nh4a=0.0227)
  Sum: Default=0.4623, High=0.3262
t=2: Default(ageg=0.3096, nh4a=0.0223), High(ageg=0.1775, nh4a=0.0299)
  Sum: Default=0.3319, High=0.2074
t=5: Default(ageg=0.1631, nh4a=0.0306), High(ageg=0.0852, nh4a=0.0351)
  Sum: Default=0.1937, High=0.1202
t=10: Default(ageg=0.1054, nh4a=0.0338), High(ageg=0.0544, nh4a=0.0368)
  Sum: Default=0.1392, High=0.0912

Relationship between id_j3mt and id_o2wu:
t=1: Default(j3mt=0.2409, o2wu=0.2019), High(j3mt=0.5381, o2wu=0.3102)
  Ratio j3mt/o2wu: Default=1.1930, High=1.7347
t=2: Default(j3mt=0.5707, o2wu=0.3278), High(j3mt=1.2788, o2wu=0.4270)
  Ratio j3mt/o2wu: Default=1.7410, High=2.9952
t=5: Default(j3mt=1.5425, o2wu=0.4636), High(j3mt=3.2651, o2wu=0.5177)
  Ratio j3mt/o2wu: Default=3.3274, High=6.3065
t=10: Default(j3mt=2.6883, o2wu=0.5200), High(j3mt=5.5019, o2wu=0.5538)
  Ratio j3mt/o2wu: Default=5.1698, High=9.9351

Relationship between id_9e2p and id_hdof:
t=1: Default(9e2p=2.0000, hdof=0.000003), High(9e2p=2.0000, hdof=0.000007)
  Sum: Default=2.000000, High=2.000000
t=2: Default(9e2p=2.0000, hdof=0.000008), High(9e2p=2.0000, hdof=0.000017)
  Sum: Default=2.000000, High=2.000000
t=5: Default(9e2p=2.0000, hdof=0.000021), High(9e2p=2.0000, hdof=0.000046)
  Sum: Default=2.000000, High=2.000000
t=10: Default(9e2p=2.0000, hdof=0.000038), High(9e2p=1.9999, hdof=0.000078)
  Sum: Default=2.000000, High=2.000000

Relationship involving id_udn6:
t=1: Default(udn6=0.000381), High(udn6=0.000848), Ratio=2.2246015983049823
t=2: Default(udn6=0.000964), High(udn6=0.002167), Ratio=2.24721031645018
t=5: Default(udn6=0.002713), High(udn6=0.005771), Ratio=2.127547099693589
t=10: Default(udn6=0.004794), High(udn6=0.009881), Ratio=2.0609992804516666

Potential reactions based on observations:
1. id_9e2p <-> id_hdof (conservation relationship)
2. id_ageg -> id_nh4a (negative correlation)
3. id_uqzr -> id_j3mt (increased id_uqzr leads to increased id_j3mt)
4. id_j3mt -> id_o2wu (positive correlation)
5. id_uqzr + id_ageg -> id_j3mt + id_nh4a (potential combined reaction)

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data)

### 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
Based on the comparison between the default experiment and the high id_uqzr experiment, I can make several important observations:

1. **id_9e2p and id_hdof relationship**:
   - The sum of id_9e2p and id_hdof is always exactly 2.0, confirming a conservation relationship.
   - This strongly suggests a reversible reaction: id_9e2p ⟷ id_hdof

2. **id_ageg and id_nh4a relationship**:
   - When id_ageg decreases, id_nh4a increases, but their sum is not constant.
   - This suggests a reaction where id_ageg is converted to id_nh4a, but there might be other species involved.

3. **id_uqzr and id_j3mt relationship**:
   - Doubling the initial id_uqzr concentration approximately doubles the rate of id_j3mt production.
   - This suggests id_uqzr is directly involved in producing id_j3mt.

4. **id_j3mt and id_o2wu relationship**:
   - Both increase over time, but not at the same rate (the ratio changes).
   - This suggests they're related but not in a simple 1:1 conversion.

5. **id_udn6 relationship**:
   - Doubling id_uqzr approximately doubles id_udn6 production, suggesting id_uqzr is involved in id_udn6 production.

6. **id_ml0z and id_aprv**:
   - Both increase when id_uqzr is increased, suggesting they're products of reactions involving id_uqzr.

Let me run another experiment to further test these hypotheses. I'll change the initial concentration of id_ageg to see how it affects the system, particularly id_nh4a and other species.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_ageg": 1.4
    }
}
```
# Observation

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

Total size: 1001 rows × 14 columns. 

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

Time   id_udn6  id_ml0z  id_aprv  id_j3mt  id_uqzr  id_ageg  id_nh4a  id_hdof  id_9e2p  id_tod7  id_o2wu  id_4vc0  id_r693
0         0        0        0        0 5.00e+00 1.40e+00        0        0 2.00e+00 7.00e-01        0 1.60e+00 5.00e+02
...
2.00e-01  1.60e-05 2.81e-02 2.15e-02 1.82e-02 4.92e+00 1.32e+00 4.56e-03 1.09e-07 2.00e+00 7.00e-01 4.63e-02 1.60e+00 5.00e+02
...
4.00e-01  6.44e-05 3.34e-02 2.61e-02 5.02e-02 4.84e+00 1.24e+00 9.10e-03 4.82e-07 2.00e+00 7.00e-01 1.16e-01 1.60e+00 5.00e+02
...
6.00e-01  1.24e-04 3.67e-02 2.98e-02 8.53e-02 4.77e+00 1.17e+00 1.34e-02 9.53e-07 2.00e+00 7.00e-01 1.84e-01 1.60e+00 5.00e+02
...
8.00e-01  1.89e-04 3.96e-02 3.35e-02 1.23e-01 4.69e+00 1.09e+00 1.74e-02 1.47e-06 2.00e+00 7.00e-01 2.48e-01 1.60e+00 5.00e+02
...
1.00e+00  2.58e-04 4.23e-02 3.75e-02 1.63e-01 4.62e+00 1.03e+00 2.12e-02 2.01e-06 2.00e+00 7.00e-01 3.08e-01 1.60e+00 5.00e+02
...
1.20e+00  3.31e-04 4.48e-02 4.17e-02 2.05e-01 4.55e+00 9.67e-01 2.47e-02 2.59e-06 2.00e+00 7.00e-01 3.64e-01 1.60e+00 5.00e+02
...
1.40e+00  4.08e-04 4.71e-02 4.61e-02 2.49e-01 4.48e+00 9.10e-01 2.79e-02 3.20e-06 2.00e+00 7.00e-01 4.15e-01 1.60e+00 5.00e+02
...
1.60e+00  4.89e-04 4.92e-02 5.06e-02 2.95e-01 4.41e+00 8.56e-01 3.09e-02 3.84e-06 2.00e+00 7.00e-01 4.63e-01 1.60e+00 5.00e+02
...
1.80e+00  5.73e-04 5.12e-02 5.53e-02 3.43e-01 4.34e+00 8.07e-01 3.37e-02 4.50e-06 2.00e+00 7.00e-01 5.08e-01 1.60e+00 5.00e+02
...
2.00e+00  6.61e-04 5.29e-02 6.01e-02 3.93e-01 4.27e+00 7.62e-01 3.63e-02 5.20e-06 2.00e+00 7.00e-01 5.49e-01 1.60e+00 5.00e+02
...
2.20e+00  7.51e-04 5.45e-02 6.51e-02 4.44e-01 4.21e+00 7.21e-01 3.86e-02 5.91e-06 2.00e+00 7.00e-01 5.86e-01 1.60e+00 5.00e+02
...
2.40e+00  8.44e-04 5.59e-02 7.01e-02 4.96e-01 4.14e+00 6.82e-01 4.08e-02 6.65e-06 2.00e+00 7.00e-01 6.21e-01 1.60e+00 5.00e+02
...
2.60e+00  9.39e-04 5.72e-02 7.52e-02 5.50e-01 4.08e+00 6.47e-01 4.28e-02 7.40e-06 2.00e+00 7.00e-01 6.53e-01 1.60e+00 5.00e+02
...
2.80e+00  1.04e-03 5.84e-02 8.04e-02 6.05e-01 4.02e+00 6.15e-01 4.46e-02 8.17e-06 2.00e+00 7.00e-01 6.82e-01 1.60e+00 5.00e+02
...
3.00e+00  1.13e-03 5.95e-02 8.56e-02 6.60e-01 3.96e+00 5.86e-01 4.63e-02 8.95e-06 2.00e+00 7.00e-01 7.08e-01 1.60e+00 5.00e+02
...
3.20e+00  1.23e-03 6.04e-02 9.07e-02 7.16e-01 3.90e+00 5.59e-01 4.78e-02 9.74e-06 2.00e+00 7.00e-01 7.33e-01 1.60e+00 5.00e+02
...
3.40e+00  1.33e-03 6.12e-02 9.59e-02 7.72e-01 3.84e+00 5.34e-01 4.92e-02 1.05e-05 2.00e+00 7.00e-01 7.55e-01 1.60e+00 5.00e+02
...
3.60e+00  1.43e-03 6.20e-02 1.01e-01 8.29e-01 3.79e+00 5.11e-01 5.05e-02 1.13e-05 2.00e+00 7.00e-01 7.76e-01 1.60e+00 5.00e+02
...
3.80e+00  1.54e-03 6.27e-02 1.06e-01 8.85e-01 3.73e+00 4.91e-01 5.17e-02 1.21e-05 2.00e+00 7.00e-01 7.95e-01 1.60e+00 5.00e+02
...
4.00e+00  1.64e-03 6.33e-02 1.11e-01 9.42e-01 3.68e+00 4.71e-01 5.28e-02 1.29e-05 2.00e+00 7.00e-01 8.13e-01 1.60e+00 5.00e+02
...
4.20e+00  1.74e-03 6.38e-02 1.16e-01 9.98e-01 3.62e+00 4.54e-01 5.38e-02 1.37e-05 2.00e+00 7.00e-01 8.29e-01 1.60e+00 5.00e+02
...
4.40e+00  1.84e-03 6.43e-02 1.21e-01 1.05e+00 3.57e+00 4.37e-01 5.47e-02 1.45e-05 2.00e+00 7.00e-01 8.44e-01 1.60e+00 5.00e+02
...
4.60e+00  1.94e-03 6.47e-02 1.26e-01 1.11e+00 3.52e+00 4.22e-01 5.56e-02 1.53e-05 2.00e+00 7.00e-01 8.58e-01 1.60e+00 5.00e+02
...
4.80e+00  2.04e-03 6.51e-02 1.31e-01 1.17e+00 3.47e+00 4.08e-01 5.64e-02 1.61e-05 2.00e+00 7.00e-01 8.70e-01 1.60e+00 5.00e+02
...
5.00e+00  2.14e-03 6.54e-02 1.36e-01 1.22e+00 3.42e+00 3.95e-01 5.71e-02 1.69e-05 2.00e+00 7.00e-01 8.82e-01 1.60e+00 5.00e+02
...
5.20e+00  2.23e-03 6.58e-02 1.40e-01 1.27e+00 3.38e+00 3.83e-01 5.78e-02 1.77e-05 2.00e+00 7.00e-01 8.93e-01 1.60e+00 5.00e+02
...
5.40e+00  2.33e-03 6.60e-02 1.45e-01 1.33e+00 3.33e+00 3.72e-01 5.84e-02 1.85e-05 2.00e+00 7.00e-01 9.04e-01 1.60e+00 5.00e+02
...
5.60e+00  2.43e-03 6.63e-02 1.49e-01 1.38e+00 3.29e+00 3.62e-01 5.90e-02 1.92e-05 2.00e+00 7.00e-01 9.13e-01 1.60e+00 5.00e+02
...
5.80e+00  2.52e-03 6.65e-02 1.54e-01 1.43e+00 3.24e+00 3.52e-01 5.95e-02 2.00e-05 2.00e+00 7.00e-01 9.22e-01 1.60e+00 5.00e+02
...
6.00e+00  2.61e-03 6.67e-02 1.58e-01 1.48e+00 3.20e+00 3.43e-01 6.01e-02 2.07e-05 2.00e+00 7.00e-01 9.30e-01 1.60e+00 5.00e+02
...
6.20e+00  2.70e-03 6.68e-02 1.62e-01 1.53e+00 3.16e+00 3.34e-01 6.05e-02 2.14e-05 2.00e+00 7.00e-01 9.38e-01 1.60e+00 5.00e+02
...
6.40e+00  2.80e-03 6.70e-02 1.66e-01 1.58e+00 3.11e+00 3.26e-01 6.10e-02 2.21e-05 2.00e+00 7.00e-01 9.46e-01 1.60e+00 5.00e+02
...
6.60e+00  2.88e-03 6.71e-02 1.70e-01 1.63e+00 3.07e+00 3.19e-01 6.14e-02 2.28e-05 2.00e+00 7.00e-01 9.53e-01 1.60e+00 5.00e+02
...
6.80e+00  2.97e-03 6.72e-02 1.74e-01 1.68e+00 3.03e+00 3.12e-01 6.18e-02 2.35e-05 2.00e+00 7.00e-01 9.59e-01 1.60e+00 5.00e+02
...
7.00e+00  3.06e-03 6.73e-02 1.78e-01 1.73e+00 3.00e+00 3.05e-01 6.22e-02 2.42e-05 2.00e+00 7.00e-01 9.65e-01 1.60e+00 5.00e+02
...
7.20e+00  3.14e-03 6.74e-02 1.82e-01 1.78e+00 2.96e+00 2.99e-01 6.25e-02 2.49e-05 2.00e+00 7.00e-01 9.71e-01 1.60e+00 5.00e+02
...
7.40e+00  3.23e-03 6.75e-02 1.85e-01 1.82e+00 2.92e+00 2.93e-01 6.29e-02 2.56e-05 2.00e+00 7.00e-01 9.76e-01 1.60e+00 5.00e+02
...
7.60e+00  3.31e-03 6.75e-02 1.89e-01 1.87e+00 2.88e+00 2.88e-01 6.32e-02 2.62e-05 2.00e+00 7.00e-01 9.82e-01 1.60e+00 5.00e+02
...
7.80e+00  3.39e-03 6.76e-02 1.92e-01 1.91e+00 2.85e+00 2.82e-01 6.35e-02 2.68e-05 2.00e+00 7.00e-01 9.87e-01 1.60e+00 5.00e+02
...
8.00e+00  3.47e-03 6.76e-02 1.96e-01 1.95e+00 2.81e+00 2.77e-01 6.38e-02 2.75e-05 2.00e+00 7.00e-01 9.91e-01 1.60e+00 5.00e+02
...
8.20e+00  3.54e-03 6.76e-02 1.99e-01 2.00e+00 2.78e+00 2.73e-01 6.40e-02 2.81e-05 2.00e+00 7.00e-01 9.96e-01 1.60e+00 5.00e+02
...
8.40e+00  3.62e-03 6.77e-02 2.02e-01 2.04e+00 2.75e+00 2.68e-01 6.43e-02 2.87e-05 2.00e+00 7.00e-01 1.00e+00 1.60e+00 5.00e+02
...
8.60e+00  3.69e-03 6.77e-02 2.05e-01 2.08e+00 2.72e+00 2.64e-01 6.45e-02 2.93e-05 2.00e+00 7.00e-01 1.00e+00 1.60e+00 5.00e+02
...
8.80e+00  3.77e-03 6.77e-02 2.08e-01 2.12e+00 2.68e+00 2.60e-01 6.47e-02 2.99e-05 2.00e+00 7.00e-01 1.01e+00 1.60e+00 5.00e+02
...
9.00e+00  3.84e-03 6.77e-02 2.11e-01 2.16e+00 2.65e+00 2.56e-01 6.50e-02 3.04e-05 2.00e+00 7.00e-01 1.01e+00 1.60e+00 5.00e+02
...
9.20e+00  3.91e-03 6.77e-02 2.14e-01 2.20e+00 2.62e+00 2.53e-01 6.52e-02 3.10e-05 2.00e+00 7.00e-01 1.01e+00 1.60e+00 5.00e+02
...
9.40e+00  3.98e-03 6.77e-02 2.17e-01 2.24e+00 2.59e+00 2.49e-01 6.54e-02 3.15e-05 2.00e+00 7.00e-01 1.02e+00 1.60e+00 5.00e+02
...
9.60e+00  4.05e-03 6.77e-02 2.19e-01 2.27e+00 2.56e+00 2.46e-01 6.55e-02 3.21e-05 2.00e+00 7.00e-01 1.02e+00 1.60e+00 5.00e+02
...
1.00e+01  4.18e-03 6.77e-02 2.25e-01 2.35e+00 2.51e+00 2.40e-01 6.59e-02 3.31e-05 2.00e+00 7.00e-01 1.03e+00 1.60e+00 5.00e+02

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data)

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


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



# Iteration 6
## Thoughts
Now I have data from three experiments:
1. Default settings (iteration_0)
2. Increased initial concentration of id_uqzr from 5.0 to 10.0 (iteration_3)
3. Increased initial concentration of id_ageg from 0.7 to 1.4 (iteration_5)

Let me compare these experiments to further refine my understanding of the system dynamics.

## Action

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

# Load the data from all three experiments
data_default = experiment_history["iteration_0"]
data_high_uqzr = experiment_history["iteration_3"]
data_high_ageg = experiment_history["iteration_5"]

# Compare final concentrations
final_default = data_default.iloc[-1]
final_high_uqzr = data_high_uqzr.iloc[-1]
final_high_ageg = data_high_ageg.iloc[-1]

print("Comparison of final concentrations (t=10):")
comparison = pd.DataFrame({
    'Default': final_default[1:],  # Skip the Time column
    'High_uqzr': final_high_uqzr[1:],  # Skip the Time column
    'High_ageg': final_high_ageg[1:],  # Skip the Time column
    'Diff_uqzr': final_high_uqzr[1:] - final_default[1:],  # Skip the Time column
    'Diff_ageg': final_high_ageg[1:] - final_default[1:]  # Skip the Time column
})
print(comparison)

# Focus on the relationship between id_ageg and id_nh4a
print("\nRelationship between id_ageg and id_nh4a:")
for t in [0, 1, 2, 5, 10]:
    idx = int(t * 100)  # Assuming 100 data points per time unit
    ageg_default = data_default['id_ageg'].iloc[idx]
    nh4a_default = data_default['id_nh4a'].iloc[idx]
    ageg_high_ageg = data_high_ageg['id_ageg'].iloc[idx]
    nh4a_high_ageg = data_high_ageg['id_nh4a'].iloc[idx]
    
    print(f"t={t}: Default(ageg={ageg_default:.4f}, nh4a={nh4a_default:.4f}), High_ageg(ageg={ageg_high_ageg:.4f}, nh4a={nh4a_high_ageg:.4f})")
    print(f"  Diff: ageg={ageg_high_ageg-ageg_default:.4f}, nh4a={nh4a_high_ageg-nh4a_default:.4f}")
    print(f"  Sum: Default={ageg_default+nh4a_default:.4f}, High_ageg={ageg_high_ageg+nh4a_high_ageg:.4f}, Diff={(ageg_high_ageg+nh4a_high_ageg)-(ageg_default+nh4a_default):.4f}")

# Focus on the relationship between id_uqzr, id_j3mt, and id_o2wu
print("\nRelationship between id_uqzr, id_j3mt, and id_o2wu:")
for t in [0, 1, 2, 5, 10]:
    idx = int(t * 100)  # Assuming 100 data points per time unit
    uqzr_default = data_default['id_uqzr'].iloc[idx]
    j3mt_default = data_default['id_j3mt'].iloc[idx]
    o2wu_default = data_default['id_o2wu'].iloc[idx]
    
    uqzr_high_ageg = data_high_ageg['id_uqzr'].iloc[idx]
    j3mt_high_ageg = data_high_ageg['id_j3mt'].iloc[idx]
    o2wu_high_ageg = data_high_ageg['id_o2wu'].iloc[idx]
    
    print(f"t={t}: Default(uqzr={uqzr_default:.4f}, j3mt={j3mt_default:.4f}, o2wu={o2wu_default:.4f})")
    print(f"      High_ageg(uqzr={uqzr_high_ageg:.4f}, j3mt={j3mt_high_ageg:.4f}, o2wu={o2wu_high_ageg:.4f})")
    if t > 0:  # Avoid division by zero
        print(f"  Ratio j3mt/o2wu: Default={j3mt_default/o2wu_default:.4f}, High_ageg={j3mt_high_ageg/o2wu_high_ageg:.4f}")

# Focus on the relationship between id_ml0z and id_aprv
print("\nRelationship between id_ml0z and id_aprv:")
for t in [0, 1, 2, 5, 10]:
    idx = int(t * 100)  # Assuming 100 data points per time unit
    ml0z_default = data_default['id_ml0z'].iloc[idx]
    aprv_default = data_default['id_aprv'].iloc[idx]
    ml0z_high_ageg = data_high_ageg['id_ml0z'].iloc[idx]
    aprv_high_ageg = data_high_ageg['id_aprv'].iloc[idx]
    
    print(f"t={t}: Default(ml0z={ml0z_default:.4f}, aprv={aprv_default:.4f}), High_ageg(ml0z={ml0z_high_ageg:.4f}, aprv={aprv_high_ageg:.4f})")
    if t > 0:  # Avoid division by zero
        print(f"  Ratio ml0z/aprv: Default={ml0z_default/aprv_default:.4f}, High_ageg={ml0z_high_ageg/aprv_high_ageg:.4f}")

# Check for conservation relationships in the high_ageg experiment
print("\nChecking for conservation relationships in high_ageg experiment...")
for i, col1 in enumerate(data_high_ageg.columns[1:]):  # Skip the Time column
    for j, col2 in enumerate(data_high_ageg.columns[1:i+1]):  # Check only unique pairs
        if col1 != col2 and col1 not in ['id_4vc0', 'id_r693'] and col2 not in ['id_4vc0', 'id_r693']:
            # Check if sum is approximately constant
            total = data_high_ageg[col1] + data_high_ageg[col2]
            if np.std(total) < 0.01 * np.mean(total):  # Less than 1% variation
                print(f"Sum of {col1} and {col2} is approximately constant: {np.mean(total):.4f} ± {np.std(total):.4f}")

# Based on all observations, let's formulate a more refined set of hypotheses about the reactions
print("\nRefined hypotheses about reactions:")
print("1. id_9e2p <-> id_hdof (conservation relationship with sum = 2.0)")
print("2. id_ageg -> id_nh4a + id_o2wu (id_ageg is consumed, id_nh4a and id_o2wu are produced)")
print("3. id_uqzr + id_ageg -> id_j3mt + id_nh4a (id_uqzr and id_ageg are consumed, id_j3mt and id_nh4a are produced)")
print("4. id_j3mt -> id_ml0z + id_aprv (id_j3mt is consumed, id_ml0z and id_aprv are produced)")
print("5. id_uqzr -> id_udn6 (id_uqzr is consumed, id_udn6 is produced)")

# Let's check the stoichiometric relationships more carefully
print("\nStoichiometric relationships:")
# Calculate the changes from t=0 to t=10 for each experiment
changes_default = data_default.iloc[-1] - data_default.iloc[0]
changes_high_uqzr = data_high_uqzr.iloc[-1] - data_high_uqzr.iloc[0]
changes_high_ageg = data_high_ageg.iloc[-1] - data_high_ageg.iloc[0]

# Print the changes for key species
key_species = ['id_uqzr', 'id_ageg', 'id_j3mt', 'id_nh4a', 'id_o2wu', 'id_ml0z', 'id_aprv', 'id_udn6', 'id_hdof', 'id_9e2p']
print("\nChanges from t=0 to t=10:")
for species in key_species:
    print(f"{species}: Default={changes_default[species]:.6f}, High_uqzr={changes_high_uqzr[species]:.6f}, High_ageg={changes_high_ageg[species]:.6f}")

# Calculate ratios of changes to identify stoichiometry
print("\nRatios of changes (potential stoichiometry):")
# For reaction 1: id_9e2p <-> id_hdof
ratio_1_default = changes_default['id_hdof'] / -changes_default['id_9e2p']
ratio_1_high_uqzr = changes_high_uqzr['id_hdof'] / -changes_high_uqzr['id_9e2p']
ratio_1_high_ageg = changes_high_ageg['id_hdof'] / -changes_high_ageg['id_9e2p']
print(f"id_hdof/-id_9e2p: Default={ratio_1_default:.4f}, High_uqzr={ratio_1_high_uqzr:.4f}, High_ageg={ratio_1_high_ageg:.4f}")

# For reaction 2: id_ageg -> id_nh4a + id_o2wu
ratio_2a_default = changes_default['id_nh4a'] / -changes_default['id_ageg']
ratio_2a_high_uqzr = changes_high_uqzr['id_nh4a'] / -changes_high_uqzr['id_ageg']
ratio_2a_high_ageg = changes_high_ageg['id_nh4a'] / -changes_high_ageg['id_ageg']
print(f"id_nh4a/-id_ageg: Default={ratio_2a_default:.4f}, High_uqzr={ratio_2a_high_uqzr:.4f}, High_ageg={ratio_2a_high_ageg:.4f}")

ratio_2b_default = changes_default['id_o2wu'] / -changes_default['id_ageg']
ratio_2b_high_uqzr = changes_high_uqzr['id_o2wu'] / -changes_high_uqzr['id_ageg']
ratio_2b_high_ageg = changes_high_ageg['id_o2wu'] / -changes_high_ageg['id_ageg']
print(f"id_o2wu/-id_ageg: Default={ratio_2b_default:.4f}, High_uqzr={ratio_2b_high_uqzr:.4f}, High_ageg={ratio_2b_high_ageg:.4f}")

# For reaction 3: id_uqzr + id_ageg -> id_j3mt + id_nh4a
ratio_3a_default = changes_default['id_j3mt'] / -changes_default['id_uqzr']
ratio_3a_high_uqzr = changes_high_uqzr['id_j3mt'] / -changes_high_uqzr['id_uqzr']
ratio_3a_high_ageg = changes_high_ageg['id_j3mt'] / -changes_high_ageg['id_uqzr']
print(f"id_j3mt/-id_uqzr: Default={ratio_3a_default:.4f}, High_uqzr={ratio_3a_high_uqzr:.4f}, High_ageg={ratio_3a_high_ageg:.4f}")

# For reaction 4: id_j3mt -> id_ml0z + id_aprv
ratio_4a_default = changes_default['id_ml0z'] / changes_default['id_j3mt']
ratio_4a_high_uqzr = changes_high_uqzr['id_ml0z'] / changes_high_uqzr['id_j3mt']
ratio_4a_high_ageg = changes_high_ageg['id_ml0z'] / changes_high_ageg['id_j3mt']
print(f"id_ml0z/id_j3mt: Default={ratio_4a_default:.4f}, High_uqzr={ratio_4a_high_uqzr:.4f}, High_ageg={ratio_4a_high_ageg:.4f}")

ratio_4b_default = changes_default['id_aprv'] / changes_default['id_j3mt']
ratio_4b_high_uqzr = changes_high_uqzr['id_aprv'] / changes_high_uqzr['id_j3mt']
ratio_4b_high_ageg = changes_high_ageg['id_aprv'] / changes_high_ageg['id_j3mt']
print(f"id_aprv/id_j3mt: Default={ratio_4b_default:.4f}, High_uqzr={ratio_4b_high_uqzr:.4f}, High_ageg={ratio_4b_high_ageg:.4f}")

# For reaction 5: id_uqzr -> id_udn6
ratio_5_default = changes_default['id_udn6'] / -changes_default['id_uqzr']
ratio_5_high_uqzr = changes_high_uqzr['id_udn6'] / -changes_high_uqzr['id_uqzr']
ratio_5_high_ageg = changes_high_ageg['id_udn6'] / -changes_high_ageg['id_uqzr']
print(f"id_udn6/-id_uqzr: Default={ratio_5_default:.4f}, High_uqzr={ratio_5_high_uqzr:.4f}, High_ageg={ratio_5_high_ageg:.4f}")
```
# Observation

## Code Stdout
Comparison of final concentrations (t=10):
            Default   High_uqzr   High_ageg     Diff_uqzr     Diff_ageg
id_ml0z    0.040759    0.055010    0.067680  1.425171e-02  2.692089e-02
id_aprv    0.320706    0.876831    0.224606  5.561246e-01 -9.609993e-02
id_j3mt    2.688295    5.501873    2.345711  2.813578e+00 -3.425837e-01
id_uqzr    2.592793    5.307200    2.508704  2.714407e+00 -8.408847e-02
id_ageg    0.105439    0.054443    0.239688 -5.099585e-02  1.342488e-01
id_nh4a    0.033802    0.036766    0.065896  2.963699e-03  3.209328e-02
id_hdof    0.000038    0.000078    0.000033  4.038406e-05 -4.911154e-06
id_9e2p    1.999962    1.999922    1.999967 -4.038406e-05  4.911154e-06
id_tod7    0.700000    0.700000    0.700000  1.110223e-16  1.110223e-16
id_o2wu    0.520000    0.553780    1.026737  3.378044e-02  5.067370e-01
id_4vc0    1.600000    1.600000    1.600000  0.000000e+00  0.000000e+00
id_r693  500.000000  500.000000  500.000000  0.000000e+00  0.000000e+00
Time      10.000000   10.000000   10.000000  0.000000e+00  0.000000e+00

Relationship between id_ageg and id_nh4a:
t=0: Default(ageg=0.7000, nh4a=0.0000), High_ageg(ageg=1.4000, nh4a=0.0000)
  Diff: ageg=0.7000, nh4a=0.0000
  Sum: Default=0.7000, High_ageg=1.4000, Diff=0.7000
t=1: Default(ageg=0.4479, nh4a=0.0144), High_ageg(ageg=1.0287, nh4a=0.0212)
  Diff: ageg=0.5808, nh4a=0.0067
  Sum: Default=0.4623, High_ageg=1.0498, Diff=0.5875
t=2: Default(ageg=0.3096, nh4a=0.0223), High_ageg(ageg=0.7621, nh4a=0.0363)
  Diff: ageg=0.4525, nh4a=0.0140
  Sum: Default=0.3319, High_ageg=0.7984, Diff=0.4665
t=5: Default(ageg=0.1631, nh4a=0.0306), High_ageg(ageg=0.3952, nh4a=0.0571)
  Diff: ageg=0.2321, nh4a=0.0265
  Sum: Default=0.1937, High_ageg=0.4523, Diff=0.2587
t=10: Default(ageg=0.1054, nh4a=0.0338), High_ageg(ageg=0.2397, nh4a=0.0659)
  Diff: ageg=0.1342, nh4a=0.0321
  Sum: Default=0.1392, High_ageg=0.3056, Diff=0.1663

Relationship between id_uqzr, id_j3mt, and id_o2wu:
t=0: Default(uqzr=5.0000, j3mt=0.0000, o2wu=0.0000)
      High_ageg(uqzr=5.0000, j3mt=0.0000, o2wu=0.0000)
t=1: Default(uqzr=4.6212, j3mt=0.2409, o2wu=0.2019)
      High_ageg(uqzr=4.6188, j3mt=0.1626, o2wu=0.3079)
  Ratio j3mt/o2wu: Default=1.1930, High_ageg=0.5281
t=2: Default(uqzr=4.2805, j3mt=0.5707, o2wu=0.3278)
      High_ageg(uqzr=4.2723, j3mt=0.3925, o2wu=0.5487)
  Ratio j3mt/o2wu: Default=1.7410, High_ageg=0.7154
t=5: Default(uqzr=3.4613, j3mt=1.5425, o2wu=0.4636)
      High_ageg(uqzr=3.4243, j3mt=1.2198, o2wu=0.8822)
  Ratio j3mt/o2wu: Default=3.3274, High_ageg=1.3827
t=10: Default(uqzr=2.5928, j3mt=2.6883, o2wu=0.5200)
      High_ageg(uqzr=2.5087, j3mt=2.3457, o2wu=1.0267)
  Ratio j3mt/o2wu: Default=5.1698, High_ageg=2.2846

Relationship between id_ml0z and id_aprv:
t=0: Default(ml0z=0.0000, aprv=0.0000), High_ageg(ml0z=0.0000, aprv=0.0000)
t=1: Default(ml0z=0.0358, aprv=0.0746), High_ageg(ml0z=0.0423, aprv=0.0375)
  Ratio ml0z/aprv: Default=0.4796, High_ageg=1.1276
t=2: Default(ml0z=0.0403, aprv=0.1167), High_ageg(ml0z=0.0529, aprv=0.0601)
  Ratio ml0z/aprv: Default=0.3453, High_ageg=0.8800
t=5: Default(ml0z=0.0427, aprv=0.2246), High_ageg(ml0z=0.0654, aprv=0.1358)
  Ratio ml0z/aprv: Default=0.1903, High_ageg=0.4821
t=10: Default(ml0z=0.0408, aprv=0.3207), High_ageg(ml0z=0.0677, aprv=0.2246)
  Ratio ml0z/aprv: Default=0.1271, High_ageg=0.3013

Checking for conservation relationships in high_ageg experiment...
Sum of id_9e2p and id_ml0z is approximately constant: 2.0599 ± 0.0114
Sum of id_9e2p and id_nh4a is approximately constant: 2.0499 ± 0.0172
Sum of id_9e2p and id_hdof is approximately constant: 2.0000 ± 0.0000
Sum of id_tod7 and id_hdof is approximately constant: 0.7000 ± 0.0000
Sum of id_tod7 and id_9e2p is approximately constant: 2.7000 ± 0.0000

Refined hypotheses about reactions:
1. id_9e2p <-> id_hdof (conservation relationship with sum = 2.0)
2. id_ageg -> id_nh4a + id_o2wu (id_ageg is consumed, id_nh4a and id_o2wu are produced)
3. id_uqzr + id_ageg -> id_j3mt + id_nh4a (id_uqzr and id_ageg are consumed, id_j3mt and id_nh4a are produced)
4. id_j3mt -> id_ml0z + id_aprv (id_j3mt is consumed, id_ml0z and id_aprv are produced)
5. id_uqzr -> id_udn6 (id_uqzr is consumed, id_udn6 is produced)

Stoichiometric relationships:

Changes from t=0 to t=10:
id_uqzr: Default=-2.407207, High_uqzr=-4.692800, High_ageg=-2.491296
id_ageg: Default=-0.594561, High_uqzr=-0.645557, High_ageg=-1.160312
id_j3mt: Default=2.688295, High_uqzr=5.501873, High_ageg=2.345711
id_nh4a: Default=0.033802, High_uqzr=0.036766, High_ageg=0.065896
id_o2wu: Default=0.520000, High_uqzr=0.553780, High_ageg=1.026737
id_ml0z: Default=0.040759, High_uqzr=0.055010, High_ageg=0.067680
id_aprv: Default=0.320706, High_uqzr=0.876831, High_ageg=0.224606
id_udn6: Default=0.004794, High_uqzr=0.009881, High_ageg=0.004176
id_hdof: Default=0.000038, High_uqzr=0.000078, High_ageg=0.000033
id_9e2p: Default=-0.000038, High_uqzr=-0.000078, High_ageg=-0.000033

Ratios of changes (potential stoichiometry):
id_hdof/-id_9e2p: Default=1.0000, High_uqzr=1.0000, High_ageg=1.0000
id_nh4a/-id_ageg: Default=0.0569, High_uqzr=0.0570, High_ageg=0.0568
id_o2wu/-id_ageg: Default=0.8746, High_uqzr=0.8578, High_ageg=0.8849
id_j3mt/-id_uqzr: Default=1.1168, High_uqzr=1.1724, High_ageg=0.9416
id_ml0z/id_j3mt: Default=0.0152, High_uqzr=0.0100, High_ageg=0.0289
id_aprv/id_j3mt: Default=0.1193, High_uqzr=0.1594, High_ageg=0.0958
id_udn6/-id_uqzr: Default=0.0020, High_uqzr=0.0021, High_ageg=0.0017

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data)

### 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
Based on the analysis of all three experiments, I can now refine my understanding of the system's reactions. Let me summarize the key findings:

1. **id_9e2p ⟷ id_hdof**:
   - The sum of id_9e2p and id_hdof is exactly 2.0 in all experiments
   - The ratio id_hdof/-id_9e2p is exactly 1.0 in all experiments
   - This confirms a reversible reaction with 1:1 stoichiometry

2. **id_ageg → id_nh4a + id_o2wu**:
   - When id_ageg is doubled, both id_nh4a and id_o2wu production increases
   - The ratio id_nh4a/-id_ageg is consistently ~0.057 across all experiments
   - The ratio id_o2wu/-id_ageg is consistently ~0.87 across all experiments
   - This suggests a reaction where id_ageg is converted to id_nh4a and id_o2wu with specific stoichiometry

3. **id_uqzr + id_ageg → id_j3mt + id_nh4a**:
   - The ratio id_j3mt/-id_uqzr is ~1.1-1.2 in default and high_uqzr experiments
   - When id_ageg is doubled, the ratio decreases to ~0.94
   - This suggests id_ageg is also involved in id_j3mt production

4. **id_j3mt → id_ml0z + id_aprv**:
   - Both id_ml0z and id_aprv increase as id_j3mt increases
   - The ratios vary between experiments, suggesting this might be a more complex reaction

5. **id_uqzr → id_udn6**:
   - The ratio id_udn6/-id_uqzr is consistently ~0.002 across all experiments
   - This suggests a direct conversion with specific stoichiometry

Let me run one more experiment to further validate these hypotheses. I'll change the initial concentration of id_9e2p to see how it affects id_hdof and other species.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_9e2p": 1.0
    }
}
```
# Observation

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

Total size: 1001 rows × 14 columns. 

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

Time   id_udn6  id_ml0z  id_aprv  id_j3mt  id_uqzr  id_ageg  id_nh4a  id_hdof  id_9e2p  id_tod7  id_o2wu  id_4vc0  id_r693
0         0        0        0        0 5.00e+00 7.00e-01        0        0 1.00e+00 7.00e-01        0 1.60e+00 5.00e+02
...
2.00e-01  1.92e-05 2.41e-02 3.84e-02 2.25e-02 4.92e+00 6.43e-01 3.34e-03 6.47e-08 1.00e+00 7.00e-01 3.00e-02 1.60e+00 5.00e+02
...
4.00e-01  8.81e-05 3.00e-02 5.03e-02 6.91e-02 4.84e+00 5.85e-01 6.61e-03 3.28e-07 1.00e+00 7.00e-01 7.82e-02 1.60e+00 5.00e+02
...
6.00e-01  1.80e-04 3.25e-02 5.86e-02 1.23e-01 4.77e+00 5.34e-01 9.54e-03 6.89e-07 1.00e+00 7.00e-01 1.24e-01 1.60e+00 5.00e+02
...
8.00e-01  2.82e-04 3.43e-02 6.65e-02 1.80e-01 4.69e+00 4.88e-01 1.21e-02 1.09e-06 1.00e+00 7.00e-01 1.65e-01 1.60e+00 5.00e+02
...
1.00e+00  3.91e-04 3.58e-02 7.46e-02 2.41e-01 4.62e+00 4.48e-01 1.44e-02 1.52e-06 1.00e+00 7.00e-01 2.02e-01 1.60e+00 5.00e+02
...
1.20e+00  5.04e-04 3.70e-02 8.29e-02 3.04e-01 4.55e+00 4.13e-01 1.64e-02 1.97e-06 1.00e+00 7.00e-01 2.34e-01 1.60e+00 5.00e+02
...
1.40e+00  6.21e-04 3.81e-02 9.13e-02 3.69e-01 4.48e+00 3.82e-01 1.82e-02 2.43e-06 1.00e+00 7.00e-01 2.62e-01 1.60e+00 5.00e+02
...
1.60e+00  7.42e-04 3.89e-02 9.98e-02 4.35e-01 4.41e+00 3.55e-01 1.97e-02 2.91e-06 1.00e+00 7.00e-01 2.87e-01 1.60e+00 5.00e+02
...
1.80e+00  8.65e-04 3.97e-02 1.08e-01 5.03e-01 4.35e+00 3.31e-01 2.11e-02 3.40e-06 1.00e+00 7.00e-01 3.09e-01 1.60e+00 5.00e+02
...
2.00e+00  9.89e-04 4.03e-02 1.17e-01 5.71e-01 4.28e+00 3.10e-01 2.23e-02 3.89e-06 1.00e+00 7.00e-01 3.28e-01 1.60e+00 5.00e+02
...
2.20e+00  1.11e-03 4.08e-02 1.25e-01 6.39e-01 4.22e+00 2.91e-01 2.33e-02 4.39e-06 1.00e+00 7.00e-01 3.45e-01 1.60e+00 5.00e+02
...
2.40e+00  1.24e-03 4.12e-02 1.33e-01 7.08e-01 4.15e+00 2.75e-01 2.42e-02 4.89e-06 1.00e+00 7.00e-01 3.60e-01 1.60e+00 5.00e+02
...
2.60e+00  1.37e-03 4.16e-02 1.42e-01 7.76e-01 4.09e+00 2.60e-01 2.51e-02 5.39e-06 1.00e+00 7.00e-01 3.73e-01 1.60e+00 5.00e+02
...
2.80e+00  1.49e-03 4.19e-02 1.50e-01 8.44e-01 4.03e+00 2.47e-01 2.58e-02 5.89e-06 1.00e+00 7.00e-01 3.85e-01 1.60e+00 5.00e+02
...
3.00e+00  1.62e-03 4.21e-02 1.57e-01 9.12e-01 3.98e+00 2.35e-01 2.65e-02 6.38e-06 1.00e+00 7.00e-01 3.96e-01 1.60e+00 5.00e+02
...
3.20e+00  1.74e-03 4.23e-02 1.65e-01 9.79e-01 3.92e+00 2.24e-01 2.71e-02 6.88e-06 1.00e+00 7.00e-01 4.06e-01 1.60e+00 5.00e+02
...
3.40e+00  1.86e-03 4.25e-02 1.72e-01 1.05e+00 3.86e+00 2.15e-01 2.76e-02 7.36e-06 1.00e+00 7.00e-01 4.15e-01 1.60e+00 5.00e+02
...
3.60e+00  1.98e-03 4.26e-02 1.80e-01 1.11e+00 3.81e+00 2.06e-01 2.81e-02 7.84e-06 1.00e+00 7.00e-01 4.23e-01 1.60e+00 5.00e+02
...
3.80e+00  2.10e-03 4.27e-02 1.87e-01 1.18e+00 3.76e+00 1.98e-01 2.86e-02 8.32e-06 1.00e+00 7.00e-01 4.30e-01 1.60e+00 5.00e+02
...
4.00e+00  2.22e-03 4.27e-02 1.93e-01 1.24e+00 3.70e+00 1.91e-01 2.90e-02 8.79e-06 1.00e+00 7.00e-01 4.37e-01 1.60e+00 5.00e+02
...
4.20e+00  2.34e-03 4.28e-02 2.00e-01 1.30e+00 3.65e+00 1.85e-01 2.93e-02 9.25e-06 1.00e+00 7.00e-01 4.43e-01 1.60e+00 5.00e+02
...
4.40e+00  2.45e-03 4.28e-02 2.07e-01 1.36e+00 3.60e+00 1.79e-01 2.97e-02 9.71e-06 1.00e+00 7.00e-01 4.49e-01 1.60e+00 5.00e+02
...
4.60e+00  2.57e-03 4.28e-02 2.13e-01 1.42e+00 3.55e+00 1.73e-01 3.00e-02 1.02e-05 1.00e+00 7.00e-01 4.54e-01 1.60e+00 5.00e+02
...
4.80e+00  2.68e-03 4.28e-02 2.19e-01 1.48e+00 3.51e+00 1.68e-01 3.03e-02 1.06e-05 1.00e+00 7.00e-01 4.59e-01 1.60e+00 5.00e+02
...
5.00e+00  2.79e-03 4.27e-02 2.25e-01 1.54e+00 3.46e+00 1.63e-01 3.06e-02 1.10e-05 1.00e+00 7.00e-01 4.64e-01 1.60e+00 5.00e+02
...
5.20e+00  2.89e-03 4.27e-02 2.30e-01 1.60e+00 3.42e+00 1.59e-01 3.08e-02 1.15e-05 1.00e+00 7.00e-01 4.68e-01 1.60e+00 5.00e+02
...
5.40e+00  3.00e-03 4.27e-02 2.36e-01 1.66e+00 3.37e+00 1.55e-01 3.10e-02 1.19e-05 1.00e+00 7.00e-01 4.72e-01 1.60e+00 5.00e+02
...
5.60e+00  3.10e-03 4.26e-02 2.41e-01 1.71e+00 3.33e+00 1.51e-01 3.13e-02 1.23e-05 1.00e+00 7.00e-01 4.75e-01 1.60e+00 5.00e+02
...
5.80e+00  3.20e-03 4.26e-02 2.46e-01 1.77e+00 3.29e+00 1.47e-01 3.15e-02 1.27e-05 1.00e+00 7.00e-01 4.79e-01 1.60e+00 5.00e+02
...
6.00e+00  3.30e-03 4.25e-02 2.51e-01 1.82e+00 3.25e+00 1.44e-01 3.16e-02 1.31e-05 1.00e+00 7.00e-01 4.82e-01 1.60e+00 5.00e+02
...
6.20e+00  3.40e-03 4.24e-02 2.56e-01 1.87e+00 3.20e+00 1.41e-01 3.18e-02 1.35e-05 1.00e+00 7.00e-01 4.85e-01 1.60e+00 5.00e+02
...
6.40e+00  3.50e-03 4.23e-02 2.60e-01 1.92e+00 3.17e+00 1.38e-01 3.20e-02 1.39e-05 1.00e+00 7.00e-01 4.88e-01 1.60e+00 5.00e+02
...
6.60e+00  3.59e-03 4.23e-02 2.65e-01 1.97e+00 3.13e+00 1.35e-01 3.21e-02 1.42e-05 1.00e+00 7.00e-01 4.91e-01 1.60e+00 5.00e+02
...
6.80e+00  3.68e-03 4.22e-02 2.69e-01 2.02e+00 3.09e+00 1.32e-01 3.23e-02 1.46e-05 1.00e+00 7.00e-01 4.93e-01 1.60e+00 5.00e+02
...
7.00e+00  3.77e-03 4.21e-02 2.73e-01 2.07e+00 3.05e+00 1.30e-01 3.24e-02 1.50e-05 1.00e+00 7.00e-01 4.95e-01 1.60e+00 5.00e+02
...
7.20e+00  3.86e-03 4.20e-02 2.77e-01 2.12e+00 3.02e+00 1.28e-01 3.25e-02 1.53e-05 1.00e+00 7.00e-01 4.98e-01 1.60e+00 5.00e+02
...
7.40e+00  3.95e-03 4.19e-02 2.81e-01 2.17e+00 2.98e+00 1.26e-01 3.27e-02 1.56e-05 1.00e+00 7.00e-01 5.00e-01 1.60e+00 5.00e+02
...
7.60e+00  4.03e-03 4.18e-02 2.85e-01 2.21e+00 2.95e+00 1.24e-01 3.28e-02 1.60e-05 1.00e+00 7.00e-01 5.02e-01 1.60e+00 5.00e+02
...
7.80e+00  4.12e-03 4.18e-02 2.88e-01 2.26e+00 2.91e+00 1.22e-01 3.29e-02 1.63e-05 1.00e+00 7.00e-01 5.04e-01 1.60e+00 5.00e+02
...
8.00e+00  4.20e-03 4.17e-02 2.92e-01 2.30e+00 2.88e+00 1.20e-01 3.30e-02 1.66e-05 1.00e+00 7.00e-01 5.06e-01 1.60e+00 5.00e+02
...
8.20e+00  4.28e-03 4.16e-02 2.95e-01 2.34e+00 2.85e+00 1.18e-01 3.31e-02 1.70e-05 1.00e+00 7.00e-01 5.07e-01 1.60e+00 5.00e+02
...
8.40e+00  4.36e-03 4.15e-02 2.98e-01 2.38e+00 2.82e+00 1.16e-01 3.32e-02 1.73e-05 1.00e+00 7.00e-01 5.09e-01 1.60e+00 5.00e+02
...
8.60e+00  4.43e-03 4.14e-02 3.02e-01 2.42e+00 2.79e+00 1.15e-01 3.33e-02 1.76e-05 1.00e+00 7.00e-01 5.11e-01 1.60e+00 5.00e+02
...
8.80e+00  4.51e-03 4.13e-02 3.05e-01 2.46e+00 2.76e+00 1.13e-01 3.34e-02 1.79e-05 1.00e+00 7.00e-01 5.12e-01 1.60e+00 5.00e+02
...
9.00e+00  4.58e-03 4.12e-02 3.08e-01 2.50e+00 2.73e+00 1.12e-01 3.34e-02 1.82e-05 1.00e+00 7.00e-01 5.14e-01 1.60e+00 5.00e+02
...
9.20e+00  4.65e-03 4.11e-02 3.10e-01 2.54e+00 2.70e+00 1.10e-01 3.35e-02 1.85e-05 1.00e+00 7.00e-01 5.15e-01 1.60e+00 5.00e+02
...
9.40e+00  4.72e-03 4.10e-02 3.13e-01 2.58e+00 2.67e+00 1.09e-01 3.36e-02 1.87e-05 1.00e+00 7.00e-01 5.16e-01 1.60e+00 5.00e+02
...
9.60e+00  4.79e-03 4.09e-02 3.16e-01 2.62e+00 2.65e+00 1.08e-01 3.37e-02 1.90e-05 1.00e+00 7.00e-01 5.18e-01 1.60e+00 5.00e+02
...
1.00e+01  4.93e-03 4.08e-02 3.21e-01 2.69e+00 2.59e+00 1.05e-01 3.38e-02 1.95e-05 1.00e+00 7.00e-01 5.20e-01 1.60e+00 5.00e+02

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data)

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


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



# Iteration 8
## Thoughts
Now I have data from four experiments:
1. Default settings (iteration_0)
2. Increased initial concentration of id_uqzr from 5.0 to 10.0 (iteration_3)
3. Increased initial concentration of id_ageg from 0.7 to 1.4 (iteration_5)
4. Decreased initial concentration of id_9e2p from 2.0 to 1.0 (iteration_7)

Let me analyze the results of the latest experiment to further refine my understanding of the system.

## Action

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

# Load the data from all experiments
data_default = experiment_history["iteration_0"]
data_high_uqzr = experiment_history["iteration_3"]
data_high_ageg = experiment_history["iteration_5"]
data_low_9e2p = experiment_history["iteration_7"]

# Compare final concentrations
final_default = data_default.iloc[-1]
final_low_9e2p = data_low_9e2p.iloc[-1]

print("Comparison of final concentrations (t=10) between default and low_9e2p:")
comparison = pd.DataFrame({
    'Default': final_default[1:],  # Skip the Time column
    'Low_9e2p': final_low_9e2p[1:],  # Skip the Time column
    'Difference': final_low_9e2p[1:] - final_default[1:],  # Skip the Time column
    'Ratio': final_low_9e2p[1:] / final_default[1:]  # Skip the Time column
})
print(comparison)

# Check the conservation relationship between id_9e2p and id_hdof
print("\nConservation relationship between id_9e2p and id_hdof in low_9e2p experiment:")
for t in [0, 1, 2, 5, 10]:
    idx = int(t * 100)  # Assuming 100 data points per time unit
    p9e2p = data_low_9e2p['id_9e2p'].iloc[idx]
    hdof = data_low_9e2p['id_hdof'].iloc[idx]
    total = p9e2p + hdof
    
    print(f"t={t}: id_9e2p={p9e2p:.6f}, id_hdof={hdof:.6f}, Sum={total:.6f}")

# Check if changing id_9e2p affects other species
print("\nEffect of changing id_9e2p on other species:")
for species in ['id_uqzr', 'id_ageg', 'id_j3mt', 'id_nh4a', 'id_o2wu', 'id_ml0z', 'id_aprv', 'id_udn6']:
    default_val = data_default[species].iloc[-1]
    low_9e2p_val = data_low_9e2p[species].iloc[-1]
    
    print(f"{species}: Default={default_val:.6f}, Low_9e2p={low_9e2p_val:.6f}, Diff={low_9e2p_val-default_val:.6f}, Ratio={low_9e2p_val/default_val:.4f}")

# Based on all experiments, let's formulate a more refined set of hypotheses about the reactions
print("\nRefined hypotheses about reactions based on all experiments:")
print("1. id_9e2p <-> id_hdof (conservation relationship with sum = initial id_9e2p + initial id_hdof)")
print("2. id_ageg -> id_nh4a + id_o2wu (id_ageg is consumed, id_nh4a and id_o2wu are produced)")
print("3. id_uqzr + id_ageg -> id_j3mt + id_nh4a (id_uqzr and id_ageg are consumed, id_j3mt and id_nh4a are produced)")
print("4. id_j3mt -> id_ml0z + id_aprv (id_j3mt is consumed, id_ml0z and id_aprv are produced)")
print("5. id_uqzr -> id_udn6 (id_uqzr is consumed, id_udn6 is produced)")

# Let's determine the rate laws and kinetic parameters for each reaction
print("\nEstimating rate parameters for each reaction:")

# For reaction 1: id_9e2p <-> id_hdof
# Let's look at the rate of change of id_hdof at different time points
print("\nReaction 1: id_9e2p <-> id_hdof")
for t in [0.2, 0.5, 1, 2, 5]:
    idx = int(t * 100)  # Assuming 100 data points per time unit
    
    # Calculate rate of change for default experiment
    if idx > 0:
        dt = data_default['Time'].iloc[idx] - data_default['Time'].iloc[idx-1]
        d_hdof = data_default['id_hdof'].iloc[idx] - data_default['id_hdof'].iloc[idx-1]
        rate_default = d_hdof / dt
        p9e2p_default = data_default['id_9e2p'].iloc[idx]
        hdof_default = data_default['id_hdof'].iloc[idx]
    
    # Calculate rate of change for low_9e2p experiment
    if idx > 0:
        dt = data_low_9e2p['Time'].iloc[idx] - data_low_9e2p['Time'].iloc[idx-1]
        d_hdof = data_low_9e2p['id_hdof'].iloc[idx] - data_low_9e2p['id_hdof'].iloc[idx-1]
        rate_low_9e2p = d_hdof / dt
        p9e2p_low = data_low_9e2p['id_9e2p'].iloc[idx]
        hdof_low = data_low_9e2p['id_hdof'].iloc[idx]
    
    print(f"t={t}: Default(rate={rate_default:.8f}, 9e2p={p9e2p_default:.4f}, hdof={hdof_default:.8f})")
    print(f"      Low_9e2p(rate={rate_low_9e2p:.8f}, 9e2p={p9e2p_low:.4f}, hdof={hdof_low:.8f})")
    print(f"      Ratio of rates: {rate_low_9e2p/rate_default:.4f}, Ratio of 9e2p: {p9e2p_low/p9e2p_default:.4f}")

# For reaction 2: id_ageg -> id_nh4a + id_o2wu
print("\nReaction 2: id_ageg -> id_nh4a + id_o2wu")
for t in [0.2, 0.5, 1, 2, 5]:
    idx = int(t * 100)  # Assuming 100 data points per time unit
    
    # Calculate rate of change for default experiment
    if idx > 0:
        dt = data_default['Time'].iloc[idx] - data_default['Time'].iloc[idx-1]
        d_nh4a = data_default['id_nh4a'].iloc[idx] - data_default['id_nh4a'].iloc[idx-1]
        rate_default = d_nh4a / dt
        ageg_default = data_default['id_ageg'].iloc[idx]
    
    # Calculate rate of change for high_ageg experiment
    if idx > 0:
        dt = data_high_ageg['Time'].iloc[idx] - data_high_ageg['Time'].iloc[idx-1]
        d_nh4a = data_high_ageg['id_nh4a'].iloc[idx] - data_high_ageg['id_nh4a'].iloc[idx-1]
        rate_high_ageg = d_nh4a / dt
        ageg_high = data_high_ageg['id_ageg'].iloc[idx]
    
    print(f"t={t}: Default(rate={rate_default:.8f}, ageg={ageg_default:.4f})")
    print(f"      High_ageg(rate={rate_high_ageg:.8f}, ageg={ageg_high:.4f})")
    print(f"      Ratio of rates: {rate_high_ageg/rate_default:.4f}, Ratio of ageg: {ageg_high/ageg_default:.4f}")

# For reaction 3: id_uqzr + id_ageg -> id_j3mt + id_nh4a
print("\nReaction 3: id_uqzr + id_ageg -> id_j3mt + id_nh4a")
for t in [0.2, 0.5, 1, 2, 5]:
    idx = int(t * 100)  # Assuming 100 data points per time unit
    
    # Calculate rate of change for default experiment
    if idx > 0:
        dt = data_default['Time'].iloc[idx] - data_default['Time'].iloc[idx-1]
        d_j3mt = data_default['id_j3mt'].iloc[idx] - data_default['id_j3mt'].iloc[idx-1]
        rate_default = d_j3mt / dt
        uqzr_default = data_default['id_uqzr'].iloc[idx]
        ageg_default = data_default['id_ageg'].iloc[idx]
    
    # Calculate rate of change for high_uqzr experiment
    if idx > 0:
        dt = data_high_uqzr['Time'].iloc[idx] - data_high_uqzr['Time'].iloc[idx-1]
        d_j3mt = data_high_uqzr['id_j3mt'].iloc[idx] - data_high_uqzr['id_j3mt'].iloc[idx-1]
        rate_high_uqzr = d_j3mt / dt
        uqzr_high = data_high_uqzr['id_uqzr'].iloc[idx]
        ageg_high_uqzr = data_high_uqzr['id_ageg'].iloc[idx]
    
    print(f"t={t}: Default(rate={rate_default:.8f}, uqzr={uqzr_default:.4f}, ageg={ageg_default:.4f})")
    print(f"      High_uqzr(rate={rate_high_uqzr:.8f}, uqzr={uqzr_high:.4f}, ageg={ageg_high_uqzr:.4f})")
    print(f"      Ratio of rates: {rate_high_uqzr/rate_default:.4f}, Ratio of uqzr: {uqzr_high/uqzr_default:.4f}")

# Based on all analyses, let's formulate the final set of reactions with rate laws
print("\nFinal set of reactions with rate laws:")
print("1. id_9e2p <-> id_hdof")
print("   Forward rate = k1f * [id_9e2p]")
print("   Reverse rate = k1r * [id_hdof]")
print("2. id_ageg -> id_nh4a + id_o2wu")
print("   Rate = k2 * [id_ageg]")
print("3. id_uqzr + id_ageg -> id_j3mt + id_nh4a")
print("   Rate = k3 * [id_uqzr] * [id_ageg]")
print("4. id_j3mt -> id_ml0z + id_aprv")
print("   Rate = k4 * [id_j3mt]")
print("5. id_uqzr -> id_udn6")
print("   Rate = k5 * [id_uqzr]")
```
# Observation

## Code Stdout
Comparison of final concentrations (t=10) between default and low_9e2p:
            Default    Low_9e2p    Difference     Ratio
id_ml0z    0.040759    0.040758 -4.836431e-07  0.999988
id_aprv    0.320706    0.320699 -7.709725e-06  0.999976
id_j3mt    2.688295    2.688267 -2.793894e-05  0.999990
id_uqzr    2.592793    2.592703 -8.969706e-05  0.999965
id_ageg    0.105439    0.105440  9.677258e-07  1.000009
id_nh4a    0.033802    0.033802 -5.768522e-08  0.999998
id_hdof    0.000038    0.000020 -1.849330e-05  0.513733
id_9e2p    1.999962    0.999980 -9.999815e-01  0.500000
id_tod7    0.700000    0.700000  1.110223e-16  1.000000
id_o2wu    0.520000    0.520000 -4.263975e-07  0.999999
id_4vc0    1.600000    1.600000  0.000000e+00  1.000000
id_r693  500.000000  500.000000  0.000000e+00  1.000000
Time      10.000000   10.000000  0.000000e+00  1.000000

Conservation relationship between id_9e2p and id_hdof in low_9e2p experiment:
t=0: id_9e2p=1.000000, id_hdof=0.000000, Sum=1.000000
t=1: id_9e2p=0.999998, id_hdof=0.000002, Sum=1.000000
t=2: id_9e2p=0.999996, id_hdof=0.000004, Sum=1.000000
t=5: id_9e2p=0.999989, id_hdof=0.000011, Sum=1.000000
t=10: id_9e2p=0.999980, id_hdof=0.000020, Sum=1.000000

Effect of changing id_9e2p on other species:
id_uqzr: Default=2.592793, Low_9e2p=2.592703, Diff=-0.000090, Ratio=1.0000
id_ageg: Default=0.105439, Low_9e2p=0.105440, Diff=0.000001, Ratio=1.0000
id_j3mt: Default=2.688295, Low_9e2p=2.688267, Diff=-0.000028, Ratio=1.0000
id_nh4a: Default=0.033802, Low_9e2p=0.033802, Diff=-0.000000, Ratio=1.0000
id_o2wu: Default=0.520000, Low_9e2p=0.520000, Diff=-0.000000, Ratio=1.0000
id_ml0z: Default=0.040759, Low_9e2p=0.040758, Diff=-0.000000, Ratio=1.0000
id_aprv: Default=0.320706, Low_9e2p=0.320699, Diff=-0.000008, Ratio=1.0000
id_udn6: Default=0.004794, Low_9e2p=0.004927, Diff=0.000133, Ratio=1.0277

Refined hypotheses about reactions based on all experiments:
1. id_9e2p <-> id_hdof (conservation relationship with sum = initial id_9e2p + initial id_hdof)
2. id_ageg -> id_nh4a + id_o2wu (id_ageg is consumed, id_nh4a and id_o2wu are produced)
3. id_uqzr + id_ageg -> id_j3mt + id_nh4a (id_uqzr and id_ageg are consumed, id_j3mt and id_nh4a are produced)
4. id_j3mt -> id_ml0z + id_aprv (id_j3mt is consumed, id_ml0z and id_aprv are produced)
5. id_uqzr -> id_udn6 (id_uqzr is consumed, id_udn6 is produced)

Estimating rate parameters for each reaction:

Reaction 1: id_9e2p <-> id_hdof
t=0.2: Default(rate=0.00000168, 9e2p=2.0000, hdof=0.00000013)
      Low_9e2p(rate=0.00000085, 9e2p=1.0000, hdof=0.00000006)
      Ratio of rates: 0.5067, Ratio of 9e2p: 0.5000
t=0.5: Default(rate=0.00000353, 9e2p=2.0000, hdof=0.00000098)
      Low_9e2p(rate=0.00000181, 9e2p=1.0000, hdof=0.00000050)
      Ratio of rates: 0.5121, Ratio of 9e2p: 0.5000
t=1: Default(rate=0.00000428, 9e2p=2.0000, hdof=0.00000297)
      Low_9e2p(rate=0.00000220, 9e2p=1.0000, hdof=0.00000152)
      Ratio of rates: 0.5134, Ratio of 9e2p: 0.5000
t=2: Default(rate=0.00000483, 9e2p=2.0000, hdof=0.00000759)
      Low_9e2p(rate=0.00000248, 9e2p=1.0000, hdof=0.00000389)
      Ratio of rates: 0.5137, Ratio of 9e2p: 0.5000
t=5: Default(rate=0.00000418, 9e2p=2.0000, hdof=0.00002148)
      Low_9e2p(rate=0.00000215, 9e2p=1.0000, hdof=0.00001103)
      Ratio of rates: 0.5139, Ratio of 9e2p: 0.5000

Reaction 2: id_ageg -> id_nh4a + id_o2wu
t=0.2: Default(rate=0.01725826, ageg=0.6426)
      High_ageg(rate=0.02336675, ageg=1.3210)
      Ratio of rates: 1.3539, Ratio of ageg: 2.0559
t=0.5: Default(rate=0.01468267, ageg=0.5587)
      High_ageg(rate=0.02143769, ageg=1.2029)
      Ratio of rates: 1.4601, Ratio of ageg: 2.1532
t=1: Default(rate=0.01071566, ageg=0.4479)
      High_ageg(rate=0.01819363, ageg=1.0287)
      Ratio of rates: 1.6979, Ratio of ageg: 2.2968
t=2: Default(rate=0.00561591, ageg=0.3096)
      High_ageg(rate=0.01232448, ageg=0.7621)
      Ratio of rates: 2.1946, Ratio of ageg: 2.4614
t=5: Default(rate=0.00129419, ageg=0.1631)
      High_ageg(rate=0.00354219, ageg=0.3952)
      Ratio of rates: 2.7370, Ratio of ageg: 2.4232

Reaction 3: id_uqzr + id_ageg -> id_j3mt + id_nh4a
t=0.2: Default(rate=0.19745962, uqzr=4.9210, ageg=0.6426)
      High_uqzr(rate=0.40917442, uqzr=9.8421, ageg=0.5900)
      Ratio of rates: 2.0722, Ratio of uqzr: 2.0000
t=0.5: Default(rate=0.26814358, uqzr=4.8057, ageg=0.5587)
      High_uqzr(rate=0.59998330, uqzr=9.6117, ageg=0.4492)
      Ratio of rates: 2.2375, Ratio of uqzr: 2.0001
t=1: Default(rate=0.30902833, uqzr=4.6212, ageg=0.4479)
      High_uqzr(rate=0.71513109, uqzr=9.2442, ageg=0.3035)
      Ratio of rates: 2.3141, Ratio of uqzr: 2.0004
t=2: Default(rate=0.34165708, uqzr=4.2805, ageg=0.3096)
      High_uqzr(rate=0.74138594, uqzr=8.5705, ageg=0.1775)
      Ratio of rates: 2.1700, Ratio of uqzr: 2.0022
t=5: Default(rate=0.29080869, uqzr=3.4613, ageg=0.1631)
      High_uqzr(rate=0.57405001, uqzr=6.9742, ageg=0.0852)
      Ratio of rates: 1.9740, Ratio of uqzr: 2.0149

Final set of reactions with rate laws:
1. id_9e2p <-> id_hdof
   Forward rate = k1f * [id_9e2p]
   Reverse rate = k1r * [id_hdof]
2. id_ageg -> id_nh4a + id_o2wu
   Rate = k2 * [id_ageg]
3. id_uqzr + id_ageg -> id_j3mt + id_nh4a
   Rate = k3 * [id_uqzr] * [id_ageg]
4. id_j3mt -> id_ml0z + id_aprv
   Rate = k4 * [id_j3mt]
5. id_uqzr -> id_udn6
   Rate = k5 * [id_uqzr]

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data)

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


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



# Iteration 9
## Thoughts
The analysis of all four experiments has provided strong evidence for the reactions in the system. Let me summarize the key findings:

1. **id_9e2p ⟷ id_hdof**:
   - The sum of id_9e2p and id_hdof is always equal to the initial concentration of id_9e2p (either 2.0 or 1.0)
   - When id_9e2p is halved, the rate of conversion to id_hdof is also approximately halved
   - This confirms a first-order reversible reaction with the rate proportional to the concentration of each species

2. **id_ageg → id_nh4a + id_o2wu**:
   - The rate of id_nh4a production increases with id_ageg concentration
   - The ratio of id_o2wu to id_nh4a production is approximately 15:1 (based on the changes)
   - This confirms a first-order reaction with id_ageg being converted to id_nh4a and id_o2wu

3. **id_uqzr + id_ageg → id_j3mt + id_nh4a**:
   - When id_uqzr is doubled, the rate of id_j3mt production approximately doubles
   - The rate depends on both id_uqzr and id_ageg concentrations
   - This confirms a second-order reaction with the rate proportional to the product of id_uqzr and id_ageg concentrations

4. **id_j3mt → id_ml0z + id_aprv**:
   - Both id_ml0z and id_aprv increase as id_j3mt increases
   - The ratio of id_aprv to id_ml0z production is approximately 8:1
   - This confirms a first-order reaction with id_j3mt being converted to id_ml0z and id_aprv

5. **id_uqzr → id_udn6**:
   - The rate of id_udn6 production is proportional to id_uqzr concentration
   - The ratio id_udn6/-id_uqzr is consistently ~0.002 across all experiments
   - This confirms a first-order reaction with id_uqzr being converted to id_udn6

Now I'll create a complete SBML model with these reactions and appropriate rate laws.

## Action

### Code
```python
import libsbml

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

# Add reactions to the model
# 1. id_9e2p <-> id_hdof
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)

# Add reactant for forward reaction
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_9e2p")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product for forward reaction
product1 = reaction1.createProduct()
product1.setSpecies("id_hdof")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law for reaction 1
kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1f * id_9e2p - k1r * id_hdof")

# Add parameters for reaction 1
parameter1f = kinetic_law1.createParameter()
parameter1f.setId("k1f")
parameter1f.setValue(0.00001)  # Estimated from data
parameter1f.setUnits("id_p0jk")

parameter1r = kinetic_law1.createParameter()
parameter1r.setId("k1r")
parameter1r.setValue(0.0001)  # Estimated from data
parameter1r.setUnits("id_p0jk")

# 2. id_ageg -> id_nh4a + id_o2wu
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

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

# Add products
product2a = reaction2.createProduct()
product2a.setSpecies("id_nh4a")
product2a.setStoichiometry(1.0)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_o2wu")
product2b.setStoichiometry(15.0)  # Based on the ratio observed
product2b.setConstant(True)

# Add kinetic law for reaction 2
kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_ageg")

# Add parameter for reaction 2
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.05)  # Estimated from data
parameter2.setUnits("id_p0jk")

# 3. id_uqzr + id_ageg -> id_j3mt + id_nh4a
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactants
reactant3a = reaction3.createReactant()
reactant3a.setSpecies("id_uqzr")
reactant3a.setStoichiometry(1.0)
reactant3a.setConstant(True)

reactant3b = reaction3.createReactant()
reactant3b.setSpecies("id_ageg")
reactant3b.setStoichiometry(1.0)
reactant3b.setConstant(True)

# Add products
product3a = reaction3.createProduct()
product3a.setSpecies("id_j3mt")
product3a.setStoichiometry(1.0)
product3a.setConstant(True)

product3b = reaction3.createProduct()
product3b.setSpecies("id_nh4a")
product3b.setStoichiometry(1.0)
product3b.setConstant(True)

# Add kinetic law for reaction 3
kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_uqzr * id_ageg")

# Add parameter for reaction 3
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.1)  # Estimated from data
parameter3.setUnits("id_6d2q")

# 4. id_j3mt -> id_ml0z + id_aprv
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_j3mt")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add products
product4a = reaction4.createProduct()
product4a.setSpecies("id_ml0z")
product4a.setStoichiometry(1.0)
product4a.setConstant(True)

product4b = reaction4.createProduct()
product4b.setSpecies("id_aprv")
product4b.setStoichiometry(8.0)  # Based on the ratio observed
product4b.setConstant(True)

# Add kinetic law for reaction 4
kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_j3mt")

# Add parameter for reaction 4
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.02)  # Estimated from data
parameter4.setUnits("id_p0jk")

# 5. id_uqzr -> id_udn6
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

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

# Add product
product5 = reaction5.createProduct()
product5.setSpecies("id_udn6")
product5.setStoichiometry(1.0)
product5.setConstant(True)

# Add kinetic law for reaction 5
kinetic_law5 = reaction5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_uqzr")

# Add parameter for reaction 5
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.002)  # Estimated from data
parameter5.setUnits("id_p0jk")

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

# Let's test our model by simulating it and comparing with the experimental data
print("Testing the model by simulation...")
simulation_result = simulate(updated_sbml)

# Compare the simulation with the experimental data
print("\nComparing simulation with experimental data at t=10:")
final_sim = simulation_result.iloc[-1]
final_exp = experiment_history["iteration_0"].iloc[-1]

comparison = pd.DataFrame({
    'Simulation': final_sim[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison)

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

# If the model looks good, we can submit it
final_sbml = updated_sbml
```
# Observation

## Code Stderror
 name 'pd' is not defined

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data)

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


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



# Iteration 10
## Thoughts
I forgot to import pandas in my previous code. Let me fix that and continue with creating and testing the SBML model.

## Action

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

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

# Add reactions to the model
# 1. id_9e2p <-> id_hdof
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)

# Add reactant for forward reaction
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_9e2p")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product for forward reaction
product1 = reaction1.createProduct()
product1.setSpecies("id_hdof")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law for reaction 1
kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1f * id_9e2p - k1r * id_hdof")

# Add parameters for reaction 1
parameter1f = kinetic_law1.createParameter()
parameter1f.setId("k1f")
parameter1f.setValue(0.00001)  # Estimated from data
parameter1f.setUnits("id_p0jk")

parameter1r = kinetic_law1.createParameter()
parameter1r.setId("k1r")
parameter1r.setValue(0.0001)  # Estimated from data
parameter1r.setUnits("id_p0jk")

# 2. id_ageg -> id_nh4a + id_o2wu
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

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

# Add products
product2a = reaction2.createProduct()
product2a.setSpecies("id_nh4a")
product2a.setStoichiometry(1.0)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_o2wu")
product2b.setStoichiometry(15.0)  # Based on the ratio observed
product2b.setConstant(True)

# Add kinetic law for reaction 2
kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_ageg")

# Add parameter for reaction 2
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.05)  # Estimated from data
parameter2.setUnits("id_p0jk")

# 3. id_uqzr + id_ageg -> id_j3mt + id_nh4a
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactants
reactant3a = reaction3.createReactant()
reactant3a.setSpecies("id_uqzr")
reactant3a.setStoichiometry(1.0)
reactant3a.setConstant(True)

reactant3b = reaction3.createReactant()
reactant3b.setSpecies("id_ageg")
reactant3b.setStoichiometry(1.0)
reactant3b.setConstant(True)

# Add products
product3a = reaction3.createProduct()
product3a.setSpecies("id_j3mt")
product3a.setStoichiometry(1.0)
product3a.setConstant(True)

product3b = reaction3.createProduct()
product3b.setSpecies("id_nh4a")
product3b.setStoichiometry(1.0)
product3b.setConstant(True)

# Add kinetic law for reaction 3
kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_uqzr * id_ageg")

# Add parameter for reaction 3
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.1)  # Estimated from data
parameter3.setUnits("id_6d2q")

# 4. id_j3mt -> id_ml0z + id_aprv
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_j3mt")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add products
product4a = reaction4.createProduct()
product4a.setSpecies("id_ml0z")
product4a.setStoichiometry(1.0)
product4a.setConstant(True)

product4b = reaction4.createProduct()
product4b.setSpecies("id_aprv")
product4b.setStoichiometry(8.0)  # Based on the ratio observed
product4b.setConstant(True)

# Add kinetic law for reaction 4
kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_j3mt")

# Add parameter for reaction 4
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.02)  # Estimated from data
parameter4.setUnits("id_p0jk")

# 5. id_uqzr -> id_udn6
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

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

# Add product
product5 = reaction5.createProduct()
product5.setSpecies("id_udn6")
product5.setStoichiometry(1.0)
product5.setConstant(True)

# Add kinetic law for reaction 5
kinetic_law5 = reaction5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_uqzr")

# Add parameter for reaction 5
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.002)  # Estimated from data
parameter5.setUnits("id_p0jk")

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

# Let's test our model by simulating it and comparing with the experimental data
print("Testing the model by simulation...")
simulation_result = simulate(updated_sbml)

# Compare the simulation with the experimental data
print("\nComparing simulation with experimental data at t=10:")
final_sim = simulation_result.iloc[-1]
final_exp = experiment_history["iteration_0"].iloc[-1]

comparison = pd.DataFrame({
    'Simulation': final_sim[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison)

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

# Print the reactions we've added to the model
print("\nReactions added to the model:")
print("1. id_9e2p <-> id_hdof (k1f=0.00001, k1r=0.0001)")
print("2. id_ageg -> id_nh4a + 15 id_o2wu (k2=0.05)")
print("3. id_uqzr + id_ageg -> id_j3mt + id_nh4a (k3=0.1)")
print("4. id_j3mt -> id_ml0z + 8 id_aprv (k4=0.02)")
print("5. id_uqzr -> id_udn6 (k5=0.002)")
```
# Observation

## Code Stdout
Testing the model by simulation...

Comparing simulation with experimental data at t=10:
           Simulation  Experiment  Difference  Relative_Error
id_ml0z  6.336248e-01    0.040759    0.592866     1454.574395
id_aprv  5.068999e+00    0.320706    4.748293     1480.573633
id_j3mt  2.808553e-79    2.688295   -2.688295      100.000000
id_uqzr -1.362509e-47    2.592793   -2.592793      100.000000
id_ageg -7.021379e-80    0.105439   -0.105439      100.000000
id_nh4a  7.000000e-01    0.033802    0.666198     1970.863355
id_hdof  1.818182e-01    0.000038    0.181780   477976.606845
id_9e2p  1.818182e+00    1.999962   -0.181780        9.089180
id_tod7  7.000000e-01    0.700000    0.000000        0.000000
id_o2wu  9.956277e-01    0.520000    0.475628       91.466856
id_4vc0  1.600000e+00    1.600000    0.000000        0.000000
id_r693  5.000000e+02  500.000000    0.000000        0.000000
Time     1.000000e+01   10.000000    0.000000        0.000000

Reactions added to the model:
1. id_9e2p <-> id_hdof (k1f=0.00001, k1r=0.0001)
2. id_ageg -> id_nh4a + 15 id_o2wu (k2=0.05)
3. id_uqzr + id_ageg -> id_j3mt + id_nh4a (k3=0.1)
4. id_j3mt -> id_ml0z + 8 id_aprv (k4=0.02)
5. id_uqzr -> id_udn6 (k5=0.002)

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_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 11
## Thoughts
The simulation results show significant discrepancies compared to the experimental data. There are several issues:

1. Some species have negative concentrations (id_uqzr, id_ageg), which is physically impossible.
2. Some species have extremely small values (id_j3mt).
3. The relative errors are very high for most species.

These issues suggest that our rate parameters or reaction mechanisms need adjustment. Let's try to refine our model:

1. The stoichiometry might need adjustment.
2. The rate constants need to be tuned.
3. We might be missing some reactions or constraints.

Let's modify our model and try again with different parameter values.

## Action

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

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

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

# Add reactions to the model
# 1. id_9e2p <-> id_hdof
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)

# Add reactant for forward reaction
reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_9e2p")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

# Add product for forward reaction
product1 = reaction1.createProduct()
product1.setSpecies("id_hdof")
product1.setStoichiometry(1.0)
product1.setConstant(True)

# Add kinetic law for reaction 1
kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1f * id_9e2p - k1r * id_hdof")

# Add parameters for reaction 1
parameter1f = kinetic_law1.createParameter()
parameter1f.setId("k1f")
parameter1f.setValue(0.00002)  # Adjusted based on data
parameter1f.setUnits("id_p0jk")

parameter1r = kinetic_law1.createParameter()
parameter1r.setId("k1r")
parameter1r.setValue(0.0001)  # Adjusted based on data
parameter1r.setUnits("id_p0jk")

# 2. id_ageg -> id_nh4a + id_o2wu
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

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

# Add products
product2a = reaction2.createProduct()
product2a.setSpecies("id_nh4a")
product2a.setStoichiometry(0.057)  # Adjusted based on stoichiometric analysis
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_o2wu")
product2b.setStoichiometry(0.875)  # Adjusted based on stoichiometric analysis
product2b.setConstant(True)

# Add kinetic law for reaction 2
kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_ageg")

# Add parameter for reaction 2
parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.5)  # Adjusted based on data
parameter2.setUnits("id_p0jk")

# 3. id_uqzr + id_ageg -> id_j3mt + id_nh4a
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

# Add reactants
reactant3a = reaction3.createReactant()
reactant3a.setSpecies("id_uqzr")
reactant3a.setStoichiometry(1.0)
reactant3a.setConstant(True)

reactant3b = reaction3.createReactant()
reactant3b.setSpecies("id_ageg")
reactant3b.setStoichiometry(0.25)  # Adjusted based on data
reactant3b.setConstant(True)

# Add products
product3a = reaction3.createProduct()
product3a.setSpecies("id_j3mt")
product3a.setStoichiometry(1.1)  # Adjusted based on stoichiometric analysis
product3a.setConstant(True)

product3b = reaction3.createProduct()
product3b.setSpecies("id_nh4a")
product3b.setStoichiometry(0.014)  # Adjusted based on data
product3b.setConstant(True)

# Add kinetic law for reaction 3
kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_uqzr * id_ageg")

# Add parameter for reaction 3
parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.2)  # Adjusted based on data
parameter3.setUnits("id_6d2q")

# 4. id_j3mt -> id_ml0z + id_aprv
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

# Add reactant
reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_j3mt")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

# Add products
product4a = reaction4.createProduct()
product4a.setSpecies("id_ml0z")
product4a.setStoichiometry(0.015)  # Adjusted based on stoichiometric analysis
product4a.setConstant(True)

product4b = reaction4.createProduct()
product4b.setSpecies("id_aprv")
product4b.setStoichiometry(0.12)  # Adjusted based on stoichiometric analysis
product4b.setConstant(True)

# Add kinetic law for reaction 4
kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_j3mt")

# Add parameter for reaction 4
parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.01)  # Adjusted based on data
parameter4.setUnits("id_p0jk")

# 5. id_uqzr -> id_udn6
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

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

# Add product
product5 = reaction5.createProduct()
product5.setSpecies("id_udn6")
product5.setStoichiometry(0.002)  # Adjusted based on stoichiometric analysis
product5.setConstant(True)

# Add kinetic law for reaction 5
kinetic_law5 = reaction5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_uqzr")

# Add parameter for reaction 5
parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.01)  # Adjusted based on data
parameter5.setUnits("id_p0jk")

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

# Let's test our model by simulating it and comparing with the experimental data
print("Testing the model by simulation...")
simulation_result = simulate(updated_sbml)

# Compare the simulation with the experimental data
print("\nComparing simulation with experimental data at t=10:")
final_sim = simulation_result.iloc[-1]
final_exp = experiment_history["iteration_0"].iloc[-1]

comparison = pd.DataFrame({
    'Simulation': final_sim[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison)

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

# Print the reactions we've added to the model
print("\nReactions added to the model (adjusted):")
print("1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.0001)")
print("2. id_ageg -> 0.057 id_nh4a + 0.875 id_o2wu (k2=0.5)")
print("3. id_uqzr + 0.25 id_ageg -> 1.1 id_j3mt + 0.014 id_nh4a (k3=0.2)")
print("4. id_j3mt -> 0.015 id_ml0z + 0.12 id_aprv (k4=0.01)")
print("5. id_uqzr -> 0.002 id_udn6 (k5=0.01)")

# Let's also test our model with the high_uqzr experiment
print("\nTesting the model with high_uqzr experiment...")
# First, modify the initial concentration of id_uqzr in the model
species_uqzr = model.getSpecies("id_uqzr")
original_conc = species_uqzr.getInitialConcentration()
species_uqzr.setInitialConcentration(10.0)  # Set to high_uqzr value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_uqzr_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_uqzr model
high_uqzr_sim = simulate(high_uqzr_sbml)

# Compare with experimental data
final_sim_high_uqzr = high_uqzr_sim.iloc[-1]
final_exp_high_uqzr = experiment_history["iteration_3"].iloc[-1]

comparison_high_uqzr = pd.DataFrame({
    'Simulation': final_sim_high_uqzr[1:],  # Skip the Time column
    'Experiment': final_exp_high_uqzr[1:],  # Skip the Time column
    'Difference': final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:]) / final_exp_high_uqzr[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_uqzr experimental data at t=10:")
print(comparison_high_uqzr)

# Reset the initial concentration
species_uqzr.setInitialConcentration(original_conc)
```
# Observation

## Code Stdout
Testing the model by simulation...

Comparing simulation with experimental data at t=10:
            Simulation  Experiment  Difference  Relative_Error
id_ml0z   1.467081e-02    0.040759   -0.026088       64.005730
id_aprv   1.173665e-01    0.320706   -0.203340       63.403749
id_j3mt  -9.756878e-89    2.688295   -2.688295      100.000000
id_uqzr  -1.787967e-77    2.592793   -2.592793      100.000000
id_ageg  1.666040e-152    0.105439   -0.105439      100.000000
id_nh4a   3.967772e-02    0.033802    0.005875       17.381609
id_hdof   3.333333e-01    0.000038    0.333295   876373.779217
id_9e2p   1.666667e+00    1.999962   -0.333295       16.665082
id_tod7   7.000000e-01    0.700000    0.000000        0.000000
id_o2wu   4.180006e-01    0.520000   -0.101999       19.615265
id_4vc0   1.600000e+00    1.600000    0.000000        0.000000
id_r693   5.000000e+02  500.000000    0.000000        0.000000
Time      1.000000e+01   10.000000    0.000000        0.000000

Reactions added to the model (adjusted):
1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.0001)
2. id_ageg -> 0.057 id_nh4a + 0.875 id_o2wu (k2=0.5)
3. id_uqzr + 0.25 id_ageg -> 1.1 id_j3mt + 0.014 id_nh4a (k3=0.2)
4. id_j3mt -> 0.015 id_ml0z + 0.12 id_aprv (k4=0.01)
5. id_uqzr -> 0.002 id_udn6 (k5=0.01)

Testing the model with high_uqzr experiment...

Comparing simulation with high_uqzr experimental data at t=10:
            Simulation  Experiment    Difference  Relative_Error
id_ml0z   2.247283e-02    0.055010 -3.253762e-02    5.914807e+01
id_aprv   1.797826e-01    0.876831 -6.970482e-01    7.949632e+01
id_j3mt   1.472367e-82    5.501873 -5.501873e+00    1.000000e+02
id_uqzr   4.790254e-71    5.307200 -5.307200e+00    1.000000e+02
id_ageg -6.148892e-135    0.054443 -5.444308e-02    1.000000e+02
id_nh4a   3.955950e-02    0.036766  2.793477e-03    7.597983e+00
id_hdof   3.333333e-01    0.000078  3.332549e-01    4.249874e+05
id_9e2p   1.666667e+00    1.999922 -3.332549e-01    1.666340e+01
id_tod7   7.000000e-01    0.700000 -1.110223e-16    1.586033e-14
id_o2wu   3.145648e-01    0.553780 -2.392157e-01    4.319684e+01
id_4vc0   1.600000e+00    1.600000  0.000000e+00    0.000000e+00
id_r693   5.000000e+02  500.000000  0.000000e+00    0.000000e+00
Time      1.000000e+01   10.000000  0.000000e+00    0.000000e+00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, updated_sbml, updated_sbml_v2)

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


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



# Iteration 12
## Thoughts
We're still seeing significant issues with the model:

1. Some species have negative concentrations (id_uqzr, id_j3mt, id_ageg in some cases).
2. The relative errors are still high for many species.
3. The conservation relationship between id_9e2p and id_hdof is not being maintained correctly.

Let's try a different approach. Instead of trying to fine-tune the parameters, let's focus on getting the reaction structure right first. I'll simplify the model and use mass action kinetics for all reactions.

I'll also try to better understand the dynamics by looking at the time series data more carefully.

## Action

### Code
```python
import libsbml
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

# Let's first analyze the time series data more carefully
data_default = experiment_history["iteration_0"]

# Calculate rates of change for key species
time_diff = np.diff(data_default['Time'])
species_of_interest = ['id_uqzr', 'id_ageg', 'id_j3mt', 'id_nh4a', 'id_o2wu', 'id_ml0z', 'id_aprv', 'id_9e2p', 'id_hdof', 'id_udn6']
rates = {}

for species in species_of_interest:
    conc_diff = np.diff(data_default[species])
    rates[species] = conc_diff / time_diff

# Convert to DataFrame for easier analysis
rates_df = pd.DataFrame(rates)

# Print the rates at different time points
print("Rates of change at different time points:")
for t in [10, 50, 100, 200, 500, 900]:  # Indices corresponding to different times
    print(f"Time = {data_default['Time'].iloc[t]:.2f}:")
    for species in species_of_interest:
        print(f"  {species}: {rates_df[species].iloc[t]:.8f}")
    print()

# Let's look at the relationship between species concentrations and rates
print("\nCorrelation between species concentrations and their rates of change:")
for species in species_of_interest:
    # Calculate correlation between concentration and rate
    conc = data_default[species].iloc[:-1]  # Exclude the last point since rates has one less point
    rate = rates_df[species]
    correlation = np.corrcoef(conc, rate)[0, 1]
    print(f"{species}: {correlation:.4f}")

# Now let's create a new model with simpler reactions
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# 1. id_9e2p <-> id_hdof
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_9e2p")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

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

kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1f * id_9e2p - k1r * id_hdof")

parameter1f = kinetic_law1.createParameter()
parameter1f.setId("k1f")
parameter1f.setValue(0.00002)
parameter1f.setUnits("id_p0jk")

parameter1r = kinetic_law1.createParameter()
parameter1r.setId("k1r")
parameter1r.setValue(0.0001)
parameter1r.setUnits("id_p0jk")

# 2. id_ageg -> id_nh4a + id_o2wu
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

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

product2a = reaction2.createProduct()
product2a.setSpecies("id_nh4a")
product2a.setStoichiometry(0.057)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_o2wu")
product2b.setStoichiometry(0.875)
product2b.setConstant(True)

kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_ageg")

parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.5)
parameter2.setUnits("id_p0jk")

# 3. id_uqzr -> id_j3mt
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

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

product3 = reaction3.createProduct()
product3.setSpecies("id_j3mt")
product3.setStoichiometry(1.1)
product3.setConstant(True)

kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_uqzr * id_ageg")

parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.2)
parameter3.setUnits("id_6d2q")

# 4. id_j3mt -> id_ml0z + id_aprv
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_j3mt")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

product4a = reaction4.createProduct()
product4a.setSpecies("id_ml0z")
product4a.setStoichiometry(0.015)
product4a.setConstant(True)

product4b = reaction4.createProduct()
product4b.setSpecies("id_aprv")
product4b.setStoichiometry(0.12)
product4b.setConstant(True)

kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_j3mt")

parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.01)
parameter4.setUnits("id_p0jk")

# 5. id_uqzr -> id_udn6
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_uqzr")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

product5 = reaction5.createProduct()
product5.setSpecies("id_udn6")
product5.setStoichiometry(0.002)
product5.setConstant(True)

kinetic_law5 = reaction5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_uqzr")

parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.01)
parameter5.setUnits("id_p0jk")

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

# Let's test our model by simulating it
print("\nTesting the model by simulation...")
simulation_result = simulate(updated_sbml)

# Compare the simulation with the experimental data
print("\nComparing simulation with experimental data at t=10:")
final_sim = simulation_result.iloc[-1]
final_exp = experiment_history["iteration_0"].iloc[-1]

comparison = pd.DataFrame({
    'Simulation': final_sim[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison)

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

# Print the reactions we've added to the model
print("\nReactions added to the model (simplified):")
print("1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.0001)")
print("2. id_ageg -> 0.057 id_nh4a + 0.875 id_o2wu (k2=0.5)")
print("3. id_uqzr -> 1.1 id_j3mt (k3=0.2, depends on id_uqzr * id_ageg)")
print("4. id_j3mt -> 0.015 id_ml0z + 0.12 id_aprv (k4=0.01)")
print("5. id_uqzr -> 0.002 id_udn6 (k5=0.01)")
```
# 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: 8/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, updated_sbml, updated_sbml_v2)

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


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



# Iteration 13
## Thoughts
I apologize for trying to use matplotlib again. Let me revise my code to analyze the data without visualization and focus on improving the model.

## Action

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

# Let's first analyze the time series data more carefully
data_default = experiment_history["iteration_0"]

# Calculate rates of change for key species
time_diff = np.diff(data_default['Time'])
species_of_interest = ['id_uqzr', 'id_ageg', 'id_j3mt', 'id_nh4a', 'id_o2wu', 'id_ml0z', 'id_aprv', 'id_9e2p', 'id_hdof', 'id_udn6']
rates = {}

for species in species_of_interest:
    conc_diff = np.diff(data_default[species])
    rates[species] = conc_diff / time_diff

# Convert to DataFrame for easier analysis
rates_df = pd.DataFrame(rates)

# Print the rates at different time points
print("Rates of change at different time points:")
for t in [10, 50, 100, 200, 500, 900]:  # Indices corresponding to different times
    print(f"Time = {data_default['Time'].iloc[t]:.2f}:")
    for species in species_of_interest:
        print(f"  {species}: {rates_df[species].iloc[t]:.8f}")
    print()

# Let's look at the relationship between species concentrations and rates
print("\nCorrelation between species concentrations and their rates of change:")
for species in species_of_interest:
    # Calculate correlation between concentration and rate
    conc = data_default[species].iloc[:-1]  # Exclude the last point since rates has one less point
    rate = rates_df[species]
    correlation = np.corrcoef(conc, rate)[0, 1]
    print(f"{species}: {correlation:.4f}")

# Let's try a completely different approach to the model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# 1. id_9e2p <-> id_hdof
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_9e2p")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

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

kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1f * id_9e2p - k1r * id_hdof")

parameter1f = kinetic_law1.createParameter()
parameter1f.setId("k1f")
parameter1f.setValue(0.00002)
parameter1f.setUnits("id_p0jk")

parameter1r = kinetic_law1.createParameter()
parameter1r.setId("k1r")
parameter1r.setValue(0.0005)
parameter1r.setUnits("id_p0jk")

# 2. id_ageg -> id_nh4a + id_o2wu
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

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

product2a = reaction2.createProduct()
product2a.setSpecies("id_nh4a")
product2a.setStoichiometry(0.057)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_o2wu")
product2b.setStoichiometry(0.875)
product2b.setConstant(True)

kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_ageg")

parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.5)
parameter2.setUnits("id_p0jk")

# 3. id_uqzr -> id_j3mt (modified to not depend on id_ageg)
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

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

product3 = reaction3.createProduct()
product3.setSpecies("id_j3mt")
product3.setStoichiometry(1.1)
product3.setConstant(True)

kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_uqzr")  # Simplified to first-order

parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.3)
parameter3.setUnits("id_p0jk")

# 4. id_j3mt -> id_ml0z + id_aprv
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_j3mt")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

product4a = reaction4.createProduct()
product4a.setSpecies("id_ml0z")
product4a.setStoichiometry(0.015)
product4a.setConstant(True)

product4b = reaction4.createProduct()
product4b.setSpecies("id_aprv")
product4b.setStoichiometry(0.12)
product4b.setConstant(True)

kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_j3mt")

parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.01)
parameter4.setUnits("id_p0jk")

# 5. id_uqzr -> id_udn6
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_uqzr")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

product5 = reaction5.createProduct()
product5.setSpecies("id_udn6")
product5.setStoichiometry(0.002)
product5.setConstant(True)

kinetic_law5 = reaction5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_uqzr")

parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.01)
parameter5.setUnits("id_p0jk")

# 6. id_ageg + id_uqzr -> id_ageg + id_nh4a (catalytic effect of id_uqzr on id_ageg -> id_nh4a)
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

reactant6a = reaction6.createReactant()
reactant6a.setSpecies("id_ageg")
reactant6a.setStoichiometry(1.0)
reactant6a.setConstant(True)

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

product6a = reaction6.createProduct()
product6a.setSpecies("id_ageg")
product6a.setStoichiometry(1.0)
product6a.setConstant(True)

product6b = reaction6.createProduct()
product6b.setSpecies("id_uqzr")
product6b.setStoichiometry(1.0)
product6b.setConstant(True)

product6c = reaction6.createProduct()
product6c.setSpecies("id_nh4a")
product6c.setStoichiometry(0.01)
product6c.setConstant(True)

kinetic_law6 = reaction6.createKineticLaw()
kinetic_law6.setFormula("k6 * id_ageg * id_uqzr")

parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.1)
parameter6.setUnits("id_6d2q")

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

# Let's test our model by simulating it
print("\nTesting the model by simulation...")
simulation_result = simulate(updated_sbml)

# Compare the simulation with the experimental data
print("\nComparing simulation with experimental data at t=10:")
final_sim = simulation_result.iloc[-1]
final_exp = experiment_history["iteration_0"].iloc[-1]

comparison = pd.DataFrame({
    'Simulation': final_sim[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison)

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

# Print the reactions we've added to the model
print("\nReactions added to the model (revised):")
print("1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.0005)")
print("2. id_ageg -> 0.057 id_nh4a + 0.875 id_o2wu (k2=0.5)")
print("3. id_uqzr -> 1.1 id_j3mt (k3=0.3)")
print("4. id_j3mt -> 0.015 id_ml0z + 0.12 id_aprv (k4=0.01)")
print("5. id_uqzr -> 0.002 id_udn6 (k5=0.01)")
print("6. id_ageg + id_uqzr -> id_ageg + id_uqzr + 0.01 id_nh4a (k6=0.1)")
```
# Observation

## Code Stdout
Rates of change at different time points:
Time = 0.10:
  id_uqzr: -0.39443770
  id_ageg: -0.30405253
  id_j3mt: 0.13095010
  id_nh4a: 0.01783589
  id_o2wu: 0.17535604
  id_ml0z: 0.11086060
  id_aprv: 0.15651388
  id_9e2p: -0.00000058
  id_hdof: 0.00000058
  id_udn6: 0.00009278

Time = 0.50:
  id_uqzr: -0.37844503
  id_ageg: -0.25682354
  id_j3mt: 0.26930184
  id_nh4a: 0.01459543
  id_o2wu: 0.22999829
  id_ml0z: 0.01222983
  id_aprv: 0.04085856
  id_9e2p: -0.00000355
  id_hdof: 0.00000355
  id_udn6: 0.00045218

Time = 1.00:
  id_uqzr: -0.35926924
  id_ageg: -0.18753425
  id_j3mt: 0.30963257
  id_nh4a: 0.01064604
  id_o2wu: 0.17020602
  id_ml0z: 0.00668219
  id_aprv: 0.04091787
  id_9e2p: -0.00000429
  id_hdof: 0.00000429
  id_udn6: 0.00054183

Time = 2.00:
  id_uqzr: -0.32213823
  id_ageg: -0.09839870
  id_j3mt: 0.34174633
  id_nh4a: 0.00558125
  id_o2wu: 0.09000891
  id_ml0z: 0.00280854
  id_aprv: 0.04214198
  id_9e2p: -0.00000483
  id_hdof: 0.00000483
  id_udn6: 0.00060872

Time = 5.00:
  id_uqzr: -0.22853482
  id_ageg: -0.02283109
  id_j3mt: 0.29054654
  id_nh4a: 0.00128930
  id_o2wu: 0.02169200
  id_ml0z: -0.00015021
  id_aprv: 0.02862954
  id_9e2p: -0.00000418
  id_hdof: 0.00000418
  id_udn6: 0.00052586

Time = 9.00:
  id_uqzr: -0.14398848
  id_ageg: -0.00703559
  id_j3mt: 0.19406834
  id_nh4a: 0.00039471
  id_o2wu: 0.00709670
  id_ml0z: -0.00045582
  id_aprv: 0.01434437
  id_9e2p: -0.00000281
  id_hdof: 0.00000281
  id_udn6: 0.00035347


Correlation between species concentrations and their rates of change:
id_uqzr: -0.9999
id_ageg: -0.9909
id_j3mt: -0.6212
id_nh4a: -0.9894
id_o2wu: -0.9547
id_ml0z: -0.8892
id_aprv: -0.5975
id_9e2p: -0.4670
id_hdof: -0.4670
id_udn6: -0.4858

Testing the model by simulation...

Comparing simulation with experimental data at t=10:
           Simulation  Experiment  Difference  Relative_Error
id_ml0z  1.197581e-01    0.040759    0.078999      193.821843
id_aprv  9.580645e-01    0.320706    0.637358      198.735821
id_j3mt -5.914904e-73    2.688295   -2.688295      100.000000
id_uqzr  0.000000e+00    2.592793   -2.592793      100.000000
id_ageg  0.000000e+00    0.105439   -0.105439      100.000000
id_nh4a  4.485277e-02    0.033802    0.011050       32.691364
id_hdof  7.692308e-02    0.000038    0.076885   202163.179819
id_9e2p  1.923077e+00    1.999962   -0.076885        3.844325
id_tod7  7.000000e-01    0.700000    0.000000        0.000000
id_o2wu  6.125000e-01    0.520000    0.092500       17.788459
id_4vc0  1.600000e+00    1.600000    0.000000        0.000000
id_r693  5.000000e+02  500.000000    0.000000        0.000000
Time     1.000000e+01   10.000000    0.000000        0.000000

Reactions added to the model (revised):
1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.0005)
2. id_ageg -> 0.057 id_nh4a + 0.875 id_o2wu (k2=0.5)
3. id_uqzr -> 1.1 id_j3mt (k3=0.3)
4. id_j3mt -> 0.015 id_ml0z + 0.12 id_aprv (k4=0.01)
5. id_uqzr -> 0.002 id_udn6 (k5=0.01)
6. id_ageg + id_uqzr -> id_ageg + id_uqzr + 0.01 id_nh4a (k6=0.1)

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, updated_sbml, updated_sbml_v2, updated_sbml_v3)

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


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



# Iteration 14
## Thoughts
We're still having issues with the model. The rate analysis provides some useful insights:

1. Strong negative correlations between species concentrations and their rates of change for id_uqzr and id_ageg suggest first-order decay.
2. The correlation for id_j3mt is weaker, suggesting more complex dynamics.
3. The simulation still shows negative concentrations for some species and large errors.

Let's try a completely different approach. Instead of trying to build the model incrementally, let's create a comprehensive model based on all our observations and then tune the parameters more carefully.

## Action

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

# Create a new model from scratch
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# Define all reactions based on our observations

# 1. id_9e2p <-> id_hdof (reversible)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_9e2p")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

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

kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1f * id_9e2p - k1r * id_hdof")

parameter1f = kinetic_law1.createParameter()
parameter1f.setId("k1f")
parameter1f.setValue(0.00002)
parameter1f.setUnits("id_p0jk")

parameter1r = kinetic_law1.createParameter()
parameter1r.setId("k1r")
parameter1r.setValue(0.0005)
parameter1r.setUnits("id_p0jk")

# 2. id_ageg -> id_nh4a + id_o2wu
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

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

product2a = reaction2.createProduct()
product2a.setSpecies("id_nh4a")
product2a.setStoichiometry(0.057)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_o2wu")
product2b.setStoichiometry(0.875)
product2b.setConstant(True)

kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_ageg")

parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.3)
parameter2.setUnits("id_p0jk")

# 3. id_uqzr -> id_j3mt
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

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

product3 = reaction3.createProduct()
product3.setSpecies("id_j3mt")
product3.setStoichiometry(1.1)
product3.setConstant(True)

kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_uqzr")

parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.1)
parameter3.setUnits("id_p0jk")

# 4. id_j3mt -> id_ml0z + id_aprv
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_j3mt")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

product4a = reaction4.createProduct()
product4a.setSpecies("id_ml0z")
product4a.setStoichiometry(0.015)
product4a.setConstant(True)

product4b = reaction4.createProduct()
product4b.setSpecies("id_aprv")
product4b.setStoichiometry(0.12)
product4b.setConstant(True)

kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_j3mt")

parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.01)
parameter4.setUnits("id_p0jk")

# 5. id_uqzr -> id_udn6
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_uqzr")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

product5 = reaction5.createProduct()
product5.setSpecies("id_udn6")
product5.setStoichiometry(0.002)
product5.setConstant(True)

kinetic_law5 = reaction5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_uqzr")

parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.001)
parameter5.setUnits("id_p0jk")

# 6. id_j3mt -> (degradation)
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

reactant6 = reaction6.createReactant()
reactant6.setSpecies("id_j3mt")
reactant6.setStoichiometry(1.0)
reactant6.setConstant(True)

kinetic_law6 = reaction6.createKineticLaw()
kinetic_law6.setFormula("k6 * id_j3mt")

parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.0)  # Initially set to 0
parameter6.setUnits("id_p0jk")

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

# Let's test our model by simulating it
print("Testing the model by simulation...")
simulation_result = simulate(updated_sbml)

# Compare the simulation with the experimental data
print("\nComparing simulation with experimental data at t=10:")
final_sim = simulation_result.iloc[-1]
final_exp = experiment_history["iteration_0"].iloc[-1]

comparison = pd.DataFrame({
    'Simulation': final_sim[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison)

# Let's try to adjust the parameters to better match the experimental data
# We'll focus on the key parameters that affect the dynamics

# Adjust parameters for better fit
sbml_doc = libsbml.readSBMLFromString(updated_sbml)
model = sbml_doc.getModel()

# Find and modify parameters
for reaction in model.getListOfReactions():
    kinetic_law = reaction.getKineticLaw()
    
    if reaction.getId() == "reaction2":  # id_ageg -> id_nh4a + id_o2wu
        parameter = kinetic_law.getParameter("k2")
        parameter.setValue(0.6)  # Increase rate to match id_ageg consumption
    
    elif reaction.getId() == "reaction3":  # id_uqzr -> id_j3mt
        parameter = kinetic_law.getParameter("k3")
        parameter.setValue(0.3)  # Increase rate to match id_j3mt production
    
    elif reaction.getId() == "reaction4":  # id_j3mt -> id_ml0z + id_aprv
        parameter = kinetic_law.getParameter("k4")
        parameter.setValue(0.05)  # Increase rate to match id_ml0z and id_aprv production
    
    elif reaction.getId() == "reaction6":  # id_j3mt -> (degradation)
        parameter = kinetic_law.getParameter("k6")
        parameter.setValue(0.05)  # Add degradation to prevent accumulation

# Write the updated SBML model with adjusted parameters
writer = libsbml.SBMLWriter()
updated_sbml_adjusted = writer.writeSBMLToString(sbml_doc)

# Test the adjusted model
print("\nTesting the model with adjusted parameters...")
simulation_result_adjusted = simulate(updated_sbml_adjusted)

# Compare the adjusted simulation with the experimental data
print("\nComparing adjusted simulation with experimental data at t=10:")
final_sim_adjusted = simulation_result_adjusted.iloc[-1]

comparison_adjusted = pd.DataFrame({
    'Simulation': final_sim_adjusted[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim_adjusted[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_adjusted[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison_adjusted)

# Store the updated SBML model
shared_variables.add("updated_sbml_v4", updated_sbml_adjusted)

# Print the reactions and adjusted parameters
print("\nReactions in the final model:")
print("1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.0005)")
print("2. id_ageg -> 0.057 id_nh4a + 0.875 id_o2wu (k2=0.6)")
print("3. id_uqzr -> 1.1 id_j3mt (k3=0.3)")
print("4. id_j3mt -> 0.015 id_ml0z + 0.12 id_aprv (k4=0.05)")
print("5. id_uqzr -> 0.002 id_udn6 (k5=0.001)")
print("6. id_j3mt -> (degradation) (k6=0.05)")

# Let's also test our model with the high_uqzr experiment
print("\nTesting the model with high_uqzr experiment...")
# First, modify the initial concentration of id_uqzr in the model
species_uqzr = model.getSpecies("id_uqzr")
original_conc = species_uqzr.getInitialConcentration()
species_uqzr.setInitialConcentration(10.0)  # Set to high_uqzr value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_uqzr_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_uqzr model
high_uqzr_sim = simulate(high_uqzr_sbml)

# Compare with experimental data
final_sim_high_uqzr = high_uqzr_sim.iloc[-1]
final_exp_high_uqzr = experiment_history["iteration_3"].iloc[-1]

comparison_high_uqzr = pd.DataFrame({
    'Simulation': final_sim_high_uqzr[1:],  # Skip the Time column
    'Experiment': final_exp_high_uqzr[1:],  # Skip the Time column
    'Difference': final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:]) / final_exp_high_uqzr[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_uqzr experimental data at t=10:")
print(comparison_high_uqzr)

# Reset the initial concentration
species_uqzr.setInitialConcentration(original_conc)
```
# Observation

## Code Stdout
Testing the model by simulation...

Comparing simulation with experimental data at t=10:
            Simulation  Experiment  Difference  Relative_Error
id_ml0z   1.225248e-01    0.040759    0.081766      200.609807
id_aprv   9.801980e-01    0.320706    0.659492      205.637309
id_j3mt   2.720342e-65    2.688295   -2.688295      100.000000
id_uqzr -2.798561e-106    2.592793   -2.592793      100.000000
id_ageg  6.687687e-132    0.105439   -0.105439      100.000000
id_nh4a   3.990000e-02    0.033802    0.006098       18.039211
id_hdof   7.692308e-02    0.000038    0.076885   202163.179819
id_9e2p   1.923077e+00    1.999962   -0.076885        3.844325
id_tod7   7.000000e-01    0.700000    0.000000        0.000000
id_o2wu   6.125000e-01    0.520000    0.092500       17.788459
id_4vc0   1.600000e+00    1.600000    0.000000        0.000000
id_r693   5.000000e+02  500.000000    0.000000        0.000000
Time      1.000000e+01   10.000000    0.000000        0.000000

Testing the model with adjusted parameters...

Comparing adjusted simulation with experimental data at t=10:
            Simulation  Experiment  Difference  Relative_Error
id_ml0z   6.166944e-02    0.040759    0.020911       51.303607
id_aprv   4.933555e-01    0.320706    0.172649       53.834061
id_j3mt  -9.042943e-93    2.688295   -2.688295      100.000000
id_uqzr -1.713439e-106    2.592793   -2.592793      100.000000
id_ageg   0.000000e+00    0.105439   -0.105439      100.000000
id_nh4a   3.990000e-02    0.033802    0.006098       18.039211
id_hdof   7.692308e-02    0.000038    0.076885   202163.179819
id_9e2p   1.923077e+00    1.999962   -0.076885        3.844325
id_tod7   7.000000e-01    0.700000    0.000000        0.000000
id_o2wu   6.125000e-01    0.520000    0.092500       17.788459
id_4vc0   1.600000e+00    1.600000    0.000000        0.000000
id_r693   5.000000e+02  500.000000    0.000000        0.000000
Time      1.000000e+01   10.000000    0.000000        0.000000

Reactions in the final model:
1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.0005)
2. id_ageg -> 0.057 id_nh4a + 0.875 id_o2wu (k2=0.6)
3. id_uqzr -> 1.1 id_j3mt (k3=0.3)
4. id_j3mt -> 0.015 id_ml0z + 0.12 id_aprv (k4=0.05)
5. id_uqzr -> 0.002 id_udn6 (k5=0.001)
6. id_j3mt -> (degradation) (k6=0.05)

Testing the model with high_uqzr experiment...

Comparing simulation with high_uqzr experimental data at t=10:
            Simulation  Experiment    Difference  Relative_Error
id_ml0z   1.233389e-01    0.055010  6.832843e-02    1.242099e+02
id_aprv   9.867110e-01    0.876831  1.098801e-01    1.253151e+01
id_j3mt  -1.703726e-92    5.501873 -5.501873e+00    1.000000e+02
id_uqzr  2.859843e-104    5.307200 -5.307200e+00    1.000000e+02
id_ageg   0.000000e+00    0.054443 -5.444308e-02    1.000000e+02
id_nh4a   3.990000e-02    0.036766  3.133974e-03    8.524103e+00
id_hdof   7.692308e-02    0.000078  7.684466e-02    9.799710e+04
id_9e2p   1.923077e+00    1.999922 -7.684466e-02    3.842384e+00
id_tod7   7.000000e-01    0.700000 -1.110223e-16    1.586033e-14
id_o2wu   6.125000e-01    0.553780  5.871955e-02    1.060340e+01
id_4vc0   1.600000e+00    1.600000  0.000000e+00    0.000000e+00
id_r693   5.000000e+02  500.000000  0.000000e+00    0.000000e+00
Time      1.000000e+01   10.000000  0.000000e+00    0.000000e+00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4)

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


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



# Iteration 15
## Thoughts
We're still facing challenges with the model. The main issues are:

1. Negative concentrations for id_uqzr and id_j3mt
2. Large errors for id_hdof and id_9e2p
3. The model doesn't capture the dynamics of id_j3mt well

Let's try a different approach. Instead of using complex reaction networks, let's start with a simpler model and focus on getting the basic dynamics right. We'll use a more direct approach to model the observed behavior.

## Action

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

# Create a new model from scratch
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# 1. id_9e2p <-> id_hdof (reversible)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_9e2p")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

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

kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1f * id_9e2p - k1r * id_hdof")

parameter1f = kinetic_law1.createParameter()
parameter1f.setId("k1f")
parameter1f.setValue(0.00002)
parameter1f.setUnits("id_p0jk")

parameter1r = kinetic_law1.createParameter()
parameter1r.setId("k1r")
parameter1r.setValue(0.5)
parameter1r.setUnits("id_p0jk")

# 2. id_ageg -> id_nh4a + id_o2wu
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

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

product2a = reaction2.createProduct()
product2a.setSpecies("id_nh4a")
product2a.setStoichiometry(0.057)
product2a.setConstant(True)

product2b = reaction2.createProduct()
product2b.setSpecies("id_o2wu")
product2b.setStoichiometry(0.875)
product2b.setConstant(True)

kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_ageg")

parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.6)
parameter2.setUnits("id_p0jk")

# 3. id_uqzr -> id_j3mt
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

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

product3 = reaction3.createProduct()
product3.setSpecies("id_j3mt")
product3.setStoichiometry(1.1)
product3.setConstant(True)

kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_uqzr")

parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.3)
parameter3.setUnits("id_p0jk")

# 4. id_j3mt -> id_ml0z + id_aprv
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_j3mt")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

product4a = reaction4.createProduct()
product4a.setSpecies("id_ml0z")
product4a.setStoichiometry(0.015)
product4a.setConstant(True)

product4b = reaction4.createProduct()
product4b.setSpecies("id_aprv")
product4b.setStoichiometry(0.12)
product4b.setConstant(True)

kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_j3mt")

parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.05)
parameter4.setUnits("id_p0jk")

# 5. id_uqzr -> id_udn6
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_uqzr")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

product5 = reaction5.createProduct()
product5.setSpecies("id_udn6")
product5.setStoichiometry(0.002)
product5.setConstant(True)

kinetic_law5 = reaction5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_uqzr")

parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.001)
parameter5.setUnits("id_p0jk")

# 6. id_j3mt -> (degradation)
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

reactant6 = reaction6.createReactant()
reactant6.setSpecies("id_j3mt")
reactant6.setStoichiometry(1.0)
reactant6.setConstant(True)

kinetic_law6 = reaction6.createKineticLaw()
kinetic_law6.setFormula("k6 * id_j3mt")

parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.05)
parameter6.setUnits("id_p0jk")

# 7. id_r693 -> id_j3mt (source for j3mt to prevent negative concentrations)
reaction7 = model.createReaction()
reaction7.setId("reaction7")
reaction7.setReversible(False)

reactant7 = reaction7.createReactant()
reactant7.setSpecies("id_r693")
reactant7.setStoichiometry(0.0)  # Zero stoichiometry since it's a boundary species
reactant7.setConstant(True)

product7 = reaction7.createProduct()
product7.setSpecies("id_j3mt")
product7.setStoichiometry(1.0)
product7.setConstant(True)

kinetic_law7 = reaction7.createKineticLaw()
kinetic_law7.setFormula("k7")  # Constant production

parameter7 = kinetic_law7.createParameter()
parameter7.setId("k7")
parameter7.setValue(0.3)  # Adjusted to match experimental data
parameter7.setUnits("id_gukt")

# 8. id_4vc0 -> id_uqzr (source for uqzr to prevent negative concentrations)
reaction8 = model.createReaction()
reaction8.setId("reaction8")
reaction8.setReversible(False)

reactant8 = reaction8.createReactant()
reactant8.setSpecies("id_4vc0")
reactant8.setStoichiometry(0.0)  # Zero stoichiometry since it's a boundary species
reactant8.setConstant(True)

product8 = reaction8.createProduct()
product8.setSpecies("id_uqzr")
product8.setStoichiometry(1.0)
product8.setConstant(True)

kinetic_law8 = reaction8.createKineticLaw()
kinetic_law8.setFormula("k8")  # Constant production

parameter8 = kinetic_law8.createParameter()
parameter8.setId("k8")
parameter8.setValue(0.1)  # Adjusted to match experimental data
parameter8.setUnits("id_gukt")

# 9. id_4vc0 -> id_ageg (source for ageg to prevent negative concentrations)
reaction9 = model.createReaction()
reaction9.setId("reaction9")
reaction9.setReversible(False)

reactant9 = reaction9.createReactant()
reactant9.setSpecies("id_4vc0")
reactant9.setStoichiometry(0.0)  # Zero stoichiometry since it's a boundary species
reactant9.setConstant(True)

product9 = reaction9.createProduct()
product9.setSpecies("id_ageg")
product9.setStoichiometry(1.0)
product9.setConstant(True)

kinetic_law9 = reaction9.createKineticLaw()
kinetic_law9.setFormula("k9")  # Constant production

parameter9 = kinetic_law9.createParameter()
parameter9.setId("k9")
parameter9.setValue(0.05)  # Adjusted to match experimental data
parameter9.setUnits("id_gukt")

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

# Let's test our model by simulating it
print("Testing the model by simulation...")
simulation_result = simulate(updated_sbml)

# Compare the simulation with the experimental data
print("\nComparing simulation with experimental data at t=10:")
final_sim = simulation_result.iloc[-1]
final_exp = experiment_history["iteration_0"].iloc[-1]

comparison = pd.DataFrame({
    'Simulation': final_sim[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison)

# Store the updated SBML model
shared_variables.add("updated_sbml_v5", updated_sbml)

# Print the reactions in the final model
print("\nReactions in the final model:")
print("1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.5)")
print("2. id_ageg -> 0.057 id_nh4a + 0.875 id_o2wu (k2=0.6)")
print("3. id_uqzr -> 1.1 id_j3mt (k3=0.3)")
print("4. id_j3mt -> 0.015 id_ml0z + 0.12 id_aprv (k4=0.05)")
print("5. id_uqzr -> 0.002 id_udn6 (k5=0.001)")
print("6. id_j3mt -> (degradation) (k6=0.05)")
print("7. id_r693 -> id_j3mt (k7=0.3, constant production)")
print("8. id_4vc0 -> id_uqzr (k8=0.1, constant production)")
print("9. id_4vc0 -> id_ageg (k9=0.05, constant production)")

# Let's also test our model with the high_uqzr experiment
print("\nTesting the model with high_uqzr experiment...")
# First, modify the initial concentration of id_uqzr in the model
species_uqzr = model.getSpecies("id_uqzr")
original_conc = species_uqzr.getInitialConcentration()
species_uqzr.setInitialConcentration(10.0)  # Set to high_uqzr value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_uqzr_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_uqzr model
high_uqzr_sim = simulate(high_uqzr_sbml)

# Compare with experimental data
final_sim_high_uqzr = high_uqzr_sim.iloc[-1]
final_exp_high_uqzr = experiment_history["iteration_3"].iloc[-1]

comparison_high_uqzr = pd.DataFrame({
    'Simulation': final_sim_high_uqzr[1:],  # Skip the Time column
    'Experiment': final_exp_high_uqzr[1:],  # Skip the Time column
    'Difference': final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:]) / final_exp_high_uqzr[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_uqzr experimental data at t=10:")
print(comparison_high_uqzr)

# Reset the initial concentration
species_uqzr.setInitialConcentration(original_conc)

# Let's also test our model with the high_ageg experiment
print("\nTesting the model with high_ageg experiment...")
# First, modify the initial concentration of id_ageg in the model
species_ageg = model.getSpecies("id_ageg")
original_ageg_conc = species_ageg.getInitialConcentration()
species_ageg.setInitialConcentration(1.4)  # Set to high_ageg value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_ageg_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_ageg model
high_ageg_sim = simulate(high_ageg_sbml)

# Compare with experimental data
final_sim_high_ageg = high_ageg_sim.iloc[-1]
final_exp_high_ageg = experiment_history["iteration_5"].iloc[-1]

comparison_high_ageg = pd.DataFrame({
    'Simulation': final_sim_high_ageg[1:],  # Skip the Time column
    'Experiment': final_exp_high_ageg[1:],  # Skip the Time column
    'Difference': final_sim_high_ageg[1:] - final_exp_high_ageg[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_ageg[1:] - final_exp_high_ageg[1:]) / final_exp_high_ageg[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_ageg experimental data at t=10:")
print(comparison_high_ageg)

# Reset the initial concentration
species_ageg.setInitialConcentration(original_ageg_conc)
```
# Observation

## Code Stdout
Testing the model by simulation...

Comparing simulation with experimental data at t=10:
           Simulation  Experiment    Difference  Relative_Error
id_ml0z  2.560216e+09    0.040759  2.560216e+09    6.281392e+12
id_aprv  2.048173e+10    0.320706  2.048173e+10    6.386444e+12
id_j3mt  4.096346e+00    2.688295  1.408051e+00    5.237711e+01
id_uqzr  3.322259e-01    2.592793 -2.260567e+00    8.718656e+01
id_ageg  8.333333e-02    0.105439 -2.210559e-02    2.096531e+01
id_nh4a  2.375000e+09    0.033802  2.375000e+09    7.026144e+12
id_hdof  7.999680e-05    0.000038  4.196562e-05    1.103453e+02
id_9e2p  1.999920e+00    1.999962 -4.196562e-05    2.098321e-03
id_tod7  7.000000e-01    0.700000  0.000000e+00    0.000000e+00
id_o2wu  3.645833e+10    0.520000  3.645833e+10    7.011218e+12
id_4vc0  1.600000e+00    1.600000  0.000000e+00    0.000000e+00
id_r693  5.000000e+02  500.000000  0.000000e+00    0.000000e+00
Time     1.000000e+01   10.000000  0.000000e+00    0.000000e+00

Reactions in the final model:
1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.5)
2. id_ageg -> 0.057 id_nh4a + 0.875 id_o2wu (k2=0.6)
3. id_uqzr -> 1.1 id_j3mt (k3=0.3)
4. id_j3mt -> 0.015 id_ml0z + 0.12 id_aprv (k4=0.05)
5. id_uqzr -> 0.002 id_udn6 (k5=0.001)
6. id_j3mt -> (degradation) (k6=0.05)
7. id_r693 -> id_j3mt (k7=0.3, constant production)
8. id_4vc0 -> id_uqzr (k8=0.1, constant production)
9. id_4vc0 -> id_ageg (k9=0.05, constant production)

Testing the model with high_uqzr experiment...

Comparing simulation with high_uqzr experimental data at t=10:
           Simulation  Experiment    Difference  Relative_Error
id_ml0z  2.560216e+09    0.055010  2.560216e+09    4.654054e+12
id_aprv  2.048173e+10    0.876831  2.048173e+10    2.335881e+12
id_j3mt  4.096346e+00    5.501873 -1.405527e+00    2.554634e+01
id_uqzr  3.322259e-01    5.307200 -4.974974e+00    9.374009e+01
id_ageg  8.333333e-02    0.054443  2.889026e-02    5.306507e+01
id_nh4a  2.375000e+09    0.036766  2.375000e+09    6.459768e+12
id_hdof  7.999680e-05    0.000078  1.581562e-06    2.016907e+00
id_9e2p  1.999920e+00    1.999922 -1.581562e-06    7.908121e-05
id_tod7  7.000000e-01    0.700000 -1.110223e-16    1.586033e-14
id_o2wu  3.645833e+10    0.553780  3.645833e+10    6.583536e+12
id_4vc0  1.600000e+00    1.600000  0.000000e+00    0.000000e+00
id_r693  5.000000e+02  500.000000  0.000000e+00    0.000000e+00
Time     1.000000e+01   10.000000  0.000000e+00    0.000000e+00

Testing the model with high_ageg experiment...

Comparing simulation with high_ageg experimental data at t=10:
           Simulation  Experiment    Difference  Relative_Error
id_ml0z  2.560216e+09    0.067680  2.560216e+09    3.782846e+12
id_aprv  2.048173e+10    0.224606  2.048173e+10    9.118944e+12
id_j3mt  4.096346e+00    2.345711  1.750635e+00    7.463131e+01
id_uqzr  3.322259e-01    2.508704 -2.176479e+00    8.675707e+01
id_ageg  8.333333e-02    0.239688 -1.563544e-01    6.523254e+01
id_nh4a  2.375000e+09    0.065896  2.375000e+09    3.604185e+12
id_hdof  7.999680e-05    0.000033  4.687677e-05    1.415360e+02
id_9e2p  1.999920e+00    1.999967 -4.687677e-05    2.343877e-03
id_tod7  7.000000e-01    0.700000 -1.110223e-16    1.586033e-14
id_o2wu  3.645833e+10    1.026737  3.645833e+10    3.550893e+12
id_4vc0  1.600000e+00    1.600000  0.000000e+00    0.000000e+00
id_r693  5.000000e+02  500.000000  0.000000e+00    0.000000e+00
Time     1.000000e+01   10.000000  0.000000e+00    0.000000e+00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5)

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


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



# Iteration 16
## Thoughts
We're still facing significant issues with the model. The simulation results show extremely large values for some species (id_ml0z, id_aprv, id_nh4a, id_o2wu), which indicates numerical instability or incorrect reaction rates.

Let's take a step back and simplify our approach. Instead of trying to model all the complex interactions at once, let's focus on getting the basic dynamics right for each species individually. We'll create a model with simpler reactions and carefully tune the parameters.

## Action

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

# Create a new model from scratch
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# 1. id_9e2p <-> id_hdof (reversible)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_9e2p")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

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

kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1f * id_9e2p - k1r * id_hdof")

parameter1f = kinetic_law1.createParameter()
parameter1f.setId("k1f")
parameter1f.setValue(0.00002)
parameter1f.setUnits("id_p0jk")

parameter1r = kinetic_law1.createParameter()
parameter1r.setId("k1r")
parameter1r.setValue(0.5)
parameter1r.setUnits("id_p0jk")

# 2. id_ageg -> id_nh4a
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

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

product2 = reaction2.createProduct()
product2.setSpecies("id_nh4a")
product2.setStoichiometry(0.057)
product2.setConstant(True)

kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_ageg")

parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.1)
parameter2.setUnits("id_p0jk")

# 3. id_ageg -> id_o2wu
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

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

product3 = reaction3.createProduct()
product3.setSpecies("id_o2wu")
product3.setStoichiometry(0.875)
product3.setConstant(True)

kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_ageg")

parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.1)
parameter3.setUnits("id_p0jk")

# 4. id_uqzr -> id_j3mt
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

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

product4 = reaction4.createProduct()
product4.setSpecies("id_j3mt")
product4.setStoichiometry(1.1)
product4.setConstant(True)

kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_uqzr")

parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.1)
parameter4.setUnits("id_p0jk")

# 5. id_j3mt -> id_ml0z
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_j3mt")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

product5 = reaction5.createProduct()
product5.setSpecies("id_ml0z")
product5.setStoichiometry(0.015)
product5.setConstant(True)

kinetic_law5 = reaction5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_j3mt")

parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.01)
parameter5.setUnits("id_p0jk")

# 6. id_j3mt -> id_aprv
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

reactant6 = reaction6.createReactant()
reactant6.setSpecies("id_j3mt")
reactant6.setStoichiometry(1.0)
reactant6.setConstant(True)

product6 = reaction6.createProduct()
product6.setSpecies("id_aprv")
product6.setStoichiometry(0.12)
product6.setConstant(True)

kinetic_law6 = reaction6.createKineticLaw()
kinetic_law6.setFormula("k6 * id_j3mt")

parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.01)
parameter6.setUnits("id_p0jk")

# 7. id_uqzr -> id_udn6
reaction7 = model.createReaction()
reaction7.setId("reaction7")
reaction7.setReversible(False)

reactant7 = reaction7.createReactant()
reactant7.setSpecies("id_uqzr")
reactant7.setStoichiometry(1.0)
reactant7.setConstant(True)

product7 = reaction7.createProduct()
product7.setSpecies("id_udn6")
product7.setStoichiometry(0.002)
product7.setConstant(True)

kinetic_law7 = reaction7.createKineticLaw()
kinetic_law7.setFormula("k7 * id_uqzr")

parameter7 = kinetic_law7.createParameter()
parameter7.setId("k7")
parameter7.setValue(0.001)
parameter7.setUnits("id_p0jk")

# 8. id_j3mt -> (degradation)
reaction8 = model.createReaction()
reaction8.setId("reaction8")
reaction8.setReversible(False)

reactant8 = reaction8.createReactant()
reactant8.setSpecies("id_j3mt")
reactant8.setStoichiometry(1.0)
reactant8.setConstant(True)

kinetic_law8 = reaction8.createKineticLaw()
kinetic_law8.setFormula("k8 * id_j3mt")

parameter8 = kinetic_law8.createParameter()
parameter8.setId("k8")
parameter8.setValue(0.01)
parameter8.setUnits("id_p0jk")

# 9. id_ml0z -> (degradation)
reaction9 = model.createReaction()
reaction9.setId("reaction9")
reaction9.setReversible(False)

reactant9 = reaction9.createReactant()
reactant9.setSpecies("id_ml0z")
reactant9.setStoichiometry(1.0)
reactant9.setConstant(True)

kinetic_law9 = reaction9.createKineticLaw()
kinetic_law9.setFormula("k9 * id_ml0z")

parameter9 = kinetic_law9.createParameter()
parameter9.setId("k9")
parameter9.setValue(0.01)
parameter9.setUnits("id_p0jk")

# 10. id_aprv -> (degradation)
reaction10 = model.createReaction()
reaction10.setId("reaction10")
reaction10.setReversible(False)

reactant10 = reaction10.createReactant()
reactant10.setSpecies("id_aprv")
reactant10.setStoichiometry(1.0)
reactant10.setConstant(True)

kinetic_law10 = reaction10.createKineticLaw()
kinetic_law10.setFormula("k10 * id_aprv")

parameter10 = kinetic_law10.createParameter()
parameter10.setId("k10")
parameter10.setValue(0.01)
parameter10.setUnits("id_p0jk")

# 11. id_nh4a -> (degradation)
reaction11 = model.createReaction()
reaction11.setId("reaction11")
reaction11.setReversible(False)

reactant11 = reaction11.createReactant()
reactant11.setSpecies("id_nh4a")
reactant11.setStoichiometry(1.0)
reactant11.setConstant(True)

kinetic_law11 = reaction11.createKineticLaw()
kinetic_law11.setFormula("k11 * id_nh4a")

parameter11 = kinetic_law11.createParameter()
parameter11.setId("k11")
parameter11.setValue(0.01)
parameter11.setUnits("id_p0jk")

# 12. id_o2wu -> (degradation)
reaction12 = model.createReaction()
reaction12.setId("reaction12")
reaction12.setReversible(False)

reactant12 = reaction12.createReactant()
reactant12.setSpecies("id_o2wu")
reactant12.setStoichiometry(1.0)
reactant12.setConstant(True)

kinetic_law12 = reaction12.createKineticLaw()
kinetic_law12.setFormula("k12 * id_o2wu")

parameter12 = kinetic_law12.createParameter()
parameter12.setId("k12")
parameter12.setValue(0.01)
parameter12.setUnits("id_p0jk")

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

# Let's test our model by simulating it
print("Testing the model by simulation...")
simulation_result = simulate(updated_sbml)

# Compare the simulation with the experimental data
print("\nComparing simulation with experimental data at t=10:")
final_sim = simulation_result.iloc[-1]
final_exp = experiment_history["iteration_0"].iloc[-1]

comparison = pd.DataFrame({
    'Simulation': final_sim[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison)

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

# Print the reactions in the final model
print("\nReactions in the final model:")
print("1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.5)")
print("2. id_ageg -> 0.057 id_nh4a (k2=0.1)")
print("3. id_ageg -> 0.875 id_o2wu (k3=0.1)")
print("4. id_uqzr -> 1.1 id_j3mt (k4=0.1)")
print("5. id_j3mt -> 0.015 id_ml0z (k5=0.01)")
print("6. id_j3mt -> 0.12 id_aprv (k6=0.01)")
print("7. id_uqzr -> 0.002 id_udn6 (k7=0.001)")
print("8. id_j3mt -> (degradation) (k8=0.01)")
print("9. id_ml0z -> (degradation) (k9=0.01)")
print("10. id_aprv -> (degradation) (k10=0.01)")
print("11. id_nh4a -> (degradation) (k11=0.01)")
print("12. id_o2wu -> (degradation) (k12=0.01)")

# Let's also test our model with the high_uqzr experiment
print("\nTesting the model with high_uqzr experiment...")
# First, modify the initial concentration of id_uqzr in the model
species_uqzr = model.getSpecies("id_uqzr")
original_conc = species_uqzr.getInitialConcentration()
species_uqzr.setInitialConcentration(10.0)  # Set to high_uqzr value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_uqzr_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_uqzr model
high_uqzr_sim = simulate(high_uqzr_sbml)

# Compare with experimental data
final_sim_high_uqzr = high_uqzr_sim.iloc[-1]
final_exp_high_uqzr = experiment_history["iteration_3"].iloc[-1]

comparison_high_uqzr = pd.DataFrame({
    'Simulation': final_sim_high_uqzr[1:],  # Skip the Time column
    'Experiment': final_exp_high_uqzr[1:],  # Skip the Time column
    'Difference': final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:]) / final_exp_high_uqzr[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_uqzr experimental data at t=10:")
print(comparison_high_uqzr)

# Reset the initial concentration
species_uqzr.setInitialConcentration(original_conc)

# Let's also test our model with the high_ageg experiment
print("\nTesting the model with high_ageg experiment...")
# First, modify the initial concentration of id_ageg in the model
species_ageg = model.getSpecies("id_ageg")
original_ageg_conc = species_ageg.getInitialConcentration()
species_ageg.setInitialConcentration(1.4)  # Set to high_ageg value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_ageg_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_ageg model
high_ageg_sim = simulate(high_ageg_sbml)

# Compare with experimental data
final_sim_high_ageg = high_ageg_sim.iloc[-1]
final_exp_high_ageg = experiment_history["iteration_5"].iloc[-1]

comparison_high_ageg = pd.DataFrame({
    'Simulation': final_sim_high_ageg[1:],  # Skip the Time column
    'Experiment': final_exp_high_ageg[1:],  # Skip the Time column
    'Difference': final_sim_high_ageg[1:] - final_exp_high_ageg[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_ageg[1:] - final_exp_high_ageg[1:]) / final_exp_high_ageg[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_ageg experimental data at t=10:")
print(comparison_high_ageg)

# Reset the initial concentration
species_ageg.setInitialConcentration(original_ageg_conc)
```
# Observation

## Code Stdout
Testing the model by simulation...

Comparing simulation with experimental data at t=10:
            Simulation  Experiment  Difference  Relative_Error
id_ml0z  -8.377060e-46    0.040759   -0.040759      100.000000
id_aprv   4.962870e-43    0.320706   -0.320706      100.000000
id_j3mt  -4.758385e-74    2.688295   -2.688295      100.000000
id_uqzr   5.770301e-86    2.592793   -2.592793      100.000000
id_ageg  9.384260e-105    0.105439   -0.105439      100.000000
id_nh4a  -1.301742e-46    0.033802   -0.033802      100.000000
id_hdof   7.999680e-05    0.000038    0.000042      110.345293
id_9e2p   1.999920e+00    1.999962   -0.000042        0.002098
id_tod7   7.000000e-01    0.700000    0.000000        0.000000
id_o2wu  -1.304651e-44    0.520000   -0.520000      100.000000
id_4vc0   1.600000e+00    1.600000    0.000000        0.000000
id_r693   5.000000e+02  500.000000    0.000000        0.000000
Time      1.000000e+01   10.000000    0.000000        0.000000

Reactions in the final model:
1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.5)
2. id_ageg -> 0.057 id_nh4a (k2=0.1)
3. id_ageg -> 0.875 id_o2wu (k3=0.1)
4. id_uqzr -> 1.1 id_j3mt (k4=0.1)
5. id_j3mt -> 0.015 id_ml0z (k5=0.01)
6. id_j3mt -> 0.12 id_aprv (k6=0.01)
7. id_uqzr -> 0.002 id_udn6 (k7=0.001)
8. id_j3mt -> (degradation) (k8=0.01)
9. id_ml0z -> (degradation) (k9=0.01)
10. id_aprv -> (degradation) (k10=0.01)
11. id_nh4a -> (degradation) (k11=0.01)
12. id_o2wu -> (degradation) (k12=0.01)

Testing the model with high_uqzr experiment...

Comparing simulation with high_uqzr experimental data at t=10:
            Simulation  Experiment    Difference  Relative_Error
id_ml0z  -3.361627e-44    0.055010 -5.501044e-02    1.000000e+02
id_aprv   8.807364e-44    0.876831 -8.768309e-01    1.000000e+02
id_j3mt   0.000000e+00    5.501873 -5.501873e+00    1.000000e+02
id_uqzr  -5.674148e-90    5.307200 -5.307200e+00    1.000000e+02
id_ageg -2.952899e-107    0.054443 -5.444308e-02    1.000000e+02
id_nh4a  -1.340736e-48    0.036766 -3.676603e-02    1.000000e+02
id_hdof   7.999680e-05    0.000078  1.581562e-06    2.016907e+00
id_9e2p   1.999920e+00    1.999922 -1.581562e-06    7.908121e-05
id_tod7   7.000000e-01    0.700000 -1.110223e-16    1.586033e-14
id_o2wu  -1.787705e-43    0.553780 -5.537805e-01    1.000000e+02
id_4vc0   1.600000e+00    1.600000  0.000000e+00    0.000000e+00
id_r693   5.000000e+02  500.000000  0.000000e+00    0.000000e+00
Time      1.000000e+01   10.000000  0.000000e+00    0.000000e+00

Testing the model with high_ageg experiment...

Comparing simulation with high_ageg experimental data at t=10:
            Simulation  Experiment    Difference  Relative_Error
id_ml0z   3.361544e-58    0.067680 -6.767962e-02    1.000000e+02
id_aprv   1.008187e-86    0.224606 -2.246063e-01    1.000000e+02
id_j3mt   0.000000e+00    2.345711 -2.345711e+00    1.000000e+02
id_uqzr  -2.333445e-95    2.508704 -2.508704e+00    1.000000e+02
id_ageg  2.232678e-109    0.239688 -2.396877e-01    1.000000e+02
id_nh4a   0.000000e+00    0.065896 -6.589561e-02    1.000000e+02
id_hdof   7.999680e-05    0.000033  4.687677e-05    1.415360e+02
id_9e2p   1.999920e+00    1.999967 -4.687677e-05    2.343877e-03
id_tod7   7.000000e-01    0.700000 -1.110223e-16    1.586033e-14
id_o2wu   4.201930e-59    1.026737 -1.026737e+00    1.000000e+02
id_4vc0   1.600000e+00    1.600000  0.000000e+00    0.000000e+00
id_r693   5.000000e+02  500.000000  0.000000e+00    0.000000e+00
Time      1.000000e+01   10.000000  0.000000e+00    0.000000e+00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5, updated_sbml_v6)

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


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



# Iteration 17
## Thoughts
We're still facing significant issues with the model. The simulation results show negative concentrations for many species, which is physically impossible. This suggests that our model structure or parameters are not correctly capturing the system dynamics.

Let's try a completely different approach. Instead of trying to model all the complex interactions, let's create a very simple model with just the essential reactions and focus on getting the basic dynamics right. We'll use mass action kinetics and avoid any complex rate laws.

## Action

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

# Create a new model from scratch
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# 1. id_9e2p <-> id_hdof (reversible)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_9e2p")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

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

kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1f * id_9e2p - k1r * id_hdof")

parameter1f = kinetic_law1.createParameter()
parameter1f.setId("k1f")
parameter1f.setValue(0.00002)
parameter1f.setUnits("id_p0jk")

parameter1r = kinetic_law1.createParameter()
parameter1r.setId("k1r")
parameter1r.setValue(0.5)
parameter1r.setUnits("id_p0jk")

# 2. id_uqzr -> id_j3mt
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

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

product2 = reaction2.createProduct()
product2.setSpecies("id_j3mt")
product2.setStoichiometry(1.0)
product2.setConstant(True)

kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_uqzr")

parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.3)
parameter2.setUnits("id_p0jk")

# 3. id_j3mt -> id_ml0z
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_j3mt")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

product3 = reaction3.createProduct()
product3.setSpecies("id_ml0z")
product3.setStoichiometry(0.015)
product3.setConstant(True)

kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_j3mt")

parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.01)
parameter3.setUnits("id_p0jk")

# 4. id_j3mt -> id_aprv
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_j3mt")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

product4 = reaction4.createProduct()
product4.setSpecies("id_aprv")
product4.setStoichiometry(0.12)
product4.setConstant(True)

kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_j3mt")

parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.01)
parameter4.setUnits("id_p0jk")

# 5. id_ageg -> id_nh4a
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_ageg")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

product5 = reaction5.createProduct()
product5.setSpecies("id_nh4a")
product5.setStoichiometry(0.057)
product5.setConstant(True)

kinetic_law5 = reaction5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_ageg")

parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.1)
parameter5.setUnits("id_p0jk")

# 6. id_ageg -> id_o2wu
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

reactant6 = reaction6.createReactant()
reactant6.setSpecies("id_ageg")
reactant6.setStoichiometry(1.0)
reactant6.setConstant(True)

product6 = reaction6.createProduct()
product6.setSpecies("id_o2wu")
product6.setStoichiometry(0.875)
product6.setConstant(True)

kinetic_law6 = reaction6.createKineticLaw()
kinetic_law6.setFormula("k6 * id_ageg")

parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.1)
parameter6.setUnits("id_p0jk")

# 7. id_uqzr -> id_udn6
reaction7 = model.createReaction()
reaction7.setId("reaction7")
reaction7.setReversible(False)

reactant7 = reaction7.createReactant()
reactant7.setSpecies("id_uqzr")
reactant7.setStoichiometry(1.0)
reactant7.setConstant(True)

product7 = reaction7.createProduct()
product7.setSpecies("id_udn6")
product7.setStoichiometry(0.002)
product7.setConstant(True)

kinetic_law7 = reaction7.createKineticLaw()
kinetic_law7.setFormula("k7 * id_uqzr")

parameter7 = kinetic_law7.createParameter()
parameter7.setId("k7")
parameter7.setValue(0.001)
parameter7.setUnits("id_p0jk")

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

# Let's test our model by simulating it
print("Testing the model by simulation...")
simulation_result = simulate(updated_sbml)

# Compare the simulation with the experimental data
print("\nComparing simulation with experimental data at t=10:")
final_sim = simulation_result.iloc[-1]
final_exp = experiment_history["iteration_0"].iloc[-1]

comparison = pd.DataFrame({
    'Simulation': final_sim[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison)

# Let's try to adjust the parameters to better match the experimental data
# We'll focus on the key parameters that affect the dynamics

# Adjust parameters for better fit
sbml_doc = libsbml.readSBMLFromString(updated_sbml)
model = sbml_doc.getModel()

# Find and modify parameters
for reaction in model.getListOfReactions():
    kinetic_law = reaction.getKineticLaw()
    
    if reaction.getId() == "reaction2":  # id_uqzr -> id_j3mt
        parameter = kinetic_law.getParameter("k2")
        parameter.setValue(0.5)  # Increase rate to match id_j3mt production
    
    elif reaction.getId() == "reaction3":  # id_j3mt -> id_ml0z
        parameter = kinetic_law.getParameter("k3")
        parameter.setValue(0.02)  # Adjust rate to match id_ml0z production
    
    elif reaction.getId() == "reaction4":  # id_j3mt -> id_aprv
        parameter = kinetic_law.getParameter("k4")
        parameter.setValue(0.15)  # Adjust rate to match id_aprv production
    
    elif reaction.getId() == "reaction5":  # id_ageg -> id_nh4a
        parameter = kinetic_law.getParameter("k5")
        parameter.setValue(0.05)  # Adjust rate to match id_nh4a production
    
    elif reaction.getId() == "reaction6":  # id_ageg -> id_o2wu
        parameter = kinetic_law.getParameter("k6")
        parameter.setValue(0.8)  # Adjust rate to match id_o2wu production

# Write the updated SBML model with adjusted parameters
writer = libsbml.SBMLWriter()
updated_sbml_adjusted = writer.writeSBMLToString(sbml_doc)

# Test the adjusted model
print("\nTesting the model with adjusted parameters...")
simulation_result_adjusted = simulate(updated_sbml_adjusted)

# Compare the adjusted simulation with the experimental data
print("\nComparing adjusted simulation with experimental data at t=10:")
final_sim_adjusted = simulation_result_adjusted.iloc[-1]

comparison_adjusted = pd.DataFrame({
    'Simulation': final_sim_adjusted[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim_adjusted[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_adjusted[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison_adjusted)

# Store the updated SBML model
shared_variables.add("updated_sbml_v7", updated_sbml_adjusted)

# Print the reactions and adjusted parameters
print("\nReactions in the final model:")
print("1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.5)")
print("2. id_uqzr -> id_j3mt (k2=0.5)")
print("3. id_j3mt -> 0.015 id_ml0z (k3=0.02)")
print("4. id_j3mt -> 0.12 id_aprv (k4=0.15)")
print("5. id_ageg -> 0.057 id_nh4a (k5=0.05)")
print("6. id_ageg -> 0.875 id_o2wu (k6=0.8)")
print("7. id_uqzr -> 0.002 id_udn6 (k7=0.001)")

# Let's also test our model with the high_uqzr experiment
print("\nTesting the model with high_uqzr experiment...")
# First, modify the initial concentration of id_uqzr in the model
species_uqzr = model.getSpecies("id_uqzr")
original_conc = species_uqzr.getInitialConcentration()
species_uqzr.setInitialConcentration(10.0)  # Set to high_uqzr value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_uqzr_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_uqzr model
high_uqzr_sim = simulate(high_uqzr_sbml)

# Compare with experimental data
final_sim_high_uqzr = high_uqzr_sim.iloc[-1]
final_exp_high_uqzr = experiment_history["iteration_3"].iloc[-1]

comparison_high_uqzr = pd.DataFrame({
    'Simulation': final_sim_high_uqzr[1:],  # Skip the Time column
    'Experiment': final_exp_high_uqzr[1:],  # Skip the Time column
    'Difference': final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:]) / final_exp_high_uqzr[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_uqzr experimental data at t=10:")
print(comparison_high_uqzr)

# Reset the initial concentration
species_uqzr.setInitialConcentration(original_conc)

# Let's also test our model with the high_ageg experiment
print("\nTesting the model with high_ageg experiment...")
# First, modify the initial concentration of id_ageg in the model
species_ageg = model.getSpecies("id_ageg")
original_ageg_conc = species_ageg.getInitialConcentration()
species_ageg.setInitialConcentration(1.4)  # Set to high_ageg value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_ageg_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_ageg model
high_ageg_sim = simulate(high_ageg_sbml)

# Compare with experimental data
final_sim_high_ageg = high_ageg_sim.iloc[-1]
final_exp_high_ageg = experiment_history["iteration_5"].iloc[-1]

comparison_high_ageg = pd.DataFrame({
    'Simulation': final_sim_high_ageg[1:],  # Skip the Time column
    'Experiment': final_exp_high_ageg[1:],  # Skip the Time column
    'Difference': final_sim_high_ageg[1:] - final_exp_high_ageg[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_ageg[1:] - final_exp_high_ageg[1:]) / final_exp_high_ageg[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_ageg experimental data at t=10:")
print(comparison_high_ageg)

# Reset the initial concentration
species_ageg.setInitialConcentration(original_ageg_conc)

# Create the final model
final_sbml = updated_sbml_adjusted
```
# Observation

## Code Stdout
Testing the model by simulation...

Comparing simulation with experimental data at t=10:
           Simulation  Experiment  Difference  Relative_Error
id_ml0z  5.606312e-02    0.040759    0.015304       37.548732
id_aprv  4.485050e-01    0.320706    0.127799       39.849144
id_j3mt -5.808451e-44    2.688295   -2.688295      100.000000
id_uqzr -1.444042e-85    2.592793   -2.592793      100.000000
id_ageg  0.000000e+00    0.105439   -0.105439      100.000000
id_nh4a  1.995000e-02    0.033802   -0.013852       40.980394
id_hdof  7.999680e-05    0.000038    0.000042      110.345293
id_9e2p  1.999920e+00    1.999962   -0.000042        0.002098
id_tod7  7.000000e-01    0.700000    0.000000        0.000000
id_o2wu  3.062500e-01    0.520000   -0.213750       41.105771
id_4vc0  1.600000e+00    1.600000    0.000000        0.000000
id_r693  5.000000e+02  500.000000    0.000000        0.000000
Time     1.000000e+01   10.000000    0.000000        0.000000

Testing the model with adjusted parameters...

Comparing adjusted simulation with experimental data at t=10:
           Simulation  Experiment  Difference  Relative_Error
id_ml0z  1.320888e-02    0.040759   -0.027550       67.592526
id_aprv  7.925326e-01    0.320706    0.471826      147.121009
id_j3mt -2.058917e-51    2.688295   -2.688295      100.000000
id_uqzr  1.792374e-79    2.592793   -2.592793      100.000000
id_ageg  0.000000e+00    0.105439   -0.105439      100.000000
id_nh4a  2.347059e-03    0.033802   -0.031455       93.056517
id_hdof  7.999680e-05    0.000038    0.000042      110.345293
id_9e2p  1.999920e+00    1.999962   -0.000042        0.002098
id_tod7  7.000000e-01    0.700000    0.000000        0.000000
id_o2wu  5.764706e-01    0.520000    0.056471       10.859726
id_4vc0  1.600000e+00    1.600000    0.000000        0.000000
id_r693  5.000000e+02  500.000000    0.000000        0.000000
Time     1.000000e+01   10.000000    0.000000        0.000000

Reactions in the final model:
1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.5)
2. id_uqzr -> id_j3mt (k2=0.5)
3. id_j3mt -> 0.015 id_ml0z (k3=0.02)
4. id_j3mt -> 0.12 id_aprv (k4=0.15)
5. id_ageg -> 0.057 id_nh4a (k5=0.05)
6. id_ageg -> 0.875 id_o2wu (k6=0.8)
7. id_uqzr -> 0.002 id_udn6 (k7=0.001)

Testing the model with high_uqzr experiment...

Comparing simulation with high_uqzr experimental data at t=10:
            Simulation  Experiment    Difference  Relative_Error
id_ml0z   2.641775e-02    0.055010 -2.859269e-02    5.197684e+01
id_aprv   1.585065e+00    0.876831  7.082343e-01    8.077206e+01
id_j3mt   2.943814e-52    5.501873 -5.501873e+00    1.000000e+02
id_uqzr  -7.810311e-83    5.307200 -5.307200e+00    1.000000e+02
id_ageg  6.615589e-104    0.054443 -5.444308e-02    1.000000e+02
id_nh4a   2.347059e-03    0.036766 -3.441897e-02    9.361623e+01
id_hdof   7.999680e-05    0.000078  1.581562e-06    2.016907e+00
id_9e2p   1.999920e+00    1.999922 -1.581562e-06    7.908121e-05
id_tod7   7.000000e-01    0.700000 -1.110223e-16    1.586033e-14
id_o2wu   5.764706e-01    0.553780  2.269014e-02    4.097316e+00
id_4vc0   1.600000e+00    1.600000  0.000000e+00    0.000000e+00
id_r693   5.000000e+02  500.000000  0.000000e+00    0.000000e+00
Time      1.000000e+01   10.000000  0.000000e+00    0.000000e+00

Testing the model with high_ageg experiment...

Comparing simulation with high_ageg experimental data at t=10:
            Simulation  Experiment    Difference  Relative_Error
id_ml0z   1.320888e-02    0.067680 -5.447075e-02    8.048323e+01
id_aprv   7.925326e-01    0.224606  5.679262e-01    2.528541e+02
id_j3mt   1.285388e-48    2.345711 -2.345711e+00    1.000000e+02
id_uqzr   5.848185e-76    2.508704 -2.508704e+00    1.000000e+02
id_ageg -2.169376e-101    0.239688 -2.396877e-01    1.000000e+02
id_nh4a   4.694118e-03    0.065896 -6.120149e-02    9.287643e+01
id_hdof   7.999680e-05    0.000033  4.687677e-05    1.415360e+02
id_9e2p   1.999920e+00    1.999967 -4.687677e-05    2.343877e-03
id_tod7   7.000000e-01    0.700000 -1.110223e-16    1.586033e-14
id_o2wu   1.152941e+00    1.026737  1.262041e-01    1.229177e+01
id_4vc0   1.600000e+00    1.600000  0.000000e+00    0.000000e+00
id_r693   5.000000e+02  500.000000  0.000000e+00    0.000000e+00
Time      1.000000e+01   10.000000  0.000000e+00    0.000000e+00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5, updated_sbml_v6, updated_sbml_v7)

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


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



# Iteration 18
## Thoughts
We're still facing issues with negative concentrations for some species (id_j3mt, id_uqzr, id_ageg). This suggests that our model structure is still not capturing the system dynamics correctly.

Let's try a different approach. Instead of trying to model all the complex interactions, let's focus on getting a model that at least produces non-negative concentrations for all species. We'll use a simpler model structure with fewer reactions and add production terms to prevent negative concentrations.

## Action

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

# Create a new model from scratch
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# 1. id_9e2p <-> id_hdof (reversible)
reaction1 = model.createReaction()
reaction1.setId("reaction1")
reaction1.setReversible(True)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_9e2p")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(True)

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

kinetic_law1 = reaction1.createKineticLaw()
kinetic_law1.setFormula("k1f * id_9e2p - k1r * id_hdof")

parameter1f = kinetic_law1.createParameter()
parameter1f.setId("k1f")
parameter1f.setValue(0.00002)
parameter1f.setUnits("id_p0jk")

parameter1r = kinetic_law1.createParameter()
parameter1r.setId("k1r")
parameter1r.setValue(0.5)
parameter1r.setUnits("id_p0jk")

# 2. Production of id_j3mt
reaction2 = model.createReaction()
reaction2.setId("reaction2")
reaction2.setReversible(False)

# Use id_r693 as a source (it's a boundary species)
reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_r693")
reactant2.setStoichiometry(0.0)  # Zero stoichiometry since it's a boundary species
reactant2.setConstant(True)

product2 = reaction2.createProduct()
product2.setSpecies("id_j3mt")
product2.setStoichiometry(1.0)
product2.setConstant(True)

kinetic_law2 = reaction2.createKineticLaw()
kinetic_law2.setFormula("k2")  # Constant production

parameter2 = kinetic_law2.createParameter()
parameter2.setId("k2")
parameter2.setValue(0.3)
parameter2.setUnits("id_gukt")

# 3. Consumption of id_j3mt
reaction3 = model.createReaction()
reaction3.setId("reaction3")
reaction3.setReversible(False)

reactant3 = reaction3.createReactant()
reactant3.setSpecies("id_j3mt")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(True)

kinetic_law3 = reaction3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_j3mt")

parameter3 = kinetic_law3.createParameter()
parameter3.setId("k3")
parameter3.setValue(0.1)
parameter3.setUnits("id_p0jk")

# 4. id_j3mt -> id_ml0z
reaction4 = model.createReaction()
reaction4.setId("reaction4")
reaction4.setReversible(False)

reactant4 = reaction4.createReactant()
reactant4.setSpecies("id_j3mt")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(True)

product4 = reaction4.createProduct()
product4.setSpecies("id_ml0z")
product4.setStoichiometry(0.015)
product4.setConstant(True)

kinetic_law4 = reaction4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_j3mt")

parameter4 = kinetic_law4.createParameter()
parameter4.setId("k4")
parameter4.setValue(0.02)
parameter4.setUnits("id_p0jk")

# 5. id_j3mt -> id_aprv
reaction5 = model.createReaction()
reaction5.setId("reaction5")
reaction5.setReversible(False)

reactant5 = reaction5.createReactant()
reactant5.setSpecies("id_j3mt")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(True)

product5 = reaction5.createProduct()
product5.setSpecies("id_aprv")
product5.setStoichiometry(0.12)
product5.setConstant(True)

kinetic_law5 = reaction5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_j3mt")

parameter5 = kinetic_law5.createParameter()
parameter5.setId("k5")
parameter5.setValue(0.15)
parameter5.setUnits("id_p0jk")

# 6. Production of id_uqzr
reaction6 = model.createReaction()
reaction6.setId("reaction6")
reaction6.setReversible(False)

# Use id_4vc0 as a source (it's a boundary species)
reactant6 = reaction6.createReactant()
reactant6.setSpecies("id_4vc0")
reactant6.setStoichiometry(0.0)  # Zero stoichiometry since it's a boundary species
reactant6.setConstant(True)

product6 = reaction6.createProduct()
product6.setSpecies("id_uqzr")
product6.setStoichiometry(1.0)
product6.setConstant(True)

kinetic_law6 = reaction6.createKineticLaw()
kinetic_law6.setFormula("k6")  # Constant production

parameter6 = kinetic_law6.createParameter()
parameter6.setId("k6")
parameter6.setValue(0.3)
parameter6.setUnits("id_gukt")

# 7. Consumption of id_uqzr
reaction7 = model.createReaction()
reaction7.setId("reaction7")
reaction7.setReversible(False)

reactant7 = reaction7.createReactant()
reactant7.setSpecies("id_uqzr")
reactant7.setStoichiometry(1.0)
reactant7.setConstant(True)

kinetic_law7 = reaction7.createKineticLaw()
kinetic_law7.setFormula("k7 * id_uqzr")

parameter7 = kinetic_law7.createParameter()
parameter7.setId("k7")
parameter7.setValue(0.1)
parameter7.setUnits("id_p0jk")

# 8. id_uqzr -> id_udn6
reaction8 = model.createReaction()
reaction8.setId("reaction8")
reaction8.setReversible(False)

reactant8 = reaction8.createReactant()
reactant8.setSpecies("id_uqzr")
reactant8.setStoichiometry(1.0)
reactant8.setConstant(True)

product8 = reaction8.createProduct()
product8.setSpecies("id_udn6")
product8.setStoichiometry(0.002)
product8.setConstant(True)

kinetic_law8 = reaction8.createKineticLaw()
kinetic_law8.setFormula("k8 * id_uqzr")

parameter8 = kinetic_law8.createParameter()
parameter8.setId("k8")
parameter8.setValue(0.001)
parameter8.setUnits("id_p0jk")

# 9. Production of id_ageg
reaction9 = model.createReaction()
reaction9.setId("reaction9")
reaction9.setReversible(False)

# Use id_4vc0 as a source (it's a boundary species)
reactant9 = reaction9.createReactant()
reactant9.setSpecies("id_4vc0")
reactant9.setStoichiometry(0.0)  # Zero stoichiometry since it's a boundary species
reactant9.setConstant(True)

product9 = reaction9.createProduct()
product9.setSpecies("id_ageg")
product9.setStoichiometry(1.0)
product9.setConstant(True)

kinetic_law9 = reaction9.createKineticLaw()
kinetic_law9.setFormula("k9")  # Constant production

parameter9 = kinetic_law9.createParameter()
parameter9.setId("k9")
parameter9.setValue(0.1)
parameter9.setUnits("id_gukt")

# 10. id_ageg -> id_nh4a
reaction10 = model.createReaction()
reaction10.setId("reaction10")
reaction10.setReversible(False)

reactant10 = reaction10.createReactant()
reactant10.setSpecies("id_ageg")
reactant10.setStoichiometry(1.0)
reactant10.setConstant(True)

product10 = reaction10.createProduct()
product10.setSpecies("id_nh4a")
product10.setStoichiometry(0.057)
product10.setConstant(True)

kinetic_law10 = reaction10.createKineticLaw()
kinetic_law10.setFormula("k10 * id_ageg")

parameter10 = kinetic_law10.createParameter()
parameter10.setId("k10")
parameter10.setValue(0.05)
parameter10.setUnits("id_p0jk")

# 11. id_ageg -> id_o2wu
reaction11 = model.createReaction()
reaction11.setId("reaction11")
reaction11.setReversible(False)

reactant11 = reaction11.createReactant()
reactant11.setSpecies("id_ageg")
reactant11.setStoichiometry(1.0)
reactant11.setConstant(True)

product11 = reaction11.createProduct()
product11.setSpecies("id_o2wu")
product11.setStoichiometry(0.875)
product11.setConstant(True)

kinetic_law11 = reaction11.createKineticLaw()
kinetic_law11.setFormula("k11 * id_ageg")

parameter11 = kinetic_law11.createParameter()
parameter11.setId("k11")
parameter11.setValue(0.8)
parameter11.setUnits("id_p0jk")

# 12. Consumption of id_ml0z
reaction12 = model.createReaction()
reaction12.setId("reaction12")
reaction12.setReversible(False)

reactant12 = reaction12.createReactant()
reactant12.setSpecies("id_ml0z")
reactant12.setStoichiometry(1.0)
reactant12.setConstant(True)

kinetic_law12 = reaction12.createKineticLaw()
kinetic_law12.setFormula("k12 * id_ml0z")

parameter12 = kinetic_law12.createParameter()
parameter12.setId("k12")
parameter12.setValue(0.01)
parameter12.setUnits("id_p0jk")

# 13. Consumption of id_aprv
reaction13 = model.createReaction()
reaction13.setId("reaction13")
reaction13.setReversible(False)

reactant13 = reaction13.createReactant()
reactant13.setSpecies("id_aprv")
reactant13.setStoichiometry(1.0)
reactant13.setConstant(True)

kinetic_law13 = reaction13.createKineticLaw()
kinetic_law13.setFormula("k13 * id_aprv")

parameter13 = kinetic_law13.createParameter()
parameter13.setId("k13")
parameter13.setValue(0.01)
parameter13.setUnits("id_p0jk")

# 14. Consumption of id_nh4a
reaction14 = model.createReaction()
reaction14.setId("reaction14")
reaction14.setReversible(False)

reactant14 = reaction14.createReactant()
reactant14.setSpecies("id_nh4a")
reactant14.setStoichiometry(1.0)
reactant14.setConstant(True)

kinetic_law14 = reaction14.createKineticLaw()
kinetic_law14.setFormula("k14 * id_nh4a")

parameter14 = kinetic_law14.createParameter()
parameter14.setId("k14")
parameter14.setValue(0.01)
parameter14.setUnits("id_p0jk")

# 15. Consumption of id_o2wu
reaction15 = model.createReaction()
reaction15.setId("reaction15")
reaction15.setReversible(False)

reactant15 = reaction15.createReactant()
reactant15.setSpecies("id_o2wu")
reactant15.setStoichiometry(1.0)
reactant15.setConstant(True)

kinetic_law15 = reaction15.createKineticLaw()
kinetic_law15.setFormula("k15 * id_o2wu")

parameter15 = kinetic_law15.createParameter()
parameter15.setId("k15")
parameter15.setValue(0.01)
parameter15.setUnits("id_p0jk")

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

# Let's test our model by simulating it
print("Testing the model by simulation...")
simulation_result = simulate(updated_sbml)

# Compare the simulation with the experimental data
print("\nComparing simulation with experimental data at t=10:")
final_sim = simulation_result.iloc[-1]
final_exp = experiment_history["iteration_0"].iloc[-1]

comparison = pd.DataFrame({
    'Simulation': final_sim[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison)

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

# Print the reactions in the final model
print("\nReactions in the final model:")
print("1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.5)")
print("2. Production of id_j3mt (k2=0.3)")
print("3. Consumption of id_j3mt (k3=0.1)")
print("4. id_j3mt -> 0.015 id_ml0z (k4=0.02)")
print("5. id_j3mt -> 0.12 id_aprv (k5=0.15)")
print("6. Production of id_uqzr (k6=0.3)")
print("7. Consumption of id_uqzr (k7=0.1)")
print("8. id_uqzr -> 0.002 id_udn6 (k8=0.001)")
print("9. Production of id_ageg (k9=0.1)")
print("10. id_ageg -> 0.057 id_nh4a (k10=0.05)")
print("11. id_ageg -> 0.875 id_o2wu (k11=0.8)")
print("12. Consumption of id_ml0z (k12=0.01)")
print("13. Consumption of id_aprv (k13=0.01)")
print("14. Consumption of id_nh4a (k14=0.01)")
print("15. Consumption of id_o2wu (k15=0.01)")

# Let's also test our model with the high_uqzr experiment
print("\nTesting the model with high_uqzr experiment...")
# First, modify the initial concentration of id_uqzr in the model
species_uqzr = model.getSpecies("id_uqzr")
original_conc = species_uqzr.getInitialConcentration()
species_uqzr.setInitialConcentration(10.0)  # Set to high_uqzr value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_uqzr_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_uqzr model
high_uqzr_sim = simulate(high_uqzr_sbml)

# Compare with experimental data
final_sim_high_uqzr = high_uqzr_sim.iloc[-1]
final_exp_high_uqzr = experiment_history["iteration_3"].iloc[-1]

comparison_high_uqzr = pd.DataFrame({
    'Simulation': final_sim_high_uqzr[1:],  # Skip the Time column
    'Experiment': final_exp_high_uqzr[1:],  # Skip the Time column
    'Difference': final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:]) / final_exp_high_uqzr[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_uqzr experimental data at t=10:")
print(comparison_high_uqzr)

# Reset the initial concentration
species_uqzr.setInitialConcentration(original_conc)

# Let's also test our model with the high_ageg experiment
print("\nTesting the model with high_ageg experiment...")
# First, modify the initial concentration of id_ageg in the model
species_ageg = model.getSpecies("id_ageg")
original_ageg_conc = species_ageg.getInitialConcentration()
species_ageg.setInitialConcentration(1.4)  # Set to high_ageg value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_ageg_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_ageg model
high_ageg_sim = simulate(high_ageg_sbml)

# Compare with experimental data
final_sim_high_ageg = high_ageg_sim.iloc[-1]
final_exp_high_ageg = experiment_history["iteration_5"].iloc[-1]

comparison_high_ageg = pd.DataFrame({
    'Simulation': final_sim_high_ageg[1:],  # Skip the Time column
    'Experiment': final_exp_high_ageg[1:],  # Skip the Time column
    'Difference': final_sim_high_ageg[1:] - final_exp_high_ageg[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_ageg[1:] - final_exp_high_ageg[1:]) / final_exp_high_ageg[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_ageg experimental data at t=10:")
print(comparison_high_ageg)

# Reset the initial concentration
species_ageg.setInitialConcentration(original_ageg_conc)

# Create the final model
final_sbml = updated_sbml
```
# Observation

## Code Stdout
Testing the model by simulation...

Comparing simulation with experimental data at t=10:
         Simulation  Experiment  Difference  Relative_Error
id_ml0z    0.033333    0.040759   -0.007425       18.217938
id_aprv    2.000000    0.320706    1.679294      523.623600
id_j3mt    1.111111    2.688295   -1.577183       58.668550
id_uqzr    2.970297    2.592793    0.377504       14.559746
id_ageg    0.117647    0.105439    0.012208       11.578391
id_nh4a    0.033529    0.033802   -0.000273        0.807386
id_hdof    0.000080    0.000038    0.000042      110.345293
id_9e2p    1.999920    1.999962   -0.000042        0.002098
id_tod7    0.700000    0.700000    0.000000        0.000000
id_o2wu    8.235294    0.520000    7.715294     1483.710371
id_4vc0    1.600000    1.600000    0.000000        0.000000
id_r693  500.000000  500.000000    0.000000        0.000000
Time      10.000000   10.000000    0.000000        0.000000

Reactions in the final model:
1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.5)
2. Production of id_j3mt (k2=0.3)
3. Consumption of id_j3mt (k3=0.1)
4. id_j3mt -> 0.015 id_ml0z (k4=0.02)
5. id_j3mt -> 0.12 id_aprv (k5=0.15)
6. Production of id_uqzr (k6=0.3)
7. Consumption of id_uqzr (k7=0.1)
8. id_uqzr -> 0.002 id_udn6 (k8=0.001)
9. Production of id_ageg (k9=0.1)
10. id_ageg -> 0.057 id_nh4a (k10=0.05)
11. id_ageg -> 0.875 id_o2wu (k11=0.8)
12. Consumption of id_ml0z (k12=0.01)
13. Consumption of id_aprv (k13=0.01)
14. Consumption of id_nh4a (k14=0.01)
15. Consumption of id_o2wu (k15=0.01)

Testing the model with high_uqzr experiment...

Comparing simulation with high_uqzr experimental data at t=10:
         Simulation  Experiment    Difference  Relative_Error
id_ml0z    0.033333    0.055010 -2.167711e-02    3.940545e+01
id_aprv    2.000000    0.876831  1.123169e+00    1.280942e+02
id_j3mt    1.111111    5.501873 -4.390762e+00    7.980486e+01
id_uqzr    2.970297    5.307200 -2.336903e+00    4.403269e+01
id_ageg    0.117647    0.054443  6.320398e-02    1.160919e+02
id_nh4a    0.033529    0.036766 -3.236614e-03    8.803275e+00
id_hdof    0.000080    0.000078  1.581562e-06    2.016907e+00
id_9e2p    1.999920    1.999922 -1.581562e-06    7.908121e-05
id_tod7    0.700000    0.700000 -1.110223e-16    1.586033e-14
id_o2wu    8.235294    0.553780  7.681514e+00    1.387105e+03
id_4vc0    1.600000    1.600000  0.000000e+00    0.000000e+00
id_r693  500.000000  500.000000  0.000000e+00    0.000000e+00
Time      10.000000   10.000000  0.000000e+00    0.000000e+00

Testing the model with high_ageg experiment...

Comparing simulation with high_ageg experimental data at t=10:
         Simulation  Experiment    Difference  Relative_Error
id_ml0z    0.033333    0.067680 -3.434629e-02    5.074835e+01
id_aprv    2.000000    0.224606  1.775394e+00    7.904468e+02
id_j3mt    1.111111    2.345711 -1.234600e+00    5.263222e+01
id_uqzr    2.970297    2.508704  4.615925e-01    1.839964e+01
id_ageg    0.117647    0.239688 -1.220407e-01    5.091653e+01
id_nh4a    0.033529    0.065896 -3.236620e-02    4.911738e+01
id_hdof    0.000080    0.000033  4.687677e-05    1.415360e+02
id_9e2p    1.999920    1.999967 -4.687677e-05    2.343877e-03
id_tod7    0.700000    0.700000 -1.110223e-16    1.586033e-14
id_o2wu    8.235294    1.026737  7.208557e+00    7.020841e+02
id_4vc0    1.600000    1.600000  0.000000e+00    0.000000e+00
id_r693  500.000000  500.000000  0.000000e+00    0.000000e+00
Time      10.000000   10.000000  0.000000e+00    0.000000e+00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5, updated_sbml_v6, updated_sbml_v7, updated_sbml_v8)

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


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



# Iteration 19
## Thoughts
We've made significant progress! Our model now produces non-negative concentrations for all species, which is a major improvement. However, there are still some discrepancies between the simulated and experimental data:

1. id_aprv is significantly overestimated (2.0 vs 0.32)
2. id_o2wu is significantly overestimated (8.23 vs 0.52)
3. id_j3mt is underestimated (1.11 vs 2.69)

Let's adjust the parameters to better match the experimental data. We'll focus on:
1. Reducing the production of id_aprv
2. Reducing the production of id_o2wu
3. Increasing the production of id_j3mt

## Action

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

# Load the model from the previous iteration
sbml_doc = libsbml.readSBMLFromString(shared_variables.access("updated_sbml_v8"))
model = sbml_doc.getModel()

# Adjust parameters to better match experimental data
for reaction in model.getListOfReactions():
    kinetic_law = reaction.getKineticLaw()
    
    if reaction.getId() == "reaction2":  # Production of id_j3mt
        parameter = kinetic_law.getParameter("k2")
        parameter.setValue(0.5)  # Increase production of id_j3mt
    
    elif reaction.getId() == "reaction3":  # Consumption of id_j3mt
        parameter = kinetic_law.getParameter("k3")
        parameter.setValue(0.15)  # Increase consumption of id_j3mt
    
    elif reaction.getId() == "reaction5":  # id_j3mt -> id_aprv
        parameter = kinetic_law.getParameter("k5")
        parameter.setValue(0.02)  # Reduce production of id_aprv
    
    elif reaction.getId() == "reaction11":  # id_ageg -> id_o2wu
        parameter = kinetic_law.getParameter("k11")
        parameter.setValue(0.1)  # Reduce production of id_o2wu
    
    elif reaction.getId() == "reaction13":  # Consumption of id_aprv
        parameter = kinetic_law.getParameter("k13")
        parameter.setValue(0.1)  # Increase consumption of id_aprv
    
    elif reaction.getId() == "reaction15":  # Consumption of id_o2wu
        parameter = kinetic_law.getParameter("k15")
        parameter.setValue(0.1)  # Increase consumption of id_o2wu

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

# Let's test our model by simulating it
print("Testing the model with adjusted parameters...")
simulation_result = simulate(updated_sbml)

# Compare the simulation with the experimental data
print("\nComparing simulation with experimental data at t=10:")
final_sim = simulation_result.iloc[-1]
final_exp = experiment_history["iteration_0"].iloc[-1]

comparison = pd.DataFrame({
    'Simulation': final_sim[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison)

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

# Print the reactions in the final model with adjusted parameters
print("\nReactions in the final model with adjusted parameters:")
print("1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.5)")
print("2. Production of id_j3mt (k2=0.5)")
print("3. Consumption of id_j3mt (k3=0.15)")
print("4. id_j3mt -> 0.015 id_ml0z (k4=0.02)")
print("5. id_j3mt -> 0.12 id_aprv (k5=0.02)")
print("6. Production of id_uqzr (k6=0.3)")
print("7. Consumption of id_uqzr (k7=0.1)")
print("8. id_uqzr -> 0.002 id_udn6 (k8=0.001)")
print("9. Production of id_ageg (k9=0.1)")
print("10. id_ageg -> 0.057 id_nh4a (k10=0.05)")
print("11. id_ageg -> 0.875 id_o2wu (k11=0.1)")
print("12. Consumption of id_ml0z (k12=0.01)")
print("13. Consumption of id_aprv (k13=0.1)")
print("14. Consumption of id_nh4a (k14=0.01)")
print("15. Consumption of id_o2wu (k15=0.1)")

# Let's also test our model with the high_uqzr experiment
print("\nTesting the model with high_uqzr experiment...")
# First, modify the initial concentration of id_uqzr in the model
species_uqzr = model.getSpecies("id_uqzr")
original_conc = species_uqzr.getInitialConcentration()
species_uqzr.setInitialConcentration(10.0)  # Set to high_uqzr value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_uqzr_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_uqzr model
high_uqzr_sim = simulate(high_uqzr_sbml)

# Compare with experimental data
final_sim_high_uqzr = high_uqzr_sim.iloc[-1]
final_exp_high_uqzr = experiment_history["iteration_3"].iloc[-1]

comparison_high_uqzr = pd.DataFrame({
    'Simulation': final_sim_high_uqzr[1:],  # Skip the Time column
    'Experiment': final_exp_high_uqzr[1:],  # Skip the Time column
    'Difference': final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:]) / final_exp_high_uqzr[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_uqzr experimental data at t=10:")
print(comparison_high_uqzr)

# Reset the initial concentration
species_uqzr.setInitialConcentration(original_conc)

# Let's also test our model with the high_ageg experiment
print("\nTesting the model with high_ageg experiment...")
# First, modify the initial concentration of id_ageg in the model
species_ageg = model.getSpecies("id_ageg")
original_ageg_conc = species_ageg.getInitialConcentration()
species_ageg.setInitialConcentration(1.4)  # Set to high_ageg value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_ageg_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_ageg model
high_ageg_sim = simulate(high_ageg_sbml)

# Compare with experimental data
final_sim_high_ageg = high_ageg_sim.iloc[-1]
final_exp_high_ageg = experiment_history["iteration_5"].iloc[-1]

comparison_high_ageg = pd.DataFrame({
    'Simulation': final_sim_high_ageg[1:],  # Skip the Time column
    'Experiment': final_exp_high_ageg[1:],  # Skip the Time column
    'Difference': final_sim_high_ageg[1:] - final_exp_high_ageg[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_ageg[1:] - final_exp_high_ageg[1:]) / final_exp_high_ageg[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_ageg experimental data at t=10:")
print(comparison_high_ageg)

# Reset the initial concentration
species_ageg.setInitialConcentration(original_ageg_conc)

# Create the final model
final_sbml = updated_sbml
```
# Observation

## Code Stdout
Testing the model with adjusted parameters...

Comparing simulation with experimental data at t=10:
         Simulation  Experiment  Difference  Relative_Error
id_ml0z    0.078947    0.040759    0.038189       93.694357
id_aprv    0.063158    0.320706   -0.257548       80.306623
id_j3mt    2.631579    2.688295   -0.056716        2.109723
id_uqzr    2.970297    2.592793    0.377504       14.559746
id_ageg    0.666667    0.105439    0.561228      532.277552
id_nh4a    0.190000    0.033802    0.156198      462.091482
id_hdof    0.000080    0.000038    0.000042      110.345293
id_9e2p    1.999920    1.999962   -0.000042        0.002098
id_tod7    0.700000    0.700000    0.000000        0.000000
id_o2wu    0.583333    0.520000    0.063333       12.179485
id_4vc0    1.600000    1.600000    0.000000        0.000000
id_r693  500.000000  500.000000    0.000000        0.000000
Time      10.000000   10.000000    0.000000        0.000000

Reactions in the final model with adjusted parameters:
1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.5)
2. Production of id_j3mt (k2=0.5)
3. Consumption of id_j3mt (k3=0.15)
4. id_j3mt -> 0.015 id_ml0z (k4=0.02)
5. id_j3mt -> 0.12 id_aprv (k5=0.02)
6. Production of id_uqzr (k6=0.3)
7. Consumption of id_uqzr (k7=0.1)
8. id_uqzr -> 0.002 id_udn6 (k8=0.001)
9. Production of id_ageg (k9=0.1)
10. id_ageg -> 0.057 id_nh4a (k10=0.05)
11. id_ageg -> 0.875 id_o2wu (k11=0.1)
12. Consumption of id_ml0z (k12=0.01)
13. Consumption of id_aprv (k13=0.1)
14. Consumption of id_nh4a (k14=0.01)
15. Consumption of id_o2wu (k15=0.1)

Testing the model with high_uqzr experiment...

Comparing simulation with high_uqzr experimental data at t=10:
         Simulation  Experiment    Difference  Relative_Error
id_ml0z    0.078947    0.055010  2.393692e-02    4.351342e+01
id_aprv    0.063158    0.876831 -8.136730e-01    9.279703e+01
id_j3mt    2.631579    5.501873 -2.870294e+00    5.216940e+01
id_uqzr    2.970297    5.307200 -2.336903e+00    4.403269e+01
id_ageg    0.666667    0.054443  6.122236e-01    1.124521e+03
id_nh4a    0.190000    0.036766  1.532340e-01    4.167814e+02
id_hdof    0.000080    0.000078  1.581562e-06    2.016907e+00
id_9e2p    1.999920    1.999922 -1.581562e-06    7.908121e-05
id_tod7    0.700000    0.700000 -1.110223e-16    1.586033e-14
id_o2wu    0.583333    0.553780  2.955288e-02    5.336570e+00
id_4vc0    1.600000    1.600000  0.000000e+00    0.000000e+00
id_r693  500.000000  500.000000  0.000000e+00    0.000000e+00
Time      10.000000   10.000000  0.000000e+00    0.000000e+00

Testing the model with high_ageg experiment...

Comparing simulation with high_ageg experimental data at t=10:
         Simulation  Experiment    Difference  Relative_Error
id_ml0z    0.078947    0.067680  1.126775e-02    1.664865e+01
id_aprv    0.063158    0.224606 -1.614484e-01    7.188063e+01
id_j3mt    2.631579    2.345711  2.858681e-01    1.218684e+01
id_uqzr    2.970297    2.508704  4.615925e-01    1.839964e+01
id_ageg    0.666667    0.239688  4.269789e-01    1.781397e+02
id_nh4a    0.190000    0.065896  1.241044e-01    1.883348e+02
id_hdof    0.000080    0.000033  4.687677e-05    1.415360e+02
id_9e2p    1.999920    1.999967 -4.687677e-05    2.343877e-03
id_tod7    0.700000    0.700000 -1.110223e-16    1.586033e-14
id_o2wu    0.583333    1.026737 -4.434037e-01    4.318571e+01
id_4vc0    1.600000    1.600000  0.000000e+00    0.000000e+00
id_r693  500.000000  500.000000  0.000000e+00    0.000000e+00
Time      10.000000   10.000000  0.000000e+00    0.000000e+00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5, updated_sbml_v6, updated_sbml_v7, updated_sbml_v8, updated_sbml_v9)

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


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



# Iteration 20
## Thoughts
We've made significant progress with our model. The current version produces non-negative concentrations for all species and matches some of the experimental data reasonably well. However, there are still some discrepancies:

1. id_j3mt is now well-matched in the default experiment (2.63 vs 2.69)
2. id_o2wu is also reasonably matched (0.58 vs 0.52)
3. However, id_ageg is overestimated (0.67 vs 0.11)
4. id_nh4a is also overestimated (0.19 vs 0.03)
5. id_aprv is underestimated (0.06 vs 0.32)

Let's make one final adjustment to the parameters to improve the match with the experimental data. We'll focus on:
1. Reducing the production of id_ageg
2. Reducing the production of id_nh4a
3. Increasing the production of id_aprv

## Action

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

# Load the model from the previous iteration
sbml_doc = libsbml.readSBMLFromString(shared_variables.access("updated_sbml_v9"))
model = sbml_doc.getModel()

# Adjust parameters to better match experimental data
for reaction in model.getListOfReactions():
    kinetic_law = reaction.getKineticLaw()
    
    if reaction.getId() == "reaction5":  # id_j3mt -> id_aprv
        parameter = kinetic_law.getParameter("k5")
        parameter.setValue(0.1)  # Increase production of id_aprv
    
    elif reaction.getId() == "reaction9":  # Production of id_ageg
        parameter = kinetic_law.getParameter("k9")
        parameter.setValue(0.02)  # Reduce production of id_ageg
    
    elif reaction.getId() == "reaction10":  # id_ageg -> id_nh4a
        parameter = kinetic_law.getParameter("k10")
        parameter.setValue(0.01)  # Reduce production of id_nh4a

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

# Let's test our model by simulating it
print("Testing the model with final parameters...")
simulation_result = simulate(updated_sbml)

# Compare the simulation with the experimental data
print("\nComparing simulation with experimental data at t=10:")
final_sim = simulation_result.iloc[-1]
final_exp = experiment_history["iteration_0"].iloc[-1]

comparison = pd.DataFrame({
    'Simulation': final_sim[1:],  # Skip the Time column
    'Experiment': final_exp[1:],  # Skip the Time column
    'Difference': final_sim[1:] - final_exp[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim[1:] - final_exp[1:]) / final_exp[1:]) * 100  # Skip the Time column
})
print(comparison)

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

# Print the reactions in the final model with adjusted parameters
print("\nReactions in the final model with final parameters:")
print("1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.5)")
print("2. Production of id_j3mt (k2=0.5)")
print("3. Consumption of id_j3mt (k3=0.15)")
print("4. id_j3mt -> 0.015 id_ml0z (k4=0.02)")
print("5. id_j3mt -> 0.12 id_aprv (k5=0.1)")
print("6. Production of id_uqzr (k6=0.3)")
print("7. Consumption of id_uqzr (k7=0.1)")
print("8. id_uqzr -> 0.002 id_udn6 (k8=0.001)")
print("9. Production of id_ageg (k9=0.02)")
print("10. id_ageg -> 0.057 id_nh4a (k10=0.01)")
print("11. id_ageg -> 0.875 id_o2wu (k11=0.1)")
print("12. Consumption of id_ml0z (k12=0.01)")
print("13. Consumption of id_aprv (k13=0.1)")
print("14. Consumption of id_nh4a (k14=0.01)")
print("15. Consumption of id_o2wu (k15=0.1)")

# Let's also test our model with the high_uqzr experiment
print("\nTesting the model with high_uqzr experiment...")
# First, modify the initial concentration of id_uqzr in the model
species_uqzr = model.getSpecies("id_uqzr")
original_conc = species_uqzr.getInitialConcentration()
species_uqzr.setInitialConcentration(10.0)  # Set to high_uqzr value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_uqzr_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_uqzr model
high_uqzr_sim = simulate(high_uqzr_sbml)

# Compare with experimental data
final_sim_high_uqzr = high_uqzr_sim.iloc[-1]
final_exp_high_uqzr = experiment_history["iteration_3"].iloc[-1]

comparison_high_uqzr = pd.DataFrame({
    'Simulation': final_sim_high_uqzr[1:],  # Skip the Time column
    'Experiment': final_exp_high_uqzr[1:],  # Skip the Time column
    'Difference': final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_uqzr[1:] - final_exp_high_uqzr[1:]) / final_exp_high_uqzr[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_uqzr experimental data at t=10:")
print(comparison_high_uqzr)

# Reset the initial concentration
species_uqzr.setInitialConcentration(original_conc)

# Let's also test our model with the high_ageg experiment
print("\nTesting the model with high_ageg experiment...")
# First, modify the initial concentration of id_ageg in the model
species_ageg = model.getSpecies("id_ageg")
original_ageg_conc = species_ageg.getInitialConcentration()
species_ageg.setInitialConcentration(1.4)  # Set to high_ageg value

# Write the modified SBML model
writer = libsbml.SBMLWriter()
high_ageg_sbml = writer.writeSBMLToString(sbml_doc)

# Simulate the high_ageg model
high_ageg_sim = simulate(high_ageg_sbml)

# Compare with experimental data
final_sim_high_ageg = high_ageg_sim.iloc[-1]
final_exp_high_ageg = experiment_history["iteration_5"].iloc[-1]

comparison_high_ageg = pd.DataFrame({
    'Simulation': final_sim_high_ageg[1:],  # Skip the Time column
    'Experiment': final_exp_high_ageg[1:],  # Skip the Time column
    'Difference': final_sim_high_ageg[1:] - final_exp_high_ageg[1:],  # Skip the Time column
    'Relative_Error': abs((final_sim_high_ageg[1:] - final_exp_high_ageg[1:]) / final_exp_high_ageg[1:]) * 100  # Skip the Time column
})
print("\nComparing simulation with high_ageg experimental data at t=10:")
print(comparison_high_ageg)

# Reset the initial concentration
species_ageg.setInitialConcentration(original_ageg_conc)

# Create the final model
final_sbml = updated_sbml
```
# Observation


            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.
            ## Code Stdout
Testing the model with final parameters...

Comparing simulation with experimental data at t=10:
         Simulation  Experiment  Difference  Relative_Error
id_ml0z    0.055556    0.040759    0.014797       36.303437
id_aprv    0.222222    0.320706   -0.098484       30.708489
id_j3mt    1.851852    2.688295   -0.836443       31.114249
id_uqzr    2.970297    2.592793    0.377504       14.559746
id_ageg    0.181818    0.105439    0.076379       72.439332
id_nh4a    0.010364    0.033802   -0.023439       69.340465
id_hdof    0.000080    0.000038    0.000042      110.345293
id_9e2p    1.999920    1.999962   -0.000042        0.002098
id_tod7    0.700000    0.700000    0.000000        0.000000
id_o2wu    0.159091    0.520000   -0.360909       69.405595
id_4vc0    1.600000    1.600000    0.000000        0.000000
id_r693  500.000000  500.000000    0.000000        0.000000
Time      10.000000   10.000000    0.000000        0.000000

Reactions in the final model with final parameters:
1. id_9e2p <-> id_hdof (k1f=0.00002, k1r=0.5)
2. Production of id_j3mt (k2=0.5)
3. Consumption of id_j3mt (k3=0.15)
4. id_j3mt -> 0.015 id_ml0z (k4=0.02)
5. id_j3mt -> 0.12 id_aprv (k5=0.1)
6. Production of id_uqzr (k6=0.3)
7. Consumption of id_uqzr (k7=0.1)
8. id_uqzr -> 0.002 id_udn6 (k8=0.001)
9. Production of id_ageg (k9=0.02)
10. id_ageg -> 0.057 id_nh4a (k10=0.01)
11. id_ageg -> 0.875 id_o2wu (k11=0.1)
12. Consumption of id_ml0z (k12=0.01)
13. Consumption of id_aprv (k13=0.1)
14. Consumption of id_nh4a (k14=0.01)
15. Consumption of id_o2wu (k15=0.1)

Testing the model with high_uqzr experiment...

Comparing simulation with high_uqzr experimental data at t=10:
         Simulation  Experiment    Difference  Relative_Error
id_ml0z    0.055556    0.055010  5.451111e-04    9.909230e-01
id_aprv    0.222222    0.876831 -6.546086e-01    7.465620e+01
id_j3mt    1.851852    5.501873 -3.650021e+00    6.634143e+01
id_uqzr    2.970297    5.307200 -2.336903e+00    4.403269e+01
id_ageg    0.181818    0.054443  1.273751e-01    2.339601e+02
id_nh4a    0.010364    0.036766 -2.640239e-02    7.181192e+01
id_hdof    0.000080    0.000078  1.581562e-06    2.016907e+00
id_9e2p    1.999920    1.999922 -1.581562e-06    7.908121e-05
id_tod7    0.700000    0.700000 -1.110223e-16    1.586033e-14
id_o2wu    0.159091    0.553780 -3.946895e-01    7.127184e+01
id_4vc0    1.600000    1.600000  0.000000e+00    0.000000e+00
id_r693  500.000000  500.000000  0.000000e+00    0.000000e+00
Time      10.000000   10.000000  0.000000e+00    0.000000e+00

Testing the model with high_ageg experiment...

Comparing simulation with high_ageg experimental data at t=10:
         Simulation  Experiment    Difference  Relative_Error
id_ml0z    0.055556    0.067680 -1.212407e-02    1.791391e+01
id_aprv    0.222222    0.224606 -2.384119e-03    1.061466e+00
id_j3mt    1.851852    2.345711 -4.938590e-01    2.105370e+01
id_uqzr    2.970297    2.508704  4.615925e-01    1.839964e+01
id_ageg    0.181818    0.239688 -5.786955e-02    2.414373e+01
id_nh4a    0.010364    0.065896 -5.553197e-02    8.427265e+01
id_hdof    0.000080    0.000033  4.687677e-05    1.415360e+02
id_9e2p    1.999920    1.999967 -4.687677e-05    2.343877e-03
id_tod7    0.700000    0.700000 -1.110223e-16    1.586033e-14
id_o2wu    0.159091    1.026737 -8.676461e-01    8.450519e+01
id_4vc0    1.600000    1.600000  0.000000e+00    0.000000e+00
id_r693  500.000000  500.000000  0.000000e+00    0.000000e+00
Time      10.000000   10.000000  0.000000e+00    0.000000e+00

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 0/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (observation_data, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_v5, updated_sbml_v6, updated_sbml_v7, updated_sbml_v8, updated_sbml_v9, updated_sbml_final)

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


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



# Iteration 21
## Thoughts
I need to submit my final model. Based on all the experiments and simulations, I've developed a model that captures the key dynamics of the system. While there are still some discrepancies between the simulated and experimental data, the model provides a reasonable representation of the biological system with non-negative concentrations for all species.

The final model includes the following reactions:
1. id_9e2p <-> id_hdof (reversible reaction)
2. Production of id_j3mt
3. Consumption of id_j3mt
4. id_j3mt -> id_ml0z
5. id_j3mt -> id_aprv
6. Production of id_uqzr
7. Consumption of id_uqzr
8. id_uqzr -> id_udn6
9. Production of id_ageg
10. id_ageg -> id_nh4a
11. id_ageg -> id_o2wu
12. Consumption of id_ml0z
13. Consumption of id_aprv
14. Consumption of id_nh4a
15. Consumption of id_o2wu

I'll submit the final model that I've developed.

## Action

### Submit
```python
import libsbml

# Use the final model from the previous iteration
final_sbml = shared_variables.access("updated_sbml_final")
```
