
                # 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_7txc">
    <listOfUnitDefinitions>
      <unitDefinition id="id_7vkb">
        <listOfUnits>
          <unit kind="mole" exponent="1" scale="-9" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_zpw5" spatialDimensions="3" size="1e-13" constant="true"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_y5zp" compartment="id_zpw5" initialConcentration="0.01" hasOnlySubstanceUnits="false" boundaryCondition="false" constant="false"/>
      <species id="id_e6wb" compartment="id_zpw5" initialConcentration="0.01" hasOnlySubstanceUnits="false" boundaryCondition="false" constant="false"/>
      <species id="id_pys4" compartment="id_zpw5" initialConcentration="0.01" hasOnlySubstanceUnits="false" boundaryCondition="false" constant="false"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

                Format your response according to the instructions in the system message.
                
## Thoughts

The provided SBML model contains three species (`id_y5zp`, `id_e6wb`, `id_pys4`) but no reactions. My goal is to discover the missing reactions/mechanisms. Since all species are observable, I should first observe the system's default behavior to get time-series data for all species. This will help me hypothesize about possible interactions or reactions.

## Action

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

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

Total size: 1001 rows × 4 columns. 

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

Time   id_y5zp  id_e6wb  id_pys4
0  1.00e-02 1.00e-02 1.00e-02
...
2.00e-01  1.70e-02 1.06e-03 7.45e-02
...
4.00e-01  4.20e-02 2.67e-03 1.86e-01
...
6.00e-01  9.49e-02 5.46e-03 3.73e-01
...
8.00e-01  1.92e-01 1.03e-02 6.81e-01
...
1.00e+00  3.59e-01 1.86e-02 1.18e+00
...
1.20e+00  6.36e-01 3.37e-02 1.97e+00
...
1.40e+00  1.09e+00 6.36e-02 3.22e+00
...
1.60e+00  1.81e+00 1.34e-01 5.17e+00
...
1.80e+00  2.96e+00 3.83e-01 8.14e+00
...
2.00e+00  4.71e+00 2.20e+00 1.20e+01
...
2.20e+00  6.91e+00 8.43e+00 1.34e+01
...
2.40e+00  8.39e+00 9.47e+00 8.92e+00
...
2.60e+00  8.68e+00 2.44e-01 6.44e+00
...
2.80e+00  8.93e+00 3.40e-01 7.74e+00
...
3.00e+00  9.52e+00 7.69e-01 9.62e+00
...
3.20e+00  1.05e+01 2.46e+00 1.16e+01
...
3.40e+00  1.17e+01 5.37e+00 1.17e+01
...
3.60e+00  1.24e+01 4.53e+00 9.48e+00
...
3.80e+00  1.27e+01 7.18e-01 8.91e+00
...
4.00e+00  1.30e+01 9.80e-01 9.91e+00
...
4.20e+00  1.36e+01 1.87e+00 1.08e+01
...
4.40e+00  1.42e+01 2.88e+00 1.09e+01
...
4.60e+00  1.47e+01 2.59e+00 1.02e+01
...
4.80e+00  1.50e+01 1.43e+00 9.87e+00
...
5.00e+00  1.53e+01 1.27e+00 1.01e+01
...
5.20e+00  1.55e+01 1.45e+00 1.02e+01
...
5.40e+00  1.58e+01 1.51e+00 1.02e+01
...
5.60e+00  1.60e+01 1.40e+00 1.00e+01
...
5.80e+00  1.62e+01 1.24e+00 9.92e+00
...
6.00e+00  1.63e+01 1.11e+00 9.81e+00
...
6.20e+00  1.64e+01 1.01e+00 9.69e+00
...
6.40e+00  1.65e+01 9.24e-01 9.57e+00
...
6.60e+00  1.65e+01 8.43e-01 9.44e+00
...
6.80e+00  1.65e+01 7.68e-01 9.30e+00
...
7.00e+00  1.65e+01 6.99e-01 9.14e+00
...
7.20e+00  1.64e+01 6.34e-01 8.97e+00
...
7.40e+00  1.63e+01 5.73e-01 8.79e+00
...
7.60e+00  1.61e+01 5.16e-01 8.58e+00
...
7.80e+00  1.59e+01 4.62e-01 8.35e+00
...
8.00e+00  1.57e+01 4.11e-01 8.09e+00
...
8.20e+00  1.54e+01 3.61e-01 7.79e+00
...
8.40e+00  1.51e+01 3.14e-01 7.45e+00
...
8.60e+00  1.47e+01 2.67e-01 7.03e+00
...
8.80e+00  1.42e+01 2.22e-01 6.53e+00
...
9.00e+00  1.37e+01 1.76e-01 5.89e+00
...
9.20e+00  1.30e+01 1.32e-01 5.07e+00
...
9.40e+00  1.22e+01 8.80e-02 3.98e+00
...
9.60e+00  1.12e+01 4.64e-02 2.52e+00
...
1.00e+01  8.35e+00 4.78e-05 3.37e-03

## 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

From the observation experiment, all three species (`id_y5zp`, `id_e6wb`, `id_pys4`) start at 0.01. Over time, their concentrations change dramatically, with some species increasing to high values and then decreasing, while others show more complex dynamics. Notably:
- `id_pys4` increases rapidly, peaks, and then decreases to near zero by t=10.
- `id_y5zp` increases, peaks, and then decreases, but not as sharply as `id_pys4`.
- `id_e6wb` increases, peaks, and then drops to near zero.

This suggests a possible cyclic or oscillatory reaction network, or a system with feedback. To further probe the system, I should perturb the initial concentrations of one or more species and observe the effect. This will help distinguish between possible reaction topologies (e.g., linear chain, autocatalysis, feedback inhibition).

A good first perturbation is to set the initial concentration of `id_pys4` to a higher value (e.g., 0.1) while keeping the others at 0.01, to see if it acts as a substrate, product, or regulator.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_pys4": 0.1
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_1
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_1]

Total size: 1001 rows × 4 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_1] for the full data

Time   id_y5zp  id_e6wb  id_pys4
0  1.00e-02 1.00e-02 1.00e-01
...
2.00e-01  4.41e-02 3.34e-03 2.31e-01
...
4.00e-01  1.10e-01 6.64e-03 4.51e-01
...
6.00e-01  2.27e-01 1.23e-02 8.09e-01
...
8.00e-01  4.24e-01 2.23e-02 1.38e+00
...
1.00e+00  7.47e-01 4.08e-02 2.30e+00
...
1.20e+00  1.27e+00 7.88e-02 3.74e+00
...
1.40e+00  2.11e+00 1.77e-01 5.97e+00
...
1.60e+00  3.43e+00 6.12e-01 9.30e+00
...
1.80e+00  5.38e+00 3.78e+00 1.30e+01
...
2.00e+00  7.51e+00 1.00e+01 1.25e+01
...
2.20e+00  8.56e+00 6.98e+00 7.40e+00
...
2.40e+00  8.72e+00 2.39e-01 6.78e+00
...
2.60e+00  9.07e+00 4.19e-01 8.27e+00
...
2.80e+00  9.79e+00 1.09e+00 1.03e+01
...
3.00e+00  1.09e+01 3.40e+00 1.19e+01
...
3.20e+00  1.20e+01 5.75e+00 1.11e+01
...
3.40e+00  1.25e+01 3.15e+00 8.95e+00
...
3.60e+00  1.28e+01 6.78e-01 9.20e+00
...
3.80e+00  1.32e+01 1.20e+00 1.02e+01
...
4.00e+00  1.38e+01 2.23e+00 1.09e+01
...
4.20e+00  1.44e+01 2.98e+00 1.07e+01
...
4.40e+00  1.48e+01 2.21e+00 1.00e+01
...
4.60e+00  1.51e+01 1.28e+00 9.91e+00
...
4.80e+00  1.53e+01 1.32e+00 1.01e+01
...
5.00e+00  1.56e+01 1.49e+00 1.02e+01
...
5.20e+00  1.59e+01 1.49e+00 1.01e+01
...
5.40e+00  1.61e+01 1.34e+00 1.00e+01
...
5.60e+00  1.63e+01 1.19e+00 9.89e+00
...
5.80e+00  1.64e+01 1.08e+00 9.77e+00
...
6.00e+00  1.65e+01 9.84e-01 9.66e+00
...
6.20e+00  1.65e+01 8.98e-01 9.53e+00
...
6.40e+00  1.65e+01 8.19e-01 9.40e+00
...
6.60e+00  1.65e+01 7.46e-01 9.25e+00
...
6.80e+00  1.64e+01 6.78e-01 9.09e+00
...
7.00e+00  1.64e+01 6.14e-01 8.92e+00
...
7.20e+00  1.62e+01 5.55e-01 8.72e+00
...
7.40e+00  1.61e+01 4.99e-01 8.51e+00
...
7.60e+00  1.59e+01 4.46e-01 8.27e+00
...
7.80e+00  1.56e+01 3.95e-01 8.00e+00
...
8.00e+00  1.53e+01 3.47e-01 7.69e+00
...
8.20e+00  1.50e+01 2.99e-01 7.33e+00
...
8.40e+00  1.46e+01 2.53e-01 6.89e+00
...
8.60e+00  1.41e+01 2.08e-01 6.34e+00
...
8.80e+00  1.35e+01 1.62e-01 5.66e+00
...
9.00e+00  1.28e+01 1.18e-01 4.76e+00
...
9.20e+00  1.19e+01 7.48e-02 3.57e+00
...
9.40e+00  1.08e+01 3.43e-02 1.98e+00
...
9.60e+00  9.38e+00 2.19e-03 1.46e-01
...
1.00e+01  6.63e+00 6.03e-05 4.25e-03

## 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, iteration_1)
- `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

Increasing the initial concentration of `id_pys4` to 0.1 (from 0.01) led to a similar qualitative pattern as the default, but with higher peaks and altered timing for all species. This suggests that `id_pys4` is involved early in the reaction network, possibly as a substrate or intermediate. The system shows a rise and fall in all species, with `id_e6wb` and `id_pys4` both peaking and then dropping to near zero, while `id_y5zp` rises and then also falls, but not as sharply.

The fact that all species eventually drop to low values suggests a possible cyclic conversion or a network with feedback and/or autocatalytic steps. To further probe the network, I should try increasing the initial concentration of a different species, such as `id_y5zp`, to see if it acts as a substrate, product, or regulator.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_y5zp": 0.1
    }
}
```
# Observation

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

Total size: 1001 rows × 4 columns. 

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

Time   id_y5zp  id_e6wb  id_pys4
0  1.00e-01 1.00e-02 1.00e-02
...
2.00e-01  8.87e-02 9.89e-04 6.96e-02
...
4.00e-01  9.71e-02 2.41e-03 1.68e-01
...
6.00e-01  1.33e-01 4.84e-03 3.32e-01
...
8.00e-01  2.09e-01 8.98e-03 6.01e-01
...
1.00e+00  3.48e-01 1.61e-02 1.04e+00
...
1.20e+00  5.85e-01 2.89e-02 1.73e+00
...
1.40e+00  9.76e-01 5.35e-02 2.84e+00
...
1.60e+00  1.61e+00 1.08e-01 4.56e+00
...
1.80e+00  2.62e+00 2.73e-01 7.22e+00
...
2.00e+00  4.19e+00 1.30e+00 1.10e+01
...
2.20e+00  6.34e+00 6.57e+00 1.36e+01
...
2.40e+00  8.14e+00 1.05e+01 1.04e+01
...
2.60e+00  8.67e+00 2.35e+00 6.36e+00
...
2.80e+00  8.85e+00 2.92e-01 7.34e+00
...
3.00e+00  9.34e+00 5.92e-01 9.07e+00
...
3.20e+00  1.02e+01 1.80e+00 1.11e+01
...
3.40e+00  1.14e+01 4.70e+00 1.19e+01
...
3.60e+00  1.23e+01 5.35e+00 1.01e+01
...
3.80e+00  1.26e+01 1.28e+00 8.76e+00
...
4.00e+00  1.29e+01 8.35e-01 9.63e+00
...
4.20e+00  1.34e+01 1.58e+00 1.06e+01
...
4.40e+00  1.41e+01 2.67e+00 1.10e+01
...
4.60e+00  1.46e+01 2.84e+00 1.04e+01
...
4.80e+00  1.49e+01 1.67e+00 9.88e+00
...
5.00e+00  1.52e+01 1.24e+00 1.00e+01
...
5.20e+00  1.55e+01 1.40e+00 1.02e+01
...
5.40e+00  1.57e+01 1.51e+00 1.02e+01
...
5.60e+00  1.60e+01 1.43e+00 1.01e+01
...
5.80e+00  1.62e+01 1.27e+00 9.95e+00
...
6.00e+00  1.63e+01 1.14e+00 9.84e+00
...
6.20e+00  1.64e+01 1.04e+00 9.72e+00
...
6.40e+00  1.65e+01 9.46e-01 9.60e+00
...
6.60e+00  1.65e+01 8.63e-01 9.48e+00
...
6.80e+00  1.65e+01 7.87e-01 9.34e+00
...
7.00e+00  1.65e+01 7.16e-01 9.18e+00
...
7.20e+00  1.64e+01 6.50e-01 9.02e+00
...
7.40e+00  1.63e+01 5.88e-01 8.83e+00
...
7.60e+00  1.62e+01 5.30e-01 8.63e+00
...
7.80e+00  1.60e+01 4.75e-01 8.41e+00
...
8.00e+00  1.58e+01 4.23e-01 8.16e+00
...
8.20e+00  1.55e+01 3.74e-01 7.87e+00
...
8.40e+00  1.52e+01 3.26e-01 7.54e+00
...
8.60e+00  1.48e+01 2.79e-01 7.14e+00
...
8.80e+00  1.44e+01 2.33e-01 6.66e+00
...
9.00e+00  1.38e+01 1.88e-01 6.06e+00
...
9.20e+00  1.32e+01 1.43e-01 5.30e+00
...
9.40e+00  1.24e+01 9.88e-02 4.28e+00
...
9.60e+00  1.15e+01 5.65e-02 2.93e+00
...
1.00e+01  8.72e+00 5.81e-05 4.03e-03

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 3
## Thoughts

Increasing the initial concentration of `id_y5zp` to 0.1 (with the others at 0.01) again produces a similar qualitative pattern: all species rise and fall, with the timing and magnitude of peaks shifted. This suggests that the system is robust to initial conditions and that the species are likely part of a cyclic or autocatalytic network, possibly with feedback.

The fact that all three species can rise to high concentrations and then fall to near zero suggests a closed loop or oscillatory system, rather than a simple linear pathway. The similar qualitative response to perturbations in both `id_pys4` and `id_y5zp` suggests that neither is a strict input or output, but rather both are intermediates in a cycle.

To further probe the network, I should perturb the initial concentration of the third species, `id_e6wb`, to see if it produces a similar pattern. This will help confirm if all three species are functionally equivalent in the network (e.g., a cycle like A→B→C→A), or if one has a distinct role.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_e6wb": 0.1
    }
}
```
# Observation

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

Total size: 1001 rows × 4 columns. 

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

Time   id_y5zp  id_e6wb  id_pys4
0  1.00e-02 1.00e-01 1.00e-02
...
2.00e-01  1.70e-02 1.06e-03 7.45e-02
...
4.00e-01  4.19e-02 2.67e-03 1.86e-01
...
6.00e-01  9.49e-02 5.46e-03 3.73e-01
...
8.00e-01  1.92e-01 1.03e-02 6.81e-01
...
1.00e+00  3.59e-01 1.86e-02 1.18e+00
...
1.20e+00  6.36e-01 3.37e-02 1.97e+00
...
1.40e+00  1.09e+00 6.36e-02 3.22e+00
...
1.60e+00  1.81e+00 1.34e-01 5.17e+00
...
1.80e+00  2.96e+00 3.83e-01 8.14e+00
...
2.00e+00  4.71e+00 2.20e+00 1.20e+01
...
2.20e+00  6.90e+00 8.43e+00 1.34e+01
...
2.40e+00  8.39e+00 9.47e+00 8.92e+00
...
2.60e+00  8.68e+00 2.45e-01 6.44e+00
...
2.80e+00  8.93e+00 3.40e-01 7.74e+00
...
3.00e+00  9.52e+00 7.69e-01 9.62e+00
...
3.20e+00  1.05e+01 2.46e+00 1.16e+01
...
3.40e+00  1.17e+01 5.37e+00 1.17e+01
...
3.60e+00  1.24e+01 4.53e+00 9.48e+00
...
3.80e+00  1.27e+01 7.19e-01 8.91e+00
...
4.00e+00  1.30e+01 9.80e-01 9.91e+00
...
4.20e+00  1.36e+01 1.87e+00 1.08e+01
...
4.40e+00  1.42e+01 2.88e+00 1.09e+01
...
4.60e+00  1.47e+01 2.59e+00 1.02e+01
...
4.80e+00  1.50e+01 1.43e+00 9.87e+00
...
5.00e+00  1.53e+01 1.27e+00 1.01e+01
...
5.20e+00  1.55e+01 1.45e+00 1.02e+01
...
5.40e+00  1.58e+01 1.51e+00 1.02e+01
...
5.60e+00  1.60e+01 1.40e+00 1.00e+01
...
5.80e+00  1.62e+01 1.24e+00 9.92e+00
...
6.00e+00  1.63e+01 1.11e+00 9.81e+00
...
6.20e+00  1.64e+01 1.01e+00 9.69e+00
...
6.40e+00  1.65e+01 9.24e-01 9.57e+00
...
6.60e+00  1.65e+01 8.43e-01 9.44e+00
...
6.80e+00  1.65e+01 7.68e-01 9.30e+00
...
7.00e+00  1.65e+01 6.99e-01 9.14e+00
...
7.20e+00  1.64e+01 6.34e-01 8.97e+00
...
7.40e+00  1.63e+01 5.73e-01 8.79e+00
...
7.60e+00  1.61e+01 5.16e-01 8.58e+00
...
7.80e+00  1.59e+01 4.62e-01 8.35e+00
...
8.00e+00  1.57e+01 4.11e-01 8.09e+00
...
8.20e+00  1.54e+01 3.61e-01 7.79e+00
...
8.40e+00  1.51e+01 3.14e-01 7.45e+00
...
8.60e+00  1.47e+01 2.67e-01 7.03e+00
...
8.80e+00  1.42e+01 2.22e-01 6.53e+00
...
9.00e+00  1.37e+01 1.76e-01 5.89e+00
...
9.20e+00  1.30e+01 1.32e-01 5.07e+00
...
9.40e+00  1.22e+01 8.80e-02 3.98e+00
...
9.60e+00  1.12e+01 4.64e-02 2.52e+00
...
1.00e+01  8.35e+00 4.78e-05 3.37e-03

## 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_1, iteration_2, iteration_3)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 4
## Thoughts

Perturbing the initial concentration of `id_e6wb` to 0.1 (with the others at 0.01) produces a time course nearly identical to the default and other perturbations, except for the timing and magnitude of the peaks. This strongly suggests that all three species are functionally equivalent in the network, likely forming a cycle (e.g., A→B→C→A).

The system's behavior is reminiscent of a cyclic reaction network, possibly with autocatalytic or feedback steps. The rise and fall of all species, with each able to drive the system when started at a higher concentration, supports the hypothesis of a closed loop.

To further test the cyclic hypothesis, I should try setting two species to high initial concentrations and the third to a low value. If the system is a simple cycle, the low-concentration species should rise as the others fall, and the overall pattern should be preserved.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_y5zp": 0.1,
        "id_e6wb": 0.1,
        "id_pys4": 0.01
    }
}
```
# Observation

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

Total size: 1001 rows × 4 columns. 

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

Time   id_y5zp  id_e6wb  id_pys4
0  1.00e-01 1.00e-01 1.00e-02
...
2.00e-01  8.87e-02 9.89e-04 6.96e-02
...
4.00e-01  9.71e-02 2.41e-03 1.68e-01
...
6.00e-01  1.33e-01 4.84e-03 3.32e-01
...
8.00e-01  2.09e-01 8.98e-03 6.01e-01
...
1.00e+00  3.48e-01 1.61e-02 1.04e+00
...
1.20e+00  5.85e-01 2.89e-02 1.73e+00
...
1.40e+00  9.76e-01 5.35e-02 2.84e+00
...
1.60e+00  1.61e+00 1.08e-01 4.56e+00
...
1.80e+00  2.62e+00 2.73e-01 7.22e+00
...
2.00e+00  4.19e+00 1.30e+00 1.10e+01
...
2.20e+00  6.34e+00 6.56e+00 1.36e+01
...
2.40e+00  8.14e+00 1.05e+01 1.04e+01
...
2.60e+00  8.67e+00 2.35e+00 6.36e+00
...
2.80e+00  8.85e+00 2.92e-01 7.34e+00
...
3.00e+00  9.34e+00 5.92e-01 9.07e+00
...
3.20e+00  1.02e+01 1.80e+00 1.11e+01
...
3.40e+00  1.14e+01 4.70e+00 1.19e+01
...
3.60e+00  1.23e+01 5.35e+00 1.01e+01
...
3.80e+00  1.26e+01 1.28e+00 8.76e+00
...
4.00e+00  1.29e+01 8.35e-01 9.63e+00
...
4.20e+00  1.34e+01 1.58e+00 1.06e+01
...
4.40e+00  1.41e+01 2.67e+00 1.10e+01
...
4.60e+00  1.46e+01 2.84e+00 1.04e+01
...
4.80e+00  1.49e+01 1.67e+00 9.88e+00
...
5.00e+00  1.52e+01 1.24e+00 1.00e+01
...
5.20e+00  1.55e+01 1.40e+00 1.02e+01
...
5.40e+00  1.57e+01 1.51e+00 1.02e+01
...
5.60e+00  1.60e+01 1.43e+00 1.01e+01
...
5.80e+00  1.62e+01 1.27e+00 9.95e+00
...
6.00e+00  1.63e+01 1.14e+00 9.84e+00
...
6.20e+00  1.64e+01 1.04e+00 9.72e+00
...
6.40e+00  1.65e+01 9.46e-01 9.60e+00
...
6.60e+00  1.65e+01 8.63e-01 9.48e+00
...
6.80e+00  1.65e+01 7.87e-01 9.34e+00
...
7.00e+00  1.65e+01 7.16e-01 9.18e+00
...
7.20e+00  1.64e+01 6.50e-01 9.02e+00
...
7.40e+00  1.63e+01 5.88e-01 8.83e+00
...
7.60e+00  1.62e+01 5.30e-01 8.63e+00
...
7.80e+00  1.60e+01 4.75e-01 8.41e+00
...
8.00e+00  1.58e+01 4.23e-01 8.16e+00
...
8.20e+00  1.55e+01 3.74e-01 7.87e+00
...
8.40e+00  1.52e+01 3.26e-01 7.54e+00
...
8.60e+00  1.48e+01 2.79e-01 7.14e+00
...
8.80e+00  1.44e+01 2.33e-01 6.66e+00
...
9.00e+00  1.38e+01 1.88e-01 6.06e+00
...
9.20e+00  1.32e+01 1.43e-01 5.30e+00
...
9.40e+00  1.24e+01 9.88e-02 4.28e+00
...
9.60e+00  1.15e+01 5.65e-02 2.93e+00
...
1.00e+01  8.72e+00 5.81e-05 4.03e-03

## 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_1, iteration_2, iteration_3, iteration_4)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 5
## Thoughts

Setting both `id_y5zp` and `id_e6wb` to high initial concentrations (0.1) and `id_pys4` to a low value (0.01) produces a time course nearly identical to the previous experiments, with the same qualitative pattern: all species rise and fall, with the timing and magnitude of peaks shifted. This further supports the hypothesis that the three species are part of a symmetric cyclic network, likely with reactions such as A→B→C→A.

Given the symmetry and the observed dynamics, a plausible minimal model is a cycle:
- `id_y5zp` → `id_e6wb`
- `id_e6wb` → `id_pys4`
- `id_pys4` → `id_y5zp`

The next step is to analyze the time series quantitatively to estimate the kinetic parameters and confirm if simple first-order reactions can explain the data, or if more complex kinetics (e.g., autocatalysis, nonlinear feedback) are needed.

## Action

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

# Load the default experiment data
df = experiment_history['iteration_0']

# Plot the time courses for all three species
plt.figure(figsize=(10,6))
plt.plot(df['Time'], df['id_y5zp'], label='id_y5zp')
plt.plot(df['Time'], df['id_e6wb'], label='id_e6wb')
plt.plot(df['Time'], df['id_pys4'], label='id_pys4')
plt.xlabel('Time')
plt.ylabel('Concentration')
plt.legend()
plt.title('Time courses for all species (default initial conditions)')
plt.show()

# Calculate the sum of all species over time to check for conservation
df['total'] = df['id_y5zp'] + df['id_e6wb'] + df['id_pys4']
plt.figure(figsize=(8,4))
plt.plot(df['Time'], df['total'])
plt.xlabel('Time')
plt.ylabel('Total concentration')
plt.title('Total concentration over time')
plt.show()

# Print the first and last few rows to check for mass conservation
print(df[['Time', 'id_y5zp', 'id_e6wb', 'id_pys4', 'total']].head())
print(df[['Time', 'id_y5zp', 'id_e6wb', 'id_pys4', 'total']].tail())
```
# 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: 15/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_3, iteration_4)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 6
## Thoughts

I attempted to use matplotlib for plotting, but it's not allowed. Instead, I'll focus on numerical analysis using numpy and pandas. I want to check if the total concentration of all species is conserved over time, which would support a simple cyclic interconversion model. If the total is not conserved, it may indicate production or degradation steps.

I'll also examine the time series to see if the transitions between species are consistent with first-order kinetics, which would further support the simple cycle hypothesis.

## Action

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

# Load the default experiment data
df = experiment_history['iteration_0']

# Calculate the sum of all species over time to check for conservation
df['total'] = df['id_y5zp'] + df['id_e6wb'] + df['id_pys4']

# Print the first and last few rows to check for mass conservation
print("First 5 rows:")
print(df[['Time', 'id_y5zp', 'id_e6wb', 'id_pys4', 'total']].head())

print("\nLast 5 rows:")
print(df[['Time', 'id_y5zp', 'id_e6wb', 'id_pys4', 'total']].tail())

# Check the min and max of the total concentration
print("\nTotal concentration min:", df['total'].min())
print("Total concentration max:", df['total'].max())
```
# Observation

## Code Stdout
First 5 rows:
   Time   id_y5zp   id_e6wb   id_pys4     total
0  0.00  0.010000  0.010000  0.010000  0.030000
1  0.01  0.010028  0.000174  0.012436  0.022638
2  0.02  0.010086  0.000209  0.014943  0.025238
3  0.03  0.010175  0.000245  0.017521  0.027942
4  0.04  0.010296  0.000283  0.020173  0.030752

Last 5 rows:
       Time   id_y5zp   id_e6wb   id_pys4     total
996    9.96  8.641808  0.000052  0.003660  8.645521
997    9.97  8.568255  0.000050  0.003479  8.571784
998    9.98  8.495185  0.000048  0.003397  8.498631
999    9.99  8.422599  0.000048  0.003368  8.426015
1000  10.00  8.350494  0.000048  0.003367  8.353908

Total concentration min: 0.022638149025383143
Total concentration max: 30.09696368584452

## 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_1, iteration_2, iteration_3, iteration_4)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 7
## Thoughts

The total concentration of all species is not conserved. It starts at 0.03 and increases dramatically, reaching over 8 by the end, with a maximum of over 30. This rules out a simple closed cycle of interconversion. Instead, there must be a source of mass (e.g., autocatalysis, external input, or a reaction that produces these species from something not modeled as a species).

The rapid increase in total concentration, followed by a decrease, suggests autocatalytic or self-amplifying reactions, possibly with a delayed negative feedback or depletion mechanism. The system is not just a cycle, but likely includes nonlinear production and/or degradation.

To further probe the mechanism, I should test what happens if all initial concentrations are set to zero. If the system still produces these species, there must be an external source/input. If not, it suggests autocatalysis or a requirement for a seed concentration.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_y5zp": 0.0,
        "id_e6wb": 0.0,
        "id_pys4": 0.0
    }
}
```
# Observation

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

Total size: 1001 rows × 4 columns. 

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

Time   id_y5zp  id_e6wb  id_pys4
0         0        0        0
...
2.00e-01  6.01e-03 8.13e-04 5.73e-02
...
4.00e-01  2.81e-02 2.26e-03 1.58e-01
...
6.00e-01  7.56e-02 4.77e-03 3.27e-01
...
8.00e-01  1.63e-01 9.09e-03 6.08e-01
...
1.00e+00  3.15e-01 1.66e-02 1.06e+00
...
1.20e+00  5.67e-01 3.00e-02 1.79e+00
...
1.40e+00  9.78e-01 5.59e-02 2.93e+00
...
1.60e+00  1.64e+00 1.14e-01 4.73e+00
...
1.80e+00  2.69e+00 2.99e-01 7.47e+00
...
2.00e+00  4.32e+00 1.52e+00 1.13e+01
...
2.20e+00  6.49e+00 7.14e+00 1.36e+01
...
2.40e+00  8.22e+00 1.03e+01 9.99e+00
...
2.60e+00  8.66e+00 1.47e+00 6.32e+00
...
2.80e+00  8.85e+00 3.04e-01 7.44e+00
...
3.00e+00  9.37e+00 6.34e-01 9.22e+00
...
3.20e+00  1.03e+01 1.97e+00 1.13e+01
...
3.40e+00  1.15e+01 4.92e+00 1.19e+01
...
3.60e+00  1.23e+01 5.17e+00 9.91e+00
...
3.80e+00  1.26e+01 1.05e+00 8.78e+00
...
4.00e+00  1.30e+01 8.71e-01 9.71e+00
...
4.20e+00  1.35e+01 1.66e+00 1.07e+01
...
4.40e+00  1.41e+01 2.74e+00 1.10e+01
...
4.60e+00  1.46e+01 2.78e+00 1.03e+01
...
4.80e+00  1.49e+01 1.60e+00 9.87e+00
...
5.00e+00  1.52e+01 1.25e+00 1.00e+01
...
5.20e+00  1.55e+01 1.42e+00 1.02e+01
...
5.40e+00  1.58e+01 1.51e+00 1.02e+01
...
5.60e+00  1.60e+01 1.43e+00 1.01e+01
...
5.80e+00  1.62e+01 1.26e+00 9.95e+00
...
6.00e+00  1.63e+01 1.13e+00 9.83e+00
...
6.20e+00  1.64e+01 1.03e+00 9.72e+00
...
6.40e+00  1.65e+01 9.40e-01 9.60e+00
...
6.60e+00  1.65e+01 8.58e-01 9.47e+00
...
6.80e+00  1.65e+01 7.82e-01 9.33e+00
...
7.00e+00  1.65e+01 7.12e-01 9.17e+00
...
7.20e+00  1.64e+01 6.46e-01 9.01e+00
...
7.40e+00  1.63e+01 5.84e-01 8.82e+00
...
7.60e+00  1.61e+01 5.27e-01 8.62e+00
...
7.80e+00  1.60e+01 4.72e-01 8.40e+00
...
8.00e+00  1.57e+01 4.20e-01 8.14e+00
...
8.20e+00  1.55e+01 3.71e-01 7.85e+00
...
8.40e+00  1.52e+01 3.23e-01 7.52e+00
...
8.60e+00  1.48e+01 2.76e-01 7.12e+00
...
8.80e+00  1.43e+01 2.30e-01 6.63e+00
...
9.00e+00  1.38e+01 1.85e-01 6.03e+00
...
9.20e+00  1.32e+01 1.40e-01 5.25e+00
...
9.40e+00  1.24e+01 9.63e-02 4.22e+00
...
9.60e+00  1.14e+01 5.42e-02 2.84e+00
...
1.00e+01  8.63e+00 5.19e-05 3.63e-03

## 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_1, iteration_2, iteration_3, iteration_4, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 8
## Thoughts

Setting all initial concentrations to zero does not prevent the system from producing all three species, which rise and fall in a similar pattern as before. This indicates there is an external source or input reaction for at least one of the species, likely a zero-order or constant influx. The system is not purely autocatalytic or dependent on initial "seed" concentrations.

Given the rapid increase in total concentration, there is likely a strong production term, possibly for one species, which then feeds into the cyclic interconversion. The subsequent decrease in total concentration suggests there is also a degradation or outflow reaction.

To further clarify, I should check if the system is symmetric with respect to which species is produced. I will set only one species (e.g., `id_y5zp`) to a nonzero initial value and the others to zero, to see if the system can still generate all three species and if the pattern is similar.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_y5zp": 0.01,
        "id_e6wb": 0.0,
        "id_pys4": 0.0
    }
}
```
# Observation

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

Total size: 1001 rows × 4 columns. 

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

Time   id_y5zp  id_e6wb  id_pys4
0  1.00e-02        0        0
...
2.00e-01  1.40e-02 8.07e-04 5.70e-02
...
4.00e-01  3.43e-02 2.24e-03 1.56e-01
...
6.00e-01  7.99e-02 4.71e-03 3.23e-01
...
8.00e-01  1.65e-01 8.97e-03 6.00e-01
...
1.00e+00  3.14e-01 1.63e-02 1.05e+00
...
1.20e+00  5.62e-01 2.95e-02 1.76e+00
...
1.40e+00  9.67e-01 5.50e-02 2.89e+00
...
1.60e+00  1.62e+00 1.12e-01 4.66e+00
...
1.80e+00  2.66e+00 2.89e-01 7.38e+00
...
2.00e+00  4.27e+00 1.44e+00 1.12e+01
...
2.20e+00  6.43e+00 6.94e+00 1.36e+01
...
2.40e+00  8.19e+00 1.04e+01 1.02e+01
...
2.60e+00  8.66e+00 1.78e+00 6.32e+00
...
2.80e+00  8.85e+00 2.99e-01 7.40e+00
...
3.00e+00  9.36e+00 6.18e-01 9.16e+00
...
3.20e+00  1.03e+01 1.90e+00 1.12e+01
...
3.40e+00  1.14e+01 4.84e+00 1.19e+01
...
3.60e+00  1.23e+01 5.24e+00 9.98e+00
...
3.80e+00  1.26e+01 1.13e+00 8.77e+00
...
4.00e+00  1.30e+01 8.57e-01 9.68e+00
...
4.20e+00  1.35e+01 1.63e+00 1.06e+01
...
4.40e+00  1.41e+01 2.72e+00 1.10e+01
...
4.60e+00  1.46e+01 2.81e+00 1.04e+01
...
4.80e+00  1.49e+01 1.63e+00 9.88e+00
...
5.00e+00  1.52e+01 1.24e+00 1.00e+01
...
5.20e+00  1.55e+01 1.41e+00 1.02e+01
...
5.40e+00  1.58e+01 1.51e+00 1.02e+01
...
5.60e+00  1.60e+01 1.43e+00 1.01e+01
...
5.80e+00  1.62e+01 1.27e+00 9.95e+00
...
6.00e+00  1.63e+01 1.14e+00 9.83e+00
...
6.20e+00  1.64e+01 1.03e+00 9.72e+00
...
6.40e+00  1.65e+01 9.43e-01 9.60e+00
...
6.60e+00  1.65e+01 8.60e-01 9.47e+00
...
6.80e+00  1.65e+01 7.84e-01 9.33e+00
...
7.00e+00  1.65e+01 7.13e-01 9.18e+00
...
7.20e+00  1.64e+01 6.48e-01 9.01e+00
...
7.40e+00  1.63e+01 5.86e-01 8.83e+00
...
7.60e+00  1.62e+01 5.28e-01 8.63e+00
...
7.80e+00  1.60e+01 4.74e-01 8.40e+00
...
8.00e+00  1.57e+01 4.22e-01 8.15e+00
...
8.20e+00  1.55e+01 3.72e-01 7.86e+00
...
8.40e+00  1.52e+01 3.24e-01 7.53e+00
...
8.60e+00  1.48e+01 2.78e-01 7.13e+00
...
8.80e+00  1.44e+01 2.32e-01 6.65e+00
...
9.00e+00  1.38e+01 1.86e-01 6.04e+00
...
9.20e+00  1.32e+01 1.41e-01 5.27e+00
...
9.40e+00  1.24e+01 9.75e-02 4.25e+00
...
9.60e+00  1.14e+01 5.53e-02 2.88e+00
...
1.00e+01  8.67e+00 5.42e-05 3.78e-03

## 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_1, iteration_2, iteration_3, iteration_4, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 9
## Thoughts

Setting only `id_y5zp` to a nonzero initial value (0.01) and the others to zero still results in the production and subsequent rise and fall of all three species, with a pattern very similar to previous experiments. This further supports the presence of an external source/input reaction for at least one species, and that the system is not strictly autocatalytic.

Given the symmetry in the system's response to different initial conditions, it is likely that the external input is not limited to just one species, or that the network is highly interconnected. The rapid increase and subsequent decrease in total concentration suggest a strong production (possibly constant or zero-order) and a delayed degradation or outflow.

To further clarify the mechanism, I will analyze the early time points to see which species appears first when all are set to zero. This may help identify which species is directly produced by the external input.

## Action

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

# Look at the first 20 time points for the all-zero initial condition experiment
df_zero = experiment_history['iteration_7']
print(df_zero[['Time', 'id_y5zp', 'id_e6wb', 'id_pys4']].head(20))
```
# Observation

## Code Stdout
    Time   id_y5zp   id_e6wb   id_pys4
0   0.00  0.000000  0.000000  0.000000
1   0.01  0.000013  0.000027  0.002151
2   0.02  0.000053  0.000059  0.004365
3   0.03  0.000120  0.000091  0.006645
4   0.04  0.000216  0.000124  0.008991
5   0.05  0.000339  0.000159  0.011407
6   0.06  0.000491  0.000194  0.013893
7   0.07  0.000673  0.000230  0.016452
8   0.08  0.000884  0.000268  0.019086
9   0.09  0.001127  0.000306  0.021797
10  0.10  0.001400  0.000346  0.024587
11  0.11  0.001706  0.000387  0.027458
12  0.12  0.002044  0.000429  0.030412
13  0.13  0.002415  0.000472  0.033453
14  0.14  0.002820  0.000516  0.036581
15  0.15  0.003260  0.000562  0.039800
16  0.16  0.003735  0.000610  0.043111
17  0.17  0.004246  0.000658  0.046518
18  0.18  0.004795  0.000708  0.050022
19  0.19  0.005381  0.000760  0.053627

## 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_1, iteration_2, iteration_3, iteration_4, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 10
## Thoughts

From the early time points with all species starting at zero, `id_pys4` increases much more rapidly than the other two species. At t=0.01, `id_pys4` is already at 0.002, while `id_y5zp` and `id_e6wb` are still at ~1e-5 to 2e-5. This suggests that the external input is primarily producing `id_pys4`, which then feeds into the rest of the network.

The pattern is consistent with:
- An external source/input reaction producing `id_pys4` (possibly zero-order or constant rate).
- `id_pys4` being converted to `id_y5zp`, which is then converted to `id_e6wb`, and possibly back to `id_pys4`, forming a cycle.
- There is also likely a degradation or outflow reaction for one or more species, given the eventual decrease in total concentration.

The next step is to check if the conversion between species is direct and if the system can be explained by a simple linear chain with an input and an output. I will now analyze the time derivatives to estimate the rates and see if first-order kinetics are plausible.

## Action

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

# Use the all-zero initial condition experiment
df = experiment_history['iteration_7']

# Estimate the time derivatives (finite differences)
dt = df['Time'].diff().values[1:]
d_pys4 = df['id_pys4'].diff().values[1:] / dt
d_y5zp = df['id_y5zp'].diff().values[1:] / dt
d_e6wb = df['id_e6wb'].diff().values[1:] / dt

# Print the first 10 time points of derivatives and concentrations
print("Time, d[id_pys4]/dt, id_pys4, d[id_y5zp]/dt, id_y5zp, d[id_e6wb]/dt, id_e6wb")
for i in range(10):
    print(f"{df['Time'].iloc[i+1]:.2f}, {d_pys4[i]:.4f}, {df['id_pys4'].iloc[i+1]:.4f}, "
          f"{d_y5zp[i]:.4f}, {df['id_y5zp'].iloc[i+1]:.4f}, "
          f"{d_e6wb[i]:.4f}, {df['id_e6wb'].iloc[i+1]:.4f}")
```
# Observation

## Code Stdout
Time, d[id_pys4]/dt, id_pys4, d[id_y5zp]/dt, id_y5zp, d[id_e6wb]/dt, id_e6wb
0.01, 0.2151, 0.0022, 0.0013, 0.0000, 0.0027, 0.0000
0.02, 0.2214, 0.0044, 0.0040, 0.0001, 0.0031, 0.0001
0.03, 0.2279, 0.0066, 0.0067, 0.0001, 0.0032, 0.0001
0.04, 0.2346, 0.0090, 0.0095, 0.0002, 0.0033, 0.0001
0.05, 0.2415, 0.0114, 0.0123, 0.0003, 0.0034, 0.0002
0.06, 0.2486, 0.0139, 0.0152, 0.0005, 0.0035, 0.0002
0.07, 0.2559, 0.0165, 0.0182, 0.0007, 0.0036, 0.0002
0.08, 0.2634, 0.0191, 0.0212, 0.0009, 0.0037, 0.0003
0.09, 0.2711, 0.0218, 0.0242, 0.0011, 0.0039, 0.0003
0.10, 0.2790, 0.0246, 0.0274, 0.0014, 0.0040, 0.0003

## 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_1, iteration_2, iteration_3, iteration_4, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 11
## Thoughts

The time derivative of `id_pys4` is much larger than those of `id_y5zp` and `id_e6wb` at early times, and increases steadily. This supports the hypothesis that `id_pys4` is being produced by an external input at a high rate, while `id_y5zp` and `id_e6wb` are produced more slowly, likely via conversion from `id_pys4` and each other.

This suggests a model with:
- An input reaction: ∅ → `id_pys4` (zero-order or constant rate)
- Conversion: `id_pys4` → `id_y5zp`
- Conversion: `id_y5zp` → `id_e6wb`
- Conversion: `id_e6wb` → `id_pys4`
- Possibly, a degradation or outflow for one or more species

Given the symmetry and the observed rise and fall, a cyclic conversion with an input and a degradation for at least one species is plausible.

I will now attempt to build a minimal SBML model with:
1. Zero-order input to `id_pys4`
2. First-order conversions: `id_pys4` → `id_y5zp` → `id_e6wb` → `id_pys4`
3. First-order degradation for all three species

I will use placeholder rate constants and simulate the model to compare with the observed data.

## Action

### Code
```python
import libsbml

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

# Remove any existing reactions (should be none, but for safety)
while model.getNumReactions() > 0:
    model.removeReaction(0)

# Add zero-order input: ∅ → id_pys4
reaction_in = model.createReaction()
reaction_in.setId("input_pys4")
reaction_in.setReversible(False)
reaction_in.setFast(False)

product = reaction_in.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)

# Add kinetic law for input (zero-order, rate = k_in)
kl_in = reaction_in.createKineticLaw()
param_in = kl_in.createParameter()
param_in.setId("k_in")
param_in.setValue(0.3)  # placeholder
kl_in.setFormula("k_in")

# id_pys4 → id_y5zp
reaction1 = model.createReaction()
reaction1.setId("pys4_to_y5zp")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant = reaction1.createReactant()
reactant.setSpecies("id_pys4")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)

product = reaction1.createProduct()
product.setSpecies("id_y5zp")
product.setStoichiometry(1.0)
product.setConstant(True)

kl1 = reaction1.createKineticLaw()
param1 = kl1.createParameter()
param1.setId("k1")
param1.setValue(0.2)  # placeholder
kl1.setFormula("k1 * id_pys4")

# id_y5zp → id_e6wb
reaction2 = model.createReaction()
reaction2.setId("y5zp_to_e6wb")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant = reaction2.createReactant()
reactant.setSpecies("id_y5zp")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)

product = reaction2.createProduct()
product.setSpecies("id_e6wb")
product.setStoichiometry(1.0)
product.setConstant(True)

kl2 = reaction2.createKineticLaw()
param2 = kl2.createParameter()
param2.setId("k2")
param2.setValue(0.15)  # placeholder
kl2.setFormula("k2 * id_y5zp")

# id_e6wb → id_pys4
reaction3 = model.createReaction()
reaction3.setId("e6wb_to_pys4")
reaction3.setReversible(False)
reaction3.setFast(False)

reactant = reaction3.createReactant()
reactant.setSpecies("id_e6wb")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)

product = reaction3.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)

kl3 = reaction3.createKineticLaw()
param3 = kl3.createParameter()
param3.setId("k3")
param3.setValue(0.1)  # placeholder
kl3.setFormula("k3 * id_e6wb")

# Add first-order degradation for all species
for sid in ["id_pys4", "id_y5zp", "id_e6wb"]:
    rxn = model.createReaction()
    rxn.setId(f"degrade_{sid}")
    rxn.setReversible(False)
    rxn.setFast(False)
    reactant = rxn.createReactant()
    reactant.setSpecies(sid)
    reactant.setStoichiometry(1.0)
    reactant.setConstant(False)
    kl = rxn.createKineticLaw()
    param = kl.createParameter()
    param.setId(f"kdeg_{sid}")
    param.setValue(0.05)  # placeholder
    kl.setFormula(f"kdeg_{sid} * {sid}")

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

# Simulate and print the first few rows
sim_result = simulate(test_sbml)
print(sim_result.head(10))
shared_variables.add("test_sbml", test_sbml)
```
# Observation

## Code Stdout
   id_y5zp  id_e6wb  id_pys4  Time
0     0.01     0.01     0.01  0.00
1     2.00     2.00     2.00  0.01
2     2.00     2.00     2.00  0.02
3     2.00     2.00     2.00  0.03
4     2.00     2.00     2.00  0.04
5     2.00     2.00     2.00  0.05
6     2.00     2.00     2.00  0.06
7     2.00     2.00     2.00  0.07
8     2.00     2.00     2.00  0.08
9     2.00     2.00     2.00  0.09

## 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_1, iteration_2, iteration_3, iteration_4, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml)

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


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



# Iteration 12
## Thoughts

The simulation of the constructed model shows that all three species (`id_y5zp`, `id_e6wb`, `id_pys4`) immediately jump to a high value (2.00) at t=0.01 and then remain constant, which is not consistent with the experimental data. In the real system, the species start low, rise, peak, and then fall, with different timing and magnitudes. This suggests that the current model is missing key features or that the parameter values are not appropriate.

Possible issues:
- The input reaction may be too strong or not properly formulated.
- The cyclic conversions and/or degradation rates may not be correct.
- There may be nonlinearities or additional feedbacks not captured by simple first-order kinetics.

To diagnose, I should check the effect of the input reaction and try reducing its rate constant, as well as check if the model is producing the expected time-dependent behavior (rise and fall, not immediate steady state).

## Action

### Code
```python
import libsbml

# Retrieve the last tested SBML
sbml_doc = libsbml.readSBMLFromString(shared_variables.access("test_sbml"))
model = sbml_doc.getModel()

# Reduce the input rate and degradation rates to see if this produces more gradual dynamics
# Update input rate
input_rxn = model.getReaction("input_pys4")
input_kl = input_rxn.getKineticLaw()
input_kl.getParameter("k_in").setValue(0.01)  # much lower input

# Update degradation rates
for sid in ["id_pys4", "id_y5zp", "id_e6wb"]:
    rxn = model.getReaction(f"degrade_{sid}")
    kl = rxn.getKineticLaw()
    kl.getParameter(f"kdeg_{sid}").setValue(0.01)  # lower degradation

# Write the updated SBML
writer = libsbml.SBMLWriter()
test_sbml2 = writer.writeSBMLToString(sbml_doc)

# Simulate and print the first 20 rows
sim_result2 = simulate(test_sbml2)
print(sim_result2.head(20))
shared_variables.add("test_sbml2", test_sbml2)
```
# Observation

## Code Stdout
     id_y5zp   id_e6wb   id_pys4  Time
0   0.010000  0.010000  0.010000  0.00
1   0.316092  0.431034  0.252874  0.01
2   0.316092  0.431034  0.252874  0.02
3   0.316092  0.431034  0.252874  0.03
4   0.316092  0.431034  0.252874  0.04
5   0.316092  0.431034  0.252874  0.05
6   0.316092  0.431034  0.252874  0.06
7   0.316092  0.431034  0.252874  0.07
8   0.316092  0.431034  0.252874  0.08
9   0.316092  0.431034  0.252874  0.09
10  0.316092  0.431034  0.252874  0.10
11  0.316092  0.431034  0.252874  0.11
12  0.316092  0.431034  0.252874  0.12
13  0.316092  0.431034  0.252874  0.13
14  0.316092  0.431034  0.252874  0.14
15  0.316092  0.431034  0.252874  0.15
16  0.316092  0.431034  0.252874  0.16
17  0.316092  0.431034  0.252874  0.17
18  0.316092  0.431034  0.252874  0.18
19  0.316092  0.431034  0.252874  0.19

## 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_1, iteration_2, iteration_3, iteration_4, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2)

### 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

Even after reducing the input and degradation rates, the model still quickly jumps to a steady state within the first time step and remains there, which is not consistent with the experimental data. The real system shows a slow rise, a peak, and then a fall for all species, with different timing and magnitudes.

This suggests that the current model structure (input + simple cycle + degradation) is missing a key feature. The rapid establishment of steady state implies that the model is too "well-mixed" and lacks the necessary delays or nonlinearities to produce the observed dynamics.

Possible missing features:
- Autocatalytic production (e.g., a species catalyzes its own production or the production of another)
- Nonlinear feedback (e.g., inhibition or activation)
- Delayed or saturating kinetics (e.g., Michaelis-Menten or Hill kinetics)

Given that `id_pys4` rises first and most rapidly, perhaps its production is autocatalytic or involves a positive feedback loop. I will try adding an autocatalytic reaction for `id_pys4` (e.g., `id_pys4` catalyzes its own production) and see if this produces the observed rise and fall.

## Action

### Code
```python
import libsbml

# Start from the previous model
sbml_doc = libsbml.readSBMLFromString(shared_variables.access("test_sbml2"))
model = sbml_doc.getModel()

# Add autocatalytic production: id_pys4 + id_pys4 -> 2 id_pys4 (or id_pys4 -> 2 id_pys4)
# We'll use a simple autocatalytic term: id_pys4 -> 2 id_pys4
reaction_auto = model.createReaction()
reaction_auto.setId("auto_pys4")
reaction_auto.setReversible(False)
reaction_auto.setFast(False)

reactant = reaction_auto.createReactant()
reactant.setSpecies("id_pys4")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)

product = reaction_auto.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(2.0)
product.setConstant(True)

kl_auto = reaction_auto.createKineticLaw()
param_auto = kl_auto.createParameter()
param_auto.setId("k_auto")
param_auto.setValue(0.01)  # placeholder
kl_auto.setFormula("k_auto * id_pys4")

# Write the updated SBML
writer = libsbml.SBMLWriter()
test_sbml3 = writer.writeSBMLToString(sbml_doc)

# Simulate and print the first 20 rows
sim_result3 = simulate(test_sbml3)
print(sim_result3.head(20))
shared_variables.add("test_sbml3", test_sbml3)
```
# Observation

## Code Stdout
     id_y5zp   id_e6wb   id_pys4  Time
0   0.010000  0.010000  0.010000  0.00
1   0.423077  0.576923  0.338462  0.01
2   0.423077  0.576923  0.338462  0.02
3   0.423077  0.576923  0.338462  0.03
4   0.423077  0.576923  0.338462  0.04
5   0.423077  0.576923  0.338462  0.05
6   0.423077  0.576923  0.338462  0.06
7   0.423077  0.576923  0.338462  0.07
8   0.423077  0.576923  0.338462  0.08
9   0.423077  0.576923  0.338462  0.09
10  0.423077  0.576923  0.338462  0.10
11  0.423077  0.576923  0.338462  0.11
12  0.423077  0.576923  0.338462  0.12
13  0.423077  0.576923  0.338462  0.13
14  0.423077  0.576923  0.338462  0.14
15  0.423077  0.576923  0.338462  0.15
16  0.423077  0.576923  0.338462  0.16
17  0.423077  0.576923  0.338462  0.17
18  0.423077  0.576923  0.338462  0.18
19  0.423077  0.576923  0.338462  0.19

## 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_1, iteration_2, iteration_3, iteration_4, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, test_sbml3)

### 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

Adding an autocatalytic reaction for `id_pys4` did not resolve the issue: the model still rapidly jumps to a new steady state within the first time step and remains there. This is inconsistent with the experimental data, which shows a gradual rise, peak, and fall for all species.

This suggests that the model is still missing a key feature. The rapid establishment of steady state implies that the system is not limited by the rates of conversion or input, but rather that the model structure is too simple or the kinetics are not capturing the necessary delays.

Given the observed data, where the total concentration rises and then falls, and all species show a peak, a plausible mechanism is:
- A zero-order input to `id_pys4`
- A cyclic conversion: `id_pys4` → `id_y5zp` → `id_e6wb` → (possibly back to) `id_pys4`
- A first-order degradation for at least one species, possibly only for `id_e6wb` (the last in the cycle), which would allow for the rise and fall in total concentration

Alternatively, the input may be saturable (e.g., Michaelis-Menten), or the degradation may be nonlinear.

I will now try a model with:
- Zero-order input to `id_pys4`
- Cyclic conversion: `id_pys4` → `id_y5zp` → `id_e6wb` → `id_pys4`
- First-order degradation only for `id_e6wb`

## Action

### Code
```python
import libsbml

# Start from the original SBML to avoid accumulating reactions
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Add zero-order input: ∅ → id_pys4
reaction_in = model.createReaction()
reaction_in.setId("input_pys4")
reaction_in.setReversible(False)
reaction_in.setFast(False)
product = reaction_in.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)
kl_in = reaction_in.createKineticLaw()
param_in = kl_in.createParameter()
param_in.setId("k_in")
param_in.setValue(0.01)  # low input
kl_in.setFormula("k_in")

# id_pys4 → id_y5zp
reaction1 = model.createReaction()
reaction1.setId("pys4_to_y5zp")
reaction1.setReversible(False)
reaction1.setFast(False)
reactant = reaction1.createReactant()
reactant.setSpecies("id_pys4")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction1.createProduct()
product.setSpecies("id_y5zp")
product.setStoichiometry(1.0)
product.setConstant(True)
kl1 = reaction1.createKineticLaw()
param1 = kl1.createParameter()
param1.setId("k1")
param1.setValue(0.1)
kl1.setFormula("k1 * id_pys4")

# id_y5zp → id_e6wb
reaction2 = model.createReaction()
reaction2.setId("y5zp_to_e6wb")
reaction2.setReversible(False)
reaction2.setFast(False)
reactant = reaction2.createReactant()
reactant.setSpecies("id_y5zp")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction2.createProduct()
product.setSpecies("id_e6wb")
product.setStoichiometry(1.0)
product.setConstant(True)
kl2 = reaction2.createKineticLaw()
param2 = kl2.createParameter()
param2.setId("k2")
param2.setValue(0.1)
kl2.setFormula("k2 * id_y5zp")

# id_e6wb → id_pys4
reaction3 = model.createReaction()
reaction3.setId("e6wb_to_pys4")
reaction3.setReversible(False)
reaction3.setFast(False)
reactant = reaction3.createReactant()
reactant.setSpecies("id_e6wb")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction3.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)
kl3 = reaction3.createKineticLaw()
param3 = kl3.createParameter()
param3.setId("k3")
param3.setValue(0.1)
kl3.setFormula("k3 * id_e6wb")

# Add first-order degradation only for id_e6wb
rxn = model.createReaction()
rxn.setId("degrade_e6wb")
rxn.setReversible(False)
rxn.setFast(False)
reactant = rxn.createReactant()
reactant.setSpecies("id_e6wb")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
kl = rxn.createKineticLaw()
param = kl.createParameter()
param.setId("kdeg_e6wb")
param.setValue(0.05)
kl.setFormula("kdeg_e6wb * id_e6wb")

# Write the updated SBML
writer = libsbml.SBMLWriter()
test_sbml4 = writer.writeSBMLToString(sbml_doc)

# Simulate and print the first 20 rows
sim_result4 = simulate(test_sbml4)
print(sim_result4.head(20))
shared_variables.add("test_sbml4", test_sbml4)
```
# Observation

## Code Stdout
    id_y5zp  id_e6wb  id_pys4  Time
0      0.01     0.01     0.01  0.00
1      0.30     0.20     0.30  0.01
2      0.30     0.20     0.30  0.02
3      0.30     0.20     0.30  0.03
4      0.30     0.20     0.30  0.04
5      0.30     0.20     0.30  0.05
6      0.30     0.20     0.30  0.06
7      0.30     0.20     0.30  0.07
8      0.30     0.20     0.30  0.08
9      0.30     0.20     0.30  0.09
10     0.30     0.20     0.30  0.10
11     0.30     0.20     0.30  0.11
12     0.30     0.20     0.30  0.12
13     0.30     0.20     0.30  0.13
14     0.30     0.20     0.30  0.14
15     0.30     0.20     0.30  0.15
16     0.30     0.20     0.30  0.16
17     0.30     0.20     0.30  0.17
18     0.30     0.20     0.30  0.18
19     0.30     0.20     0.30  0.19

## 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_1, iteration_2, iteration_3, iteration_4, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, test_sbml3, test_sbml4)

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


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



# Iteration 15
## Thoughts

The model still rapidly reaches a steady state within the first time step, which is inconsistent with the experimental data. The real system shows a gradual rise, a peak, and then a fall for all species, with the total concentration increasing and then decreasing over time. This suggests that the model is missing a mechanism that introduces a delay or a nonlinear amplification, such as autocatalysis or a positive feedback loop.

Given that the total concentration increases dramatically and then falls, and that all species can be produced from zero initial conditions, the system likely involves:
- A nonlinear, possibly autocatalytic, production of at least one species (likely `id_pys4`)
- A degradation or outflow for at least one species

The rapid establishment of steady state in the current models suggests that the input and conversion reactions are too fast relative to the degradation, or that the model is missing a key nonlinear step.

I will now try a model where the production of `id_pys4` is autocatalytic (e.g., ∅ + `id_pys4` → 2 `id_pys4`), which can produce the observed exponential rise and subsequent fall if coupled with degradation.

## Action

### Code
```python
import libsbml

# Start from the original SBML to avoid accumulating reactions
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Add autocatalytic input: ∅ + id_pys4 → 2 id_pys4
reaction_auto = model.createReaction()
reaction_auto.setId("auto_input_pys4")
reaction_auto.setReversible(False)
reaction_auto.setFast(False)
product = reaction_auto.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(2.0)
product.setConstant(True)
reactant = reaction_auto.createReactant()
reactant.setSpecies("id_pys4")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
kl_auto = reaction_auto.createKineticLaw()
param_auto = kl_auto.createParameter()
param_auto.setId("k_auto")
param_auto.setValue(0.01)
kl_auto.setFormula("k_auto * id_pys4")

# id_pys4 → id_y5zp
reaction1 = model.createReaction()
reaction1.setId("pys4_to_y5zp")
reaction1.setReversible(False)
reaction1.setFast(False)
reactant = reaction1.createReactant()
reactant.setSpecies("id_pys4")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction1.createProduct()
product.setSpecies("id_y5zp")
product.setStoichiometry(1.0)
product.setConstant(True)
kl1 = reaction1.createKineticLaw()
param1 = kl1.createParameter()
param1.setId("k1")
param1.setValue(0.1)
kl1.setFormula("k1 * id_pys4")

# id_y5zp → id_e6wb
reaction2 = model.createReaction()
reaction2.setId("y5zp_to_e6wb")
reaction2.setReversible(False)
reaction2.setFast(False)
reactant = reaction2.createReactant()
reactant.setSpecies("id_y5zp")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction2.createProduct()
product.setSpecies("id_e6wb")
product.setStoichiometry(1.0)
product.setConstant(True)
kl2 = reaction2.createKineticLaw()
param2 = kl2.createParameter()
param2.setId("k2")
param2.setValue(0.1)
kl2.setFormula("k2 * id_y5zp")

# id_e6wb → (degradation)
rxn = model.createReaction()
rxn.setId("degrade_e6wb")
rxn.setReversible(False)
rxn.setFast(False)
reactant = rxn.createReactant()
reactant.setSpecies("id_e6wb")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
kl = rxn.createKineticLaw()
param = kl.createParameter()
param.setId("kdeg_e6wb")
param.setValue(0.05)
kl.setFormula("kdeg_e6wb * id_e6wb")

# Write the updated SBML
writer = libsbml.SBMLWriter()
test_sbml5 = writer.writeSBMLToString(sbml_doc)

# Simulate and print the first 20 rows
sim_result5 = simulate(test_sbml5)
print(sim_result5.head(20))
shared_variables.add("test_sbml5", test_sbml5)
```
# Observation

## Code Stdout
         id_y5zp       id_e6wb       id_pys4  Time
0   1.000000e-02  1.000000e-02  1.000000e-02  0.00
1   5.511047e-62 -2.161690e-47  2.302523e-66  0.01
2   4.507834e-62 -1.768103e-47  1.883402e-66  0.02
3   3.504620e-62 -1.374516e-47  1.464281e-66  0.03
4   2.501407e-62 -9.809287e-48  1.045161e-66  0.04
5   1.498194e-62 -5.873417e-48  6.260400e-67  0.05
6   4.949802e-63 -1.937547e-48  2.069194e-67  0.06
7   1.063633e-66  3.935040e-51  1.707985e-70  0.07
8   1.045273e-66  3.867143e-51  1.678503e-70  0.08
9   1.026913e-66  3.799246e-51  1.649020e-70  0.09
10  1.008552e-66  3.731348e-51  1.619538e-70  0.10
11  9.901922e-67  3.663451e-51  1.590056e-70  0.11
12  9.718321e-67  3.595554e-51  1.560574e-70  0.12
13  9.534719e-67  3.527656e-51  1.531092e-70  0.13
14  9.351117e-67  3.459759e-51  1.501610e-70  0.14
15  9.167515e-67  3.391861e-51  1.472128e-70  0.15
16  8.983913e-67  3.323964e-51  1.442645e-70  0.16
17  8.800311e-67  3.256067e-51  1.413163e-70  0.17
18  8.616709e-67  3.188169e-51  1.383681e-70  0.18
19  8.433108e-67  3.120272e-51  1.354199e-70  0.19

## 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_1, iteration_2, iteration_3, iteration_4, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, test_sbml3, test_sbml4, test_sbml5)

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


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



# Iteration 16
## Thoughts

The autocatalytic model (∅ + `id_pys4` → 2 `id_pys4`) results in the concentrations of all species rapidly dropping to near zero or even negative/very small values, which is not physically plausible and does not match the experimental data. This suggests that the model structure or parameterization is still incorrect.

Key observations from the real data:
- All species can be produced from zero initial conditions, indicating an external input.
- The total concentration rises dramatically, peaks, and then falls, indicating a strong production phase followed by a depletion or degradation phase.
- The system is robust to initial conditions, suggesting a strong driving force (input) and a delayed negative feedback (degradation or outflow).

Given these, a plausible mechanism is:
- A strong, time-limited input (e.g., a pulse or a self-limiting input)
- A cyclic conversion between species
- A delayed degradation or outflow, possibly with a threshold or nonlinear dependence

Alternatively, the input could be a constant influx, but the degradation is nonlinear (e.g., second-order or cooperative).

I will now try a model with:
- Constant input to `id_pys4`
- Cyclic conversion: `id_pys4` → `id_y5zp` → `id_e6wb` → `id_pys4`
- Nonlinear (second-order) degradation for `id_e6wb`

## Action

### Code
```python
import libsbml

# Start from the original SBML to avoid accumulating reactions
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Add zero-order input: ∅ → id_pys4
reaction_in = model.createReaction()
reaction_in.setId("input_pys4")
reaction_in.setReversible(False)
reaction_in.setFast(False)
product = reaction_in.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)
kl_in = reaction_in.createKineticLaw()
param_in = kl_in.createParameter()
param_in.setId("k_in")
param_in.setValue(0.5)  # strong input
kl_in.setFormula("k_in")

# id_pys4 → id_y5zp
reaction1 = model.createReaction()
reaction1.setId("pys4_to_y5zp")
reaction1.setReversible(False)
reaction1.setFast(False)
reactant = reaction1.createReactant()
reactant.setSpecies("id_pys4")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction1.createProduct()
product.setSpecies("id_y5zp")
product.setStoichiometry(1.0)
product.setConstant(True)
kl1 = reaction1.createKineticLaw()
param1 = kl1.createParameter()
param1.setId("k1")
param1.setValue(0.2)
kl1.setFormula("k1 * id_pys4")

# id_y5zp → id_e6wb
reaction2 = model.createReaction()
reaction2.setId("y5zp_to_e6wb")
reaction2.setReversible(False)
reaction2.setFast(False)
reactant = reaction2.createReactant()
reactant.setSpecies("id_y5zp")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction2.createProduct()
product.setSpecies("id_e6wb")
product.setStoichiometry(1.0)
product.setConstant(True)
kl2 = reaction2.createKineticLaw()
param2 = kl2.createParameter()
param2.setId("k2")
param2.setValue(0.15)
kl2.setFormula("k2 * id_y5zp")

# id_e6wb → id_pys4
reaction3 = model.createReaction()
reaction3.setId("e6wb_to_pys4")
reaction3.setReversible(False)
reaction3.setFast(False)
reactant = reaction3.createReactant()
reactant.setSpecies("id_e6wb")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction3.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)
kl3 = reaction3.createKineticLaw()
param3 = kl3.createParameter()
param3.setId("k3")
param3.setValue(0.1)
kl3.setFormula("k3 * id_e6wb")

# Add second-order degradation for id_e6wb: id_e6wb + id_e6wb -> ∅
rxn = model.createReaction()
rxn.setId("degrade_e6wb")
rxn.setReversible(False)
rxn.setFast(False)
reactant1 = rxn.createReactant()
reactant1.setSpecies("id_e6wb")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)
reactant2 = rxn.createReactant()
reactant2.setSpecies("id_e6wb")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
kl = rxn.createKineticLaw()
param = kl.createParameter()
param.setId("kdeg_e6wb")
param.setValue(0.01)
kl.setFormula("kdeg_e6wb * id_e6wb * id_e6wb")

# Write the updated SBML
writer = libsbml.SBMLWriter()
test_sbml6 = writer.writeSBMLToString(sbml_doc)

# Simulate and print the first 20 rows
sim_result6 = simulate(test_sbml6)
print(sim_result6.head(20))
shared_variables.add("test_sbml6", test_sbml6)
```
# Observation

## Code Stdout
     id_y5zp  id_e6wb  id_pys4  Time
0   0.010000     0.01     0.01  0.00
1   6.666667     5.00     5.00  0.01
2   6.666667     5.00     5.00  0.02
3   6.666667     5.00     5.00  0.03
4   6.666667     5.00     5.00  0.04
5   6.666667     5.00     5.00  0.05
6   6.666667     5.00     5.00  0.06
7   6.666667     5.00     5.00  0.07
8   6.666667     5.00     5.00  0.08
9   6.666667     5.00     5.00  0.09
10  6.666667     5.00     5.00  0.10
11  6.666667     5.00     5.00  0.11
12  6.666667     5.00     5.00  0.12
13  6.666667     5.00     5.00  0.13
14  6.666667     5.00     5.00  0.14
15  6.666667     5.00     5.00  0.15
16  6.666667     5.00     5.00  0.16
17  6.666667     5.00     5.00  0.17
18  6.666667     5.00     5.00  0.18
19  6.666667     5.00     5.00  0.19

## 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_1, iteration_2, iteration_3, iteration_4, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, test_sbml3, test_sbml4, test_sbml5, test_sbml6)

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


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



# Iteration 17
## Thoughts

The model with a strong input and second-order degradation still immediately jumps to a high steady state for all species, which is not consistent with the experimental data. The real system shows a gradual rise, a peak, and then a fall for all species, with the total concentration increasing and then decreasing over time.

This persistent issue suggests that the model is missing a key regulatory or feedback mechanism that introduces a delay or limits the accumulation of species. The rapid establishment of steady state in all tested models indicates that the input and conversion reactions are too fast relative to the degradation, or that the model is missing a negative feedback loop or a saturating (nonlinear) step.

Given the experimental data, a plausible mechanism is:
- A constant input to `id_pys4`
- Cyclic conversion: `id_pys4` → `id_y5zp` → `id_e6wb` → `id_pys4`
- First-order degradation for all three species (to allow for the observed fall in total concentration)
- Lower rate constants for all reactions to slow down the dynamics

I will now try a model with all first-order reactions (including degradation for all species) and much lower rate constants to see if this produces the observed gradual dynamics.

## Action

### Code
```python
import libsbml

# Start from the original SBML to avoid accumulating reactions
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Add zero-order input: ∅ → id_pys4
reaction_in = model.createReaction()
reaction_in.setId("input_pys4")
reaction_in.setReversible(False)
reaction_in.setFast(False)
product = reaction_in.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)
kl_in = reaction_in.createKineticLaw()
param_in = kl_in.createParameter()
param_in.setId("k_in")
param_in.setValue(0.01)  # much lower input
kl_in.setFormula("k_in")

# id_pys4 → id_y5zp
reaction1 = model.createReaction()
reaction1.setId("pys4_to_y5zp")
reaction1.setReversible(False)
reaction1.setFast(False)
reactant = reaction1.createReactant()
reactant.setSpecies("id_pys4")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction1.createProduct()
product.setSpecies("id_y5zp")
product.setStoichiometry(1.0)
product.setConstant(True)
kl1 = reaction1.createKineticLaw()
param1 = kl1.createParameter()
param1.setId("k1")
param1.setValue(0.01)
kl1.setFormula("k1 * id_pys4")

# id_y5zp → id_e6wb
reaction2 = model.createReaction()
reaction2.setId("y5zp_to_e6wb")
reaction2.setReversible(False)
reaction2.setFast(False)
reactant = reaction2.createReactant()
reactant.setSpecies("id_y5zp")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction2.createProduct()
product.setSpecies("id_e6wb")
product.setStoichiometry(1.0)
product.setConstant(True)
kl2 = reaction2.createKineticLaw()
param2 = kl2.createParameter()
param2.setId("k2")
param2.setValue(0.01)
kl2.setFormula("k2 * id_y5zp")

# id_e6wb → id_pys4
reaction3 = model.createReaction()
reaction3.setId("e6wb_to_pys4")
reaction3.setReversible(False)
reaction3.setFast(False)
reactant = reaction3.createReactant()
reactant.setSpecies("id_e6wb")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction3.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)
kl3 = reaction3.createKineticLaw()
param3 = kl3.createParameter()
param3.setId("k3")
param3.setValue(0.01)
kl3.setFormula("k3 * id_e6wb")

# Add first-order degradation for all species
for sid in ["id_pys4", "id_y5zp", "id_e6wb"]:
    rxn = model.createReaction()
    rxn.setId(f"degrade_{sid}")
    rxn.setReversible(False)
    rxn.setFast(False)
    reactant = rxn.createReactant()
    reactant.setSpecies(sid)
    reactant.setStoichiometry(1.0)
    reactant.setConstant(False)
    kl = rxn.createKineticLaw()
    param = kl.createParameter()
    param.setId(f"kdeg_{sid}")
    param.setValue(0.01)  # lower degradation
    kl.setFormula(f"kdeg_{sid} * {sid}")

# Write the updated SBML
writer = libsbml.SBMLWriter()
test_sbml7 = writer.writeSBMLToString(sbml_doc)

# Simulate and print the first 20 rows
sim_result7 = simulate(test_sbml7)
print(sim_result7.head(20))
shared_variables.add("test_sbml7", test_sbml7)
```
# Observation

## Code Stdout
     id_y5zp   id_e6wb   id_pys4  Time
0   0.010000  0.010000  0.010000  0.00
1   0.285714  0.142857  0.571429  0.01
2   0.285714  0.142857  0.571429  0.02
3   0.285714  0.142857  0.571429  0.03
4   0.285714  0.142857  0.571429  0.04
5   0.285714  0.142857  0.571429  0.05
6   0.285714  0.142857  0.571429  0.06
7   0.285714  0.142857  0.571429  0.07
8   0.285714  0.142857  0.571429  0.08
9   0.285714  0.142857  0.571429  0.09
10  0.285714  0.142857  0.571429  0.10
11  0.285714  0.142857  0.571429  0.11
12  0.285714  0.142857  0.571429  0.12
13  0.285714  0.142857  0.571429  0.13
14  0.285714  0.142857  0.571429  0.14
15  0.285714  0.142857  0.571429  0.15
16  0.285714  0.142857  0.571429  0.16
17  0.285714  0.142857  0.571429  0.17
18  0.285714  0.142857  0.571429  0.18
19  0.285714  0.142857  0.571429  0.19

## 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_1, iteration_2, iteration_3, iteration_4, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, test_sbml3, test_sbml4, test_sbml5, test_sbml6, test_sbml7)

### 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

Even with all rate constants set low, the model still rapidly reaches a steady state within the first time step, which is not consistent with the experimental data. The real system shows a slow, dramatic rise, a peak, and then a fall for all species, with the total concentration increasing and then decreasing over time.

This suggests that the system is not governed by simple first-order kinetics. The rapid approach to steady state in the model, regardless of rate constants, suggests that the model is missing a key nonlinear or time-dependent feature.

Given the experimental data:
- All species can be produced from zero initial conditions.
- The total concentration increases dramatically, peaks, and then falls.
- The system is robust to initial conditions.

A plausible mechanism is a time-dependent input (e.g., a pulse or a burst), or a self-limiting autocatalytic process (e.g., substrate inhibition or depletion of a hidden resource). Alternatively, the input could be a function of time, such as a pulse or a step function.

I will now try a model with a time-dependent input: a pulse of input to `id_pys4` for a limited time, then zero input. This could produce the observed rise and fall.

## Action

### Code
```python
import libsbml

# Start from the original SBML to avoid accumulating reactions
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Add a time-dependent input: input to id_pys4 for t < 2, then zero
# This requires an assignment rule for the input parameter
# Add parameter for time-dependent input
param_in = model.createParameter()
param_in.setId("k_in")
param_in.setValue(0.0)
param_in.setConstant(False)

# Add assignment rule for k_in: k_in = 0.5 if time < 2 else 0
rule = model.createAssignmentRule()
rule.setVariable("k_in")
rule.setFormula("piecewise(0.5, time < 2, 0)")

# Add input reaction: ∅ → id_pys4
reaction_in = model.createReaction()
reaction_in.setId("input_pys4")
reaction_in.setReversible(False)
reaction_in.setFast(False)
product = reaction_in.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)
kl_in = reaction_in.createKineticLaw()
kl_in.setFormula("k_in")

# id_pys4 → id_y5zp
reaction1 = model.createReaction()
reaction1.setId("pys4_to_y5zp")
reaction1.setReversible(False)
reaction1.setFast(False)
reactant = reaction1.createReactant()
reactant.setSpecies("id_pys4")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction1.createProduct()
product.setSpecies("id_y5zp")
product.setStoichiometry(1.0)
product.setConstant(True)
kl1 = reaction1.createKineticLaw()
param1 = kl1.createParameter()
param1.setId("k1")
param1.setValue(0.1)
kl1.setFormula("k1 * id_pys4")

# id_y5zp → id_e6wb
reaction2 = model.createReaction()
reaction2.setId("y5zp_to_e6wb")
reaction2.setReversible(False)
reaction2.setFast(False)
reactant = reaction2.createReactant()
reactant.setSpecies("id_y5zp")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction2.createProduct()
product.setSpecies("id_e6wb")
product.setStoichiometry(1.0)
product.setConstant(True)
kl2 = reaction2.createKineticLaw()
param2 = kl2.createParameter()
param2.setId("k2")
param2.setValue(0.1)
kl2.setFormula("k2 * id_y5zp")

# id_e6wb → id_pys4
reaction3 = model.createReaction()
reaction3.setId("e6wb_to_pys4")
reaction3.setReversible(False)
reaction3.setFast(False)
reactant = reaction3.createReactant()
reactant.setSpecies("id_e6wb")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction3.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)
kl3 = reaction3.createKineticLaw()
param3 = kl3.createParameter()
param3.setId("k3")
param3.setValue(0.1)
kl3.setFormula("k3 * id_e6wb")

# Add first-order degradation for all species
for sid in ["id_pys4", "id_y5zp", "id_e6wb"]:
    rxn = model.createReaction()
    rxn.setId(f"degrade_{sid}")
    rxn.setReversible(False)
    rxn.setFast(False)
    reactant = rxn.createReactant()
    reactant.setSpecies(sid)
    reactant.setStoichiometry(1.0)
    reactant.setConstant(False)
    kl = rxn.createKineticLaw()
    param = kl.createParameter()
    param.setId(f"kdeg_{sid}")
    param.setValue(0.05)
    kl.setFormula(f"kdeg_{sid} * {sid}")

# Write the updated SBML
writer = libsbml.SBMLWriter()
test_sbml8 = writer.writeSBMLToString(sbml_doc)

# Simulate and print the first 20 rows
sim_result8 = simulate(test_sbml8)
print(sim_result8.head(20))
shared_variables.add("test_sbml8", test_sbml8)
```
# Observation

## Code Stdout
         id_y5zp       id_e6wb       id_pys4  Time
0   1.000000e-02  1.000000e-02  1.000000e-02  0.00
1   3.213744e-48 -3.201851e-49 -2.337723e-47  0.01
2   2.790915e-48 -2.780704e-49 -2.030304e-47  0.02
3   2.368087e-48 -2.359557e-49 -1.722884e-47  0.03
4   1.945258e-48 -1.938410e-49 -1.415465e-47  0.04
5   1.522429e-48 -1.517263e-49 -1.108046e-47  0.05
6   1.099600e-48 -1.096117e-49 -8.006266e-48  0.06
7   6.767707e-49 -6.749696e-50 -4.932073e-48  0.07
8   2.539417e-49 -2.538227e-50 -1.857880e-48  0.08
9  -5.515979e-52 -3.371985e-53 -7.517872e-51  0.09
10 -5.444381e-52 -3.328213e-53 -7.420288e-51  0.10
11 -5.372783e-52 -3.284441e-53 -7.322704e-51  0.11
12 -5.301184e-52 -3.240668e-53 -7.225120e-51  0.12
13 -5.229586e-52 -3.196896e-53 -7.127535e-51  0.13
14 -5.157987e-52 -3.153124e-53 -7.029951e-51  0.14
15 -5.086389e-52 -3.109351e-53 -6.932367e-51  0.15
16 -5.014791e-52 -3.065579e-53 -6.834783e-51  0.16
17 -4.943192e-52 -3.021807e-53 -6.737198e-51  0.17
18 -4.871594e-52 -2.978034e-53 -6.639614e-51  0.18
19 -4.799995e-52 -2.934262e-53 -6.542030e-51  0.19

## 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_1, iteration_2, iteration_3, iteration_4, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, test_sbml3, test_sbml4, test_sbml5, test_sbml6, test_sbml7, test_sbml8)

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


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



# Iteration 19
## Thoughts

The time-dependent input model (pulse input for t < 2) still fails: the concentrations of all species quickly drop to near zero or negative/small values, which is not consistent with the experimental data. This suggests that the model structure is fundamentally missing a key feature.

Key observations from the data:
- All species can be produced from zero initial conditions.
- The total concentration increases dramatically, peaks, and then falls.
- The system is robust to initial conditions and shows a delayed, nonlinear response.

The persistent failure of all tested models (including those with time-dependent input, autocatalysis, and nonlinear degradation) suggests that the system may involve a positive feedback loop or autocatalytic production that is not simply first-order, or that the input is not a simple constant or pulse but is itself regulated by the concentrations of the species.

Given the dramatic rise and fall, a plausible mechanism is:
- Strong autocatalytic production of one species (e.g., `id_pys4` catalyzes its own production, possibly with a threshold or Hill-type nonlinearity)
- Cyclic conversion between species
- First-order degradation for all species

I will now try a model with Hill-type autocatalytic production for `id_pys4` (e.g., ∅ → `id_pys4` with rate proportional to `id_pys4^n / (K^n + id_pys4^n)`), which can produce a sharp rise and fall.

## Action

### Code
```python
import libsbml

# Start from the original SBML to avoid accumulating reactions
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Add parameters for Hill kinetics
param_kcat = model.createParameter()
param_kcat.setId("kcat")
param_kcat.setValue(2.0)
param_kcat.setConstant(True)
param_K = model.createParameter()
param_K.setId("K")
param_K.setValue(0.1)
param_K.setConstant(True)
param_n = model.createParameter()
param_n.setId("n")
param_n.setValue(3.0)
param_n.setConstant(True)

# Add autocatalytic Hill input: ∅ → id_pys4, rate = kcat * id_pys4^n / (K^n + id_pys4^n)
reaction_in = model.createReaction()
reaction_in.setId("auto_hill_input_pys4")
reaction_in.setReversible(False)
reaction_in.setFast(False)
product = reaction_in.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)
kl_in = reaction_in.createKineticLaw()
kl_in.setFormula("kcat * pow(id_pys4, n) / (pow(K, n) + pow(id_pys4, n))")

# id_pys4 → id_y5zp
reaction1 = model.createReaction()
reaction1.setId("pys4_to_y5zp")
reaction1.setReversible(False)
reaction1.setFast(False)
reactant = reaction1.createReactant()
reactant.setSpecies("id_pys4")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction1.createProduct()
product.setSpecies("id_y5zp")
product.setStoichiometry(1.0)
product.setConstant(True)
kl1 = reaction1.createKineticLaw()
param1 = kl1.createParameter()
param1.setId("k1")
param1.setValue(0.1)
kl1.setFormula("k1 * id_pys4")

# id_y5zp → id_e6wb
reaction2 = model.createReaction()
reaction2.setId("y5zp_to_e6wb")
reaction2.setReversible(False)
reaction2.setFast(False)
reactant = reaction2.createReactant()
reactant.setSpecies("id_y5zp")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction2.createProduct()
product.setSpecies("id_e6wb")
product.setStoichiometry(1.0)
product.setConstant(True)
kl2 = reaction2.createKineticLaw()
param2 = kl2.createParameter()
param2.setId("k2")
param2.setValue(0.1)
kl2.setFormula("k2 * id_y5zp")

# id_e6wb → id_pys4
reaction3 = model.createReaction()
reaction3.setId("e6wb_to_pys4")
reaction3.setReversible(False)
reaction3.setFast(False)
reactant = reaction3.createReactant()
reactant.setSpecies("id_e6wb")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction3.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)
kl3 = reaction3.createKineticLaw()
param3 = kl3.createParameter()
param3.setId("k3")
param3.setValue(0.1)
kl3.setFormula("k3 * id_e6wb")

# Add first-order degradation for all species
for sid in ["id_pys4", "id_y5zp", "id_e6wb"]:
    rxn = model.createReaction()
    rxn.setId(f"degrade_{sid}")
    rxn.setReversible(False)
    rxn.setFast(False)
    reactant = rxn.createReactant()
    reactant.setSpecies(sid)
    reactant.setStoichiometry(1.0)
    reactant.setConstant(False)
    kl = rxn.createKineticLaw()
    param = kl.createParameter()
    param.setId(f"kdeg_{sid}")
    param.setValue(0.05)
    kl.setFormula(f"kdeg_{sid} * {sid}")

# Write the updated SBML
writer = libsbml.SBMLWriter()
test_sbml9 = writer.writeSBMLToString(sbml_doc)

# Simulate and print the first 20 rows
sim_result9 = simulate(test_sbml9)
print(sim_result9.head(20))
shared_variables.add("test_sbml9", test_sbml9)
```
# Observation

## Code Stdout
      id_y5zp   id_e6wb    id_pys4  Time
0    0.010000  0.010000   0.010000  0.00
1   12.631577  8.421051  18.947366  0.01
2   12.631577  8.421051  18.947366  0.02
3   12.631577  8.421051  18.947366  0.03
4   12.631577  8.421051  18.947366  0.04
5   12.631577  8.421051  18.947366  0.05
6   12.631577  8.421051  18.947366  0.06
7   12.631577  8.421051  18.947366  0.07
8   12.631577  8.421051  18.947366  0.08
9   12.631577  8.421051  18.947366  0.09
10  12.631577  8.421051  18.947366  0.10
11  12.631577  8.421051  18.947366  0.11
12  12.631577  8.421051  18.947366  0.12
13  12.631577  8.421051  18.947366  0.13
14  12.631577  8.421051  18.947366  0.14
15  12.631577  8.421051  18.947366  0.15
16  12.631577  8.421051  18.947366  0.16
17  12.631577  8.421051  18.947366  0.17
18  12.631577  8.421051  18.947366  0.18
19  12.631577  8.421051  18.947366  0.19

## 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_1, iteration_2, iteration_3, iteration_4, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, test_sbml3, test_sbml4, test_sbml5, test_sbml6, test_sbml7, test_sbml8, test_sbml9)

### 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

The Hill-type autocatalytic input for `id_pys4` results in all species immediately jumping to high steady-state values, with no gradual rise, peak, or fall as seen in the experimental data. This is a persistent issue across all tested models, regardless of the introduction of nonlinearities, time-dependent inputs, or feedbacks.

Key observations from the data:
- All species can be produced from zero initial conditions.
- The total concentration rises dramatically, peaks, and then falls.
- The system is robust to initial conditions and shows a delayed, nonlinear response.

Despite extensive exploration, none of the tested models reproduce the observed gradual rise, peak, and fall. The models all rapidly reach a steady state, suggesting that the real system may involve a hidden resource or substrate that is depleted over time, or a delayed negative feedback that is not captured by the current models.

Given the constraints and the time limit, I will submit the model with the most plausible mechanistic structure based on the data:
- Constant input to `id_pys4`
- Cyclic conversion: `id_pys4` → `id_y5zp` → `id_e6wb` → `id_pys4`
- First-order degradation for all species

This structure is the most consistent with the observed robustness and the ability to generate all species from zero initial conditions, even if the parameterization does not capture the full dynamics.

## Action

### Submit
```python
import libsbml

# Start from the original SBML to avoid accumulating reactions
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Add zero-order input: ∅ → id_pys4
reaction_in = model.createReaction()
reaction_in.setId("input_pys4")
reaction_in.setReversible(False)
reaction_in.setFast(False)
product = reaction_in.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)
kl_in = reaction_in.createKineticLaw()
param_in = kl_in.createParameter()
param_in.setId("k_in")
param_in.setValue(0.1)
kl_in.setFormula("k_in")

# id_pys4 → id_y5zp
reaction1 = model.createReaction()
reaction1.setId("pys4_to_y5zp")
reaction1.setReversible(False)
reaction1.setFast(False)
reactant = reaction1.createReactant()
reactant.setSpecies("id_pys4")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction1.createProduct()
product.setSpecies("id_y5zp")
product.setStoichiometry(1.0)
product.setConstant(True)
kl1 = reaction1.createKineticLaw()
param1 = kl1.createParameter()
param1.setId("k1")
param1.setValue(0.05)
kl1.setFormula("k1 * id_pys4")

# id_y5zp → id_e6wb
reaction2 = model.createReaction()
reaction2.setId("y5zp_to_e6wb")
reaction2.setReversible(False)
reaction2.setFast(False)
reactant = reaction2.createReactant()
reactant.setSpecies("id_y5zp")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction2.createProduct()
product.setSpecies("id_e6wb")
product.setStoichiometry(1.0)
product.setConstant(True)
kl2 = reaction2.createKineticLaw()
param2 = kl2.createParameter()
param2.setId("k2")
param2.setValue(0.05)
kl2.setFormula("k2 * id_y5zp")

# id_e6wb → id_pys4
reaction3 = model.createReaction()
reaction3.setId("e6wb_to_pys4")
reaction3.setReversible(False)
reaction3.setFast(False)
reactant = reaction3.createReactant()
reactant.setSpecies("id_e6wb")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = reaction3.createProduct()
product.setSpecies("id_pys4")
product.setStoichiometry(1.0)
product.setConstant(True)
kl3 = reaction3.createKineticLaw()
param3 = kl3.createParameter()
param3.setId("k3")
param3.setValue(0.05)
kl3.setFormula("k3 * id_e6wb")

# Add first-order degradation for all species
for sid in ["id_pys4", "id_y5zp", "id_e6wb"]:
    rxn = model.createReaction()
    rxn.setId(f"degrade_{sid}")
    rxn.setReversible(False)
    rxn.setFast(False)
    reactant = rxn.createReactant()
    reactant.setSpecies(sid)
    reactant.setStoichiometry(1.0)
    reactant.setConstant(False)
    kl = rxn.createKineticLaw()
    param = kl.createParameter()
    param.setId(f"kdeg_{sid}")
    param.setValue(0.05)
    kl.setFormula(f"kdeg_{sid} * {sid}")

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