
                # Interation 0

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


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

                <?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level2/version4" level="2" version="4">
  <model id="id_wciq">
    <listOfUnitDefinitions>
      <unitDefinition id="id_xx42">
        <listOfUnits>
          <unit kind="litre" exponent="1" scale="-3" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_wyjy">
        <listOfUnits>
          <unit kind="second" exponent="1" scale="0" multiplier="86400"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_wvh6">
        <listOfUnits>
          <unit kind="mole" exponent="1" scale="-3" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_48wi" spatialDimensions="3" size="1" constant="true"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_vzxw" compartment="id_48wi" initialConcentration="1" boundaryCondition="false" constant="false"/>
      <species id="id_gufr" compartment="id_48wi" initialConcentration="1" boundaryCondition="false" constant="false"/>
      <species id="id_c5ov" compartment="id_48wi" initialConcentration="1" boundaryCondition="false" constant="false"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

                Format your response according to the instructions in the system message.
                
## Thoughts
I notice that the SBML model contains three species (id_vzxw, id_gufr, id_c5ov) with initial concentrations of 1, but no reactions are defined. To understand the system's dynamics, I'll first observe the default behavior by running an experiment to see how these species change over time.

## Action

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

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

Total size: 1001 rows × 4 columns. 

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

Time   id_vzxw  id_gufr  id_c5ov
0  1.00e+00 1.00e+00 1.00e+00
...
2.00e+01  6.81e-03 3.98e+00 3.66e+01
...
4.00e+01  5.70e+00 1.28e+02 1.34e+03
...
6.00e+01  6.42e+02 4.48e+03 4.55e+04
...
8.00e+01  1.38e+04 9.00e+04 6.57e+05
...
1.00e+02  5.70e+04 3.67e+05 8.35e+05
...
1.20e+02  7.28e+01 2.35e+05 5.98e+00
...
1.40e+02  2.25e-02 1.29e+05 3.48e-03
...
1.60e+02  1.03e-03 7.08e+04 2.97e-04
...
1.80e+02  7.37e-04 3.89e+04 3.89e-04
...
2.00e+02  2.37e-03 2.13e+04 2.29e-03
...
2.20e+02  1.74e-02 1.17e+04 3.08e-02
...
2.40e+02  2.01e-01 6.42e+03 6.51e-01
...
2.60e+02  2.97e+00 3.53e+03 1.76e+01
...
2.80e+02  4.47e+01 1.99e+03 5.45e+02
...
3.00e+02  3.67e+02 2.80e+03 1.77e+04
...
3.20e+02  6.74e+03 4.41e+04 3.63e+05
...
3.40e+02  4.61e+04 2.97e+05 1.19e+06
...
3.60e+02  3.25e+03 2.74e+05 2.44e+02
...
3.80e+02  1.70e-01 1.51e+05 2.24e-02
...
4.00e+02  2.83e-03 8.26e+04 6.93e-04
...
4.20e+02  1.15e-03 4.54e+04 5.21e-04
...
4.40e+02  2.73e-03 2.49e+04 2.26e-03
...
4.60e+02  1.70e-02 1.37e+04 2.57e-02
...
4.80e+02  1.79e-01 7.50e+03 4.95e-01
...
5.00e+02  2.52e+00 4.12e+03 1.27e+01
...
5.20e+02  3.80e+01 2.30e+03 3.84e+02
...
5.40e+02  3.02e+02 2.46e+03 1.24e+04
...
5.60e+02  5.04e+03 3.31e+04 2.82e+05
...
5.80e+02  4.09e+04 2.64e+05 1.20e+06
...
6.00e+02  1.22e+04 2.92e+05 1.08e+03
...
6.20e+02  3.57e-01 1.60e+05 4.40e-02
...
6.40e+02  3.78e-03 8.79e+04 8.70e-04
...
6.60e+02  1.21e-03 4.82e+04 5.13e-04
...
6.80e+02  2.50e-03 2.65e+04 1.95e-03
...
7.00e+02  1.44e-02 1.45e+04 2.05e-02
...
7.20e+02  1.46e-01 7.97e+03 3.80e-01
...
7.40e+02  2.01e+00 4.38e+03 9.55e+00
...
7.60e+02  3.06e+01 2.43e+03 2.84e+02
...
7.80e+02  2.54e+02 2.22e+03 9.16e+03
...
8.00e+02  3.92e+03 2.58e+04 2.25e+05
...
8.20e+02  3.65e+04 2.36e+05 1.17e+06
...
8.40e+02  2.77e+04 3.07e+05 4.01e+03
...
8.60e+02  6.79e-01 1.69e+05 7.93e-02
...
8.80e+02  4.79e-03 9.26e+04 1.05e-03
...
9.00e+02  1.22e-03 5.08e+04 4.93e-04
...
9.20e+02  2.24e-03 2.79e+04 1.66e-03
...
9.40e+02  1.21e-02 1.53e+04 1.64e-02
...
9.60e+02  1.18e-01 8.40e+03 2.92e-01
...
1.00e+03  2.44e+01 2.55e+03 2.12e+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
The observation reveals a complex, oscillatory behavior in the system. The concentrations of the three species (id_vzxw, id_gufr, id_c5ov) show interesting dynamics:
1. They start at initial concentrations of 1
2. They exhibit multiple peaks and troughs over time
3. The oscillations seem to have a somewhat regular pattern, but with varying amplitudes

This suggests there are likely multiple interconnected reactions between these species. To better understand the system, I'll analyze the data more closely and then design a targeted experiment to probe the system's behavior.

I'll first visualize the data to get a clearer picture of the dynamics.

## Action

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

# Retrieve the full experiment data
data = experiment_history['iteration_0']

# Plot the time series for each species
plt.figure(figsize=(12, 6))
plt.plot(data['Time'], data['id_vzxw'], label='Species 1 (id_vzxw)')
plt.plot(data['Time'], data['id_gufr'], label='Species 2 (id_gufr)')
plt.plot(data['Time'], data['id_c5ov'], label='Species 3 (id_c5ov)')
plt.xlabel('Time')
plt.ylabel('Concentration')
plt.title('Species Concentration Over Time')
plt.legend()
plt.xscale('log')
plt.yscale('log')
plt.grid(True)
plt.tight_layout()
plt.show()

# Calculate some basic statistics
print("Peak times and values:")
for species in ['id_vzxw', 'id_gufr', 'id_c5ov']:
    peak_indices = data[species].diff().gt(0) & data[species].diff(1).lt(0)
    peak_times = data.loc[peak_indices, 'Time']
    peak_values = data.loc[peak_indices, species]
    print(f"\n{species}:")
    print("Peak Times:", peak_times.tolist())
    print("Peak Values:", peak_values.tolist())
```
# 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 the unauthorized matplotlib use. I'll modify my analysis to use only allowed libraries and focus on understanding the system's dynamics through numerical analysis.

Key observations from the previous data:
1. The system shows clear oscillatory behavior
2. Species concentrations vary by several orders of magnitude
3. There seem to be periodic patterns with different characteristics for each species

My goal is to understand the potential reaction mechanisms that could generate such dynamics. I'll analyze the data statistically and look for relationships between species.

## Action

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

# Retrieve the full experiment data
data = experiment_history['iteration_0']

# Calculate key statistical properties
stats = {}
for species in ['id_vzxw', 'id_gufr', 'id_c5ov']:
    stats[species] = {
        'mean': data[species].mean(),
        'median': data[species].median(),
        'max': data[species].max(),
        'min': data[species].min(),
        'std': data[species].std()
    }

# Print statistics
print("Species Statistics:")
for species, stat_dict in stats.items():
    print(f"\n{species}:")
    for stat_name, stat_value in stat_dict.items():
        print(f"{stat_name}: {stat_value}")

# Calculate correlations between species
correlation_matrix = data[['id_vzxw', 'id_gufr', 'id_c5ov']].corr()
print("\nCorrelation Matrix:")
print(correlation_matrix)

# Identify potential periodic behavior
def find_peaks(series):
    # Simple peak detection
    peaks = []
    for i in range(1, len(series)-1):
        if series.iloc[i] > series.iloc[i-1] and series.iloc[i] > series.iloc[i+1]:
            peaks.append(series.iloc[i])
    return peaks

peak_stats = {}
for species in ['id_vzxw', 'id_gufr', 'id_c5ov']:
    peaks = find_peaks(data[species])
    peak_stats[species] = {
        'num_peaks': len(peaks),
        'peak_mean': np.mean(peaks) if peaks else None,
        'peak_std': np.std(peaks) if peaks else None
    }

print("\nPeak Statistics:")
for species, stats in peak_stats.items():
    print(f"\n{species}:")
    for stat_name, stat_value in stats.items():
        print(f"{stat_name}: {stat_value}")
```

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 0.1,  // Reduce initial concentration of first species
        "id_gufr": 0.1,  // Reduce initial concentration of second species
        "id_c5ov": 0.1   // Reduce initial concentration of third species
    }
}
```
# Observation

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

Total size: 1001 rows × 4 columns. 

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

Time   id_vzxw  id_gufr  id_c5ov
0  1.00e-01 1.00e-01 1.00e-01
...
2.00e+01  6.88e-05 3.98e-01 3.66e+00
...
4.00e+01  7.75e-02 1.28e+01 1.34e+02
...
6.00e+01  4.27e+01 4.65e+02 4.86e+03
...
8.00e+01  2.26e+03 1.50e+04 1.43e+05
...
1.00e+02  2.87e+04 1.86e+05 1.07e+06
...
1.20e+02  5.07e+04 3.44e+05 4.69e+04
...
1.40e+02  1.81e+00 1.89e+05 1.87e-01
...
1.60e+02  4.82e-03 1.04e+05 9.34e-04
...
1.80e+02  7.22e-04 5.70e+04 2.59e-04
...
2.00e+02  9.86e-04 3.13e+04 6.48e-04
...
2.20e+02  4.53e-03 1.72e+04 5.45e-03
...
2.40e+02  4.05e-02 9.43e+03 8.89e-02
...
2.60e+02  5.21e-01 5.17e+03 2.09e+00
...
2.80e+02  8.07e+00 2.85e+03 6.00e+01
...
3.00e+02  1.01e+02 1.75e+03 1.91e+03
...
3.20e+02  9.99e+02 6.84e+03 5.93e+04
...
3.40e+02  1.63e+04 1.06e+05 7.33e+05
...
3.60e+02  5.68e+04 3.66e+05 6.36e+05
...
3.80e+02  3.93e+01 2.21e+05 3.45e+00
...
4.00e+02  2.36e-02 1.21e+05 3.89e-03
...
4.20e+02  1.55e-03 6.66e+04 4.75e-04
...
4.40e+02  1.35e-03 3.65e+04 7.62e-04
...
4.60e+02  4.86e-03 2.01e+04 5.01e-03
...
4.80e+02  3.79e-02 1.10e+04 7.14e-02
...
5.00e+02  4.53e-01 6.04e+03 1.56e+00
...
5.20e+02  6.77e+00 3.32e+03 4.29e+01
...
5.40e+02  8.91e+01 1.95e+03 1.34e+03
...
5.60e+02  7.46e+02 5.21e+03 4.22e+04
...
5.80e+02  1.29e+04 8.39e+04 6.13e+05
...
6.00e+02  5.53e+04 3.56e+05 8.80e+05
...
6.20e+02  1.31e+02 2.35e+05 1.08e+01
...
6.40e+02  4.07e-02 1.29e+05 6.30e-03
...
6.60e+02  1.87e-03 7.08e+04 5.37e-04
...
6.80e+02  1.34e-03 3.88e+04 7.06e-04
...
7.00e+02  4.30e-03 2.13e+04 4.17e-03
...
7.20e+02  3.16e-02 1.17e+04 5.60e-02
...
7.40e+02  3.66e-01 6.42e+03 1.18e+00
...
7.60e+02  5.38e+00 3.53e+03 3.20e+01
...
7.80e+02  7.42e+01 2.03e+03 9.91e+02
...
8.00e+02  5.86e+02 4.19e+03 3.15e+04
...
8.20e+02  1.04e+04 6.80e+04 5.20e+05
...
8.40e+02  5.29e+04 3.40e+05 1.03e+06
...
8.60e+02  3.76e+02 2.48e+05 2.94e+01
...
8.80e+02  6.49e-02 1.36e+05 9.51e-03
...
9.00e+02  2.15e-03 7.46e+04 5.86e-04
...
9.20e+02  1.29e-03 4.09e+04 6.45e-04
...
9.40e+02  3.75e-03 2.25e+04 3.45e-03
...
9.60e+02  2.61e-02 1.23e+04 4.39e-02
...
1.00e+03  4.26e+00 3.72e+03 2.40e+01

## Code Stdout
Species Statistics:

id_vzxw:
mean: 5582.885941265174
median: 0.7830123991368849
max: 57923.74927156997
min: 6.794606041976765e-05
std: 14169.508403227504

id_gufr:
mean: 76502.05902275197
median: 24185.674417460767
max: 372778.92648269323
min: 0.9885800930104088
std: 102532.358930375

id_c5ov:
mean: 114878.34752507546
median: 2.5607277879876253
max: 1232240.013139291
min: 0.0002585323974491048
std: 294041.23973388737

Correlation Matrix:
         id_vzxw   id_gufr   id_c5ov
id_vzxw  1.00000  0.786650  0.757920
id_gufr  0.78665  1.000000  0.522735
id_c5ov  0.75792  0.522735  1.000000

Peak Statistics:

id_vzxw:
num_peaks: 4
peak_mean: 57093.64466284885
peak_std: 481.5311503324353

id_gufr:
num_peaks: 4
peak_mean: 367517.81094693264
peak_std: 3051.2852440990237

id_c5ov:
num_peaks: 4
peak_mean: 1210937.981870841
peak_std: 12328.071191590541

## Reminder

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



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

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


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



# Iteration 3
## Thoughts
The analysis of both experiments reveals fascinating insights:

1. Correlation Analysis:
- Strong positive correlations between all species (0.52-0.79)
- This suggests interconnected reactions where species influence each other's concentrations

2. Dynamics Observations:
- Oscillatory behavior persists even with reduced initial concentrations
- Similar periodic patterns in both experiments
- High variability in concentrations (large standard deviations)

3. Peak Characteristics:
- Consistent number of peaks (4) in both experiments
- Different peak magnitudes when initial concentrations are changed

These observations suggest a complex reaction network with potential feedback loops or autocatalytic processes.

Hypothesis: There might be reactions involving:
- Mutual conversion between species
- Autocatalytic production
- Inhibitory interactions

To test this, I'll design an experiment to perturb one species significantly to probe the system's response.

## Action

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 0.01,  // Dramatically reduce first species
        "id_gufr": 10,    // Increase second species
        "id_c5ov": 0.5    // Moderate change in third species
    }
}
```
# 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 × 4 columns. 

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

Time   id_vzxw  id_gufr  id_c5ov
0  1.00e-02 1.00e+01 5.00e-01
...
2.00e+01  6.27e-03 7.20e+00 1.83e+01
...
4.00e+01  1.75e+00 6.67e+01 6.69e+02
...
6.00e+01  3.08e+02 2.29e+03 2.36e+04
...
8.00e+01  8.55e+03 5.58e+04 4.51e+05
...
1.00e+02  5.10e+04 3.29e+05 1.15e+06
...
1.20e+02  8.15e+02 2.64e+05 6.02e+01
...
1.40e+02  6.60e-02 1.45e+05 9.04e-03
...
1.60e+02  1.44e-03 7.95e+04 3.66e-04
...
1.80e+02  6.80e-04 4.36e+04 3.20e-04
...
2.00e+02  1.75e-03 2.39e+04 1.51e-03
...
2.20e+02  1.14e-02 1.31e+04 1.79e-02
...
2.40e+02  1.23e-01 7.21e+03 3.53e-01
...
2.60e+02  1.75e+00 3.96e+03 9.21e+00
...
2.80e+02  2.73e+01 2.20e+03 2.80e+02
...
3.00e+02  2.39e+02 2.08e+03 9.11e+03
...
3.20e+02  3.90e+03 2.57e+04 2.25e+05
...
3.40e+02  3.65e+04 2.36e+05 1.17e+06
...
3.60e+02  2.76e+04 3.08e+05 3.98e+03
...
3.80e+02  6.57e-01 1.69e+05 7.65e-02
...
4.00e+02  4.57e-03 9.28e+04 9.94e-04
...
4.20e+02  1.16e-03 5.09e+04 4.65e-04
...
4.40e+02  2.11e-03 2.79e+04 1.56e-03
...
4.60e+02  1.13e-02 1.53e+04 1.53e-02
...
4.80e+02  1.11e-01 8.42e+03 2.73e-01
...
5.00e+02  1.49e+00 4.62e+03 6.72e+00
...
5.20e+02  2.29e+01 2.55e+03 1.98e+02
...
5.40e+02  2.08e+02 2.02e+03 6.36e+03
...
5.60e+02  2.87e+03 1.90e+04 1.69e+05
...
5.80e+02  3.12e+04 2.02e+05 1.10e+06
...
6.00e+02  4.48e+04 3.27e+05 2.06e+04
...
6.20e+02  1.55e+00 1.80e+05 1.70e-01
...
6.40e+02  6.53e-03 9.86e+04 1.33e-03
...
6.60e+02  1.26e-03 5.41e+04 4.74e-04
...
6.80e+02  1.97e-03 2.97e+04 1.36e-03
...
7.00e+02  9.74e-03 1.63e+04 1.24e-02
...
7.20e+02  9.07e-02 8.95e+03 2.10e-01
...
7.40e+02  1.19e+00 4.91e+03 5.05e+00
...
7.60e+02  1.83e+01 2.71e+03 1.47e+02
...
7.80e+02  1.79e+02 1.94e+03 4.70e+03
...
8.00e+02  2.20e+03 1.47e+04 1.31e+05
...
8.20e+02  2.69e+04 1.74e+05 1.02e+06
...
8.40e+02  5.17e+04 3.43e+05 7.58e+04
...
8.60e+02  3.30e+00 1.89e+05 3.41e-01
...
8.80e+02  8.79e-03 1.04e+05 1.70e-03
...
9.00e+02  1.32e-03 5.70e+04 4.71e-04
...
9.20e+02  1.80e-03 3.13e+04 1.18e-03
...
9.40e+02  8.25e-03 1.72e+04 9.94e-03
...
9.60e+02  7.38e-02 9.43e+03 1.62e-01
...
1.00e+03  1.45e+01 2.85e+03 1.09e+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_2, iteration_3)
- `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 4
## Thoughts
The latest experiment provides crucial insights into the system's behavior:

1. Robustness of Oscillatory Dynamics:
- Despite dramatically different initial concentrations, the system maintains its oscillatory pattern
- Similar periodic behavior observed across all three experiments
- Suggests a robust, self-regulating network with complex interactions

2. Concentration Dynamics:
- Rapid growth and decline phases for all species
- Interdependence between species is evident
- Initial perturbations quickly get absorbed into the system's characteristic dynamics

3. Key Observations:
- The system seems to have an intrinsic "reset" mechanism
- Concentrations tend to converge to similar patterns regardless of initial conditions
- Indicates potential feedback loops or autocatalytic processes

Hypothesis: The system likely involves:
- Mutual catalysis between species
- Autocatalytic reactions
- Potential inhibitory interactions that prevent unlimited growth

To further probe the system, I'll analyze the rate of change and look for potential reaction mechanisms.

## Action

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

# Analyze rate of change for each species across experiments
def analyze_rate_of_change(experiment_ids):
    rate_of_change = {}
    for species in ['id_vzxw', 'id_gufr', 'id_c5ov']:
        species_changes = []
        for exp_id in experiment_ids:
            data = experiment_history[exp_id]
            # Calculate numerical derivative
            changes = data[species].diff() / data['Time'].diff()
            species_changes.append(changes)
        
        rate_of_change[species] = {
            'mean_rate': np.mean([np.nanmean(changes) for changes in species_changes]),
            'std_rate': np.mean([np.nanstd(changes) for changes in species_changes]),
            'max_rate': np.max([np.nanmax(np.abs(changes)) for changes in species_changes]),
            'min_rate': np.min([np.nanmin(np.abs(changes)) for changes in species_changes])
        }
    
    print("Rate of Change Analysis:")
    for species, stats in rate_of_change.items():
        print(f"\n{species}:")
        for stat_name, stat_value in stats.items():
            print(f"{stat_name}: {stat_value}")
    
    return rate_of_change

# Analyze rate of change across all experiments
analyze_rate_of_change(['iteration_0', 'iteration_2', 'iteration_3'])
```

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 5,    // Moderate increase
        "id_gufr": 0.05, // Significant decrease
        "id_c5ov": 20    // Large increase
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_4
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_4]

Total size: 1001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_4] for the full data

Time   id_vzxw  id_gufr  id_c5ov
0  5.00e+00 5.00e-02 2.00e+01
...
2.00e+01  1.93e+00 6.87e+01 7.31e+02
...
4.00e+01  3.40e+02 2.49e+03 2.57e+04
...
6.00e+01  9.13e+03 5.96e+04 4.75e+05
...
8.00e+01  5.20e+04 3.35e+05 1.13e+06
...
1.00e+02  5.86e+02 2.60e+05 4.37e+01
...
1.20e+02  5.67e-02 1.43e+05 7.90e-03
...
1.40e+02  1.37e-03 7.83e+04 3.54e-04
...
1.60e+02  6.84e-04 4.30e+04 3.27e-04
...
1.80e+02  1.81e-03 2.36e+04 1.59e-03
...
2.00e+02  1.20e-02 1.29e+04 1.92e-02
...
2.20e+02  1.31e-01 7.10e+03 3.82e-01
...
2.40e+02  1.87e+00 3.90e+03 1.00e+01
...
2.60e+02  2.91e+01 2.17e+03 3.05e+02
...
2.80e+02  2.51e+02 2.15e+03 9.92e+03
...
3.00e+02  4.20e+03 2.76e+04 2.40e+05
...
3.20e+02  3.78e+04 2.44e+05 1.19e+06
...
3.40e+02  2.28e+04 3.03e+05 2.73e+03
...
3.60e+02  5.45e-01 1.67e+05 6.46e-02
...
3.80e+02  4.26e-03 9.14e+04 9.42e-04
...
4.00e+02  1.15e-03 5.02e+04 4.70e-04
...
4.20e+02  2.18e-03 2.75e+04 1.63e-03
...
4.40e+02  1.19e-02 1.51e+04 1.63e-02
...
4.60e+02  1.18e-01 8.29e+03 2.94e-01
...
4.80e+02  1.59e+00 4.55e+03 7.29e+00
...
5.00e+02  2.45e+01 2.52e+03 2.15e+02
...
5.20e+02  2.17e+02 2.05e+03 6.93e+03
...
5.40e+02  3.09e+03 2.04e+04 1.81e+05
...
5.60e+02  3.24e+04 2.10e+05 1.12e+06
...
5.80e+02  4.17e+04 3.22e+05 1.40e+04
...
6.00e+02  1.27e+00 1.77e+05 1.41e-01
...
6.20e+02  6.04e-03 9.72e+04 1.25e-03
...
6.40e+02  1.24e-03 5.33e+04 4.77e-04
...
6.60e+02  2.02e-03 2.93e+04 1.42e-03
...
6.80e+02  1.02e-02 1.61e+04 1.32e-02
...
7.00e+02  9.63e-02 8.81e+03 2.27e-01
...
7.20e+02  1.28e+00 4.84e+03 5.48e+00
...
7.40e+02  1.96e+01 2.67e+03 1.60e+02
...
7.60e+02  1.87e+02 1.96e+03 5.12e+03
...
7.80e+02  2.38e+03 1.58e+04 1.41e+05
...
8.00e+02  2.81e+04 1.82e+05 1.04e+06
...
8.20e+02  5.02e+04 3.38e+05 5.34e+04
...
8.40e+02  2.65e+00 1.87e+05 2.79e-01
...
8.60e+02  8.07e-03 1.02e+05 1.59e-03
...
8.80e+02  1.30e-03 5.62e+04 4.72e-04
...
9.00e+02  1.84e-03 3.08e+04 1.23e-03
...
9.20e+02  8.66e-03 1.69e+04 1.06e-02
...
9.40e+02  7.83e-02 9.29e+03 1.75e-01
...
9.60e+02  1.01e+00 5.10e+03 4.13e+00
...
1.00e+03  1.60e+02 1.91e+03 3.80e+03

## Code Stdout
Rate of Change Analysis:

id_vzxw:
mean_rate: 0.014027819848540216
std_rate: 1375.9405294220899
max_rate: 10241.024451626221
min_rate: 1.348222317600787e-07

id_gufr:
mean_rate: 3.0352230492880623
std_rate: 5011.302359259204
max_rate: 16783.974655146594
min_rate: 0.0001739090808578897

id_c5ov:
mean_rate: 0.11450773118961864
std_rate: 26093.940589090274
max_rate: 136788.84481291875
min_rate: 2.428785462661341e-07

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4)
- `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 5
## Thoughts
The rate of change analysis reveals critical insights into the system's dynamics:

1. Highly Variable Reaction Rates:
- Enormous standard deviations in rates for all species
- Extremely wide range between min and max rates
- Suggests complex, non-linear interactions

2. Species-Specific Characteristics:
- id_c5ov shows the highest variability in rate of change
- id_gufr has most consistent mean rate of change
- id_vzxw demonstrates most erratic behavior

3. Key Observations:
- Rates are not linear or predictable
- Strong interdependence between species
- Potential for multiple simultaneous reaction mechanisms

Hypothesis: The system likely involves:
- Autocatalytic reactions
- Mutual inhibition
- Complex feedback loops with non-linear kinetics

Proposed Reaction Mechanisms:
1. Autocatalytic production of species
2. Cross-catalysis between species
3. Saturation-based inhibition

To validate this, I'll design an experiment to test these potential mechanisms by introducing a more extreme initial condition.

## Action

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 100,   // Large increase
        "id_gufr": 0.001, // Extremely low concentration
        "id_c5ov": 0.1    // Low concentration
    }
}
```

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

def analyze_reaction_characteristics(experiment_ids):
    characteristics = {}
    for species in ['id_vzxw', 'id_gufr', 'id_c5ov']:
        species_data = []
        for exp_id in experiment_ids:
            data = experiment_history[exp_id]
            
            # Calculate time to first peak
            peak_time = data.loc[data[species].idxmax(), 'Time']
            
            # Calculate peak height and width
            peak_height = data[species].max()
            peak_width = data.loc[data[species] > peak_height/2, 'Time'].max() - \
                         data.loc[data[species] > peak_height/2, 'Time'].min()
            
            species_data.append({
                'peak_time': peak_time,
                'peak_height': peak_height,
                'peak_width': peak_width
            })
        
        # Aggregate statistics
        characteristics[species] = {
            'avg_peak_time': np.mean([d['peak_time'] for d in species_data]),
            'avg_peak_height': np.mean([d['peak_height'] for d in species_data]),
            'avg_peak_width': np.mean([d['peak_width'] for d in species_data]),
            'peak_time_variation': np.std([d['peak_time'] for d in species_data]),
            'peak_height_variation': np.std([d['peak_height'] for d in species_data])
        }
    
    print("Reaction Characteristics:")
    for species, stats in characteristics.items():
        print(f"\n{species}:")
        for stat_name, stat_value in stats.items():
            print(f"{stat_name}: {stat_value}")
    
    return characteristics

# Analyze characteristics across experiments
analyze_reaction_characteristics(['iteration_0', 'iteration_2', 'iteration_3', 'iteration_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 × 4 columns. 

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

Time   id_vzxw  id_gufr  id_c5ov
0  1.00e+02 1.00e-03 1.00e-01
...
2.00e+01  5.92e-05 3.44e-01 3.66e+00
...
4.00e+01  7.73e-02 1.28e+01 1.34e+02
...
6.00e+01  4.27e+01 4.65e+02 4.86e+03
...
8.00e+01  2.26e+03 1.50e+04 1.43e+05
...
1.00e+02  2.87e+04 1.86e+05 1.07e+06
...
1.20e+02  5.07e+04 3.44e+05 4.69e+04
...
1.40e+02  1.81e+00 1.89e+05 1.87e-01
...
1.60e+02  4.82e-03 1.04e+05 9.34e-04
...
1.80e+02  7.22e-04 5.70e+04 2.59e-04
...
2.00e+02  9.86e-04 3.13e+04 6.48e-04
...
2.20e+02  4.53e-03 1.72e+04 5.45e-03
...
2.40e+02  4.05e-02 9.43e+03 8.90e-02
...
2.60e+02  5.21e-01 5.17e+03 2.09e+00
...
2.80e+02  8.07e+00 2.85e+03 6.00e+01
...
3.00e+02  1.01e+02 1.75e+03 1.92e+03
...
3.20e+02  9.99e+02 6.84e+03 5.93e+04
...
3.40e+02  1.63e+04 1.06e+05 7.33e+05
...
3.60e+02  5.68e+04 3.66e+05 6.36e+05
...
3.80e+02  3.93e+01 2.21e+05 3.45e+00
...
4.00e+02  2.36e-02 1.21e+05 3.89e-03
...
4.20e+02  1.55e-03 6.66e+04 4.75e-04
...
4.40e+02  1.35e-03 3.65e+04 7.62e-04
...
4.60e+02  4.86e-03 2.01e+04 5.01e-03
...
4.80e+02  3.79e-02 1.10e+04 7.14e-02
...
5.00e+02  4.53e-01 6.04e+03 1.56e+00
...
5.20e+02  6.77e+00 3.32e+03 4.29e+01
...
5.40e+02  8.91e+01 1.95e+03 1.34e+03
...
5.60e+02  7.46e+02 5.21e+03 4.22e+04
...
5.80e+02  1.29e+04 8.39e+04 6.13e+05
...
6.00e+02  5.53e+04 3.56e+05 8.80e+05
...
6.20e+02  1.31e+02 2.35e+05 1.08e+01
...
6.40e+02  4.07e-02 1.29e+05 6.30e-03
...
6.60e+02  1.87e-03 7.08e+04 5.37e-04
...
6.80e+02  1.34e-03 3.88e+04 7.06e-04
...
7.00e+02  4.30e-03 2.13e+04 4.16e-03
...
7.20e+02  3.16e-02 1.17e+04 5.60e-02
...
7.40e+02  3.66e-01 6.42e+03 1.18e+00
...
7.60e+02  5.38e+00 3.53e+03 3.20e+01
...
7.80e+02  7.42e+01 2.03e+03 9.90e+02
...
8.00e+02  5.86e+02 4.19e+03 3.15e+04
...
8.20e+02  1.04e+04 6.80e+04 5.20e+05
...
8.40e+02  5.29e+04 3.40e+05 1.03e+06
...
8.60e+02  3.76e+02 2.48e+05 2.95e+01
...
8.80e+02  6.49e-02 1.36e+05 9.52e-03
...
9.00e+02  2.15e-03 7.46e+04 5.86e-04
...
9.20e+02  1.29e-03 4.09e+04 6.44e-04
...
9.40e+02  3.75e-03 2.25e+04 3.44e-03
...
9.60e+02  2.61e-02 1.23e+04 4.39e-02
...
1.00e+03  4.25e+00 3.72e+03 2.39e+01

## Code Stdout
Reaction Characteristics:

id_vzxw:
avg_peak_time: 102.0
avg_peak_height: 57912.752034216275
avg_peak_width: 751.25
peak_time_variation: 10.88577052853862
peak_height_variation: 18.34214510074537

id_gufr:
avg_peak_time: 102.25
avg_peak_height: 372725.25472993206
avg_peak_width: 768.25
peak_time_variation: 10.497023387608508
peak_height_variation: 130.4426423752567

id_c5ov:
avg_peak_time: 93.0
avg_peak_height: 1231929.974740499
avg_peak_width: 750.75
peak_time_variation: 10.88577052853862
peak_height_variation: 267.6526487363707

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5)
- `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 6
## Thoughts
The reaction characteristics analysis reveals profound insights into the system's dynamics:

1. Consistent Peak Timing:
- All species have remarkably similar average peak times (93-102 time units)
- Low variation in peak timing (around 10-11 time units)
- Suggests a synchronized, coordinated response mechanism

2. Peak Height Characteristics:
- Significant variations in peak heights
- id_c5ov shows highest peak height and greatest variation
- Indicates potential non-linear amplification mechanisms

3. Robustness of System:
- Consistent peak width across experiments (750-768 time units)
- System maintains similar dynamic behavior despite extreme initial conditions
- Strong evidence of complex, self-regulating interactions

Key Observations:
- Synchronized oscillatory behavior
- Non-linear interaction dynamics
- Potential for mutual catalysis and inhibition

Hypothesis Refinement:
1. Autocatalytic reactions with cross-species interactions
2. Saturation-based inhibition mechanisms
3. Feedback loops that maintain system stability

Next Strategy:
- Design an experiment to probe the system's response to asymmetric perturbations
- Focus on understanding the interaction mechanisms between species

## Action

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 0.5,   // Low concentration
        "id_gufr": 50,    // High concentration
        "id_c5ov": 0.01   // Very low concentration
    }
}
```

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

def analyze_interaction_dynamics(experiment_ids):
    interaction_metrics = {}
    
    for species1 in ['id_vzxw', 'id_gufr', 'id_c5ov']:
        for species2 in ['id_vzxw', 'id_gufr', 'id_c5ov']:
            if species1 != species2:
                cross_correlations = []
                phase_shifts = []
                
                for exp_id in experiment_ids:
                    data = experiment_history[exp_id]
                    
                    # Calculate cross-correlation
                    correlation = data[species1].corr(data[species2])
                    cross_correlations.append(correlation)
                    
                    # Estimate phase shift
                    max_s1 = data[species1].idxmax()
                    max_s2 = data[species2].idxmax()
                    phase_shift = abs(data.loc[max_s1, 'Time'] - data.loc[max_s2, 'Time'])
                    phase_shifts.append(phase_shift)
                
                interaction_metrics[f'{species1}_vs_{species2}'] = {
                    'avg_correlation': np.mean(cross_correlations),
                    'correlation_variation': np.std(cross_correlations),
                    'avg_phase_shift': np.mean(phase_shifts),
                    'phase_shift_variation': np.std(phase_shifts)
                }
    
    print("Species Interaction Dynamics:")
    for interaction, metrics in interaction_metrics.items():
        print(f"\n{interaction}:")
        for metric_name, metric_value in metrics.items():
            print(f"{metric_name}: {metric_value}")
    
    return interaction_metrics

# Analyze interaction dynamics across experiments
analyze_interaction_dynamics(['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5'])
```
# Observation

## Experiment Result
Experiment ID: iteration_6
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_6]

Total size: 1001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_6] for the full data

Time   id_vzxw  id_gufr  id_c5ov
0  5.00e-01 5.00e+01 1.00e-02
...
2.00e+01  4.83e-04 2.75e+01 3.65e-01
...
4.00e+01  1.04e-02 1.63e+01 1.33e+01
...
6.00e+01  1.10e+00 5.47e+01 4.88e+02
...
8.00e+01  2.17e+02 1.68e+03 1.74e+04
...
1.00e+02  6.73e+03 4.41e+04 3.70e+05
...
1.20e+02  4.71e+04 3.04e+05 1.22e+06
...
1.40e+02  2.66e+03 2.78e+05 1.94e+02
...
1.60e+02  1.15e-01 1.53e+05 1.49e-02
...
1.80e+02  1.73e-03 8.38e+04 4.18e-04
...
2.00e+02  6.70e-04 4.60e+04 2.98e-04
...
2.20e+02  1.54e-03 2.52e+04 1.26e-03
...
2.40e+02  9.41e-03 1.38e+04 1.41e-02
...
2.60e+02  9.84e-02 7.60e+03 2.69e-01
...
2.80e+02  1.38e+00 4.17e+03 6.88e+00
...
3.00e+02  2.16e+01 2.31e+03 2.07e+02
...
3.20e+02  2.01e+02 1.91e+03 6.72e+03
...
3.40e+02  3.01e+03 1.99e+04 1.77e+05
...
3.60e+02  3.21e+04 2.08e+05 1.12e+06
...
3.80e+02  4.27e+04 3.24e+05 1.56e+04
...
4.00e+02  1.31e+00 1.78e+05 1.44e-01
...
4.20e+02  5.92e-03 9.77e+04 1.22e-03
...
4.40e+02  1.19e-03 5.36e+04 4.52e-04
...
4.60e+02  1.90e-03 2.94e+04 1.33e-03
...
4.80e+02  9.52e-03 1.62e+04 1.22e-02
...
5.00e+02  8.93e-02 8.87e+03 2.09e-01
...
5.20e+02  1.18e+00 4.87e+03 5.04e+00
...
5.40e+02  1.81e+01 2.69e+03 1.47e+02
...
5.60e+02  1.77e+02 1.93e+03 4.70e+03
...
5.80e+02  2.20e+03 1.47e+04 1.31e+05
...
6.00e+02  2.69e+04 1.75e+05 1.02e+06
...
6.20e+02  5.17e+04 3.43e+05 7.55e+04
...
6.40e+02  3.28e+00 1.89e+05 3.39e-01
...
6.60e+02  8.74e-03 1.04e+05 1.69e-03
...
6.80e+02  1.31e-03 5.70e+04 4.69e-04
...
7.00e+02  1.79e-03 3.13e+04 1.18e-03
...
7.20e+02  8.21e-03 1.72e+04 9.89e-03
...
7.40e+02  7.34e-02 9.43e+03 1.61e-01
...
7.60e+02  9.45e-01 5.17e+03 3.79e+00
...
7.80e+02  1.45e+01 2.85e+03 1.09e+02
...
8.00e+02  1.53e+02 1.90e+03 3.47e+03
...
8.20e+02  1.69e+03 1.13e+04 1.01e+05
...
8.40e+02  2.30e+04 1.49e+05 9.25e+05
...
8.60e+02  5.50e+04 3.56e+05 2.13e+05
...
8.80e+02  7.34e+00 2.00e+05 7.18e-01
...
9.00e+02  1.21e-02 1.09e+05 2.22e-03
...
9.20e+02  1.40e-03 6.01e+04 4.74e-04
...
9.40e+02  1.65e-03 3.30e+04 1.03e-03
...
9.60e+02  7.00e-03 1.81e+04 7.99e-03
...
1.00e+03  7.53e-01 5.45e+03 2.87e+00

## Code Stdout
Species Interaction Dynamics:

id_vzxw_vs_id_gufr:
avg_correlation: 0.7866253877321483
correlation_variation: 3.5965933038471685e-05
avg_phase_shift: 0.2
phase_shift_variation: 0.4

id_vzxw_vs_id_c5ov:
avg_correlation: 0.7579173403934502
correlation_variation: 7.1010235499872695e-06
avg_phase_shift: 9.0
phase_shift_variation: 0.0

id_gufr_vs_id_vzxw:
avg_correlation: 0.7866253877321483
correlation_variation: 3.596593303846049e-05
avg_phase_shift: 0.2
phase_shift_variation: 0.4

id_gufr_vs_id_c5ov:
avg_correlation: 0.5227286164070606
correlation_variation: 1.8284097633159176e-05
avg_phase_shift: 9.2
phase_shift_variation: 0.39999999999999997

id_c5ov_vs_id_vzxw:
avg_correlation: 0.7579173403934502
correlation_variation: 7.1010235499872695e-06
avg_phase_shift: 9.0
phase_shift_variation: 0.0

id_c5ov_vs_id_gufr:
avg_correlation: 0.5227286164070606
correlation_variation: 1.82840976331726e-05
avg_phase_shift: 9.2
phase_shift_variation: 0.39999999999999997

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6)
- `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 7
## Thoughts
The interaction dynamics analysis reveals profound insights into the system's behavior:

1. Correlation Characteristics:
- Strong positive correlations between species
  - id_vzxw and id_gufr: 0.787 (highest correlation)
  - id_vzxw and id_c5ov: 0.758
  - id_gufr and id_c5ov: 0.523 (weakest, but still significant)

2. Phase Shift Dynamics:
- Consistent phase shifts between species
- Most interactions show ~9 time unit shifts
- Suggests synchronized but slightly offset oscillatory behavior

3. Key Observations:
- Highly interconnected system
- Non-linear, mutually dependent interactions
- Potential for complex feedback mechanisms

Refined Hypothesis:
1. Autocatalytic reactions with cross-species interactions
2. Saturation-based inhibition mechanisms
3. Delayed feedback loops causing phase shifts

Proposed Reaction Mechanisms:
- Mutual activation between species
- Saturation-based inhibition preventing unlimited growth
- Time-delayed feedback loops

Strategy:
- Design an experiment to test the inhibition hypothesis
- Introduce an extreme initial condition to probe system's response

## Action

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 0.001,  // Extremely low concentration
        "id_gufr": 100,    // Very high concentration
        "id_c5ov": 500     // Extremely high concentration
    }
}
```

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

def analyze_nonlinear_dynamics(experiment_ids):
    nonlinear_metrics = {}
    
    for species in ['id_vzxw', 'id_gufr', 'id_c5ov']:
        species_metrics = {}
        
        for exp_id in experiment_ids:
            data = experiment_history[exp_id]
            
            # Calculate growth rates at different concentration ranges
            low_conc = data[data[species] < data[species].quantile(0.25)]
            mid_conc = data[(data[species] >= data[species].quantile(0.25)) & 
                            (data[species] <= data[species].quantile(0.75))]
            high_conc = data[data[species] > data[species].quantile(0.75)]
            
            species_metrics[exp_id] = {
                'low_conc_growth_rate': np.mean(np.diff(low_conc[species]) / np.diff(low_conc['Time'])),
                'mid_conc_growth_rate': np.mean(np.diff(mid_conc[species]) / np.diff(mid_conc['Time'])),
                'high_conc_growth_rate': np.mean(np.diff(high_conc[species]) / np.diff(high_conc['Time']))
            }
        
        # Aggregate metrics across experiments
        nonlinear_metrics[species] = {
            'avg_low_conc_growth_rate': np.mean([m['low_conc_growth_rate'] for m in species_metrics.values()]),
            'avg_mid_conc_growth_rate': np.mean([m['mid_conc_growth_rate'] for m in species_metrics.values()]),
            'avg_high_conc_growth_rate': np.mean([m['high_conc_growth_rate'] for m in species_metrics.values()]),
            'growth_rate_variation': np.std([m['high_conc_growth_rate'] - m['low_conc_growth_rate'] for m in species_metrics.values()])
        }
    
    print("Nonlinear Growth Dynamics:")
    for species, metrics in nonlinear_metrics.items():
        print(f"\n{species}:")
        for metric_name, metric_value in metrics.items():
            print(f"{metric_name}: {metric_value}")
    
    return nonlinear_metrics

# Analyze nonlinear dynamics across experiments
analyze_nonlinear_dynamics(['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 'iteration_6'])
```
# 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 × 4 columns. 

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

Time   id_vzxw  id_gufr  id_c5ov
0  1.00e-03 1.00e+02 5.00e+02
...
2.00e+01  2.26e+02 1.74e+03 1.77e+04
...
4.00e+01  6.85e+03 4.48e+04 3.75e+05
...
6.00e+01  4.73e+04 3.05e+05 1.21e+06
...
8.00e+01  2.46e+03 2.77e+05 1.79e+02
...
1.00e+02  1.11e-01 1.52e+05 1.45e-02
...
1.20e+02  1.73e-03 8.34e+04 4.19e-04
...
1.40e+02  6.79e-04 4.58e+04 3.04e-04
...
1.60e+02  1.57e-03 2.51e+04 1.29e-03
...
1.80e+02  9.67e-03 1.38e+04 1.45e-02
...
2.00e+02  1.01e-01 7.57e+03 2.78e-01
...
2.20e+02  1.42e+00 4.16e+03 7.12e+00
...
2.40e+02  2.23e+01 2.30e+03 2.14e+02
...
2.60e+02  2.05e+02 1.93e+03 6.97e+03
...
2.80e+02  3.11e+03 2.05e+04 1.82e+05
...
3.00e+02  3.26e+04 2.11e+05 1.12e+06
...
3.20e+02  4.13e+04 3.22e+05 1.33e+04
...
3.40e+02  1.20e+00 1.77e+05 1.33e-01
...
3.60e+02  5.74e-03 9.71e+04 1.19e-03
...
3.80e+02  1.18e-03 5.33e+04 4.53e-04
...
4.00e+02  1.92e-03 2.93e+04 1.35e-03
...
4.20e+02  9.73e-03 1.61e+04 1.25e-02
...
4.40e+02  9.17e-02 8.81e+03 2.16e-01
...
4.60e+02  1.21e+00 4.84e+03 5.22e+00
...
4.80e+02  1.87e+01 2.67e+03 1.52e+02
...
5.00e+02  1.81e+02 1.93e+03 4.87e+03
...
5.20e+02  2.28e+03 1.51e+04 1.35e+05
...
5.40e+02  2.74e+04 1.78e+05 1.03e+06
...
5.60e+02  5.11e+04 3.41e+05 6.52e+04
...
5.80e+02  2.99e+00 1.88e+05 3.11e-01
...
6.00e+02  8.43e-03 1.03e+05 1.64e-03
...
6.20e+02  1.30e-03 5.67e+04 4.69e-04
...
6.40e+02  1.81e-03 3.11e+04 1.20e-03
...
6.60e+02  8.38e-03 1.71e+04 1.02e-02
...
6.80e+02  7.53e-02 9.37e+03 1.67e-01
...
7.00e+02  9.72e-01 5.14e+03 3.93e+00
...
7.20e+02  1.49e+01 2.83e+03 1.13e+02
...
7.40e+02  1.56e+02 1.90e+03 3.60e+03
...
7.60e+02  1.74e+03 1.17e+04 1.04e+05
...
7.80e+02  2.34e+04 1.52e+05 9.37e+05
...
8.00e+02  5.47e+04 3.55e+05 1.91e+05
...
8.20e+02  6.64e+00 1.98e+05 6.54e-01
...
8.40e+02  1.16e-02 1.09e+05 2.15e-03
...
8.60e+02  1.38e-03 5.97e+04 4.73e-04
...
8.80e+02  1.67e-03 3.28e+04 1.05e-03
...
9.00e+02  7.14e-03 1.80e+04 8.21e-03
...
9.20e+02  6.14e-02 9.87e+03 1.29e-01
...
9.40e+02  7.74e-01 5.42e+03 2.97e+00
...
9.60e+02  1.18e+01 2.98e+03 8.42e+01
...
1.00e+03  1.34e+03 9.07e+03 7.98e+04

## Code Stdout
Nonlinear Growth Dynamics:

id_vzxw:
avg_low_conc_growth_rate: 2.0504632713244484e-05
avg_mid_conc_growth_rate: 0.7640426568136222
avg_high_conc_growth_rate: 1.507920233665421
growth_rate_variation: 1.170550532015936

id_gufr:
avg_low_conc_growth_rate: 8.690084896193705
avg_mid_conc_growth_rate: -33.11081424412453
avg_high_conc_growth_rate: -73.99660698675535
growth_rate_variation: 37.54819051181354

id_c5ov:
avg_low_conc_growth_rate: 2.9198103319458362e-06
avg_mid_conc_growth_rate: 9.346086139396538
avg_high_conc_growth_rate: 42.86658079654621
growth_rate_variation: 16.576291539404046

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7)
- `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 8
## Thoughts
The nonlinear growth dynamics analysis reveals critical insights into the system's complex behavior:

1. Species-Specific Growth Dynamics:
- id_vzxw: 
  - Relatively stable growth rates
  - Moderate nonlinearity (growth rate variation: 1.17)
  - Transitions smoothly between concentration ranges

- id_gufr:
  - Highly nonlinear behavior
  - Dramatic shift from positive to negative growth rates
  - Large growth rate variation (37.55)
  - Suggests strong inhibitory mechanisms

- id_c5ov:
  - Moderate nonlinearity (growth rate variation: 16.58)
  - Increasing growth rates at higher concentrations
  - Potential autocatalytic behavior

2. Key Observations:
- Complex, non-monotonic growth dynamics
- Strong interdependence between species
- Presence of saturation and inhibition mechanisms

Refined Hypothesis:
1. Autocatalytic reactions with concentration-dependent rates
2. Mutual inhibition preventing unlimited growth
3. Complex feedback loops with time-delayed interactions

Proposed Reaction Mechanisms:
- Nonlinear catalysis
- Concentration-dependent inhibition
- Cooperative interactions between species

Strategy:
- Design an experiment to test the cooperative interaction hypothesis
- Introduce asymmetric initial conditions to probe system's response

## Action

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 10,    // Moderate concentration
        "id_gufr": 0.01,  // Very low concentration
        "id_c5ov": 1000   // Extremely high concentration
    }
}
```

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

def analyze_cooperative_dynamics(experiment_ids):
    cooperative_metrics = {}
    
    for species in ['id_vzxw', 'id_gufr', 'id_c5ov']:
        cooperative_metrics[species] = {}
        
        for exp_id in experiment_ids:
            data = experiment_history[exp_id]
            
            # Calculate cooperative index
            # Measure how concentration changes depend on other species
            cooperative_index = {}
            for other_species in ['id_vzxw', 'id_gufr', 'id_c5ov']:
                if other_species != species:
                    # Calculate correlation of growth rates
                    species_growth_rate = np.diff(data[species]) / np.diff(data['Time'])
                    other_species_conc = data[other_species][:-1]
                    
                    correlation = np.corrcoef(species_growth_rate, other_species_conc)[0, 1]
                    cooperative_index[other_species] = correlation
            
            cooperative_metrics[species][exp_id] = cooperative_index
        
        # Aggregate cooperative indices
        cooperative_metrics[species]['avg_cooperative_indices'] = {
            species: np.mean([exp[species] for exp in cooperative_metrics[species].values() if isinstance(exp, dict)])
            for species in ['id_vzxw', 'id_gufr', 'id_c5ov']
            if species != species
        }
    
    print("Cooperative Interaction Dynamics:")
    for species, metrics in cooperative_metrics.items():
        print(f"\n{species}:")
        for metric_name, metric_value in metrics['avg_cooperative_indices'].items():
            print(f"Cooperation with {metric_name}: {metric_value}")
    
    return cooperative_metrics

# Analyze cooperative dynamics across experiments
analyze_cooperative_dynamics(['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 'iteration_6', 'iteration_7'])
```
# Observation

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

Total size: 1001 rows × 4 columns. 

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

Time   id_vzxw  id_gufr  id_c5ov
0  1.00e+01 1.00e-02 1.00e+03
...
2.00e+01  4.69e+02 3.34e+03 3.48e+04
...
4.00e+01  1.14e+04 7.45e+04 5.68e+05
...
6.00e+01  5.51e+04 3.55e+05 9.98e+05
...
8.00e+01  1.87e+02 2.47e+05 1.46e+01
...
1.00e+02  3.34e-02 1.35e+05 4.92e-03
...
1.20e+02  1.13e-03 7.43e+04 3.10e-04
...
1.40e+02  6.86e-04 4.08e+04 3.45e-04
...
1.60e+02  2.02e-03 2.24e+04 1.86e-03
...
1.80e+02  1.41e-02 1.23e+04 2.38e-02
...
2.00e+02  1.59e-01 6.74e+03 4.88e-01
...
2.20e+02  2.31e+00 3.70e+03 1.30e+01
...
2.40e+02  3.55e+01 2.07e+03 4.00e+02
...
2.60e+02  2.97e+02 2.39e+03 1.30e+04
...
2.80e+02  5.26e+03 3.45e+04 2.93e+05
...
3.00e+02  4.18e+04 2.70e+05 1.21e+06
...
3.20e+02  1.01e+04 2.89e+05 8.47e+02
...
3.40e+02  3.09e-01 1.59e+05 3.84e-02
...
3.60e+02  3.47e-03 8.72e+04 8.04e-04
...
3.80e+02  1.14e-03 4.78e+04 4.89e-04
...
4.00e+02  2.41e-03 2.63e+04 1.89e-03
...
4.20e+02  1.40e-02 1.44e+04 2.01e-02
...
4.40e+02  1.43e-01 7.91e+03 3.74e-01
...
4.60e+02  1.97e+00 4.34e+03 9.44e+00
...
4.80e+02  3.01e+01 2.41e+03 2.82e+02
...
5.00e+02  2.52e+02 2.20e+03 9.08e+03
...
5.20e+02  3.89e+03 2.56e+04 2.23e+05
...
5.40e+02  3.64e+04 2.35e+05 1.17e+06
...
5.60e+02  2.82e+04 3.08e+05 4.16e+03
...
5.80e+02  6.89e-01 1.69e+05 8.04e-02
...
6.00e+02  4.80e-03 9.27e+04 1.05e-03
...
6.20e+02  1.22e-03 5.09e+04 4.90e-04
...
6.40e+02  2.22e-03 2.79e+04 1.64e-03
...
6.60e+02  1.20e-02 1.53e+04 1.61e-02
...
6.80e+02  1.17e-01 8.41e+03 2.87e-01
...
7.00e+02  1.57e+00 4.62e+03 7.08e+00
...
7.20e+02  2.41e+01 2.55e+03 2.09e+02
...
7.40e+02  2.15e+02 2.05e+03 6.71e+03
...
7.60e+02  3.00e+03 1.99e+04 1.76e+05
...
7.80e+02  3.19e+04 2.06e+05 1.11e+06
...
8.00e+02  4.30e+04 3.24e+05 1.63e+04
...
8.20e+02  1.38e+00 1.78e+05 1.52e-01
...
8.40e+02  6.26e-03 9.77e+04 1.29e-03
...
8.60e+02  1.25e-03 5.36e+04 4.78e-04
...
8.80e+02  2.01e-03 2.94e+04 1.41e-03
...
9.00e+02  1.01e-02 1.62e+04 1.29e-02
...
9.20e+02  9.46e-02 8.87e+03 2.21e-01
...
9.40e+02  1.25e+00 4.87e+03 5.34e+00
...
9.60e+02  1.92e+01 2.69e+03 1.55e+02
...
1.00e+03  2.32e+03 1.54e+04 1.38e+05

## Code Stdout
Cooperative Interaction Dynamics:

id_vzxw:

id_gufr:

id_c5ov:

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7, iteration_8)
- `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 9
## Thoughts
I noticed an issue with the previous code that resulted in no output. I'll modify the analysis approach to directly investigate the cooperative dynamics.

The experimental data continues to reveal the system's remarkable properties:
1. Persistent Oscillatory Behavior
- Despite extreme initial conditions, the system maintains characteristic dynamics
- Rapid growth and decline phases for all species
- Consistent periodicity across different initial states

2. Key Observations:
- Robust self-regulating mechanism
- Complex interdependencies between species
- Nonlinear interaction dynamics

Refined Hypothesis:
- The system likely involves:
  1. Mutual catalysis with saturation
  2. Concentration-dependent inhibition
  3. Time-delayed feedback loops

Strategy:
- Develop a more direct method to quantify species interactions
- Investigate how species influence each other's growth rates

## Action

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

def analyze_species_interactions():
    interaction_matrix = np.zeros((3, 3))
    species_list = ['id_vzxw', 'id_gufr', 'id_c5ov']
    
    for i, species1 in enumerate(species_list):
        for j, species2 in enumerate(species_list):
            if i != j:
                correlations = []
                for exp_id in ['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 'iteration_6', 'iteration_7', 'iteration_8']:
                    data = experiment_history[exp_id]
                    
                    # Calculate growth rates
                    growth_rate1 = np.diff(data[species1]) / np.diff(data['Time'])
                    conc2 = data[species2][:-1]
                    
                    # Compute correlation between growth rate of species1 and concentration of species2
                    correlation = np.corrcoef(growth_rate1, conc2)[0, 1]
                    correlations.append(correlation)
                
                interaction_matrix[i, j] = np.mean(correlations)
    
    print("Species Interaction Matrix:")
    for i, species1 in enumerate(species_list):
        print(f"\n{species1}:")
        for j, species2 in enumerate(species_list):
            if i != j:
                print(f"Influence from {species2}: {interaction_matrix[i, j]:.4f}")
    
    return interaction_matrix

analyze_species_interactions()
```

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 0.1,   // Very low concentration
        "id_gufr": 500,   // Extremely high concentration
        "id_c5ov": 0.5    // Low concentration
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_9
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_9]

Total size: 1001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_9] for the full data

Time   id_vzxw  id_gufr  id_c5ov
0  1.00e-01 5.00e+02 5.00e-01
...
2.00e+01  2.36e-01 2.76e+02 1.79e+01
...
4.00e+01  5.46e+00 2.12e+02 6.45e+02
...
6.00e+01  3.06e+02 2.28e+03 2.26e+04
...
8.00e+01  8.27e+03 5.40e+04 4.38e+05
...
1.00e+02  5.04e+04 3.25e+05 1.16e+06
...
1.20e+02  9.77e+02 2.66e+05 7.19e+01
...
1.40e+02  7.34e-02 1.46e+05 1.00e-02
...
1.60e+02  1.53e-03 8.00e+04 3.88e-04
...
1.80e+02  7.09e-04 4.39e+04 3.31e-04
...
2.00e+02  1.80e-03 2.41e+04 1.54e-03
...
2.20e+02  1.16e-02 1.32e+04 1.82e-02
...
2.40e+02  1.25e-01 7.26e+03 3.57e-01
...
2.60e+02  1.78e+00 3.98e+03 9.29e+00
...
2.80e+02  2.76e+01 2.21e+03 2.82e+02
...
3.00e+02  2.41e+02 2.10e+03 9.17e+03
...
3.20e+02  3.93e+03 2.59e+04 2.26e+05
...
3.40e+02  3.66e+04 2.37e+05 1.18e+06
...
3.60e+02  2.73e+04 3.07e+05 3.86e+03
...
3.80e+02  6.48e-01 1.69e+05 7.57e-02
...
4.00e+02  4.56e-03 9.26e+04 9.93e-04
...
4.20e+02  1.16e-03 5.08e+04 4.67e-04
...
4.40e+02  2.12e-03 2.79e+04 1.57e-03
...
4.60e+02  1.14e-02 1.53e+04 1.55e-02
...
4.80e+02  1.12e-01 8.40e+03 2.75e-01
...
5.00e+02  1.51e+00 4.61e+03 6.79e+00
...
5.20e+02  2.31e+01 2.55e+03 2.00e+02
...
5.40e+02  2.09e+02 2.02e+03 6.43e+03
...
5.60e+02  2.90e+03 1.92e+04 1.70e+05
...
5.80e+02  3.13e+04 2.03e+05 1.10e+06
...
6.00e+02  4.44e+04 3.26e+05 1.96e+04
...
6.20e+02  1.51e+00 1.79e+05 1.66e-01
...
6.40e+02  6.47e-03 9.84e+04 1.32e-03
...
6.60e+02  1.25e-03 5.40e+04 4.75e-04
...
6.80e+02  1.97e-03 2.96e+04 1.37e-03
...
7.00e+02  9.80e-03 1.63e+04 1.25e-02
...
7.20e+02  9.14e-02 8.93e+03 2.12e-01
...
7.40e+02  1.20e+00 4.90e+03 5.11e+00
...
7.60e+02  1.85e+01 2.70e+03 1.48e+02
...
7.80e+02  1.80e+02 1.94e+03 4.75e+03
...
8.00e+02  2.23e+03 1.48e+04 1.32e+05
...
8.20e+02  2.71e+04 1.75e+05 1.02e+06
...
8.40e+02  5.15e+04 3.42e+05 7.24e+04
...
8.60e+02  3.20e+00 1.89e+05 3.32e-01
...
8.80e+02  8.69e-03 1.04e+05 1.69e-03
...
9.00e+02  1.31e-03 5.69e+04 4.71e-04
...
9.20e+02  1.80e-03 3.12e+04 1.19e-03
...
9.40e+02  8.31e-03 1.71e+04 1.00e-02
...
9.60e+02  7.44e-02 9.41e+03 1.64e-01
...
1.00e+03  1.47e+01 2.84e+03 1.11e+02

## Code Stdout
Species Interaction Matrix:

id_vzxw:
Influence from id_gufr: -0.2218
Influence from id_c5ov: 0.4678

id_gufr:
Influence from id_vzxw: 0.3731
Influence from id_c5ov: 0.8385

id_c5ov:
Influence from id_vzxw: -0.5323
Influence from id_gufr: -0.4768

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7, iteration_8, iteration_9)
- `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 10
## Thoughts
The species interaction matrix reveals profound insights into the system's complex dynamics:

1. Interaction Characteristics:
- id_gufr → id_c5ov: Strong positive influence (0.8385)
  - Suggests strong activation or catalytic relationship
- id_vzxw → id_c5ov: Strong negative influence (-0.5323)
  - Indicates potential inhibitory mechanism
- id_gufr → id_vzxw: Moderate positive influence (0.3731)
- id_vzxw → id_gufr: Negative influence (-0.2218)

2. Key Observations:
- Non-linear, asymmetric interactions
- Complex feedback loops
- Concentration-dependent regulatory mechanisms

Refined Hypothesis:
1. Competitive/inhibitory interactions between some species
2. Autocatalytic processes with saturation
3. Time-delayed feedback mechanisms

Proposed Reaction Mechanisms:
- Mutual inhibition between certain species
- Concentration-dependent activation/suppression
- Non-linear catalytic interactions

Strategy:
- Design an experiment to test the inhibition and activation hypotheses
- Introduce intermediate initial concentrations to probe transition dynamics

## Action

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 5,     // Moderate concentration
        "id_gufr": 25,    // Moderate-high concentration
        "id_c5ov": 15     // Moderate concentration
    }
}
```

### Code
```python
import numpy as np
import pandas as pd
import scipy.signal as signal

def analyze_oscillation_dynamics():
    species_list = ['id_vzxw', 'id_gufr', 'id_c5ov']
    oscillation_metrics = {}
    
    for species in species_list:
        # Collect data across all experiments
        all_data = []
        for exp_id in ['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 'iteration_6', 'iteration_7', 'iteration_8', 'iteration_9']:
            data = experiment_history[exp_id]
            all_data.append(data[species])
        
        # Combine and analyze
        combined_data = np.concatenate(all_data)
        
        # Peak detection
        peaks, _ = signal.find_peaks(combined_data)
        troughs, _ = signal.find_peaks(-combined_data)
        
        oscillation_metrics[species] = {
            'num_peaks': len(peaks),
            'num_troughs': len(troughs),
            'avg_peak_height': np.mean(combined_data[peaks]) if len(peaks) > 0 else np.nan,
            'avg_trough_depth': np.mean(combined_data[troughs]) if len(troughs) > 0 else np.nan,
            'peak_variability': np.std(combined_data[peaks]) if len(peaks) > 1 else np.nan,
            'trough_variability': np.std(combined_data[troughs]) if len(troughs) > 1 else np.nan
        }
    
    print("Oscillation Dynamics:")
    for species, metrics in oscillation_metrics.items():
        print(f"\n{species}:")
        for metric_name, metric_value in metrics.items():
            print(f"{metric_name}: {metric_value}")
    
    return oscillation_metrics

analyze_oscillation_dynamics()
```
# Observation

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

Total size: 1001 rows × 4 columns. 

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

Time   id_vzxw  id_gufr  id_c5ov
0  5.00e+00 2.50e+01 1.50e+01
...
2.00e+01  1.45e+00 6.51e+01 5.48e+02
...
4.00e+01  2.48e+02 1.88e+03 1.94e+04
...
6.00e+01  7.36e+03 4.81e+04 3.99e+05
...
8.00e+01  4.86e+04 3.13e+05 1.20e+06
...
1.00e+02  1.72e+03 2.73e+05 1.25e+02
...
1.20e+02  9.34e-02 1.50e+05 1.24e-02
...
1.40e+02  1.61e-03 8.22e+04 3.98e-04
...
1.60e+02  6.74e-04 4.51e+04 3.06e-04
...
1.80e+02  1.62e-03 2.47e+04 1.35e-03
...
2.00e+02  1.01e-02 1.36e+04 1.54e-02
...
2.20e+02  1.07e-01 7.45e+03 2.98e-01
...
2.40e+02  1.51e+00 4.09e+03 7.67e+00
...
2.60e+02  2.36e+01 2.27e+03 2.32e+02
...
2.80e+02  2.14e+02 1.97e+03 7.54e+03
...
3.00e+02  3.32e+03 2.19e+04 1.94e+05
...
3.20e+02  3.37e+04 2.18e+05 1.14e+06
...
3.40e+02  3.78e+04 3.18e+05 9.29e+03
...
3.60e+02  1.00e+00 1.75e+05 1.13e-01
...
3.80e+02  5.35e-03 9.58e+04 1.13e-03
...
4.00e+02  1.17e-03 5.26e+04 4.56e-04
...
4.20e+02  1.97e-03 2.89e+04 1.41e-03
...
4.40e+02  1.02e-02 1.58e+04 1.33e-02
...
4.60e+02  9.68e-02 8.69e+03 2.31e-01
...
4.80e+02  1.29e+00 4.77e+03 5.61e+00
...
5.00e+02  1.98e+01 2.64e+03 1.64e+02
...
5.20e+02  1.88e+02 1.95e+03 5.26e+03
...
5.40e+02  2.43e+03 1.62e+04 1.44e+05
...
5.60e+02  2.85e+04 1.85e+05 1.05e+06
...
5.80e+02  4.97e+04 3.37e+05 4.73e+04
...
6.00e+02  2.46e+00 1.86e+05 2.60e-01
...
6.20e+02  7.81e-03 1.02e+05 1.54e-03
...
6.40e+02  1.29e-03 5.59e+04 4.70e-04
...
6.60e+02  1.85e-03 3.07e+04 1.24e-03
...
6.80e+02  8.75e-03 1.68e+04 1.07e-02
...
7.00e+02  7.95e-02 9.24e+03 1.78e-01
...
7.20e+02  1.03e+00 5.07e+03 4.22e+00
...
7.40e+02  1.58e+01 2.80e+03 1.22e+02
...
7.60e+02  1.62e+02 1.91e+03 3.89e+03
...
7.80e+02  1.87e+03 1.25e+04 1.11e+05
...
8.00e+02  2.44e+04 1.58e+05 9.61e+05
...
8.20e+02  5.40e+04 3.52e+05 1.50e+05
...
8.40e+02  5.40e+00 1.96e+05 5.39e-01
...
8.60e+02  1.07e-02 1.07e+05 2.00e-03
...
8.80e+02  1.36e-03 5.89e+04 4.72e-04
...
9.00e+02  1.70e-03 3.23e+04 1.08e-03
...
9.20e+02  7.45e-03 1.77e+04 8.67e-03
...
9.40e+02  6.48e-02 9.74e+03 1.38e-01
...
9.60e+02  8.21e-01 5.35e+03 3.19e+00
...
1.00e+03  1.39e+02 1.89e+03 2.88e+03

## Code Stdout
Oscillation Dynamics:

id_vzxw:
num_peaks: 44
num_troughs: 45
avg_peak_height: 46789.26975428049
avg_trough_depth: 0.019261618948266085
peak_variability: 21835.71057549348
trough_variability: 0.11961637159838961

id_gufr:
num_peaks: 39
num_troughs: 39
avg_peak_height: 339833.21397119545
avg_trough_depth: 1424.1527393981696
peak_variability: 95619.03090925621
trough_variability: 763.4260684949106

id_c5ov:
num_peaks: 43
num_troughs: 43
avg_peak_height: 1019137.2006203742
avg_trough_depth: 23.74941405390791
peak_variability: 436059.85439643444
trough_variability: 150.66882128251598

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7, iteration_8, iteration_9, iteration_10)
- `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 11
## Thoughts
The oscillation dynamics analysis reveals extraordinary insights into the system's behavior:

1. Oscillation Characteristics:
- Consistent Periodicity:
  - id_vzxw: 44-45 peaks/troughs
  - id_gufr: 39 peaks/troughs
  - id_c5ov: 43 peaks/troughs

2. Peak Height Variations:
- Dramatic differences in magnitude:
  - id_c5ov: Highest peaks (avg 1,019,137)
  - id_gufr: Intermediate peaks (avg 339,833)
  - id_vzxw: Lowest peaks (avg 46,789)

3. Trough Depth Characteristics:
- Extremely low trough depths
- Suggests rapid recovery mechanisms
- Indicates strong self-regulation

Key Observations:
- Synchronized but asymmetric oscillations
- Complex, multi-scale interaction dynamics
- Potential for nested feedback loops

Refined Hypothesis:
1. Hierarchical regulatory network
2. Concentration-dependent activation/inhibition
3. Multi-timescale interaction mechanisms

Proposed Reaction Mechanisms:
- Nested autocatalytic processes
- Hierarchical inhibition networks
- Time-delayed cooperative interactions

Strategy:
- Design an experiment to test hierarchical interaction hypothesis
- Probe system's response to asymmetric perturbations

## Action

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 0.001,  // Extremely low concentration
        "id_gufr": 0.1,    // Very low concentration
        "id_c5ov": 100     // High concentration
    }
}
```

### Code
```python
import numpy as np
import scipy.signal as signal

def analyze_interaction_hierarchy():
    species_list = ['id_vzxw', 'id_gufr', 'id_c5ov']
    hierarchy_metrics = {}
    
    for species in species_list:
        # Collect data across all experiments
        all_data = []
        for exp_id in ['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 'iteration_6', 'iteration_7', 'iteration_8', 'iteration_9', 'iteration_10']:
            data = experiment_history[exp_id]
            all_data.append(data[species])
        
        combined_data = np.concatenate(all_data)
        
        # Advanced spectral analysis
        frequencies, power_spectrum = signal.welch(combined_data)
        
        hierarchy_metrics[species] = {
            'dominant_frequency': frequencies[np.argmax(power_spectrum)],
            'frequency_entropy': -np.sum(power_spectrum * np.log(power_spectrum + 1e-10)),
            'spectral_centroid': np.sum(frequencies * power_spectrum) / np.sum(power_spectrum),
            'spectral_spread': np.sqrt(np.sum(((frequencies - hierarchy_metrics[species]['spectral_centroid'])**2) * power_spectrum) / np.sum(power_spectrum))
        }
    
    print("Interaction Hierarchy Metrics:")
    for species, metrics in hierarchy_metrics.items():
        print(f"\n{species}:")
        for metric_name, metric_value in metrics.items():
            print(f"{metric_name}: {metric_value}")
    
    return hierarchy_metrics

analyze_interaction_hierarchy()
```
# Observation

## Experiment Result
Experiment ID: iteration_11
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_11]

Total size: 1001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_11] for the full data

Time   id_vzxw  id_gufr  id_c5ov
0  1.00e-03 1.00e-01 1.00e+02
...
2.00e+01  2.77e+01 3.42e+02 3.64e+03
...
4.00e+01  1.72e+03 1.15e+04 1.12e+05
...
6.00e+01  2.49e+04 1.61e+05 9.86e+05
...
8.00e+01  5.49e+04 3.58e+05 1.42e+05
...
1.00e+02  3.80e+00 1.99e+05 3.73e-01
...
1.20e+02  6.49e-03 1.09e+05 1.19e-03
...
1.40e+02  7.61e-04 5.99e+04 2.59e-04
...
1.60e+02  9.08e-04 3.29e+04 5.69e-04
...
1.80e+02  3.88e-03 1.80e+04 4.44e-03
...
2.00e+02  3.33e-02 9.90e+03 6.97e-02
...
2.20e+02  4.19e-01 5.43e+03 1.60e+00
...
2.40e+02  6.44e+00 2.99e+03 4.54e+01
...
2.60e+02  8.53e+01 1.78e+03 1.44e+03
...
2.80e+02  7.83e+02 5.44e+03 4.54e+04
...
3.00e+02  1.36e+04 8.85e+04 6.40e+05
...
3.20e+02  5.58e+04 3.59e+05 8.32e+05
...
3.40e+02  9.77e+01 2.32e+05 8.15e+00
...
3.60e+02  3.48e-02 1.27e+05 5.46e-03
...
3.80e+02  1.72e-03 6.99e+04 5.02e-04
...
4.00e+02  1.28e-03 3.84e+04 6.87e-04
...
4.20e+02  4.22e-03 2.11e+04 4.14e-03
...
4.40e+02  3.15e-02 1.16e+04 5.64e-02
...
4.60e+02  3.66e-01 6.34e+03 1.20e+00
...
4.80e+02  5.41e+00 3.48e+03 3.26e+01
...
5.00e+02  7.45e+01 2.01e+03 1.01e+03
...
5.20e+02  5.94e+02 4.24e+03 3.21e+04
...
5.40e+02  1.06e+04 6.90e+04 5.26e+05
...
5.60e+02  5.31e+04 3.42e+05 1.03e+06
...
5.80e+02  3.49e+02 2.47e+05 2.74e+01
...
6.00e+02  6.26e-02 1.35e+05 9.21e-03
...
6.20e+02  2.12e-03 7.43e+04 5.80e-04
...
6.40e+02  1.28e-03 4.08e+04 6.45e-04
...
6.60e+02  3.76e-03 2.24e+04 3.47e-03
...
6.80e+02  2.63e-02 1.23e+04 4.43e-02
...
7.00e+02  2.96e-01 6.74e+03 9.11e-01
...
7.20e+02  4.30e+00 3.70e+03 2.43e+01
...
7.40e+02  6.14e+01 2.10e+03 7.46e+02
...
7.60e+02  4.73e+02 3.48e+03 2.39e+04
...
7.80e+02  8.49e+03 5.54e+04 4.39e+05
...
8.00e+02  4.98e+04 3.21e+05 1.13e+06
...
8.20e+02  1.06e+03 2.60e+05 8.01e+01
...
8.40e+02  1.04e-01 1.43e+05 1.44e-02
...
8.60e+02  2.49e-03 7.83e+04 6.45e-04
...
8.80e+02  1.25e-03 4.30e+04 5.95e-04
...
9.00e+02  3.30e-03 2.36e+04 2.89e-03
...
9.20e+02  2.18e-02 1.29e+04 3.49e-02
...
9.40e+02  2.38e-01 7.11e+03 6.95e-01
...
9.60e+02  3.40e+00 3.90e+03 1.82e+01
...
1.00e+03  3.84e+02 2.93e+03 1.78e+04

## Code Stderror
 'id_vzxw'

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7, iteration_8, iteration_9, iteration_10, iteration_11)
- `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 12
## Thoughts
I noticed an error in the previous code execution. I'll modify the analysis to be more robust and focus on extracting key insights from the experimental data.

The latest experiment reveals fascinating dynamics:

1. Resilience and Adaptability:
- Despite extremely low initial concentrations for id_vzxw and id_gufr
- System quickly reaches characteristic oscillatory state
- Demonstrates remarkable self-organizing capabilities

2. Concentration Dynamics:
- Rapid growth phases for all species
- Synchronized but asymmetric oscillations
- Quick transitions between high and low concentration states

Key Observations:
- Complex, non-linear interaction network
- Potential for emergent self-regulation
- Hierarchical feedback mechanisms

Refined Hypothesis:
1. Nested autocatalytic processes
2. Concentration-dependent activation/inhibition
3. Multi-timescale interaction dynamics

Strategy:
- Develop a more direct method to quantify species interactions
- Focus on understanding transition dynamics between concentration ranges

## Action

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

def analyze_transition_dynamics():
    species_list = ['id_vzxw', 'id_gufr', 'id_c5ov']
    transition_metrics = {}
    
    for species in species_list:
        # Collect data across all experiments
        all_data = []
        for exp_id in ['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 
                       'iteration_6', 'iteration_7', 'iteration_8', 'iteration_9', 'iteration_10', 'iteration_11']:
            data = experiment_history[exp_id]
            all_data.append(data[species])
        
        combined_data = np.concatenate(all_data)
        
        # Define concentration ranges
        low_threshold = np.percentile(combined_data, 25)
        high_threshold = np.percentile(combined_data, 75)
        
        # Transition analysis
        transition_metrics[species] = {
            'low_range_mean': np.mean(combined_data[combined_data < low_threshold]),
            'mid_range_mean': np.mean(combined_data[(combined_data >= low_threshold) & (combined_data <= high_threshold)]),
            'high_range_mean': np.mean(combined_data[combined_data > high_threshold]),
            'transition_speed': np.std(np.diff(combined_data)) / np.mean(np.diff(combined_data)),
            'concentration_range': np.max(combined_data) / np.min(combined_data)
        }
    
    print("Transition Dynamics:")
    for species, metrics in transition_metrics.items():
        print(f"\n{species}:")
        for metric_name, metric_value in metrics.items():
            print(f"{metric_name}: {metric_value}")
    
    return transition_metrics

analyze_transition_dynamics()
```

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 50,    // Moderate-high concentration
        "id_gufr": 0.05,  // Very low concentration
        "id_c5ov": 0.5    // Low concentration
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_12
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_12]

Total size: 1001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_12] for the full data

Time   id_vzxw  id_gufr  id_c5ov
0  5.00e+01 5.00e-02 5.00e-01
...
2.00e+01  1.50e-03 1.74e+00 1.83e+01
...
4.00e+01  1.67e+00 6.37e+01 6.69e+02
...
6.00e+01  3.08e+02 2.29e+03 2.36e+04
...
8.00e+01  8.55e+03 5.59e+04 4.51e+05
...
1.00e+02  5.10e+04 3.29e+05 1.15e+06
...
1.20e+02  8.12e+02 2.64e+05 6.00e+01
...
1.40e+02  6.58e-02 1.45e+05 9.03e-03
...
1.60e+02  1.43e-03 7.95e+04 3.66e-04
...
1.80e+02  6.79e-04 4.36e+04 3.19e-04
...
2.00e+02  1.75e-03 2.39e+04 1.51e-03
...
2.20e+02  1.13e-02 1.31e+04 1.79e-02
...
2.40e+02  1.23e-01 7.21e+03 3.53e-01
...
2.60e+02  1.75e+00 3.96e+03 9.21e+00
...
2.80e+02  2.73e+01 2.20e+03 2.80e+02
...
3.00e+02  2.38e+02 2.08e+03 9.11e+03
...
3.20e+02  3.90e+03 2.57e+04 2.25e+05
...
3.40e+02  3.65e+04 2.36e+05 1.17e+06
...
3.60e+02  2.76e+04 3.08e+05 3.98e+03
...
3.80e+02  6.56e-01 1.69e+05 7.65e-02
...
4.00e+02  4.57e-03 9.28e+04 9.94e-04
...
4.20e+02  1.16e-03 5.09e+04 4.65e-04
...
4.40e+02  2.11e-03 2.79e+04 1.55e-03
...
4.60e+02  1.13e-02 1.53e+04 1.53e-02
...
4.80e+02  1.11e-01 8.42e+03 2.72e-01
...
5.00e+02  1.49e+00 4.62e+03 6.72e+00
...
5.20e+02  2.29e+01 2.55e+03 1.98e+02
...
5.40e+02  2.08e+02 2.01e+03 6.36e+03
...
5.60e+02  2.87e+03 1.90e+04 1.69e+05
...
5.80e+02  3.12e+04 2.02e+05 1.10e+06
...
6.00e+02  4.48e+04 3.27e+05 2.07e+04
...
6.20e+02  1.56e+00 1.80e+05 1.70e-01
...
6.40e+02  6.53e-03 9.86e+04 1.34e-03
...
6.60e+02  1.26e-03 5.41e+04 4.74e-04
...
6.80e+02  1.97e-03 2.97e+04 1.36e-03
...
7.00e+02  9.73e-03 1.63e+04 1.23e-02
...
7.20e+02  9.07e-02 8.95e+03 2.10e-01
...
7.40e+02  1.19e+00 4.91e+03 5.05e+00
...
7.60e+02  1.83e+01 2.71e+03 1.47e+02
...
7.80e+02  1.79e+02 1.94e+03 4.69e+03
...
8.00e+02  2.20e+03 1.47e+04 1.31e+05
...
8.20e+02  2.69e+04 1.74e+05 1.02e+06
...
8.40e+02  5.17e+04 3.43e+05 7.59e+04
...
8.60e+02  3.30e+00 1.89e+05 3.41e-01
...
8.80e+02  8.80e-03 1.04e+05 1.70e-03
...
9.00e+02  1.32e-03 5.70e+04 4.71e-04
...
9.20e+02  1.80e-03 3.13e+04 1.18e-03
...
9.40e+02  8.26e-03 1.72e+04 9.94e-03
...
9.60e+02  7.38e-02 9.43e+03 1.62e-01
...
1.00e+03  1.45e+01 2.85e+03 1.09e+02

## Code Stdout
Transition Dynamics:

id_vzxw:
low_range_mean: 0.002269934380051413
mid_range_mean: 34.405571598152484
high_range_mean: 22273.03459852944
transition_speed: 39557.959021969444
concentration_range: 853495786692.9135

id_gufr:
low_range_mean: 2447.254640695998
mid_range_mean: 34933.68217476698
high_range_mean: 233744.7467796134
transition_speed: 18832.960581980282
concentration_range: 373091289.07455444

id_c5ov:
low_range_mean: 0.0012936566998235336
mid_range_mean: 370.58349331913996
high_range_mean: 459296.79216085223
transition_speed: 16136.437818690987
concentration_range: 4912126472.961379

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7, iteration_8, iteration_9, iteration_10, iteration_11, iteration_12)
- `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 13
## Thoughts
The transition dynamics analysis reveals extraordinary insights into the system's behavior:

1. Concentration Range Characteristics:
- id_vzxw: Extreme range (853,495,786,692x)
- id_gufr: High range (373,091,289x)
- id_c5ov: Massive range (4,912,126,472x)

2. Transition Dynamics:
- Extremely high transition speeds
- Dramatic shifts between concentration ranges
- Non-linear, highly responsive system

3. Concentration Range Means:
- Low Range:
  - id_vzxw: 0.0023
  - id_gufr: 2,447
  - id_c5ov: 0.0013
- High Range:
  - id_vzxw: 22,273
  - id_gufr: 233,745
  - id_c5ov: 459,297

Key Observations:
- Hierarchical, multi-scale interaction network
- Extreme sensitivity to initial conditions
- Complex, non-linear regulatory mechanisms

Refined Hypothesis:
1. Nested autocatalytic processes with concentration-dependent switching
2. Hierarchical inhibition and activation networks
3. Emergent self-organizing criticality

Proposed Reaction Mechanisms:
- Concentration-triggered switch mechanisms
- Nested feedback loops with variable time constants
- Cooperative/competitive interactions

Strategy:
- Design an experiment to test the switching hypothesis
- Probe system's response at critical transition points

## Action

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 0.1,   // Very low concentration
        "id_gufr": 10,    // Low-moderate concentration
        "id_c5ov": 0.01   // Extremely low concentration
    }
}
```

### Code
```python
import numpy as np
import scipy.stats as stats

def analyze_switching_dynamics():
    species_list = ['id_vzxw', 'id_gufr', 'id_c5ov']
    switching_metrics = {}
    
    for species in species_list:
        # Collect data across all experiments
        all_data = []
        for exp_id in ['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 
                       'iteration_6', 'iteration_7', 'iteration_8', 'iteration_9', 'iteration_10', 
                       'iteration_11', 'iteration_12']:
            data = experiment_history[exp_id]
            all_data.append(data[species])
        
        combined_data = np.concatenate(all_data)
        
        # Advanced switching analysis
        switching_metrics[species] = {
            'kurtosis': stats.kurtosis(combined_data),  # Measure of tail heaviness
            'skewness': stats.skew(combined_data),      # Asymmetry of distribution
            'coefficient_of_variation': np.std(combined_data) / np.mean(combined_data),
            'mode_switching_index': len(np.unique(np.digitize(combined_data, bins=10))) / 10,
            'concentration_entropy': -np.sum(np.histogram(combined_data, bins=10)[0] * 
                                             np.log(np.histogram(combined_data, bins=10)[0] + 1e-10))
        }
    
    print("Switching Dynamics:")
    for species, metrics in switching_metrics.items():
        print(f"\n{species}:")
        for metric_name, metric_value in metrics.items():
            print(f"{metric_name}: {metric_value}")
    
    return switching_metrics

analyze_switching_dynamics()
```
# Observation

## Experiment Result
Experiment ID: iteration_13
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_13]

Total size: 1001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_13] for the full data

Time   id_vzxw  id_gufr  id_c5ov
0  1.00e-01 1.00e+01 1.00e-02
...
2.00e+01  9.72e-05 5.52e+00 3.66e-01
...
4.00e+01  2.73e-03 4.29e+00 1.34e+01
...
6.00e+01  9.69e-01 4.83e+01 4.89e+02
...
8.00e+01  2.18e+02 1.68e+03 1.74e+04
...
1.00e+02  6.75e+03 4.42e+04 3.71e+05
...
1.20e+02  4.71e+04 3.04e+05 1.22e+06
...
1.40e+02  2.62e+03 2.78e+05 1.91e+02
...
1.60e+02  1.14e-01 1.53e+05 1.48e-02
...
1.80e+02  1.72e-03 8.37e+04 4.17e-04
...
2.00e+02  6.69e-04 4.60e+04 2.98e-04
...
2.20e+02  1.54e-03 2.52e+04 1.26e-03
...
2.40e+02  9.42e-03 1.38e+04 1.41e-02
...
2.60e+02  9.85e-02 7.60e+03 2.69e-01
...
2.80e+02  1.38e+00 4.17e+03 6.89e+00
...
3.00e+02  2.16e+01 2.31e+03 2.07e+02
...
3.20e+02  2.01e+02 1.91e+03 6.74e+03
...
3.40e+02  3.02e+03 1.99e+04 1.77e+05
...
3.60e+02  3.21e+04 2.08e+05 1.12e+06
...
3.80e+02  4.26e+04 3.24e+05 1.54e+04
...
4.00e+02  1.30e+00 1.78e+05 1.43e-01
...
4.20e+02  5.91e-03 9.77e+04 1.22e-03
...
4.40e+02  1.19e-03 5.36e+04 4.52e-04
...
4.60e+02  1.90e-03 2.94e+04 1.33e-03
...
4.80e+02  9.53e-03 1.62e+04 1.22e-02
...
5.00e+02  8.94e-02 8.86e+03 2.09e-01
...
5.20e+02  1.18e+00 4.87e+03 5.04e+00
...
5.40e+02  1.82e+01 2.68e+03 1.47e+02
...
5.60e+02  1.78e+02 1.93e+03 4.71e+03
...
5.80e+02  2.21e+03 1.47e+04 1.31e+05
...
6.00e+02  2.70e+04 1.75e+05 1.02e+06
...
6.20e+02  5.16e+04 3.43e+05 7.50e+04
...
6.40e+02  3.26e+00 1.89e+05 3.38e-01
...
6.60e+02  8.73e-03 1.04e+05 1.69e-03
...
6.80e+02  1.31e-03 5.70e+04 4.69e-04
...
7.00e+02  1.79e-03 3.13e+04 1.18e-03
...
7.20e+02  8.22e-03 1.72e+04 9.90e-03
...
7.40e+02  7.35e-02 9.42e+03 1.62e-01
...
7.60e+02  9.46e-01 5.17e+03 3.80e+00
...
7.80e+02  1.45e+01 2.85e+03 1.09e+02
...
8.00e+02  1.53e+02 1.90e+03 3.47e+03
...
8.20e+02  1.69e+03 1.13e+04 1.01e+05
...
8.40e+02  2.30e+04 1.49e+05 9.26e+05
...
8.60e+02  5.50e+04 3.56e+05 2.12e+05
...
8.80e+02  7.31e+00 1.99e+05 7.15e-01
...
9.00e+02  1.21e-02 1.09e+05 2.22e-03
...
9.20e+02  1.39e-03 6.01e+04 4.74e-04
...
9.40e+02  1.65e-03 3.30e+04 1.03e-03
...
9.60e+02  7.01e-03 1.81e+04 8.00e-03
...
1.00e+03  7.54e-01 5.45e+03 2.87e+00

## Code Stderror
 object of too small depth for desired array

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7, iteration_8, iteration_9, iteration_10, iteration_11, iteration_12, iteration_13)
- `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 14
## Thoughts
I noticed an error in the previous code execution. I'll modify the analysis to be more robust and focus on extracting key insights from the experimental data.

The latest experiment reveals fascinating dynamics:

1. Resilience and Adaptability:
- System demonstrates remarkable self-organization
- Consistent oscillatory behavior across different initial conditions
- Rapid transitions between concentration ranges

2. Concentration Dynamics:
- Quick growth and decline phases
- Synchronized but asymmetric oscillations
- Ability to converge to characteristic dynamics regardless of initial state

Key Observations:
- Complex, non-linear interaction network
- Potential for emergent self-regulation
- Hierarchical feedback mechanisms

Refined Hypothesis:
1. Nested autocatalytic processes
2. Concentration-dependent activation/inhibition
3. Multi-timescale interaction dynamics

Strategy:
- Develop a more direct method to quantify species interactions
- Focus on understanding transition dynamics and interaction strengths

## Action

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

def analyze_interaction_strengths():
    species_list = ['id_vzxw', 'id_gufr', 'id_c5ov']
    interaction_matrix = np.zeros((3, 3))
    
    for i, species1 in enumerate(species_list):
        for j, species2 in enumerate(species_list):
            if i != j:
                correlations = []
                for exp_id in ['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 
                               'iteration_6', 'iteration_7', 'iteration_8', 'iteration_9', 
                               'iteration_10', 'iteration_11', 'iteration_12', 'iteration_13']:
                    data = experiment_history[exp_id]
                    
                    # Calculate growth rate of species1
                    growth_rate = np.diff(data[species1]) / np.diff(data['Time'])
                    
                    # Calculate concentration of species2
                    conc_species2 = data[species2][:-1]
                    
                    # Compute correlation
                    correlation = np.corrcoef(growth_rate, conc_species2)[0, 1]
                    correlations.append(correlation)
                
                interaction_matrix[i, j] = np.mean(correlations)
    
    print("Interaction Strength Matrix:")
    for i, species1 in enumerate(species_list):
        print(f"\n{species1}:")
        for j, species2 in enumerate(species_list):
            if i != j:
                print(f"Influence from {species2}: {interaction_matrix[i, j]:.4f}")
    
    # Calculate additional metrics
    print("\nAdditional Interaction Metrics:")
    for species in species_list:
        # Collect data across all experiments
        all_data = []
        for exp_id in ['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 
                       'iteration_6', 'iteration_7', 'iteration_8', 'iteration_9', 
                       'iteration_10', 'iteration_11', 'iteration_12', 'iteration_13']:
            data = experiment_history[exp_id]
            all_data.append(data[species])
        
        combined_data = np.concatenate(all_data)
        
        print(f"\n{species}:")
        print(f"Concentration Range: {np.max(combined_data) / np.min(combined_data):.2f}")
        print(f"Variability (Coefficient of Variation): {np.std(combined_data) / np.mean(combined_data):.4f}")
    
    return interaction_matrix

analyze_interaction_strengths()
```

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 0.5,   // Low concentration
        "id_gufr": 75,    // Moderate-high concentration
        "id_c5ov": 0.01   // Extremely low concentration
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_14
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_14]

Total size: 1001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_14] for the full data

Time   id_vzxw  id_gufr  id_c5ov
0  5.00e-01 7.50e+01 1.00e-02
...
2.00e+01  7.23e-04 4.12e+01 3.65e-01
...
4.00e+01  1.52e-02 2.39e+01 1.33e+01
...
6.00e+01  1.18e+00 5.88e+01 4.87e+02
...
8.00e+01  2.17e+02 1.68e+03 1.73e+04
...
1.00e+02  6.72e+03 4.40e+04 3.70e+05
...
1.20e+02  4.70e+04 3.03e+05 1.22e+06
...
1.40e+02  2.69e+03 2.78e+05 1.96e+02
...
1.60e+02  1.16e-01 1.53e+05 1.50e-02
...
1.80e+02  1.74e-03 8.38e+04 4.19e-04
...
2.00e+02  6.70e-04 4.60e+04 2.99e-04
...
2.20e+02  1.54e-03 2.52e+04 1.26e-03
...
2.40e+02  9.41e-03 1.39e+04 1.41e-02
...
2.60e+02  9.84e-02 7.60e+03 2.68e-01
...
2.80e+02  1.38e+00 4.17e+03 6.87e+00
...
3.00e+02  2.16e+01 2.31e+03 2.07e+02
...
3.20e+02  2.01e+02 1.91e+03 6.72e+03
...
3.40e+02  3.01e+03 1.99e+04 1.77e+05
...
3.60e+02  3.21e+04 2.07e+05 1.12e+06
...
3.80e+02  4.27e+04 3.24e+05 1.56e+04
...
4.00e+02  1.31e+00 1.78e+05 1.44e-01
...
4.20e+02  5.92e-03 9.78e+04 1.22e-03
...
4.40e+02  1.19e-03 5.37e+04 4.52e-04
...
4.60e+02  1.90e-03 2.94e+04 1.33e-03
...
4.80e+02  9.52e-03 1.62e+04 1.22e-02
...
5.00e+02  8.92e-02 8.87e+03 2.09e-01
...
5.20e+02  1.18e+00 4.87e+03 5.03e+00
...
5.40e+02  1.81e+01 2.69e+03 1.46e+02
...
5.60e+02  1.77e+02 1.93e+03 4.69e+03
...
5.80e+02  2.20e+03 1.47e+04 1.31e+05
...
6.00e+02  2.69e+04 1.74e+05 1.02e+06
...
6.20e+02  5.17e+04 3.43e+05 7.58e+04
...
6.40e+02  3.29e+00 1.89e+05 3.40e-01
...
6.60e+02  8.75e-03 1.04e+05 1.69e-03
...
6.80e+02  1.31e-03 5.70e+04 4.69e-04
...
7.00e+02  1.79e-03 3.13e+04 1.18e-03
...
7.20e+02  8.21e-03 1.72e+04 9.88e-03
...
7.40e+02  7.34e-02 9.43e+03 1.61e-01
...
7.60e+02  9.44e-01 5.17e+03 3.79e+00
...
7.80e+02  1.44e+01 2.85e+03 1.09e+02
...
8.00e+02  1.53e+02 1.90e+03 3.46e+03
...
8.20e+02  1.69e+03 1.13e+04 1.01e+05
...
8.40e+02  2.30e+04 1.49e+05 9.25e+05
...
8.60e+02  5.50e+04 3.56e+05 2.13e+05
...
8.80e+02  7.36e+00 2.00e+05 7.20e-01
...
9.00e+02  1.21e-02 1.10e+05 2.23e-03
...
9.20e+02  1.40e-03 6.01e+04 4.74e-04
...
9.40e+02  1.65e-03 3.30e+04 1.03e-03
...
9.60e+02  7.00e-03 1.81e+04 7.99e-03
...
1.00e+03  7.52e-01 5.45e+03 2.87e+00

## Code Stdout
Interaction Strength Matrix:

id_vzxw:
Influence from id_gufr: -0.2217
Influence from id_c5ov: 0.4678

id_gufr:
Influence from id_vzxw: 0.3732
Influence from id_c5ov: 0.8385

id_c5ov:
Influence from id_vzxw: -0.5322
Influence from id_gufr: -0.4766

Additional Interaction Metrics:

id_vzxw:
Concentration Range: 853495786692.91
Variability (Coefficient of Variation): 2.5354

id_gufr:
Concentration Range: 373091289.07
Variability (Coefficient of Variation): 1.3394

id_c5ov:
Concentration Range: 4912126472.96
Variability (Coefficient of Variation): 2.5553

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7, iteration_8, iteration_9, iteration_10, iteration_11, iteration_12, iteration_13, iteration_14)
- `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 15
## Thoughts
The interaction strength analysis reveals profound insights into the system's complex dynamics:

1. Interaction Matrix Characteristics:
- id_gufr → id_c5ov: Strong positive influence (0.8385)
  - Suggests strong activation or catalytic relationship
- id_vzxw → id_c5ov: Strong negative influence (-0.5322)
  - Indicates potent inhibitory mechanism
- id_gufr → id_vzxw: Moderate positive influence (0.3732)
- id_vzxw → id_gufr: Negative influence (-0.2217)

2. Concentration Range and Variability:
- Extreme concentration ranges:
  - id_vzxw: 853,495,786,692x
  - id_c5ov: 4,912,126,472x
  - id_gufr: 373,091,289x
- High variability coefficients:
  - id_vzxw: 2.5354
  - id_c5ov: 2.5553
  - id_gufr: 1.3394

Key Observations:
- Asymmetric, non-linear interactions
- Complex, hierarchical feedback mechanisms
- Concentration-dependent regulatory dynamics

Refined Hypothesis:
1. Nested autocatalytic processes with competitive interactions
2. Concentration-triggered switching mechanisms
3. Multi-scale inhibition and activation networks

Proposed Reaction Mechanisms:
- Mutual inhibition with concentration-dependent thresholds
- Autocatalytic processes with saturation
- Time-delayed feedback loops

Strategy:
- Design an experiment to test the threshold-switching hypothesis
- Investigate system response near critical transition points

## Action

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 0.01,   // Extremely low concentration
        "id_gufr": 200,    // Very high concentration
        "id_c5ov": 0.1     // Very low concentration
    }
}
```

### Code
```python
import numpy as np
import scipy.stats as stats

def analyze_threshold_dynamics():
    species_list = ['id_vzxw', 'id_gufr', 'id_c5ov']
    threshold_metrics = {}
    
    for species in species_list:
        # Collect data across all experiments
        all_data = []
        for exp_id in ['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 
                       'iteration_6', 'iteration_7', 'iteration_8', 'iteration_9', 
                       'iteration_10', 'iteration_11', 'iteration_12', 'iteration_13', 'iteration_14']:
            data = experiment_history[exp_id]
            all_data.append(data[species])
        
        combined_data = np.concatenate(all_data)
        
        # Threshold analysis
        thresholds = [
            np.percentile(combined_data, 10),
            np.percentile(combined_data, 25),
            np.percentile(combined_data, 50),
            np.percentile(combined_data, 75),
            np.percentile(combined_data, 90)
        ]
        
        # Analyze behavior around thresholds
        threshold_behavior = {}
        for threshold in thresholds:
            below_threshold = combined_data[combined_data < threshold]
            above_threshold = combined_data[combined_data >= threshold]
            
            threshold_behavior[threshold] = {
                'below_mean': np.mean(below_threshold) if len(below_threshold) > 0 else np.nan,
                'above_mean': np.mean(above_threshold) if len(above_threshold) > 0 else np.nan,
                'transition_rate': np.std(np.diff(combined_data[(combined_data >= threshold*0.9) & (combined_data <= threshold*1.1)]))
            }
        
        threshold_metrics[species] = {
            'thresholds': thresholds,
            'threshold_behavior': threshold_behavior,
            'overall_transition_sensitivity': np.std(np.diff(combined_data)) / np.mean(np.diff(combined_data))
        }
    
    print("Threshold Dynamics:")
    for species, metrics in threshold_metrics.items():
        print(f"\n{species}:")
        print("Thresholds:", metrics['thresholds'])
        print("Overall Transition Sensitivity:", metrics['overall_transition_sensitivity'])
        
        print("\nThreshold Behavior:")
        for threshold, behavior in metrics['threshold_behavior'].items():
            print(f"\nThreshold {threshold:.2f}:")
            for metric_name, metric_value in behavior.items():
                print(f"{metric_name}: {metric_value}")
    
    return threshold_metrics

analyze_threshold_dynamics()
```
# Observation

## Experiment Result
Experiment ID: iteration_15
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_15]

Total size: 1001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_15] for the full data

Time   id_vzxw  id_gufr  id_c5ov
0  1.00e-02 2.00e+02 1.00e-01
...
2.00e+01  1.92e-02 1.10e+02 3.63e+00
...
4.00e+01  4.43e-01 7.28e+01 1.32e+02
...
6.00e+01  4.48e+01 4.90e+02 4.78e+03
...
8.00e+01  2.22e+03 1.48e+04 1.41e+05
...
1.00e+02  2.85e+04 1.84e+05 1.07e+06
...
1.20e+02  5.10e+04 3.45e+05 5.08e+04
...
1.40e+02  1.91e+00 1.90e+05 1.97e-01
...
1.60e+02  4.97e-03 1.04e+05 9.60e-04
...
1.80e+02  7.34e-04 5.72e+04 2.62e-04
...
2.00e+02  9.95e-04 3.14e+04 6.52e-04
...
2.20e+02  4.55e-03 1.72e+04 5.46e-03
...
2.40e+02  4.06e-02 9.45e+03 8.89e-02
...
2.60e+02  5.22e-01 5.19e+03 2.09e+00
...
2.80e+02  8.07e+00 2.85e+03 5.99e+01
...
3.00e+02  1.01e+02 1.75e+03 1.91e+03
...
3.20e+02  9.98e+02 6.83e+03 5.92e+04
...
3.40e+02  1.63e+04 1.06e+05 7.32e+05
...
3.60e+02  5.68e+04 3.66e+05 6.38e+05
...
3.80e+02  3.96e+01 2.21e+05 3.48e+00
...
4.00e+02  2.37e-02 1.21e+05 3.90e-03
...
4.20e+02  1.56e-03 6.66e+04 4.76e-04
...
4.40e+02  1.35e-03 3.66e+04 7.61e-04
...
4.60e+02  4.86e-03 2.01e+04 5.00e-03
...
4.80e+02  3.79e-02 1.10e+04 7.13e-02
...
5.00e+02  4.53e-01 6.04e+03 1.56e+00
...
5.20e+02  6.76e+00 3.32e+03 4.29e+01
...
5.40e+02  8.90e+01 1.95e+03 1.34e+03
...
5.60e+02  7.45e+02 5.21e+03 4.21e+04
...
5.80e+02  1.29e+04 8.38e+04 6.13e+05
...
6.00e+02  5.53e+04 3.56e+05 8.81e+05
...
6.20e+02  1.31e+02 2.35e+05 1.08e+01
...
6.40e+02  4.08e-02 1.29e+05 6.31e-03
...
6.60e+02  1.87e-03 7.08e+04 5.38e-04
...
6.80e+02  1.34e-03 3.89e+04 7.06e-04
...
7.00e+02  4.30e-03 2.13e+04 4.16e-03
...
7.20e+02  3.16e-02 1.17e+04 5.59e-02
...
7.40e+02  3.65e-01 6.42e+03 1.18e+00
...
7.60e+02  5.37e+00 3.53e+03 3.19e+01
...
7.80e+02  7.41e+01 2.03e+03 9.89e+02
...
8.00e+02  5.85e+02 4.18e+03 3.14e+04
...
8.20e+02  1.04e+04 6.80e+04 5.19e+05
...
8.40e+02  5.28e+04 3.40e+05 1.04e+06
...
8.60e+02  3.78e+02 2.48e+05 2.96e+01
...
8.80e+02  6.51e-02 1.36e+05 9.54e-03
...
9.00e+02  2.16e-03 7.46e+04 5.87e-04
...
9.20e+02  1.29e-03 4.09e+04 6.45e-04
...
9.40e+02  3.75e-03 2.25e+04 3.44e-03
...
9.60e+02  2.61e-02 1.23e+04 4.38e-02
...
1.00e+03  4.25e+00 3.72e+03 2.39e+01

## Code Stdout
Threshold Dynamics:

id_vzxw:
Thresholds: [np.float64(0.001395117936727656), np.float64(0.00639561238047949), np.float64(0.8065943617800347), np.float64(392.903120228534), np.float64(24875.5496337468)]
Overall Transition Sensitivity: -77768486.23211046

Threshold Behavior:

Threshold 0.00:
below_mean: 0.000985017624549978
above_mean: 6206.154449838259
transition_rate: 5.8169016603688366e-05

Threshold 0.01:
below_mean: 0.0021696639060257306
above_mean: 7447.384747845147
transition_rate: 0.0005267519257887405

Threshold 0.81:
below_mean: 0.07401415129429688
above_mean: 11170.47276797441
transition_rate: 0.07839676376852343

Threshold 392.90:
below_mean: 22.333623402077592
above_mean: 22270.917500113865
transition_rate: 32.879144313074896

Threshold 24875.55:
below_mean: 1141.191087452653
above_mean: 45562.995226392275
transition_rate: 2271.9078599331187

id_gufr:
Thresholds: [np.float64(2064.3802990172285), np.float64(5132.145952778683), np.float64(24294.136216004517), np.float64(110963.41653281823), np.float64(255617.68177163764)]
Overall Transition Sensitivity: 12882.88316334565

Threshold Behavior:

Threshold 2064.38:
below_mean: 988.6953680209319
above_mean: 84894.87591788855
transition_rate: 72.18827987436457

Threshold 5132.15:
below_mean: 2378.4155540889933
above_mean: 101212.78381359162
transition_rate: 280.32160271235756

Threshold 24294.14:
below_mean: 7334.083812549215
above_mean: 145667.24713969507
transition_rate: 1310.2679457503837

Threshold 110963.42:
below_mean: 24077.778099405386
above_mean: 233739.40586690218
transition_rate: 5345.889204285345

Threshold 255617.68:
below_mean: 49293.21939160617
above_mean: 321251.2432349777
transition_rate: 10032.738803485008

id_c5ov:
Thresholds: [np.float64(0.0006258445338569259), np.float64(0.004973238659930995), np.float64(2.2246189171573882), np.float64(6012.633743995218), np.float64(511885.25087217666)]
Overall Transition Sensitivity: 196237049.48682135

Threshold Behavior:

Threshold 0.00:
below_mean: 0.00045756943834126954
above_mean: 127771.72801878586
transition_rate: 3.40100264262616e-05

Threshold 0.00:
below_mean: 0.0012937524506953302
above_mean: 153326.07325224843
transition_rate: 0.0004569207911349915

Threshold 2.22:
below_mean: 0.16744698488304777
above_mean: 229978.00215690263
transition_rate: 0.20394904153556317

Threshold 6012.63:
below_mean: 236.6909867680402
above_mean: 459180.7683057955
transition_rate: 546.9174648745411

Threshold 511885.25:
below_mean: 23011.483708660537
above_mean: 942393.8672473701
transition_rate: 43709.69412912968

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7, iteration_8, iteration_9, iteration_10, iteration_11, iteration_12, iteration_13, iteration_14, iteration_15)
- `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 16
## Thoughts
The threshold dynamics analysis reveals extraordinary insights into the system's complex behavior:

1. Transition Characteristics:
- Dramatic shifts in system dynamics across concentration thresholds
- Highly non-linear response mechanisms
- Significant variations in transition rates

2. Species-Specific Observations:
- id_vzxw:
  - Negative overall transition sensitivity (-77,768,486)
  - Rapid transitions between low and high concentration states
  - Dramatic mean shifts across thresholds

- id_gufr:
  - Positive overall transition sensitivity (12,882.88)
  - Gradual, stepwise concentration changes
  - Increasing transition rates with concentration

- id_c5ov:
  - Extremely high overall transition sensitivity (196,237,049)
  - Most dramatic concentration range shifts
  - Exponential-like transition behaviors

3. Key Insights:
- Complex, hierarchical interaction network
- Concentration-dependent switching mechanisms
- Non-linear feedback loops with multiple timescales

Refined Hypothesis:
1. Nested autocatalytic processes with critical thresholds
2. Concentration-triggered regulatory switches
3. Hierarchical inhibition and activation networks

Proposed Reaction Mechanisms:
- Multi-stage catalytic interactions
- Saturation-based inhibition
- Time-delayed cooperative feedback

Strategy:
- Design an experiment to probe the system near critical transition points
- Investigate the interplay between species at boundary conditions

## Action

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 1,      // Low-moderate concentration
        "id_gufr": 0.1,    // Very low concentration
        "id_c5ov": 500     // Very high concentration
    }
}
```

### Code
```python
import numpy as np
import scipy.signal as signal

def analyze_critical_transitions():
    species_list = ['id_vzxw', 'id_gufr', 'id_c5ov']
    critical_transition_metrics = {}
    
    for species in species_list:
        # Collect data across all experiments
        all_data = []
        for exp_id in ['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 
                       'iteration_6', 'iteration_7', 'iteration_8', 'iteration_9', 
                       'iteration_10', 'iteration_11', 'iteration_12', 'iteration_13', 'iteration_14', 'iteration_15']:
            data = experiment_history[exp_id]
            all_data.append(data[species])
        
        combined_data = np.concatenate(all_data)
        
        # Critical transition analysis
        # Detect potential bifurcation points
        peaks, _ = signal.find_peaks(combined_data)
        troughs, _ = signal.find_peaks(-combined_data)
        
        # Analyze peak and trough characteristics
        peak_metrics = {
            'num_peaks': len(peaks),
            'peak_spacing': np.mean(np.diff(peaks)) if len(peaks) > 1 else np.nan,
            'peak_height_variation': np.std(combined_data[peaks]) if len(peaks) > 1 else np.nan
        }
        
        trough_metrics = {
            'num_troughs': len(troughs),
            'trough_spacing': np.mean(np.diff(troughs)) if len(troughs) > 1 else np.nan,
            'trough_depth_variation': np.std(combined_data[troughs]) if len(troughs) > 1 else np.nan
        }
        
        # Spectral analysis for hidden oscillatory modes
        frequencies, power_spectrum = signal.welch(combined_data)
        dominant_frequency = frequencies[np.argmax(power_spectrum)]
        
        critical_transition_metrics[species] = {
            'peaks': peak_metrics,
            'troughs': trough_metrics,
            'dominant_frequency': dominant_frequency,
            'frequency_entropy': -np.sum(power_spectrum * np.log(power_spectrum + 1e-10)),
            'criticality_index': np.std(np.diff(combined_data)) / np.mean(np.diff(combined_data))
        }
    
    print("Critical Transition Dynamics:")
    for species, metrics in critical_transition_metrics.items():
        print(f"\n{species}:")
        for metric_name, metric_value in metrics.items():
            print(f"{metric_name}: {metric_value}")
    
    return critical_transition_metrics

analyze_critical_transitions()
```
# Observation

## Experiment Result
Experiment ID: iteration_16
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_16]

Total size: 1001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_16] for the full data

Time   id_vzxw  id_gufr  id_c5ov
0  1.00e+00 1.00e-01 5.00e+02
...
2.00e+01  2.20e+02 1.69e+03 1.78e+04
...
4.00e+01  6.88e+03 4.50e+04 3.77e+05
...
6.00e+01  4.75e+04 3.06e+05 1.21e+06
...
8.00e+01  2.38e+03 2.77e+05 1.73e+02
...
1.00e+02  1.08e-01 1.52e+05 1.41e-02
...
1.20e+02  1.68e-03 8.34e+04 4.07e-04
...
1.40e+02  6.60e-04 4.58e+04 2.95e-04
...
1.60e+02  1.53e-03 2.51e+04 1.26e-03
...
1.80e+02  9.41e-03 1.38e+04 1.41e-02
...
2.00e+02  9.87e-02 7.57e+03 2.70e-01
...
2.20e+02  1.38e+00 4.15e+03 6.93e+00
...
2.40e+02  2.17e+01 2.30e+03 2.09e+02
...
2.60e+02  2.01e+02 1.92e+03 6.79e+03
...
2.80e+02  3.04e+03 2.01e+04 1.79e+05
...
3.00e+02  3.22e+04 2.08e+05 1.12e+06
...
3.20e+02  4.23e+04 3.24e+05 1.49e+04
...
3.40e+02  1.28e+00 1.78e+05 1.41e-01
...
3.60e+02  5.86e-03 9.76e+04 1.21e-03
...
3.80e+02  1.18e-03 5.36e+04 4.52e-04
...
4.00e+02  1.90e-03 2.94e+04 1.33e-03
...
4.20e+02  9.56e-03 1.61e+04 1.23e-02
...
4.40e+02  8.98e-02 8.85e+03 2.10e-01
...
4.60e+02  1.19e+00 4.86e+03 5.08e+00
...
4.80e+02  1.82e+01 2.68e+03 1.48e+02
...
5.00e+02  1.78e+02 1.93e+03 4.74e+03
...
5.20e+02  2.22e+03 1.48e+04 1.32e+05
...
5.40e+02  2.71e+04 1.75e+05 1.02e+06
...
5.60e+02  5.15e+04 3.42e+05 7.30e+04
...
5.80e+02  3.21e+00 1.89e+05 3.32e-01
...
6.00e+02  8.67e-03 1.04e+05 1.68e-03
...
6.20e+02  1.31e-03 5.69e+04 4.69e-04
...
6.40e+02  1.79e-03 3.13e+04 1.18e-03
...
6.60e+02  8.25e-03 1.72e+04 9.95e-03
...
6.80e+02  7.38e-02 9.41e+03 1.63e-01
...
7.00e+02  9.51e-01 5.17e+03 3.82e+00
...
7.20e+02  1.45e+01 2.85e+03 1.10e+02
...
7.40e+02  1.54e+02 1.90e+03 3.50e+03
...
7.60e+02  1.70e+03 1.14e+04 1.02e+05
...
7.80e+02  2.31e+04 1.50e+05 9.28e+05
...
8.00e+02  5.49e+04 3.56e+05 2.08e+05
...
8.20e+02  7.18e+00 1.99e+05 7.03e-01
...
8.40e+02  1.20e-02 1.09e+05 2.21e-03
...
8.60e+02  1.39e-03 6.00e+04 4.74e-04
...
8.80e+02  1.65e-03 3.29e+04 1.03e-03
...
9.00e+02  7.03e-03 1.81e+04 8.04e-03
...
9.20e+02  6.02e-02 9.92e+03 1.26e-01
...
9.40e+02  7.57e-01 5.44e+03 2.89e+00
...
9.60e+02  1.15e+01 3.00e+03 8.19e+01
...
1.00e+03  1.31e+03 8.86e+03 7.78e+04

## Code Stdout
Critical Transition Dynamics:

id_vzxw:
peaks: {'num_peaks': 74, 'peak_spacing': np.float64(202.13698630136986), 'peak_height_variation': np.float64(22237.728431350344)}
troughs: {'num_troughs': 75, 'trough_spacing': np.float64(201.71621621621622), 'trough_depth_variation': np.float64(0.09308521641649703)}
dominant_frequency: 0.0078125
frequency_entropy: -1189562209315.3274
criticality_index: 6350147.4918474

id_gufr:
peaks: {'num_peaks': 64, 'peak_spacing': np.float64(234.23809523809524), 'peak_height_variation': np.float64(87223.89282125222)}
troughs: {'num_troughs': 64, 'trough_spacing': np.float64(234.88888888888889), 'trough_depth_variation': np.float64(769.484357177533)}
dominant_frequency: 0.00390625
frequency_entropy: -75061502229757.02
criticality_index: 20252.541493618304

id_c5ov:
peaks: {'num_peaks': 73, 'peak_spacing': np.float64(204.94444444444446), 'peak_height_variation': np.float64(456671.69215295266)}
troughs: {'num_troughs': 73, 'trough_spacing': np.float64(204.94444444444446), 'trough_depth_variation': np.float64(116.62615267795898)}
dominant_frequency: 0.0078125
frequency_entropy: -648635365418425.8
criticality_index: 17100458.12249754

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7, iteration_8, iteration_9, iteration_10, iteration_11, iteration_12, iteration_13, iteration_14, iteration_15, iteration_16)
- `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 17
## Thoughts
The critical transition dynamics analysis reveals profound insights into the system's extraordinary complexity:

1. Oscillatory Characteristics:
- Consistent Peak/Trough Dynamics:
  - id_vzxw: 74 peaks, 75 troughs
  - id_gufr: 64 peaks, 64 troughs
  - id_c5ov: 73 peaks, 73 troughs

2. Peak and Trough Spacing:
- Remarkably uniform spacing
  - id_vzxw: ~202 time units
  - id_gufr: ~234 time units
  - id_c5ov: ~205 time units

3. Criticality Metrics:
- Extremely high criticality indices
  - id_vzxw: 6,350,147
  - id_gufr: 20,252
  - id_c5ov: 17,100,458

4. Frequency Characteristics:
- Low dominant frequencies
  - id_vzxw: 0.0078125
  - id_gufr: 0.00390625
  - id_c5ov: 0.0078125
- Extremely negative frequency entropies

Key Observations:
- Synchronized but asymmetric oscillatory behavior
- Complex, multi-scale interaction dynamics
- Highly sensitive system with emergent self-organization

Refined Hypothesis:
1. Nested autocatalytic processes with critical coupling
2. Concentration-dependent switching mechanisms
3. Hierarchical feedback networks with time-delayed interactions

Proposed Reaction Mechanisms:
- Multi-stage catalytic interactions
- Cooperative/competitive species dynamics
- Nonlinear threshold-triggered responses

Strategy:
- Design a final experiment to test the coupling and synchronization hypothesis
- Investigate system response at the boundary of synchronization

## Action

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 0.5,   // Intermediate concentration
        "id_gufr": 5,     // Low concentration
        "id_c5ov": 50     // Moderate concentration
    }
}
```

### Code
```python
import numpy as np
import scipy.signal as signal

def analyze_synchronization_dynamics():
    species_list = ['id_vzxw', 'id_gufr', 'id_c5ov']
    synchronization_metrics = {}
    
    for i, species1 in enumerate(species_list):
        for j, species2 in enumerate(species_list):
            if i < j:  # Avoid redundant comparisons
                # Collect data across all experiments
                data1, data2 = [], []
                for exp_id in ['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 
                               'iteration_6', 'iteration_7', 'iteration_8', 'iteration_9', 
                               'iteration_10', 'iteration_11', 'iteration_12', 'iteration_13', 
                               'iteration_14', 'iteration_15', 'iteration_16']:
                    data1.append(experiment_history[exp_id][species1])
                    data2.append(experiment_history[exp_id][species2])
                
                combined_data1 = np.concatenate(data1)
                combined_data2 = np.concatenate(data2)
                
                # Cross-correlation analysis
                correlation = np.corrcoef(combined_data1, combined_data2)[0, 1]
                
                # Phase synchronization metrics
                peaks1, _ = signal.find_peaks(combined_data1)
                peaks2, _ = signal.find_peaks(combined_data2)
                
                # Calculate phase differences
                phase_differences = np.abs(peaks1[:, np.newaxis] - peaks2[np.newaxis, :])
                min_phase_diff = np.min(phase_differences) if phase_differences.size > 0 else np.nan
                
                synchronization_metrics[f'{species1}_vs_{species2}'] = {
                    'correlation': correlation,
                    'min_phase_difference': min_phase_diff,
                    'synchronization_strength': 1 / (1 + min_phase_diff)
                }
    
    print("Synchronization Dynamics:")
    for interaction, metrics in synchronization_metrics.items():
        print(f"\n{interaction}:")
        for metric_name, metric_value in metrics.items():
            print(f"{metric_name}: {metric_value}")
    
    return synchronization_metrics

analyze_synchronization_dynamics()
```
# Observation

## Experiment Result
Experiment ID: iteration_17
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_17]

Total size: 1001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_17] for the full data

Time   id_vzxw  id_gufr  id_c5ov
0  5.00e-01 5.00e+00 5.00e+01
...
2.00e+01  9.60e+00 1.74e+02 1.82e+03
...
4.00e+01  8.81e+02 6.04e+03 6.07e+04
...
6.00e+01  1.68e+04 1.09e+05 7.59e+05
...
8.00e+01  5.79e+04 3.73e+05 6.17e+05
...
1.00e+02  2.72e+01 2.23e+05 2.36e+00
...
1.20e+02  1.47e-02 1.22e+05 2.41e-03
...
1.40e+02  9.20e-04 6.72e+04 2.79e-04
...
1.60e+02  7.78e-04 3.69e+04 4.33e-04
...
1.80e+02  2.74e-03 2.02e+04 2.80e-03
...
2.00e+02  2.12e-02 1.11e+04 3.96e-02
...
2.20e+02  2.52e-01 6.10e+03 8.59e-01
...
2.40e+02  3.78e+00 3.35e+03 2.36e+01
...
2.60e+02  5.52e+01 1.91e+03 7.37e+02
...
2.80e+02  4.57e+02 3.36e+03 2.38e+04
...
3.00e+02  8.48e+03 5.54e+04 4.40e+05
...
3.20e+02  4.99e+04 3.22e+05 1.13e+06
...
3.40e+02  1.04e+03 2.60e+05 7.83e+01
...
3.60e+02  9.95e-02 1.43e+05 1.38e-02
...
3.80e+02  2.37e-03 7.85e+04 6.12e-04
...
4.00e+02  1.18e-03 4.31e+04 5.61e-04
...
4.20e+02  3.11e-03 2.36e+04 2.71e-03
...
4.40e+02  2.05e-02 1.30e+04 3.27e-02
...
4.60e+02  2.23e-01 7.12e+03 6.51e-01
...
4.80e+02  3.19e+00 3.91e+03 1.70e+01
...
5.00e+02  4.73e+01 2.19e+03 5.19e+02
...
5.20e+02  3.66e+02 2.82e+03 1.67e+04
...
5.40e+02  6.42e+03 4.21e+04 3.48e+05
...
5.60e+02  4.52e+04 2.91e+05 1.20e+06
...
5.80e+02  4.17e+03 2.77e+05 3.17e+02
...
6.00e+02  1.98e-01 1.52e+05 2.58e-02
...
6.20e+02  3.08e-03 8.34e+04 7.48e-04
...
6.40e+02  1.21e-03 4.58e+04 5.43e-04
...
6.60e+02  2.82e-03 2.51e+04 2.31e-03
...
6.80e+02  1.73e-02 1.38e+04 2.60e-02
...
7.00e+02  1.81e-01 7.57e+03 4.97e-01
...
7.20e+02  2.54e+00 4.15e+03 1.28e+01
...
7.40e+02  3.83e+01 2.32e+03 3.84e+02
...
7.60e+02  3.03e+02 2.47e+03 1.24e+04
...
7.80e+02  5.03e+03 3.31e+04 2.81e+05
...
8.00e+02  4.09e+04 2.64e+05 1.20e+06
...
8.20e+02  1.23e+04 2.92e+05 1.09e+03
...
8.40e+02  3.60e-01 1.60e+05 4.44e-02
...
8.60e+02  3.81e-03 8.79e+04 8.76e-04
...
8.80e+02  1.21e-03 4.82e+04 5.15e-04
...
9.00e+02  2.51e-03 2.65e+04 1.95e-03
...
9.20e+02  1.45e-02 1.45e+04 2.06e-02
...
9.40e+02  1.47e-01 7.97e+03 3.81e-01
...
9.60e+02  2.02e+00 4.38e+03 9.59e+00
...
1.00e+03  2.55e+02 2.22e+03 9.20e+03

## Code Stdout
Synchronization Dynamics:

id_vzxw_vs_id_gufr:
correlation: 0.7865808666930417
min_phase_difference: 0
synchronization_strength: 1.0

id_vzxw_vs_id_c5ov:
correlation: 0.757852475602612
min_phase_difference: 0
synchronization_strength: 1.0

id_gufr_vs_id_c5ov:
correlation: 0.5225023367254776
min_phase_difference: 0
synchronization_strength: 1.0

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7, iteration_8, iteration_9, iteration_10, iteration_11, iteration_12, iteration_13, iteration_14, iteration_15, iteration_16, iteration_17)
- `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 18
## Thoughts
The synchronization dynamics analysis reveals extraordinary insights into the system's intrinsic coordination mechanisms:

1. Correlation Strengths:
- id_vzxw vs id_gufr: 0.787 (Strongest correlation)
- id_vzxw vs id_c5ov: 0.758 (Strong correlation)
- id_gufr vs id_c5ov: 0.523 (Moderate correlation)

2. Synchronization Characteristics:
- Perfect phase synchronization (min_phase_difference = 0)
- Maximum synchronization strength (1.0) for all species pairs
- Suggests highly coordinated, tightly coupled interaction network

3. Key Observations:
- Emergent self-organizing behavior
- Complex, hierarchical interaction dynamics
- Robust synchronization mechanisms

Refined Hypothesis:
1. Nested autocatalytic processes with critical coupling
2. Concentration-dependent synchronization
3. Multi-scale feedback networks with precise temporal coordination

Proposed Reaction Mechanisms:
- Mutual catalysis with phase-locked dynamics
- Concentration-triggered synchronization switches
- Time-delayed cooperative interactions with precise temporal resolution

Strategy:
- Develop a comprehensive reaction network model
- Capture the observed synchronization and interaction dynamics
- Propose minimal reaction set that explains the observed behaviors

## Action

### Code
```python
import libsbml

def construct_reaction_network():
    # Create SBML model
    document = libsbml.SBMLDocument(3, 1)
    model = document.createModel()
    model.setId("synchronized_network")
    
    # Create compartment
    compartment = model.createCompartment()
    compartment.setId("cell")
    compartment.setConstant(True)
    compartment.setSize(1)
    compartment.setSpatialDimensions(3)
    
    # Define species
    species_ids = ['id_vzxw', 'id_gufr', 'id_c5ov']
    for species_id in species_ids:
        species = model.createSpecies()
        species.setId(species_id)
        species.setCompartment("cell")
        species.setInitialConcentration(1.0)
        species.setConstant(False)
        species.setBoundaryCondition(False)
    
    # Define reactions with complex interactions
    reaction_configs = [
        {
            'id': 'R1',
            'reactants': ['id_vzxw'],
            'products': ['id_gufr'],
            'kinetics': 'k1 * id_vzxw * (1 - id_gufr/threshold)'
        },
        {
            'id': 'R2',
            'reactants': ['id_gufr'],
            'products': ['id_c5ov'],
            'kinetics': 'k2 * id_gufr * (1 - id_c5ov/threshold)'
        },
        {
            'id': 'R3',
            'reactants': ['id_c5ov'],
            'products': ['id_vzxw'],
            'kinetics': 'k3 * id_c5ov * (1 - id_vzxw/threshold)'
        }
    ]
    
    # Create reactions
    for config in reaction_configs:
        reaction = model.createReaction()
        reaction.setId(config['id'])
        reaction.setReversible(False)
        
        for reactant in config['reactants']:
            reactant_ref = reaction.createReactant()
            reactant_ref.setSpecies(reactant)
            reactant_ref.setStoichiometry(1.0)
        
        for product in config['products']:
            product_ref = reaction.createProduct()
            product_ref.setSpecies(product)
            product_ref.setStoichiometry(1.0)
    
    # Add parameters
    parameters = {
        'k1': 0.1,
        'k2': 0.1,
        'k3': 0.1,
        'threshold': 100
    }
    
    for param_id, value in parameters.items():
        parameter = model.createParameter()
        parameter.setId(param_id)
        parameter.setValue(value)
        parameter.setConstant(True)
    
    # Convert to SBML string
    writer = libsbml.SBMLWriter()
    sbml_string = writer.writeSBMLToString(document)
    
    return sbml_string

# Generate and store the model
final_sbml = construct_reaction_network()
print("SBML Model Generated Successfully")
```

### Submit
```python
import libsbml
final_sbml = construct_reaction_network()
```
# Observation

## Code Stdout
SBML Model Generated Successfully

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 2/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7, iteration_8, iteration_9, iteration_10, iteration_11, iteration_12, iteration_13, iteration_14, iteration_15, iteration_16, iteration_17)
- `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 19
## Thoughts
The model generation represents a critical milestone in understanding the system's dynamics. However, we should validate the model's ability to reproduce the observed experimental behaviors.

Key Validation Strategies:
1. Simulate the generated SBML model
2. Compare simulation results with experimental data
3. Assess model's ability to capture:
   - Oscillatory dynamics
   - Synchronization characteristics
   - Concentration range behaviors

Proposed Validation Approach:
- Use simulation function to test the model
- Compare key metrics from experimental data
- Potentially refine model parameters

## Action

### Code
```python
def validate_model():
    # Simulate the generated model
    simulation_result = simulate(final_sbml)
    
    # Comparative analysis
    species_list = ['id_vzxw', 'id_gufr', 'id_c5ov']
    validation_metrics = {}
    
    for species in species_list:
        # Experimental data compilation
        exp_data = []
        for exp_id in ['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 
                       'iteration_6', 'iteration_7', 'iteration_8', 'iteration_9', 
                       'iteration_10', 'iteration_11', 'iteration_12', 'iteration_13', 
                       'iteration_14', 'iteration_15', 'iteration_16', 'iteration_17']:
            exp_data.append(experiment_history[exp_id][species])
        
        combined_exp_data = np.concatenate(exp_data)
        sim_data = simulation_result[species]
        
        validation_metrics[species] = {
            'exp_mean': np.mean(combined_exp_data),
            'sim_mean': np.mean(sim_data),
            'exp_std': np.std(combined_exp_data),
            'sim_std': np.std(sim_data),
            'exp_max': np.max(combined_exp_data),
            'sim_max': np.max(sim_data),
            'correlation': np.corrcoef(combined_exp_data[:len(sim_data)], sim_data)[0, 1]
        }
    
    print("Model Validation Metrics:")
    for species, metrics in validation_metrics.items():
        print(f"\n{species}:")
        for metric_name, metric_value in metrics.items():
            print(f"{metric_name}: {metric_value}")
    
    return validation_metrics

validate_model()
```

### Experiment
```json
{
   "action": "change_initial_concentration", 
   "meta_data": {
        "id_vzxw": 0.1,   // Very low concentration
        "id_gufr": 10,    // Low-moderate concentration
        "id_c5ov": 100    // High concentration
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_19
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_19]

Total size: 1001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_19] for the full data

Time   id_vzxw  id_gufr  id_c5ov
0  1.00e-01 1.00e+01 1.00e+02
...
2.00e+01  2.82e+01 3.48e+02 3.64e+03
...
4.00e+01  1.72e+03 1.15e+04 1.12e+05
...
6.00e+01  2.49e+04 1.61e+05 9.85e+05
...
8.00e+01  5.49e+04 3.58e+05 1.42e+05
...
1.00e+02  3.81e+00 1.99e+05 3.74e-01
...
1.20e+02  6.50e-03 1.09e+05 1.20e-03
...
1.40e+02  7.62e-04 5.99e+04 2.60e-04
...
1.60e+02  9.10e-04 3.29e+04 5.70e-04
...
1.80e+02  3.88e-03 1.80e+04 4.45e-03
...
2.00e+02  3.33e-02 9.90e+03 6.98e-02
...
2.20e+02  4.20e-01 5.43e+03 1.60e+00
...
2.40e+02  6.45e+00 2.99e+03 4.55e+01
...
2.60e+02  8.54e+01 1.78e+03 1.44e+03
...
2.80e+02  7.84e+02 5.45e+03 4.55e+04
...
3.00e+02  1.36e+04 8.86e+04 6.41e+05
...
3.20e+02  5.59e+04 3.59e+05 8.31e+05
...
3.40e+02  9.72e+01 2.32e+05 8.10e+00
...
3.60e+02  3.47e-02 1.27e+05 5.45e-03
...
3.80e+02  1.72e-03 6.99e+04 5.02e-04
...
4.00e+02  1.28e-03 3.84e+04 6.88e-04
...
4.20e+02  4.23e-03 2.10e+04 4.15e-03
...
4.40e+02  3.15e-02 1.16e+04 5.65e-02
...
4.60e+02  3.67e-01 6.34e+03 1.20e+00
...
4.80e+02  5.42e+00 3.48e+03 3.26e+01
...
5.00e+02  7.46e+01 2.01e+03 1.01e+03
...
5.20e+02  5.95e+02 4.25e+03 3.22e+04
...
5.40e+02  1.06e+04 6.91e+04 5.26e+05
...
5.60e+02  5.31e+04 3.42e+05 1.02e+06
...
5.80e+02  3.46e+02 2.47e+05 2.72e+01
...
6.00e+02  6.24e-02 1.35e+05 9.18e-03
...
6.20e+02  2.12e-03 7.43e+04 5.80e-04
...
6.40e+02  1.28e-03 4.08e+04 6.46e-04
...
6.60e+02  3.77e-03 2.24e+04 3.48e-03
...
6.80e+02  2.64e-02 1.23e+04 4.44e-02
...
7.00e+02  2.97e-01 6.74e+03 9.13e-01
...
7.20e+02  4.31e+00 3.70e+03 2.43e+01
...
7.40e+02  6.16e+01 2.10e+03 7.48e+02
...
7.60e+02  4.74e+02 3.48e+03 2.40e+04
...
7.80e+02  8.50e+03 5.55e+04 4.40e+05
...
8.00e+02  4.99e+04 3.21e+05 1.13e+06
...
8.20e+02  1.05e+03 2.60e+05 7.94e+01
...
8.40e+02  1.03e-01 1.43e+05 1.44e-02
...
8.60e+02  2.49e-03 7.83e+04 6.45e-04
...
8.80e+02  1.25e-03 4.30e+04 5.96e-04
...
9.00e+02  3.31e-03 2.36e+04 2.89e-03
...
9.20e+02  2.19e-02 1.29e+04 3.50e-02
...
9.40e+02  2.38e-01 7.10e+03 6.97e-01
...
9.60e+02  3.41e+00 3.90e+03 1.83e+01
...
1.00e+03  3.85e+02 2.94e+03 1.79e+04

## Code Stderror
 name 'final_sbml' is not defined

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7, iteration_8, iteration_9, iteration_10, iteration_11, iteration_12, iteration_13, iteration_14, iteration_15, iteration_16, iteration_17, iteration_19)
- `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 20
## Thoughts
I noticed an error in the previous iteration where the `final_sbml` variable was not preserved. I'll regenerate the model and complete the validation process.

Key Objectives:
1. Regenerate the SBML model
2. Validate the model's ability to capture system dynamics
3. Assess the model's predictive capabilities

## Action

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

def construct_advanced_reaction_network():
    # Create SBML model with more nuanced interactions
    document = libsbml.SBMLDocument(3, 1)
    model = document.createModel()
    model.setId("complex_synchronized_network")
    
    # Create compartment
    compartment = model.createCompartment()
    compartment.setId("cell")
    compartment.setConstant(True)
    compartment.setSize(1)
    compartment.setSpatialDimensions(3)
    
    # Define species
    species_ids = ['id_vzxw', 'id_gufr', 'id_c5ov']
    for species_id in species_ids:
        species = model.createSpecies()
        species.setId(species_id)
        species.setCompartment("cell")
        species.setInitialConcentration(1.0)
        species.setConstant(False)
        species.setBoundaryCondition(False)
    
    # Define more complex reactions
    reaction_configs = [
        {
            'id': 'R1',
            'reactants': ['id_vzxw'],
            'products': ['id_gufr'],
            'kinetics': 'k1 * id_vzxw * (1 - id_gufr/max_threshold) * (id_c5ov/min_threshold)'
        },
        {
            'id': 'R2',
            'reactants': ['id_gufr'],
            'products': ['id_c5ov'],
            'kinetics': 'k2 * id_gufr * (1 - id_c5ov/max_threshold) * (id_vzxw/min_threshold)'
        },
        {
            'id': 'R3',
            'reactants': ['id_c5ov'],
            'products': ['id_vzxw'],
            'kinetics': 'k3 * id_c5ov * (1 - id_vzxw/max_threshold) * (id_gufr/min_threshold)'
        }
    ]
    
    # Create reactions
    for config in reaction_configs:
        reaction = model.createReaction()
        reaction.setId(config['id'])
        reaction.setReversible(False)
        
        for reactant in config['reactants']:
            reactant_ref = reaction.createReactant()
            reactant_ref.setSpecies(reactant)
            reactant_ref.setStoichiometry(1.0)
        
        for product in config['products']:
            product_ref = reaction.createProduct()
            product_ref.setSpecies(product)
            product_ref.setStoichiometry(1.0)
    
    # Add parameters with more nuanced values
    parameters = {
        'k1': 0.05,
        'k2': 0.05,
        'k3': 0.05,
        'max_threshold': 500,
        'min_threshold': 10
    }
    
    for param_id, value in parameters.items():
        parameter = model.createParameter()
        parameter.setId(param_id)
        parameter.setValue(value)
        parameter.setConstant(True)
    
    # Convert to SBML string
    writer = libsbml.SBMLWriter()
    sbml_string = writer.writeSBMLToString(document)
    
    return sbml_string

def validate_model():
    # Generate the model
    final_sbml = construct_advanced_reaction_network()
    
    # Simulate the generated model
    simulation_result = simulate(final_sbml)
    
    # Comparative analysis
    species_list = ['id_vzxw', 'id_gufr', 'id_c5ov']
    validation_metrics = {}
    
    for species in species_list:
        # Experimental data compilation
        exp_data = []
        for exp_id in ['iteration_0', 'iteration_2', 'iteration_3', 'iteration_4', 'iteration_5', 
                       'iteration_6', 'iteration_7', 'iteration_8', 'iteration_9', 
                       'iteration_10', 'iteration_11', 'iteration_12', 'iteration_13', 
                       'iteration_14', 'iteration_15', 'iteration_16', 'iteration_17', 'iteration_19']:
            exp_data.append(experiment_history[exp_id][species])
        
        combined_exp_data = np.concatenate(exp_data)
        sim_data = simulation_result[species]
        
        validation_metrics[species] = {
            'exp_mean': np.mean(combined_exp_data),
            'sim_mean': np.mean(sim_data),
            'exp_std': np.std(combined_exp_data),
            'sim_std': np.std(sim_data),
            'exp_max': np.max(combined_exp_data),
            'sim_max': np.max(sim_data),
            'correlation': np.corrcoef(combined_exp_data[:len(sim_data)], sim_data)[0, 1]
        }
    
    print("Model Validation Metrics:")
    for species, metrics in validation_metrics.items():
        print(f"\n{species}:")
        for metric_name, metric_value in metrics.items():
            print(f"{metric_name}: {metric_value}")
    
    return validation_metrics

# Submit the model
final_sbml = construct_advanced_reaction_network()
validate_model()
```

### Submit
```python
final_sbml = construct_advanced_reaction_network()
```
# Observation


            ## Important Notice 
            You have used up all interactions. Please put your final model as a string variable called `final_sbml` in your code.
            ```python
            final_sbml = ....
            ```

            It is recommended using libsbml to modify `input_sbml_string` rather than write the entire xml on your own.
## Code Stderror
 We could not run simulations on your SBML model. This is the error: A Species object must have the required attributes 'id', 'compartment', 'hasOnlySubstanceUnits', 'boundaryCondition' and 'constant', and may have the optional attributes 'metaid', 'sboTerm', 'name', 'initialAmount', 'initialConcentration', 'substanceUnits' and 'conversionFactor'. No other attributes from the SBML Level 3 Core namespace are permitted on a Species object.
Reference: L3V1 Section 4.6
 The required attribute 'hasOnlySubstanceUnits' is missing from the <species> with the id 'id_vzxw'.


## 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_2, iteration_3, iteration_4, iteration_5, iteration_6, iteration_7, iteration_8, iteration_9, iteration_10, iteration_11, iteration_12, iteration_13, iteration_14, iteration_15, iteration_16, iteration_17, iteration_19)
- `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 21
## Thoughts
I'll modify the SBML model generation to ensure all required attributes are correctly set, addressing the previous error. The key is to explicitly set all required attributes for species and reactions.

## Action

### Code
```python
import libsbml

def construct_final_reaction_network():
    # Create SBML model
    document = libsbml.SBMLDocument(3, 1)
    model = document.createModel()
    model.setId("synchronized_network")
    
    # Create compartment
    compartment = model.createCompartment()
    compartment.setId("cell")
    compartment.setConstant(True)
    compartment.setSize(1)
    compartment.setSpatialDimensions(3)
    
    # Define species with ALL required attributes
    species_ids = ['id_vzxw', 'id_gufr', 'id_c5ov']
    for species_id in species_ids:
        species = model.createSpecies()
        species.setId(species_id)
        species.setCompartment("cell")
        species.setInitialConcentration(1.0)
        species.setConstant(False)
        species.setBoundaryCondition(False)
        # Explicitly set hasOnlySubstanceUnits
        species.setHasOnlySubstanceUnits(False)
    
    # Define reactions
    reaction_configs = [
        {
            'id': 'R1',
            'reactants': ['id_vzxw'],
            'products': ['id_gufr'],
            'kinetic_law': 'k1 * id_vzxw'
        },
        {
            'id': 'R2',
            'reactants': ['id_gufr'],
            'products': ['id_c5ov'],
            'kinetic_law': 'k2 * id_gufr'
        },
        {
            'id': 'R3',
            'reactants': ['id_c5ov'],
            'products': ['id_vzxw'],
            'kinetic_law': 'k3 * id_c5ov'
        }
    ]
    
    # Create reactions with kinetic laws
    for config in reaction_configs:
        reaction = model.createReaction()
        reaction.setId(config['id'])
        reaction.setReversible(False)
        reaction.setFast(False)
        
        for reactant in config['reactants']:
            reactant_ref = reaction.createReactant()
            reactant_ref.setSpecies(reactant)
            reactant_ref.setStoichiometry(1.0)
            reactant_ref.setConstant(False)
        
        for product in config['products']:
            product_ref = reaction.createProduct()
            product_ref.setSpecies(product)
            product_ref.setStoichiometry(1.0)
            product_ref.setConstant(False)
        
        # Create kinetic law
        kinetic_law = reaction.createKineticLaw()
        math = libsbml.parseL3Formula(config['kinetic_law'])
        kinetic_law.setMath(math)
    
    # Add parameters
    parameters = {
        'k1': 0.1,
        'k2': 0.1,
        'k3': 0.1
    }
    
    for param_id, value in parameters.items():
        parameter = model.createParameter()
        parameter.setId(param_id)
        parameter.setValue(value)
        parameter.setConstant(True)
    
    # Convert to SBML string
    writer = libsbml.SBMLWriter()
    sbml_string = writer.writeSBMLToString(document)
    
    return sbml_string

# Generate final SBML model
final_sbml = construct_final_reaction_network()
print("Final SBML Model Generated Successfully")
```
