
                # 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_m277">
    <listOfUnitDefinitions>
      <unitDefinition id="id_4k5w">
        <listOfUnits>
          <unit kind="litre" scale="-3"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_i2bi">
        <listOfUnits>
          <unit kind="second" multiplier="60"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_azy6">
        <listOfUnits>
          <unit kind="mole" scale="-3"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_motv" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_wq5e" compartment="id_motv" initialConcentration="0"/>
      <species id="id_9z5o" compartment="id_motv" initialConcentration="0"/>
      <species id="id_dukt" compartment="id_motv" initialConcentration="0"/>
      <species id="id_gbbq" compartment="id_motv" initialConcentration="0"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

                Format your response according to the instructions in the system message.
                
## Thoughts
I'm investigating a biological system with four species: id_wq5e, id_9z5o, id_dukt, and id_gbbq. All of these species have initial concentrations of 0. My goal is to discover the missing reactions between these species.

To start, I need to gather some data about how these species behave in the system. I'll first run an observation experiment to see if there's any activity in the system with the default settings. This will help me understand if there are any spontaneous reactions or if the system requires some initial concentrations to show activity.

## 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: 1341 rows × 5 columns. 

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

Time   id_wq5e  id_9z5o  id_dukt  id_gbbq
0         0        0        0        0
...
5.24e-01  1.47e-01 1.48e-01 1.47e-01 1.48e-01
...
1.05e+00  1.53e-01 1.57e-01 1.53e-01 1.57e-01
...
1.57e+00  1.53e-01 1.60e-01 1.53e-01 1.60e-01
...
2.10e+00  1.53e-01 1.63e-01 1.53e-01 1.63e-01
...
2.62e+00  1.53e-01 1.65e-01 1.53e-01 1.65e-01
...
3.14e+00  1.53e-01 1.66e-01 1.53e-01 1.66e-01
...
3.67e+00  1.53e-01 1.67e-01 1.53e-01 1.67e-01
...
4.19e+00  1.53e-01 1.69e-01 1.53e-01 1.69e-01
...
4.71e+00  1.53e-01 1.70e-01 1.53e-01 1.70e-01
...
5.24e+00  1.53e-01 1.71e-01 1.53e-01 1.71e-01
...
5.76e+00  1.53e-01 1.72e-01 1.53e-01 1.72e-01
...
6.29e+00  1.53e-01 1.72e-01 1.53e-01 1.72e-01
...
6.81e+00  1.53e-01 1.73e-01 1.53e-01 1.73e-01
...
7.33e+00  1.53e-01 1.74e-01 1.53e-01 1.74e-01
...
7.86e+00  1.53e-01 1.75e-01 1.53e-01 1.75e-01
...
8.38e+00  1.53e-01 1.76e-01 1.53e-01 1.76e-01
...
8.91e+00  1.53e-01 1.77e-01 1.53e-01 1.77e-01
...
9.43e+00  1.53e-01 1.78e-01 1.53e-01 1.78e-01
...
9.95e+00  1.53e-01 1.79e-01 1.53e-01 1.79e-01
...
1.05e+01  1.53e-01 1.80e-01 1.53e-01 1.80e-01
...
1.10e+01  1.53e-01 1.81e-01 1.53e-01 1.81e-01
...
1.15e+01  1.53e-01 1.83e-01 1.53e-01 1.83e-01
...
1.20e+01  1.53e-01 1.84e-01 1.53e-01 1.84e-01
...
1.26e+01  1.53e-01 1.87e-01 1.53e-01 1.86e-01
...
1.31e+01  1.53e-01 1.90e-01 1.54e-01 1.89e-01
...
1.36e+01  1.51e-01 1.97e-01 1.55e-01 1.92e-01
...
1.41e+01  1.46e-01 2.12e-01 1.61e-01 1.93e-01
...
1.47e+01  1.30e-01 2.60e-01 1.82e-01 1.87e-01
...
1.52e+01  9.63e-02 4.31e-01 2.65e-01 1.70e-01
...
1.57e+01  6.00e-02 6.49e-01 4.61e-01 1.28e-01
...
1.62e+01  3.60e-02 7.89e-01 6.61e-01 7.90e-02
...
1.68e+01  2.14e-02 8.74e-01 7.97e-01 4.72e-02
...
1.73e+01  1.28e-02 9.25e-01 8.79e-01 2.80e-02
...
1.78e+01  7.62e-03 9.56e-01 9.29e-01 1.67e-02
...
1.83e+01  4.57e-03 9.74e-01 9.58e-01 9.92e-03
...
1.89e+01  2.75e-03 9.84e-01 9.75e-01 5.92e-03
...
1.94e+01  1.67e-03 9.91e-01 9.85e-01 3.55e-03
...
1.99e+01  1.03e-03 9.95e-01 9.91e-01 2.15e-03
...
2.04e+01  6.54e-04 9.97e-01 9.95e-01 1.31e-03
...
2.10e+01  4.29e-04 9.98e-01 9.97e-01 8.19e-04
...
2.15e+01  2.95e-04 9.99e-01 9.98e-01 5.26e-04
...
2.20e+01  2.16e-04 9.99e-01 9.99e-01 3.53e-04
...
2.25e+01  1.69e-04 1.00e+00 9.99e-01 2.50e-04
...
2.31e+01  1.41e-04 1.00e+00 1.00e+00 1.89e-04
...
2.36e+01  1.24e-04 1.00e+00 1.00e+00 1.53e-04
...
2.41e+01  1.14e-04 1.00e+00 1.00e+00 1.31e-04
...
2.46e+01  1.09e-04 1.00e+00 1.00e+00 1.18e-04
...
2.51e+01  1.05e-04 1.00e+00 1.00e+00 1.11e-04
...
2.60e+01  1.02e-04 1.00e+00 1.00e+00 1.05e-04

## 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
Interesting! Even though all species start with an initial concentration of 0, we observe that they all increase in concentration over time. This suggests there might be some spontaneous generation or influx of these species from outside the system.

Looking at the data more closely:
1. All four species (id_wq5e, id_9z5o, id_dukt, id_gbbq) start at 0 and increase.
2. Around time 13-15, there's a significant change in dynamics:
   - id_9z5o and id_dukt continue to increase rapidly, eventually approaching 1.0
   - id_wq5e and id_gbbq peak and then decrease, eventually approaching very small values

This suggests a system where:
- There might be some influx of all species initially
- id_9z5o and id_dukt might be products of reactions consuming id_wq5e and id_gbbq
- There could be feedback mechanisms or catalytic relationships

Let me analyze the data more thoroughly to understand the relationships between these species.

## Action

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

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

# Let's look at the first few and last few rows to understand the dynamics
print("First few rows:")
print(data.head())
print("\nLast few rows:")
print(data.tail())

# Let's calculate the rates of change for each species
data['d_wq5e'] = np.gradient(data['id_wq5e'], data['Time'])
data['d_9z5o'] = np.gradient(data['id_9z5o'], data['Time'])
data['d_dukt'] = np.gradient(data['id_dukt'], data['Time'])
data['d_gbbq'] = np.gradient(data['id_gbbq'], data['Time'])

# Let's look at the correlation between species concentrations
correlation = data[['id_wq5e', 'id_9z5o', 'id_dukt', 'id_gbbq']].corr()
print("\nCorrelation between species concentrations:")
print(correlation)

# Let's also look at the correlation between rates of change
rate_correlation = data[['d_wq5e', 'd_9z5o', 'd_dukt', 'd_gbbq']].corr()
print("\nCorrelation between rates of change:")
print(rate_correlation)

# Let's examine if there are any conservation laws
# If species are interconverted, their sum might be constant
data['sum_all'] = data['id_wq5e'] + data['id_9z5o'] + data['id_dukt'] + data['id_gbbq']
data['sum_wq5e_9z5o'] = data['id_wq5e'] + data['id_9z5o']
data['sum_dukt_gbbq'] = data['id_dukt'] + data['id_gbbq']
data['sum_wq5e_dukt'] = data['id_wq5e'] + data['id_dukt']
data['sum_9z5o_gbbq'] = data['id_9z5o'] + data['id_gbbq']

print("\nChecking for conservation laws:")
print("Min and max of sum of all species:", data['sum_all'].min(), data['sum_all'].max())
print("Min and max of sum of wq5e and 9z5o:", data['sum_wq5e_9z5o'].min(), data['sum_wq5e_9z5o'].max())
print("Min and max of sum of dukt and gbbq:", data['sum_dukt_gbbq'].min(), data['sum_dukt_gbbq'].max())
print("Min and max of sum of wq5e and dukt:", data['sum_wq5e_dukt'].min(), data['sum_wq5e_dukt'].max())
print("Min and max of sum of 9z5o and gbbq:", data['sum_9z5o_gbbq'].min(), data['sum_9z5o_gbbq'].max())

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

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

## Reminder

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



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

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


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



# Iteration 2
## Thoughts
I apologize for the error. I tried to use matplotlib which is not in the allowed libraries. Let me revise my code to only use the authorized libraries for analyzing the data.

I'll focus on understanding the relationships between the species by examining:
1. The dynamics of each species over time
2. Correlations between species concentrations
3. Rates of change and their correlations
4. Potential conservation laws

This analysis should help me identify the missing reactions in the system.

## Action

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

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

# Let's look at the first few and last few rows to understand the dynamics
print("First few rows:")
print(data.head())
print("\nLast few rows:")
print(data.tail())

# Let's calculate the rates of change for each species
data['d_wq5e'] = np.gradient(data['id_wq5e'], data['Time'])
data['d_9z5o'] = np.gradient(data['id_9z5o'], data['Time'])
data['d_dukt'] = np.gradient(data['id_dukt'], data['Time'])
data['d_gbbq'] = np.gradient(data['id_gbbq'], data['Time'])

# Let's look at the correlation between species concentrations
correlation = data[['id_wq5e', 'id_9z5o', 'id_dukt', 'id_gbbq']].corr()
print("\nCorrelation between species concentrations:")
print(correlation)

# Let's also look at the correlation between rates of change
rate_correlation = data[['d_wq5e', 'd_9z5o', 'd_dukt', 'd_gbbq']].corr()
print("\nCorrelation between rates of change:")
print(rate_correlation)

# Let's examine if there are any conservation laws
# If species are interconverted, their sum might be constant
data['sum_all'] = data['id_wq5e'] + data['id_9z5o'] + data['id_dukt'] + data['id_gbbq']
data['sum_wq5e_9z5o'] = data['id_wq5e'] + data['id_9z5o']
data['sum_dukt_gbbq'] = data['id_dukt'] + data['id_gbbq']
data['sum_wq5e_dukt'] = data['id_wq5e'] + data['id_dukt']
data['sum_9z5o_gbbq'] = data['id_9z5o'] + data['id_gbbq']

print("\nChecking for conservation laws:")
print("Min and max of sum of all species:", data['sum_all'].min(), data['sum_all'].max())
print("Min and max of sum of wq5e and 9z5o:", data['sum_wq5e_9z5o'].min(), data['sum_wq5e_9z5o'].max())
print("Min and max of sum of dukt and gbbq:", data['sum_dukt_gbbq'].min(), data['sum_dukt_gbbq'].max())
print("Min and max of sum of wq5e and dukt:", data['sum_wq5e_dukt'].min(), data['sum_wq5e_dukt'].max())
print("Min and max of sum of 9z5o and gbbq:", data['sum_9z5o_gbbq'].min(), data['sum_9z5o_gbbq'].max())

# Let's also check the values at specific time points to understand the dynamics better
print("\nValues at specific time points:")
for t in [0, 5, 10, 15, 20, 25]:
    closest_idx = (data['Time'] - t).abs().idxmin()
    print(f"Time ≈ {t}:")
    print(data.loc[closest_idx, ['Time', 'id_wq5e', 'id_9z5o', 'id_dukt', 'id_gbbq']])

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

## Code Stdout
First few rows:
    id_wq5e   id_9z5o   id_dukt   id_gbbq      Time
0  0.000000  0.000000  0.000000  0.000000  0.000000
1  0.019211  0.019211  0.019211  0.019211  0.019403
2  0.037902  0.037902  0.037902  0.037902  0.038806
3  0.055455  0.055455  0.055455  0.055455  0.058209
4  0.070889  0.070889  0.070889  0.070889  0.077612

Last few rows:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
1336  0.000102  0.999987  0.999979  0.000105  25.922388
1337  0.000102  0.999987  0.999979  0.000105  25.941791
1338  0.000102  0.999987  0.999979  0.000105  25.961194
1339  0.000102  0.999987  0.999980  0.000105  25.980597
1340  0.000102  0.999988  0.999980  0.000105  26.000000

Correlation between species concentrations:
          id_wq5e   id_9z5o   id_dukt   id_gbbq
id_wq5e  1.000000 -0.989528 -0.984091  0.980334
id_9z5o -0.989528  1.000000  0.995115 -0.969733
id_dukt -0.984091  0.995115  1.000000 -0.982678
id_gbbq  0.980334 -0.969733 -0.982678  1.000000

Correlation between rates of change:
          d_wq5e    d_9z5o    d_dukt    d_gbbq
d_wq5e  1.000000  0.350956  0.367946  0.984335
d_9z5o  0.350956  1.000000  0.934287  0.310233
d_dukt  0.367946  0.934287  1.000000  0.269911
d_gbbq  0.984335  0.310233  0.269911  1.000000

Checking for conservation laws:
Min and max of sum of all species: 0.0 2.0001746253979684
Min and max of sum of wq5e and 9z5o: 0.0 1.000089831959628
Min and max of sum of dukt and gbbq: 0.0 1.0000847934383403
Min and max of sum of wq5e and dukt: 0.0 1.0000822794201716
Min and max of sum of 9z5o and gbbq: 0.0 1.0000923459777968

Values at specific time points:
Time ≈ 0:
Time       0.0
id_wq5e    0.0
id_9z5o    0.0
id_dukt    0.0
id_gbbq    0.0
Name: 0, dtype: float64
Time ≈ 5:
Time       5.005970
id_wq5e    0.153301
id_9z5o    0.170195
id_dukt    0.153301
id_gbbq    0.170195
Name: 258, dtype: float64
Time ≈ 10:
Time       9.992537
id_wq5e    0.153301
id_9z5o    0.178741
id_dukt    0.153302
id_gbbq    0.178740
Name: 515, dtype: float64
Time ≈ 15:
Time       14.998507
id_wq5e     0.110779
id_9z5o     0.347772
id_dukt     0.221478
id_gbbq     0.177324
Name: 773, dtype: float64
Time ≈ 20:
Time       20.004478
id_wq5e     0.000947
id_9z5o     0.995054
id_dukt     0.992021
id_gbbq     0.001957
Name: 1031, dtype: float64
Time ≈ 25:
Time       24.991045
id_wq5e     0.000106
id_9z5o     0.999966
id_dukt     0.999946
id_gbbq     0.000113
Name: 1288, dtype: float64

## Reminder

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



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

### 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 provides valuable insights into the system dynamics:

1. **Initial Behavior**: All species start at 0 and increase to around 0.15-0.17 by time 5.

2. **Correlation Analysis**:
   - Strong negative correlations between id_wq5e and id_9z5o (-0.99), and between id_wq5e and id_dukt (-0.98)
   - Strong negative correlation between id_gbbq and id_9z5o (-0.97), and between id_gbbq and id_dukt (-0.98)
   - Strong positive correlation between id_wq5e and id_gbbq (0.98)
   - Strong positive correlation between id_9z5o and id_dukt (0.995)

3. **Rate Correlation Analysis**:
   - Strong positive correlation between rates of change of id_wq5e and id_gbbq (0.98)
   - Strong positive correlation between rates of change of id_9z5o and id_dukt (0.93)

4. **Conservation Laws**:
   - The sum of all species reaches approximately 2.0, suggesting that the total concentration in the system increases over time.
   - No perfect conservation laws between pairs of species, but the sums all approach 1.0.

5. **Time Point Analysis**:
   - At time 0: All species are at 0
   - At time 5: All species are around 0.15-0.17
   - At time 10: Similar to time 5, with slight increases in id_9z5o and id_gbbq
   - At time 15: Significant changes - id_wq5e and id_gbbq decreasing, id_9z5o and id_dukt increasing
   - At time 20: id_wq5e and id_gbbq have nearly disappeared (~0.001), while id_9z5o and id_dukt have reached ~0.99
   - At time 25: System has stabilized with id_9z5o and id_dukt at ~1.0, id_wq5e and id_gbbq at ~0.0001

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

1. There appears to be an influx of all species from outside the system (since they all start at 0 and increase).
2. id_wq5e and id_gbbq seem to be consumed to produce id_9z5o and id_dukt.
3. The strong correlation between id_wq5e and id_gbbq, and between id_9z5o and id_dukt, suggests they might be involved in similar reactions.

Let me try to formulate a more specific hypothesis and test it with another experiment. I'll try changing the initial concentrations to see how the system responds.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_wq5e": 0.5,
        "id_9z5o": 0.0,
        "id_dukt": 0.0,
        "id_gbbq": 0.5
    }
}
```
# 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: 1341 rows × 5 columns. 

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

Time   id_wq5e  id_9z5o  id_dukt  id_gbbq
0  5.00e-01        0        0 5.00e-01
...
5.24e-01  7.04e-01 3.04e-04 3.04e-04 7.04e-01
...
1.05e+00  8.25e-01 2.95e-04 2.95e-04 8.25e-01
...
1.57e+00  8.96e-01 2.48e-04 2.48e-04 8.96e-01
...
2.10e+00  9.38e-01 2.03e-04 2.03e-04 9.38e-01
...
2.62e+00  9.64e-01 1.70e-04 1.70e-04 9.64e-01
...
3.14e+00  9.78e-01 1.46e-04 1.46e-04 9.78e-01
...
3.67e+00  9.87e-01 1.30e-04 1.30e-04 9.87e-01
...
4.19e+00  9.92e-01 1.19e-04 1.19e-04 9.92e-01
...
4.71e+00  9.96e-01 1.12e-04 1.12e-04 9.96e-01
...
5.24e+00  9.97e-01 1.08e-04 1.08e-04 9.97e-01
...
5.76e+00  9.98e-01 1.05e-04 1.05e-04 9.98e-01
...
6.29e+00  9.99e-01 1.03e-04 1.03e-04 9.99e-01
...
6.81e+00  9.99e-01 1.02e-04 1.02e-04 9.99e-01
...
7.33e+00  1.00e+00 1.01e-04 1.01e-04 1.00e+00
...
7.86e+00  1.00e+00 1.01e-04 1.01e-04 1.00e+00
...
8.38e+00  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
8.91e+00  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
9.43e+00  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
9.95e+00  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.05e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.10e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.15e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.20e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.26e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.31e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.36e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.41e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.47e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.52e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.57e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.62e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.68e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.73e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.78e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.83e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.89e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.94e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.99e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.04e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.10e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.15e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.20e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.25e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.31e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.36e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.41e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.46e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.51e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.60e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00

## Reminder

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



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

### 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
This experiment provides crucial insights into the system dynamics. I started with high concentrations of id_wq5e and id_gbbq (both at 0.5) and zero concentrations of id_9z5o and id_dukt. The results show:

1. id_wq5e and id_gbbq both increase from 0.5 to approximately 1.0 over time.
2. id_9z5o and id_dukt remain at very low levels (around 0.0001).

This is the opposite of what happened in the first experiment, where all species started at 0, and eventually id_9z5o and id_dukt increased to ~1.0 while id_wq5e and id_gbbq decreased to near zero.

These observations suggest:

1. The system has two stable states:
   - State 1: High id_wq5e and id_gbbq, low id_9z5o and id_dukt
   - State 2: Low id_wq5e and id_gbbq, high id_9z5o and id_dukt

2. The initial conditions determine which stable state the system reaches.

3. There appears to be a bistable switch mechanism, which is common in biological systems with mutual inhibition or positive feedback loops.

Let me try another experiment with different initial conditions to further understand the system. I'll set id_9z5o and id_dukt to high values and id_wq5e and id_gbbq to zero.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_wq5e": 0.0,
        "id_9z5o": 0.5,
        "id_dukt": 0.5,
        "id_gbbq": 0.0
    }
}
```
# 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: 1341 rows × 5 columns. 

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

Time   id_wq5e  id_9z5o  id_dukt  id_gbbq
0         0 5.00e-01 5.00e-01        0
...
5.24e-01  3.04e-04 7.04e-01 7.04e-01 3.04e-04
...
1.05e+00  2.95e-04 8.25e-01 8.25e-01 2.95e-04
...
1.57e+00  2.48e-04 8.96e-01 8.96e-01 2.48e-04
...
2.10e+00  2.03e-04 9.38e-01 9.38e-01 2.03e-04
...
2.62e+00  1.70e-04 9.64e-01 9.64e-01 1.70e-04
...
3.14e+00  1.46e-04 9.78e-01 9.78e-01 1.46e-04
...
3.67e+00  1.30e-04 9.87e-01 9.87e-01 1.30e-04
...
4.19e+00  1.19e-04 9.92e-01 9.92e-01 1.19e-04
...
4.71e+00  1.12e-04 9.96e-01 9.96e-01 1.12e-04
...
5.24e+00  1.08e-04 9.97e-01 9.97e-01 1.08e-04
...
5.76e+00  1.05e-04 9.98e-01 9.98e-01 1.05e-04
...
6.29e+00  1.03e-04 9.99e-01 9.99e-01 1.03e-04
...
6.81e+00  1.02e-04 9.99e-01 9.99e-01 1.02e-04
...
7.33e+00  1.01e-04 1.00e+00 1.00e+00 1.01e-04
...
7.86e+00  1.01e-04 1.00e+00 1.00e+00 1.01e-04
...
8.38e+00  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
8.91e+00  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
9.43e+00  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
9.95e+00  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.05e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.10e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.15e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.20e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.26e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.31e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.36e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.41e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.47e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.52e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.57e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.62e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.68e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.73e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.78e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.83e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.89e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.94e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.99e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.04e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.10e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.15e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.20e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.25e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.31e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.36e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.41e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.46e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.51e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.60e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis)

### 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
This experiment confirms my hypothesis about the bistable nature of the system. When I started with high concentrations of id_9z5o and id_dukt (both at 0.5) and zero concentrations of id_wq5e and id_gbbq, the system evolved to a state where id_9z5o and id_dukt are at high concentrations (~1.0) and id_wq5e and id_gbbq are at very low concentrations (~0.0001).

The symmetry in the results is striking:
1. In experiment 3: High id_wq5e and id_gbbq → System stabilizes with high id_wq5e and id_gbbq, low id_9z5o and id_dukt
2. In experiment 4: High id_9z5o and id_dukt → System stabilizes with high id_9z5o and id_dukt, low id_wq5e and id_gbbq

This strongly suggests a mutual inhibition network between two pairs of species:
- The pair (id_wq5e, id_gbbq) inhibits the pair (id_9z5o, id_dukt)
- The pair (id_9z5o, id_dukt) inhibits the pair (id_wq5e, id_gbbq)

Additionally, there seems to be positive feedback within each pair, as they tend to increase or decrease together.

Let me try one more experiment with mixed initial conditions to see if there's a threshold that determines which stable state the system reaches. I'll set all species to moderate values but with id_wq5e and id_gbbq slightly higher.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_wq5e": 0.3,
        "id_9z5o": 0.2,
        "id_dukt": 0.2,
        "id_gbbq": 0.3
    }
}
```
# 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: 1341 rows × 5 columns. 

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

Time   id_wq5e  id_9z5o  id_dukt  id_gbbq
0  3.00e-01 2.00e-01 2.00e-01 3.00e-01
...
5.24e-01  2.41e-01 1.36e-01 1.28e-01 2.81e-01
...
1.05e+00  3.40e-01 9.04e-02 8.29e-02 3.93e-01
...
1.57e+00  5.47e-01 5.51e-02 5.03e-02 5.91e-01
...
2.10e+00  7.22e-01 3.29e-02 3.00e-02 7.49e-01
...
2.62e+00  8.34e-01 1.96e-02 1.79e-02 8.50e-01
...
3.14e+00  9.02e-01 1.17e-02 1.07e-02 9.11e-01
...
3.67e+00  9.42e-01 6.97e-03 6.37e-03 9.47e-01
...
4.19e+00  9.65e-01 4.18e-03 3.82e-03 9.69e-01
...
4.71e+00  9.80e-01 2.52e-03 2.31e-03 9.82e-01
...
5.24e+00  9.88e-01 1.54e-03 1.41e-03 9.89e-01
...
5.76e+00  9.93e-01 9.52e-04 8.78e-04 9.94e-01
...
6.29e+00  9.96e-01 6.05e-04 5.62e-04 9.96e-01
...
6.81e+00  9.97e-01 4.00e-04 3.74e-04 9.98e-01
...
7.33e+00  9.99e-01 2.78e-04 2.63e-04 9.99e-01
...
7.86e+00  9.99e-01 2.06e-04 1.96e-04 9.99e-01
...
8.38e+00  9.99e-01 1.63e-04 1.57e-04 1.00e+00
...
8.91e+00  1.00e+00 1.37e-04 1.34e-04 1.00e+00
...
9.43e+00  1.00e+00 1.22e-04 1.20e-04 1.00e+00
...
9.95e+00  1.00e+00 1.13e-04 1.12e-04 1.00e+00
...
1.05e+01  1.00e+00 1.08e-04 1.07e-04 1.00e+00
...
1.10e+01  1.00e+00 1.05e-04 1.04e-04 1.00e+00
...
1.15e+01  1.00e+00 1.03e-04 1.02e-04 1.00e+00
...
1.20e+01  1.00e+00 1.02e-04 1.01e-04 1.00e+00
...
1.26e+01  1.00e+00 1.01e-04 1.01e-04 1.00e+00
...
1.31e+01  1.00e+00 1.01e-04 1.01e-04 1.00e+00
...
1.36e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.41e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.47e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.52e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.57e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.62e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.68e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.73e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.78e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.83e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.89e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.94e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
1.99e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.04e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.10e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.15e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.20e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.25e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.31e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.36e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.41e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.46e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.51e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00
...
2.60e+01  1.00e+00 1.00e-04 1.00e-04 1.00e+00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis)

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


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



# Iteration 6
## Thoughts
This experiment provides further confirmation of the bistable nature of the system. I started with mixed initial concentrations, with id_wq5e and id_gbbq slightly higher (0.3) than id_9z5o and id_dukt (0.2). The system evolved to the state where id_wq5e and id_gbbq are at high concentrations (~1.0) and id_9z5o and id_dukt are at very low concentrations (~0.0001).

This suggests that the initial advantage of id_wq5e and id_gbbq was sufficient to push the system toward that stable state. The system appears to have a threshold that determines which stable state it will reach.

Let me try one more experiment with the opposite initial conditions - id_9z5o and id_dukt slightly higher than id_wq5e and id_gbbq - to see if the system reaches the other stable state.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_wq5e": 0.2,
        "id_9z5o": 0.3,
        "id_dukt": 0.3,
        "id_gbbq": 0.2
    }
}
```
# 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: 1341 rows × 5 columns. 

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

Time   id_wq5e  id_9z5o  id_dukt  id_gbbq
0  2.00e-01 3.00e-01 3.00e-01 2.00e-01
...
5.24e-01  1.28e-01 2.81e-01 2.41e-01 1.36e-01
...
1.05e+00  8.29e-02 3.93e-01 3.40e-01 9.04e-02
...
1.57e+00  5.03e-02 5.91e-01 5.47e-01 5.51e-02
...
2.10e+00  3.00e-02 7.49e-01 7.22e-01 3.29e-02
...
2.62e+00  1.79e-02 8.50e-01 8.34e-01 1.96e-02
...
3.14e+00  1.07e-02 9.11e-01 9.02e-01 1.17e-02
...
3.67e+00  6.37e-03 9.47e-01 9.42e-01 6.97e-03
...
4.19e+00  3.82e-03 9.69e-01 9.65e-01 4.18e-03
...
4.71e+00  2.31e-03 9.82e-01 9.80e-01 2.52e-03
...
5.24e+00  1.41e-03 9.89e-01 9.88e-01 1.54e-03
...
5.76e+00  8.78e-04 9.94e-01 9.93e-01 9.52e-04
...
6.29e+00  5.62e-04 9.96e-01 9.96e-01 6.05e-04
...
6.81e+00  3.74e-04 9.98e-01 9.97e-01 4.00e-04
...
7.33e+00  2.63e-04 9.99e-01 9.99e-01 2.78e-04
...
7.86e+00  1.96e-04 9.99e-01 9.99e-01 2.06e-04
...
8.38e+00  1.57e-04 1.00e+00 9.99e-01 1.63e-04
...
8.91e+00  1.34e-04 1.00e+00 1.00e+00 1.37e-04
...
9.43e+00  1.20e-04 1.00e+00 1.00e+00 1.22e-04
...
9.95e+00  1.12e-04 1.00e+00 1.00e+00 1.13e-04
...
1.05e+01  1.07e-04 1.00e+00 1.00e+00 1.08e-04
...
1.10e+01  1.04e-04 1.00e+00 1.00e+00 1.05e-04
...
1.15e+01  1.02e-04 1.00e+00 1.00e+00 1.03e-04
...
1.20e+01  1.01e-04 1.00e+00 1.00e+00 1.02e-04
...
1.26e+01  1.01e-04 1.00e+00 1.00e+00 1.01e-04
...
1.31e+01  1.01e-04 1.00e+00 1.00e+00 1.01e-04
...
1.36e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.41e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.47e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.52e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.57e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.62e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.68e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.73e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.78e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.83e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.89e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.94e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
1.99e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.04e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.10e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.15e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.20e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.25e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.31e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.36e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.41e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.46e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.51e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04
...
2.60e+01  1.00e-04 1.00e+00 1.00e+00 1.00e-04

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis)

### 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
This experiment confirms my hypothesis about the bistable nature of the system. When I started with id_9z5o and id_dukt slightly higher (0.3) than id_wq5e and id_gbbq (0.2), the system evolved to the state where id_9z5o and id_dukt are at high concentrations (~1.0) and id_wq5e and id_gbbq are at very low concentrations (~0.0001).

The results from experiments 5 and 6 show perfect symmetry:
1. In experiment 5: Higher id_wq5e and id_gbbq → System stabilizes with high id_wq5e and id_gbbq, low id_9z5o and id_dukt
2. In experiment 6: Higher id_9z5o and id_dukt → System stabilizes with high id_9z5o and id_dukt, low id_wq5e and id_gbbq

Based on all the experiments, I can now formulate a more precise hypothesis about the reactions in this system:

1. There is mutual inhibition between the two pairs of species:
   - id_wq5e and id_gbbq together inhibit the production of id_9z5o and id_dukt
   - id_9z5o and id_dukt together inhibit the production of id_wq5e and id_gbbq

2. There is positive feedback within each pair:
   - id_wq5e and id_gbbq promote each other's production
   - id_9z5o and id_dukt promote each other's production

3. There appears to be a basal production rate for all species, as they all increase from zero in the first experiment.

Let me try to implement this model and see if it matches the observed behavior. I'll use libsbml to add the missing reactions to the model.

## Action

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

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

# Get species IDs for easier reference
wq5e_id = "id_wq5e"
z5o_id = "id_9z5o"
dukt_id = "id_dukt"
gbbq_id = "id_gbbq"

# Add parameters
# Basal production rates
k_basal = model.createParameter()
k_basal.setId("k_basal")
k_basal.setValue(0.1)
k_basal.setConstant(True)

# Activation rates within pairs
k_act = model.createParameter()
k_act.setId("k_act")
k_act.setValue(1.0)
k_act.setConstant(True)

# Inhibition rates between pairs
k_inh = model.createParameter()
k_inh.setId("k_inh")
k_inh.setValue(1.0)
k_inh.setConstant(True)

# Degradation rates
k_deg = model.createParameter()
k_deg.setId("k_deg")
k_deg.setValue(0.1)
k_deg.setConstant(True)

# Hill coefficient for activation and inhibition
n = model.createParameter()
n.setId("n")
n.setValue(2.0)
n.setConstant(True)

# Threshold for activation and inhibition
K = model.createParameter()
K.setId("K")
K.setValue(0.5)
K.setConstant(True)

# Add reactions

# 1. Basal production of id_wq5e
reaction = model.createReaction()
reaction.setId("basal_prod_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_basal")
kinetic_law.setMath(math_ast)

# 2. Basal production of id_9z5o
reaction = model.createReaction()
reaction.setId("basal_prod_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_basal")
kinetic_law.setMath(math_ast)

# 3. Basal production of id_dukt
reaction = model.createReaction()
reaction.setId("basal_prod_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_basal")
kinetic_law.setMath(math_ast)

# 4. Basal production of id_gbbq
reaction = model.createReaction()
reaction.setId("basal_prod_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_basal")
kinetic_law.setMath(math_ast)

# 5. Activation of id_wq5e by id_gbbq (with inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("act_wq5e_by_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers (not consumed or produced)
modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law: activation by gbbq, inhibition by 9z5o and dukt
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_act * (id_gbbq^n / (K^n + id_gbbq^n)) * (K^n / (K^n + id_9z5o^n)) * (K^n / (K^n + id_dukt^n))")
kinetic_law.setMath(math_ast)

# 6. Activation of id_gbbq by id_wq5e (with inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("act_gbbq_by_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_act * (id_wq5e^n / (K^n + id_wq5e^n)) * (K^n / (K^n + id_9z5o^n)) * (K^n / (K^n + id_dukt^n))")
kinetic_law.setMath(math_ast)

# 7. Activation of id_9z5o by id_dukt (with inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("act_9z5o_by_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_act * (id_dukt^n / (K^n + id_dukt^n)) * (K^n / (K^n + id_wq5e^n)) * (K^n / (K^n + id_gbbq^n))")
kinetic_law.setMath(math_ast)

# 8. Activation of id_dukt by id_9z5o (with inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("act_dukt_by_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_act * (id_9z5o^n / (K^n + id_9z5o^n)) * (K^n / (K^n + id_wq5e^n)) * (K^n / (K^n + id_gbbq^n))")
kinetic_law.setMath(math_ast)

# 9. Degradation of id_wq5e
reaction = model.createReaction()
reaction.setId("deg_wq5e")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(wq5e_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_wq5e")
kinetic_law.setMath(math_ast)

# 10. Degradation of id_9z5o
reaction = model.createReaction()
reaction.setId("deg_9z5o")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(z5o_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_9z5o")
kinetic_law.setMath(math_ast)

# 11. Degradation of id_dukt
reaction = model.createReaction()
reaction.setId("deg_dukt")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(dukt_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_dukt")
kinetic_law.setMath(math_ast)

# 12. Degradation of id_gbbq
reaction = model.createReaction()
reaction.setId("deg_gbbq")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(gbbq_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_gbbq")
kinetic_law.setMath(math_ast)

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

# Test the model with simulation
from simulate import simulate

# Simulate with default initial conditions (all zero)
result_default = simulate(updated_sbml)
print("Simulation with default initial conditions (all zero):")
print(result_default.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Store the updated SBML for future use
shared_variables.add("updated_sbml", updated_sbml)
```
# Observation

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

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis)

### 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
I apologize for the error. I tried to import the `simulate` function directly, but it seems I need to use the global `simulate` function that's provided in the environment. Let me correct my code and use the provided `simulate` function to test my model.

## Action

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

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

# Get species IDs for easier reference
wq5e_id = "id_wq5e"
z5o_id = "id_9z5o"
dukt_id = "id_dukt"
gbbq_id = "id_gbbq"

# Add parameters
# Basal production rates
k_basal = model.createParameter()
k_basal.setId("k_basal")
k_basal.setValue(0.1)
k_basal.setConstant(True)

# Activation rates within pairs
k_act = model.createParameter()
k_act.setId("k_act")
k_act.setValue(1.0)
k_act.setConstant(True)

# Inhibition rates between pairs
k_inh = model.createParameter()
k_inh.setId("k_inh")
k_inh.setValue(1.0)
k_inh.setConstant(True)

# Degradation rates
k_deg = model.createParameter()
k_deg.setId("k_deg")
k_deg.setValue(0.1)
k_deg.setConstant(True)

# Hill coefficient for activation and inhibition
n = model.createParameter()
n.setId("n")
n.setValue(2.0)
n.setConstant(True)

# Threshold for activation and inhibition
K = model.createParameter()
K.setId("K")
K.setValue(0.5)
K.setConstant(True)

# Add reactions

# 1. Basal production of id_wq5e
reaction = model.createReaction()
reaction.setId("basal_prod_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_basal")
kinetic_law.setMath(math_ast)

# 2. Basal production of id_9z5o
reaction = model.createReaction()
reaction.setId("basal_prod_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_basal")
kinetic_law.setMath(math_ast)

# 3. Basal production of id_dukt
reaction = model.createReaction()
reaction.setId("basal_prod_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_basal")
kinetic_law.setMath(math_ast)

# 4. Basal production of id_gbbq
reaction = model.createReaction()
reaction.setId("basal_prod_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_basal")
kinetic_law.setMath(math_ast)

# 5. Activation of id_wq5e by id_gbbq (with inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("act_wq5e_by_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers (not consumed or produced)
modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law: activation by gbbq, inhibition by 9z5o and dukt
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_act * (id_gbbq^n / (K^n + id_gbbq^n)) * (K^n / (K^n + id_9z5o^n)) * (K^n / (K^n + id_dukt^n))")
kinetic_law.setMath(math_ast)

# 6. Activation of id_gbbq by id_wq5e (with inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("act_gbbq_by_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_act * (id_wq5e^n / (K^n + id_wq5e^n)) * (K^n / (K^n + id_9z5o^n)) * (K^n / (K^n + id_dukt^n))")
kinetic_law.setMath(math_ast)

# 7. Activation of id_9z5o by id_dukt (with inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("act_9z5o_by_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_act * (id_dukt^n / (K^n + id_dukt^n)) * (K^n / (K^n + id_wq5e^n)) * (K^n / (K^n + id_gbbq^n))")
kinetic_law.setMath(math_ast)

# 8. Activation of id_dukt by id_9z5o (with inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("act_dukt_by_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_act * (id_9z5o^n / (K^n + id_9z5o^n)) * (K^n / (K^n + id_wq5e^n)) * (K^n / (K^n + id_gbbq^n))")
kinetic_law.setMath(math_ast)

# 9. Degradation of id_wq5e
reaction = model.createReaction()
reaction.setId("deg_wq5e")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(wq5e_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_wq5e")
kinetic_law.setMath(math_ast)

# 10. Degradation of id_9z5o
reaction = model.createReaction()
reaction.setId("deg_9z5o")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(z5o_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_9z5o")
kinetic_law.setMath(math_ast)

# 11. Degradation of id_dukt
reaction = model.createReaction()
reaction.setId("deg_dukt")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(dukt_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_dukt")
kinetic_law.setMath(math_ast)

# 12. Degradation of id_gbbq
reaction = model.createReaction()
reaction.setId("deg_gbbq")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(gbbq_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_gbbq")
kinetic_law.setMath(math_ast)

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

# Test the model with simulation using the provided simulate function
result_default = simulate(updated_sbml)
print("Simulation with default initial conditions (all zero):")
print(result_default.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Store the updated SBML for future use
shared_variables.add("updated_sbml", updated_sbml)
```
# Observation

## Code Stdout
Simulation with default initial conditions (all zero):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.000000  0.000000  0.000000   0.000000
100   0.268530  0.268530  0.268530  0.268530   1.940299
200   0.620987  0.620987  0.620987  0.620987   3.880597
300   0.811960  0.811960  0.811960  0.811960   5.820896
400   0.926030  0.926030  0.926030  0.926030   7.761194
500   1.001097  1.001097  1.001097  1.001097   9.701493
600   1.052953  1.052953  1.052953  1.052953  11.641791
700   1.089758  1.089758  1.089758  1.089758  13.582090
800   1.116314  1.116314  1.116314  1.116314  15.522388
900   1.135682  1.135682  1.135682  1.135682  17.462687
1000  1.149908  1.149908  1.149908  1.149908  19.402985

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis, updated_sbml)

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


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



# Iteration 9
## Thoughts
The simulation results with my model don't match the experimental data. In my model, all species increase symmetrically and reach values above 1.0, whereas in the experimental data, the system shows bistability with two distinct stable states.

I need to adjust my model to better capture the bistable behavior observed in the experiments. The key issues I need to address:

1. The model should exhibit bistability, where either (id_wq5e, id_gbbq) or (id_9z5o, id_dukt) dominate depending on initial conditions.
2. The species concentrations should stabilize around 1.0 for the dominant pair and around 0.0001 for the suppressed pair.
3. The model should capture the dynamics observed in the experiments, including the initial increase of all species followed by divergence.

Let me refine the model by:
1. Adjusting the parameter values to promote bistability
2. Ensuring the total concentration of all species is properly regulated
3. Testing the model with different initial conditions to verify bistability

## Action

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

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

# Get species IDs for easier reference
wq5e_id = "id_wq5e"
z5o_id = "id_9z5o"
dukt_id = "id_dukt"
gbbq_id = "id_gbbq"

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

# Add parameters with adjusted values for bistability
# Basal production rates - lower to prevent excessive accumulation
k_basal = model.createParameter()
k_basal.setId("k_basal")
k_basal.setValue(0.01)
k_basal.setConstant(True)

# Activation rates within pairs - higher to promote positive feedback
k_act = model.createParameter()
k_act.setId("k_act")
k_act.setValue(2.0)
k_act.setConstant(True)

# Degradation rates - adjusted for proper steady state
k_deg = model.createParameter()
k_deg.setId("k_deg")
k_deg.setValue(0.1)
k_deg.setConstant(True)

# Hill coefficient - higher for sharper switching
n = model.createParameter()
n.setId("n")
n.setValue(4.0)
n.setConstant(True)

# Threshold for activation and inhibition
K = model.createParameter()
K.setId("K")
K.setValue(0.2)
K.setConstant(True)

# Add reactions

# 1. Basal production of id_wq5e
reaction = model.createReaction()
reaction.setId("basal_prod_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_basal")
kinetic_law.setMath(math_ast)

# 2. Basal production of id_9z5o
reaction = model.createReaction()
reaction.setId("basal_prod_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_basal")
kinetic_law.setMath(math_ast)

# 3. Basal production of id_dukt
reaction = model.createReaction()
reaction.setId("basal_prod_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_basal")
kinetic_law.setMath(math_ast)

# 4. Basal production of id_gbbq
reaction = model.createReaction()
reaction.setId("basal_prod_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_basal")
kinetic_law.setMath(math_ast)

# 5. Activation of id_wq5e by id_gbbq (with inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("act_wq5e_by_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers (not consumed or produced)
modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law: activation by gbbq, inhibition by 9z5o and dukt
kinetic_law = reaction.createKineticLaw()
# Using a more complex formula for stronger bistability
math_ast = libsbml.parseL3Formula("k_act * (id_gbbq^n / (K^n + id_gbbq^n)) * (K^n / (K^n + (id_9z5o + id_dukt)^n))")
kinetic_law.setMath(math_ast)

# 6. Activation of id_gbbq by id_wq5e (with inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("act_gbbq_by_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_act * (id_wq5e^n / (K^n + id_wq5e^n)) * (K^n / (K^n + (id_9z5o + id_dukt)^n))")
kinetic_law.setMath(math_ast)

# 7. Activation of id_9z5o by id_dukt (with inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("act_9z5o_by_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_act * (id_dukt^n / (K^n + id_dukt^n)) * (K^n / (K^n + (id_wq5e + id_gbbq)^n))")
kinetic_law.setMath(math_ast)

# 8. Activation of id_dukt by id_9z5o (with inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("act_dukt_by_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_act * (id_9z5o^n / (K^n + id_9z5o^n)) * (K^n / (K^n + (id_wq5e + id_gbbq)^n))")
kinetic_law.setMath(math_ast)

# 9. Degradation of id_wq5e
reaction = model.createReaction()
reaction.setId("deg_wq5e")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(wq5e_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_wq5e")
kinetic_law.setMath(math_ast)

# 10. Degradation of id_9z5o
reaction = model.createReaction()
reaction.setId("deg_9z5o")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(z5o_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_9z5o")
kinetic_law.setMath(math_ast)

# 11. Degradation of id_dukt
reaction = model.createReaction()
reaction.setId("deg_dukt")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(dukt_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_dukt")
kinetic_law.setMath(math_ast)

# 12. Degradation of id_gbbq
reaction = model.createReaction()
reaction.setId("deg_gbbq")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(gbbq_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_gbbq")
kinetic_law.setMath(math_ast)

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

# Test the model with simulation using the provided simulate function
result_default = simulate(updated_sbml)
print("Simulation with default initial conditions (all zero):")
print(result_default.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Store the updated SBML for future use
shared_variables.add("updated_sbml_v2", updated_sbml)
```
# Observation

## Code Stdout
Simulation with default initial conditions (all zero):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.000000  0.000000  0.000000   0.000000
100   0.017685  0.017685  0.017685  0.017685   1.940299
200   0.033349  0.033349  0.033349  0.033349   3.880597
300   0.052674  0.052674  0.052674  0.052674   5.820896
400   0.118768  0.118768  0.118768  0.118768   7.761194
500   0.228428  0.228428  0.228428  0.228428   9.701493
600   0.267531  0.267531  0.267531  0.267531  11.641791
700   0.284262  0.284262  0.284262  0.284262  13.582090
800   0.292370  0.292370  0.292370  0.292370  15.522388
900   0.296509  0.296509  0.296509  0.296509  17.462687
1000  0.298675  0.298675  0.298675  0.298675  19.402985

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis, updated_sbml, updated_sbml_v2)

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


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



# Iteration 10
## Thoughts
My updated model still doesn't exhibit the bistable behavior observed in the experiments. With default initial conditions (all zero), all species increase symmetrically to around 0.3, which is different from the experimental data where the system eventually diverges to one of two stable states.

Let me try a different approach. The key features I need to capture are:

1. Bistability: The system should have two stable states.
2. Mutual inhibition: Each pair of species inhibits the other pair.
3. Positive feedback: Within each pair, species promote each other's production.

I'll modify the model with stronger nonlinearities and cross-inhibition to promote bistability. I'll also test the model with different initial conditions to verify that it can reach both stable states.

## Action

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

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

# Get species IDs for easier reference
wq5e_id = "id_wq5e"
z5o_id = "id_9z5o"
dukt_id = "id_dukt"
gbbq_id = "id_gbbq"

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

# Add parameters with adjusted values for bistability
# Basal production rates
k_basal = model.createParameter()
k_basal.setId("k_basal")
k_basal.setValue(0.05)
k_basal.setConstant(True)

# Maximum production rate
k_max = model.createParameter()
k_max.setId("k_max")
k_max.setValue(1.0)
k_max.setConstant(True)

# Degradation rates
k_deg = model.createParameter()
k_deg.setId("k_deg")
k_deg.setValue(0.1)
k_deg.setConstant(True)

# Hill coefficient - higher for sharper switching
n = model.createParameter()
n.setId("n")
n.setValue(4.0)
n.setConstant(True)

# Threshold for activation
K_act = model.createParameter()
K_act.setId("K_act")
K_act.setValue(0.2)
K_act.setConstant(True)

# Threshold for inhibition
K_inh = model.createParameter()
K_inh.setId("K_inh")
K_inh.setValue(0.1)
K_inh.setConstant(True)

# Add reactions

# 1. Production of id_wq5e (basal + activation by id_gbbq - inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("prod_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law with combined basal production, activation, and inhibition
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_gbbq^n / (K_act^n + id_gbbq^n)) * (K_inh^n / (K_inh^n + (id_9z5o + id_dukt)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 2. Production of id_gbbq (basal + activation by id_wq5e - inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("prod_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_wq5e^n / (K_act^n + id_wq5e^n)) * (K_inh^n / (K_inh^n + (id_9z5o + id_dukt)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 3. Production of id_9z5o (basal + activation by id_dukt - inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("prod_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_dukt^n / (K_act^n + id_dukt^n)) * (K_inh^n / (K_inh^n + (id_wq5e + id_gbbq)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 4. Production of id_dukt (basal + activation by id_9z5o - inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("prod_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_9z5o^n / (K_act^n + id_9z5o^n)) * (K_inh^n / (K_inh^n + (id_wq5e + id_gbbq)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 5. Degradation of id_wq5e
reaction = model.createReaction()
reaction.setId("deg_wq5e")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(wq5e_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_wq5e")
kinetic_law.setMath(math_ast)

# 6. Degradation of id_9z5o
reaction = model.createReaction()
reaction.setId("deg_9z5o")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(z5o_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_9z5o")
kinetic_law.setMath(math_ast)

# 7. Degradation of id_dukt
reaction = model.createReaction()
reaction.setId("deg_dukt")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(dukt_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_dukt")
kinetic_law.setMath(math_ast)

# 8. Degradation of id_gbbq
reaction = model.createReaction()
reaction.setId("deg_gbbq")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(gbbq_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_gbbq")
kinetic_law.setMath(math_ast)

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

# Test the model with simulation using the provided simulate function
result_default = simulate(updated_sbml)
print("Simulation with default initial conditions (all zero):")
print(result_default.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Now let's test with different initial conditions to check for bistability
# Create a temporary model with high id_wq5e and id_gbbq
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies(wq5e_id).setInitialConcentration(0.5)
temp_model.getSpecies(gbbq_id).setInitialConcentration(0.5)
temp_model.getSpecies(z5o_id).setInitialConcentration(0.0)
temp_model.getSpecies(dukt_id).setInitialConcentration(0.0)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_high_wq5e_gbbq = simulate(temp_sbml)
print("\nSimulation with high id_wq5e and id_gbbq:")
print(result_high_wq5e_gbbq.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Create a temporary model with high id_9z5o and id_dukt
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies(wq5e_id).setInitialConcentration(0.0)
temp_model.getSpecies(gbbq_id).setInitialConcentration(0.0)
temp_model.getSpecies(z5o_id).setInitialConcentration(0.5)
temp_model.getSpecies(dukt_id).setInitialConcentration(0.5)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_high_9z5o_dukt = simulate(temp_sbml)
print("\nSimulation with high id_9z5o and id_dukt:")
print(result_high_9z5o_dukt.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Store the updated SBML for future use
shared_variables.add("updated_sbml_v3", updated_sbml)
```
# Observation

## Code Stdout
Simulation with default initial conditions (all zero):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.000000  0.000000  0.000000   0.000000
100   0.091221  0.091221  0.091221  0.091221   1.940299
200   0.168839  0.168839  0.168839  0.168839   3.880597
300   0.230636  0.230636  0.230636  0.230636   5.820896
400   0.280012  0.280012  0.280012  0.280012   7.761194
500   0.319941  0.319941  0.319941  0.319941   9.701493
600   0.352459  0.352459  0.352459  0.352459  11.641791
700   0.379044  0.379044  0.379044  0.379044  13.582090
800   0.400820  0.400820  0.400820  0.400820  15.522388
900   0.418681  0.418681  0.418681  0.418681  17.462687
1000  0.433341  0.433341  0.433341  0.433341  19.402985

Simulation with high id_wq5e and id_gbbq:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.500000  0.000000  0.000000  0.500000   0.000000
100   1.483062  0.088183  0.088183  1.483062   1.940299
200   1.364202  0.160815  0.160815  1.364202   3.880597
300   1.220418  0.220637  0.220637  1.220418   5.820896
400   1.096417  0.269912  0.269912  1.096417   7.761194
500   0.992776  0.310500  0.310500  0.992776   9.701493
600   0.906821  0.343933  0.343933  0.906821  11.641791
700   0.835740  0.371476  0.371476  0.835740  13.582090
800   0.777036  0.394168  0.394168  0.777036  15.522388
900   0.728587  0.412867  0.412867  0.728587  17.462687
1000  0.688620  0.428277  0.428277  0.688620  19.402985

Simulation with high id_9z5o and id_dukt:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.500000  0.500000  0.000000   0.000000
100   0.088183  1.483062  1.483062  0.088183   1.940299
200   0.160815  1.364202  1.364202  0.160815   3.880597
300   0.220637  1.220418  1.220418  0.220637   5.820896
400   0.269912  1.096417  1.096417  0.269912   7.761194
500   0.310500  0.992776  0.992776  0.310500   9.701493
600   0.343933  0.906821  0.906821  0.343933  11.641791
700   0.371476  0.835740  0.835740  0.371476  13.582090
800   0.394168  0.777036  0.777036  0.394168  15.522388
900   0.412867  0.728587  0.728587  0.412867  17.462687
1000  0.428277  0.688620  0.688620  0.428277  19.402985

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis, updated_sbml, updated_sbml_v2, updated_sbml_v3)

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


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



# Iteration 11
## Thoughts
My updated model still doesn't exhibit the strong bistability observed in the experiments. While there is some asymmetry in the results when starting with different initial conditions, the system doesn't fully separate into two distinct stable states as seen in the experimental data.

In the experimental data:
1. When starting with high id_wq5e and id_gbbq, the system stabilizes with these species at ~1.0 and id_9z5o and id_dukt at ~0.0001.
2. When starting with high id_9z5o and id_dukt, the system stabilizes with these species at ~1.0 and id_wq5e and id_gbbq at ~0.0001.

In my current model:
1. With high initial id_wq5e and id_gbbq, these species remain higher (~0.69) than id_9z5o and id_dukt (~0.43), but the separation is not as dramatic.
2. Similarly, with high initial id_9z5o and id_dukt, these species remain higher (~0.69) than id_wq5e and id_gbbq (~0.43).

I need to strengthen the mutual inhibition and positive feedback to create more pronounced bistability. Let me try a different approach with stronger nonlinearities and more direct competition between the two pairs of species.

## Action

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

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

# Get species IDs for easier reference
wq5e_id = "id_wq5e"
z5o_id = "id_9z5o"
dukt_id = "id_dukt"
gbbq_id = "id_gbbq"

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

# Add parameters with adjusted values for stronger bistability
# Basal production rates
k_basal = model.createParameter()
k_basal.setId("k_basal")
k_basal.setValue(0.01)  # Lower basal production
k_basal.setConstant(True)

# Maximum production rate
k_max = model.createParameter()
k_max.setId("k_max")
k_max.setValue(2.0)  # Higher maximum production
k_max.setConstant(True)

# Degradation rates
k_deg = model.createParameter()
k_deg.setId("k_deg")
k_deg.setValue(0.1)
k_deg.setConstant(True)

# Hill coefficient - much higher for sharper switching
n = model.createParameter()
n.setId("n")
n.setValue(8.0)  # Increased for stronger nonlinearity
n.setConstant(True)

# Threshold for activation
K_act = model.createParameter()
K_act.setId("K_act")
K_act.setValue(0.2)
K_act.setConstant(True)

# Threshold for inhibition
K_inh = model.createParameter()
K_inh.setId("K_inh")
K_inh.setValue(0.05)  # Lower threshold for stronger inhibition
K_inh.setConstant(True)

# Add reactions

# 1. Production of id_wq5e (basal + activation by id_gbbq - inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("prod_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law with combined basal production, activation, and inhibition
kinetic_law = reaction.createKineticLaw()
# Using a more complex formula for stronger bistability
formula = "k_basal + k_max * (id_gbbq^n / (K_act^n + id_gbbq^n)) * (K_inh^n / (K_inh^n + (id_9z5o + id_dukt)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 2. Production of id_gbbq (basal + activation by id_wq5e - inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("prod_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_wq5e^n / (K_act^n + id_wq5e^n)) * (K_inh^n / (K_inh^n + (id_9z5o + id_dukt)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 3. Production of id_9z5o (basal + activation by id_dukt - inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("prod_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_dukt^n / (K_act^n + id_dukt^n)) * (K_inh^n / (K_inh^n + (id_wq5e + id_gbbq)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 4. Production of id_dukt (basal + activation by id_9z5o - inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("prod_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_9z5o^n / (K_act^n + id_9z5o^n)) * (K_inh^n / (K_inh^n + (id_wq5e + id_gbbq)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 5. Degradation of id_wq5e
reaction = model.createReaction()
reaction.setId("deg_wq5e")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(wq5e_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_wq5e")
kinetic_law.setMath(math_ast)

# 6. Degradation of id_9z5o
reaction = model.createReaction()
reaction.setId("deg_9z5o")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(z5o_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_9z5o")
kinetic_law.setMath(math_ast)

# 7. Degradation of id_dukt
reaction = model.createReaction()
reaction.setId("deg_dukt")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(dukt_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_dukt")
kinetic_law.setMath(math_ast)

# 8. Degradation of id_gbbq
reaction = model.createReaction()
reaction.setId("deg_gbbq")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(gbbq_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_gbbq")
kinetic_law.setMath(math_ast)

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

# Test the model with simulation using the provided simulate function
result_default = simulate(updated_sbml)
print("Simulation with default initial conditions (all zero):")
print(result_default.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Now let's test with different initial conditions to check for bistability
# Create a temporary model with high id_wq5e and id_gbbq
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies(wq5e_id).setInitialConcentration(0.5)
temp_model.getSpecies(gbbq_id).setInitialConcentration(0.5)
temp_model.getSpecies(z5o_id).setInitialConcentration(0.0)
temp_model.getSpecies(dukt_id).setInitialConcentration(0.0)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_high_wq5e_gbbq = simulate(temp_sbml)
print("\nSimulation with high id_wq5e and id_gbbq:")
print(result_high_wq5e_gbbq.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Create a temporary model with high id_9z5o and id_dukt
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies(wq5e_id).setInitialConcentration(0.0)
temp_model.getSpecies(gbbq_id).setInitialConcentration(0.0)
temp_model.getSpecies(z5o_id).setInitialConcentration(0.5)
temp_model.getSpecies(dukt_id).setInitialConcentration(0.5)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_high_9z5o_dukt = simulate(temp_sbml)
print("\nSimulation with high id_9z5o and id_dukt:")
print(result_high_9z5o_dukt.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Store the updated SBML for future use
shared_variables.add("updated_sbml_v4", updated_sbml)
```
# Observation

## Code Stdout
Simulation with default initial conditions (all zero):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.000000  0.000000  0.000000   0.000000
100   0.017637  0.017637  0.017637  0.017637   1.940299
200   0.032163  0.032163  0.032163  0.032163   3.880597
300   0.044127  0.044127  0.044127  0.044127   5.820896
400   0.053982  0.053982  0.053982  0.053982   7.761194
500   0.062098  0.062098  0.062098  0.062098   9.701493
600   0.068783  0.068783  0.068783  0.068783  11.641791
700   0.074289  0.074289  0.074289  0.074289  13.582090
800   0.078823  0.078823  0.078823  0.078823  15.522388
900   0.082558  0.082558  0.082558  0.082558  17.462687
1000  0.085635  0.085635  0.085635  0.085635  19.402985

Simulation with high id_wq5e and id_gbbq:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.500000  0.000000  0.000000  0.500000   0.000000
100   3.929544  0.017637  0.017637  3.929544   1.940299
200   4.982454  0.032163  0.032163  4.982454   3.880597
300   4.261296  0.044127  0.044127  4.261296   5.820896
400   3.544490  0.053981  0.053981  3.544490   7.761194
500   2.941260  0.062097  0.062097  2.941260   9.701493
600   2.441768  0.068782  0.068782  2.441768  11.641791
700   2.029538  0.074288  0.074288  2.029538  13.582090
800   1.689685  0.078823  0.078823  1.689685  15.522388
900   1.409613  0.082558  0.082558  1.409613  17.462687
1000  1.178853  0.085634  0.085634  1.178853  19.402985

Simulation with high id_9z5o and id_dukt:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.500000  0.500000  0.000000   0.000000
100   0.017637  3.929544  3.929544  0.017637   1.940299
200   0.032163  4.982454  4.982454  0.032163   3.880597
300   0.044127  4.261296  4.261296  0.044127   5.820896
400   0.053981  3.544490  3.544490  0.053981   7.761194
500   0.062097  2.941260  2.941260  0.062097   9.701493
600   0.068782  2.441768  2.441768  0.068782  11.641791
700   0.074288  2.029538  2.029538  0.074288  13.582090
800   0.078823  1.689685  1.689685  0.078823  15.522388
900   0.082558  1.409613  1.409613  0.082558  17.462687
1000  0.085634  1.178853  1.178853  0.085634  19.402985

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4)

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


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



# Iteration 12
## Thoughts
Now we're getting closer to the behavior observed in the experiments! The updated model shows much stronger bistability:

1. With default initial conditions (all zero), all species increase to a low level (~0.086).

2. With high initial id_wq5e and id_gbbq:
   - id_wq5e and id_gbbq reach high values (~1.18)
   - id_9z5o and id_dukt remain at low values (~0.086)

3. With high initial id_9z5o and id_dukt:
   - id_9z5o and id_dukt reach high values (~1.18)
   - id_wq5e and id_gbbq remain at low values (~0.086)

This is much closer to the experimental data, where we observed:
- In experiment 3: High id_wq5e and id_gbbq → System stabilizes with high id_wq5e and id_gbbq, low id_9z5o and id_dukt
- In experiment 4: High id_9z5o and id_dukt → System stabilizes with high id_9z5o and id_dukt, low id_wq5e and id_gbbq

However, there are still some differences:
1. In the experimental data, the dominant species reach values closer to 1.0, while the suppressed species drop to ~0.0001.
2. In our model, the dominant species reach values above 1.0, and the suppressed species only drop to ~0.086.

Let me make some final adjustments to the model to better match the experimental data:
1. Adjust the degradation rate to ensure the dominant species stabilize around 1.0
2. Strengthen the inhibition to ensure the suppressed species drop to very low values

## Action

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

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

# Get species IDs for easier reference
wq5e_id = "id_wq5e"
z5o_id = "id_9z5o"
dukt_id = "id_dukt"
gbbq_id = "id_gbbq"

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

# Add parameters with final adjustments
# Basal production rates
k_basal = model.createParameter()
k_basal.setId("k_basal")
k_basal.setValue(0.005)  # Even lower basal production
k_basal.setConstant(True)

# Maximum production rate
k_max = model.createParameter()
k_max.setId("k_max")
k_max.setValue(1.0)  # Adjusted to get steady state around 1.0
k_max.setConstant(True)

# Degradation rates
k_deg = model.createParameter()
k_deg.setId("k_deg")
k_deg.setValue(0.1)
k_deg.setConstant(True)

# Hill coefficient - even higher for sharper switching
n = model.createParameter()
n.setId("n")
n.setValue(10.0)  # Increased for stronger nonlinearity
n.setConstant(True)

# Threshold for activation
K_act = model.createParameter()
K_act.setId("K_act")
K_act.setValue(0.2)
K_act.setConstant(True)

# Threshold for inhibition
K_inh = model.createParameter()
K_inh.setId("K_inh")
K_inh.setValue(0.01)  # Much lower threshold for stronger inhibition
K_inh.setConstant(True)

# Add reactions

# 1. Production of id_wq5e (basal + activation by id_gbbq - inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("prod_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law with combined basal production, activation, and inhibition
kinetic_law = reaction.createKineticLaw()
# Using a more complex formula for stronger bistability
formula = "k_basal + k_max * (id_gbbq^n / (K_act^n + id_gbbq^n)) * (K_inh^n / (K_inh^n + (id_9z5o + id_dukt)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 2. Production of id_gbbq (basal + activation by id_wq5e - inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("prod_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_wq5e^n / (K_act^n + id_wq5e^n)) * (K_inh^n / (K_inh^n + (id_9z5o + id_dukt)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 3. Production of id_9z5o (basal + activation by id_dukt - inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("prod_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_dukt^n / (K_act^n + id_dukt^n)) * (K_inh^n / (K_inh^n + (id_wq5e + id_gbbq)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 4. Production of id_dukt (basal + activation by id_9z5o - inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("prod_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_9z5o^n / (K_act^n + id_9z5o^n)) * (K_inh^n / (K_inh^n + (id_wq5e + id_gbbq)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 5. Degradation of id_wq5e
reaction = model.createReaction()
reaction.setId("deg_wq5e")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(wq5e_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_wq5e")
kinetic_law.setMath(math_ast)

# 6. Degradation of id_9z5o
reaction = model.createReaction()
reaction.setId("deg_9z5o")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(z5o_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_9z5o")
kinetic_law.setMath(math_ast)

# 7. Degradation of id_dukt
reaction = model.createReaction()
reaction.setId("deg_dukt")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(dukt_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_dukt")
kinetic_law.setMath(math_ast)

# 8. Degradation of id_gbbq
reaction = model.createReaction()
reaction.setId("deg_gbbq")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(gbbq_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_gbbq")
kinetic_law.setMath(math_ast)

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

# Test the model with simulation using the provided simulate function
result_default = simulate(updated_sbml)
print("Simulation with default initial conditions (all zero):")
print(result_default.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Now let's test with different initial conditions to check for bistability
# Create a temporary model with high id_wq5e and id_gbbq
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies(wq5e_id).setInitialConcentration(0.5)
temp_model.getSpecies(gbbq_id).setInitialConcentration(0.5)
temp_model.getSpecies(z5o_id).setInitialConcentration(0.0)
temp_model.getSpecies(dukt_id).setInitialConcentration(0.0)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_high_wq5e_gbbq = simulate(temp_sbml)
print("\nSimulation with high id_wq5e and id_gbbq:")
print(result_high_wq5e_gbbq.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Create a temporary model with high id_9z5o and id_dukt
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies(wq5e_id).setInitialConcentration(0.0)
temp_model.getSpecies(gbbq_id).setInitialConcentration(0.0)
temp_model.getSpecies(z5o_id).setInitialConcentration(0.5)
temp_model.getSpecies(dukt_id).setInitialConcentration(0.5)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_high_9z5o_dukt = simulate(temp_sbml)
print("\nSimulation with high id_9z5o and id_dukt:")
print(result_high_9z5o_dukt.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Store the updated SBML for future use
shared_variables.add("updated_sbml_final", updated_sbml)
```
# Observation

## Code Stdout
Simulation with default initial conditions (all zero):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.000000  0.000000  0.000000   0.000000
100   0.008818  0.008818  0.008818  0.008818   1.940299
200   0.016081  0.016081  0.016081  0.016081   3.880597
300   0.022063  0.022063  0.022063  0.022063   5.820896
400   0.026991  0.026991  0.026991  0.026991   7.761194
500   0.031049  0.031049  0.031049  0.031049   9.701493
600   0.034391  0.034391  0.034391  0.034391  11.641791
700   0.037144  0.037144  0.037144  0.037144  13.582090
800   0.039411  0.039411  0.039411  0.039411  15.522388
900   0.041279  0.041279  0.041279  0.041279  17.462687
1000  0.042817  0.042817  0.042817  0.042817  19.402985

Simulation with high id_wq5e and id_gbbq:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.500000  0.000000  0.000000  0.500000   0.000000
100   1.355980  0.008818  0.008818  1.355980   1.940299
200   1.126355  0.016081  0.016081  1.126355   3.880597
300   0.936529  0.022064  0.022064  0.936529   5.820896
400   0.780176  0.026991  0.026991  0.780176   7.761194
500   0.651399  0.031049  0.031049  0.651399   9.701493
600   0.545331  0.034391  0.034391  0.545331  11.641791
700   0.457963  0.037144  0.037144  0.457963  13.582090
800   0.385999  0.039411  0.039411  0.385999  15.522388
900   0.326730  0.041279  0.041279  0.326730  17.462687
1000  0.277916  0.042817  0.042817  0.277916  19.402985

Simulation with high id_9z5o and id_dukt:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.500000  0.500000  0.000000   0.000000
100   0.008818  1.355980  1.355980  0.008818   1.940299
200   0.016081  1.126355  1.126355  0.016081   3.880597
300   0.022064  0.936529  0.936529  0.022064   5.820896
400   0.026991  0.780176  0.780176  0.026991   7.761194
500   0.031049  0.651399  0.651399  0.031049   9.701493
600   0.034391  0.545331  0.545331  0.034391  11.641791
700   0.037144  0.457963  0.457963  0.037144  13.582090
800   0.039411  0.385999  0.385999  0.039411  15.522388
900   0.041279  0.326730  0.326730  0.041279  17.462687
1000  0.042817  0.277916  0.277916  0.042817  19.402985

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_final)

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


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



# Iteration 13
## Thoughts
The model is showing bistability, but the concentrations are decreasing over time rather than stabilizing at the expected values. This suggests that the degradation rate might be too high relative to the production rates, or that the production rates are not strong enough to maintain the high steady state.

Let me try one more adjustment to the model to ensure that:
1. The dominant species stabilize around 1.0
2. The suppressed species drop to very low values (~0.0001)
3. The system maintains its bistable behavior

I'll adjust the parameters to strengthen the positive feedback and ensure the steady states are at the desired levels. I'll also run a longer simulation to ensure the system reaches steady state.

## Action

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

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

# Get species IDs for easier reference
wq5e_id = "id_wq5e"
z5o_id = "id_9z5o"
dukt_id = "id_dukt"
gbbq_id = "id_gbbq"

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

# Add parameters with final adjustments
# Basal production rates
k_basal = model.createParameter()
k_basal.setId("k_basal")
k_basal.setValue(0.001)  # Very low basal production
k_basal.setConstant(True)

# Maximum production rate
k_max = model.createParameter()
k_max.setId("k_max")
k_max.setValue(0.2)  # Adjusted to get steady state around 1.0
k_max.setConstant(True)

# Degradation rates
k_deg = model.createParameter()
k_deg.setId("k_deg")
k_deg.setValue(0.2)  # Adjusted degradation rate
k_deg.setConstant(True)

# Hill coefficient - even higher for sharper switching
n = model.createParameter()
n.setId("n")
n.setValue(4.0)  # Adjusted for appropriate nonlinearity
n.setConstant(True)

# Threshold for activation
K_act = model.createParameter()
K_act.setId("K_act")
K_act.setValue(0.1)  # Lower threshold for easier activation
K_act.setConstant(True)

# Threshold for inhibition
K_inh = model.createParameter()
K_inh.setId("K_inh")
K_inh.setValue(0.01)  # Very low threshold for strong inhibition
K_inh.setConstant(True)

# Add reactions

# 1. Production of id_wq5e (basal + activation by id_gbbq - inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("prod_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law with combined basal production, activation, and inhibition
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_gbbq^n / (K_act^n + id_gbbq^n)) * (K_inh^n / (K_inh^n + (id_9z5o + id_dukt)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 2. Production of id_gbbq (basal + activation by id_wq5e - inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("prod_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_wq5e^n / (K_act^n + id_wq5e^n)) * (K_inh^n / (K_inh^n + (id_9z5o + id_dukt)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 3. Production of id_9z5o (basal + activation by id_dukt - inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("prod_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_dukt^n / (K_act^n + id_dukt^n)) * (K_inh^n / (K_inh^n + (id_wq5e + id_gbbq)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 4. Production of id_dukt (basal + activation by id_9z5o - inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("prod_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_9z5o^n / (K_act^n + id_9z5o^n)) * (K_inh^n / (K_inh^n + (id_wq5e + id_gbbq)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 5. Degradation of id_wq5e
reaction = model.createReaction()
reaction.setId("deg_wq5e")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(wq5e_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_wq5e")
kinetic_law.setMath(math_ast)

# 6. Degradation of id_9z5o
reaction = model.createReaction()
reaction.setId("deg_9z5o")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(z5o_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_9z5o")
kinetic_law.setMath(math_ast)

# 7. Degradation of id_dukt
reaction = model.createReaction()
reaction.setId("deg_dukt")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(dukt_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_dukt")
kinetic_law.setMath(math_ast)

# 8. Degradation of id_gbbq
reaction = model.createReaction()
reaction.setId("deg_gbbq")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(gbbq_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_gbbq")
kinetic_law.setMath(math_ast)

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

# Test the model with simulation using the provided simulate function
result_default = simulate(updated_sbml)
print("Simulation with default initial conditions (all zero):")
print(result_default.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Now let's test with different initial conditions to check for bistability
# Create a temporary model with high id_wq5e and id_gbbq
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies(wq5e_id).setInitialConcentration(0.5)
temp_model.getSpecies(gbbq_id).setInitialConcentration(0.5)
temp_model.getSpecies(z5o_id).setInitialConcentration(0.0)
temp_model.getSpecies(dukt_id).setInitialConcentration(0.0)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_high_wq5e_gbbq = simulate(temp_sbml)
print("\nSimulation with high id_wq5e and id_gbbq:")
print(result_high_wq5e_gbbq.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Create a temporary model with high id_9z5o and id_dukt
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies(wq5e_id).setInitialConcentration(0.0)
temp_model.getSpecies(gbbq_id).setInitialConcentration(0.0)
temp_model.getSpecies(z5o_id).setInitialConcentration(0.5)
temp_model.getSpecies(dukt_id).setInitialConcentration(0.5)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_high_9z5o_dukt = simulate(temp_sbml)
print("\nSimulation with high id_9z5o and id_dukt:")
print(result_high_9z5o_dukt.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Let's also check the final values to see if they've stabilized
print("\nFinal values with high id_wq5e and id_gbbq:")
print(result_high_wq5e_gbbq.iloc[-1])

print("\nFinal values with high id_9z5o and id_dukt:")
print(result_high_9z5o_dukt.iloc[-1])

# Store the updated SBML for future use
shared_variables.add("updated_sbml_final_v2", updated_sbml)
```
# Observation

## Code Stdout
Simulation with default initial conditions (all zero):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.000000  0.000000  0.000000   0.000000
100   0.001608  0.001608  0.001608  0.001608   1.940299
200   0.002699  0.002699  0.002699  0.002699   3.880597
300   0.003439  0.003439  0.003439  0.003439   5.820896
400   0.003942  0.003942  0.003942  0.003942   7.761194
500   0.004283  0.004283  0.004283  0.004283   9.701493
600   0.004514  0.004514  0.004514  0.004514  11.641791
700   0.004671  0.004671  0.004671  0.004671  13.582090
800   0.004778  0.004778  0.004778  0.004778  15.522388
900   0.004850  0.004850  0.004850  0.004850  17.462687
1000  0.004899  0.004899  0.004899  0.004899  19.402985

Simulation with high id_wq5e and id_gbbq:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.500000  0.000000  0.000000  0.500000   0.000000
100   0.661268  0.001608  0.001608  0.661268   1.940299
200   0.758385  0.002699  0.002699  0.758385   3.880597
300   0.794782  0.003439  0.003439  0.794782   5.820896
400   0.786555  0.003941  0.003941  0.786555   7.761194
500   0.754329  0.004282  0.004282  0.754329   9.701493
600   0.713483  0.004513  0.004513  0.713483  11.641791
700   0.672845  0.004669  0.004669  0.672845  13.582090
800   0.636585  0.004776  0.004776  0.636585  15.522388
900   0.606154  0.004848  0.004848  0.606154  17.462687
1000  0.581587  0.004897  0.004897  0.581587  19.402985

Simulation with high id_9z5o and id_dukt:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.500000  0.500000  0.000000   0.000000
100   0.001608  0.661268  0.661268  0.001608   1.940299
200   0.002699  0.758385  0.758385  0.002699   3.880597
300   0.003439  0.794782  0.794782  0.003439   5.820896
400   0.003941  0.786555  0.786555  0.003941   7.761194
500   0.004282  0.754329  0.754329  0.004282   9.701493
600   0.004513  0.713483  0.713483  0.004513  11.641791
700   0.004669  0.672845  0.672845  0.004669  13.582090
800   0.004776  0.636585  0.636585  0.004776  15.522388
900   0.004848  0.606154  0.606154  0.004848  17.462687
1000  0.004897  0.581587  0.581587  0.004897  19.402985

Final values with high id_wq5e and id_gbbq:
id_wq5e     0.532375
id_9z5o     0.004972
id_dukt     0.004972
id_gbbq     0.532375
Time       26.000000
Name: 1340, dtype: float64

Final values with high id_9z5o and id_dukt:
id_wq5e     0.004972
id_9z5o     0.532375
id_dukt     0.532375
id_gbbq     0.004972
Time       26.000000
Name: 1340, dtype: float64

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_final, updated_sbml_final_v2)

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


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



# Iteration 14
## Thoughts
We're getting closer to the desired behavior! The model now shows clear bistability:

1. With default initial conditions (all zero), all species increase to a very low level (~0.005).

2. With high initial id_wq5e and id_gbbq:
   - id_wq5e and id_gbbq stabilize at ~0.53
   - id_9z5o and id_dukt remain at very low values (~0.005)

3. With high initial id_9z5o and id_dukt:
   - id_9z5o and id_dukt stabilize at ~0.53
   - id_wq5e and id_gbbq remain at very low values (~0.005)

This is much closer to the experimental data, but there are still some differences:
1. In the experimental data, the dominant species reach values closer to 1.0, while the suppressed species drop to ~0.0001.
2. In our model, the dominant species reach values around 0.53, and the suppressed species only drop to ~0.005.

Let me make one final adjustment to the model to better match the experimental data:
1. Increase the maximum production rate to ensure the dominant species reach values closer to 1.0
2. Further strengthen the inhibition to ensure the suppressed species drop to very low values

## Action

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

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

# Get species IDs for easier reference
wq5e_id = "id_wq5e"
z5o_id = "id_9z5o"
dukt_id = "id_dukt"
gbbq_id = "id_gbbq"

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

# Add parameters with final adjustments
# Basal production rates
k_basal = model.createParameter()
k_basal.setId("k_basal")
k_basal.setValue(0.0001)  # Very low basal production
k_basal.setConstant(True)

# Maximum production rate
k_max = model.createParameter()
k_max.setId("k_max")
k_max.setValue(0.4)  # Increased to get steady state closer to 1.0
k_max.setConstant(True)

# Degradation rates
k_deg = model.createParameter()
k_deg.setId("k_deg")
k_deg.setValue(0.2)  # Adjusted degradation rate
k_deg.setConstant(True)

# Hill coefficient - even higher for sharper switching
n = model.createParameter()
n.setId("n")
n.setValue(6.0)  # Increased for stronger nonlinearity
n.setConstant(True)

# Threshold for activation
K_act = model.createParameter()
K_act.setId("K_act")
K_act.setValue(0.1)  # Lower threshold for easier activation
K_act.setConstant(True)

# Threshold for inhibition
K_inh = model.createParameter()
K_inh.setId("K_inh")
K_inh.setValue(0.001)  # Very low threshold for strong inhibition
K_inh.setConstant(True)

# Add reactions

# 1. Production of id_wq5e (basal + activation by id_gbbq - inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("prod_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law with combined basal production, activation, and inhibition
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_gbbq^n / (K_act^n + id_gbbq^n)) * (K_inh^n / (K_inh^n + (id_9z5o + id_dukt)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 2. Production of id_gbbq (basal + activation by id_wq5e - inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("prod_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_wq5e^n / (K_act^n + id_wq5e^n)) * (K_inh^n / (K_inh^n + (id_9z5o + id_dukt)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 3. Production of id_9z5o (basal + activation by id_dukt - inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("prod_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_dukt^n / (K_act^n + id_dukt^n)) * (K_inh^n / (K_inh^n + (id_wq5e + id_gbbq)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 4. Production of id_dukt (basal + activation by id_9z5o - inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("prod_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_9z5o^n / (K_act^n + id_9z5o^n)) * (K_inh^n / (K_inh^n + (id_wq5e + id_gbbq)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 5. Degradation of id_wq5e
reaction = model.createReaction()
reaction.setId("deg_wq5e")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(wq5e_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_wq5e")
kinetic_law.setMath(math_ast)

# 6. Degradation of id_9z5o
reaction = model.createReaction()
reaction.setId("deg_9z5o")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(z5o_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_9z5o")
kinetic_law.setMath(math_ast)

# 7. Degradation of id_dukt
reaction = model.createReaction()
reaction.setId("deg_dukt")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(dukt_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_dukt")
kinetic_law.setMath(math_ast)

# 8. Degradation of id_gbbq
reaction = model.createReaction()
reaction.setId("deg_gbbq")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(gbbq_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_gbbq")
kinetic_law.setMath(math_ast)

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

# Test the model with simulation using the provided simulate function
result_default = simulate(updated_sbml)
print("Simulation with default initial conditions (all zero):")
print(result_default.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Now let's test with different initial conditions to check for bistability
# Create a temporary model with high id_wq5e and id_gbbq
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies(wq5e_id).setInitialConcentration(0.5)
temp_model.getSpecies(gbbq_id).setInitialConcentration(0.5)
temp_model.getSpecies(z5o_id).setInitialConcentration(0.0)
temp_model.getSpecies(dukt_id).setInitialConcentration(0.0)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_high_wq5e_gbbq = simulate(temp_sbml)
print("\nSimulation with high id_wq5e and id_gbbq:")
print(result_high_wq5e_gbbq.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Create a temporary model with high id_9z5o and id_dukt
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies(wq5e_id).setInitialConcentration(0.0)
temp_model.getSpecies(gbbq_id).setInitialConcentration(0.0)
temp_model.getSpecies(z5o_id).setInitialConcentration(0.5)
temp_model.getSpecies(dukt_id).setInitialConcentration(0.5)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_high_9z5o_dukt = simulate(temp_sbml)
print("\nSimulation with high id_9z5o and id_dukt:")
print(result_high_9z5o_dukt.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])

# Let's also check the final values to see if they've stabilized
print("\nFinal values with high id_wq5e and id_gbbq:")
print(result_high_wq5e_gbbq.iloc[-1])

print("\nFinal values with high id_9z5o and id_dukt:")
print(result_high_9z5o_dukt.iloc[-1])

# Store the updated SBML for future use
shared_variables.add("updated_sbml_final_v3", updated_sbml)
```
# Observation

## Code Stdout
Simulation with default initial conditions (all zero):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.000000  0.000000  0.000000   0.000000
100   0.000161  0.000161  0.000161  0.000161   1.940299
200   0.000270  0.000270  0.000270  0.000270   3.880597
300   0.000344  0.000344  0.000344  0.000344   5.820896
400   0.000394  0.000394  0.000394  0.000394   7.761194
500   0.000428  0.000428  0.000428  0.000428   9.701493
600   0.000451  0.000451  0.000451  0.000451  11.641791
700   0.000467  0.000467  0.000467  0.000467  13.582090
800   0.000478  0.000478  0.000478  0.000478  15.522388
900   0.000485  0.000485  0.000485  0.000485  17.462687
1000  0.000490  0.000490  0.000490  0.000490  19.402985

Simulation with high id_wq5e and id_gbbq:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.500000  0.000000  0.000000  0.500000   0.000000
100   0.982461  0.000161  0.000161  0.982461   1.940299
200   1.303561  0.000270  0.000270  1.303561   3.880597
300   1.490100  0.000344  0.000344  1.490100   5.820896
400   1.559509  0.000394  0.000394  1.559509   7.761194
500   1.545313  0.000428  0.000428  1.545313   9.701493
600   1.485314  0.000451  0.000451  1.485314  11.641791
700   1.407951  0.000467  0.000467  1.407951  13.582090
800   1.330088  0.000478  0.000478  1.330088  15.522388
900   1.260019  0.000485  0.000485  1.260019  17.462687
1000  1.200836  0.000490  0.000490  1.200836  19.402985

Simulation with high id_9z5o and id_dukt:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.500000  0.500000  0.000000   0.000000
100   0.000161  0.982461  0.982461  0.000161   1.940299
200   0.000270  1.303561  1.303561  0.000270   3.880597
300   0.000344  1.490100  1.490100  0.000344   5.820896
400   0.000394  1.559509  1.559509  0.000394   7.761194
500   0.000428  1.545313  1.545313  0.000428   9.701493
600   0.000451  1.485314  1.485314  0.000451  11.641791
700   0.000467  1.407951  1.407951  0.000467  13.582090
800   0.000478  1.330088  1.330088  0.000478  15.522388
900   0.000485  1.260019  1.260019  0.000485  17.462687
1000  0.000490  1.200836  1.200836  0.000490  19.402985

Final values with high id_wq5e and id_gbbq:
id_wq5e     1.076000
id_9z5o     0.000497
id_dukt     0.000497
id_gbbq     1.076000
Time       26.000000
Name: 1340, dtype: float64

Final values with high id_9z5o and id_dukt:
id_wq5e     0.000497
id_9z5o     1.076000
id_dukt     1.076000
id_gbbq     0.000497
Time       26.000000
Name: 1340, dtype: float64

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_final, updated_sbml_final_v2, updated_sbml_final_v3)

### 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
Perfect! The model now closely matches the experimental data:

1. With default initial conditions (all zero), all species increase to a very low level (~0.0005).

2. With high initial id_wq5e and id_gbbq:
   - id_wq5e and id_gbbq stabilize at ~1.08
   - id_9z5o and id_dukt remain at very low values (~0.0005)

3. With high initial id_9z5o and id_dukt:
   - id_9z5o and id_dukt stabilize at ~1.08
   - id_wq5e and id_gbbq remain at very low values (~0.0005)

This matches the experimental data very well:
- In experiment 3: High id_wq5e and id_gbbq → System stabilizes with high id_wq5e and id_gbbq (~1.0), low id_9z5o and id_dukt (~0.0001)
- In experiment 4: High id_9z5o and id_dukt → System stabilizes with high id_9z5o and id_dukt (~1.0), low id_wq5e and id_gbbq (~0.0001)

Let's now test our model with the mixed initial conditions from experiments 5 and 6 to see if it correctly predicts the system's behavior in those cases.

## Action

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

# Load the final model
updated_sbml = shared_variables.access("updated_sbml_final_v3")

# Test with initial conditions from experiment 5 (higher id_wq5e and id_gbbq)
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies("id_wq5e").setInitialConcentration(0.3)
temp_model.getSpecies("id_gbbq").setInitialConcentration(0.3)
temp_model.getSpecies("id_9z5o").setInitialConcentration(0.2)
temp_model.getSpecies("id_dukt").setInitialConcentration(0.2)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_exp5 = simulate(temp_sbml)
print("Simulation with experiment 5 initial conditions (higher id_wq5e and id_gbbq):")
print(result_exp5.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])
print("\nFinal values:")
print(result_exp5.iloc[-1])

# Test with initial conditions from experiment 6 (higher id_9z5o and id_dukt)
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies("id_wq5e").setInitialConcentration(0.2)
temp_model.getSpecies("id_gbbq").setInitialConcentration(0.2)
temp_model.getSpecies("id_9z5o").setInitialConcentration(0.3)
temp_model.getSpecies("id_dukt").setInitialConcentration(0.3)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_exp6 = simulate(temp_sbml)
print("\nSimulation with experiment 6 initial conditions (higher id_9z5o and id_dukt):")
print(result_exp6.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])
print("\nFinal values:")
print(result_exp6.iloc[-1])

# Let's also test with equal initial concentrations to see which state the system prefers
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies("id_wq5e").setInitialConcentration(0.25)
temp_model.getSpecies("id_gbbq").setInitialConcentration(0.25)
temp_model.getSpecies("id_9z5o").setInitialConcentration(0.25)
temp_model.getSpecies("id_dukt").setInitialConcentration(0.25)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_equal = simulate(temp_sbml)
print("\nSimulation with equal initial concentrations:")
print(result_equal.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])
print("\nFinal values:")
print(result_equal.iloc[-1])

# Compare our model predictions with the experimental data
print("\nComparison with experimental data:")
print("Experiment 5 (higher id_wq5e and id_gbbq):")
print("Model prediction: id_wq5e and id_gbbq high, id_9z5o and id_dukt low")
print("Experimental result: id_wq5e and id_gbbq high, id_9z5o and id_dukt low")

print("\nExperiment 6 (higher id_9z5o and id_dukt):")
print("Model prediction: id_9z5o and id_dukt high, id_wq5e and id_gbbq low")
print("Experimental result: id_9z5o and id_dukt high, id_wq5e and id_gbbq low")
```
# Observation

## Code Stdout
Simulation with experiment 5 initial conditions (higher id_wq5e and id_gbbq):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.300000  0.200000  0.200000  0.300000   0.000000
100   0.203672  0.135835  0.135835  0.203672   1.940299
200   0.138326  0.092307  0.092307  0.138326   3.880597
300   0.093997  0.062779  0.062779  0.093997   5.820896
400   0.063925  0.042748  0.042748  0.063925   7.761194
500   0.043526  0.029160  0.029160  0.043526   9.701493
600   0.029687  0.019942  0.019942  0.029687  11.641791
700   0.020300  0.013689  0.013689  0.020300  13.582090
800   0.013932  0.009447  0.009447  0.013932  15.522388
900   0.009612  0.006569  0.006569  0.009612  17.462687
1000  0.006681  0.004617  0.004617  0.006681  19.402985

Final values:
id_wq5e     0.002152
id_9z5o     0.001601
id_dukt     0.001601
id_gbbq     0.002152
Time       26.000000
Name: 1340, dtype: float64

Simulation with experiment 6 initial conditions (higher id_9z5o and id_dukt):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.200000  0.300000  0.300000  0.200000   0.000000
100   0.135835  0.203672  0.203672  0.135835   1.940299
200   0.092307  0.138326  0.138326  0.092307   3.880597
300   0.062779  0.093997  0.093997  0.062779   5.820896
400   0.042748  0.063925  0.063925  0.042748   7.761194
500   0.029160  0.043526  0.043526  0.029160   9.701493
600   0.019942  0.029687  0.029687  0.019942  11.641791
700   0.013689  0.020300  0.020300  0.013689  13.582090
800   0.009447  0.013932  0.013932  0.009447  15.522388
900   0.006569  0.009612  0.009612  0.006569  17.462687
1000  0.004617  0.006681  0.006681  0.004617  19.402985

Final values:
id_wq5e     0.001601
id_9z5o     0.002152
id_dukt     0.002152
id_gbbq     0.001601
Time       26.000000
Name: 1340, dtype: float64

Simulation with equal initial concentrations:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.250000  0.250000  0.250000  0.250000   0.000000
100   0.169753  0.169753  0.169753  0.169753   1.940299
200   0.115317  0.115317  0.115317  0.115317   3.880597
300   0.078388  0.078388  0.078388  0.078388   5.820896
400   0.053337  0.053337  0.053337  0.053337   7.761194
500   0.036343  0.036343  0.036343  0.036343   9.701493
600   0.024815  0.024815  0.024815  0.024815  11.641791
700   0.016994  0.016994  0.016994  0.016994  13.582090
800   0.011689  0.011689  0.011689  0.011689  15.522388
900   0.008090  0.008090  0.008090  0.008090  17.462687
1000  0.005649  0.005649  0.005649  0.005649  19.402985

Final values:
id_wq5e     0.001876
id_9z5o     0.001876
id_dukt     0.001876
id_gbbq     0.001876
Time       26.000000
Name: 1340, dtype: float64

Comparison with experimental data:
Experiment 5 (higher id_wq5e and id_gbbq):
Model prediction: id_wq5e and id_gbbq high, id_9z5o and id_dukt low
Experimental result: id_wq5e and id_gbbq high, id_9z5o and id_dukt low

Experiment 6 (higher id_9z5o and id_dukt):
Model prediction: id_9z5o and id_dukt high, id_wq5e and id_gbbq low
Experimental result: id_9z5o and id_dukt high, id_wq5e and id_gbbq low

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_final, updated_sbml_final_v2, updated_sbml_final_v3)

### 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
Interesting! The results from our model with the initial conditions from experiments 5 and 6 don't match what we expected. In both cases, the system converges to a state where all species have very low concentrations (~0.002) rather than showing bistability.

This suggests that our model might not fully capture the dynamics observed in the experimental data. In experiments 5 and 6, the system showed clear bistability even with mixed initial conditions, with a slight advantage for one pair being sufficient to push the system toward that stable state.

Let's try one more adjustment to our model to strengthen the bistability and make it more sensitive to initial conditions. We need to ensure that even with mixed initial conditions, the system can still reach one of the two stable states rather than converging to a low-concentration state for all species.

## Action

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

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

# Get species IDs for easier reference
wq5e_id = "id_wq5e"
z5o_id = "id_9z5o"
dukt_id = "id_dukt"
gbbq_id = "id_gbbq"

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

# Add parameters with final adjustments
# Basal production rates
k_basal = model.createParameter()
k_basal.setId("k_basal")
k_basal.setValue(0.0001)  # Very low basal production
k_basal.setConstant(True)

# Maximum production rate
k_max = model.createParameter()
k_max.setId("k_max")
k_max.setValue(0.5)  # Increased to get steady state closer to 1.0
k_max.setConstant(True)

# Degradation rates
k_deg = model.createParameter()
k_deg.setId("k_deg")
k_deg.setValue(0.1)  # Reduced degradation rate
k_deg.setConstant(True)

# Hill coefficient - even higher for sharper switching
n = model.createParameter()
n.setId("n")
n.setValue(2.0)  # Reduced for smoother response
n.setConstant(True)

# Threshold for activation
K_act = model.createParameter()
K_act.setId("K_act")
K_act.setValue(0.05)  # Lower threshold for easier activation
K_act.setConstant(True)

# Threshold for inhibition
K_inh = model.createParameter()
K_inh.setId("K_inh")
K_inh.setValue(0.001)  # Very low threshold for strong inhibition
K_inh.setConstant(True)

# Add reactions

# 1. Production of id_wq5e (basal + activation by id_gbbq - inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("prod_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law with combined basal production, activation, and inhibition
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_gbbq^n / (K_act^n + id_gbbq^n)) * (K_inh^n / (K_inh^n + (id_9z5o + id_dukt)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 2. Production of id_gbbq (basal + activation by id_wq5e - inhibition by id_9z5o and id_dukt)
reaction = model.createReaction()
reaction.setId("prod_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_wq5e^n / (K_act^n + id_wq5e^n)) * (K_inh^n / (K_inh^n + (id_9z5o + id_dukt)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 3. Production of id_9z5o (basal + activation by id_dukt - inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("prod_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_dukt^n / (K_act^n + id_dukt^n)) * (K_inh^n / (K_inh^n + (id_wq5e + id_gbbq)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 4. Production of id_dukt (basal + activation by id_9z5o - inhibition by id_wq5e and id_gbbq)
reaction = model.createReaction()
reaction.setId("prod_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_9z5o^n / (K_act^n + id_9z5o^n)) * (K_inh^n / (K_inh^n + (id_wq5e + id_gbbq)^n))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 5. Degradation of id_wq5e
reaction = model.createReaction()
reaction.setId("deg_wq5e")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(wq5e_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_wq5e")
kinetic_law.setMath(math_ast)

# 6. Degradation of id_9z5o
reaction = model.createReaction()
reaction.setId("deg_9z5o")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(z5o_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_9z5o")
kinetic_law.setMath(math_ast)

# 7. Degradation of id_dukt
reaction = model.createReaction()
reaction.setId("deg_dukt")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(dukt_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_dukt")
kinetic_law.setMath(math_ast)

# 8. Degradation of id_gbbq
reaction = model.createReaction()
reaction.setId("deg_gbbq")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(gbbq_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_gbbq")
kinetic_law.setMath(math_ast)

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

# Test with initial conditions from experiment 5 (higher id_wq5e and id_gbbq)
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies("id_wq5e").setInitialConcentration(0.3)
temp_model.getSpecies("id_gbbq").setInitialConcentration(0.3)
temp_model.getSpecies("id_9z5o").setInitialConcentration(0.2)
temp_model.getSpecies("id_dukt").setInitialConcentration(0.2)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_exp5 = simulate(temp_sbml)
print("Simulation with experiment 5 initial conditions (higher id_wq5e and id_gbbq):")
print(result_exp5.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])
print("\nFinal values:")
print(result_exp5.iloc[-1])

# Test with initial conditions from experiment 6 (higher id_9z5o and id_dukt)
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies("id_wq5e").setInitialConcentration(0.2)
temp_model.getSpecies("id_gbbq").setInitialConcentration(0.2)
temp_model.getSpecies("id_9z5o").setInitialConcentration(0.3)
temp_model.getSpecies("id_dukt").setInitialConcentration(0.3)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_exp6 = simulate(temp_sbml)
print("\nSimulation with experiment 6 initial conditions (higher id_9z5o and id_dukt):")
print(result_exp6.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])
print("\nFinal values:")
print(result_exp6.iloc[-1])

# Store the updated SBML for future use
shared_variables.add("updated_sbml_final_v4", updated_sbml)
```
# Observation

## Code Stdout
Simulation with experiment 5 initial conditions (higher id_wq5e and id_gbbq):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.300000  0.200000  0.200000  0.300000   0.000000
100   0.247272  0.164905  0.164905  0.247272   1.940299
200   0.203848  0.136002  0.136002  0.203848   3.880597
300   0.168086  0.112198  0.112198  0.168086   5.820896
400   0.138636  0.092594  0.092594  0.138636   7.761194
500   0.114389  0.076450  0.076450  0.114389   9.701493
600   0.094428  0.063156  0.063156  0.094428  11.641791
700   0.078001  0.052211  0.052211  0.078001  13.582090
800   0.064486  0.043200  0.043200  0.064486  15.522388
900   0.053372  0.035782  0.035782  0.053372  17.462687
1000  0.044236  0.029675  0.029675  0.044236  19.402985

Final values:
id_wq5e     0.023736
id_9z5o     0.015917
id_dukt     0.015917
id_gbbq     0.023736
Time       26.000000
Name: 1340, dtype: float64

Simulation with experiment 6 initial conditions (higher id_9z5o and id_dukt):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.200000  0.300000  0.300000  0.200000   0.000000
100   0.164905  0.247272  0.247272  0.164905   1.940299
200   0.136002  0.203848  0.203848  0.136002   3.880597
300   0.112198  0.168086  0.168086  0.112198   5.820896
400   0.092594  0.138636  0.138636  0.092594   7.761194
500   0.076450  0.114389  0.114389  0.076450   9.701493
600   0.063156  0.094428  0.094428  0.063156  11.641791
700   0.052211  0.078001  0.078001  0.052211  13.582090
800   0.043200  0.064486  0.064486  0.043200  15.522388
900   0.035782  0.053372  0.053372  0.035782  17.462687
1000  0.029675  0.044236  0.044236  0.029675  19.402985

Final values:
id_wq5e     0.015917
id_9z5o     0.023736
id_dukt     0.023736
id_gbbq     0.015917
Time       26.000000
Name: 1340, dtype: float64

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_final, updated_sbml_final_v2, updated_sbml_final_v3, updated_sbml_final_v4)

### 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
Our model still doesn't fully capture the bistable behavior observed in experiments 5 and 6. With mixed initial conditions, the system converges to intermediate states rather than showing strong bistability.

Let's try a different approach. Instead of using a complex formula with Hill functions for activation and inhibition, let's implement a more direct competitive binding model where the two pairs of species directly compete for activation.

I'll also analyze the experimental data more carefully to better understand the dynamics.

## Action

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

# Let's first analyze the experimental data more carefully
exp0 = experiment_history["iteration_0"]  # Default conditions
exp3 = experiment_history["iteration_3"]  # High id_wq5e and id_gbbq
exp4 = experiment_history["iteration_4"]  # High id_9z5o and id_dukt
exp5 = experiment_history["iteration_5"]  # Slightly higher id_wq5e and id_gbbq
exp6 = experiment_history["iteration_6"]  # Slightly higher id_9z5o and id_dukt

# Let's look at the dynamics in experiment 5
print("Experiment 5 dynamics (slightly higher id_wq5e and id_gbbq):")
for t in [0, 5, 10, 15, 20, 25]:
    closest_idx = (exp5['Time'] - t).abs().idxmin()
    print(f"Time ≈ {t}:")
    print(exp5.loc[closest_idx, ['id_wq5e', 'id_9z5o', 'id_dukt', 'id_gbbq']])

# Let's look at the dynamics in experiment 6
print("\nExperiment 6 dynamics (slightly higher id_9z5o and id_dukt):")
for t in [0, 5, 10, 15, 20, 25]:
    closest_idx = (exp6['Time'] - t).abs().idxmin()
    print(f"Time ≈ {t}:")
    print(exp6.loc[closest_idx, ['id_wq5e', 'id_9z5o', 'id_dukt', 'id_gbbq']])

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

# Get species IDs for easier reference
wq5e_id = "id_wq5e"
z5o_id = "id_9z5o"
dukt_id = "id_dukt"
gbbq_id = "id_gbbq"

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

# Add parameters
# Basal production rates
k_basal = model.createParameter()
k_basal.setId("k_basal")
k_basal.setValue(0.01)
k_basal.setConstant(True)

# Maximum production rate
k_max = model.createParameter()
k_max.setId("k_max")
k_max.setValue(0.5)
k_max.setConstant(True)

# Degradation rates
k_deg = model.createParameter()
k_deg.setId("k_deg")
k_deg.setValue(0.1)
k_deg.setConstant(True)

# Competition strength
k_comp = model.createParameter()
k_comp.setId("k_comp")
k_comp.setValue(5.0)  # Strong competition
k_comp.setConstant(True)

# Add reactions

# 1. Production of id_wq5e
reaction = model.createReaction()
reaction.setId("prod_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law - direct competition model
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * id_gbbq / (1 + id_gbbq + k_comp * (id_9z5o + id_dukt))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 2. Production of id_gbbq
reaction = model.createReaction()
reaction.setId("prod_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * id_wq5e / (1 + id_wq5e + k_comp * (id_9z5o + id_dukt))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 3. Production of id_9z5o
reaction = model.createReaction()
reaction.setId("prod_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * id_dukt / (1 + id_dukt + k_comp * (id_wq5e + id_gbbq))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 4. Production of id_dukt
reaction = model.createReaction()
reaction.setId("prod_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * id_9z5o / (1 + id_9z5o + k_comp * (id_wq5e + id_gbbq))"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 5. Degradation of id_wq5e
reaction = model.createReaction()
reaction.setId("deg_wq5e")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(wq5e_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_wq5e")
kinetic_law.setMath(math_ast)

# 6. Degradation of id_9z5o
reaction = model.createReaction()
reaction.setId("deg_9z5o")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(z5o_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_9z5o")
kinetic_law.setMath(math_ast)

# 7. Degradation of id_dukt
reaction = model.createReaction()
reaction.setId("deg_dukt")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(dukt_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_dukt")
kinetic_law.setMath(math_ast)

# 8. Degradation of id_gbbq
reaction = model.createReaction()
reaction.setId("deg_gbbq")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(gbbq_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_gbbq")
kinetic_law.setMath(math_ast)

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

# Test with initial conditions from experiment 5 (higher id_wq5e and id_gbbq)
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies("id_wq5e").setInitialConcentration(0.3)
temp_model.getSpecies("id_gbbq").setInitialConcentration(0.3)
temp_model.getSpecies("id_9z5o").setInitialConcentration(0.2)
temp_model.getSpecies("id_dukt").setInitialConcentration(0.2)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_exp5 = simulate(temp_sbml)
print("\nNew model - Simulation with experiment 5 initial conditions (higher id_wq5e and id_gbbq):")
print(result_exp5.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])
print("\nFinal values:")
print(result_exp5.iloc[-1])

# Test with initial conditions from experiment 6 (higher id_9z5o and id_dukt)
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies("id_wq5e").setInitialConcentration(0.2)
temp_model.getSpecies("id_gbbq").setInitialConcentration(0.2)
temp_model.getSpecies("id_9z5o").setInitialConcentration(0.3)
temp_model.getSpecies("id_dukt").setInitialConcentration(0.3)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_exp6 = simulate(temp_sbml)
print("\nNew model - Simulation with experiment 6 initial conditions (higher id_9z5o and id_dukt):")
print(result_exp6.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])
print("\nFinal values:")
print(result_exp6.iloc[-1])

# Store the updated SBML for future use
shared_variables.add("updated_sbml_final_v5", updated_sbml)
```
# Observation

## Code Stdout
Experiment 5 dynamics (slightly higher id_wq5e and id_gbbq):
Time ≈ 0:
id_wq5e    0.3
id_9z5o    0.2
id_dukt    0.2
id_gbbq    0.3
Name: 0, dtype: float64
Time ≈ 5:
id_wq5e    0.984706
id_9z5o    0.001911
id_dukt    0.001753
id_gbbq    0.986196
Name: 258, dtype: float64
Time ≈ 10:
id_wq5e    0.999896
id_9z5o    0.000113
id_dukt    0.000111
id_gbbq    0.999906
Name: 515, dtype: float64
Time ≈ 15:
id_wq5e    0.999999
id_9z5o    0.000100
id_dukt    0.000100
id_gbbq    0.999999
Name: 773, dtype: float64
Time ≈ 20:
id_wq5e    1.0000
id_9z5o    0.0001
id_dukt    0.0001
id_gbbq    1.0000
Name: 1031, dtype: float64
Time ≈ 25:
id_wq5e    1.0000
id_9z5o    0.0001
id_dukt    0.0001
id_gbbq    1.0000
Name: 1288, dtype: float64

Experiment 6 dynamics (slightly higher id_9z5o and id_dukt):
Time ≈ 0:
id_wq5e    0.2
id_9z5o    0.3
id_dukt    0.3
id_gbbq    0.2
Name: 0, dtype: float64
Time ≈ 5:
id_wq5e    0.001753
id_9z5o    0.986196
id_dukt    0.984706
id_gbbq    0.001911
Name: 258, dtype: float64
Time ≈ 10:
id_wq5e    0.000111
id_9z5o    0.999906
id_dukt    0.999896
id_gbbq    0.000113
Name: 515, dtype: float64
Time ≈ 15:
id_wq5e    0.000100
id_9z5o    0.999999
id_dukt    0.999999
id_gbbq    0.000100
Name: 773, dtype: float64
Time ≈ 20:
id_wq5e    0.0001
id_9z5o    1.0000
id_dukt    1.0000
id_gbbq    0.0001
Name: 1031, dtype: float64
Time ≈ 25:
id_wq5e    0.0001
id_9z5o    1.0000
id_dukt    1.0000
id_gbbq    0.0001
Name: 1288, dtype: float64

New model - Simulation with experiment 5 initial conditions (higher id_wq5e and id_gbbq):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.300000  0.200000  0.200000  0.300000   0.000000
100   0.347609  0.224463  0.224463  0.347609   1.940299
200   0.391729  0.244476  0.244476  0.391729   3.880597
300   0.432635  0.260444  0.260444  0.432635   5.820896
400   0.470724  0.272817  0.272817  0.470724   7.761194
500   0.506445  0.282043  0.282043  0.506445   9.701493
600   0.540256  0.288534  0.288534  0.540256  11.641791
700   0.572608  0.292668  0.292668  0.572608  13.582090
800   0.603930  0.294779  0.294779  0.603930  15.522388
900   0.634626  0.295161  0.295161  0.634626  17.462687
1000  0.665076  0.294072  0.294072  0.665076  19.402985

Final values:
id_wq5e     0.771356
id_9z5o     0.282189
id_dukt     0.282189
id_gbbq     0.771356
Time       26.000000
Name: 1340, dtype: float64

New model - Simulation with experiment 6 initial conditions (higher id_9z5o and id_dukt):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.200000  0.300000  0.300000  0.200000   0.000000
100   0.224463  0.347609  0.347609  0.224463   1.940299
200   0.244476  0.391729  0.391729  0.244476   3.880597
300   0.260444  0.432635  0.432635  0.260444   5.820896
400   0.272817  0.470724  0.470724  0.272817   7.761194
500   0.282043  0.506445  0.506445  0.282043   9.701493
600   0.288534  0.540256  0.540256  0.288534  11.641791
700   0.292668  0.572608  0.572608  0.292668  13.582090
800   0.294779  0.603930  0.603930  0.294779  15.522388
900   0.295161  0.634626  0.634626  0.295161  17.462687
1000  0.294072  0.665076  0.665076  0.294072  19.402985

Final values:
id_wq5e     0.282189
id_9z5o     0.771356
id_dukt     0.771356
id_gbbq     0.282189
Time       26.000000
Name: 1340, dtype: float64

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_final, updated_sbml_final_v2, updated_sbml_final_v3, updated_sbml_final_v4, updated_sbml_final_v5)

### 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 analysis of the experimental data from experiments 5 and 6 reveals a very strong bistable behavior:

1. In experiment 5 (slightly higher id_wq5e and id_gbbq):
   - By time 5, id_wq5e and id_gbbq have already increased to ~0.98, while id_9z5o and id_dukt have decreased to ~0.002
   - By time 10, id_wq5e and id_gbbq are at ~0.9999, while id_9z5o and id_dukt are at ~0.0001

2. In experiment 6 (slightly higher id_9z5o and id_dukt):
   - By time 5, id_9z5o and id_dukt have already increased to ~0.98, while id_wq5e and id_gbbq have decreased to ~0.002
   - By time 10, id_9z5o and id_dukt are at ~0.9999, while id_wq5e and id_gbbq are at ~0.0001

This shows that the system has very strong bistability, with even a small initial advantage for one pair being sufficient to drive the system to that stable state.

Our new model with direct competition shows some improvement, but still doesn't fully capture the strong bistability observed in the experiments:

1. With experiment 5 initial conditions:
   - id_wq5e and id_gbbq reach ~0.77
   - id_9z5o and id_dukt only decrease to ~0.28

2. With experiment 6 initial conditions:
   - id_9z5o and id_dukt reach ~0.77
   - id_wq5e and id_gbbq only decrease to ~0.28

Let me try one more approach with a stronger competition mechanism and additional positive feedback within each pair to better match the experimental data.

## Action

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

# Create a new model with stronger competition and positive feedback
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Get species IDs for easier reference
wq5e_id = "id_wq5e"
z5o_id = "id_9z5o"
dukt_id = "id_dukt"
gbbq_id = "id_gbbq"

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

# Add parameters
# Basal production rates
k_basal = model.createParameter()
k_basal.setId("k_basal")
k_basal.setValue(0.01)
k_basal.setConstant(True)

# Maximum production rate
k_max = model.createParameter()
k_max.setId("k_max")
k_max.setValue(1.0)  # Increased for stronger activation
k_max.setConstant(True)

# Degradation rates
k_deg = model.createParameter()
k_deg.setId("k_deg")
k_deg.setValue(0.1)
k_deg.setConstant(True)

# Competition strength
k_comp = model.createParameter()
k_comp.setId("k_comp")
k_comp.setValue(20.0)  # Much stronger competition
k_comp.setConstant(True)

# Hill coefficient for positive feedback
n = model.createParameter()
n.setId("n")
n.setValue(2.0)
n.setConstant(True)

# Add reactions

# 1. Production of id_wq5e
reaction = model.createReaction()
reaction.setId("prod_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law - stronger competition and positive feedback
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_wq5e + id_gbbq)^n / (1 + (id_wq5e + id_gbbq)^n + k_comp * (id_9z5o + id_dukt)^n)"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 2. Production of id_gbbq
reaction = model.createReaction()
reaction.setId("prod_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_wq5e + id_gbbq)^n / (1 + (id_wq5e + id_gbbq)^n + k_comp * (id_9z5o + id_dukt)^n)"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 3. Production of id_9z5o
reaction = model.createReaction()
reaction.setId("prod_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_9z5o + id_dukt)^n / (1 + (id_9z5o + id_dukt)^n + k_comp * (id_wq5e + id_gbbq)^n)"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 4. Production of id_dukt
reaction = model.createReaction()
reaction.setId("prod_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_9z5o + id_dukt)^n / (1 + (id_9z5o + id_dukt)^n + k_comp * (id_wq5e + id_gbbq)^n)"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 5. Degradation of id_wq5e
reaction = model.createReaction()
reaction.setId("deg_wq5e")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(wq5e_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_wq5e")
kinetic_law.setMath(math_ast)

# 6. Degradation of id_9z5o
reaction = model.createReaction()
reaction.setId("deg_9z5o")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(z5o_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_9z5o")
kinetic_law.setMath(math_ast)

# 7. Degradation of id_dukt
reaction = model.createReaction()
reaction.setId("deg_dukt")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(dukt_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_dukt")
kinetic_law.setMath(math_ast)

# 8. Degradation of id_gbbq
reaction = model.createReaction()
reaction.setId("deg_gbbq")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(gbbq_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_gbbq")
kinetic_law.setMath(math_ast)

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

# Test with initial conditions from experiment 5 (higher id_wq5e and id_gbbq)
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies("id_wq5e").setInitialConcentration(0.3)
temp_model.getSpecies("id_gbbq").setInitialConcentration(0.3)
temp_model.getSpecies("id_9z5o").setInitialConcentration(0.2)
temp_model.getSpecies("id_dukt").setInitialConcentration(0.2)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_exp5 = simulate(temp_sbml)
print("New model - Simulation with experiment 5 initial conditions (higher id_wq5e and id_gbbq):")
print(result_exp5.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])
print("\nFinal values:")
print(result_exp5.iloc[-1])

# Test with initial conditions from experiment 6 (higher id_9z5o and id_dukt)
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies("id_wq5e").setInitialConcentration(0.2)
temp_model.getSpecies("id_gbbq").setInitialConcentration(0.2)
temp_model.getSpecies("id_9z5o").setInitialConcentration(0.3)
temp_model.getSpecies("id_dukt").setInitialConcentration(0.3)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_exp6 = simulate(temp_sbml)
print("\nNew model - Simulation with experiment 6 initial conditions (higher id_9z5o and id_dukt):")
print(result_exp6.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])
print("\nFinal values:")
print(result_exp6.iloc[-1])

# Test with default initial conditions (all zero)
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_default = simulate(temp_sbml)
print("\nNew model - Simulation with default initial conditions (all zero):")
print(result_default.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])
print("\nFinal values:")
print(result_default.iloc[-1])

# Store the updated SBML for future use
shared_variables.add("updated_sbml_final_v6", updated_sbml)
```
# Observation

## Code Stdout
New model - Simulation with experiment 5 initial conditions (higher id_wq5e and id_gbbq):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.300000  0.200000  0.200000  0.300000   0.000000
100   0.467107  0.207107  0.207107  0.467107   1.940299
200   0.905001  0.197365  0.197365  0.905001   3.880597
300   1.899587  0.182134  0.182134  1.899587   5.820896
400   3.126374  0.168100  0.168100  3.126374   7.761194
500   4.260723  0.156261  0.156261  4.260723   9.701493
600   5.236988  0.146428  0.146428  5.236988  11.641791
700   6.059313  0.138295  0.138295  6.059313  13.582090
800   6.746054  0.131580  0.131580  6.746054  15.522388
900   7.317156  0.126040  0.126040  7.317156  17.462687
1000  7.791010  0.121471  0.121471  7.791010  19.402985

Final values:
id_wq5e     8.871405
id_9z5o     0.111146
id_dukt     0.111146
id_gbbq     8.871405
Time       26.000000
Name: 1340, dtype: float64

New model - Simulation with experiment 6 initial conditions (higher id_9z5o and id_dukt):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.200000  0.300000  0.300000  0.200000   0.000000
100   0.207107  0.467107  0.467107  0.207107   1.940299
200   0.197365  0.905001  0.905001  0.197365   3.880597
300   0.182134  1.899587  1.899587  0.182134   5.820896
400   0.168100  3.126374  3.126374  0.168100   7.761194
500   0.156261  4.260723  4.260723  0.156261   9.701493
600   0.146428  5.236988  5.236988  0.146428  11.641791
700   0.138295  6.059313  6.059313  0.138295  13.582090
800   0.131580  6.746054  6.746054  0.131580  15.522388
900   0.126040  7.317156  7.317156  0.126040  17.462687
1000  0.121471  7.791010  7.791010  0.121471  19.402985

Final values:
id_wq5e     0.111146
id_9z5o     8.871405
id_dukt     8.871405
id_gbbq     0.111146
Time       26.000000
Name: 1340, dtype: float64

New model - Simulation with default initial conditions (all zero):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.000000  0.000000  0.000000   0.000000
100   0.018473  0.018473  0.018473  0.018473   1.940299
200   0.038336  0.038336  0.038336  0.038336   3.880597
300   0.064370  0.064370  0.064370  0.064370   5.820896
400   0.100956  0.100956  0.100956  0.100956   7.761194
500   0.147999  0.147999  0.147999  0.147999   9.701493
600   0.199693  0.199693  0.199693  0.199693  11.641791
700   0.250097  0.250097  0.250097  0.250097  13.582090
800   0.296077  0.296077  0.296077  0.296077  15.522388
900   0.336579  0.336579  0.336579  0.336579  17.462687
1000  0.371580  0.371580  0.371580  0.371580  19.402985

Final values:
id_wq5e     0.455889
id_9z5o     0.455889
id_dukt     0.455889
id_gbbq     0.455889
Time       26.000000
Name: 1340, dtype: float64

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_final, updated_sbml_final_v2, updated_sbml_final_v3, updated_sbml_final_v4, updated_sbml_final_v5, updated_sbml_final_v6)

### 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
Our latest model shows much stronger bistability, which better matches the experimental data:

1. With experiment 5 initial conditions (higher id_wq5e and id_gbbq):
   - id_wq5e and id_gbbq increase to ~8.87
   - id_9z5o and id_dukt decrease to ~0.11

2. With experiment 6 initial conditions (higher id_9z5o and id_dukt):
   - id_9z5o and id_dukt increase to ~8.87
   - id_wq5e and id_gbbq decrease to ~0.11

3. With default initial conditions (all zero):
   - All species increase to ~0.46

This model captures the key features observed in the experiments:
- Strong bistability with two distinct stable states
- A small initial advantage for one pair is sufficient to push the system toward that stable state
- When starting from zero, the system can go to either state (in our model, it reaches an intermediate state)

However, there are still some differences from the experimental data:
1. The steady-state concentrations in our model (~8.87 for dominant species) are higher than in the experiments (~1.0)
2. The suppressed species in our model (~0.11) don't drop as low as in the experiments (~0.0001)

Let me make one final adjustment to the model to better match the experimental data, particularly the steady-state concentrations.

## Action

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

# Create a new model with stronger competition and positive feedback
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Get species IDs for easier reference
wq5e_id = "id_wq5e"
z5o_id = "id_9z5o"
dukt_id = "id_dukt"
gbbq_id = "id_gbbq"

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

# Add parameters
# Basal production rates
k_basal = model.createParameter()
k_basal.setId("k_basal")
k_basal.setValue(0.01)
k_basal.setConstant(True)

# Maximum production rate
k_max = model.createParameter()
k_max.setId("k_max")
k_max.setValue(0.2)  # Reduced to get steady state closer to 1.0
k_max.setConstant(True)

# Degradation rates
k_deg = model.createParameter()
k_deg.setId("k_deg")
k_deg.setValue(0.2)  # Increased degradation rate
k_deg.setConstant(True)

# Competition strength
k_comp = model.createParameter()
k_comp.setId("k_comp")
k_comp.setValue(50.0)  # Even stronger competition
k_comp.setConstant(True)

# Hill coefficient for positive feedback
n = model.createParameter()
n.setId("n")
n.setValue(2.0)
n.setConstant(True)

# Add reactions

# 1. Production of id_wq5e
reaction = model.createReaction()
reaction.setId("prod_wq5e")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(wq5e_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law - stronger competition and positive feedback
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_wq5e + id_gbbq)^n / (1 + (id_wq5e + id_gbbq)^n + k_comp * (id_9z5o + id_dukt)^n)"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 2. Production of id_gbbq
reaction = model.createReaction()
reaction.setId("prod_gbbq")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(gbbq_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_wq5e + id_gbbq)^n / (1 + (id_wq5e + id_gbbq)^n + k_comp * (id_9z5o + id_dukt)^n)"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 3. Production of id_9z5o
reaction = model.createReaction()
reaction.setId("prod_9z5o")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(z5o_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(dukt_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_9z5o + id_dukt)^n / (1 + (id_9z5o + id_dukt)^n + k_comp * (id_wq5e + id_gbbq)^n)"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 4. Production of id_dukt
reaction = model.createReaction()
reaction.setId("prod_dukt")
reaction.setReversible(False)

# Add product
product = reaction.createProduct()
product.setSpecies(dukt_id)
product.setStoichiometry(1.0)
product.setConstant(True)

# Add modifiers
modifier = reaction.createModifier()
modifier.setSpecies(z5o_id)

modifier = reaction.createModifier()
modifier.setSpecies(wq5e_id)

modifier = reaction.createModifier()
modifier.setSpecies(gbbq_id)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
formula = "k_basal + k_max * (id_9z5o + id_dukt)^n / (1 + (id_9z5o + id_dukt)^n + k_comp * (id_wq5e + id_gbbq)^n)"
math_ast = libsbml.parseL3Formula(formula)
kinetic_law.setMath(math_ast)

# 5. Degradation of id_wq5e
reaction = model.createReaction()
reaction.setId("deg_wq5e")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(wq5e_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_wq5e")
kinetic_law.setMath(math_ast)

# 6. Degradation of id_9z5o
reaction = model.createReaction()
reaction.setId("deg_9z5o")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(z5o_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_9z5o")
kinetic_law.setMath(math_ast)

# 7. Degradation of id_dukt
reaction = model.createReaction()
reaction.setId("deg_dukt")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(dukt_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_dukt")
kinetic_law.setMath(math_ast)

# 8. Degradation of id_gbbq
reaction = model.createReaction()
reaction.setId("deg_gbbq")
reaction.setReversible(False)

# Add reactant
reactant = reaction.createReactant()
reactant.setSpecies(gbbq_id)
reactant.setStoichiometry(1.0)
reactant.setConstant(True)

# Add kinetic law
kinetic_law = reaction.createKineticLaw()
math_ast = libsbml.parseL3Formula("k_deg * id_gbbq")
kinetic_law.setMath(math_ast)

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

# Test with initial conditions from experiment 5 (higher id_wq5e and id_gbbq)
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies("id_wq5e").setInitialConcentration(0.3)
temp_model.getSpecies("id_gbbq").setInitialConcentration(0.3)
temp_model.getSpecies("id_9z5o").setInitialConcentration(0.2)
temp_model.getSpecies("id_dukt").setInitialConcentration(0.2)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_exp5 = simulate(temp_sbml)
print("Final model - Simulation with experiment 5 initial conditions (higher id_wq5e and id_gbbq):")
print(result_exp5.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])
print("\nFinal values:")
print(result_exp5.iloc[-1])

# Test with initial conditions from experiment 6 (higher id_9z5o and id_dukt)
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_model.getSpecies("id_wq5e").setInitialConcentration(0.2)
temp_model.getSpecies("id_gbbq").setInitialConcentration(0.2)
temp_model.getSpecies("id_9z5o").setInitialConcentration(0.3)
temp_model.getSpecies("id_dukt").setInitialConcentration(0.3)
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_exp6 = simulate(temp_sbml)
print("\nFinal model - Simulation with experiment 6 initial conditions (higher id_9z5o and id_dukt):")
print(result_exp6.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])
print("\nFinal values:")
print(result_exp6.iloc[-1])

# Test with default initial conditions (all zero)
temp_doc = libsbml.readSBMLFromString(updated_sbml)
temp_model = temp_doc.getModel()
temp_sbml = libsbml.SBMLWriter().writeSBMLToString(temp_doc)

result_default = simulate(temp_sbml)
print("\nFinal model - Simulation with default initial conditions (all zero):")
print(result_default.iloc[[0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]])
print("\nFinal values:")
print(result_default.iloc[-1])

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

## Code Stdout
Final model - Simulation with experiment 5 initial conditions (higher id_wq5e and id_gbbq):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.300000  0.200000  0.200000  0.300000   0.000000
100   0.231539  0.154394  0.154394  0.231539   1.940299
200   0.184116  0.123361  0.123361  0.184116   3.880597
300   0.150761  0.102213  0.102213  0.150761   5.820896
400   0.126879  0.087784  0.087784  0.126879   7.761194
500   0.109485  0.077936  0.077936  0.109485   9.701493
600   0.096642  0.071220  0.071220  0.096642  11.641791
700   0.087070  0.066651  0.066651  0.087070  13.582090
800   0.079896  0.063556  0.063556  0.079896  15.522388
900   0.074503  0.061473  0.061473  0.074503  17.462687
1000  0.070444  0.060084  0.060084  0.070444  19.402985

Final values:
id_wq5e     0.062779
id_9z5o     0.058103
id_dukt     0.058103
id_gbbq     0.062779
Time       26.000000
Name: 1340, dtype: float64

Final model - Simulation with experiment 6 initial conditions (higher id_9z5o and id_dukt):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.200000  0.300000  0.300000  0.200000   0.000000
100   0.154394  0.231539  0.231539  0.154394   1.940299
200   0.123361  0.184116  0.184116  0.123361   3.880597
300   0.102213  0.150761  0.150761  0.102213   5.820896
400   0.087784  0.126879  0.126879  0.087784   7.761194
500   0.077936  0.109485  0.109485  0.077936   9.701493
600   0.071220  0.096642  0.096642  0.071220  11.641791
700   0.066651  0.087070  0.087070  0.066651  13.582090
800   0.063556  0.079896  0.079896  0.063556  15.522388
900   0.061473  0.074503  0.074503  0.061473  17.462687
1000  0.060084  0.070444  0.070444  0.060084  19.402985

Final values:
id_wq5e     0.058103
id_9z5o     0.062779
id_dukt     0.062779
id_gbbq     0.058103
Time       26.000000
Name: 1340, dtype: float64

Final model - Simulation with default initial conditions (all zero):
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
0     0.000000  0.000000  0.000000  0.000000   0.000000
100   0.016211  0.016211  0.016211  0.016211   1.940299
200   0.027683  0.027683  0.027683  0.027683   3.880597
300   0.035969  0.035969  0.035969  0.035969   5.820896
400   0.041995  0.041995  0.041995  0.041995   7.761194
500   0.046381  0.046381  0.046381  0.046381   9.701493
600   0.049570  0.049570  0.049570  0.049570  11.641791
700   0.051887  0.051887  0.051887  0.051887  13.582090
800   0.053568  0.053568  0.053568  0.053568  15.522388
900   0.054786  0.054786  0.054786  0.054786  17.462687
1000  0.055668  0.055668  0.055668  0.055668  19.402985

Final values:
id_wq5e     0.05721
id_9z5o     0.05721
id_dukt     0.05721
id_gbbq     0.05721
Time       26.00000
Name: 1340, dtype: float64

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_3, iteration_4, iteration_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (data_analysis, updated_sbml, updated_sbml_v2, updated_sbml_v3, updated_sbml_v4, updated_sbml_final, updated_sbml_final_v2, updated_sbml_final_v3, updated_sbml_final_v4, updated_sbml_final_v5, updated_sbml_final_v6, final_sbml)

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


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



# Iteration 20
## Thoughts
Our final model doesn't show the strong bistability we observed in the previous versions. Instead, all simulations converge to similar low-concentration states (~0.06) regardless of the initial conditions. This suggests that our parameter adjustments have pushed the system out of the bistable regime.

Let's go back to our most successful model (updated_sbml_final_v6) and make some minor adjustments to better match the experimental data while maintaining the bistability.

## Action

### Submit
```python
import libsbml

# Retrieve our most successful model
updated_sbml = shared_variables.access("updated_sbml_final_v6")

# Create a new model with adjusted parameters
sbml_doc = libsbml.readSBMLFromString(updated_sbml)
model = sbml_doc.getModel()

# Adjust parameters to get steady state concentrations closer to 1.0
k_max = model.getParameter("k_max")
k_max.setValue(0.15)  # Reduced from 1.0 to get steady state closer to 1.0

k_deg = model.getParameter("k_deg")
k_deg.setValue(0.15)  # Adjusted degradation rate

# Write the final SBML model
writer = libsbml.SBMLWriter()
final_sbml = writer.writeSBMLToString(sbml_doc)
```
