
                # Interation 0

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


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

                <?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level2" level="2" version="1">
  <model id="id_y16y">
    <listOfUnitDefinitions>
      <unitDefinition id="id_0yqd">
        <listOfUnits>
          <unit kind="mole" scale="-6" multiplier="1" offset="0"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_4fev">
        <listOfUnits>
          <unit kind="second" multiplier="60" offset="0"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_52il" size="1" outside="id_cyas"/>
      <compartment id="id_rt6a" size="1"/>
      <compartment id="id_cyas" size="1" outside="id_rt6a"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_x589" compartment="id_cyas" initialConcentration="0"/>
      <species id="id_r7xb" compartment="id_52il" initialConcentration="0.36"/>
      <species id="id_22ta" compartment="id_cyas" initialConcentration="0"/>
      <species id="id_plsk" compartment="id_cyas" initialConcentration="0"/>
      <species id="id_0nyd" compartment="id_rt6a" initialConcentration="0"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

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

The provided SBML model contains five species distributed across three compartments, but no reactions are defined. All species are observable, and my goal is to discover the missing reactions. To begin, I need to observe the system's default behavior to see how the concentrations of the species change over time. This will provide a baseline for understanding the system's dynamics and help identify which species are being produced or consumed, suggesting possible reactions.

## Action

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

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

Total size: 10001 rows × 6 columns. 

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

Time   id_x589  id_r7xb  id_22ta   id_plsk   id_0nyd
0         0 3.60e-01        0         0         0
...
1.99e+01  2.05e-01 3.48e-01 3.26e-01 -3.26e-01 -1.93e-01
...
3.98e+01  2.32e-01 3.43e-01 2.71e-01 -2.71e-01 -2.16e-01
...
5.97e+01  2.26e-01 3.84e-01 2.53e-01 -2.53e-01 -2.49e-01
...
7.96e+01  2.30e-01 4.27e-01 2.52e-01 -2.52e-01 -2.97e-01
...
9.95e+01  2.47e-01 4.62e-01 2.28e-01 -2.28e-01 -3.49e-01
...
1.19e+02  2.53e-01 5.11e-01 1.95e-01 -1.95e-01 -4.05e-01
...
1.39e+02  2.39e-01 5.88e-01 1.91e-01 -1.91e-01 -4.67e-01
...
1.59e+02  2.17e-01 6.83e-01 2.31e-01 -2.31e-01 -5.40e-01
...
1.79e+02  2.11e-01 7.73e-01 3.52e-01 -3.52e-01 -6.24e-01
...
1.99e+02  3.15e-01 6.78e-01 6.26e-02 -6.26e-02 -6.33e-01
...
2.19e+02  9.18e-02 8.97e-01 8.83e-01 -8.83e-01 -6.29e-01
...
2.39e+02  7.77e-02 7.50e-01 8.11e-01 -8.11e-01 -4.68e-01
...
2.59e+02  7.23e-02 5.82e-01 6.46e-01 -6.46e-01 -2.94e-01
...
2.78e+02  1.67e-01 3.61e-01 3.71e-01 -3.71e-01 -1.68e-01
...
2.98e+02  2.33e-01 3.08e-01 3.07e-01 -3.07e-01 -1.81e-01
...
3.18e+02  2.15e-01 3.43e-01 2.81e-01 -2.81e-01 -1.98e-01
...
3.38e+02  2.21e-01 3.73e-01 2.83e-01 -2.83e-01 -2.35e-01
...
3.58e+02  2.39e-01 3.93e-01 2.45e-01 -2.45e-01 -2.72e-01
...
3.78e+02  2.37e-01 4.41e-01 2.24e-01 -2.24e-01 -3.18e-01
...
3.98e+02  2.34e-01 5.02e-01 2.27e-01 -2.27e-01 -3.76e-01
...
4.18e+02  2.45e-01 5.57e-01 2.30e-01 -2.30e-01 -4.42e-01
...
4.38e+02  2.77e-01 5.91e-01 1.95e-01 -1.95e-01 -5.09e-01
...
4.57e+02  2.72e-01 6.50e-01 1.29e-01 -1.29e-01 -5.63e-01
...
4.77e+02  1.84e-01 7.88e-01 2.33e-01 -2.33e-01 -6.12e-01
...
4.97e+02  1.20e-01 9.38e-01 8.88e-01 -8.88e-01 -6.98e-01
...
5.17e+02  8.34e-02 8.29e-01 8.56e-01 -8.56e-01 -5.52e-01
...
5.37e+02  7.34e-02 6.70e-01 7.45e-01 -7.45e-01 -3.84e-01
...
5.57e+02  9.93e-02 4.74e-01 5.13e-01 -5.13e-01 -2.13e-01
...
5.77e+02  2.12e-01 3.09e-01 2.84e-01 -2.84e-01 -1.61e-01
...
5.97e+02  2.05e-01 3.48e-01 3.27e-01 -3.27e-01 -1.93e-01
...
6.17e+02  2.32e-01 3.43e-01 2.70e-01 -2.70e-01 -2.15e-01
...
6.36e+02  2.25e-01 3.84e-01 2.54e-01 -2.54e-01 -2.49e-01
...
6.56e+02  2.30e-01 4.26e-01 2.52e-01 -2.52e-01 -2.96e-01
...
6.76e+02  2.47e-01 4.61e-01 2.27e-01 -2.27e-01 -3.48e-01
...
6.96e+02  2.52e-01 5.11e-01 1.96e-01 -1.96e-01 -4.04e-01
...
7.16e+02  2.38e-01 5.88e-01 1.92e-01 -1.92e-01 -4.66e-01
...
7.36e+02  2.17e-01 6.83e-01 2.33e-01 -2.33e-01 -5.40e-01
...
7.56e+02  2.17e-01 7.67e-01 3.51e-01 -3.51e-01 -6.24e-01
...
7.76e+02  3.07e-01 6.84e-01 6.61e-02 -6.61e-02 -6.31e-01
...
7.96e+02  9.22e-02 8.99e-01 8.84e-01 -8.84e-01 -6.31e-01
...
8.15e+02  7.78e-02 7.53e-01 8.13e-01 -8.13e-01 -4.71e-01
...
8.35e+02  7.22e-02 5.85e-01 6.49e-01 -6.49e-01 -2.97e-01
...
8.55e+02  1.66e-01 3.63e-01 3.75e-01 -3.75e-01 -1.68e-01
...
8.75e+02  2.34e-01 3.07e-01 3.05e-01 -3.05e-01 -1.80e-01
...
8.95e+02  2.15e-01 3.43e-01 2.82e-01 -2.82e-01 -1.97e-01
...
9.15e+02  2.22e-01 3.73e-01 2.84e-01 -2.84e-01 -2.34e-01
...
9.35e+02  2.39e-01 3.92e-01 2.44e-01 -2.44e-01 -2.71e-01
...
9.55e+02  2.36e-01 4.41e-01 2.24e-01 -2.24e-01 -3.17e-01
...
9.75e+02  2.20e-01 3.80e-01 2.76e-01 -2.76e-01 -2.39e-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:
- `id_r7xb` starts at 0.36 and generally increases over time, sometimes with oscillatory or periodic behavior.
- `id_x589`, `id_22ta`, and `id_0nyd` all start at 0 and become nonzero, with `id_x589` and `id_22ta` remaining positive, while `id_0nyd` and `id_plsk` take on negative values.
- `id_plsk` and `id_0nyd` are always negative and seem to mirror the positive values of `id_22ta` and `id_x589` respectively.

This suggests:
- There may be reactions that interconvert these species, possibly with stoichiometry that causes some to be negative (though negative concentrations are unphysical, this may be a modeling artifact or indicate a missing constraint).
- The periodicity hints at a possible oscillatory system or a cycle.

To further probe the system, I will perturb the initial concentration of `id_r7xb` (the only species with a nonzero initial concentration) to see how the system responds. This will help determine if `id_r7xb` is a substrate or a driver for the other species' dynamics.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_r7xb": 0.7
    }
}
```
# 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: 10001 rows × 6 columns. 

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

Time   id_x589  id_r7xb  id_22ta   id_plsk   id_0nyd
0         0 7.00e-01        0         0         0
...
1.99e+01  2.32e-01 4.39e-01 2.32e-01 -2.32e-01  2.84e-02
...
3.98e+01  2.35e-01 4.94e-01 2.34e-01 -2.34e-01 -2.95e-02
...
5.97e+01  2.54e-01 5.39e-01 2.20e-01 -2.20e-01 -9.28e-02
...
7.96e+01  2.73e-01 5.81e-01 1.72e-01 -1.72e-01 -1.54e-01
...
9.95e+01  2.44e-01 6.68e-01 1.52e-01 -1.52e-01 -2.12e-01
...
1.19e+02  1.76e-01 8.00e-01 2.78e-01 -2.78e-01 -2.76e-01
...
1.39e+02  1.72e-01 8.97e-01 8.67e-01 -8.67e-01 -3.70e-01
...
1.59e+02  8.54e-02 8.49e-01 8.65e-01 -8.65e-01 -2.34e-01
...
1.79e+02  7.45e-02 6.93e-01 7.66e-01 -7.66e-01 -6.76e-02
...
1.99e+02  8.50e-02 5.09e-01 5.53e-01 -5.53e-01  1.06e-01
...
2.19e+02  2.00e-01 3.20e-01 3.02e-01 -3.02e-01  1.80e-01
...
2.39e+02  2.10e-01 3.42e-01 3.33e-01 -3.33e-01  1.49e-01
...
2.59e+02  2.30e-01 3.39e-01 2.67e-01 -2.67e-01  1.31e-01
...
2.78e+02  2.21e-01 3.83e-01 2.64e-01 -2.64e-01  9.56e-02
...
2.98e+02  2.33e-01 4.17e-01 2.54e-01 -2.54e-01  4.97e-02
...
3.18e+02  2.48e-01 4.51e-01 2.21e-01 -2.21e-01  9.55e-04
...
3.38e+02  2.45e-01 5.09e-01 2.00e-01 -2.00e-01 -5.42e-02
...
3.58e+02  2.32e-01 5.87e-01 2.11e-01 -2.11e-01 -1.19e-01
...
3.78e+02  2.27e-01 6.68e-01 2.50e-01 -2.50e-01 -1.95e-01
...
3.98e+02  2.92e-01 6.82e-01 2.83e-01 -2.83e-01 -2.74e-01
...
4.18e+02  2.47e-01 7.29e-01 1.08e-01 -1.08e-01 -2.76e-01
...
4.38e+02  9.61e-02 9.16e-01 8.88e-01 -8.88e-01 -3.12e-01
...
4.57e+02  7.93e-02 7.75e-01 8.27e-01 -8.27e-01 -1.54e-01
...
4.77e+02  7.18e-02 6.10e-01 6.80e-01 -6.80e-01  1.82e-02
...
4.97e+02  1.50e-01 3.87e-01 4.10e-01 -4.10e-01  1.63e-01
...
5.17e+02  2.35e-01 2.98e-01 2.86e-01 -2.86e-01  1.67e-01
...
5.37e+02  2.09e-01 3.46e-01 2.95e-01 -2.95e-01  1.45e-01
...
5.57e+02  2.26e-01 3.64e-01 2.84e-01 -2.84e-01  1.10e-01
...
5.77e+02  2.37e-01 3.87e-01 2.42e-01 -2.42e-01  7.60e-02
...
5.97e+02  2.32e-01 4.39e-01 2.33e-01 -2.33e-01  2.94e-02
...
6.17e+02  2.36e-01 4.93e-01 2.35e-01 -2.35e-01 -2.84e-02
...
6.36e+02  2.56e-01 5.35e-01 2.18e-01 -2.18e-01 -9.10e-02
...
6.56e+02  2.71e-01 5.81e-01 1.70e-01 -1.70e-01 -1.52e-01
...
6.76e+02  2.40e-01 6.70e-01 1.57e-01 -1.57e-01 -2.11e-01
...
6.96e+02  1.75e-01 8.02e-01 2.86e-01 -2.86e-01 -2.77e-01
...
7.16e+02  2.06e-01 8.64e-01 8.51e-01 -8.51e-01 -3.70e-01
...
7.36e+02  8.58e-02 8.52e-01 8.67e-01 -8.67e-01 -2.38e-01
...
7.56e+02  7.47e-02 6.98e-01 7.70e-01 -7.70e-01 -7.22e-02
...
7.76e+02  8.29e-02 5.15e-01 5.61e-01 -5.61e-01  1.02e-01
...
7.96e+02  1.97e-01 3.23e-01 3.06e-01 -3.06e-01  1.80e-01
...
8.15e+02  2.11e-01 3.40e-01 3.34e-01 -3.34e-01  1.49e-01
...
8.35e+02  2.29e-01 3.39e-01 2.67e-01 -2.67e-01  1.32e-01
...
8.55e+02  2.21e-01 3.83e-01 2.66e-01 -2.66e-01  9.63e-02
...
8.75e+02  2.34e-01 4.15e-01 2.54e-01 -2.54e-01  5.10e-02
...
8.95e+02  2.47e-01 4.50e-01 2.20e-01 -2.20e-01  2.78e-03
...
9.15e+02  2.43e-01 5.09e-01 2.02e-01 -2.02e-01 -5.24e-02
...
9.35e+02  2.32e-01 5.86e-01 2.14e-01 -2.14e-01 -1.18e-01
...
9.55e+02  2.31e-01 6.63e-01 2.51e-01 -2.51e-01 -1.94e-01
...
9.75e+02  2.53e-01 5.11e-01 1.95e-01 -1.95e-01 -6.39e-02

## 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 system's response to doubling the initial concentration of `id_r7xb` shows:
- The oscillatory or periodic pattern persists, but the amplitude and timing of the peaks for other species (e.g., `id_22ta`, `id_x589`) are affected.
- `id_0nyd` and `id_plsk` still take on negative values, but now `id_0nyd` sometimes becomes positive, suggesting a more complex relationship.
- The system appears to cycle through phases where `id_22ta` and `id_x589` rise and fall, with `id_r7xb` peaking and dipping in a related but not identical pattern.

This suggests:
- There may be a cyclic or oscillatory network, possibly involving feedback.
- The negative values for `id_plsk` and `id_0nyd` are likely due to missing reactions or incorrect stoichiometry in the model.
- The system is not simply a linear conversion from `id_r7xb` to the other species.

To further probe the system, I will set the initial concentration of `id_r7xb` to zero and see if any dynamics occur. This will help determine if `id_r7xb` is essential for the observed oscillations and if the other species can be produced without it.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_r7xb": 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: 10001 rows × 6 columns. 

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

Time   id_x589  id_r7xb  id_22ta   id_plsk   id_0nyd
0         0        0        0         0         0
...
1.99e+01  3.91e-01 6.26e-01 5.44e-02 -5.44e-02 -1.02e+00
...
3.98e+01  8.94e-02 8.82e-01 8.78e-01 -8.78e-01 -9.71e-01
...
5.97e+01  7.66e-02 7.32e-01 7.98e-01 -7.98e-01 -8.08e-01
...
7.96e+01  7.40e-02 5.60e-01 6.17e-01 -6.17e-01 -6.34e-01
...
9.95e+01  1.78e-01 3.45e-01 3.45e-01 -3.45e-01 -5.23e-01
...
1.19e+02  2.26e-01 3.20e-01 3.23e-01 -3.23e-01 -5.46e-01
...
1.39e+02  2.21e-01 3.40e-01 2.73e-01 -2.73e-01 -5.61e-01
...
1.59e+02  2.20e-01 3.78e-01 2.79e-01 -2.79e-01 -5.98e-01
...
1.79e+02  2.38e-01 4.00e-01 2.49e-01 -2.49e-01 -6.39e-01
...
1.99e+02  2.41e-01 4.43e-01 2.19e-01 -2.19e-01 -6.84e-01
...
2.19e+02  2.35e-01 5.06e-01 2.18e-01 -2.18e-01 -7.41e-01
...
2.39e+02  2.37e-01 5.72e-01 2.30e-01 -2.30e-01 -8.09e-01
...
2.59e+02  2.66e-01 6.14e-01 2.26e-01 -2.26e-01 -8.80e-01
...
2.78e+02  3.02e-01 6.35e-01 1.28e-01 -1.28e-01 -9.37e-01
...
2.98e+02  1.97e-01 7.73e-01 1.92e-01 -1.92e-01 -9.70e-01
...
3.18e+02  1.07e-01 9.37e-01 8.91e-01 -8.91e-01 -1.04e+00
...
3.38e+02  8.20e-02 8.11e-01 8.48e-01 -8.48e-01 -8.93e-01
...
3.58e+02  7.27e-02 6.51e-01 7.26e-01 -7.26e-01 -7.24e-01
...
3.78e+02  1.16e-01 4.43e-01 4.78e-01 -4.78e-01 -5.58e-01
...
3.98e+02  2.22e-01 3.02e-01 2.77e-01 -2.77e-01 -5.24e-01
...
4.18e+02  2.04e-01 3.49e-01 3.18e-01 -3.18e-01 -5.53e-01
...
4.38e+02  2.32e-01 3.48e-01 2.76e-01 -2.76e-01 -5.80e-01
...
4.57e+02  2.29e-01 3.84e-01 2.48e-01 -2.48e-01 -6.13e-01
...
4.77e+02  2.29e-01 4.32e-01 2.47e-01 -2.47e-01 -6.61e-01
...
4.97e+02  2.44e-01 4.72e-01 2.33e-01 -2.33e-01 -7.16e-01
...
5.17e+02  2.58e-01 5.15e-01 1.98e-01 -1.98e-01 -7.73e-01
...
5.37e+02  2.48e-01 5.85e-01 1.78e-01 -1.78e-01 -8.33e-01
...
5.57e+02  2.18e-01 6.84e-01 2.10e-01 -2.10e-01 -9.02e-01
...
5.77e+02  1.86e-01 7.98e-01 3.44e-01 -3.44e-01 -9.84e-01
...
5.97e+02  3.82e-01 6.32e-01 5.22e-02 -5.22e-02 -1.01e+00
...
6.17e+02  8.96e-02 8.83e-01 8.79e-01 -8.79e-01 -9.73e-01
...
6.36e+02  7.67e-02 7.34e-01 7.99e-01 -7.99e-01 -8.10e-01
...
6.56e+02  7.38e-02 5.62e-01 6.20e-01 -6.20e-01 -6.35e-01
...
6.76e+02  1.77e-01 3.46e-01 3.47e-01 -3.47e-01 -5.24e-01
...
6.96e+02  2.26e-01 3.19e-01 3.22e-01 -3.22e-01 -5.45e-01
...
7.16e+02  2.20e-01 3.40e-01 2.73e-01 -2.73e-01 -5.60e-01
...
7.36e+02  2.20e-01 3.78e-01 2.79e-01 -2.79e-01 -5.98e-01
...
7.56e+02  2.39e-01 3.99e-01 2.48e-01 -2.48e-01 -6.38e-01
...
7.76e+02  2.41e-01 4.43e-01 2.19e-01 -2.19e-01 -6.84e-01
...
7.96e+02  2.35e-01 5.06e-01 2.19e-01 -2.19e-01 -7.41e-01
...
8.15e+02  2.37e-01 5.71e-01 2.31e-01 -2.31e-01 -8.08e-01
...
8.35e+02  2.68e-01 6.12e-01 2.24e-01 -2.24e-01 -8.80e-01
...
8.55e+02  3.00e-01 6.36e-01 1.27e-01 -1.27e-01 -9.36e-01
...
8.75e+02  1.96e-01 7.74e-01 1.94e-01 -1.94e-01 -9.70e-01
...
8.95e+02  1.08e-01 9.37e-01 8.91e-01 -8.91e-01 -1.04e+00
...
9.15e+02  8.20e-02 8.12e-01 8.48e-01 -8.48e-01 -8.94e-01
...
9.35e+02  7.27e-02 6.52e-01 7.26e-01 -7.26e-01 -7.24e-01
...
9.55e+02  1.15e-01 4.44e-01 4.79e-01 -4.79e-01 -5.59e-01
...
9.75e+02  8.00e-02 7.85e-01 8.33e-01 -8.33e-01 -8.65e-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 `id_r7xb` to zero does not stop the oscillatory dynamics. In fact, `id_r7xb` itself increases from zero, and the other species also show oscillatory or periodic changes. This suggests:
- There is a source for `id_r7xb` (possibly a reaction that produces it from another species or from an implicit source).
- The system is inherently oscillatory, likely involving feedback loops.
- The negative values for `id_plsk` and `id_0nyd` persist, which is unphysical and likely due to missing or mis-specified reactions.

To further probe the system, I will set the initial concentration of `id_x589` to a nonzero value (e.g., 0.5) while keeping `id_r7xb` at its default (0.36). This will help determine if `id_x589` can drive the system or if it is downstream of other species.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_x589": 0.5
    }
}
```
# Observation

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

Total size: 10001 rows × 6 columns. 

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

Time   id_x589  id_r7xb  id_22ta   id_plsk   id_0nyd
0  5.00e-01 3.60e-01        0         0         0
...
1.99e+01  2.29e-01 3.84e-01 2.48e-01 -2.48e-01  2.47e-01
...
3.98e+01  2.29e-01 4.32e-01 2.47e-01 -2.47e-01  1.99e-01
...
5.97e+01  2.44e-01 4.72e-01 2.33e-01 -2.33e-01  1.44e-01
...
7.96e+01  2.58e-01 5.15e-01 1.98e-01 -1.98e-01  8.75e-02
...
9.95e+01  2.48e-01 5.85e-01 1.79e-01 -1.79e-01  2.70e-02
...
1.19e+02  2.18e-01 6.84e-01 2.10e-01 -2.10e-01 -4.22e-02
...
1.39e+02  1.86e-01 7.98e-01 3.44e-01 -3.44e-01 -1.24e-01
...
1.59e+02  3.82e-01 6.32e-01 5.23e-02 -5.23e-02 -1.54e-01
...
1.79e+02  8.96e-02 8.83e-01 8.79e-01 -8.79e-01 -1.13e-01
...
1.99e+02  7.67e-02 7.34e-01 7.99e-01 -7.99e-01  4.92e-02
...
2.19e+02  7.37e-02 5.62e-01 6.21e-01 -6.21e-01  2.24e-01
...
2.39e+02  1.77e-01 3.47e-01 3.48e-01 -3.48e-01  3.36e-01
...
2.59e+02  2.27e-01 3.18e-01 3.21e-01 -3.21e-01  3.15e-01
...
2.78e+02  2.20e-01 3.40e-01 2.73e-01 -2.73e-01  3.00e-01
...
2.98e+02  2.20e-01 3.78e-01 2.79e-01 -2.79e-01  2.62e-01
...
3.18e+02  2.39e-01 3.99e-01 2.48e-01 -2.48e-01  2.22e-01
...
3.38e+02  2.41e-01 4.43e-01 2.20e-01 -2.20e-01  1.77e-01
...
3.58e+02  2.35e-01 5.06e-01 2.19e-01 -2.19e-01  1.19e-01
...
3.78e+02  2.38e-01 5.70e-01 2.31e-01 -2.31e-01  5.21e-02
...
3.98e+02  2.68e-01 6.11e-01 2.22e-01 -2.22e-01 -1.90e-02
...
4.18e+02  2.98e-01 6.36e-01 1.26e-01 -1.26e-01 -7.49e-02
...
4.38e+02  1.95e-01 7.75e-01 1.97e-01 -1.97e-01 -1.10e-01
...
4.57e+02  1.08e-01 9.37e-01 8.91e-01 -8.91e-01 -1.86e-01
...
4.77e+02  8.22e-02 8.14e-01 8.49e-01 -8.49e-01 -3.60e-02
...
4.97e+02  7.28e-02 6.53e-01 7.28e-01 -7.28e-01  1.34e-01
...
5.17e+02  1.14e-01 4.46e-01 4.82e-01 -4.82e-01  3.00e-01
...
5.37e+02  2.21e-01 3.02e-01 2.77e-01 -2.77e-01  3.37e-01
...
5.57e+02  2.04e-01 3.49e-01 3.19e-01 -3.19e-01  3.07e-01
...
5.77e+02  2.32e-01 3.47e-01 2.75e-01 -2.75e-01  2.80e-01
...
5.97e+02  2.29e-01 3.84e-01 2.48e-01 -2.48e-01  2.47e-01
...
6.17e+02  2.29e-01 4.31e-01 2.48e-01 -2.48e-01  2.00e-01
...
6.36e+02  2.45e-01 4.70e-01 2.32e-01 -2.32e-01  1.45e-01
...
6.56e+02  2.57e-01 5.14e-01 1.97e-01 -1.97e-01  8.91e-02
...
6.76e+02  2.46e-01 5.86e-01 1.81e-01 -1.81e-01  2.82e-02
...
6.96e+02  2.17e-01 6.85e-01 2.14e-01 -2.14e-01 -4.18e-02
...
7.16e+02  1.89e-01 7.95e-01 3.47e-01 -3.47e-01 -1.24e-01
...
7.36e+02  3.67e-01 6.42e-01 5.13e-02 -5.13e-02 -1.49e-01
...
7.56e+02  9.01e-02 8.86e-01 8.80e-01 -8.80e-01 -1.16e-01
...
7.76e+02  7.69e-02 7.38e-01 8.02e-01 -8.02e-01  4.54e-02
...
7.96e+02  7.33e-02 5.67e-01 6.27e-01 -6.27e-01  2.20e-01
...
8.15e+02  1.75e-01 3.50e-01 3.53e-01 -3.53e-01  3.35e-01
...
8.35e+02  2.28e-01 3.16e-01 3.18e-01 -3.18e-01  3.16e-01
...
8.55e+02  2.19e-01 3.41e-01 2.75e-01 -2.75e-01  3.00e-01
...
8.75e+02  2.20e-01 3.77e-01 2.80e-01 -2.80e-01  2.63e-01
...
8.95e+02  2.39e-01 3.98e-01 2.47e-01 -2.47e-01  2.23e-01
...
9.15e+02  2.40e-01 4.42e-01 2.20e-01 -2.20e-01  1.78e-01
...
9.35e+02  2.34e-01 5.05e-01 2.21e-01 -2.21e-01  1.20e-01
...
9.55e+02  2.39e-01 5.68e-01 2.31e-01 -2.31e-01  5.32e-02
...
9.75e+02  2.46e-01 4.47e-01 2.18e-01 -2.18e-01  1.67e-01

## Reminder

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



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

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


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



# Iteration 4
## Thoughts

Setting the initial concentration of `id_x589` to 0.5 (with `id_r7xb` at its default) results in:
- The system still exhibits oscillatory behavior.
- `id_x589` quickly drops from its initial value and then oscillates in a pattern similar to previous experiments.
- `id_0nyd` now takes on positive values for a significant portion of the cycle, suggesting a direct or indirect relationship with `id_x589`.
- The overall pattern of oscillations and the relationships between the species are preserved, but the phase and amplitude are affected.

This suggests:
- `id_x589` is not strictly downstream; it can influence the system when set high, but the system returns to its oscillatory regime.
- The system is robust to initial conditions, indicating strong feedback or cyclic reactions.
- The negative values for `id_plsk` and the oscillatory sign of `id_0nyd` suggest these may be intermediates or products in a cycle, or there may be missing constraints or reactions.

To better understand the relationships, I will analyze the time series data quantitatively to look for correlations, phase relationships, and possible stoichiometric relationships between the species. This may help hypothesize the missing reactions.

## Action

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

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

# Calculate correlations between species
corr = df.drop(columns='Time').corr()

# Calculate time lags for peak values to look for phase relationships
def get_peak_times(series):
    from scipy.signal import find_peaks
    peaks, _ = find_peaks(series)
    return df['Time'].iloc[peaks].values

peak_times = {col: get_peak_times(df[col].values) for col in df.columns if col != 'Time'}

# Print correlation matrix and peak time differences
print("Correlation matrix:\n", corr)
print("\nPeak times for each species:")
for k, v in peak_times.items():
    print(f"{k}: {v[:5]} ...")  # print first 5 peak times for brevity

# Also, check if the sum of all species is conserved (suggesting a closed cycle)
df['sum_species'] = df[['id_x589', 'id_r7xb', 'id_22ta', 'id_plsk', 'id_0nyd']].sum(axis=1)
print("\nSum of all species (first 10):", df['sum_species'].head(10).values)
print("Sum of all species (last 10):", df['sum_species'].tail(10).values)
print("Range of sum of all species:", df['sum_species'].min(), df['sum_species'].max())
```
# Observation

## Code Stdout
Correlation matrix:
           id_x589   id_r7xb   id_22ta   id_plsk   id_0nyd
id_x589  1.000000 -0.393122 -0.865650  0.865650 -0.000716
id_r7xb -0.393122  1.000000  0.558578 -0.558578 -0.919205
id_22ta -0.865650  0.558578  1.000000 -1.000000 -0.236766
id_plsk  0.865650 -0.558578 -1.000000  1.000000  0.236766
id_0nyd -0.000716 -0.919205 -0.236766  0.236766  1.000000

Peak times for each species:
id_x589: [0.585 0.78  0.975 1.17  1.365] ...
id_r7xb: [0.4875 0.6825 0.8775 1.8525 2.535 ] ...
id_22ta: [0.4875 0.78   1.0725 1.2675 1.4625] ...
id_plsk: [0.6825 0.975  1.17   1.365  1.56  ] ...
id_0nyd: [0.6825 2.0475 3.9975 4.68   6.045 ] ...

Sum of all species (first 10): [0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36]
Sum of all species (last 10): [0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36]
Range of sum of all species: 0.3599999999995097 0.36000000000000465

## Reminder

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



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

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


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



# Iteration 5
## Thoughts

Key findings from the analysis:
- The sum of all species is strictly conserved at 0.36 throughout the simulation. This strongly suggests a closed cycle with no external input or output.
- Strong negative correlation between `id_22ta` and `id_plsk` (-1.0), and strong positive correlation between `id_x589` and `id_plsk` (0.87), as well as perfect negative correlation between `id_22ta` and `id_plsk`. This suggests that `id_plsk` is essentially `-id_22ta`, and these two are tightly coupled, possibly as product/reactant pairs in a reversible reaction.
- `id_r7xb` and `id_0nyd` are strongly negatively correlated (-0.92), suggesting a direct conversion or tight coupling.
- The peak times for the species are offset, indicating a cyclic conversion (e.g., A→B→C→D→A).
- The negative values for `id_plsk` and `id_0nyd` are unphysical, suggesting that the model is missing constraints or that the reactions should be reversible and/or have correct stoichiometry.

Given the conservation and the correlations, a plausible hypothesis is that the system is a closed cycle, e.g.,

`id_r7xb` → `id_22ta` → `id_plsk` → `id_0nyd` → `id_x589` → `id_r7xb`

But the perfect negative correlation between `id_22ta` and `id_plsk` suggests a direct reversible reaction between them. Similarly, the strong negative correlation between `id_r7xb` and `id_0nyd` suggests a direct relationship.

To further test the hypothesis, I will perturb the initial concentration of `id_22ta` to 0.5 and observe the system's response. This will help clarify the directionality and coupling of the cycle.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_22ta": 0.5
    }
}
```
# 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: 10001 rows × 6 columns. 

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

Time   id_x589  id_r7xb  id_22ta   id_plsk   id_0nyd
0         0 3.60e-01 5.00e-01         0         0
...
1.99e+01  2.04e-01 3.49e-01 3.24e-01  1.76e-01 -1.93e-01
...
3.98e+01  2.32e-01 3.45e-01 2.72e-01  2.28e-01 -2.17e-01
...
5.97e+01  2.27e-01 3.84e-01 2.51e-01  2.49e-01 -2.51e-01
...
7.96e+01  2.29e-01 4.29e-01 2.51e-01  2.49e-01 -2.98e-01
...
9.95e+01  2.46e-01 4.65e-01 2.30e-01  2.70e-01 -3.51e-01
...
1.19e+02  2.55e-01 5.12e-01 1.96e-01  3.04e-01 -4.07e-01
...
1.39e+02  2.42e-01 5.87e-01 1.86e-01  3.14e-01 -4.69e-01
...
1.59e+02  2.16e-01 6.84e-01 2.24e-01  2.76e-01 -5.41e-01
...
1.79e+02  1.99e-01 7.85e-01 3.52e-01  1.48e-01 -6.25e-01
...
1.99e+02  3.37e-01 6.62e-01 5.55e-02  4.45e-01 -6.40e-01
...
2.19e+02  9.10e-02 8.92e-01 8.81e-01 -3.81e-01 -6.23e-01
...
2.39e+02  7.73e-02 7.44e-01 8.07e-01 -3.07e-01 -4.62e-01
...
2.59e+02  7.27e-02 5.74e-01 6.36e-01 -1.36e-01 -2.87e-01
...
2.78e+02  1.71e-01 3.55e-01 3.62e-01  1.38e-01 -1.66e-01
...
2.98e+02  2.31e-01 3.12e-01 3.13e-01  1.87e-01 -1.83e-01
...
3.18e+02  2.17e-01 3.42e-01 2.78e-01  2.22e-01 -1.99e-01
...
3.38e+02  2.21e-01 3.75e-01 2.82e-01  2.18e-01 -2.36e-01
...
3.58e+02  2.39e-01 3.96e-01 2.46e-01  2.54e-01 -2.75e-01
...
3.78e+02  2.39e-01 4.42e-01 2.22e-01  2.78e-01 -3.20e-01
...
3.98e+02  2.34e-01 5.04e-01 2.24e-01  2.76e-01 -3.78e-01
...
4.18e+02  2.42e-01 5.63e-01 2.31e-01  2.69e-01 -4.45e-01
...
4.38e+02  2.75e-01 5.98e-01 2.07e-01  2.93e-01 -5.13e-01
...
4.57e+02  2.84e-01 6.44e-01 1.25e-01  3.75e-01 -5.68e-01
...
4.77e+02  1.89e-01 7.82e-01 2.16e-01  2.84e-01 -6.11e-01
...
4.97e+02  1.13e-01 9.39e-01 8.90e-01 -3.90e-01 -6.92e-01
...
5.17e+02  8.28e-02 8.21e-01 8.53e-01 -3.53e-01 -5.44e-01
...
5.37e+02  7.31e-02 6.62e-01 7.36e-01 -2.36e-01 -3.75e-01
...
5.57e+02  1.07e-01 4.60e-01 4.97e-01  3.16e-03 -2.06e-01
...
5.77e+02  2.17e-01 3.05e-01 2.80e-01  2.20e-01 -1.62e-01
...
5.97e+02  2.04e-01 3.49e-01 3.23e-01  1.77e-01 -1.93e-01
...
6.17e+02  2.32e-01 3.45e-01 2.73e-01  2.27e-01 -2.18e-01
...
6.36e+02  2.27e-01 3.84e-01 2.51e-01  2.49e-01 -2.51e-01
...
6.56e+02  2.29e-01 4.29e-01 2.50e-01  2.50e-01 -2.99e-01
...
6.76e+02  2.46e-01 4.66e-01 2.30e-01  2.70e-01 -3.52e-01
...
6.96e+02  2.55e-01 5.13e-01 1.96e-01  3.04e-01 -4.08e-01
...
7.16e+02  2.42e-01 5.87e-01 1.85e-01  3.15e-01 -4.69e-01
...
7.36e+02  2.16e-01 6.84e-01 2.23e-01  2.77e-01 -5.41e-01
...
7.56e+02  1.97e-01 7.87e-01 3.51e-01  1.49e-01 -6.25e-01
...
7.76e+02  3.43e-01 6.58e-01 5.42e-02  4.46e-01 -6.41e-01
...
7.96e+02  9.08e-02 8.91e-01 8.81e-01 -3.81e-01 -6.21e-01
...
8.15e+02  7.72e-02 7.43e-01 8.05e-01 -3.05e-01 -4.60e-01
...
8.35e+02  7.29e-02 5.72e-01 6.34e-01 -1.34e-01 -2.85e-01
...
8.55e+02  1.72e-01 3.54e-01 3.60e-01  1.40e-01 -1.66e-01
...
8.75e+02  2.30e-01 3.13e-01 3.15e-01  1.85e-01 -1.83e-01
...
8.95e+02  2.18e-01 3.41e-01 2.77e-01  2.23e-01 -1.99e-01
...
9.15e+02  2.20e-01 3.76e-01 2.81e-01  2.19e-01 -2.36e-01
...
9.35e+02  2.39e-01 3.96e-01 2.46e-01  2.54e-01 -2.75e-01
...
9.55e+02  2.39e-01 4.42e-01 2.21e-01  2.79e-01 -3.21e-01
...
9.75e+02  2.20e-01 3.81e-01 2.72e-01  2.28e-01 -2.41e-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_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 6
## Thoughts

Perturbing `id_22ta` to 0.5 (with all others at default) again results in oscillatory behavior, with the system returning to its characteristic cycles. The sum of all species remains conserved, and the relationships between the species are preserved, though the phase and amplitude of oscillations are affected.

Key insights:
- The system is robust to initial conditions, always returning to a conserved sum and oscillatory regime.
- The strong correlations and anti-correlations, along with the conservation, suggest a closed cycle with reversible reactions.
- The negative values for `id_plsk` and `id_0nyd` are likely due to missing or mis-specified reactions or stoichiometry.

Given the perfect negative correlation between `id_22ta` and `id_plsk`, and the strong negative correlation between `id_r7xb` and `id_0nyd`, I hypothesize the following reactions:
1. `id_22ta <-> id_plsk` (reversible)
2. `id_r7xb <-> id_0nyd` (reversible)
3. The remaining species (`id_x589`) may be involved in a conversion with one of the others, possibly closing the cycle.

To further clarify the relationships, I will analyze the time series for stoichiometric relationships (e.g., does an increase in one species always correspond to a decrease in another of equal magnitude?). This will help determine the correct stoichiometry for the reactions.

## Action

### Code
```python
df = experiment_history['iteration_0']

# Check if id_22ta + id_plsk is always zero (perfect anti-correlation)
sum_22ta_plsk = df['id_22ta'] + df['id_plsk']
print("id_22ta + id_plsk (first 10):", sum_22ta_plsk.head(10).values)
print("Range of id_22ta + id_plsk:", sum_22ta_plsk.min(), sum_22ta_plsk.max())

# Check if id_r7xb + id_0nyd is always constant (strong anti-correlation)
sum_r7xb_0nyd = df['id_r7xb'] + df['id_0nyd']
print("id_r7xb + id_0nyd (first 10):", sum_r7xb_0nyd.head(10).values)
print("Range of id_r7xb + id_0nyd:", sum_r7xb_0nyd.min(), sum_r7xb_0nyd.max())

# Check if id_x589 is related to the others in a similar way
sum_x589_others = df['id_x589'] + df['id_r7xb'] + df['id_22ta']
print("id_x589 + id_r7xb + id_22ta (first 10):", sum_x589_others.head(10).values)
print("Range of id_x589 + id_r7xb + id_22ta:", sum_x589_others.min(), sum_x589_others.max())
```
# Observation

## Code Stdout
id_22ta + id_plsk (first 10): [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00
  0.00000000e+00  0.00000000e+00  0.00000000e+00 -1.11022302e-16
 -1.11022302e-16 -1.38777878e-16]
Range of id_22ta + id_plsk: -2.7478019859472624e-15 3.6637359812630166e-15
id_r7xb + id_0nyd (first 10): [ 0.36        0.29707112  0.29162407  0.28594787  0.27888159  0.26742912
 -0.01572453  0.1691578   0.06897159  0.14010669]
Range of id_r7xb + id_0nyd: -0.07845174779661779 0.36
id_x589 + id_r7xb + id_22ta (first 10): [0.36       0.89244379 1.25684148 1.52268042 1.72395354 1.87757951
 1.66266766 1.18205183 1.25805206 1.10559743]
Range of id_x589 + id_r7xb + id_22ta: 0.36 1.947838904255853

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_3, iteration_5)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 7
## Thoughts

- `id_22ta + id_plsk` is always zero (within numerical error), confirming these two are perfectly anti-correlated and likely interconverted in a 1:1 reversible reaction.
- `id_r7xb + id_0nyd` is not constant, but ranges from 0.36 to about -0.08, suggesting a more complex relationship, possibly involving other species or non-1:1 stoichiometry.
- `id_x589 + id_r7xb + id_22ta` is not constant, but always ≥ 0.36, suggesting that `id_x589` is not simply a direct product of the other two.

Given the above, the most certain reaction is:
- `id_22ta <-> id_plsk` (1:1 reversible)

The other relationships are less clear, but the strong negative correlation between `id_r7xb` and `id_0nyd` suggests a direct or indirect conversion, possibly with involvement of `id_x589`.

To further clarify, I will perturb the initial concentration of `id_plsk` to 0.5 and observe the system's response. This will help confirm the direct relationship between `id_22ta` and `id_plsk` and may provide more insight into the role of the other species.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_plsk": 0.5
    }
}
```
# 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: 10001 rows × 6 columns. 

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

Time   id_x589  id_r7xb  id_22ta   id_plsk   id_0nyd
0         0 3.60e-01        0  5.00e-01         0
...
1.99e+01  2.05e-01 3.48e-01 3.26e-01  1.74e-01 -1.93e-01
...
3.98e+01  2.32e-01 3.43e-01 2.71e-01  2.29e-01 -2.16e-01
...
5.97e+01  2.26e-01 3.84e-01 2.53e-01  2.47e-01 -2.50e-01
...
7.96e+01  2.30e-01 4.27e-01 2.52e-01  2.48e-01 -2.97e-01
...
9.95e+01  2.47e-01 4.63e-01 2.28e-01  2.72e-01 -3.50e-01
...
1.19e+02  2.54e-01 5.12e-01 1.95e-01  3.05e-01 -4.05e-01
...
1.39e+02  2.40e-01 5.88e-01 1.90e-01  3.10e-01 -4.67e-01
...
1.59e+02  2.16e-01 6.84e-01 2.29e-01  2.71e-01 -5.40e-01
...
1.79e+02  2.08e-01 7.76e-01 3.53e-01  1.47e-01 -6.24e-01
...
1.99e+02  3.20e-01 6.74e-01 6.07e-02  4.39e-01 -6.35e-01
...
2.19e+02  9.16e-02 8.96e-01 8.83e-01 -3.83e-01 -6.27e-01
...
2.39e+02  7.76e-02 7.49e-01 8.10e-01 -3.10e-01 -4.66e-01
...
2.59e+02  7.24e-02 5.80e-01 6.43e-01 -1.43e-01 -2.92e-01
...
2.78e+02  1.68e-01 3.59e-01 3.68e-01  1.32e-01 -1.67e-01
...
2.98e+02  2.32e-01 3.09e-01 3.09e-01  1.91e-01 -1.82e-01
...
3.18e+02  2.16e-01 3.42e-01 2.80e-01  2.20e-01 -1.98e-01
...
3.38e+02  2.21e-01 3.74e-01 2.83e-01  2.17e-01 -2.35e-01
...
3.58e+02  2.39e-01 3.94e-01 2.45e-01  2.55e-01 -2.73e-01
...
3.78e+02  2.38e-01 4.41e-01 2.23e-01  2.77e-01 -3.19e-01
...
3.98e+02  2.34e-01 5.03e-01 2.26e-01  2.74e-01 -3.77e-01
...
4.18e+02  2.43e-01 5.60e-01 2.31e-01  2.69e-01 -4.43e-01
...
4.38e+02  2.76e-01 5.94e-01 2.00e-01  3.00e-01 -5.11e-01
...
4.57e+02  2.78e-01 6.47e-01 1.27e-01  3.73e-01 -5.65e-01
...
4.77e+02  1.86e-01 7.85e-01 2.25e-01  2.75e-01 -6.11e-01
...
4.97e+02  1.16e-01 9.39e-01 8.89e-01 -3.89e-01 -6.95e-01
...
5.17e+02  8.31e-02 8.25e-01 8.55e-01 -3.55e-01 -5.48e-01
...
5.37e+02  7.33e-02 6.66e-01 7.41e-01 -2.41e-01 -3.79e-01
...
5.57e+02  1.03e-01 4.67e-01 5.05e-01 -4.89e-03 -2.10e-01
...
5.77e+02  2.15e-01 3.07e-01 2.82e-01  2.18e-01 -1.61e-01
...
5.97e+02  2.04e-01 3.48e-01 3.25e-01  1.75e-01 -1.93e-01
...
6.17e+02  2.32e-01 3.44e-01 2.71e-01  2.29e-01 -2.16e-01
...
6.36e+02  2.26e-01 3.84e-01 2.52e-01  2.48e-01 -2.50e-01
...
6.56e+02  2.29e-01 4.28e-01 2.51e-01  2.49e-01 -2.98e-01
...
6.76e+02  2.47e-01 4.64e-01 2.29e-01  2.71e-01 -3.50e-01
...
6.96e+02  2.54e-01 5.12e-01 1.96e-01  3.04e-01 -4.06e-01
...
7.16e+02  2.40e-01 5.87e-01 1.88e-01  3.12e-01 -4.68e-01
...
7.36e+02  2.16e-01 6.84e-01 2.27e-01  2.73e-01 -5.40e-01
...
7.56e+02  2.05e-01 7.80e-01 3.53e-01  1.47e-01 -6.25e-01
...
7.76e+02  3.26e-01 6.70e-01 5.86e-02  4.41e-01 -6.36e-01
...
7.96e+02  9.14e-02 8.94e-01 8.82e-01 -3.82e-01 -6.26e-01
...
8.15e+02  7.75e-02 7.47e-01 8.09e-01 -3.09e-01 -4.65e-01
...
8.35e+02  7.25e-02 5.77e-01 6.40e-01 -1.40e-01 -2.90e-01
...
8.55e+02  1.69e-01 3.57e-01 3.66e-01  1.34e-01 -1.67e-01
...
8.75e+02  2.32e-01 3.10e-01 3.11e-01  1.89e-01 -1.82e-01
...
8.95e+02  2.16e-01 3.42e-01 2.79e-01  2.21e-01 -1.98e-01
...
9.15e+02  2.21e-01 3.75e-01 2.82e-01  2.18e-01 -2.35e-01
...
9.35e+02  2.39e-01 3.95e-01 2.46e-01  2.54e-01 -2.74e-01
...
9.55e+02  2.38e-01 4.42e-01 2.22e-01  2.78e-01 -3.20e-01
...
9.75e+02  2.20e-01 3.81e-01 2.74e-01  2.26e-01 -2.40e-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_3, iteration_5, iteration_7)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 8
## Thoughts

Setting the initial concentration of `id_plsk` to 0.5 (with all others at default) produces a time series nearly identical to when `id_22ta` is set to 0.5, but with the sign of `id_plsk` and `id_22ta` swapped. This further confirms that `id_22ta` and `id_plsk` are perfectly anti-correlated and are interconverted in a 1:1 reversible reaction.

The other species (`id_r7xb`, `id_x589`, `id_0nyd`) show the same oscillatory behavior as before, with the system always returning to its characteristic regime. The sum of all species remains conserved.

Given the evidence, the following reactions are strongly supported:
1. `id_22ta <-> id_plsk` (1:1 reversible)
2. The remaining relationships are less clear, but the strong negative correlation between `id_r7xb` and `id_0nyd` suggests a direct or indirect conversion, possibly involving `id_x589`.

To further clarify the role of `id_0nyd`, I will set its initial concentration to 0.5 and observe the system's response. This will help determine if it is directly interconverted with `id_r7xb` or if other species are involved.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_0nyd": 0.5
    }
}
```
# 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: 10001 rows × 6 columns. 

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

Time   id_x589  id_r7xb  id_22ta   id_plsk   id_0nyd
0         0 3.60e-01        0         0  5.00e-01
...
1.99e+01  2.05e-01 3.48e-01 3.26e-01 -3.26e-01  3.07e-01
...
3.98e+01  2.32e-01 3.43e-01 2.71e-01 -2.71e-01  2.84e-01
...
5.97e+01  2.26e-01 3.84e-01 2.53e-01 -2.53e-01  2.50e-01
...
7.96e+01  2.30e-01 4.27e-01 2.52e-01 -2.52e-01  2.03e-01
...
9.95e+01  2.47e-01 4.62e-01 2.28e-01 -2.28e-01  1.51e-01
...
1.19e+02  2.53e-01 5.11e-01 1.95e-01 -1.95e-01  9.54e-02
...
1.39e+02  2.39e-01 5.88e-01 1.90e-01 -1.90e-01  3.30e-02
...
1.59e+02  2.17e-01 6.83e-01 2.31e-01 -2.31e-01 -3.99e-02
...
1.79e+02  2.11e-01 7.73e-01 3.53e-01 -3.53e-01 -1.24e-01
...
1.99e+02  3.16e-01 6.77e-01 6.22e-02 -6.22e-02 -1.33e-01
...
2.19e+02  9.18e-02 8.97e-01 8.83e-01 -8.83e-01 -1.28e-01
...
2.39e+02  7.77e-02 7.50e-01 8.11e-01 -8.11e-01  3.19e-02
...
2.59e+02  7.23e-02 5.81e-01 6.45e-01 -6.45e-01  2.06e-01
...
2.78e+02  1.67e-01 3.61e-01 3.71e-01 -3.71e-01  3.32e-01
...
2.98e+02  2.33e-01 3.08e-01 3.08e-01 -3.08e-01  3.19e-01
...
3.18e+02  2.15e-01 3.42e-01 2.81e-01 -2.81e-01  3.02e-01
...
3.38e+02  2.21e-01 3.73e-01 2.83e-01 -2.83e-01  2.65e-01
...
3.58e+02  2.39e-01 3.93e-01 2.45e-01 -2.45e-01  2.28e-01
...
3.78e+02  2.37e-01 4.41e-01 2.24e-01 -2.24e-01  1.82e-01
...
3.98e+02  2.34e-01 5.02e-01 2.27e-01 -2.27e-01  1.24e-01
...
4.18e+02  2.45e-01 5.57e-01 2.30e-01 -2.30e-01  5.79e-02
...
4.38e+02  2.77e-01 5.91e-01 1.96e-01 -1.96e-01 -8.73e-03
...
4.57e+02  2.73e-01 6.50e-01 1.29e-01 -1.29e-01 -6.30e-02
...
4.77e+02  1.84e-01 7.88e-01 2.32e-01 -2.32e-01 -1.12e-01
...
4.97e+02  1.19e-01 9.38e-01 8.88e-01 -8.88e-01 -1.98e-01
...
5.17e+02  8.34e-02 8.29e-01 8.56e-01 -8.56e-01 -5.20e-02
...
5.37e+02  7.34e-02 6.70e-01 7.45e-01 -7.45e-01  1.17e-01
...
5.57e+02  9.96e-02 4.73e-01 5.12e-01 -5.12e-01  2.87e-01
...
5.77e+02  2.12e-01 3.09e-01 2.84e-01 -2.84e-01  3.39e-01
...
5.97e+02  2.05e-01 3.48e-01 3.27e-01 -3.27e-01  3.07e-01
...
6.17e+02  2.32e-01 3.43e-01 2.70e-01 -2.70e-01  2.85e-01
...
6.36e+02  2.25e-01 3.84e-01 2.54e-01 -2.54e-01  2.51e-01
...
6.56e+02  2.30e-01 4.26e-01 2.52e-01 -2.52e-01  2.04e-01
...
6.76e+02  2.47e-01 4.61e-01 2.27e-01 -2.27e-01  1.52e-01
...
6.96e+02  2.52e-01 5.11e-01 1.96e-01 -1.96e-01  9.66e-02
...
7.16e+02  2.38e-01 5.88e-01 1.93e-01 -1.93e-01  3.39e-02
...
7.36e+02  2.17e-01 6.82e-01 2.34e-01 -2.34e-01 -3.95e-02
...
7.56e+02  2.18e-01 7.66e-01 3.51e-01 -3.51e-01 -1.24e-01
...
7.76e+02  3.05e-01 6.85e-01 6.67e-02 -6.67e-02 -1.31e-01
...
7.96e+02  9.23e-02 8.99e-01 8.84e-01 -8.84e-01 -1.31e-01
...
8.15e+02  7.79e-02 7.53e-01 8.13e-01 -8.13e-01  2.88e-02
...
8.35e+02  7.22e-02 5.85e-01 6.50e-01 -6.50e-01  2.03e-01
...
8.55e+02  1.65e-01 3.63e-01 3.75e-01 -3.75e-01  3.31e-01
...
8.75e+02  2.34e-01 3.06e-01 3.05e-01 -3.05e-01  3.20e-01
...
8.95e+02  2.14e-01 3.43e-01 2.82e-01 -2.82e-01  3.03e-01
...
9.15e+02  2.22e-01 3.72e-01 2.84e-01 -2.84e-01  2.66e-01
...
9.35e+02  2.39e-01 3.92e-01 2.44e-01 -2.44e-01  2.29e-01
...
9.55e+02  2.36e-01 4.41e-01 2.25e-01 -2.25e-01  1.83e-01
...
9.75e+02  2.20e-01 3.80e-01 2.77e-01 -2.77e-01  2.61e-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_3, iteration_5, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 9
## Thoughts

Setting the initial concentration of `id_0nyd` to 0.5 (with all others at default) results in:
- `id_0nyd` starts positive and then oscillates, but its pattern is a phase-shifted version of the default, with the sign flipped compared to when it starts at zero.
- The other species (`id_r7xb`, `id_x589`, `id_22ta`, `id_plsk`) show the same oscillatory behavior as before, with the system returning to its characteristic regime.
- The sum of all species remains conserved.

This further supports the idea that `id_0nyd` is tightly coupled to the cycle, and its dynamics are phase-shifted depending on its initial value. The strong negative correlation with `id_r7xb` suggests a direct or indirect conversion, but the relationship is not as perfect as between `id_22ta` and `id_plsk`.

Given the evidence, I am confident in adding the reversible reaction:
- `id_22ta <-> id_plsk`

For the other species, the oscillatory and phase-shifted behavior suggests a cycle involving all five species. The conservation of the sum and the phase relationships suggest a closed loop, possibly:
- `id_r7xb <-> id_0nyd`
- `id_0nyd <-> id_x589`
- `id_x589 <-> id_22ta`

I will now analyze the time derivatives of the species to look for direct conversion relationships (e.g., does the rate of change of one species match the negative rate of change of another?).

## Action

### Code
```python
df = experiment_history['iteration_0']

# Compute time derivatives (finite difference)
dt = df['Time'].diff().fillna(0)
derivatives = df.drop(columns='Time').diff().divide(dt, axis=0).fillna(0)

# Correlate derivatives to look for direct conversion relationships
deriv_corr = derivatives.corr()
print("Correlation matrix of time derivatives:\n", deriv_corr)

# Print a few rows of derivatives for inspection
print("\nFirst 5 rows of derivatives:\n", derivatives.head())
```
# Observation

## Code Stdout
Correlation matrix of time derivatives:
           id_x589   id_r7xb   id_22ta   id_plsk   id_0nyd
id_x589  1.000000 -0.736441 -0.679068  0.679068 -0.000392
id_r7xb -0.736441  1.000000  0.758432 -0.758432 -0.676213
id_22ta -0.679068  0.758432  1.000000 -1.000000 -0.381608
id_plsk  0.679068 -0.758432 -1.000000  1.000000  0.381608
id_0nyd -0.000392 -0.676213 -0.381608  0.381608  1.000000

First 5 rows of derivatives:
     id_x589   id_r7xb   id_22ta   id_plsk   id_0nyd
0  0.000000  0.000000  0.000000  0.000000  0.000000
1  0.645424  0.868650  3.946887 -3.946887 -1.514075
2  0.055867  1.286667  2.394878 -2.394878 -1.342534
3  0.058217  1.230385  1.437951 -1.437951 -1.288602
4  0.072475  1.153400  0.838465 -0.838465 -1.225875

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_3, iteration_5, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 10
## Thoughts

- The time derivative of `id_22ta` and `id_plsk` are perfectly anti-correlated (-1.0), confirming a direct reversible reaction: `id_22ta <-> id_plsk`.
- The time derivative of `id_r7xb` is strongly positively correlated with `id_22ta` (0.76) and negatively with `id_x589` (-0.74), suggesting a flow: `id_r7xb` → `id_22ta` → `id_plsk` and possibly `id_r7xb` → `id_x589`.
- The time derivative of `id_0nyd` is negatively correlated with `id_r7xb` (-0.68) and weakly with `id_22ta` (-0.38), and positively with `id_plsk` (0.38), suggesting it is downstream of these.
- The sum of all derivatives at each time point should be zero (since the sum of all species is conserved), which is consistent with a closed cycle.

Given these relationships, a plausible minimal cycle is:
1. `id_r7xb → id_22ta`
2. `id_22ta <-> id_plsk`
3. `id_plsk → id_0nyd`
4. `id_0nyd → id_x589`
5. `id_x589 → id_r7xb`

This would close the loop and explain the conservation and oscillatory behavior.

I will now attempt to add these reactions (with mass-action kinetics and arbitrary rate constants) to the SBML model and simulate to see if the qualitative behavior matches the observed data.

## Action

### Code
```python
import libsbml

# Load the incomplete SBML model
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 id_r7xb → id_22ta
r1 = model.createReaction()
r1.setId("r1")
r1.setReversible(False)
r1.setFast(False)
reactant = r1.createReactant()
reactant.setSpecies("id_r7xb")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = r1.createProduct()
product.setSpecies("id_22ta")
product.setStoichiometry(1.0)
product.setConstant(False)
kl1 = model.createParameter()
kl1.setId("k1")
kl1.setValue(1.0)
kl1.setConstant(True)
kinetic_law1 = r1.createKineticLaw()
kinetic_law1.setFormula("k1 * id_r7xb")

# Add id_22ta <-> id_plsk
r2 = model.createReaction()
r2.setId("r2")
r2.setReversible(True)
r2.setFast(False)
reactant = r2.createReactant()
reactant.setSpecies("id_22ta")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = r2.createProduct()
product.setSpecies("id_plsk")
product.setStoichiometry(1.0)
product.setConstant(False)
k2f = model.createParameter()
k2f.setId("k2f")
k2f.setValue(1.0)
k2f.setConstant(True)
k2r = model.createParameter()
k2r.setId("k2r")
k2r.setValue(1.0)
k2r.setConstant(True)
kinetic_law2 = r2.createKineticLaw()
kinetic_law2.setFormula("k2f * id_22ta - k2r * id_plsk")

# Add id_plsk → id_0nyd
r3 = model.createReaction()
r3.setId("r3")
r3.setReversible(False)
r3.setFast(False)
reactant = r3.createReactant()
reactant.setSpecies("id_plsk")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = r3.createProduct()
product.setSpecies("id_0nyd")
product.setStoichiometry(1.0)
product.setConstant(False)
k3 = model.createParameter()
k3.setId("k3")
k3.setValue(1.0)
k3.setConstant(True)
kinetic_law3 = r3.createKineticLaw()
kinetic_law3.setFormula("k3 * id_plsk")

# Add id_0nyd → id_x589
r4 = model.createReaction()
r4.setId("r4")
r4.setReversible(False)
r4.setFast(False)
reactant = r4.createReactant()
reactant.setSpecies("id_0nyd")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = r4.createProduct()
product.setSpecies("id_x589")
product.setStoichiometry(1.0)
product.setConstant(False)
k4 = model.createParameter()
k4.setId("k4")
k4.setValue(1.0)
k4.setConstant(True)
kinetic_law4 = r4.createKineticLaw()
kinetic_law4.setFormula("k4 * id_0nyd")

# Add id_x589 → id_r7xb
r5 = model.createReaction()
r5.setId("r5")
r5.setReversible(False)
r5.setFast(False)
reactant = r5.createReactant()
reactant.setSpecies("id_x589")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = r5.createProduct()
product.setSpecies("id_r7xb")
product.setStoichiometry(1.0)
product.setConstant(False)
k5 = model.createParameter()
k5.setId("k5")
k5.setValue(1.0)
k5.setConstant(True)
kinetic_law5 = r5.createKineticLaw()
kinetic_law5.setFormula("k5 * id_x589")

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

# Simulate and compare to experiment
sim_df = simulate(updated_sbml)
print(sim_df.head(10))
shared_variables.add("cycle_model_sbml", updated_sbml)
```
# Observation

## Code Stdout
    id_x589   id_r7xb   id_22ta   id_plsk   id_0nyd    Time
0  0.000000  0.360000  0.000000  0.000000  0.000000  0.0000
1  0.000001  0.326557  0.031889  0.001504  0.000049  0.0975
2  0.000017  0.296221  0.058113  0.005300  0.000350  0.1950
3  0.000078  0.268707  0.079643  0.010524  0.001048  0.2925
4  0.000219  0.243758  0.097268  0.016547  0.002208  0.3900
5  0.000477  0.221145  0.111628  0.022911  0.003839  0.4875
6  0.000884  0.200663  0.123250  0.029290  0.005913  0.5850
7  0.001465  0.182130  0.132567  0.035460  0.008378  0.6825
8  0.002237  0.165382  0.139939  0.041271  0.011172  0.7800
9  0.003209  0.150270  0.145668  0.046629  0.014224  0.8775

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_3, iteration_5, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (cycle_model_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 simulated model with the closed cycle of five reactions produces a monotonic redistribution of concentrations, not the oscillatory behavior observed in the experimental data. In the simulation, `id_x589` starts at zero and slowly increases, while `id_r7xb` decreases, and the other species gradually change as well. There are no oscillations or negative concentrations, which is an improvement, but the model does not capture the periodicity seen in the real system.

This suggests that the real system likely involves additional feedback or nonlinearities, such as autocatalysis, inhibition, or higher-order reactions, which are necessary to produce sustained oscillations.

Given the perfect anti-correlation between `id_22ta` and `id_plsk`, and the strong negative correlation between `id_r7xb` and `id_0nyd`, it is possible that one or more reactions are autocatalytic or involve nonlinear feedback.

A classic motif for oscillations is the presence of a negative feedback loop with a delay, or an autocatalytic step. I will now analyze the time series for evidence of such nonlinearities (e.g., does the rate of change of a species depend nonlinearly on its own concentration or that of another?).

## Action

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

df = experiment_history['iteration_0']

# Plot time series for all species to visually inspect for phase relationships and oscillatory behavior
plt.figure(figsize=(10,6))
for col in ['id_x589', 'id_r7xb', 'id_22ta', 'id_plsk', 'id_0nyd']:
    plt.plot(df['Time'], df[col], label=col)
plt.legend()
plt.xlabel('Time')
plt.ylabel('Concentration')
plt.title('Time Series of All Species (iteration_0)')
plt.show()

# Plot phase plane: id_r7xb vs id_0nyd and id_22ta vs id_plsk
plt.figure(figsize=(6,6))
plt.plot(df['id_r7xb'], df['id_0nyd'], label='id_r7xb vs id_0nyd')
plt.xlabel('id_r7xb')
plt.ylabel('id_0nyd')
plt.title('Phase Plane: id_r7xb vs id_0nyd')
plt.show()

plt.figure(figsize=(6,6))
plt.plot(df['id_22ta'], df['id_plsk'], label='id_22ta vs id_plsk')
plt.xlabel('id_22ta')
plt.ylabel('id_plsk')
plt.title('Phase Plane: id_22ta vs id_plsk')
plt.show()
```
# 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: 9/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_3, iteration_5, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (cycle_model_sbml)

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


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



# Iteration 12
## Thoughts

I attempted to visualize the time series and phase planes to look for nonlinearities and feedback, but plotting is not allowed. Instead, I will analyze the data numerically for evidence of nonlinear relationships, such as:
- Whether the rate of change of a species depends nonlinearly on its own concentration or that of another (e.g., quadratic or product terms).
- Whether there is evidence for autocatalysis or inhibition.

I will fit simple linear and nonlinear models to the time derivatives of key species (e.g., `id_22ta`, `id_r7xb`) as a function of the concentrations of all species, and compare the fit quality. This may reveal the need for nonlinear terms in the reaction kinetics.

## Action

### Code
```python
import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures

df = experiment_history['iteration_0']
dt = df['Time'].diff().fillna(0)
derivatives = df.drop(columns='Time').diff().divide(dt, axis=0).fillna(0)

# Focus on d(id_22ta)/dt as a function of all species
X = df[['id_x589', 'id_r7xb', 'id_22ta', 'id_plsk', 'id_0nyd']].values
y = derivatives['id_22ta'].values

# Linear fit
linreg = LinearRegression().fit(X, y)
r2_linear = linreg.score(X, y)

# Quadratic fit
poly = PolynomialFeatures(degree=2, include_bias=False)
X_poly = poly.fit_transform(X)
linreg2 = LinearRegression().fit(X_poly, y)
r2_quadratic = linreg2.score(X_poly, y)

print("R^2 for linear fit (d(id_22ta)/dt):", r2_linear)
print("R^2 for quadratic fit (d(id_22ta)/dt):", r2_quadratic)

# Print coefficients for quadratic fit to see which terms are important
coefs = linreg2.coef_
feature_names = poly.get_feature_names_out(['id_x589', 'id_r7xb', 'id_22ta', 'id_plsk', 'id_0nyd'])
coef_table = pd.DataFrame({'feature': feature_names, 'coef': coefs})
print(coef_table.sort_values('coef', key=np.abs, ascending=False).head(10))
```
# Observation

## Code Stdout
R^2 for linear fit (d(id_22ta)/dt): 0.37327517273873945
R^2 for quadratic fit (d(id_22ta)/dt): 0.8654513093869135
            feature       coef
5         id_x589^2 -84.534950
6   id_x589 id_r7xb  60.465751
10        id_r7xb^2 -39.107747
12  id_r7xb id_plsk -34.954769
11  id_r7xb id_22ta  34.954769
9   id_x589 id_0nyd  34.165638
8   id_x589 id_plsk  32.457181
7   id_x589 id_22ta -32.457181
0           id_x589  28.045665
14        id_22ta^2 -25.309882

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_3, iteration_5, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (cycle_model_sbml)

### 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 linear model explains only ~37% of the variance in d(id_22ta)/dt, while the quadratic model explains ~87%. This is strong evidence that the system's dynamics are highly nonlinear.
- The most important terms in the quadratic fit are cross-terms and squared terms, especially `id_x589^2`, `id_x589 * id_r7xb`, `id_r7xb^2`, and mixed terms involving `id_22ta`, `id_plsk`, and `id_0nyd`.
- This suggests that the production or consumption of `id_22ta` depends on nonlinear interactions, possibly autocatalysis or inhibition, and not just simple mass-action kinetics.

Given this, the model should include at least one nonlinear (e.g., quadratic or product) term in the reaction rates. A classic oscillatory motif is the Lotka-Volterra or Brusselator, which includes autocatalytic and inhibitory terms.

I will now attempt to modify the SBML model to include a nonlinear (autocatalytic) term in the conversion of `id_r7xb` to `id_22ta`, e.g., rate = k1 * id_r7xb * id_x589, and see if this produces oscillations.

## Action

### Code
```python
import libsbml

# Load the previous cycle model
sbml_doc = libsbml.readSBMLFromString(shared_variables.access("cycle_model_sbml"))
model = sbml_doc.getModel()

# Modify the first reaction to be autocatalytic: id_r7xb + id_x589 -> id_22ta
r1 = model.getReaction("r1")
# Remove all reactants and products first
while r1.getNumReactants() > 0:
    r1.removeReactant(0)
while r1.getNumProducts() > 0:
    r1.removeProduct(0)
# Add new reactants
reactant1 = r1.createReactant()
reactant1.setSpecies("id_r7xb")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)
reactant2 = r1.createReactant()
reactant2.setSpecies("id_x589")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
# Add product
product = r1.createProduct()
product.setSpecies("id_22ta")
product.setStoichiometry(1.0)
product.setConstant(False)
# Update kinetic law
r1.getKineticLaw().setFormula("k1 * id_r7xb * id_x589")

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

# Simulate and compare to experiment
sim_df = simulate(updated_sbml)
print(sim_df.head(10))
shared_variables.add("autocat_model_sbml", updated_sbml)
```
# Observation

## Code Stdout
   id_x589  id_r7xb  id_22ta  id_plsk  id_0nyd    Time
0      0.0     0.36      0.0      0.0      0.0  0.0000
1      0.0     0.36      0.0      0.0      0.0  0.0975
2      0.0     0.36      0.0      0.0      0.0  0.1950
3      0.0     0.36      0.0      0.0      0.0  0.2925
4      0.0     0.36      0.0      0.0      0.0  0.3900
5      0.0     0.36      0.0      0.0      0.0  0.4875
6      0.0     0.36      0.0      0.0      0.0  0.5850
7      0.0     0.36      0.0      0.0      0.0  0.6825
8      0.0     0.36      0.0      0.0      0.0  0.7800
9      0.0     0.36      0.0      0.0      0.0  0.8775

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_3, iteration_5, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (cycle_model_sbml, autocat_model_sbml)

### 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

The autocatalytic model (`id_r7xb + id_x589 -> id_22ta`) fails to produce any dynamics: all species except `id_r7xb` remain at zero. This is because both reactants are required for the reaction, but `id_x589` starts at zero, so the reaction cannot proceed. This suggests that the autocatalytic step alone is insufficient, or that the cycle needs to be closed in a way that allows for the initial production of `id_x589`.

Given the strong quadratic and cross-terms in the regression, it is possible that more than one reaction needs to be nonlinear, or that a combination of linear and nonlinear terms is required. Alternatively, the system may require a "leak" or basal production of `id_x589` to initiate the cycle.

A classic oscillatory system is the Brusselator, which includes both linear and nonlinear terms. I will try modifying the model so that the conversion of `id_0nyd` to `id_x589` is also autocatalytic (e.g., `id_0nyd + id_x589 -> 2 id_x589`), and restore the original mass-action for the other steps.

## Action

### Code
```python
import libsbml

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

# Modify r4: id_0nyd + id_x589 -> 2 id_x589 (autocatalytic)
r4 = model.getReaction("r4")
while r4.getNumReactants() > 0:
    r4.removeReactant(0)
while r4.getNumProducts() > 0:
    r4.removeProduct(0)
reactant1 = r4.createReactant()
reactant1.setSpecies("id_0nyd")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)
reactant2 = r4.createReactant()
reactant2.setSpecies("id_x589")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product = r4.createProduct()
product.setSpecies("id_x589")
product.setStoichiometry(2.0)
product.setConstant(False)
r4.getKineticLaw().setFormula("k4 * id_0nyd * id_x589")

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

# Simulate and compare to experiment
sim_df = simulate(updated_sbml)
print(sim_df.head(10))
shared_variables.add("autocat2_model_sbml", updated_sbml)
```
# Observation

## Code Stdout
   id_x589   id_r7xb   id_22ta   id_plsk   id_0nyd    Time
0      0.0  0.360000  0.000000  0.000000  0.000000  0.0000
1      0.0  0.326557  0.031889  0.001504  0.000050  0.0975
2      0.0  0.296220  0.058113  0.005300  0.000367  0.1950
3      0.0  0.268702  0.079643  0.010524  0.001130  0.2925
4      0.0  0.243740  0.097267  0.016547  0.002445  0.3900
5      0.0  0.221098  0.111624  0.022910  0.004368  0.4875
6      0.0  0.200558  0.123239  0.029289  0.006913  0.5850
7      0.0  0.181927  0.132543  0.035458  0.010072  0.6825
8      0.0  0.165026  0.139892  0.041266  0.013816  0.7800
9      0.0  0.149696  0.145581  0.046619  0.018104  0.8775

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_3, iteration_5, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (cycle_model_sbml, autocat_model_sbml, autocat2_model_sbml)

### 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 modified model, where `id_0nyd + id_x589 -> 2 id_x589` is autocatalytic, still does not produce oscillations or significant dynamics for `id_x589`. `id_x589` remains at zero, indicating that the cycle cannot start because there is no initial `id_x589` to catalyze its own production. This suggests that the system needs a basal production or "leak" reaction to initiate the cycle, or that the autocatalytic step is not the correct mechanism.

Given the strong quadratic and cross-terms in the regression, and the classic motifs for oscillatory systems, I will try adding a small basal production of `id_x589` from nothing (zero-order reaction), which can act as a seed for the cycle. This is analogous to the "A" inflow in the Brusselator model.

## Action

### Code
```python
import libsbml

# Start from the previous autocatalytic model
sbml_doc = libsbml.readSBMLFromString(shared_variables.access("autocat2_model_sbml"))
model = sbml_doc.getModel()

# Add a zero-order production of id_x589: null -> id_x589
r_seed = model.createReaction()
r_seed.setId("r_seed")
r_seed.setReversible(False)
r_seed.setFast(False)
product = r_seed.createProduct()
product.setSpecies("id_x589")
product.setStoichiometry(1.0)
product.setConstant(False)
k_seed = model.createParameter()
k_seed.setId("k_seed")
k_seed.setValue(0.01)
k_seed.setConstant(True)
kinetic_law_seed = r_seed.createKineticLaw()
kinetic_law_seed.setFormula("k_seed")

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

# Simulate and compare to experiment
sim_df = simulate(updated_sbml)
print(sim_df.head(10))
shared_variables.add("autocat2_seed_model_sbml", updated_sbml)
```
# Observation

## Code Stdout
    id_x589   id_r7xb   id_22ta   id_plsk   id_0nyd    Time
0  0.000000  0.360000  0.000000  0.000000  0.000000  0.0000
1  0.000929  0.326601  0.031890  0.001504  0.000050  0.0975
2  0.001772  0.296388  0.058123  0.005300  0.000367  0.1950
3  0.002536  0.269055  0.079677  0.010527  0.001130  0.2925
4  0.003230  0.244329  0.097341  0.016554  0.002445  0.3900
5  0.003860  0.221962  0.111760  0.022925  0.004367  0.4875
6  0.004433  0.201728  0.123459  0.029317  0.006913  0.5850
7  0.004954  0.183425  0.132870  0.035505  0.010071  0.6825
8  0.005428  0.166868  0.140349  0.041340  0.013815  0.7800
9  0.005861  0.151892  0.146192  0.046727  0.018103  0.8775

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_3, iteration_5, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (cycle_model_sbml, autocat_model_sbml, autocat2_model_sbml, autocat2_seed_model_sbml)

### 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 basal production of `id_x589` allows the cycle to start, but the system still does not produce oscillations. Instead, the concentrations change monotonically, similar to previous linear models. This suggests that the current set of reactions and nonlinearities is still insufficient to generate the observed oscillatory behavior.

Given the strong quadratic and cross-terms in the regression, and the classic motifs for oscillatory systems (e.g., the Brusselator or Oregonator), it is likely that the system requires both autocatalytic production and nonlinear inhibition or depletion.

A common feature in such models is a nonlinear consumption or inhibition step. I will try modifying the conversion of `id_22ta` to `id_plsk` to include a nonlinear inhibition term, such as `rate = k2f * id_22ta - k2r * id_plsk * id_x589`, introducing a cross-term that could provide the necessary feedback for oscillations.

## Action

### Code
```python
import libsbml

# Start from the previous model with basal production
sbml_doc = libsbml.readSBMLFromString(shared_variables.access("autocat2_seed_model_sbml"))
model = sbml_doc.getModel()

# Modify r2: id_22ta <-> id_plsk, with nonlinear inhibition by id_x589
r2 = model.getReaction("r2")
r2.getKineticLaw().setFormula("k2f * id_22ta - k2r * id_plsk * id_x589")

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

# Simulate and compare to experiment
sim_df = simulate(updated_sbml)
print(sim_df.head(10))
shared_variables.add("oscillator_model_sbml", updated_sbml)
```
# Observation

## Code Stdout
    id_x589   id_r7xb   id_22ta   id_plsk   id_0nyd    Time
0  0.000000  0.360000  0.000000  0.000000  0.000000  0.0000
1  0.000929  0.326601  0.031841  0.001552  0.000052  0.0975
2  0.001772  0.296388  0.057774  0.005632  0.000385  0.1950
3  0.002536  0.269055  0.078631  0.011495  0.001208  0.2925
4  0.003230  0.244329  0.095139  0.018538  0.002664  0.3900
5  0.003860  0.221962  0.107933  0.026277  0.004843  0.4875
6  0.004433  0.201728  0.117567  0.034328  0.007794  0.5850
7  0.004954  0.183425  0.124524  0.042391  0.011530  0.6825
8  0.005430  0.166868  0.129224  0.050237  0.016042  0.7800
9  0.005864  0.151892  0.132030  0.057692  0.021297  0.8775

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_3, iteration_5, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (cycle_model_sbml, autocat_model_sbml, autocat2_model_sbml, autocat2_seed_model_sbml, oscillator_model_sbml)

### 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

Even after introducing a nonlinear inhibition term (`- k2r * id_plsk * id_x589`) in the reversible reaction between `id_22ta` and `id_plsk`, the model still does not produce oscillations. The concentrations change monotonically, and there is no sign of the periodic behavior observed in the experimental data.

This suggests that the current model structure is still missing a crucial element for oscillatory dynamics. In classic chemical oscillators (e.g., Brusselator, Oregonator), oscillations arise from a combination of autocatalysis and nonlinear inhibition, often with a "sink" or outflow reaction that prevents the system from reaching a static equilibrium.

Given the conservation of total mass in the experimental data, it is likely that all reactions should be interconverting species, but the system may require a more complex nonlinear feedback, such as a quadratic depletion or a higher-order autocatalytic step.

Given the strong quadratic term for `id_x589^2` in the regression, I will try making the conversion of `id_x589` to `id_r7xb` a quadratic (autocatalytic) reaction: `id_x589 + id_r7xb -> 2 id_r7xb`, and see if this produces oscillations.

## Action

### Code
```python
import libsbml

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

# Modify r5: id_x589 + id_r7xb -> 2 id_r7xb (autocatalytic)
r5 = model.getReaction("r5")
while r5.getNumReactants() > 0:
    r5.removeReactant(0)
while r5.getNumProducts() > 0:
    r5.removeProduct(0)
reactant1 = r5.createReactant()
reactant1.setSpecies("id_x589")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)
reactant2 = r5.createReactant()
reactant2.setSpecies("id_r7xb")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product = r5.createProduct()
product.setSpecies("id_r7xb")
product.setStoichiometry(2.0)
product.setConstant(False)
r5.getKineticLaw().setFormula("k5 * id_x589 * id_r7xb")

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

# Simulate and compare to experiment
sim_df = simulate(updated_sbml)
print(sim_df.head(10))
shared_variables.add("oscillator2_model_sbml", updated_sbml)
```
# Observation

## Code Stdout
    id_x589   id_r7xb   id_22ta   id_plsk   id_0nyd    Time
0  0.000000  0.360000  0.000000  0.000000  0.000000  0.0000
1  0.000959  0.326572  0.031840  0.001552  0.000052  0.0975
2  0.001891  0.296276  0.057767  0.005632  0.000385  0.1950
3  0.002802  0.268814  0.078609  0.011493  0.001207  0.2925
4  0.003696  0.243919  0.095089  0.018533  0.002663  0.3900
5  0.004579  0.221349  0.107841  0.026264  0.004842  0.4875
6  0.005454  0.200884  0.117418  0.034303  0.007790  0.5850
7  0.006325  0.182327  0.124303  0.042347  0.011522  0.6825
8  0.007195  0.165499  0.128916  0.050166  0.016026  0.7800
9  0.008066  0.150236  0.131620  0.057584  0.021268  0.8775

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_3, iteration_5, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (cycle_model_sbml, autocat_model_sbml, autocat2_model_sbml, autocat2_seed_model_sbml, oscillator_model_sbml, oscillator2_model_sbml)

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


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



# Iteration 18
## Thoughts

Even after making the conversion of `id_x589` to `id_r7xb` autocatalytic (`id_x589 + id_r7xb -> 2 id_r7xb`), the model still does not produce oscillations. The concentrations change monotonically, and there is no sign of the periodic behavior observed in the experimental data.

This suggests that the current model structure, even with nonlinearities and a basal production, is still missing a crucial element for oscillatory dynamics. In classic chemical oscillators, oscillations often arise from a combination of autocatalysis, nonlinear inhibition, and a "sink" or outflow reaction. However, the experimental data show strict conservation of total mass, so all reactions must be interconversions.

Given the strong quadratic and cross-terms in the regression, perhaps more than one reaction needs to be nonlinear, or the rates need to be tuned. Alternatively, the system may require a delay or a higher-order feedback loop.

As a final attempt, I will make both the conversion of `id_r7xb` to `id_22ta` and `id_x589` to `id_r7xb` autocatalytic, and keep the nonlinear inhibition in the reversible step. This will maximize the nonlinear feedback in the system and may produce oscillations.

## Action

### Code
```python
import libsbml

# Start from the previous oscillator2 model
sbml_doc = libsbml.readSBMLFromString(shared_variables.access("oscillator2_model_sbml"))
model = sbml_doc.getModel()

# Modify r1: id_r7xb + id_x589 -> id_22ta (autocatalytic)
r1 = model.getReaction("r1")
while r1.getNumReactants() > 0:
    r1.removeReactant(0)
while r1.getNumProducts() > 0:
    r1.removeProduct(0)
reactant1 = r1.createReactant()
reactant1.setSpecies("id_r7xb")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)
reactant2 = r1.createReactant()
reactant2.setSpecies("id_x589")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product = r1.createProduct()
product.setSpecies("id_22ta")
product.setStoichiometry(1.0)
product.setConstant(False)
r1.getKineticLaw().setFormula("k1 * id_r7xb * id_x589")

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

# Simulate and compare to experiment
sim_df = simulate(updated_sbml)
print(sim_df.head(10))
shared_variables.add("oscillator3_model_sbml", updated_sbml)
```
# Observation

## Code Stdout
    id_x589  id_r7xb   id_22ta       id_plsk       id_0nyd    Time
0  0.000000     0.36  0.000000  0.000000e+00  0.000000e+00  0.0000
1  0.000942     0.36  0.000016  5.205118e-07  1.285815e-08  0.0975
2  0.001819     0.36  0.000061  3.898674e-06  1.951597e-07  0.1950
3  0.002638     0.36  0.000130  1.232291e-05  9.376264e-07  0.2925
4  0.003400     0.36  0.000220  2.736434e-05  2.813084e-06  0.3900
5  0.004111     0.36  0.000325  5.008492e-05  6.521500e-06  0.4875
6  0.004774     0.36  0.000444  8.113019e-05  1.284478e-05  0.5850
7  0.005392     0.36  0.000573  1.208085e-04  2.260998e-05  0.6825
8  0.005968     0.36  0.000710  1.691584e-04  3.665958e-05  0.7800
9  0.006505     0.36  0.000853  2.260060e-04  5.582803e-05  0.8775

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_3, iteration_5, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (cycle_model_sbml, autocat_model_sbml, autocat2_model_sbml, autocat2_seed_model_sbml, oscillator_model_sbml, oscillator2_model_sbml, oscillator3_model_sbml)

### 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

Even with both `id_r7xb + id_x589 -> id_22ta` and `id_x589 + id_r7xb -> 2 id_r7xb` as autocatalytic steps, and nonlinear inhibition in the reversible step, the model still does not produce oscillations. The concentrations change very slowly and monotonically, and the system does not exhibit the periodic behavior seen in the experimental data.

This suggests that the true system may involve a more complex network of nonlinear feedbacks, or that the rate constants need to be tuned to a regime that supports oscillations. Alternatively, the system may require a different topology, such as a negative feedback loop with a delay, or a higher-order autocatalytic or inhibitory step.

Given the strong evidence for quadratic and cross-terms, and the failure of the current models to produce oscillations, I will try one last approach: I will increase the rate constants for the nonlinear steps by an order of magnitude to see if this pushes the system into an oscillatory regime.

## Action

### Code
```python
import libsbml

# Start from the previous oscillator3 model
sbml_doc = libsbml.readSBMLFromString(shared_variables.access("oscillator3_model_sbml"))
model = sbml_doc.getModel()

# Increase all rate constants by a factor of 10
for pid in ["k1", "k2f", "k2r", "k3", "k4", "k5", "k_seed"]:
    p = model.getParameter(pid) if model.getParameter(pid) else None
    if p:
        p.setValue(p.getValue() * 10)

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

# Simulate and compare to experiment
sim_df = simulate(updated_sbml)
print(sim_df.head(10))
shared_variables.add("oscillator3_fast_model_sbml", updated_sbml)
```
# Observation

## Code Stdout
    id_x589  id_r7xb   id_22ta   id_plsk   id_0nyd    Time
0  0.000000     0.36  0.000000  0.000000  0.000000  0.0000
1  0.007006     0.36  0.001000  0.000291  0.000081  0.0975
2  0.010480     0.36  0.002449  0.001262  0.000798  0.1950
3  0.012214     0.36  0.003534  0.002402  0.002572  0.2925
4  0.013095     0.36  0.004220  0.003349  0.005349  0.3900
5  0.013564     0.36  0.004625  0.004018  0.008869  0.4875
6  0.013834     0.36  0.004860  0.004451  0.012869  0.5850
7  0.014011     0.36  0.004999  0.004719  0.017146  0.6825
8  0.014143     0.36  0.005087  0.004885  0.021569  0.7800
9  0.014254     0.36  0.005148  0.004990  0.026057  0.8775

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_2, iteration_3, iteration_5, iteration_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (cycle_model_sbml, autocat_model_sbml, autocat2_model_sbml, autocat2_seed_model_sbml, oscillator_model_sbml, oscillator2_model_sbml, oscillator3_model_sbml, oscillator3_fast_model_sbml)

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


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



# Iteration 20
## Thoughts

Even after increasing all rate constants by a factor of 10, the model still does not produce oscillations. The concentrations change slightly faster, but the system remains monotonic and does not capture the periodic, oscillatory behavior observed in the experimental data. 

Despite extensive attempts with various nonlinearities, autocatalytic steps, and nonlinear inhibition, the current model structure is unable to reproduce the true system's oscillations. The experimental data suggest a highly nonlinear, possibly higher-order feedback system, but the exact mechanism remains elusive with the current information and time.

Given that this is the last iteration, I will submit the most mechanistically plausible model that incorporates the key findings:
- Conservation of total mass (closed cycle)
- Strong quadratic and cross-terms (nonlinear feedback)
- Autocatalytic and nonlinear inhibition steps

This model is the last one tested, with all nonlinearities and increased rate constants.

## Action

### Submit
```python
import libsbml
final_sbml = shared_variables.access("oscillator3_fast_model_sbml")
```
