
                # 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_gs9e">
    <listOfUnitDefinitions>
      <unitDefinition id="id_y5me">
        <listOfUnits>
          <unit kind="second" exponent="1" scale="0" multiplier="3600"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_yufe" spatialDimensions="3" size="1" constant="true"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_k8mo" compartment="id_yufe" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_smxa" compartment="id_yufe" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_q2yx" compartment="id_yufe" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_9wyg" compartment="id_yufe" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_piw6" compartment="id_yufe" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_xee0" compartment="id_yufe" initialConcentration="0.999999999999971" 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 six species, all with initial concentrations of zero except for `id_xee0`, which starts at approximately 1. There are no reactions defined in the model, so the system as it stands will not change over time. To begin uncovering the missing reactions, I should first observe the system's behavior under default conditions. This will provide a baseline time-course for all species and may reveal which species change over time, suggesting possible reaction pathways.

## 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: 4189 rows × 7 columns. 

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

Time   id_k8mo  id_smxa  id_q2yx  id_9wyg  id_piw6  id_xee0
0         0        0        0        0        0 1.00e+00
...
1.68e+00  2.07e-02 3.90e-02 1.74e-01 1.54e-01 1.15e-03 2.83e-01
...
3.37e+00  1.25e-01 1.39e-01 3.85e-01 2.82e-01 3.27e-02 1.21e-01
...
5.05e+00  3.16e-01 2.70e-01 5.66e-01 3.88e-01 1.91e-01 6.95e-02
...
6.74e+00  4.78e-01 4.08e-01 5.52e-01 4.76e-01 5.50e-01 5.56e-02
...
8.42e+00  4.17e-01 5.37e-01 2.65e-01 5.49e-01 8.98e-01 7.34e-02
...
1.01e+01  1.66e-01 6.46e-01 5.24e-02 6.10e-01 4.28e-01 1.99e-01
...
1.18e+01  1.16e-01 7.33e-01 9.80e-02 6.61e-01 2.30e-01 2.10e-01
...
1.35e+01  1.36e-01 8.00e-01 9.82e-02 7.03e-01 3.04e-01 1.90e-01
...
1.52e+01  1.26e-01 8.49e-01 7.90e-02 7.38e-01 3.13e-01 2.05e-01
...
1.68e+01  1.14e-01 8.85e-01 7.21e-02 7.67e-01 2.93e-01 2.19e-01
...
1.85e+01  1.10e-01 9.10e-01 6.83e-02 7.91e-01 2.87e-01 2.26e-01
...
2.02e+01  1.07e-01 9.27e-01 6.50e-02 8.11e-01 2.84e-01 2.31e-01
...
2.19e+01  1.05e-01 9.39e-01 6.26e-02 8.27e-01 2.81e-01 2.35e-01
...
2.36e+01  1.03e-01 9.47e-01 6.09e-02 8.41e-01 2.79e-01 2.39e-01
...
2.53e+01  1.02e-01 9.52e-01 5.96e-02 8.53e-01 2.78e-01 2.41e-01
...
2.70e+01  1.01e-01 9.56e-01 5.86e-02 8.62e-01 2.76e-01 2.43e-01
...
2.86e+01  1.01e-01 9.59e-01 5.78e-02 8.70e-01 2.76e-01 2.44e-01
...
3.03e+01  1.01e-01 9.60e-01 5.72e-02 8.77e-01 2.75e-01 2.46e-01
...
3.20e+01  1.00e-01 9.61e-01 5.67e-02 8.82e-01 2.74e-01 2.47e-01
...
3.37e+01  1.00e-01 9.62e-01 5.63e-02 8.87e-01 2.74e-01 2.47e-01
...
3.54e+01  9.98e-02 9.63e-01 5.60e-02 8.91e-01 2.73e-01 2.48e-01
...
3.71e+01  9.97e-02 9.63e-01 5.57e-02 8.94e-01 2.73e-01 2.48e-01
...
3.87e+01  9.96e-02 9.64e-01 5.55e-02 8.96e-01 2.73e-01 2.49e-01
...
4.04e+01  9.95e-02 9.64e-01 5.54e-02 8.98e-01 2.73e-01 2.49e-01
...
4.21e+01  9.94e-02 9.64e-01 5.52e-02 9.00e-01 2.73e-01 2.50e-01
...
4.38e+01  9.94e-02 9.64e-01 5.51e-02 9.02e-01 2.72e-01 2.50e-01
...
4.55e+01  9.94e-02 9.64e-01 5.50e-02 9.03e-01 2.72e-01 2.50e-01
...
4.72e+01  9.93e-02 9.64e-01 5.49e-02 9.04e-01 2.72e-01 2.50e-01
...
4.89e+01  9.93e-02 9.64e-01 5.49e-02 9.05e-01 2.72e-01 2.50e-01
...
5.05e+01  9.93e-02 9.64e-01 5.48e-02 9.06e-01 2.72e-01 2.50e-01
...
5.22e+01  9.92e-02 9.64e-01 5.48e-02 9.06e-01 2.72e-01 2.50e-01
...
5.39e+01  9.92e-02 9.64e-01 5.47e-02 9.07e-01 2.72e-01 2.50e-01
...
5.56e+01  9.92e-02 9.65e-01 5.47e-02 9.07e-01 2.72e-01 2.51e-01
...
5.73e+01  9.92e-02 9.65e-01 5.47e-02 9.07e-01 2.72e-01 2.51e-01
...
5.90e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.06e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.23e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.40e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.57e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.74e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
6.91e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.08e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.24e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.41e+01  9.92e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.58e+01  9.92e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.75e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.92e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.09e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.30e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01

## 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, we see that all species except `id_xee0` start at zero, and `id_xee0` starts at ~1. Over time, `id_xee0` decreases while all other species increase, but at different rates and to different extents. This suggests that `id_xee0` is being converted into the other species, possibly through a series of reactions or a network with branching.

Notably:
- `id_smxa` increases the most, reaching ~0.96 at steady state.
- `id_9wyg` also increases substantially, reaching ~0.9.
- `id_piw6` and `id_k8mo` reach ~0.27 and ~0.1, respectively.
- `id_q2yx` increases only slightly, reaching ~0.054.

The sum of all species at steady state is greater than 1, which suggests that there may be autocatalytic or branching reactions, or that the system is not strictly mass-conserving (possibly due to external sources or sinks, or the units are not strictly molar).

To further probe the system, I should perturb the initial concentration of `id_xee0` (e.g., set it to 0.5) and observe how the other species respond. This will help determine if the system is linear, if there are thresholds, or if the reactions are saturable or cooperative.

## Action

### Experiment

```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_xee0": 0.5
    }
}
```
# 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: 4189 rows × 7 columns. 

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

Time   id_k8mo  id_smxa  id_q2yx  id_9wyg  id_piw6  id_xee0
0         0        0        0        0        0 5.00e-01
...
1.68e+00  3.22e-02 3.90e-02 2.60e-01 1.54e-01 1.82e-03 1.95e-01
...
3.37e+00  1.72e-01 1.39e-01 5.14e-01 2.82e-01 4.57e-02 9.05e-02
...
5.05e+00  4.01e-01 2.70e-01 6.96e-01 3.88e-01 2.50e-01 5.54e-02
...
6.74e+00  5.60e-01 4.08e-01 6.14e-01 4.76e-01 6.92e-01 4.79e-02
...
8.42e+00  4.02e-01 5.37e-01 1.54e-01 5.49e-01 1.22e+00 8.25e-02
...
1.01e+01  9.44e-02 6.46e-01 2.70e-02 6.10e-01 2.62e-01 3.25e-01
...
1.18e+01  1.02e-01 7.33e-01 1.03e-01 6.61e-01 1.84e-01 2.25e-01
...
1.35e+01  1.37e-01 8.00e-01 9.96e-02 7.03e-01 3.03e-01 1.90e-01
...
1.52e+01  1.26e-01 8.49e-01 7.87e-02 7.38e-01 3.14e-01 2.04e-01
...
1.68e+01  1.14e-01 8.85e-01 7.21e-02 7.67e-01 2.92e-01 2.19e-01
...
1.85e+01  1.10e-01 9.10e-01 6.84e-02 7.91e-01 2.87e-01 2.25e-01
...
2.02e+01  1.07e-01 9.27e-01 6.50e-02 8.11e-01 2.84e-01 2.31e-01
...
2.19e+01  1.05e-01 9.39e-01 6.26e-02 8.27e-01 2.81e-01 2.35e-01
...
2.36e+01  1.03e-01 9.47e-01 6.09e-02 8.41e-01 2.79e-01 2.39e-01
...
2.53e+01  1.02e-01 9.52e-01 5.96e-02 8.53e-01 2.78e-01 2.41e-01
...
2.70e+01  1.01e-01 9.56e-01 5.86e-02 8.62e-01 2.76e-01 2.43e-01
...
2.86e+01  1.01e-01 9.59e-01 5.78e-02 8.70e-01 2.76e-01 2.44e-01
...
3.03e+01  1.01e-01 9.60e-01 5.72e-02 8.77e-01 2.75e-01 2.46e-01
...
3.20e+01  1.00e-01 9.61e-01 5.67e-02 8.82e-01 2.74e-01 2.47e-01
...
3.37e+01  1.00e-01 9.62e-01 5.63e-02 8.87e-01 2.74e-01 2.47e-01
...
3.54e+01  9.98e-02 9.63e-01 5.60e-02 8.91e-01 2.73e-01 2.48e-01
...
3.71e+01  9.97e-02 9.63e-01 5.57e-02 8.94e-01 2.73e-01 2.48e-01
...
3.87e+01  9.96e-02 9.64e-01 5.55e-02 8.96e-01 2.73e-01 2.49e-01
...
4.04e+01  9.95e-02 9.64e-01 5.54e-02 8.98e-01 2.73e-01 2.49e-01
...
4.21e+01  9.94e-02 9.64e-01 5.52e-02 9.00e-01 2.73e-01 2.50e-01
...
4.38e+01  9.94e-02 9.64e-01 5.51e-02 9.02e-01 2.72e-01 2.50e-01
...
4.55e+01  9.94e-02 9.64e-01 5.50e-02 9.03e-01 2.72e-01 2.50e-01
...
4.72e+01  9.93e-02 9.64e-01 5.49e-02 9.04e-01 2.72e-01 2.50e-01
...
4.89e+01  9.93e-02 9.64e-01 5.49e-02 9.05e-01 2.72e-01 2.50e-01
...
5.05e+01  9.93e-02 9.64e-01 5.48e-02 9.06e-01 2.72e-01 2.50e-01
...
5.22e+01  9.92e-02 9.64e-01 5.48e-02 9.06e-01 2.72e-01 2.50e-01
...
5.39e+01  9.92e-02 9.64e-01 5.47e-02 9.07e-01 2.72e-01 2.50e-01
...
5.56e+01  9.92e-02 9.65e-01 5.47e-02 9.07e-01 2.72e-01 2.51e-01
...
5.73e+01  9.92e-02 9.65e-01 5.47e-02 9.07e-01 2.72e-01 2.51e-01
...
5.90e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.06e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.23e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.40e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.57e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.74e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
6.91e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.08e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.24e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.41e+01  9.92e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.58e+01  9.92e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.75e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.92e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.09e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.30e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01

## 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

The results from the experiment with `id_xee0` initial concentration set to 0.5 show that the system's qualitative behavior is similar to the default case, but the quantitative details differ. Notably, the steady-state values for the other species are almost identical to the previous experiment, despite starting with half the initial `id_xee0`. This suggests that the system is not simply linear with respect to the initial amount of `id_xee0`, and there may be autocatalytic or feedback mechanisms, or external sources for some species.

Additionally, the sum of all species at steady state is still greater than the initial amount of `id_xee0`, which further supports the idea of autocatalysis or an external source.

To further probe the system, I will set the initial concentration of `id_xee0` to zero. If the other species still increase, it would strongly suggest the presence of an external source or autocatalytic reactions.

## Action

### Experiment

```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_xee0": 0.0
    }
}
```
# 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: 4189 rows × 7 columns. 

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

Time   id_k8mo  id_smxa  id_q2yx  id_9wyg  id_piw6  id_xee0
0         0        0        0        0        0        0
...
1.68e+00  3.76e-01 3.90e-02 2.60e+00 1.54e-01 2.25e-02 1.62e-02
...
3.37e+00  1.13e+00 1.39e-01 2.69e+00 2.82e-01 3.49e-01 1.31e-02
...
5.05e+00  1.47e+00 2.70e-01 1.76e+00 3.88e-01 2.06e+00 1.50e-02
...
6.74e+00  5.05e-01 4.08e-01 8.67e-04 4.76e-01 4.29e+00 2.81e-01
...
8.42e+00  9.44e-02 5.37e-01 1.03e-03 5.49e-01 2.59e+00 4.00e-01
...
1.01e+01  2.16e-02 6.46e-01 1.37e-02 6.10e-01 2.92e-01 3.91e-01
...
1.18e+01  9.73e-02 7.33e-01 1.14e-01 6.61e-01 1.58e-01 2.26e-01
...
1.35e+01  1.40e-01 8.00e-01 1.00e-01 7.03e-01 3.13e-01 1.87e-01
...
1.52e+01  1.26e-01 8.49e-01 7.78e-02 7.38e-01 3.15e-01 2.05e-01
...
1.68e+01  1.14e-01 8.85e-01 7.22e-02 7.67e-01 2.91e-01 2.19e-01
...
1.85e+01  1.10e-01 9.10e-01 6.84e-02 7.91e-01 2.87e-01 2.25e-01
...
2.02e+01  1.07e-01 9.27e-01 6.49e-02 8.11e-01 2.84e-01 2.31e-01
...
2.19e+01  1.05e-01 9.39e-01 6.26e-02 8.27e-01 2.81e-01 2.35e-01
...
2.36e+01  1.03e-01 9.47e-01 6.09e-02 8.41e-01 2.79e-01 2.39e-01
...
2.53e+01  1.02e-01 9.52e-01 5.96e-02 8.53e-01 2.78e-01 2.41e-01
...
2.70e+01  1.01e-01 9.56e-01 5.86e-02 8.62e-01 2.76e-01 2.43e-01
...
2.86e+01  1.01e-01 9.59e-01 5.78e-02 8.70e-01 2.76e-01 2.44e-01
...
3.03e+01  1.01e-01 9.60e-01 5.72e-02 8.77e-01 2.75e-01 2.46e-01
...
3.20e+01  1.00e-01 9.61e-01 5.67e-02 8.82e-01 2.74e-01 2.47e-01
...
3.37e+01  1.00e-01 9.62e-01 5.63e-02 8.87e-01 2.74e-01 2.47e-01
...
3.54e+01  9.98e-02 9.63e-01 5.60e-02 8.91e-01 2.73e-01 2.48e-01
...
3.71e+01  9.97e-02 9.63e-01 5.57e-02 8.94e-01 2.73e-01 2.48e-01
...
3.87e+01  9.96e-02 9.64e-01 5.55e-02 8.96e-01 2.73e-01 2.49e-01
...
4.04e+01  9.95e-02 9.64e-01 5.54e-02 8.98e-01 2.73e-01 2.49e-01
...
4.21e+01  9.94e-02 9.64e-01 5.52e-02 9.00e-01 2.73e-01 2.50e-01
...
4.38e+01  9.94e-02 9.64e-01 5.51e-02 9.02e-01 2.72e-01 2.50e-01
...
4.55e+01  9.94e-02 9.64e-01 5.50e-02 9.03e-01 2.72e-01 2.50e-01
...
4.72e+01  9.93e-02 9.64e-01 5.49e-02 9.04e-01 2.72e-01 2.50e-01
...
4.89e+01  9.93e-02 9.64e-01 5.49e-02 9.05e-01 2.72e-01 2.50e-01
...
5.05e+01  9.93e-02 9.64e-01 5.48e-02 9.06e-01 2.72e-01 2.50e-01
...
5.22e+01  9.92e-02 9.64e-01 5.48e-02 9.06e-01 2.72e-01 2.50e-01
...
5.39e+01  9.92e-02 9.64e-01 5.47e-02 9.07e-01 2.72e-01 2.50e-01
...
5.56e+01  9.92e-02 9.65e-01 5.47e-02 9.07e-01 2.72e-01 2.51e-01
...
5.73e+01  9.92e-02 9.65e-01 5.47e-02 9.07e-01 2.72e-01 2.51e-01
...
5.90e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.06e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.23e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.40e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.57e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.74e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
6.91e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.08e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.24e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.41e+01  9.92e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.58e+01  9.92e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.75e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.92e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.09e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.30e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01

## 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

Setting the initial concentration of `id_xee0` to zero does not prevent the other species from increasing over time. In fact, some species (e.g., `id_piw6`, `id_q2yx`) reach even higher concentrations than in the previous experiments, and `id_xee0` itself increases from zero to a nonzero steady-state value. This strongly suggests that there is an external source for at least some of the species, and possibly for all of them. The system is not closed, and the dynamics are not simply a conversion of `id_xee0` into the other species.

Given this, the next step is to analyze the time courses quantitatively to look for patterns, such as:
- Which species appear first and at what rates?
- Are there lag phases or sequential rises, suggesting a reaction chain?
- Are the rates of increase for some species correlated, suggesting direct conversion or shared sources?

A code-based analysis of the time series will help clarify these relationships and guide the construction of plausible reactions.

## Action

### Code

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

# Load the three experiments
df0 = experiment_history['iteration_0']
df1 = experiment_history['iteration_1']
df2 = experiment_history['iteration_2']

# For each, plot all species over time
for i, (df, title) in enumerate(zip([df0, df1, df2], ['xee0=1', 'xee0=0.5', 'xee0=0']), 1):
    plt.figure(figsize=(10, 6))
    for col in df.columns:
        if col != 'Time':
            plt.plot(df['Time'], df[col], label=col)
    plt.title(f"Time courses for initial {title}")
    plt.xlabel('Time')
    plt.ylabel('Concentration')
    plt.legend()
    plt.show()

# Calculate and print the steady-state values for each species in each experiment
def get_steady_state(df):
    return df.iloc[-10:].mean()

print("Steady-state values for each experiment:")
print("xee0=1:", get_steady_state(df0))
print("xee0=0.5:", get_steady_state(df1))
print("xee0=0:", get_steady_state(df2))

# Save steady-state values for further analysis
shared_variables.add("steady_states", {
    "xee0=1": get_steady_state(df0),
    "xee0=0.5": get_steady_state(df1),
    "xee0=0": get_steady_state(df2)
})
```
# 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: 17/20



### 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 4
## Thoughts

I mistakenly used `matplotlib`, which is not allowed. Instead, I will focus on numerical analysis using `pandas` and `numpy`. I will:
- Calculate the steady-state values for each species in each experiment.
- Examine the time to reach half-maximal concentration for each species to infer the order of appearance and possible reaction chains.
- Look for correlations in the time derivatives to infer direct conversions or shared sources.

This analysis will help clarify the relationships between the species and guide the construction of plausible reactions.

## Action

### Code

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

# Helper function to get steady-state (last 10 time points) means
def get_steady_state(df):
    return df.iloc[-10:].mean()

# Helper function to get time to half-max for each species
def get_half_max_times(df):
    half_max_times = {}
    for col in df.columns:
        if col != 'Time':
            max_val = df[col].max()
            half_max = max_val / 2
            above_half = df[df[col] >= half_max]
            if not above_half.empty:
                half_max_times[col] = above_half.iloc[0]['Time']
            else:
                half_max_times[col] = np.nan
    return half_max_times

# Analyze all three experiments
results = {}
for key in ['iteration_0', 'iteration_1', 'iteration_2']:
    df = experiment_history[key]
    results[key] = {
        'steady_state': get_steady_state(df),
        'half_max_times': get_half_max_times(df)
    }

# Print steady-state values and half-max times for each experiment
for key in results:
    print(f"\nExperiment {key}:")
    print("Steady-state concentrations:")
    print(results[key]['steady_state'])
    print("Time to half-max for each species:")
    print(results[key]['half_max_times'])

# Save results for further analysis
shared_variables.add("analysis_results", results)
```
# Observation

## Code Stdout

Experiment iteration_0:
Steady-state concentrations:
id_k8mo     0.099147
id_smxa     0.964624
id_q2yx     0.054537
id_9wyg     0.908991
id_piw6     0.271831
id_xee0     0.250829
Time       82.910817
dtype: float64
Time to half-max for each species:
{'id_k8mo': np.float64(4.478987583572111), 'id_smxa': np.float64(7.689589302769819), 'id_q2yx': np.float64(2.6953199617956063), 'id_9wyg': np.float64(6.302292263610315), 'id_piw6': np.float64(6.341929321872016), 'id_xee0': np.float64(0.0)}

Experiment iteration_1:
Steady-state concentrations:
id_k8mo     0.099147
id_smxa     0.964624
id_q2yx     0.054537
id_9wyg     0.908991
id_piw6     0.271831
id_xee0     0.250829
Time       82.910817
dtype: float64
Time to half-max for each species:
{'id_k8mo': np.float64(4.22134670487106), 'id_smxa': np.float64(7.689589302769819), 'id_q2yx': np.float64(2.3187679083094554), 'id_9wyg': np.float64(6.302292263610315), 'id_piw6': np.float64(6.480659025787966), 'id_xee0': np.float64(0.0)}

Experiment iteration_2:
Steady-state concentrations:
id_k8mo     0.099147
id_smxa     0.964624
id_q2yx     0.054537
id_9wyg     0.908991
id_piw6     0.271831
id_xee0     0.250829
Time       82.910817
dtype: float64
Time to half-max for each species:
{'id_k8mo': np.float64(2.497134670487106), 'id_smxa': np.float64(7.689589302769819), 'id_q2yx': np.float64(0.43600764087870103), 'id_9wyg': np.float64(6.302292263610315), 'id_piw6': np.float64(5.113180515759312), 'id_xee0': np.float64(6.460840496657116)}

## 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)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results)

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


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



# Iteration 5
## Thoughts

The steady-state concentrations for all species are identical across all three experiments, regardless of the initial concentration of `id_xee0`. This is highly indicative of a system with strong homeostatic regulation, likely involving external sources and/or sinks for the species. The time to half-max for each species varies somewhat with the initial conditions, but the final values do not.

Key observations:
- `id_xee0` always returns to ~0.25 at steady state, even if started at 0 or 1.
- All other species also reach the same steady-state values regardless of initial `id_xee0`.
- Some species (e.g., `id_q2yx`, `id_k8mo`) reach half-max much earlier when `id_xee0` is started at 0, suggesting that their production is not dependent on `id_xee0` but may be from an external source or a fast reaction.

Given these results, the next step is to test whether the system is robust to perturbations in other species. For example, set the initial concentration of `id_smxa` to 1 and all others to 0, and observe if the system returns to the same steady state. This will help determine if the system is globally stable and if there are interconversions or independent sources for each species.

## Action

### Experiment

```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_k8mo": 0.0,
        "id_smxa": 1.0,
        "id_q2yx": 0.0,
        "id_9wyg": 0.0,
        "id_piw6": 0.0,
        "id_xee0": 0.0
    }
}
```
# Observation

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

Total size: 4189 rows × 7 columns. 

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

Time   id_k8mo  id_smxa  id_q2yx  id_9wyg  id_piw6  id_xee0
0         0 1.00e+00        0        0        0        0
...
1.68e+00  3.57e-01 9.84e-01 2.34e+00 1.54e-01 8.15e-01 1.66e-02
...
3.37e+00  4.00e-01 9.70e-01 1.35e-03 2.82e-01 5.61e+00 1.41e-01
...
5.05e+00  7.45e-02 9.60e-01 6.42e-04 3.88e-01 4.09e+00 3.93e-01
...
6.74e+00  1.47e-02 9.53e-01 1.66e-03 4.76e-01 1.65e+00 4.05e-01
...
8.42e+00  3.93e-02 9.50e-01 8.94e-02 5.49e-01 7.74e-02 2.95e-01
...
1.01e+01  1.16e-01 9.49e-01 1.11e-01 6.10e-01 2.91e-01 1.92e-01
...
1.18e+01  1.18e-01 9.49e-01 8.37e-02 6.61e-01 3.33e-01 1.98e-01
...
1.35e+01  1.09e-01 9.51e-01 7.61e-02 7.03e-01 3.02e-01 2.13e-01
...
1.52e+01  1.08e-01 9.52e-01 7.24e-02 7.38e-01 2.95e-01 2.20e-01
...
1.68e+01  1.06e-01 9.54e-01 6.83e-02 7.67e-01 2.90e-01 2.26e-01
...
1.85e+01  1.04e-01 9.56e-01 6.55e-02 7.91e-01 2.86e-01 2.31e-01
...
2.02e+01  1.03e-01 9.57e-01 6.34e-02 8.11e-01 2.83e-01 2.34e-01
...
2.19e+01  1.02e-01 9.59e-01 6.16e-02 8.27e-01 2.81e-01 2.37e-01
...
2.36e+01  1.02e-01 9.60e-01 6.03e-02 8.41e-01 2.79e-01 2.40e-01
...
2.53e+01  1.01e-01 9.61e-01 5.92e-02 8.53e-01 2.77e-01 2.42e-01
...
2.70e+01  1.01e-01 9.61e-01 5.84e-02 8.62e-01 2.76e-01 2.43e-01
...
2.86e+01  1.01e-01 9.62e-01 5.77e-02 8.70e-01 2.76e-01 2.45e-01
...
3.03e+01  1.00e-01 9.62e-01 5.71e-02 8.77e-01 2.75e-01 2.46e-01
...
3.20e+01  1.00e-01 9.63e-01 5.67e-02 8.82e-01 2.74e-01 2.47e-01
...
3.37e+01  9.99e-02 9.63e-01 5.63e-02 8.87e-01 2.74e-01 2.47e-01
...
3.54e+01  9.98e-02 9.63e-01 5.60e-02 8.91e-01 2.73e-01 2.48e-01
...
3.71e+01  9.97e-02 9.64e-01 5.57e-02 8.94e-01 2.73e-01 2.49e-01
...
3.87e+01  9.96e-02 9.64e-01 5.55e-02 8.96e-01 2.73e-01 2.49e-01
...
4.04e+01  9.95e-02 9.64e-01 5.54e-02 8.98e-01 2.73e-01 2.49e-01
...
4.21e+01  9.94e-02 9.64e-01 5.52e-02 9.00e-01 2.73e-01 2.50e-01
...
4.38e+01  9.94e-02 9.64e-01 5.51e-02 9.02e-01 2.72e-01 2.50e-01
...
4.55e+01  9.93e-02 9.64e-01 5.50e-02 9.03e-01 2.72e-01 2.50e-01
...
4.72e+01  9.93e-02 9.64e-01 5.49e-02 9.04e-01 2.72e-01 2.50e-01
...
4.89e+01  9.93e-02 9.64e-01 5.49e-02 9.05e-01 2.72e-01 2.50e-01
...
5.05e+01  9.93e-02 9.64e-01 5.48e-02 9.06e-01 2.72e-01 2.50e-01
...
5.22e+01  9.92e-02 9.64e-01 5.48e-02 9.06e-01 2.72e-01 2.50e-01
...
5.39e+01  9.92e-02 9.64e-01 5.47e-02 9.07e-01 2.72e-01 2.50e-01
...
5.56e+01  9.92e-02 9.65e-01 5.47e-02 9.07e-01 2.72e-01 2.51e-01
...
5.73e+01  9.92e-02 9.65e-01 5.47e-02 9.07e-01 2.72e-01 2.51e-01
...
5.90e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.06e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.23e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.40e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.57e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.74e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
6.91e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.08e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.24e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.41e+01  9.92e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.58e+01  9.92e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.75e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.92e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.09e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.30e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01

## 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_5)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results)

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


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



# Iteration 6
## Thoughts

The system again returns to the same steady-state concentrations for all species, regardless of the initial condition (here, `id_smxa` started at 1, all others at 0). This confirms that the system is globally stable and that each species is being driven toward a fixed point, likely by external sources and/or sinks. The transient dynamics differ, but the endpoint is invariant.

Given this, the most parsimonious explanation is that each species is produced from an external source and possibly degraded, with little or no interconversion between species. However, the transient overshoots and the time to half-max suggest there may be some interconversion or feedback, or at least that the production/degradation rates differ.

To test for possible interconversion, I will set the initial concentration of one of the minor species (e.g., `id_q2yx`) to a high value (e.g., 1), with all others at 0, and observe if it is converted into other species or simply decays to its steady-state value.

## Action

### Experiment

```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_k8mo": 0.0,
        "id_smxa": 0.0,
        "id_q2yx": 1.0,
        "id_9wyg": 0.0,
        "id_piw6": 0.0,
        "id_xee0": 0.0
    }
}
```
# Observation

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

Total size: 4189 rows × 7 columns. 

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

Time   id_k8mo  id_smxa  id_q2yx  id_9wyg  id_piw6  id_xee0
0         0        0 1.00e+00        0        0        0
...
1.68e+00  6.89e-01 3.90e-02 4.42e+00 1.54e-01 4.25e-02 7.43e-03
...
3.37e+00  1.65e+00 1.39e-01 3.59e+00 2.82e-01 5.56e-01 8.44e-03
...
5.05e+00  1.69e+00 2.70e-01 1.53e+00 3.88e-01 3.54e+00 1.34e-02
...
6.74e+00  4.22e-01 4.08e-01 6.43e-04 4.76e-01 4.73e+00 3.39e-01
...
8.42e+00  7.89e-02 5.37e-01 1.01e-03 5.49e-01 2.60e+00 4.04e-01
...
1.01e+01  1.92e-02 6.46e-01 1.60e-02 6.10e-01 2.55e-01 3.89e-01
...
1.18e+01  9.98e-02 7.33e-01 1.15e-01 6.61e-01 1.63e-01 2.23e-01
...
1.35e+01  1.41e-01 8.00e-01 1.00e-01 7.03e-01 3.15e-01 1.86e-01
...
1.52e+01  1.25e-01 8.49e-01 7.77e-02 7.38e-01 3.14e-01 2.05e-01
...
1.68e+01  1.14e-01 8.85e-01 7.23e-02 7.67e-01 2.91e-01 2.19e-01
...
1.85e+01  1.10e-01 9.10e-01 6.84e-02 7.91e-01 2.87e-01 2.25e-01
...
2.02e+01  1.07e-01 9.27e-01 6.49e-02 8.11e-01 2.84e-01 2.31e-01
...
2.19e+01  1.05e-01 9.39e-01 6.26e-02 8.27e-01 2.81e-01 2.35e-01
...
2.36e+01  1.03e-01 9.47e-01 6.09e-02 8.41e-01 2.79e-01 2.39e-01
...
2.53e+01  1.02e-01 9.52e-01 5.96e-02 8.53e-01 2.78e-01 2.41e-01
...
2.70e+01  1.01e-01 9.56e-01 5.86e-02 8.62e-01 2.76e-01 2.43e-01
...
2.86e+01  1.01e-01 9.59e-01 5.78e-02 8.70e-01 2.76e-01 2.44e-01
...
3.03e+01  1.01e-01 9.60e-01 5.72e-02 8.77e-01 2.75e-01 2.46e-01
...
3.20e+01  1.00e-01 9.61e-01 5.67e-02 8.82e-01 2.74e-01 2.47e-01
...
3.37e+01  1.00e-01 9.62e-01 5.63e-02 8.87e-01 2.74e-01 2.47e-01
...
3.54e+01  9.98e-02 9.63e-01 5.60e-02 8.91e-01 2.73e-01 2.48e-01
...
3.71e+01  9.97e-02 9.63e-01 5.57e-02 8.94e-01 2.73e-01 2.48e-01
...
3.87e+01  9.96e-02 9.64e-01 5.55e-02 8.96e-01 2.73e-01 2.49e-01
...
4.04e+01  9.95e-02 9.64e-01 5.54e-02 8.98e-01 2.73e-01 2.49e-01
...
4.21e+01  9.94e-02 9.64e-01 5.52e-02 9.00e-01 2.73e-01 2.50e-01
...
4.38e+01  9.94e-02 9.64e-01 5.51e-02 9.02e-01 2.72e-01 2.50e-01
...
4.55e+01  9.94e-02 9.64e-01 5.50e-02 9.03e-01 2.72e-01 2.50e-01
...
4.72e+01  9.93e-02 9.64e-01 5.49e-02 9.04e-01 2.72e-01 2.50e-01
...
4.89e+01  9.93e-02 9.64e-01 5.49e-02 9.05e-01 2.72e-01 2.50e-01
...
5.05e+01  9.93e-02 9.64e-01 5.48e-02 9.06e-01 2.72e-01 2.50e-01
...
5.22e+01  9.92e-02 9.64e-01 5.48e-02 9.06e-01 2.72e-01 2.50e-01
...
5.39e+01  9.92e-02 9.64e-01 5.47e-02 9.07e-01 2.72e-01 2.50e-01
...
5.56e+01  9.92e-02 9.65e-01 5.47e-02 9.07e-01 2.72e-01 2.51e-01
...
5.73e+01  9.92e-02 9.65e-01 5.47e-02 9.07e-01 2.72e-01 2.51e-01
...
5.90e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.06e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.23e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.40e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.57e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.74e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
6.91e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.08e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.24e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.41e+01  9.92e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.58e+01  9.92e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.75e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.92e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.09e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.30e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01

## 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_5, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results)

### 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

Once again, the system returns to the same steady-state concentrations for all species, regardless of the initial condition (here, `id_q2yx` started at 1, all others at 0). However, the transient dynamics show that `id_q2yx` initially increases to a much higher value before decaying to its steady-state, and other species (e.g., `id_k8mo`, `id_piw6`) also show transient increases. This suggests that there may be some interconversion between species, or at least that the production/degradation rates are coupled.

Given the strong homeostatic behavior and the transient overshoots, the most likely model is that each species is produced from an external source and degraded, possibly with some weak interconversion between species. To test for direct interconversion, I will set two species to high initial concentrations and the rest to zero, and observe if the system still returns to the same steady state and if there are any notable transient effects.

## Action

### Experiment

```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_k8mo": 1.0,
        "id_smxa": 1.0,
        "id_q2yx": 0.0,
        "id_9wyg": 0.0,
        "id_piw6": 0.0,
        "id_xee0": 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: 4189 rows × 7 columns. 

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

Time   id_k8mo  id_smxa  id_q2yx  id_9wyg  id_piw6  id_xee0
0  1.00e+00 1.00e+00        0        0        0        0
...
1.68e+00  1.99e-01 9.84e-01 7.33e-04 1.54e-01 4.62e+00 3.07e-01
...
3.37e+00  3.72e-02 9.70e-01 1.05e-03 2.82e-01 2.54e+00 4.02e-01
...
5.05e+00  1.08e-02 9.60e-01 2.31e-02 3.88e-01 1.91e-01 3.81e-01
...
6.74e+00  8.57e-02 9.53e-01 1.43e-01 4.76e-01 1.83e-01 2.04e-01
...
8.42e+00  1.33e-01 9.50e-01 1.26e-01 5.49e-01 3.59e-01 1.64e-01
...
1.01e+01  1.23e-01 9.49e-01 9.28e-02 6.10e-01 3.54e-01 1.84e-01
...
1.18e+01  1.13e-01 9.49e-01 8.33e-02 6.61e-01 3.13e-01 2.03e-01
...
1.35e+01  1.10e-01 9.51e-01 7.76e-02 7.03e-01 3.03e-01 2.11e-01
...
1.52e+01  1.08e-01 9.52e-01 7.21e-02 7.38e-01 2.96e-01 2.19e-01
...
1.68e+01  1.06e-01 9.54e-01 6.83e-02 7.67e-01 2.90e-01 2.26e-01
...
1.85e+01  1.04e-01 9.56e-01 6.55e-02 7.91e-01 2.86e-01 2.31e-01
...
2.02e+01  1.03e-01 9.57e-01 6.33e-02 8.11e-01 2.83e-01 2.34e-01
...
2.19e+01  1.02e-01 9.59e-01 6.16e-02 8.27e-01 2.81e-01 2.37e-01
...
2.36e+01  1.02e-01 9.60e-01 6.03e-02 8.41e-01 2.79e-01 2.40e-01
...
2.53e+01  1.01e-01 9.61e-01 5.92e-02 8.53e-01 2.77e-01 2.42e-01
...
2.70e+01  1.01e-01 9.61e-01 5.84e-02 8.62e-01 2.76e-01 2.43e-01
...
2.86e+01  1.01e-01 9.62e-01 5.77e-02 8.70e-01 2.76e-01 2.45e-01
...
3.03e+01  1.00e-01 9.62e-01 5.71e-02 8.77e-01 2.75e-01 2.46e-01
...
3.20e+01  1.00e-01 9.63e-01 5.67e-02 8.82e-01 2.74e-01 2.47e-01
...
3.37e+01  9.99e-02 9.63e-01 5.63e-02 8.87e-01 2.74e-01 2.47e-01
...
3.54e+01  9.98e-02 9.63e-01 5.60e-02 8.91e-01 2.73e-01 2.48e-01
...
3.71e+01  9.97e-02 9.64e-01 5.57e-02 8.94e-01 2.73e-01 2.49e-01
...
3.87e+01  9.96e-02 9.64e-01 5.55e-02 8.96e-01 2.73e-01 2.49e-01
...
4.04e+01  9.95e-02 9.64e-01 5.54e-02 8.98e-01 2.73e-01 2.49e-01
...
4.21e+01  9.94e-02 9.64e-01 5.52e-02 9.00e-01 2.73e-01 2.50e-01
...
4.38e+01  9.94e-02 9.64e-01 5.51e-02 9.02e-01 2.72e-01 2.50e-01
...
4.55e+01  9.93e-02 9.64e-01 5.50e-02 9.03e-01 2.72e-01 2.50e-01
...
4.72e+01  9.93e-02 9.64e-01 5.49e-02 9.04e-01 2.72e-01 2.50e-01
...
4.89e+01  9.93e-02 9.64e-01 5.49e-02 9.05e-01 2.72e-01 2.50e-01
...
5.05e+01  9.93e-02 9.64e-01 5.48e-02 9.06e-01 2.72e-01 2.50e-01
...
5.22e+01  9.92e-02 9.64e-01 5.48e-02 9.06e-01 2.72e-01 2.50e-01
...
5.39e+01  9.92e-02 9.64e-01 5.47e-02 9.07e-01 2.72e-01 2.50e-01
...
5.56e+01  9.92e-02 9.65e-01 5.47e-02 9.07e-01 2.72e-01 2.51e-01
...
5.73e+01  9.92e-02 9.65e-01 5.47e-02 9.07e-01 2.72e-01 2.51e-01
...
5.90e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.06e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.23e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.40e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.57e+01  9.92e-02 9.65e-01 5.46e-02 9.08e-01 2.72e-01 2.51e-01
...
6.74e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
6.91e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.08e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.24e+01  9.92e-02 9.65e-01 5.46e-02 9.09e-01 2.72e-01 2.51e-01
...
7.41e+01  9.92e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.58e+01  9.92e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.75e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.92e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.09e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.30e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01

## 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_5, iteration_6, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results)

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


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



# Iteration 8
## Thoughts

The system continues to show strong homeostatic behavior: regardless of the initial concentrations of two species (`id_k8mo` and `id_smxa` at 1, others at 0), all species return to the same steady-state values as in previous experiments. The transient dynamics show that some species can overshoot or undershoot, but the endpoint is always the same.

This pattern is consistent with a model where each species is produced from an external source and degraded, with little or no interconversion. The transient overshoots could be explained by fast initial production or decay, but the lack of persistent changes in other species suggests that interconversion is minimal or absent.

To further test for possible interconversion, I will set all species to high initial concentrations (e.g., 1) and observe if the system still returns to the same steady state. If so, this would strongly support the hypothesis of independent production and degradation for each species.

## Action

### Experiment

```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_k8mo": 1.0,
        "id_smxa": 1.0,
        "id_q2yx": 1.0,
        "id_9wyg": 1.0,
        "id_piw6": 1.0,
        "id_xee0": 1.0
    }
}
```
# 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: 4189 rows × 7 columns. 

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

Time   id_k8mo  id_smxa  id_q2yx  id_9wyg  id_piw6  id_xee0
0  1.00e+00 1.00e+00 1.00e+00 1.00e+00 1.00e+00 1.00e+00
...
1.68e+00  2.42e-01 9.87e-01 3.42e-04 9.85e-01 6.64e+00 4.43e-01
...
3.37e+00  4.58e-02 9.79e-01 6.49e-04 9.72e-01 3.86e+00 4.11e-01
...
5.05e+00  1.06e-02 9.74e-01 2.13e-03 9.61e-01 1.32e+00 4.05e-01
...
6.74e+00  6.91e-02 9.71e-01 6.99e-02 9.52e-01 1.38e-01 2.88e-01
...
8.42e+00  1.05e-01 9.69e-01 5.19e-02 9.45e-01 2.91e-01 2.49e-01
...
1.01e+01  9.68e-02 9.68e-01 5.14e-02 9.39e-01 2.67e-01 2.57e-01
...
1.18e+01  9.83e-02 9.67e-01 5.30e-02 9.34e-01 2.69e-01 2.54e-01
...
1.35e+01  9.85e-02 9.66e-01 5.29e-02 9.30e-01 2.70e-01 2.54e-01
...
1.52e+01  9.86e-02 9.66e-01 5.32e-02 9.26e-01 2.70e-01 2.53e-01
...
1.68e+01  9.87e-02 9.66e-01 5.35e-02 9.23e-01 2.71e-01 2.53e-01
...
1.85e+01  9.88e-02 9.65e-01 5.36e-02 9.21e-01 2.71e-01 2.53e-01
...
2.02e+01  9.88e-02 9.65e-01 5.38e-02 9.19e-01 2.71e-01 2.52e-01
...
2.19e+01  9.89e-02 9.65e-01 5.39e-02 9.17e-01 2.71e-01 2.52e-01
...
2.36e+01  9.89e-02 9.65e-01 5.40e-02 9.16e-01 2.71e-01 2.52e-01
...
2.53e+01  9.90e-02 9.65e-01 5.41e-02 9.15e-01 2.71e-01 2.52e-01
...
2.70e+01  9.90e-02 9.65e-01 5.42e-02 9.14e-01 2.71e-01 2.52e-01
...
2.86e+01  9.90e-02 9.65e-01 5.42e-02 9.13e-01 2.71e-01 2.51e-01
...
3.03e+01  9.90e-02 9.65e-01 5.43e-02 9.12e-01 2.72e-01 2.51e-01
...
3.20e+01  9.91e-02 9.65e-01 5.43e-02 9.12e-01 2.72e-01 2.51e-01
...
3.37e+01  9.91e-02 9.65e-01 5.44e-02 9.11e-01 2.72e-01 2.51e-01
...
3.54e+01  9.91e-02 9.65e-01 5.44e-02 9.11e-01 2.72e-01 2.51e-01
...
3.71e+01  9.91e-02 9.65e-01 5.44e-02 9.11e-01 2.72e-01 2.51e-01
...
3.87e+01  9.91e-02 9.65e-01 5.44e-02 9.10e-01 2.72e-01 2.51e-01
...
4.04e+01  9.91e-02 9.65e-01 5.44e-02 9.10e-01 2.72e-01 2.51e-01
...
4.21e+01  9.91e-02 9.65e-01 5.45e-02 9.10e-01 2.72e-01 2.51e-01
...
4.38e+01  9.91e-02 9.65e-01 5.45e-02 9.10e-01 2.72e-01 2.51e-01
...
4.55e+01  9.91e-02 9.65e-01 5.45e-02 9.10e-01 2.72e-01 2.51e-01
...
4.72e+01  9.91e-02 9.65e-01 5.45e-02 9.10e-01 2.72e-01 2.51e-01
...
4.89e+01  9.91e-02 9.65e-01 5.45e-02 9.10e-01 2.72e-01 2.51e-01
...
5.05e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
5.22e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
5.39e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
5.56e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
5.73e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
5.90e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
6.06e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
6.23e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
6.40e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
6.57e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
6.74e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
6.91e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.08e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.24e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.41e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.58e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.75e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
7.92e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.09e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01
...
8.30e+01  9.91e-02 9.65e-01 5.45e-02 9.09e-01 2.72e-01 2.51e-01

## 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_5, iteration_6, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results)

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


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



# Iteration 9
## Thoughts

The system is extremely robust: regardless of the initial concentrations of all species (all set to 1), the system always returns to the same steady-state values for each species. This is strong evidence that each species is independently produced from an external source and degraded, with little or no interconversion between species. The transient overshoots and undershoots are likely due to differences in production and degradation rates, not interconversion.

Given this, the most plausible minimal model is:
- Each species is produced from an external source (zero-order or constant rate).
- Each species is degraded (first-order decay).
- There is no significant interconversion between species.

To confirm this, I will analyze the time series for each species to estimate the production and degradation rates. If the time courses fit a simple production-degradation model, this will support the hypothesis.

## Action

### Code

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

# Use the experiment with all species starting at 0 (iteration_2) for cleanest fit
df = experiment_history['iteration_2']

# Fit each species to a simple ODE: dX/dt = k_prod - k_deg * X
# Use early time points to estimate k_prod, and late time points to estimate k_deg

fit_results = {}

for species in ['id_k8mo', 'id_smxa', 'id_q2yx', 'id_9wyg', 'id_piw6', 'id_xee0']:
    t = df['Time'].values
    x = df[species].values

    # Estimate k_deg from late time points (steady state: k_prod = k_deg * X_ss)
    X_ss = np.mean(x[-10:])
    # Estimate k_prod from early slope (first 10 time points)
    dt = t[1] - t[0]
    dxdt_early = (x[1:11] - x[0:10]) / dt
    k_prod_est = np.mean(dxdt_early)
    # Estimate k_deg = k_prod / X_ss
    k_deg_est = k_prod_est / X_ss if X_ss > 0 else np.nan

    fit_results[species] = {
        'X_ss': X_ss,
        'k_prod_est': k_prod_est,
        'k_deg_est': k_deg_est
    }

print("Production and degradation rate estimates for each species:")
for species, vals in fit_results.items():
    print(f"{species}: steady-state={vals['X_ss']:.4f}, k_prod~{vals['k_prod_est']:.4e}, k_deg~{vals['k_deg_est']:.4e}")

shared_variables.add("fit_results", fit_results)
```
# Observation

## Code Stdout
Production and degradation rate estimates for each species:
id_k8mo: steady-state=0.0991, k_prod~1.1621e-02, k_deg~1.1721e-01
id_smxa: steady-state=0.9646, k_prod~2.9485e-03, k_deg~3.0566e-03
id_q2yx: steady-state=0.0545, k_prod~4.2703e+00, k_deg~7.8301e+01
id_9wyg: steady-state=0.9090, k_prod~9.8918e-02, k_deg~1.0882e-01
id_piw6: steady-state=0.2718, k_prod~2.1184e-06, k_deg~7.7929e-06
id_xee0: steady-state=0.2508, k_prod~8.1319e-02, k_deg~3.2420e-01

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_5, iteration_6, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results, fit_results)

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


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



# Iteration 10
## Thoughts

The estimated production and degradation rates for each species support the hypothesis that each species is produced from an external source and degraded independently:
- The steady-state concentrations, production rates, and degradation rates are consistent with the simple ODE: \( dX/dt = k_{prod} - k_{deg} \cdot X \).
- The values of \( k_{prod} \) and \( k_{deg} \) differ widely between species, explaining the different steady-state levels and transient dynamics.
- There is no evidence of significant interconversion between species, as the system always returns to the same steady state regardless of initial conditions.

The next step is to construct an SBML model with the following for each species:
- A zero-order production reaction (external source).
- A first-order degradation reaction.

I will implement this minimal model using libSBML.

## Action

### Code

```python
import libsbml

# Use the fit results from previous analysis
fit_results = shared_variables.access("fit_results")

# Start from the input SBML string
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Remove any existing reactions (if any)
while model.getNumReactions() > 0:
    model.removeReaction(0)

# Add production and degradation reactions for each species
for species_id, params in fit_results.items():
    # Production reaction: --> species
    prod_rxn = model.createReaction()
    prod_rxn.setId(f"prod_{species_id}")
    prod_rxn.setReversible(False)
    prod_rxn.setFast(False)
    # Product
    prod_product = prod_rxn.createProduct()
    prod_product.setSpecies(species_id)
    prod_product.setStoichiometry(1.0)
    prod_product.setConstant(True)
    # Kinetic law (zero-order)
    klaw_prod = prod_rxn.createKineticLaw()
    param_prod = klaw_prod.createParameter()
    param_prod.setId(f"k_prod_{species_id}")
    param_prod.setValue(params['k_prod_est'])
    klaw_prod.setFormula(f"k_prod_{species_id}")

    # Degradation reaction: species -->
    deg_rxn = model.createReaction()
    deg_rxn.setId(f"deg_{species_id}")
    deg_rxn.setReversible(False)
    deg_rxn.setFast(False)
    # Reactant
    deg_reactant = deg_rxn.createReactant()
    deg_reactant.setSpecies(species_id)
    deg_reactant.setStoichiometry(1.0)
    deg_reactant.setConstant(False)
    # Kinetic law (first-order)
    klaw_deg = deg_rxn.createKineticLaw()
    param_deg = klaw_deg.createParameter()
    param_deg.setId(f"k_deg_{species_id}")
    param_deg.setValue(params['k_deg_est'])
    klaw_deg.setFormula(f"k_deg_{species_id}*{species_id}")

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

# Print the updated SBML for review
print(updated_sbml)

# Save for possible submission
shared_variables.add("candidate_sbml", updated_sbml)
```

# Observation

## Code Stdout
<?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level2/version4" level="2" version="4">
  <model id="id_gs9e">
    <listOfUnitDefinitions>
      <unitDefinition id="id_y5me">
        <listOfUnits>
          <unit kind="second" exponent="1" scale="0" multiplier="3600"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_yufe" spatialDimensions="3" size="1" constant="true"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_k8mo" compartment="id_yufe" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_smxa" compartment="id_yufe" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_q2yx" compartment="id_yufe" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_9wyg" compartment="id_yufe" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_piw6" compartment="id_yufe" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_xee0" compartment="id_yufe" initialConcentration="0.999999999999971" boundaryCondition="false" constant="false"/>
    </listOfSpecies>
    <listOfReactions>
      <reaction id="prod_id_k8mo" reversible="false" fast="false">
        <listOfProducts>
          <speciesReference species="id_k8mo" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <ci> k_prod_id_k8mo </ci>
          </math>
          <listOfParameters>
            <parameter id="k_prod_id_k8mo" value="0.0116208488102044"/>
          </listOfParameters>
        </kineticLaw>
      </reaction>
      <reaction id="deg_id_k8mo" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_k8mo" stoichiometry="1"/>
        </listOfReactants>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k_deg_id_k8mo </ci>
              <ci> id_k8mo </ci>
            </apply>
          </math>
          <listOfParameters>
            <parameter id="k_deg_id_k8mo" value="0.117208471459942"/>
          </listOfParameters>
        </kineticLaw>
      </reaction>
      <reaction id="prod_id_smxa" reversible="false" fast="false">
        <listOfProducts>
          <speciesReference species="id_smxa" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <ci> k_prod_id_smxa </ci>
          </math>
          <listOfParameters>
            <parameter id="k_prod_id_smxa" value="0.00294847963029535"/>
          </listOfParameters>
        </kineticLaw>
      </reaction>
      <reaction id="deg_id_smxa" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_smxa" stoichiometry="1"/>
        </listOfReactants>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k_deg_id_smxa </ci>
              <ci> id_smxa </ci>
            </apply>
          </math>
          <listOfParameters>
            <parameter id="k_deg_id_smxa" value="0.00305660992799834"/>
          </listOfParameters>
        </kineticLaw>
      </reaction>
      <reaction id="prod_id_q2yx" reversible="false" fast="false">
        <listOfProducts>
          <speciesReference species="id_q2yx" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <ci> k_prod_id_q2yx </ci>
          </math>
          <listOfParameters>
            <parameter id="k_prod_id_q2yx" value="4.27027890905162"/>
          </listOfParameters>
        </kineticLaw>
      </reaction>
      <reaction id="deg_id_q2yx" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_q2yx" stoichiometry="1"/>
        </listOfReactants>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k_deg_id_q2yx </ci>
              <ci> id_q2yx </ci>
            </apply>
          </math>
          <listOfParameters>
            <parameter id="k_deg_id_q2yx" value="78.3012727475991"/>
          </listOfParameters>
        </kineticLaw>
      </reaction>
      <reaction id="prod_id_9wyg" reversible="false" fast="false">
        <listOfProducts>
          <speciesReference species="id_9wyg" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <ci> k_prod_id_9wyg </ci>
          </math>
          <listOfParameters>
            <parameter id="k_prod_id_9wyg" value="0.0989178588597301"/>
          </listOfParameters>
        </kineticLaw>
      </reaction>
      <reaction id="deg_id_9wyg" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_9wyg" stoichiometry="1"/>
        </listOfReactants>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k_deg_id_9wyg </ci>
              <ci> id_9wyg </ci>
            </apply>
          </math>
          <listOfParameters>
            <parameter id="k_deg_id_9wyg" value="0.108821553882444"/>
          </listOfParameters>
        </kineticLaw>
      </reaction>
      <reaction id="prod_id_piw6" reversible="false" fast="false">
        <listOfProducts>
          <speciesReference species="id_piw6" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <ci> k_prod_id_piw6 </ci>
          </math>
          <listOfParameters>
            <parameter id="k_prod_id_piw6" value="2.11835384012093e-06"/>
          </listOfParameters>
        </kineticLaw>
      </reaction>
      <reaction id="deg_id_piw6" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_piw6" stoichiometry="1"/>
        </listOfReactants>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k_deg_id_piw6 </ci>
              <ci> id_piw6 </ci>
            </apply>
          </math>
          <listOfParameters>
            <parameter id="k_deg_id_piw6" value="7.79290466241517e-06"/>
          </listOfParameters>
        </kineticLaw>
      </reaction>
      <reaction id="prod_id_xee0" reversible="false" fast="false">
        <listOfProducts>
          <speciesReference species="id_xee0" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <ci> k_prod_id_xee0 </ci>
          </math>
          <listOfParameters>
            <parameter id="k_prod_id_xee0" value="0.0813191583281228"/>
          </listOfParameters>
        </kineticLaw>
      </reaction>
      <reaction id="deg_id_xee0" reversible="false" fast="false">
        <listOfReactants>
          <speciesReference species="id_xee0" stoichiometry="1"/>
        </listOfReactants>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">
            <apply>
              <times/>
              <ci> k_deg_id_xee0 </ci>
              <ci> id_xee0 </ci>
            </apply>
          </math>
          <listOfParameters>
            <parameter id="k_deg_id_xee0" value="0.324201381914596"/>
          </listOfParameters>
        </kineticLaw>
      </reaction>
    </listOfReactions>
  </model>
</sbml>


## 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_5, iteration_6, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results, fit_results, candidate_sbml)

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


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



# Iteration 11
## Thoughts

The constructed SBML model now includes, for each species:
- A zero-order production reaction (external source).
- A first-order degradation reaction.

This matches the observed system behavior: robust return to steady state regardless of initial conditions, and no evidence of interconversion. The estimated parameters are based on the data and should reproduce the observed dynamics.

Before submitting, I should simulate this candidate model and compare its output to the experimental data, especially for the default and perturbed initial conditions. If the model matches well, it is likely complete. If not, further refinement may be needed.

## Action

### Code

```python
# Retrieve the candidate SBML model
candidate_sbml = shared_variables.access("candidate_sbml")

# Simulate the candidate model for the default initial condition
sim_df = simulate(candidate_sbml)

# Compare to the original experiment (iteration_0)
exp_df = experiment_history['iteration_0']

# Print a summary: steady-state values and first few time points for both
print("Simulated model steady-state (last 10 time points):")
print(sim_df.iloc[-10:].mean())
print("\nExperimental steady-state (last 10 time points):")
print(exp_df.iloc[-10:].mean())

print("\nSimulated model (first 5 time points):")
print(sim_df.head())

print("\nExperimental data (first 5 time points):")
print(exp_df.head())

# Save simulation for further analysis
shared_variables.add("sim_df", sim_df)
```
# Observation

## Code Stdout
Simulated model steady-state (last 10 time points):
id_k8mo     0.099141
id_smxa     0.215943
id_q2yx     0.054537
id_9wyg     0.908881
id_piw6     0.000176
id_xee0     0.250829
Time       82.910817
dtype: float64

Experimental steady-state (last 10 time points):
id_k8mo     0.099147
id_smxa     0.964624
id_q2yx     0.054537
id_9wyg     0.908991
id_piw6     0.271831
id_xee0     0.250829
Time       82.910817
dtype: float64

Simulated model (first 5 time points):
    id_k8mo   id_smxa   id_q2yx   id_9wyg       id_piw6   id_xee0      Time
0  0.000000  0.000000  0.000000  0.000000  0.000000e+00  1.000000  0.000000
1  0.000230  0.000058  0.042983  0.001958  4.198265e-08  0.995202  0.019819
2  0.000460  0.000117  0.052088  0.003912  8.396530e-08  0.990434  0.039637
3  0.000689  0.000175  0.054017  0.005862  1.259479e-07  0.985698  0.059456
4  0.000917  0.000234  0.054426  0.007808  1.679306e-07  0.980991  0.079274

Experimental data (first 5 time points):
        id_k8mo   id_smxa   id_q2yx   id_9wyg       id_piw6   id_xee0      Time
0  0.000000e+00  0.000000  0.000000  0.000000  0.000000e+00  1.000000  0.000000
1  5.107273e-08  0.000006  0.001962  0.001980  1.004311e-14  0.980508  0.019819
2  4.062643e-07  0.000024  0.003924  0.003955  6.214792e-13  0.961643  0.039637
3  1.363195e-06  0.000053  0.005885  0.005926  6.977448e-12  0.943367  0.059456
4  3.212532e-06  0.000094  0.007845  0.007893  3.843889e-11  0.925646  0.079274

## 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_5, iteration_6, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results, fit_results, candidate_sbml, sim_df)

### 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 simulated model matches the experimental steady-state values well for most species, but there are significant discrepancies for `id_smxa` and `id_piw6`:
- `id_smxa` (simulated: 0.22, experimental: 0.96)
- `id_piw6` (simulated: 0.00018, experimental: 0.27)

Other species (`id_k8mo`, `id_q2yx`, `id_9wyg`, `id_xee0`) are well matched. This suggests that the simple production-degradation model is insufficient for `id_smxa` and `id_piw6`. The large difference for `id_smxa` (the most abundant species at steady state) and the very low simulated value for `id_piw6` (vs. a substantial experimental value) suggest that there may be additional reactions, possibly:
- Interconversion between species (e.g., `id_piw6` or `id_smxa` produced from another species)
- Nonlinear production or degradation (e.g., autocatalysis or inhibition)

To investigate, I will analyze the time derivatives and correlations between `id_smxa`, `id_piw6`, and the other species to look for evidence of interconversion or nonlinear effects.

## Action

### Code

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

# Use the experiment with all species starting at 0 (iteration_2)
df = experiment_history['iteration_2']

# Compute time derivatives for all species
dt = df['Time'].diff().values[1:]
derivs = {}
for species in ['id_k8mo', 'id_smxa', 'id_q2yx', 'id_9wyg', 'id_piw6', 'id_xee0']:
    dx = df[species].diff().values[1:]
    derivs[species] = dx / dt

# Correlate d(id_smxa)/dt and d(id_piw6)/dt with other species' concentrations
corrs_smxa = {}
corrs_piw6 = {}
for species in ['id_k8mo', 'id_q2yx', 'id_9wyg', 'id_piw6', 'id_xee0']:
    corrs_smxa[species] = np.corrcoef(derivs['id_smxa'], df[species].values[1:])[0,1]
    corrs_piw6[species] = np.corrcoef(derivs['id_piw6'], df[species].values[1:])[0,1]

print("Correlation of d(id_smxa)/dt with other species:")
print(corrs_smxa)
print("\nCorrelation of d(id_piw6)/dt with other species:")
print(corrs_piw6)
```
# Observation

## Code Stdout
Correlation of d(id_smxa)/dt with other species:
{'id_k8mo': np.float64(0.6875710000860629), 'id_q2yx': np.float64(0.531473137425847), 'id_9wyg': np.float64(-0.8100547740933474), 'id_piw6': np.float64(0.6836710094510997), 'id_xee0': np.float64(-0.32400509993990095)}

Correlation of d(id_piw6)/dt with other species:
{'id_k8mo': np.float64(0.6466800969613187), 'id_q2yx': np.float64(0.380826677071971), 'id_9wyg': np.float64(-0.13884390270390645), 'id_piw6': np.float64(0.0018078249310882499), 'id_xee0': np.float64(-0.7067443090346053)}

## 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_5, iteration_6, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results, fit_results, candidate_sbml, sim_df)

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


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



# Iteration 13
## Thoughts

The correlations reveal important clues:
- The rate of change of `id_smxa` (`d(id_smxa)/dt`) is **strongly positively correlated** with `id_k8mo`, `id_q2yx`, and `id_piw6`, and **strongly negatively correlated** with `id_9wyg`. This suggests that `id_smxa` may be produced from or with the help of `id_k8mo`, `id_q2yx`, and `id_piw6`, and/or is consumed to make `id_9wyg`.
- The rate of change of `id_piw6` (`d(id_piw6)/dt`) is **strongly positively correlated** with `id_k8mo` and `id_q2yx`, and **strongly negatively correlated** with `id_xee0`. This suggests that `id_piw6` may be produced from `id_k8mo` and `id_q2yx`, and/or is consumed to make `id_xee0`.

The strong positive correlations between `d(id_smxa)/dt` and `id_piw6`, and between `d(id_piw6)/dt` and `id_k8mo`, suggest a possible reaction chain or network:
- `id_k8mo` and `id_q2yx` may be precursors for `id_piw6`, which in turn may be a precursor for `id_smxa`.
- The negative correlation with `id_9wyg` for `id_smxa` suggests a conversion or competition.

Given the high steady-state value of `id_smxa` in the data (but not in the model), a plausible missing reaction is the conversion of `id_piw6` to `id_smxa`. I will add a reaction: `id_piw6` → `id_smxa` (first-order), and refit the model.

## Action

### Code

```python
import libsbml

# Retrieve the candidate SBML model
candidate_sbml = shared_variables.access("candidate_sbml")
sbml_doc = libsbml.readSBMLFromString(candidate_sbml)
model = sbml_doc.getModel()

# Add a conversion reaction: id_piw6 --> id_smxa
reaction = model.createReaction()
reaction.setId("conv_piw6_to_smxa")
reaction.setReversible(False)
reaction.setFast(False)

# Reactant: id_piw6
reactant = reaction.createReactant()
reactant.setSpecies("id_piw6")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)

# Product: id_smxa
product = reaction.createProduct()
product.setSpecies("id_smxa")
product.setStoichiometry(1.0)
product.setConstant(True)

# Kinetic law: k_conv * id_piw6 (guess a rate constant, e.g., 0.1)
klaw = reaction.createKineticLaw()
param = klaw.createParameter()
param.setId("k_conv_piw6_smxa")
param.setValue(0.1)
klaw.setFormula("k_conv_piw6_smxa*id_piw6")

# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml2 = writer.writeSBMLToString(sbml_doc)

# Simulate and compare to experiment
sim_df2 = simulate(updated_sbml2)
exp_df = experiment_history['iteration_0']

print("Simulated model with piw6->smxa conversion (steady-state, last 10 time points):")
print(sim_df2.iloc[-10:].mean())
print("\nExperimental steady-state (last 10 time points):")
print(exp_df.iloc[-10:].mean())

# Save for further analysis
shared_variables.add("updated_sbml2", updated_sbml2)
shared_variables.add("sim_df2", sim_df2)
```
# Observation

## Code Stdout
Simulated model with piw6->smxa conversion (steady-state, last 10 time points):
id_k8mo     0.099141
id_smxa     0.216082
id_q2yx     0.054537
id_9wyg     0.908881
id_piw6     0.000021
id_xee0     0.250829
Time       82.910817
dtype: float64

Experimental steady-state (last 10 time points):
id_k8mo     0.099147
id_smxa     0.964624
id_q2yx     0.054537
id_9wyg     0.908991
id_piw6     0.271831
id_xee0     0.250829
Time       82.910817
dtype: float64

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_5, iteration_6, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results, fit_results, candidate_sbml, sim_df, updated_sbml2, sim_df2)

### 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 the conversion reaction `id_piw6` → `id_smxa` (with a rate constant of 0.1) did not significantly increase the steady-state value of `id_smxa` (still ~0.22 vs. experimental ~0.96), nor did it rescue the low value of `id_piw6` (now even lower). This suggests that the simple conversion is not sufficient to explain the high steady-state of `id_smxa` and the substantial value of `id_piw6`.

Given the strong positive correlation between `d(id_smxa)/dt` and `id_piw6`, `id_k8mo`, and `id_q2yx`, and the negative correlation with `id_9wyg`, it is possible that `id_smxa` is produced from a combination of these species, or that its production is autocatalytic (i.e., depends on its own concentration).

A plausible next step is to test for autocatalysis in `id_smxa` production. I will modify the production reaction for `id_smxa` to be first-order in `id_smxa` (autocatalytic), i.e., production rate = k * `id_smxa`, and see if this can account for the high steady-state value.

## Action

### Code

```python
import libsbml

# Start from the original candidate model (without piw6->smxa conversion)
candidate_sbml = shared_variables.access("candidate_sbml")
sbml_doc = libsbml.readSBMLFromString(candidate_sbml)
model = sbml_doc.getModel()

# Remove the existing production reaction for id_smxa
for i in range(model.getNumReactions()):
    rxn = model.getReaction(i)
    if rxn.getId() == "prod_id_smxa":
        model.removeReaction(i)
        break

# Add autocatalytic production: id_smxa --> 2 id_smxa (rate = k_auto * id_smxa)
reaction = model.createReaction()
reaction.setId("auto_prod_smxa")
reaction.setReversible(False)
reaction.setFast(False)

# Reactant: id_smxa
reactant = reaction.createReactant()
reactant.setSpecies("id_smxa")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)

# Product: id_smxa (2 produced, 1 consumed, net +1)
product = reaction.createProduct()
product.setSpecies("id_smxa")
product.setStoichiometry(2.0)
product.setConstant(True)

# Kinetic law: k_auto * id_smxa (guess k_auto = 0.1)
klaw = reaction.createKineticLaw()
param = klaw.createParameter()
param.setId("k_auto_smxa")
param.setValue(0.1)
klaw.setFormula("k_auto_smxa*id_smxa")

# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml3 = writer.writeSBMLToString(sbml_doc)

# Simulate and compare to experiment
sim_df3 = simulate(updated_sbml3)
exp_df = experiment_history['iteration_0']

print("Simulated model with autocatalytic smxa production (steady-state, last 10 time points):")
print(sim_df3.iloc[-10:].mean())
print("\nExperimental steady-state (last 10 time points):")
print(exp_df.iloc[-10:].mean())

# Save for further analysis
shared_variables.add("updated_sbml3", updated_sbml3)
shared_variables.add("sim_df3", sim_df3)
```
# Observation

## Code Stdout
Simulated model with autocatalytic smxa production (steady-state, last 10 time points):
id_k8mo     0.099141
id_smxa     0.000000
id_q2yx     0.054537
id_9wyg     0.908881
id_piw6     0.000176
id_xee0     0.250829
Time       82.910817
dtype: float64

Experimental steady-state (last 10 time points):
id_k8mo     0.099147
id_smxa     0.964624
id_q2yx     0.054537
id_9wyg     0.908991
id_piw6     0.271831
id_xee0     0.250829
Time       82.910817
dtype: float64

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_5, iteration_6, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results, fit_results, candidate_sbml, sim_df, updated_sbml2, sim_df2, updated_sbml3, sim_df3)

### 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 autocatalytic production model for `id_smxa` failed: the steady-state value of `id_smxa` dropped to zero, indicating that this mechanism is not responsible for the high steady-state observed in the experimental data. The simple production-degradation model also underestimates `id_smxa` and `id_piw6`.

Given the strong positive correlations between `d(id_smxa)/dt` and `id_k8mo`, `id_q2yx`, and `id_piw6`, and the negative correlation with `id_9wyg`, a plausible hypothesis is that `id_smxa` is produced from a combination of these species, possibly in a multi-substrate reaction or a network of conversions.

A reasonable next step is to try a reaction where `id_k8mo`, `id_q2yx`, and `id_piw6` are all reactants for the production of `id_smxa`. I will add a reaction: `id_k8mo + id_q2yx + id_piw6 → id_smxa` (with a guessed rate constant), and see if this improves the fit.

## Action

### Code

```python
import libsbml

# Start from the original candidate model (without previous failed modifications)
candidate_sbml = shared_variables.access("candidate_sbml")
sbml_doc = libsbml.readSBMLFromString(candidate_sbml)
model = sbml_doc.getModel()

# Add a multi-substrate conversion: id_k8mo + id_q2yx + id_piw6 --> id_smxa
reaction = model.createReaction()
reaction.setId("conv_k8mo_q2yx_piw6_to_smxa")
reaction.setReversible(False)
reaction.setFast(False)

# Reactants
for species in ["id_k8mo", "id_q2yx", "id_piw6"]:
    reactant = reaction.createReactant()
    reactant.setSpecies(species)
    reactant.setStoichiometry(1.0)
    reactant.setConstant(False)

# Product
product = reaction.createProduct()
product.setSpecies("id_smxa")
product.setStoichiometry(1.0)
product.setConstant(True)

# Kinetic law: k_conv * id_k8mo * id_q2yx * id_piw6 (guess k_conv = 10)
klaw = reaction.createKineticLaw()
param = klaw.createParameter()
param.setId("k_conv_k8mo_q2yx_piw6_smxa")
param.setValue(10.0)
klaw.setFormula("k_conv_k8mo_q2yx_piw6_smxa*id_k8mo*id_q2yx*id_piw6")

# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml4 = writer.writeSBMLToString(sbml_doc)

# Simulate and compare to experiment
sim_df4 = simulate(updated_sbml4)
exp_df = experiment_history['iteration_0']

print("Simulated model with k8mo+q2yx+piw6->smxa (steady-state, last 10 time points):")
print(sim_df4.iloc[-10:].mean())
print("\nExperimental steady-state (last 10 time points):")
print(exp_df.iloc[-10:].mean())

# Save for further analysis
shared_variables.add("updated_sbml4", updated_sbml4)
shared_variables.add("sim_df4", sim_df4)
```
# Observation

## Code Stdout
Simulated model with k8mo+q2yx+piw6->smxa (steady-state, last 10 time points):
id_k8mo     0.099123
id_smxa     0.216067
id_q2yx     0.054536
id_9wyg     0.908881
id_piw6     0.000039
id_xee0     0.250829
Time       82.910817
dtype: float64

Experimental steady-state (last 10 time points):
id_k8mo     0.099147
id_smxa     0.964624
id_q2yx     0.054537
id_9wyg     0.908991
id_piw6     0.271831
id_xee0     0.250829
Time       82.910817
dtype: float64

## 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_5, iteration_6, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results, fit_results, candidate_sbml, sim_df, updated_sbml2, sim_df2, updated_sbml3, sim_df3, updated_sbml4, sim_df4)

### 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

Adding a multi-substrate reaction (`id_k8mo + id_q2yx + id_piw6 → id_smxa`) did not significantly improve the steady-state value of `id_smxa` (still ~0.22 vs. experimental ~0.96), nor did it rescue the low value of `id_piw6`. This suggests that the missing mechanism is not a simple conversion from these three species.

Given the strong negative correlation between `d(id_smxa)/dt` and `id_9wyg`, and the fact that `id_9wyg` and `id_smxa` both reach high steady-state values, it is possible that there is a reversible reaction or a competitive relationship between these two species. Alternatively, the production of `id_smxa` may be inhibited by `id_9wyg`, or `id_9wyg` may be produced from `id_smxa`.

A plausible next step is to add a reversible reaction between `id_smxa` and `id_9wyg` (i.e., `id_smxa <-> id_9wyg`) and see if this improves the fit.

## Action

### Code

```python
import libsbml

# Start from the original candidate model
candidate_sbml = shared_variables.access("candidate_sbml")
sbml_doc = libsbml.readSBMLFromString(candidate_sbml)
model = sbml_doc.getModel()

# Add reversible reaction: id_smxa <-> id_9wyg
# Forward: id_smxa -> id_9wyg
rxn_fwd = model.createReaction()
rxn_fwd.setId("smxa_to_9wyg")
rxn_fwd.setReversible(False)
rxn_fwd.setFast(False)
reactant_fwd = rxn_fwd.createReactant()
reactant_fwd.setSpecies("id_smxa")
reactant_fwd.setStoichiometry(1.0)
reactant_fwd.setConstant(False)
product_fwd = rxn_fwd.createProduct()
product_fwd.setSpecies("id_9wyg")
product_fwd.setStoichiometry(1.0)
product_fwd.setConstant(True)
klaw_fwd = rxn_fwd.createKineticLaw()
param_fwd = klaw_fwd.createParameter()
param_fwd.setId("k_smxa_9wyg")
param_fwd.setValue(0.1)
klaw_fwd.setFormula("k_smxa_9wyg*id_smxa")

# Reverse: id_9wyg -> id_smxa
rxn_rev = model.createReaction()
rxn_rev.setId("9wyg_to_smxa")
rxn_rev.setReversible(False)
rxn_rev.setFast(False)
reactant_rev = rxn_rev.createReactant()
reactant_rev.setSpecies("id_9wyg")
reactant_rev.setStoichiometry(1.0)
reactant_rev.setConstant(False)
product_rev = rxn_rev.createProduct()
product_rev.setSpecies("id_smxa")
product_rev.setStoichiometry(1.0)
product_rev.setConstant(True)
klaw_rev = rxn_rev.createKineticLaw()
param_rev = klaw_rev.createParameter()
param_rev.setId("k_9wyg_smxa")
param_rev.setValue(0.1)
klaw_rev.setFormula("k_9wyg_smxa*id_9wyg")

# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml5 = writer.writeSBMLToString(sbml_doc)

# Simulate and compare to experiment
sim_df5 = simulate(updated_sbml5)
exp_df = experiment_history['iteration_0']

print("Simulated model with smxa <-> 9wyg (steady-state, last 10 time points):")
print(sim_df5.iloc[-10:].mean())
print("\nExperimental steady-state (last 10 time points):")
print(exp_df.iloc[-10:].mean())

# Save for further analysis
shared_variables.add("updated_sbml5", updated_sbml5)
shared_variables.add("sim_df5", sim_df5)
```
# Observation

## Code Stderror
 We could not run simulations on your SBML model. This is the error: Missing a required XML attribute. The http://www.sbml.org/sbml/level2/version4 reaction attribute 'id' is required.


## 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_5, iteration_6, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results, fit_results, candidate_sbml, sim_df, updated_sbml2, sim_df2, updated_sbml3, sim_df3, updated_sbml4, sim_df4)

### 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

There was an error in the previous code, likely due to a missing or duplicate reaction ID or a malformed SBML structure. To avoid this, I will:
- Start from the original candidate model.
- Carefully check for existing reactions with the same IDs before adding new ones.
- Use unique IDs for the new reactions.

Additionally, I will try different rate constants for the reversible reaction to see if this can better match the high steady-state value of `id_smxa` and the substantial value of `id_piw6`.

## Action

### Code

```python
import libsbml

# Start from the original candidate model
candidate_sbml = shared_variables.access("candidate_sbml")
sbml_doc = libsbml.readSBMLFromString(candidate_sbml)
model = sbml_doc.getModel()

# Ensure no duplicate reaction IDs
existing_ids = set(rxn.getId() for rxn in [model.getReaction(i) for i in range(model.getNumReactions())])

# Add forward reaction: id_smxa -> id_9wyg
if "smxa_to_9wyg" not in existing_ids:
    rxn_fwd = model.createReaction()
    rxn_fwd.setId("smxa_to_9wyg")
    rxn_fwd.setReversible(False)
    rxn_fwd.setFast(False)
    reactant_fwd = rxn_fwd.createReactant()
    reactant_fwd.setSpecies("id_smxa")
    reactant_fwd.setStoichiometry(1.0)
    reactant_fwd.setConstant(False)
    product_fwd = rxn_fwd.createProduct()
    product_fwd.setSpecies("id_9wyg")
    product_fwd.setStoichiometry(1.0)
    product_fwd.setConstant(True)
    klaw_fwd = rxn_fwd.createKineticLaw()
    param_fwd = klaw_fwd.createParameter()
    param_fwd.setId("k_smxa_9wyg")
    param_fwd.setValue(0.05)  # Try a lower rate
    klaw_fwd.setFormula("k_smxa_9wyg*id_smxa")

# Add reverse reaction: id_9wyg -> id_smxa
if "n9wyg_to_smxa" not in existing_ids:
    rxn_rev = model.createReaction()
    rxn_rev.setId("n9wyg_to_smxa")
    rxn_rev.setReversible(False)
    rxn_rev.setFast(False)
    reactant_rev = rxn_rev.createReactant()
    reactant_rev.setSpecies("id_9wyg")
    reactant_rev.setStoichiometry(1.0)
    reactant_rev.setConstant(False)
    product_rev = rxn_rev.createProduct()
    product_rev.setSpecies("id_smxa")
    product_rev.setStoichiometry(1.0)
    product_rev.setConstant(True)
    klaw_rev = rxn_rev.createKineticLaw()
    param_rev = klaw_rev.createParameter()
    param_rev.setId("k_9wyg_smxa")
    param_rev.setValue(0.2)  # Try a higher rate for reverse
    klaw_rev.setFormula("k_9wyg_smxa*id_9wyg")

# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml6 = writer.writeSBMLToString(sbml_doc)

# Simulate and compare to experiment
sim_df6 = simulate(updated_sbml6)
exp_df = experiment_history['iteration_0']

print("Simulated model with smxa <-> 9wyg (steady-state, last 10 time points):")
print(sim_df6.iloc[-10:].mean())
print("\nExperimental steady-state (last 10 time points):")
print(exp_df.iloc[-10:].mean())

# Save for further analysis
shared_variables.add("updated_sbml6", updated_sbml6)
shared_variables.add("sim_df6", sim_df6)
```
# Observation

## Code Stdout
Simulated model with smxa <-> 9wyg (steady-state, last 10 time points):
id_k8mo     0.099141
id_smxa     2.509941
id_q2yx     0.054537
id_9wyg     0.719095
id_piw6     0.000176
id_xee0     0.250829
Time       82.910817
dtype: float64

Experimental steady-state (last 10 time points):
id_k8mo     0.099147
id_smxa     0.964624
id_q2yx     0.054537
id_9wyg     0.908991
id_piw6     0.271831
id_xee0     0.250829
Time       82.910817
dtype: float64

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_5, iteration_6, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results, fit_results, candidate_sbml, sim_df, updated_sbml2, sim_df2, updated_sbml3, sim_df3, updated_sbml4, sim_df4, updated_sbml6, sim_df6)

### 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

Adding the reversible reaction `id_smxa <-> id_9wyg` with different forward and reverse rates resulted in a much higher steady-state value for `id_smxa` (~2.51, overshooting the experimental value of ~0.96) and a lower value for `id_9wyg` (~0.72 vs. experimental ~0.91). However, `id_piw6` is still much lower than the experimental value (~0.00018 vs. ~0.27). This suggests that while the reversible reaction can tune the balance between `id_smxa` and `id_9wyg`, it does not address the low value of `id_piw6`.

Given that `id_piw6` is consistently underestimated, it is likely that its production is not solely from an external source, but may also be produced from another species, possibly `id_smxa` or `id_9wyg`. The strong positive correlation between `d(id_piw6)/dt` and `id_k8mo` and `id_q2yx` also suggests a possible conversion.

A reasonable next step is to add a reaction for the production of `id_piw6` from `id_smxa` (e.g., `id_smxa` → `id_piw6`) and see if this improves the fit.

## Action

### Code

```python
import libsbml

# Start from the previous model with smxa <-> 9wyg
updated_sbml6 = shared_variables.access("updated_sbml6")
sbml_doc = libsbml.readSBMLFromString(updated_sbml6)
model = sbml_doc.getModel()

# Add conversion: id_smxa -> id_piw6
rxn = model.createReaction()
rxn.setId("smxa_to_piw6")
rxn.setReversible(False)
rxn.setFast(False)
reactant = rxn.createReactant()
reactant.setSpecies("id_smxa")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = rxn.createProduct()
product.setSpecies("id_piw6")
product.setStoichiometry(1.0)
product.setConstant(True)
klaw = rxn.createKineticLaw()
param = klaw.createParameter()
param.setId("k_smxa_piw6")
param.setValue(0.1)
klaw.setFormula("k_smxa_piw6*id_smxa")

# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml7 = writer.writeSBMLToString(sbml_doc)

# Simulate and compare to experiment
sim_df7 = simulate(updated_sbml7)
exp_df = experiment_history['iteration_0']

print("Simulated model with smxa <-> 9wyg and smxa -> piw6 (steady-state, last 10 time points):")
print(sim_df7.iloc[-10:].mean())
print("\nExperimental steady-state (last 10 time points):")
print(exp_df.iloc[-10:].mean())

# Save for further analysis
shared_variables.add("updated_sbml7", updated_sbml7)
shared_variables.add("sim_df7", sim_df7)
```
# Observation

## Code Stdout
Simulated model with smxa <-> 9wyg and smxa -> piw6 (steady-state, last 10 time points):
id_k8mo     0.099141
id_smxa     0.555153
id_q2yx     0.054537
id_9wyg     0.410179
id_piw6     3.922869
id_xee0     0.250829
Time       82.910817
dtype: float64

Experimental steady-state (last 10 time points):
id_k8mo     0.099147
id_smxa     0.964624
id_q2yx     0.054537
id_9wyg     0.908991
id_piw6     0.271831
id_xee0     0.250829
Time       82.910817
dtype: float64

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_5, iteration_6, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results, fit_results, candidate_sbml, sim_df, updated_sbml2, sim_df2, updated_sbml3, sim_df3, updated_sbml4, sim_df4, updated_sbml6, sim_df6, updated_sbml7, sim_df7)

### 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

Adding the reaction `id_smxa` → `id_piw6` resulted in a much higher steady-state value for `id_piw6` (~3.92, overshooting the experimental value of ~0.27), and a lower value for `id_9wyg` (~0.41 vs. ~0.91). The value for `id_smxa` (~0.56) is still below the experimental value (~0.96), but closer than before.

This suggests that the conversion rates between these species need to be tuned, and/or that the model may require additional reactions or feedbacks to balance the steady-state values. However, with only two iterations left, the best course is to tune the rate constants for the reversible reaction (`id_smxa <-> id_9wyg`) and the conversion (`id_smxa` → `id_piw6`) to better match the experimental steady-state values.

## Action

### Code

```python
import libsbml

# Start from the model with smxa <-> 9wyg and smxa -> piw6
updated_sbml7 = shared_variables.access("updated_sbml7")
sbml_doc = libsbml.readSBMLFromString(updated_sbml7)
model = sbml_doc.getModel()

# Adjust rate constants for smxa <-> 9wyg and smxa -> piw6
for rxn_id, new_k in [("smxa_to_9wyg", 0.02), ("n9wyg_to_smxa", 0.15), ("smxa_to_piw6", 0.01)]:
    rxn = model.getReaction(rxn_id)
    klaw = rxn.getKineticLaw()
    param = klaw.getParameter(0)
    param.setValue(new_k)

# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml8 = writer.writeSBMLToString(sbml_doc)

# Simulate and compare to experiment
sim_df8 = simulate(updated_sbml8)
exp_df = experiment_history['iteration_0']

print("Simulated model with tuned rates (steady-state, last 10 time points):")
print(sim_df8.iloc[-10:].mean())
print("\nExperimental steady-state (last 10 time points):")
print(exp_df.iloc[-10:].mean())

# Save for possible submission
shared_variables.add("updated_sbml8", updated_sbml8)
shared_variables.add("sim_df8", sim_df8)
```
# Observation

## Code Stdout
Simulated model with tuned rates (steady-state, last 10 time points):
id_k8mo     0.099141
id_smxa     2.253806
id_q2yx     0.054537
id_9wyg     0.552666
id_piw6     1.128908
id_xee0     0.250829
Time       82.910817
dtype: float64

Experimental steady-state (last 10 time points):
id_k8mo     0.099147
id_smxa     0.964624
id_q2yx     0.054537
id_9wyg     0.908991
id_piw6     0.271831
id_xee0     0.250829
Time       82.910817
dtype: float64

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_5, iteration_6, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (analysis_results, fit_results, candidate_sbml, sim_df, updated_sbml2, sim_df2, updated_sbml3, sim_df3, updated_sbml4, sim_df4, updated_sbml6, sim_df6, updated_sbml7, sim_df7, updated_sbml8, sim_df8)

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


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



# Iteration 20
## Thoughts

After tuning the rate constants, the model still does not quantitatively match the experimental steady-state values for `id_smxa`, `id_9wyg`, and `id_piw6`. The qualitative behavior is correct (all species reach a steady state, and the direction of changes is reasonable), but the quantitative fit is off, especially for `id_smxa` (simulated: 2.25, experimental: 0.96) and `id_piw6` (simulated: 1.13, experimental: 0.27).

With only one iteration left, further fine-tuning is unlikely to yield a perfect match. However, the current model captures the main features:
- Each species has external production and degradation.
- There is reversible conversion between `id_smxa` and `id_9wyg`.
- There is conversion from `id_smxa` to `id_piw6`.

This structure is consistent with the observed homeostasis and the correlations in the data. I will submit this as the final model.

## Action

### Submit

```python
import libsbml
final_sbml = shared_variables.access("updated_sbml8")
```
