
                # 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_ewbh">
    <listOfUnitDefinitions>
      <unitDefinition id="id_hxrc">
        <listOfUnits>
          <unit kind="item"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_twzy">
        <listOfUnits>
          <unit kind="second" multiplier="3600"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_f4nr" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_x8lp" compartment="id_f4nr" initialConcentration="0.8"/>
      <species id="id_ddfe" compartment="id_f4nr" initialConcentration="0.1"/>
      <species id="id_y5nu" compartment="id_f4nr" initialConcentration="0"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

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

The provided SBML model defines three species (`id_x8lp`, `id_ddfe`, `id_y5nu`) but does not include any reactions. My first step should be to observe the time-course behavior of these species under default conditions. This will help me infer possible reactions and their directions (e.g., conversion, production, or degradation). 

## Action

### Experiment

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

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

Total size: 1001 rows × 4 columns. 

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

Time   id_x8lp  id_ddfe  id_y5nu
0  8.00e-01 1.00e-01        0
...
2.00e-01  6.95e-01 8.53e-02 3.18e-04
...
4.00e-01  6.04e-01 7.28e-02 6.86e-04
...
6.00e-01  5.25e-01 6.23e-02 3.33e-03
...
8.00e-01  4.56e-01 5.51e-02 1.91e-02
...
1.00e+00  3.96e-01 5.43e-02 5.50e-02
...
1.20e+00  3.46e-01 6.28e-02 1.09e-01
...
1.40e+00  3.06e-01 8.27e-02 1.79e-01
...
1.60e+00  2.75e-01 1.15e-01 2.60e-01
...
1.80e+00  2.55e-01 1.60e-01 3.51e-01
...
2.00e+00  2.45e-01 2.18e-01 4.46e-01
...
2.20e+00  2.46e-01 2.86e-01 5.43e-01
...
2.40e+00  2.58e-01 3.64e-01 6.37e-01
...
2.60e+00  2.80e-01 4.49e-01 7.26e-01
...
2.80e+00  3.12e-01 5.39e-01 8.06e-01
...
3.00e+00  3.52e-01 6.31e-01 8.73e-01
...
3.20e+00  4.00e-01 7.21e-01 9.26e-01
...
3.40e+00  4.54e-01 8.06e-01 9.60e-01
...
3.60e+00  5.12e-01 8.84e-01 9.76e-01
...
3.80e+00  5.73e-01 9.52e-01 9.72e-01
...
4.00e+00  6.33e-01 1.01e+00 9.47e-01
...
4.20e+00  6.91e-01 1.05e+00 9.02e-01
...
4.40e+00  7.46e-01 1.07e+00 8.37e-01
...
4.60e+00  7.94e-01 1.07e+00 7.55e-01
...
4.80e+00  8.34e-01 1.06e+00 6.58e-01
...
5.00e+00  8.65e-01 1.02e+00 5.49e-01
...
5.20e+00  8.85e-01 9.72e-01 4.32e-01
...
5.40e+00  8.92e-01 9.03e-01 3.09e-01
...
5.60e+00  8.88e-01 8.20e-01 1.86e-01
...
5.80e+00  8.71e-01 7.24e-01 6.74e-02
...
6.00e+00  8.41e-01 6.21e-01 1.70e-04
...
6.20e+00  8.01e-01 5.29e-01 1.95e-04
...
6.40e+00  7.55e-01 4.51e-01 2.34e-04
...
6.60e+00  7.05e-01 3.84e-01 3.01e-04
...
6.80e+00  6.53e-01 3.27e-01 4.26e-04
...
7.00e+00  6.01e-01 2.79e-01 7.22e-04
...
7.20e+00  5.50e-01 2.38e-01 1.87e-03
...
7.40e+00  5.01e-01 2.04e-01 8.11e-03
...
7.60e+00  4.55e-01 1.77e-01 2.67e-02
...
7.80e+00  4.13e-01 1.59e-01 5.96e-02
...
8.00e+00  3.75e-01 1.53e-01 1.06e-01
...
8.20e+00  3.42e-01 1.58e-01 1.65e-01
...
8.40e+00  3.16e-01 1.75e-01 2.33e-01
...
8.60e+00  2.97e-01 2.04e-01 3.09e-01
...
8.80e+00  2.86e-01 2.45e-01 3.90e-01
...
9.00e+00  2.84e-01 2.97e-01 4.73e-01
...
9.20e+00  2.90e-01 3.58e-01 5.56e-01
...
9.40e+00  3.06e-01 4.26e-01 6.35e-01
...
9.60e+00  3.29e-01 5.00e-01 7.07e-01
...
1.00e+01  3.98e-01 6.54e-01 8.22e-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 data, all three species (`id_x8lp`, `id_ddfe`, `id_y5nu`) show oscillatory or cyclic behavior: their concentrations rise and fall over time. This suggests the presence of a cyclic or feedback network, possibly similar to a reversible or oscillatory reaction system (e.g., a simple cycle or a repressilator-like motif).

- `id_x8lp` starts high, decreases, then increases again.
- `id_ddfe` starts low, increases, then decreases, then increases again.
- `id_y5nu` starts at zero, increases, then decreases, then increases again.

This pattern suggests that the species are interconverted, possibly in a cycle (A → B → C → A). To further probe the system, I should perturb the initial concentrations of one or more species and observe the system's response. This will help clarify the directionality and connectivity of the reactions.

I will set the initial concentration of `id_x8lp` to 0 and `id_y5nu` to 1, to see if the system's dynamics are consistent with a cyclic conversion.

## Action

### Experiment

```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_x8lp": 0.0,
        "id_y5nu": 1.0
    }
}
```
# Observation

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

Total size: 1001 rows × 4 columns. 

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

Time   id_x8lp  id_ddfe  id_y5nu
0         0 1.00e-01 1.00e+00
...
2.00e-01  3.04e-02 3.07e-01 1.18e+00
...
4.00e-01  8.73e-02 5.18e-01 1.34e+00
...
6.00e-01  1.67e-01 7.28e-01 1.47e+00
...
8.00e-01  2.65e-01 9.31e-01 1.58e+00
...
1.00e+00  3.79e-01 1.12e+00 1.65e+00
...
1.20e+00  5.02e-01 1.30e+00 1.68e+00
...
1.40e+00  6.31e-01 1.45e+00 1.67e+00
...
1.60e+00  7.61e-01 1.57e+00 1.61e+00
...
1.80e+00  8.87e-01 1.65e+00 1.51e+00
...
2.00e+00  1.00e+00 1.70e+00 1.37e+00
...
2.20e+00  1.11e+00 1.71e+00 1.19e+00
...
2.40e+00  1.20e+00 1.68e+00 9.78e-01
...
2.60e+00  1.26e+00 1.60e+00 7.40e-01
...
2.80e+00  1.30e+00 1.49e+00 4.83e-01
...
3.00e+00  1.32e+00 1.34e+00 2.16e-01
...
3.20e+00  1.31e+00 1.16e+00 6.78e-05
...
3.40e+00  1.28e+00 9.88e-01 7.10e-05
...
3.60e+00  1.22e+00 8.42e-01 7.65e-05
...
3.80e+00  1.16e+00 7.18e-01 8.46e-05
...
4.00e+00  1.08e+00 6.11e-01 9.57e-05
...
4.20e+00  1.01e+00 5.21e-01 1.11e-04
...
4.40e+00  9.28e-01 4.44e-01 1.33e-04
...
4.60e+00  8.51e-01 3.78e-01 1.64e-04
...
4.80e+00  7.77e-01 3.23e-01 2.13e-04
...
5.00e+00  7.06e-01 2.75e-01 2.99e-04
...
5.20e+00  6.39e-01 2.34e-01 4.78e-04
...
5.40e+00  5.77e-01 2.00e-01 1.04e-03
...
5.60e+00  5.19e-01 1.71e-01 4.45e-03
...
5.80e+00  4.65e-01 1.48e-01 1.92e-02
...
6.00e+00  4.17e-01 1.33e-01 4.98e-02
...
6.20e+00  3.75e-01 1.28e-01 9.55e-02
...
6.40e+00  3.38e-01 1.34e-01 1.55e-01
...
6.60e+00  3.10e-01 1.53e-01 2.25e-01
...
6.80e+00  2.89e-01 1.84e-01 3.03e-01
...
7.00e+00  2.76e-01 2.27e-01 3.88e-01
...
7.20e+00  2.73e-01 2.81e-01 4.74e-01
...
7.40e+00  2.79e-01 3.45e-01 5.61e-01
...
7.60e+00  2.94e-01 4.17e-01 6.44e-01
...
7.80e+00  3.18e-01 4.94e-01 7.20e-01
...
8.00e+00  3.50e-01 5.75e-01 7.86e-01
...
8.20e+00  3.90e-01 6.56e-01 8.41e-01
...
8.40e+00  4.35e-01 7.34e-01 8.81e-01
...
8.60e+00  4.85e-01 8.07e-01 9.05e-01
...
8.80e+00  5.38e-01 8.73e-01 9.11e-01
...
9.00e+00  5.92e-01 9.28e-01 8.99e-01
...
9.20e+00  6.45e-01 9.71e-01 8.69e-01
...
9.40e+00  6.95e-01 9.99e-01 8.21e-01
...
9.60e+00  7.41e-01 1.01e+00 7.57e-01
...
1.00e+01  8.13e-01 9.87e-01 5.86e-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 new experiment, where `id_x8lp` starts at 0 and `id_y5nu` at 1, shows a similar oscillatory pattern as the default, but phase-shifted. This strongly supports the hypothesis that the three species are interconverted in a cycle, likely with reactions such as:

- `id_x8lp` → `id_ddfe`
- `id_ddfe` → `id_y5nu`
- `id_y5nu` → `id_x8lp`

The oscillatory behavior and the way the system "rotates" through the species when initial conditions are changed suggest that each species is converted to the next in a unidirectional cycle. The total concentration of all species appears to increase and decrease, which may indicate that the reactions are not strictly mass-conserving, or that the system is being driven by some external input or nonlinear kinetics.

Before building a model, I should check if the total concentration is conserved, and if not, whether there is a net production or degradation. This will help determine if I need to include source/sink terms or nonlinearities.

## Action

### Code

```python
import pandas as pd

# Access the experiment data
df0 = experiment_history['iteration_0']
df1 = experiment_history['iteration_1']

# Calculate total concentration for each time point
df0['total'] = df0['id_x8lp'] + df0['id_ddfe'] + df0['id_y5nu']
df1['total'] = df1['id_x8lp'] + df1['id_ddfe'] + df1['id_y5nu']

# Print summary statistics and a few rows to check conservation
print("Iteration 0: total concentration min/max/mean")
print(df0['total'].min(), df0['total'].max(), df0['total'].mean())
print(df0[['Time', 'total']].head(10))
print(df0[['Time', 'total']].tail(10))

print("\nIteration 1: total concentration min/max/mean")
print(df1['total'].min(), df1['total'].max(), df1['total'].mean())
print(df1[['Time', 'total']].head(10))
print(df1[['Time', 'total']].tail(10))
```
# Observation

## Code Stdout
Iteration 0: total concentration min/max/mean
0.505173750149956 2.6519271057878595 1.361870981183557
   Time     total
0  0.00  0.900000
1  0.01  0.893824
2  0.02  0.887497
3  0.03  0.881215
4  0.04  0.874977
5  0.05  0.868782
6  0.06  0.862631
7  0.07  0.856524
8  0.08  0.850459
9  0.09  0.844437
       Time     total
991    9.91  1.799470
992    9.92  1.807762
993    9.93  1.816033
994    9.94  1.824283
995    9.95  1.832511
996    9.96  1.840716
997    9.97  1.848897
998    9.98  1.857054
999    9.99  1.865186
1000  10.00  1.873292

Iteration 1: total concentration min/max/mean
0.5947791329212504 4.079606932199141 2.0368782915883465
   Time     total
0  0.00  1.100000
1  0.01  1.120039
2  0.02  1.140155
3  0.03  1.160346
4  0.04  1.180610
5  0.05  1.200945
6  0.06  1.221349
7  0.07  1.241819
8  0.08  1.262354
9  0.09  1.282952
       Time     total
991    9.91  2.427579
992    9.92  2.423452
993    9.93  2.419235
994    9.94  2.414929
995    9.95  2.410533
996    9.96  2.406047
997    9.97  2.401473
998    9.98  2.396809
999    9.99  2.392058
1000  10.00  2.387218

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

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


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



# Iteration 3
## Thoughts

The total concentration of all species is not conserved; it increases over time in both experiments. This suggests that there is a net production of mass in the system, possibly due to an external source or autocatalytic reactions. The oscillatory pattern and the increase in total concentration suggest a system with both cyclic interconversion and net production.

A plausible minimal model is:
- Each species is converted to the next in a cycle (A → B → C → A).
- There is an additional production term for at least one species (possibly all).
- There may or may not be degradation.

To further clarify, I should test what happens if I start with all species at zero except one, to see if the system can "self-start" (i.e., if there is spontaneous production from nothing). This will help distinguish between autocatalytic and source-driven production.

## Action

### Experiment

```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_x8lp": 0.0,
        "id_ddfe": 0.0,
        "id_y5nu": 1.0
    }
}
```
# Observation

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

Total size: 1001 rows × 4 columns. 

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

Time   id_x8lp  id_ddfe  id_y5nu
0         0        0 1.00e+00
...
2.00e-01  1.68e-02 2.22e-01 1.18e+00
...
4.00e-01  6.42e-02 4.46e-01 1.35e+00
...
6.00e-01  1.38e-01 6.70e-01 1.49e+00
...
8.00e-01  2.33e-01 8.87e-01 1.61e+00
...
1.00e+00  3.45e-01 1.09e+00 1.69e+00
...
1.20e+00  4.70e-01 1.28e+00 1.73e+00
...
1.40e+00  6.03e-01 1.44e+00 1.73e+00
...
1.60e+00  7.37e-01 1.58e+00 1.68e+00
...
1.80e+00  8.70e-01 1.68e+00 1.59e+00
...
2.00e+00  9.94e-01 1.74e+00 1.45e+00
...
2.20e+00  1.11e+00 1.76e+00 1.27e+00
...
2.40e+00  1.20e+00 1.74e+00 1.06e+00
...
2.60e+00  1.28e+00 1.67e+00 8.20e-01
...
2.80e+00  1.33e+00 1.56e+00 5.57e-01
...
3.00e+00  1.35e+00 1.42e+00 2.81e-01
...
3.20e+00  1.35e+00 1.24e+00 2.25e-03
...
3.40e+00  1.32e+00 1.05e+00 6.72e-05
...
3.60e+00  1.27e+00 8.97e-01 7.19e-05
...
3.80e+00  1.20e+00 7.64e-01 7.88e-05
...
4.00e+00  1.13e+00 6.51e-01 8.85e-05
...
4.20e+00  1.05e+00 5.55e-01 1.02e-04
...
4.40e+00  9.70e-01 4.73e-01 1.20e-04
...
4.60e+00  8.91e-01 4.03e-01 1.46e-04
...
4.80e+00  8.14e-01 3.44e-01 1.86e-04
...
5.00e+00  7.41e-01 2.93e-01 2.50e-04
...
5.20e+00  6.71e-01 2.50e-01 3.72e-04
...
5.40e+00  6.06e-01 2.13e-01 6.76e-04
...
5.60e+00  5.45e-01 1.82e-01 2.06e-03
...
5.80e+00  4.90e-01 1.56e-01 1.04e-02
...
6.00e+00  4.39e-01 1.37e-01 3.36e-02
...
6.20e+00  3.93e-01 1.27e-01 7.26e-02
...
6.40e+00  3.54e-01 1.29e-01 1.26e-01
...
6.60e+00  3.21e-01 1.42e-01 1.91e-01
...
6.80e+00  2.97e-01 1.68e-01 2.67e-01
...
7.00e+00  2.80e-01 2.05e-01 3.49e-01
...
7.20e+00  2.73e-01 2.55e-01 4.35e-01
...
7.40e+00  2.75e-01 3.15e-01 5.22e-01
...
7.60e+00  2.86e-01 3.83e-01 6.07e-01
...
7.80e+00  3.06e-01 4.59e-01 6.87e-01
...
8.00e+00  3.34e-01 5.38e-01 7.58e-01
...
8.20e+00  3.71e-01 6.19e-01 8.19e-01
...
8.40e+00  4.13e-01 6.99e-01 8.66e-01
...
8.60e+00  4.62e-01 7.75e-01 8.97e-01
...
8.80e+00  5.13e-01 8.45e-01 9.11e-01
...
9.00e+00  5.67e-01 9.05e-01 9.08e-01
...
9.20e+00  6.21e-01 9.54e-01 8.86e-01
...
9.40e+00  6.73e-01 9.89e-01 8.46e-01
...
9.60e+00  7.21e-01 1.01e+00 7.89e-01
...
1.00e+01  8.00e-01 1.00e+00 6.30e-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_3)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 4
## Thoughts

The system can "self-start" from a single species, and the oscillatory, cyclic pattern is preserved. This further supports the hypothesis of a cyclic conversion network, possibly with autocatalytic or source-driven production. The total concentration still increases over time, so there must be a net production term in the system.

Given the data, a minimal model would be:
- Three unidirectional reactions forming a cycle:  
  `id_x8lp` → `id_ddfe`  
  `id_ddfe` → `id_y5nu`  
  `id_y5nu` → `id_x8lp`
- Each reaction could be first-order in the reactant.
- There is a net production term, likely as a zero-order (constant) source for at least one species.

To distinguish whether the source is for a specific species or all, I should try starting with all species at zero and see if any production occurs.

## Action

### Experiment

```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_x8lp": 0.0,
        "id_ddfe": 0.0,
        "id_y5nu": 0.0
    }
}
```
# Observation

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

Total size: 1001 rows × 4 columns. 

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

Time   id_x8lp  id_ddfe  id_y5nu
0         0        0        0
...
2.00e-01  9.75e-04 1.88e-02 1.80e-01
...
4.00e-01  7.21e-03 7.13e-02 3.59e-01
...
6.00e-01  2.25e-02 1.52e-01 5.34e-01
...
8.00e-01  4.93e-02 2.56e-01 7.02e-01
...
1.00e+00  8.89e-02 3.77e-01 8.59e-01
...
1.20e+00  1.42e-01 5.11e-01 1.00e+00
...
1.40e+00  2.07e-01 6.52e-01 1.12e+00
...
1.60e+00  2.83e-01 7.94e-01 1.22e+00
...
1.80e+00  3.70e-01 9.32e-01 1.29e+00
...
2.00e+00  4.63e-01 1.06e+00 1.33e+00
...
2.20e+00  5.60e-01 1.17e+00 1.33e+00
...
2.40e+00  6.58e-01 1.27e+00 1.31e+00
...
2.60e+00  7.54e-01 1.34e+00 1.25e+00
...
2.80e+00  8.45e-01 1.39e+00 1.15e+00
...
3.00e+00  9.27e-01 1.40e+00 1.03e+00
...
3.20e+00  9.97e-01 1.39e+00 8.84e-01
...
3.40e+00  1.05e+00 1.35e+00 7.15e-01
...
3.60e+00  1.09e+00 1.28e+00 5.31e-01
...
3.80e+00  1.11e+00 1.17e+00 3.36e-01
...
4.00e+00  1.11e+00 1.05e+00 1.38e-01
...
4.20e+00  1.09e+00 9.03e-01 9.43e-05
...
4.40e+00  1.05e+00 7.69e-01 1.01e-04
...
4.60e+00  1.00e+00 6.56e-01 1.12e-04
...
4.80e+00  9.43e-01 5.59e-01 1.28e-04
...
5.00e+00  8.80e-01 4.76e-01 1.51e-04
...
5.20e+00  8.15e-01 4.06e-01 1.85e-04
...
5.40e+00  7.50e-01 3.46e-01 2.40e-04
...
5.60e+00  6.86e-01 2.95e-01 3.37e-04
...
5.80e+00  6.25e-01 2.51e-01 5.49e-04
...
6.00e+00  5.67e-01 2.14e-01 1.27e-03
...
6.20e+00  5.12e-01 1.83e-01 5.59e-03
...
6.40e+00  4.61e-01 1.59e-01 2.18e-02
...
6.60e+00  4.15e-01 1.43e-01 5.33e-02
...
6.80e+00  3.74e-01 1.37e-01 9.94e-02
...
7.00e+00  3.40e-01 1.43e-01 1.58e-01
...
7.20e+00  3.12e-01 1.61e-01 2.28e-01
...
7.40e+00  2.92e-01 1.92e-01 3.05e-01
...
7.60e+00  2.80e-01 2.34e-01 3.89e-01
...
7.80e+00  2.77e-01 2.87e-01 4.74e-01
...
8.00e+00  2.83e-01 3.50e-01 5.59e-01
...
8.20e+00  2.98e-01 4.21e-01 6.41e-01
...
8.40e+00  3.22e-01 4.97e-01 7.15e-01
...
8.60e+00  3.54e-01 5.76e-01 7.81e-01
...
8.80e+00  3.93e-01 6.55e-01 8.34e-01
...
9.00e+00  4.37e-01 7.32e-01 8.73e-01
...
9.20e+00  4.87e-01 8.04e-01 8.96e-01
...
9.40e+00  5.38e-01 8.68e-01 9.02e-01
...
9.60e+00  5.91e-01 9.22e-01 8.90e-01
...
1.00e+01  6.93e-01 9.92e-01 8.12e-01

## 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_3, iteration_4)
- `shared_variables`: all variables you have saved from the previous iterations. ()

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


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



# Iteration 5
## Thoughts

With all initial concentrations set to zero, the system still produces all three species and exhibits the same oscillatory, cyclic pattern. This means there is a zero-order (constant) source term for at least one species, likely for `id_y5nu` (since it rises first), but possibly for all. The cyclic interconversion is also evident.

A minimal model that fits all observations:
- Three unidirectional, first-order reactions forming a cycle:
  - `id_x8lp` → `id_ddfe`
  - `id_ddfe` → `id_y5nu`
  - `id_y5nu` → `id_x8lp`
- A constant source term for at least `id_y5nu` (possibly for all, but the data suggest `id_y5nu` is the main entry point).

Next, I will attempt to fit a simple model with these reactions and a constant source for `id_y5nu`. I will implement this in SBML and simulate it to compare with 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 (should be none, but for safety)
while model.getNumReactions() > 0:
    model.removeReaction(0)

# Add reaction: id_x8lp -> id_ddfe
r1 = model.createReaction()
r1.setId("r_x8lp_to_ddfe")
r1.setReversible(False)
r1.setFast(False)
reactant1 = r1.createReactant()
reactant1.setSpecies("id_x8lp")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)
product1 = r1.createProduct()
product1.setSpecies("id_ddfe")
product1.setStoichiometry(1.0)
product1.setConstant(False)
klp = model.createParameter()
klp.setId("k_x8lp_to_ddfe")
klp.setValue(0.5)
klp.setConstant(True)
kinetics1 = r1.createKineticLaw()
kinetics1.setFormula("k_x8lp_to_ddfe * id_x8lp")

# Add reaction: id_ddfe -> id_y5nu
r2 = model.createReaction()
r2.setId("r_ddfe_to_y5nu")
r2.setReversible(False)
r2.setFast(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_ddfe")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_y5nu")
product2.setStoichiometry(1.0)
product2.setConstant(False)
kde = model.createParameter()
kde.setId("k_ddfe_to_y5nu")
kde.setValue(0.5)
kde.setConstant(True)
kinetics2 = r2.createKineticLaw()
kinetics2.setFormula("k_ddfe_to_y5nu * id_ddfe")

# Add reaction: id_y5nu -> id_x8lp
r3 = model.createReaction()
r3.setId("r_y5nu_to_x8lp")
r3.setReversible(False)
r3.setFast(False)
reactant3 = r3.createReactant()
reactant3.setSpecies("id_y5nu")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(False)
product3 = r3.createProduct()
product3.setSpecies("id_x8lp")
product3.setStoichiometry(1.0)
product3.setConstant(False)
kyn = model.createParameter()
kyn.setId("k_y5nu_to_x8lp")
kyn.setValue(0.5)
kyn.setConstant(True)
kinetics3 = r3.createKineticLaw()
kinetics3.setFormula("k_y5nu_to_x8lp * id_y5nu")

# Add a constant source for id_y5nu
r4 = model.createReaction()
r4.setId("r_source_y5nu")
r4.setReversible(False)
r4.setFast(False)
product4 = r4.createProduct()
product4.setSpecies("id_y5nu")
product4.setStoichiometry(1.0)
product4.setConstant(False)
ksrc = model.createParameter()
ksrc.setId("k_source_y5nu")
ksrc.setValue(0.2)
ksrc.setConstant(True)
kinetics4 = r4.createKineticLaw()
kinetics4.setFormula("k_source_y5nu")

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

# Simulate and compare with experiment 0
sim_df = simulate(test_sbml)
shared_variables.add("test_sbml", test_sbml)
print(sim_df.head(20))
print(sim_df.tail(10))
```
# Observation

## Code Stdout
     id_x8lp   id_ddfe   id_y5nu  Time
0   0.800000  0.100000  0.000000  0.00
1   0.796016  0.103481  0.002502  0.01
2   0.792065  0.106925  0.005010  0.02
3   0.788146  0.110333  0.007522  0.03
4   0.784259  0.113704  0.010038  0.04
5   0.780403  0.117038  0.012558  0.05
6   0.776580  0.120337  0.015083  0.06
7   0.772788  0.123601  0.017611  0.07
8   0.769028  0.126829  0.020142  0.08
9   0.765299  0.130023  0.022677  0.09
10  0.761602  0.133182  0.025216  0.10
11  0.757936  0.136307  0.027757  0.11
12  0.754300  0.139399  0.030301  0.12
13  0.750696  0.142457  0.032848  0.13
14  0.747122  0.145481  0.035397  0.14
15  0.743578  0.148473  0.037949  0.15
16  0.740065  0.151432  0.040502  0.16
17  0.736583  0.154359  0.043058  0.17
18  0.733130  0.157255  0.045615  0.18
19  0.729707  0.160118  0.048174  0.19
       id_x8lp   id_ddfe   id_y5nu   Time
991   0.960660  0.827059  1.094281   9.91
992   0.961328  0.827727  1.094945   9.92
993   0.961996  0.828395  1.095609   9.93
994   0.962664  0.829063  1.096273   9.94
995   0.963332  0.829731  1.096937   9.95
996   0.964000  0.830399  1.097601   9.96
997   0.964668  0.831067  1.098265   9.97
998   0.965336  0.831735  1.098929   9.98
999   0.966004  0.832403  1.099593   9.99
1000  0.966672  0.833071  1.100257  10.00

## Reminder

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



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

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


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



# Iteration 6
## Thoughts

The simulated model with three cyclic first-order reactions and a constant source for `id_y5nu` produces a monotonic increase in all species, but does not reproduce the oscillatory/cyclic behavior seen in the experimental data. In the simulation, all species rise smoothly and approach a steady state, while in the real system, the concentrations oscillate and cycle through peaks and troughs.

This suggests that the real system has a delay or nonlinearity that is not captured by simple first-order mass-action kinetics and a constant source. Possible missing mechanisms:
- The conversion reactions may be nonlinear (e.g., autocatalytic, or involve inhibition/activation).
- There may be negative feedback or time delays.
- The source term may be autocatalytic or regulated, not constant.

A classic way to generate oscillations in a three-species cycle is to use nonlinear kinetics, such as:
- Autocatalysis (e.g., a species promotes its own production or the conversion of another).
- Inhibition (e.g., one species inhibits the production of another).

To probe for nonlinearity, I should test the system's response to a high initial concentration of one species and zero for the others, to see if the amplitude or period of oscillations changes.

## Action

### Experiment

```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_x8lp": 2.0,
        "id_ddfe": 0.0,
        "id_y5nu": 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: 1001 rows × 4 columns. 

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

Time   id_x8lp  id_ddfe  id_y5nu
0  2.00e+00        0        0
...
2.00e-01  1.70e+00 8.22e-06 4.51e-05
...
4.00e-01  1.45e+00 1.74e-05 5.74e-05
...
6.00e-01  1.24e+00 2.82e-05 7.47e-05
...
8.00e-01  1.05e+00 4.17e-05 1.01e-04
...
1.00e+00  8.99e-01 6.01e-05 1.43e-04
...
1.20e+00  7.66e-01 8.77e-05 2.23e-04
...
1.40e+00  6.53e-01 1.37e-04 4.25e-04
...
1.60e+00  5.56e-01 2.78e-04 1.49e-03
...
1.80e+00  4.74e-01 1.29e-03 1.16e-02
...
2.00e+00  4.04e-01 6.39e-03 4.33e-02
...
2.20e+00  3.46e-01 1.94e-02 9.62e-02
...
2.40e+00  3.00e-01 4.32e-02 1.67e-01
...
2.60e+00  2.64e-01 7.93e-02 2.51e-01
...
2.80e+00  2.41e-01 1.28e-01 3.46e-01
...
3.00e+00  2.29e-01 1.90e-01 4.46e-01
...
3.20e+00  2.28e-01 2.63e-01 5.49e-01
...
3.40e+00  2.40e-01 3.47e-01 6.50e-01
...
3.60e+00  2.62e-01 4.38e-01 7.45e-01
...
3.80e+00  2.95e-01 5.33e-01 8.30e-01
...
4.00e+00  3.38e-01 6.31e-01 9.03e-01
...
4.20e+00  3.89e-01 7.28e-01 9.59e-01
...
4.40e+00  4.46e-01 8.19e-01 9.98e-01
...
4.60e+00  5.08e-01 9.03e-01 1.02e+00
...
4.80e+00  5.72e-01 9.76e-01 1.01e+00
...
5.00e+00  6.36e-01 1.04e+00 9.87e-01
...
5.20e+00  6.99e-01 1.08e+00 9.40e-01
...
5.40e+00  7.57e-01 1.10e+00 8.72e-01
...
5.60e+00  8.09e-01 1.11e+00 7.86e-01
...
5.80e+00  8.52e-01 1.09e+00 6.83e-01
...
6.00e+00  8.86e-01 1.06e+00 5.68e-01
...
6.20e+00  9.08e-01 1.01e+00 4.42e-01
...
6.40e+00  9.17e-01 9.33e-01 3.12e-01
...
6.60e+00  9.13e-01 8.45e-01 1.81e-01
...
6.80e+00  8.95e-01 7.43e-01 5.34e-02
...
7.00e+00  8.64e-01 6.36e-01 1.58e-04
...
7.20e+00  8.23e-01 5.42e-01 1.80e-04
...
7.40e+00  7.75e-01 4.62e-01 2.15e-04
...
7.60e+00  7.24e-01 3.93e-01 2.72e-04
...
7.80e+00  6.70e-01 3.35e-01 3.75e-04
...
8.00e+00  6.17e-01 2.86e-01 5.97e-04
...
8.20e+00  5.65e-01 2.44e-01 1.33e-03
...
8.40e+00  5.14e-01 2.08e-01 5.40e-03
...
8.60e+00  4.67e-01 1.80e-01 2.03e-02
...
8.80e+00  4.23e-01 1.60e-01 4.96e-02
...
9.00e+00  3.83e-01 1.51e-01 9.30e-02
...
9.20e+00  3.49e-01 1.53e-01 1.49e-01
...
9.40e+00  3.21e-01 1.68e-01 2.15e-01
...
9.60e+00  3.00e-01 1.94e-01 2.90e-01
...
1.00e+01  2.83e-01 2.82e-01 4.54e-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_3, iteration_4, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml)

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


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



# Iteration 7
## Thoughts

The system, when started with a high concentration of `id_x8lp` and zero for the others, still shows the same oscillatory/cyclic pattern, with the amplitude and period of oscillations similar to previous experiments. This suggests that the oscillations are robust to initial conditions and are an intrinsic property of the network, not just a result of initial transients.

The failure of the simple first-order cyclic model with a constant source to reproduce oscillations indicates that the real system likely involves nonlinear kinetics, such as:
- Autocatalysis (e.g., a species catalyzes its own production or the conversion of another).
- Inhibition (e.g., one species inhibits the production of another).
- Delayed negative feedback.

A classic model that produces oscillations in a three-species cycle is the Lotka-Volterra or repressilator-type network, where each species inhibits the next. Since all species are observable, I can try to fit a model where each conversion is autocatalytic or has a nonlinear term.

I will now attempt to fit a model where each conversion is second-order (e.g., `id_x8lp + id_ddfe → 2 id_ddfe`), which can produce oscillations, and see if this better matches the data.

## Action

### Code

```python
import libsbml

# Start from the original model again
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# id_x8lp + id_ddfe -> 2 id_ddfe (autocatalytic conversion)
r1 = model.createReaction()
r1.setId("r_x8lp_ddfe")
r1.setReversible(False)
r1.setFast(False)
reactant1a = r1.createReactant()
reactant1a.setSpecies("id_x8lp")
reactant1a.setStoichiometry(1.0)
reactant1a.setConstant(False)
reactant1b = r1.createReactant()
reactant1b.setSpecies("id_ddfe")
reactant1b.setStoichiometry(1.0)
reactant1b.setConstant(False)
product1 = r1.createProduct()
product1.setSpecies("id_ddfe")
product1.setStoichiometry(2.0)
product1.setConstant(False)
k1 = model.createParameter()
k1.setId("k1")
k1.setValue(0.5)
k1.setConstant(True)
kinetics1 = r1.createKineticLaw()
kinetics1.setFormula("k1 * id_x8lp * id_ddfe")

# id_ddfe + id_y5nu -> 2 id_y5nu
r2 = model.createReaction()
r2.setId("r_ddfe_y5nu")
r2.setReversible(False)
r2.setFast(False)
reactant2a = r2.createReactant()
reactant2a.setSpecies("id_ddfe")
reactant2a.setStoichiometry(1.0)
reactant2a.setConstant(False)
reactant2b = r2.createReactant()
reactant2b.setSpecies("id_y5nu")
reactant2b.setStoichiometry(1.0)
reactant2b.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_y5nu")
product2.setStoichiometry(2.0)
product2.setConstant(False)
k2 = model.createParameter()
k2.setId("k2")
k2.setValue(0.5)
k2.setConstant(True)
kinetics2 = r2.createKineticLaw()
kinetics2.setFormula("k2 * id_ddfe * id_y5nu")

# id_y5nu + id_x8lp -> 2 id_x8lp
r3 = model.createReaction()
r3.setId("r_y5nu_x8lp")
r3.setReversible(False)
r3.setFast(False)
reactant3a = r3.createReactant()
reactant3a.setSpecies("id_y5nu")
reactant3a.setStoichiometry(1.0)
reactant3a.setConstant(False)
reactant3b = r3.createReactant()
reactant3b.setSpecies("id_x8lp")
reactant3b.setStoichiometry(1.0)
reactant3b.setConstant(False)
product3 = r3.createProduct()
product3.setSpecies("id_x8lp")
product3.setStoichiometry(2.0)
product3.setConstant(False)
k3 = model.createParameter()
k3.setId("k3")
k3.setValue(0.5)
k3.setConstant(True)
kinetics3 = r3.createKineticLaw()
kinetics3.setFormula("k3 * id_y5nu * id_x8lp")

# Add a constant source for id_y5nu (as before)
r4 = model.createReaction()
r4.setId("r_source_y5nu")
r4.setReversible(False)
r4.setFast(False)
product4 = r4.createProduct()
product4.setSpecies("id_y5nu")
product4.setStoichiometry(1.0)
product4.setConstant(False)
ksrc = model.createParameter()
ksrc.setId("k_source_y5nu")
ksrc.setValue(0.2)
ksrc.setConstant(True)
kinetics4 = r4.createKineticLaw()
kinetics4.setFormula("k_source_y5nu")

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

# Simulate and compare with experiment 0
sim_df2 = simulate(test_sbml2)
shared_variables.add("test_sbml2", test_sbml2)
print(sim_df2.head(20))
print(sim_df2.tail(10))
```
# Observation

## Code Stdout
     id_x8lp   id_ddfe   id_y5nu  Time
0   0.800000  0.100000  0.000000  0.00
1   0.799603  0.100400  0.001997  0.01
2   0.799213  0.100801  0.003986  0.02
3   0.798830  0.101202  0.005969  0.03
4   0.798452  0.101603  0.007944  0.04
5   0.798082  0.102005  0.009913  0.05
6   0.797717  0.102407  0.011875  0.06
7   0.797359  0.102810  0.013831  0.07
8   0.797008  0.103213  0.015779  0.08
9   0.796663  0.103616  0.017721  0.09
10  0.796324  0.104020  0.019657  0.10
11  0.795991  0.104424  0.021585  0.11
12  0.795664  0.104828  0.023507  0.12
13  0.795344  0.105233  0.025423  0.13
14  0.795029  0.105639  0.027332  0.14
15  0.794721  0.106044  0.029234  0.15
16  0.794419  0.106450  0.031131  0.16
17  0.794123  0.106857  0.033020  0.17
18  0.793833  0.107264  0.034904  0.18
19  0.793548  0.107671  0.036781  0.19
       id_x8lp   id_ddfe   id_y5nu   Time
991   0.999014  0.905973  0.977013   9.91
992   0.999373  0.906070  0.978558   9.92
993   0.999739  0.906161  0.980100   9.93
994   1.000112  0.906247  0.981641   9.94
995   1.000493  0.906329  0.983179   9.95
996   1.000881  0.906404  0.984715   9.96
997   1.001277  0.906475  0.986249   9.97
998   1.001680  0.906540  0.987780   9.98
999   1.002090  0.906601  0.989309   9.99
1000  1.002508  0.906656  0.990835  10.00

## 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_3, iteration_4, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2)

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


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



# Iteration 8
## Thoughts

The model with autocatalytic (second-order) cyclic reactions and a constant source for `id_y5nu` still does not reproduce the oscillatory/cyclic behavior seen in the experimental data. The simulated concentrations increase smoothly and approach a steady state, rather than oscillating.

This suggests that the system's oscillations are not due to simple autocatalysis or mass-action cycles, but likely involve negative feedback or inhibition, possibly with a delay. A classic motif for oscillations is the repressilator, where each species inhibits the next in a cycle (e.g., A inhibits B, B inhibits C, C inhibits A), often modeled with Hill-type (sigmoidal) inhibition.

To test for inhibition, I should perturb the system by starting with high concentrations of two species and zero for the third, and see if the third is suppressed or delayed in its rise.

## Action

### Experiment

```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_x8lp": 2.0,
        "id_ddfe": 2.0,
        "id_y5nu": 0.0
    }
}
```
# Observation

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

Total size: 1001 rows × 4 columns. 

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

Time   id_x8lp  id_ddfe  id_y5nu
0  2.00e+00 2.00e+00        0
...
2.00e-01  1.98e+00 1.70e+00 3.66e-05
...
4.00e-01  1.92e+00 1.45e+00 3.82e-05
...
6.00e-01  1.83e+00 1.24e+00 4.07e-05
...
8.00e-01  1.73e+00 1.05e+00 4.41e-05
...
1.00e+00  1.62e+00 8.99e-01 4.86e-05
...
1.20e+00  1.50e+00 7.66e-01 5.45e-05
...
1.40e+00  1.38e+00 6.53e-01 6.20e-05
...
1.60e+00  1.27e+00 5.56e-01 7.17e-05
...
1.80e+00  1.16e+00 4.74e-01 8.44e-05
...
2.00e+00  1.05e+00 4.04e-01 1.02e-04
...
2.20e+00  9.50e-01 3.44e-01 1.26e-04
...
2.40e+00  8.56e-01 2.93e-01 1.62e-04
...
2.60e+00  7.70e-01 2.50e-01 2.20e-04
...
2.80e+00  6.90e-01 2.13e-01 3.29e-04
...
3.00e+00  6.17e-01 1.82e-01 5.94e-04
...
3.20e+00  5.51e-01 1.55e-01 1.79e-03
...
3.40e+00  4.90e-01 1.33e-01 9.71e-03
...
3.60e+00  4.36e-01 1.18e-01 3.33e-02
...
3.80e+00  3.88e-01 1.11e-01 7.35e-02
...
4.00e+00  3.48e-01 1.15e-01 1.29e-01
...
4.20e+00  3.14e-01 1.31e-01 1.97e-01
...
4.40e+00  2.89e-01 1.60e-01 2.74e-01
...
4.60e+00  2.73e-01 2.00e-01 3.59e-01
...
4.80e+00  2.66e-01 2.53e-01 4.48e-01
...
5.00e+00  2.69e-01 3.16e-01 5.37e-01
...
5.20e+00  2.81e-01 3.88e-01 6.24e-01
...
5.40e+00  3.03e-01 4.66e-01 7.05e-01
...
5.60e+00  3.33e-01 5.48e-01 7.77e-01
...
5.80e+00  3.71e-01 6.31e-01 8.37e-01
...
6.00e+00  4.16e-01 7.13e-01 8.84e-01
...
6.20e+00  4.66e-01 7.91e-01 9.14e-01
...
6.40e+00  5.19e-01 8.61e-01 9.27e-01
...
6.60e+00  5.75e-01 9.22e-01 9.21e-01
...
6.80e+00  6.30e-01 9.71e-01 8.96e-01
...
7.00e+00  6.83e-01 1.01e+00 8.53e-01
...
7.20e+00  7.32e-01 1.02e+00 7.92e-01
...
7.40e+00  7.76e-01 1.03e+00 7.16e-01
...
7.60e+00  8.12e-01 1.01e+00 6.25e-01
...
7.80e+00  8.39e-01 9.78e-01 5.25e-01
...
8.00e+00  8.56e-01 9.29e-01 4.16e-01
...
8.20e+00  8.62e-01 8.64e-01 3.04e-01
...
8.40e+00  8.57e-01 7.87e-01 1.92e-01
...
8.60e+00  8.40e-01 6.98e-01 8.31e-02
...
8.80e+00  8.11e-01 6.01e-01 1.88e-04
...
9.00e+00  7.73e-01 5.12e-01 2.17e-04
...
9.20e+00  7.29e-01 4.37e-01 2.65e-04
...
9.40e+00  6.81e-01 3.72e-01 3.49e-04
...
9.60e+00  6.31e-01 3.17e-01 5.18e-04
...
1.00e+01  5.32e-01 2.31e-01 3.18e-03

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_3, iteration_4, iteration_6, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2)

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


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



# Iteration 9
## Thoughts

The experiment with high initial concentrations of `id_x8lp` and `id_ddfe` and zero `id_y5nu` shows that `id_y5nu` remains suppressed for a while, then rises, and the system resumes its oscillatory/cyclic pattern. This is consistent with a system where the presence of certain species inhibits or delays the production of others, supporting the idea of negative feedback or inhibition.

The failure of both first-order and autocatalytic models to reproduce oscillations suggests that the real system likely involves nonlinear inhibition, such as Hill-type repression (as in the repressilator). In such a model, each species inhibits the production of the next, and the production rate is a decreasing function of the inhibitor's concentration.

I will now attempt to build a repressilator-like model, where each species is produced at a constant rate, but this production is inhibited by the next species in the cycle via a Hill function. I will implement this in SBML and simulate it.

## Action

### Code

```python
import libsbml

# Start from the original model again
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# Parameters for Hill repression
n = 2  # Hill coefficient
K = 0.5  # Dissociation constant
alpha = 2.0  # Max production rate
delta = 0.5  # Degradation rate

# id_x8lp production repressed by id_y5nu, degraded linearly
r1 = model.createReaction()
r1.setId("r_prod_x8lp")
r1.setReversible(False)
r1.setFast(False)
product1 = r1.createProduct()
product1.setSpecies("id_x8lp")
product1.setStoichiometry(1.0)
product1.setConstant(False)
kinetics1 = r1.createKineticLaw()
kinetics1.setFormula(f"{alpha}/(1 + (id_y5nu/{K})^{n})")

r1d = model.createReaction()
r1d.setId("r_deg_x8lp")
r1d.setReversible(False)
r1d.setFast(False)
reactant1d = r1d.createReactant()
reactant1d.setSpecies("id_x8lp")
reactant1d.setStoichiometry(1.0)
reactant1d.setConstant(False)
kinetics1d = r1d.createKineticLaw()
kinetics1d.setFormula(f"{delta}*id_x8lp")

# id_ddfe production repressed by id_x8lp, degraded linearly
r2 = model.createReaction()
r2.setId("r_prod_ddfe")
r2.setReversible(False)
r2.setFast(False)
product2 = r2.createProduct()
product2.setSpecies("id_ddfe")
product2.setStoichiometry(1.0)
product2.setConstant(False)
kinetics2 = r2.createKineticLaw()
kinetics2.setFormula(f"{alpha}/(1 + (id_x8lp/{K})^{n})")

r2d = model.createReaction()
r2d.setId("r_deg_ddfe")
r2d.setReversible(False)
r2d.setFast(False)
reactant2d = r2d.createReactant()
reactant2d.setSpecies("id_ddfe")
reactant2d.setStoichiometry(1.0)
reactant2d.setConstant(False)
kinetics2d = r2d.createKineticLaw()
kinetics2d.setFormula(f"{delta}*id_ddfe")

# id_y5nu production repressed by id_ddfe, degraded linearly
r3 = model.createReaction()
r3.setId("r_prod_y5nu")
r3.setReversible(False)
r3.setFast(False)
product3 = r3.createProduct()
product3.setSpecies("id_y5nu")
product3.setStoichiometry(1.0)
product3.setConstant(False)
kinetics3 = r3.createKineticLaw()
kinetics3.setFormula(f"{alpha}/(1 + (id_ddfe/{K})^{n})")

r3d = model.createReaction()
r3d.setId("r_deg_y5nu")
r3d.setReversible(False)
r3d.setFast(False)
reactant3d = r3d.createReactant()
reactant3d.setSpecies("id_y5nu")
reactant3d.setStoichiometry(1.0)
reactant3d.setConstant(False)
kinetics3d = r3d.createKineticLaw()
kinetics3d.setFormula(f"{delta}*id_y5nu")

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

# Simulate and compare with experiment 0
sim_df3 = simulate(repressilator_sbml)
shared_variables.add("repressilator_sbml", repressilator_sbml)
print(sim_df3.head(20))
print(sim_df3.tail(10))
```
# Observation

## Code Stdout
     id_x8lp   id_ddfe   id_y5nu  Time
0   0.800000  0.100000  0.000000  0.00
1   0.815950  0.105026  0.019145  0.01
2   0.831762  0.109872  0.038118  0.02
3   0.847383  0.114547  0.056922  0.03
4   0.862761  0.119059  0.075555  0.04
5   0.877849  0.123416  0.094020  0.05
6   0.892604  0.127626  0.112318  0.06
7   0.906990  0.131696  0.130451  0.07
8   0.920975  0.135634  0.148419  0.08
9   0.934533  0.139448  0.166225  0.09
10  0.947642  0.143144  0.183871  0.10
11  0.960287  0.146729  0.201357  0.11
12  0.972454  0.150210  0.218686  0.12
13  0.984137  0.153593  0.235859  0.13
14  0.995331  0.156883  0.252879  0.14
15  1.006035  0.160086  0.269746  0.15
16  1.016253  0.163207  0.286463  0.16
17  1.025989  0.166251  0.303031  0.17
18  1.035250  0.169222  0.319451  0.18
19  1.044044  0.172126  0.335726  0.19
       id_x8lp   id_ddfe   id_y5nu   Time
991   1.121085  0.749723  0.938744   9.91
992   1.119897  0.749296  0.940206   9.92
993   1.118705  0.748878  0.941665   9.93
994   1.117507  0.748467  0.943122   9.94
995   1.116305  0.748065  0.944577   9.95
996   1.115099  0.747671  0.946028   9.96
997   1.113888  0.747284  0.947477   9.97
998   1.112673  0.746906  0.948923   9.98
999   1.111454  0.746535  0.950366   9.99
1000  1.110230  0.746173  0.951806  10.00

## 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_3, iteration_4, iteration_6, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, repressilator_sbml)

### 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 repressilator-like model (Hill-type inhibition, linear degradation, and constant production) produces a monotonic increase in all species, but still does not reproduce the oscillatory/cyclic behavior seen in the experimental data. The simulated concentrations rise and approach a steady state, rather than oscillating.

This suggests that the parameter values (Hill coefficient, production/degradation rates, or dissociation constant) may not be in the regime that produces oscillations. In the classic repressilator, oscillations require sufficiently high Hill coefficients (n ≥ 2–3) and appropriate ratios of production to degradation rates.

I will try increasing the Hill coefficient and the production rate, and decreasing the degradation rate, to see if this produces oscillations. If this works, I can then tune the parameters to better match the observed period and amplitude.

## Action

### Code

```python
import libsbml

# Start from the original model again
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# Try higher Hill coefficient and production, lower degradation
n = 4  # Hill coefficient
K = 0.5  # Dissociation constant
alpha = 5.0  # Max production rate
delta = 0.2  # Degradation rate

# id_x8lp production repressed by id_y5nu, degraded linearly
r1 = model.createReaction()
r1.setId("r_prod_x8lp")
r1.setReversible(False)
r1.setFast(False)
product1 = r1.createProduct()
product1.setSpecies("id_x8lp")
product1.setStoichiometry(1.0)
product1.setConstant(False)
kinetics1 = r1.createKineticLaw()
kinetics1.setFormula(f"{alpha}/(1 + (id_y5nu/{K})^{n})")

r1d = model.createReaction()
r1d.setId("r_deg_x8lp")
r1d.setReversible(False)
r1d.setFast(False)
reactant1d = r1d.createReactant()
reactant1d.setSpecies("id_x8lp")
reactant1d.setStoichiometry(1.0)
reactant1d.setConstant(False)
kinetics1d = r1d.createKineticLaw()
kinetics1d.setFormula(f"{delta}*id_x8lp")

# id_ddfe production repressed by id_x8lp, degraded linearly
r2 = model.createReaction()
r2.setId("r_prod_ddfe")
r2.setReversible(False)
r2.setFast(False)
product2 = r2.createProduct()
product2.setSpecies("id_ddfe")
product2.setStoichiometry(1.0)
product2.setConstant(False)
kinetics2 = r2.createKineticLaw()
kinetics2.setFormula(f"{alpha}/(1 + (id_x8lp/{K})^{n})")

r2d = model.createReaction()
r2d.setId("r_deg_ddfe")
r2d.setReversible(False)
r2d.setFast(False)
reactant2d = r2d.createReactant()
reactant2d.setSpecies("id_ddfe")
reactant2d.setStoichiometry(1.0)
reactant2d.setConstant(False)
kinetics2d = r2d.createKineticLaw()
kinetics2d.setFormula(f"{delta}*id_ddfe")

# id_y5nu production repressed by id_ddfe, degraded linearly
r3 = model.createReaction()
r3.setId("r_prod_y5nu")
r3.setReversible(False)
r3.setFast(False)
product3 = r3.createProduct()
product3.setSpecies("id_y5nu")
product3.setStoichiometry(1.0)
product3.setConstant(False)
kinetics3 = r3.createKineticLaw()
kinetics3.setFormula(f"{alpha}/(1 + (id_ddfe/{K})^{n})")

r3d = model.createReaction()
r3d.setId("r_deg_y5nu")
r3d.setReversible(False)
r3d.setFast(False)
reactant3d = r3d.createReactant()
reactant3d.setSpecies("id_y5nu")
reactant3d.setStoichiometry(1.0)
reactant3d.setConstant(False)
kinetics3d = r3d.createKineticLaw()
kinetics3d.setFormula(f"{delta}*id_y5nu")

# Write the updated SBML
writer = libsbml.SBMLWriter()
repressilator_sbml2 = writer.writeSBMLToString(sbml_doc)

# Simulate and compare with experiment 0
sim_df4 = simulate(repressilator_sbml2)
shared_variables.add("repressilator_sbml2", repressilator_sbml2)
print(sim_df4.head(20))
print(sim_df4.tail(10))
```
# Observation

## Code Stdout
     id_x8lp   id_ddfe   id_y5nu  Time
0   0.800000  0.100000  0.000000  0.00
1   0.848351  0.105771  0.049860  0.01
2   0.896575  0.110432  0.099601  0.02
3   0.944526  0.114217  0.149225  0.03
4   0.991839  0.117310  0.198733  0.04
5   1.037851  0.119858  0.248129  0.05
6   1.081616  0.121978  0.297412  0.06
7   1.122029  0.123766  0.346587  0.07
8   1.158080  0.125300  0.395652  0.08
9   1.189092  0.126641  0.444611  0.09
10  1.214873  0.127838  0.493464  0.10
11  1.235692  0.128930  0.542212  0.11
12  1.252112  0.129942  0.590856  0.12
13  1.264818  0.130895  0.639395  0.13
14  1.274489  0.131806  0.687831  0.14
15  1.281735  0.132685  0.736163  0.15
16  1.287062  0.133541  0.784393  0.16
17  1.290878  0.134380  0.832519  0.17
18  1.293506  0.135206  0.880544  0.18
19  1.295195  0.136024  0.928465  0.19
       id_x8lp    id_ddfe   id_y5nu   Time
991   0.212022  14.569861  1.924491   9.91
992   0.211826  14.589139  1.920646   9.92
993   0.211632  14.608384  1.916808   9.93
994   0.211441  14.627596  1.912978   9.94
995   0.211251  14.646775  1.909156   9.95
996   0.211064  14.665921  1.905342   9.96
997   0.210879  14.685034  1.901535   9.97
998   0.210696  14.704113  1.897736   9.98
999   0.210516  14.723160  1.893944   9.99
1000  0.210337  14.742174  1.890160  10.00

## 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_3, iteration_4, iteration_6, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, repressilator_sbml, repressilator_sbml2)

### 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

Even with a high Hill coefficient and increased production rate, the repressilator model does not produce oscillations; instead, one species (`id_ddfe`) grows without bound, while the others remain low. This suggests that the parameter regime is not yet correct, or that the model structure is still missing a key feature.

In the classic repressilator, oscillations require:
- High Hill coefficient (n ≥ 2–4)
- Balanced production and degradation rates
- No constant source term (production is only via regulated synthesis)
- All species degrade at similar rates

The unbounded growth of `id_ddfe` suggests that the negative feedback is not strong enough, or that the system is not closed (i.e., mass is not conserved or there is a net source). The original data show that the total concentration increases, but not without bound, and the system cycles through all three species.

I will try the following adjustments:
- Lower the production rate (`alpha`)
- Increase the degradation rate (`delta`)
- Keep the Hill coefficient high
- Ensure all species have the same production and degradation structure

If this still does not produce oscillations, I may need to consider adding explicit delays or more complex feedback.

## Action

### Code

```python
import libsbml

# Start from the original model again
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# Try more balanced parameters
n = 4  # Hill coefficient
K = 0.5  # Dissociation constant
alpha = 1.5  # Max production rate
delta = 0.5  # Degradation rate

# id_x8lp production repressed by id_y5nu, degraded linearly
r1 = model.createReaction()
r1.setId("r_prod_x8lp")
r1.setReversible(False)
r1.setFast(False)
product1 = r1.createProduct()
product1.setSpecies("id_x8lp")
product1.setStoichiometry(1.0)
product1.setConstant(False)
kinetics1 = r1.createKineticLaw()
kinetics1.setFormula(f"{alpha}/(1 + (id_y5nu/{K})^{n})")

r1d = model.createReaction()
r1d.setId("r_deg_x8lp")
r1d.setReversible(False)
r1d.setFast(False)
reactant1d = r1d.createReactant()
reactant1d.setSpecies("id_x8lp")
reactant1d.setStoichiometry(1.0)
reactant1d.setConstant(False)
kinetics1d = r1d.createKineticLaw()
kinetics1d.setFormula(f"{delta}*id_x8lp")

# id_ddfe production repressed by id_x8lp, degraded linearly
r2 = model.createReaction()
r2.setId("r_prod_ddfe")
r2.setReversible(False)
r2.setFast(False)
product2 = r2.createProduct()
product2.setSpecies("id_ddfe")
product2.setStoichiometry(1.0)
product2.setConstant(False)
kinetics2 = r2.createKineticLaw()
kinetics2.setFormula(f"{alpha}/(1 + (id_x8lp/{K})^{n})")

r2d = model.createReaction()
r2d.setId("r_deg_ddfe")
r2d.setReversible(False)
r2d.setFast(False)
reactant2d = r2d.createReactant()
reactant2d.setSpecies("id_ddfe")
reactant2d.setStoichiometry(1.0)
reactant2d.setConstant(False)
kinetics2d = r2d.createKineticLaw()
kinetics2d.setFormula(f"{delta}*id_ddfe")

# id_y5nu production repressed by id_ddfe, degraded linearly
r3 = model.createReaction()
r3.setId("r_prod_y5nu")
r3.setReversible(False)
r3.setFast(False)
product3 = r3.createProduct()
product3.setSpecies("id_y5nu")
product3.setStoichiometry(1.0)
product3.setConstant(False)
kinetics3 = r3.createKineticLaw()
kinetics3.setFormula(f"{alpha}/(1 + (id_ddfe/{K})^{n})")

r3d = model.createReaction()
r3d.setId("r_deg_y5nu")
r3d.setReversible(False)
r3d.setFast(False)
reactant3d = r3d.createReactant()
reactant3d.setSpecies("id_y5nu")
reactant3d.setStoichiometry(1.0)
reactant3d.setConstant(False)
kinetics3d = r3d.createKineticLaw()
kinetics3d.setFormula(f"{delta}*id_y5nu")

# Write the updated SBML
writer = libsbml.SBMLWriter()
repressilator_sbml3 = writer.writeSBMLToString(sbml_doc)

# Simulate and compare with experiment 0
sim_df5 = simulate(repressilator_sbml3)
shared_variables.add("repressilator_sbml3", repressilator_sbml3)
print(sim_df5.head(20))
print(sim_df5.tail(10))
```
# Observation

## Code Stdout
     id_x8lp   id_ddfe   id_y5nu  Time
0   0.800000  0.100000  0.000000  0.00
1   0.810973  0.101436  0.014938  0.01
2   0.821890  0.102775  0.029800  0.02
3   0.832753  0.104024  0.044587  0.03
4   0.843560  0.105187  0.059298  0.04
5   0.854310  0.106269  0.073935  0.05
6   0.865001  0.107276  0.088498  0.06
7   0.875628  0.108210  0.102987  0.07
8   0.886188  0.109078  0.117403  0.08
9   0.896672  0.109881  0.131745  0.09
10  0.907072  0.110625  0.146015  0.10
11  0.917379  0.111312  0.160213  0.11
12  0.927580  0.111945  0.174340  0.12
13  0.937660  0.112529  0.188395  0.13
14  0.947603  0.113065  0.202379  0.14
15  0.957392  0.113557  0.216293  0.15
16  0.967006  0.114007  0.230137  0.16
17  0.976424  0.114419  0.243911  0.17
18  0.985625  0.114794  0.257616  0.18
19  0.994585  0.115135  0.271252  0.19
       id_x8lp   id_ddfe   id_y5nu   Time
991   1.143268  0.262773  1.485394   9.91
992   1.137754  0.261995  1.491893   9.92
993   1.132264  0.261231  1.498372   9.93
994   1.126799  0.260482  1.504829   9.94
995   1.121358  0.259746  1.511265   9.95
996   1.115940  0.259025  1.517680   9.96
997   1.110547  0.258318  1.524073   9.97
998   1.105178  0.257626  1.530444   9.98
999   1.099833  0.256948  1.536793   9.99
1000  1.094512  0.256286  1.543120  10.00

## 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_3, iteration_4, iteration_6, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, repressilator_sbml, repressilator_sbml2, repressilator_sbml3)

### 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

Despite tuning the parameters (lowering production, increasing degradation, keeping a high Hill coefficient), the repressilator model still does not produce oscillations. The simulated concentrations rise and approach a steady state, rather than oscillating. This suggests that either:
- The parameter regime is still not correct for oscillations, or
- The model structure is missing a key feature, such as explicit time delays, additional feedback, or a different form of nonlinearity.

Given that the experimental data show robust, sustained oscillations and cycling of all three species, and that the repressilator model is not oscillating even with high nonlinearity, I suspect that the system may require an explicit delay or a different feedback structure.

Before moving to more complex models, I should check the period and amplitude of the oscillations in the experimental data to guide further modeling. This will help determine if the system is underdamped, has a fixed period, or if the oscillations decay over time.

## Action

### Code

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

# Use experiment 0 (default initial conditions)
df = experiment_history['iteration_0']

# Find peaks in id_x8lp to estimate period and amplitude
from scipy.signal import find_peaks

x = df['id_x8lp'].values
peaks, _ = find_peaks(x)
peak_times = df['Time'].iloc[peaks].values
peak_vals = x[peaks]

# Print peak times and values
print("Peak times (id_x8lp):", peak_times)
print("Peak values (id_x8lp):", peak_vals)

# Estimate period (mean difference between peaks)
if len(peak_times) > 1:
    periods = np.diff(peak_times)
    print("Estimated period (mean):", periods.mean())
    print("Estimated amplitude (mean):", peak_vals.mean())
else:
    print("Not enough peaks to estimate period.")
```
# Observation

## Code Stdout
Peak times (id_x8lp): [5.43]
Peak values (id_x8lp): [0.89255623]
Not enough peaks to estimate period.

## 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_3, iteration_4, iteration_6, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, repressilator_sbml, repressilator_sbml2, repressilator_sbml3)

### 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 peak-finding analysis on `id_x8lp` only detected a single peak, suggesting that the oscillations in the experimental data may not be strictly periodic, or that the period is long compared to the simulation window. However, visual inspection of the data (from earlier experiment outputs) shows clear rises and falls in all three species, with each species cycling through high and low values in a sequence. This is consistent with a relaxation oscillator or a system with strong, sequential activation and inhibition.

Given that the repressilator model with Hill-type inhibition does not oscillate, and that the system can "self-start" from zero, it is possible that the system is driven by a combination of:
- Cyclic conversion (A → B → C → A)
- Nonlinear feedback (possibly with threshold or switch-like behavior)
- A constant or autocatalytic source

Alternatively, the system may be best described by a set of irreversible, sequential reactions with a source and a sink, or by a model with explicit time delays.

Before moving to delay differential equations (which are not supported in standard SBML), I will try a model with both cyclic conversion and nonlinear (Hill-type) feedback, and include a constant source for one species. This hybrid approach may capture the observed dynamics.

## Action

### Code

```python
import libsbml

# Start from the original model again
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# Parameters
k1 = 1.0  # rate for id_x8lp -> id_ddfe
k2 = 1.0  # rate for id_ddfe -> id_y5nu
k3 = 1.0  # rate for id_y5nu -> id_x8lp
alpha = 0.2  # constant source for id_y5nu
n = 4  # Hill coefficient for feedback
K = 0.5  # Dissociation constant

# id_x8lp -> id_ddfe, repressed by id_y5nu
r1 = model.createReaction()
r1.setId("r_x8lp_to_ddfe")
r1.setReversible(False)
r1.setFast(False)
reactant1 = r1.createReactant()
reactant1.setSpecies("id_x8lp")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)
product1 = r1.createProduct()
product1.setSpecies("id_ddfe")
product1.setStoichiometry(1.0)
product1.setConstant(False)
kinetics1 = r1.createKineticLaw()
kinetics1.setFormula(f"{k1} * id_x8lp / (1 + (id_y5nu/{K})^{n})")

# id_ddfe -> id_y5nu, repressed by id_x8lp
r2 = model.createReaction()
r2.setId("r_ddfe_to_y5nu")
r2.setReversible(False)
r2.setFast(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_ddfe")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_y5nu")
product2.setStoichiometry(1.0)
product2.setConstant(False)
kinetics2 = r2.createKineticLaw()
kinetics2.setFormula(f"{k2} * id_ddfe / (1 + (id_x8lp/{K})^{n})")

# id_y5nu -> id_x8lp, repressed by id_ddfe
r3 = model.createReaction()
r3.setId("r_y5nu_to_x8lp")
r3.setReversible(False)
r3.setFast(False)
reactant3 = r3.createReactant()
reactant3.setSpecies("id_y5nu")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(False)
product3 = r3.createProduct()
product3.setSpecies("id_x8lp")
product3.setStoichiometry(1.0)
product3.setConstant(False)
kinetics3 = r3.createKineticLaw()
kinetics3.setFormula(f"{k3} * id_y5nu / (1 + (id_ddfe/{K})^{n})")

# Constant source for id_y5nu
r4 = model.createReaction()
r4.setId("r_source_y5nu")
r4.setReversible(False)
r4.setFast(False)
product4 = r4.createProduct()
product4.setSpecies("id_y5nu")
product4.setStoichiometry(1.0)
product4.setConstant(False)
kinetics4 = r4.createKineticLaw()
kinetics4.setFormula(f"{alpha}")

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

# Simulate and compare with experiment 0
sim_df6 = simulate(hybrid_sbml)
shared_variables.add("hybrid_sbml", hybrid_sbml)
print(sim_df6.head(20))
print(sim_df6.tail(10))
```
# Observation

## Code Stdout
     id_x8lp   id_ddfe   id_y5nu  Time
0   0.800000  0.100000  0.000000  0.00
1   0.792050  0.107820  0.002129  0.01
2   0.784201  0.115546  0.004253  0.02
3   0.776451  0.123176  0.006373  0.03
4   0.768799  0.130713  0.008488  0.04
5   0.761244  0.138156  0.010601  0.05
6   0.753784  0.145504  0.012711  0.06
7   0.746420  0.152759  0.014821  0.07
8   0.739149  0.159921  0.016930  0.08
9   0.731972  0.166989  0.019040  0.09
10  0.724886  0.173963  0.021151  0.10
11  0.717891  0.180844  0.023265  0.11
12  0.710985  0.187632  0.025383  0.12
13  0.704168  0.194326  0.027505  0.13
14  0.697439  0.200927  0.029633  0.14
15  0.690797  0.207435  0.031768  0.15
16  0.684240  0.213850  0.033910  0.16
17  0.677768  0.220171  0.036061  0.17
18  0.671380  0.226399  0.038221  0.18
19  0.665075  0.232533  0.040393  0.19
       id_x8lp   id_ddfe   id_y5nu   Time
991   1.102740  0.768714  1.010546   9.91
992   1.103651  0.769026  1.011323   9.92
993   1.104562  0.769337  1.012101   9.93
994   1.105473  0.769648  1.012879   9.94
995   1.106385  0.769958  1.013657   9.95
996   1.107297  0.770268  1.014435   9.96
997   1.108210  0.770577  1.015213   9.97
998   1.109123  0.770887  1.015991   9.98
999   1.110036  0.771195  1.016769   9.99
1000  1.110950  0.771503  1.017547  10.00

## 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_3, iteration_4, iteration_6, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, repressilator_sbml, repressilator_sbml2, repressilator_sbml3, hybrid_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 hybrid model with cyclic conversion and nonlinear (Hill-type) feedback, plus a constant source, still does not produce oscillations. The simulated concentrations increase smoothly and approach a steady state, rather than oscillating. This suggests that the system's oscillations are not due to the types of feedback or conversion mechanisms tested so far.

Given the robust oscillatory/cyclic behavior in the experimental data, and the failure of all tested models (first-order, autocatalytic, repressilator, hybrid) to reproduce oscillations, it is likely that the real system includes a mechanism not captured by these models. Possibilities include:
- Explicit time delays (not supported in standard SBML ODEs)
- Nonlinear degradation or removal (e.g., zero-order or cooperative degradation)
- Additional hidden feedback loops or autocatalytic cycles

Since the system can "self-start" from zero and the total concentration increases over time, a constant or autocatalytic source is likely. However, the key missing ingredient for oscillations may be a nonlinear or saturating degradation term.

I will now try a model with Michaelis-Menten (saturating) degradation for each species, which can sometimes produce oscillations in combination with cyclic feedback.

## Action

### Code

```python
import libsbml

# Start from the original model again
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# Parameters
k1 = 1.0  # rate for id_x8lp -> id_ddfe
k2 = 1.0  # rate for id_ddfe -> id_y5nu
k3 = 1.0  # rate for id_y5nu -> id_x8lp
alpha = 0.2  # constant source for id_y5nu
Km = 0.2  # Michaelis constant for degradation
Vmax = 0.5  # Max degradation rate

# id_x8lp -> id_ddfe
r1 = model.createReaction()
r1.setId("r_x8lp_to_ddfe")
r1.setReversible(False)
r1.setFast(False)
reactant1 = r1.createReactant()
reactant1.setSpecies("id_x8lp")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)
product1 = r1.createProduct()
product1.setSpecies("id_ddfe")
product1.setStoichiometry(1.0)
product1.setConstant(False)
kinetics1 = r1.createKineticLaw()
kinetics1.setFormula(f"{k1} * id_x8lp")

# id_ddfe -> id_y5nu
r2 = model.createReaction()
r2.setId("r_ddfe_to_y5nu")
r2.setReversible(False)
r2.setFast(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_ddfe")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_y5nu")
product2.setStoichiometry(1.0)
product2.setConstant(False)
kinetics2 = r2.createKineticLaw()
kinetics2.setFormula(f"{k2} * id_ddfe")

# id_y5nu -> id_x8lp
r3 = model.createReaction()
r3.setId("r_y5nu_to_x8lp")
r3.setReversible(False)
r3.setFast(False)
reactant3 = r3.createReactant()
reactant3.setSpecies("id_y5nu")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(False)
product3 = r3.createProduct()
product3.setSpecies("id_x8lp")
product3.setStoichiometry(1.0)
product3.setConstant(False)
kinetics3 = r3.createKineticLaw()
kinetics3.setFormula(f"{k3} * id_y5nu")

# Constant source for id_y5nu
r4 = model.createReaction()
r4.setId("r_source_y5nu")
r4.setReversible(False)
r4.setFast(False)
product4 = r4.createProduct()
product4.setSpecies("id_y5nu")
product4.setStoichiometry(1.0)
product4.setConstant(False)
kinetics4 = r4.createKineticLaw()
kinetics4.setFormula(f"{alpha}")

# Michaelis-Menten degradation for id_x8lp
r5 = model.createReaction()
r5.setId("r_deg_x8lp")
r5.setReversible(False)
r5.setFast(False)
reactant5 = r5.createReactant()
reactant5.setSpecies("id_x8lp")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(False)
kinetics5 = r5.createKineticLaw()
kinetics5.setFormula(f"{Vmax}*id_x8lp/({Km}+id_x8lp)")

# Michaelis-Menten degradation for id_ddfe
r6 = model.createReaction()
r6.setId("r_deg_ddfe")
r6.setReversible(False)
r6.setFast(False)
reactant6 = r6.createReactant()
reactant6.setSpecies("id_ddfe")
reactant6.setStoichiometry(1.0)
reactant6.setConstant(False)
kinetics6 = r6.createKineticLaw()
kinetics6.setFormula(f"{Vmax}*id_ddfe/({Km}+id_ddfe)")

# Michaelis-Menten degradation for id_y5nu
r7 = model.createReaction()
r7.setId("r_deg_y5nu")
r7.setReversible(False)
r7.setFast(False)
reactant7 = r7.createReactant()
reactant7.setSpecies("id_y5nu")
reactant7.setStoichiometry(1.0)
reactant7.setConstant(False)
kinetics7 = r7.createKineticLaw()
kinetics7.setFormula(f"{Vmax}*id_y5nu/({Km}+id_y5nu)")

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

# Simulate and compare with experiment 0
sim_df7 = simulate(mmdeg_sbml)
shared_variables.add("mmdeg_sbml", mmdeg_sbml)
print(sim_df7.head(20))
print(sim_df7.tail(10))
```
# Observation

## Code Stdout
     id_x8lp   id_ddfe   id_y5nu  Time
0   0.800000  0.100000  0.000000  0.00
1   0.788081  0.105218  0.002974  0.01
2   0.776321  0.110213  0.005899  0.02
3   0.764720  0.114990  0.008775  0.03
4   0.753275  0.119559  0.011603  0.04
5   0.741984  0.123925  0.014386  0.05
6   0.730846  0.128096  0.017123  0.06
7   0.719858  0.132078  0.019817  0.07
8   0.709018  0.135877  0.022467  0.08
9   0.698326  0.139497  0.025075  0.09
10  0.687779  0.142946  0.027642  0.10
11  0.677376  0.146228  0.030167  0.11
12  0.667114  0.149347  0.032653  0.12
13  0.656992  0.152310  0.035098  0.13
14  0.647009  0.155119  0.037504  0.14
15  0.637163  0.157781  0.039871  0.15
16  0.627452  0.160298  0.042200  0.16
17  0.617874  0.162676  0.044491  0.17
18  0.608429  0.164918  0.046744  0.18
19  0.599114  0.167028  0.048960  0.19
       id_x8lp   id_ddfe   id_y5nu   Time
991   0.022461  0.006566  0.072943   9.91
992   0.022461  0.006566  0.072943   9.92
993   0.022461  0.006566  0.072943   9.93
994   0.022461  0.006566  0.072943   9.94
995   0.022461  0.006566  0.072943   9.95
996   0.022461  0.006566  0.072943   9.96
997   0.022461  0.006566  0.072943   9.97
998   0.022461  0.006566  0.072943   9.98
999   0.022461  0.006566  0.072943   9.99
1000  0.022461  0.006566  0.072943  10.00

## 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_3, iteration_4, iteration_6, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, repressilator_sbml, repressilator_sbml2, repressilator_sbml3, hybrid_sbml, mmdeg_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 model with Michaelis-Menten (saturating) degradation and cyclic conversion still does not produce oscillations. Instead, the system approaches a steady state, with all species reaching low, constant values. This further supports the idea that the oscillatory behavior in the experimental data is not due to the types of feedback, conversion, or degradation mechanisms tested so far.

Given the robust, sequential cycling in the experimental data, and the failure of all ODE-based models to reproduce oscillations, it is likely that the real system includes a mechanism not captured by standard ODEs, such as:
- Explicit time delays (which are not supported in standard SBML ODEs)
- Piecewise or switch-like kinetics
- Additional hidden feedback loops

However, the experimental data show that the system can "self-start" from zero, and the total concentration increases over time, suggesting a constant or autocatalytic source. The cycling pattern is reminiscent of a relaxation oscillator, which can be modeled with strong, nonlinear feedback and slow/fast timescales.

As a last attempt, I will try a model with strong positive feedback (autocatalysis) for each species, in addition to the cyclic conversion and a constant source. This can sometimes produce relaxation oscillations.

## Action

### Code

```python
import libsbml

# Start from the original model again
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# Parameters
k1 = 1.0  # rate for id_x8lp -> id_ddfe
k2 = 1.0  # rate for id_ddfe -> id_y5nu
k3 = 1.0  # rate for id_y5nu -> id_x8lp
alpha = 0.2  # constant source for id_y5nu
k_auto = 2.0  # autocatalytic rate

# id_x8lp -> id_ddfe
r1 = model.createReaction()
r1.setId("r_x8lp_to_ddfe")
r1.setReversible(False)
r1.setFast(False)
reactant1 = r1.createReactant()
reactant1.setSpecies("id_x8lp")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)
product1 = r1.createProduct()
product1.setSpecies("id_ddfe")
product1.setStoichiometry(1.0)
product1.setConstant(False)
kinetics1 = r1.createKineticLaw()
kinetics1.setFormula(f"{k1} * id_x8lp")

# id_ddfe -> id_y5nu
r2 = model.createReaction()
r2.setId("r_ddfe_to_y5nu")
r2.setReversible(False)
r2.setFast(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_ddfe")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_y5nu")
product2.setStoichiometry(1.0)
product2.setConstant(False)
kinetics2 = r2.createKineticLaw()
kinetics2.setFormula(f"{k2} * id_ddfe")

# id_y5nu -> id_x8lp
r3 = model.createReaction()
r3.setId("r_y5nu_to_x8lp")
r3.setReversible(False)
r3.setFast(False)
reactant3 = r3.createReactant()
reactant3.setSpecies("id_y5nu")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(False)
product3 = r3.createProduct()
product3.setSpecies("id_x8lp")
product3.setStoichiometry(1.0)
product3.setConstant(False)
kinetics3 = r3.createKineticLaw()
kinetics3.setFormula(f"{k3} * id_y5nu")

# Constant source for id_y5nu
r4 = model.createReaction()
r4.setId("r_source_y5nu")
r4.setReversible(False)
r4.setFast(False)
product4 = r4.createProduct()
product4.setSpecies("id_y5nu")
product4.setStoichiometry(1.0)
product4.setConstant(False)
kinetics4 = r4.createKineticLaw()
kinetics4.setFormula(f"{alpha}")

# Autocatalytic production for each species
# id_x8lp autocatalysis
r5 = model.createReaction()
r5.setId("r_auto_x8lp")
r5.setReversible(False)
r5.setFast(False)
reactant5 = r5.createReactant()
reactant5.setSpecies("id_x8lp")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(False)
product5 = r5.createProduct()
product5.setSpecies("id_x8lp")
product5.setStoichiometry(2.0)
product5.setConstant(False)
kinetics5 = r5.createKineticLaw()
kinetics5.setFormula(f"{k_auto} * id_x8lp")

# id_ddfe autocatalysis
r6 = model.createReaction()
r6.setId("r_auto_ddfe")
r6.setReversible(False)
r6.setFast(False)
reactant6 = r6.createReactant()
reactant6.setSpecies("id_ddfe")
reactant6.setStoichiometry(1.0)
reactant6.setConstant(False)
product6 = r6.createProduct()
product6.setSpecies("id_ddfe")
product6.setStoichiometry(2.0)
product6.setConstant(False)
kinetics6 = r6.createKineticLaw()
kinetics6.setFormula(f"{k_auto} * id_ddfe")

# id_y5nu autocatalysis
r7 = model.createReaction()
r7.setId("r_auto_y5nu")
r7.setReversible(False)
r7.setFast(False)
reactant7 = r7.createReactant()
reactant7.setSpecies("id_y5nu")
reactant7.setStoichiometry(1.0)
reactant7.setConstant(False)
product7 = r7.createProduct()
product7.setSpecies("id_y5nu")
product7.setStoichiometry(2.0)
product7.setConstant(False)
kinetics7 = r7.createKineticLaw()
kinetics7.setFormula(f"{k_auto} * id_y5nu")

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

# Simulate and compare with experiment 0
sim_df8 = simulate(auto_sbml)
shared_variables.add("auto_sbml", auto_sbml)
print(sim_df8.head(20))
print(sim_df8.tail(10))
```
# Observation

## Code Stdout
     id_x8lp   id_ddfe   id_y5nu  Time
0   0.800000  0.100000  0.000000  0.00
1   0.808055  0.109085  0.003060  0.01
2   0.816223  0.118344  0.006244  0.02
3   0.824506  0.127778  0.009553  0.03
4   0.832905  0.137390  0.012992  0.04
5   0.841424  0.147185  0.016562  0.05
6   0.850066  0.157164  0.020268  0.06
7   0.858832  0.167330  0.024112  0.07
8   0.867726  0.177688  0.028098  0.08
9   0.876749  0.188240  0.032229  0.09
10  0.885906  0.198989  0.036508  0.10
11  0.895199  0.209939  0.040940  0.11
12  0.904630  0.221093  0.045527  0.12
13  0.914203  0.232454  0.050273  0.13
14  0.923920  0.244027  0.055183  0.14
15  0.933786  0.255815  0.060259  0.15
16  0.943802  0.267820  0.065506  0.16
17  0.953973  0.280048  0.070927  0.17
18  0.964302  0.292502  0.076527  0.18
19  0.974791  0.305186  0.082309  0.19
           id_x8lp       id_ddfe       id_y5nu   Time
991   1.350848e+08  1.350849e+08  1.350849e+08   9.91
992   1.378137e+08  1.378138e+08  1.378138e+08   9.92
993   1.405978e+08  1.405979e+08  1.405978e+08   9.93
994   1.434380e+08  1.434381e+08  1.434381e+08   9.94
995   1.463357e+08  1.463358e+08  1.463357e+08   9.95
996   1.492919e+08  1.492919e+08  1.492919e+08   9.96
997   1.523078e+08  1.523078e+08  1.523078e+08   9.97
998   1.553846e+08  1.553847e+08  1.553846e+08   9.98
999   1.585236e+08  1.585237e+08  1.585236e+08   9.99
1000  1.617260e+08  1.617260e+08  1.617260e+08  10.00

## 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_3, iteration_4, iteration_6, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (test_sbml, test_sbml2, repressilator_sbml, repressilator_sbml2, repressilator_sbml3, hybrid_sbml, mmdeg_sbml, auto_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

The model with strong autocatalysis for each species, in addition to cyclic conversion and a constant source, leads to runaway exponential growth in all species, not oscillations. This confirms that positive feedback alone is not the mechanism behind the observed oscillatory/cyclic behavior.

All tested ODE-based models (first-order, autocatalytic, repressilator, hybrid, Michaelis-Menten degradation, and strong positive feedback) have failed to reproduce the robust, sequential oscillations seen in the experimental data. The real system likely includes a mechanism not captured by these models, such as:
- Explicit time delays (not supported in standard SBML ODEs)
- Piecewise or switch-like kinetics
- Additional hidden feedback loops or a more complex network topology

Given the constraints of SBML and the available data, the most plausible ODE-based model is a cyclic conversion network with a constant source for one species. This model at least captures the sequential conversion and the increase in total concentration, even if it does not reproduce oscillations.

Since further iterations are unlikely to yield a better ODE-based fit, I will submit the best mechanistic model supported by the data: a cyclic conversion network with a constant source for `id_y5nu`.

## Action

### Submit

```python
import libsbml

# Start from the original model again
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

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

# Parameters
k1 = 1.0  # rate for id_x8lp -> id_ddfe
k2 = 1.0  # rate for id_ddfe -> id_y5nu
k3 = 1.0  # rate for id_y5nu -> id_x8lp
alpha = 0.2  # constant source for id_y5nu

# id_x8lp -> id_ddfe
r1 = model.createReaction()
r1.setId("r_x8lp_to_ddfe")
r1.setReversible(False)
r1.setFast(False)
reactant1 = r1.createReactant()
reactant1.setSpecies("id_x8lp")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)
product1 = r1.createProduct()
product1.setSpecies("id_ddfe")
product1.setStoichiometry(1.0)
product1.setConstant(False)
kinetics1 = r1.createKineticLaw()
kinetics1.setFormula(f"{k1} * id_x8lp")

# id_ddfe -> id_y5nu
r2 = model.createReaction()
r2.setId("r_ddfe_to_y5nu")
r2.setReversible(False)
r2.setFast(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_ddfe")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_y5nu")
product2.setStoichiometry(1.0)
product2.setConstant(False)
kinetics2 = r2.createKineticLaw()
kinetics2.setFormula(f"{k2} * id_ddfe")

# id_y5nu -> id_x8lp
r3 = model.createReaction()
r3.setId("r_y5nu_to_x8lp")
r3.setReversible(False)
r3.setFast(False)
reactant3 = r3.createReactant()
reactant3.setSpecies("id_y5nu")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(False)
product3 = r3.createProduct()
product3.setSpecies("id_x8lp")
product3.setStoichiometry(1.0)
product3.setConstant(False)
kinetics3 = r3.createKineticLaw()
kinetics3.setFormula(f"{k3} * id_y5nu")

# Constant source for id_y5nu
r4 = model.createReaction()
r4.setId("r_source_y5nu")
r4.setReversible(False)
r4.setFast(False)
product4 = r4.createProduct()
product4.setSpecies("id_y5nu")
product4.setStoichiometry(1.0)
product4.setConstant(False)
kinetics4 = r4.createKineticLaw()
kinetics4.setFormula(f"{alpha}")

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