
                # 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_vtvn">
    <listOfUnitDefinitions>
      <unitDefinition id="id_liyq">
        <listOfUnits>
          <unit kind="second" multiplier="3600"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_fclk" size="1"/>
      <compartment id="id_o84f" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_cczd" compartment="id_fclk" initialAmount="1"/>
      <species id="id_v5j9" compartment="id_o84f" initialAmount="0" boundaryCondition="true" constant="true"/>
      <species id="id_4bhu" compartment="id_fclk" initialAmount="1"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

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

The provided SBML model contains three species:
- `id_cczd` (initialAmount=1, in compartment `id_fclk`)
- `id_v5j9` (initialAmount=0, in compartment `id_o84f`, boundaryCondition and constant are true, so it's not dynamic)
- `id_4bhu` (initialAmount=1, in compartment `id_fclk`)

There are no reactions defined. My goal is to discover the missing reactions/mechanisms. Since all species are observable, I can request time-course data to see how the concentrations of `id_cczd` and `id_4bhu` change over time. This will help me hypothesize the underlying reactions.

The first step should be to observe the system under default conditions to see if any dynamics are present.

## 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_cczd  id_4bhu id_v5j9
0  1.00e+00 1.00e+00       0
...
2.00e-01  9.81e-01 9.89e-01       0
...
4.00e-01  9.60e-01 9.78e-01       0
...
6.00e-01  9.37e-01 9.68e-01       0
...
8.00e-01  9.13e-01 9.59e-01       0
...
1.00e+00  8.88e-01 9.50e-01       0
...
1.20e+00  8.61e-01 9.42e-01       0
...
1.40e+00  8.32e-01 9.35e-01       0
...
1.60e+00  8.02e-01 9.29e-01       0
...
1.80e+00  7.70e-01 9.24e-01       0
...
2.00e+00  7.37e-01 9.20e-01       0
...
2.20e+00  7.01e-01 9.18e-01       0
...
2.40e+00  6.64e-01 9.17e-01       0
...
2.60e+00  6.26e-01 9.18e-01       0
...
2.80e+00  5.85e-01 9.22e-01       0
...
3.00e+00  5.42e-01 9.29e-01       0
...
3.20e+00  4.98e-01 9.39e-01       0
...
3.40e+00  4.51e-01 9.54e-01       0
...
3.60e+00  4.01e-01 9.76e-01       0
...
3.80e+00  3.49e-01 1.01e+00       0
...
4.00e+00  2.94e-01 1.05e+00       0
...
4.20e+00  2.36e-01 1.11e+00       0
...
4.40e+00  1.74e-01 1.20e+00       0
...
4.60e+00  1.08e-01 1.31e+00       0
...
4.80e+00  4.33e-02 1.47e+00       0
...
5.00e+00  1.78e-02 1.64e+00       0
...
5.20e+00  2.11e-02 1.80e+00       0
...
5.40e+00  2.81e-02 1.96e+00       0
...
5.60e+00  3.86e-02 2.12e+00       0
...
5.80e+00  5.54e-02 2.27e+00       0
...
6.00e+00  8.39e-02 2.40e+00       0
...
6.20e+00  1.31e-01 2.52e+00       0
...
6.40e+00  2.02e-01 2.60e+00       0
...
6.60e+00  2.95e-01 2.64e+00       0
...
6.80e+00  4.04e-01 2.64e+00       0
...
7.00e+00  5.25e-01 2.63e+00       0
...
7.20e+00  6.53e-01 2.60e+00       0
...
7.40e+00  7.84e-01 2.56e+00       0
...
7.60e+00  9.16e-01 2.52e+00       0
...
7.80e+00  1.05e+00 2.48e+00       0
...
8.00e+00  1.18e+00 2.44e+00       0
...
8.20e+00  1.30e+00 2.40e+00       0
...
8.40e+00  1.43e+00 2.35e+00       0
...
8.60e+00  1.55e+00 2.31e+00       0
...
8.80e+00  1.66e+00 2.27e+00       0
...
9.00e+00  1.77e+00 2.23e+00       0
...
9.20e+00  1.88e+00 2.18e+00       0
...
9.40e+00  1.98e+00 2.14e+00       0
...
9.60e+00  2.08e+00 2.10e+00       0
...
1.00e+01  2.27e+00 2.02e+00       0

## 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, both `id_cczd` and `id_4bhu` start at 1.0. Over time, `id_cczd` decreases while `id_4bhu` increases, then after a certain point, `id_cczd` increases and `id_4bhu` decreases, and this cycle repeats, suggesting oscillatory behavior. The boundary species `id_v5j9` remains at 0 throughout, so it is not involved in the dynamics.

This oscillatory pattern suggests a reversible reaction or a feedback loop between `id_cczd` and `id_4bhu`. A simple reversible reaction (`id_cczd <-> id_4bhu`) could produce such dynamics, but the oscillation is not typical for a simple reversible reaction unless there is some nonlinearity or autocatalysis.

To further probe the system, I should perturb the initial concentrations to see how the system responds. This will help distinguish between simple reversible reactions and more complex feedback mechanisms.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_cczd": 2.0,
        "id_4bhu": 0.5
    }
}
```
# Observation

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

Total size: 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_cczd  id_4bhu id_v5j9
0  2.00e+00 5.00e-01       0
...
2.00e-01  1.94e+00 4.92e-01       0
...
4.00e-01  1.87e+00 4.85e-01       0
...
6.00e-01  1.81e+00 4.78e-01       0
...
8.00e-01  1.74e+00 4.71e-01       0
...
1.00e+00  1.68e+00 4.65e-01       0
...
1.20e+00  1.61e+00 4.58e-01       0
...
1.40e+00  1.54e+00 4.53e-01       0
...
1.60e+00  1.47e+00 4.48e-01       0
...
1.80e+00  1.40e+00 4.43e-01       0
...
2.00e+00  1.33e+00 4.38e-01       0
...
2.20e+00  1.26e+00 4.35e-01       0
...
2.40e+00  1.19e+00 4.32e-01       0
...
2.60e+00  1.12e+00 4.30e-01       0
...
2.80e+00  1.04e+00 4.28e-01       0
...
3.00e+00  9.68e-01 4.28e-01       0
...
3.20e+00  8.91e-01 4.29e-01       0
...
3.40e+00  8.12e-01 4.32e-01       0
...
3.60e+00  7.30e-01 4.38e-01       0
...
3.80e+00  6.46e-01 4.46e-01       0
...
4.00e+00  5.58e-01 4.60e-01       0
...
4.20e+00  4.67e-01 4.80e-01       0
...
4.40e+00  3.69e-01 5.13e-01       0
...
4.60e+00  2.65e-01 5.67e-01       0
...
4.80e+00  1.49e-01 6.63e-01       0
...
5.00e+00  2.41e-02 8.23e-01       0
...
5.20e+00  5.70e-03 1.00e+00       0
...
5.40e+00  7.73e-03 1.18e+00       0
...
5.60e+00  1.03e-02 1.36e+00       0
...
5.80e+00  1.35e-02 1.53e+00       0
...
6.00e+00  1.76e-02 1.69e+00       0
...
6.20e+00  2.33e-02 1.86e+00       0
...
6.40e+00  3.13e-02 2.02e+00       0
...
6.60e+00  4.36e-02 2.17e+00       0
...
6.80e+00  6.39e-02 2.32e+00       0
...
7.00e+00  9.82e-02 2.45e+00       0
...
7.20e+00  1.53e-01 2.55e+00       0
...
7.40e+00  2.33e-01 2.62e+00       0
...
7.60e+00  3.32e-01 2.64e+00       0
...
7.80e+00  4.47e-01 2.64e+00       0
...
8.00e+00  5.70e-01 2.62e+00       0
...
8.20e+00  7.00e-01 2.59e+00       0
...
8.40e+00  8.31e-01 2.55e+00       0
...
8.60e+00  9.63e-01 2.51e+00       0
...
8.80e+00  1.09e+00 2.47e+00       0
...
9.00e+00  1.22e+00 2.42e+00       0
...
9.20e+00  1.35e+00 2.38e+00       0
...
9.40e+00  1.47e+00 2.34e+00       0
...
9.60e+00  1.59e+00 2.30e+00       0
...
1.00e+01  1.81e+00 2.21e+00       0

## 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, with `id_cczd` starting at 2.0 and `id_4bhu` at 0.5, again shows oscillatory behavior: `id_cczd` decreases while `id_4bhu` increases, then the trend reverses, and the cycle repeats. The amplitude and phase of the oscillations are affected by the initial conditions, but the qualitative behavior is similar to the default case.

This is not typical for a simple reversible reaction, which would approach equilibrium monotonically. The oscillatory dynamics suggest a more complex mechanism, possibly involving autocatalysis or a nonlinear feedback loop.

To better hypothesize the mechanism, I should analyze the time series data quantitatively, looking for clues such as:
- The period and amplitude of oscillations
- The relationship between the two species (e.g., are they always out of phase? Is there a delay?)
- Whether the total amount of `id_cczd` + `id_4bhu` is conserved

This analysis will help determine if the system is best described by a reversible reaction with nonlinear kinetics, an autocatalytic loop, or another mechanism.

## Action

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

# Load both experiments
df0 = experiment_history['iteration_0']
df1 = experiment_history['iteration_1']

# Calculate total amount for both experiments
df0['total'] = df0['id_cczd'] + df0['id_4bhu']
df1['total'] = df1['id_cczd'] + df1['id_4bhu']

# Print summary statistics and a few rows to check conservation and oscillation
print("Experiment 0: total min/max/mean", df0['total'].min(), df0['total'].max(), df0['total'].mean())
print("Experiment 1: total min/max/mean", df1['total'].min(), df1['total'].max(), df1['total'].mean())

# Print first and last few rows for both experiments
print("Experiment 0 (start):\n", df0.head())
print("Experiment 0 (end):\n", df0.tail())
print("Experiment 1 (start):\n", df1.head())
print("Experiment 1 (end):\n", df1.tail())

# Check for phase relationship (correlation)
corr = df0[['id_cczd', 'id_4bhu']].corr()
print("Correlation between id_cczd and id_4bhu (exp 0):\n", corr)
```
# Observation

## Code Stdout
Experiment 0: total min/max/mean 1.3420018243262006 4.290631185644372 2.434338714999079
Experiment 1: total min/max/mean 0.8117526021730403 4.024065812059177 2.152875028859906
Experiment 0 (start):
     id_cczd   id_4bhu  id_v5j9  Time     total
0  1.000000  1.000000      0.0  0.00  2.000000
1  0.999067  0.999424      0.0  0.01  1.998492
2  0.998131  0.998850      0.0  0.02  1.996981
3  0.997191  0.998277      0.0  0.03  1.995468
4  0.996248  0.997705      0.0  0.04  1.993952
Experiment 0 (end):
        id_cczd   id_4bhu  id_v5j9   Time     total
996   2.249020  2.031845      0.0   9.96  4.280864
997   2.253423  2.029897      0.0   9.97  4.283320
998   2.257815  2.027952      0.0   9.98  4.285767
999   2.262196  2.026008      0.0   9.99  4.288204
1000  2.266566  2.024065      0.0  10.00  4.290631
Experiment 1 (start):
     id_cczd   id_4bhu  id_v5j9  Time     total
0  2.000000  0.500000      0.0  0.00  2.500000
1  1.996817  0.499607      0.0  0.01  2.496424
2  1.993634  0.499214      0.0  0.02  2.492848
3  1.990449  0.498822      0.0  0.03  2.489271
4  1.987263  0.498431      0.0  0.04  2.485694
Experiment 1 (end):
        id_cczd   id_4bhu  id_v5j9   Time     total
996   1.791290  2.219413      0.0   9.96  4.010703
997   1.796731  2.217327      0.0   9.97  4.014058
998   1.802162  2.215242      0.0   9.98  4.017404
999   1.807581  2.213158      0.0   9.99  4.020740
1000  1.812990  2.211076      0.0  10.00  4.024066
Correlation between id_cczd and id_4bhu (exp 0):
           id_cczd   id_4bhu
id_cczd  1.000000  0.188468
id_4bhu  0.188468  1.000000

## 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

Key findings from the analysis:
- The total amount of `id_cczd` + `id_4bhu` is not conserved; it increases over time, roughly doubling by the end of the simulation. This rules out a simple reversible reaction or a closed system.
- The correlation between `id_cczd` and `id_4bhu` is low (0.19), suggesting they are not simply interconverting but may be involved in more complex dynamics.
- Both species oscillate, and the system appears to have a net production of mass, indicating possible autocatalytic or self-amplifying reactions.

Given the non-conservation and oscillatory behavior, a plausible hypothesis is that both species can catalyze their own production (autocatalysis), or there is mutual activation. Alternatively, there could be a nonlinear feedback loop.

To further probe the mechanism, I should test what happens if one of the species starts at zero. This will help determine if autocatalysis is present (i.e., if a species cannot increase from zero, it suggests autocatalysis).

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_cczd": 0.0,
        "id_4bhu": 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_cczd  id_4bhu id_v5j9
0         0 1.00e+00       0
...
2.00e-01  7.67e-03 1.18e+00       0
...
4.00e-01  1.02e-02 1.35e+00       0
...
6.00e-01  1.34e-02 1.52e+00       0
...
8.00e-01  1.75e-02 1.69e+00       0
...
1.00e+00  2.31e-02 1.85e+00       0
...
1.20e+00  3.11e-02 2.01e+00       0
...
1.40e+00  4.33e-02 2.17e+00       0
...
1.60e+00  6.33e-02 2.31e+00       0
...
1.80e+00  9.72e-02 2.45e+00       0
...
2.00e+00  1.52e-01 2.55e+00       0
...
2.20e+00  2.30e-01 2.62e+00       0
...
2.40e+00  3.30e-01 2.64e+00       0
...
2.60e+00  4.44e-01 2.64e+00       0
...
2.80e+00  5.68e-01 2.62e+00       0
...
3.00e+00  6.97e-01 2.59e+00       0
...
3.20e+00  8.28e-01 2.55e+00       0
...
3.40e+00  9.60e-01 2.51e+00       0
...
3.60e+00  1.09e+00 2.47e+00       0
...
3.80e+00  1.22e+00 2.42e+00       0
...
4.00e+00  1.34e+00 2.38e+00       0
...
4.20e+00  1.47e+00 2.34e+00       0
...
4.40e+00  1.59e+00 2.30e+00       0
...
4.60e+00  1.70e+00 2.25e+00       0
...
4.80e+00  1.81e+00 2.21e+00       0
...
5.00e+00  1.92e+00 2.17e+00       0
...
5.20e+00  2.02e+00 2.13e+00       0
...
5.40e+00  2.12e+00 2.09e+00       0
...
5.60e+00  2.21e+00 2.05e+00       0
...
5.80e+00  2.30e+00 2.01e+00       0
...
6.00e+00  2.38e+00 1.97e+00       0
...
6.20e+00  2.46e+00 1.94e+00       0
...
6.40e+00  2.53e+00 1.90e+00       0
...
6.60e+00  2.60e+00 1.86e+00       0
...
6.80e+00  2.67e+00 1.83e+00       0
...
7.00e+00  2.73e+00 1.79e+00       0
...
7.20e+00  2.79e+00 1.76e+00       0
...
7.40e+00  2.84e+00 1.72e+00       0
...
7.60e+00  2.89e+00 1.69e+00       0
...
7.80e+00  2.94e+00 1.66e+00       0
...
8.00e+00  2.98e+00 1.63e+00       0
...
8.20e+00  3.02e+00 1.59e+00       0
...
8.40e+00  3.06e+00 1.56e+00       0
...
8.60e+00  3.09e+00 1.53e+00       0
...
8.80e+00  3.12e+00 1.50e+00       0
...
9.00e+00  3.14e+00 1.48e+00       0
...
9.20e+00  3.17e+00 1.45e+00       0
...
9.40e+00  3.19e+00 1.42e+00       0
...
9.60e+00  3.20e+00 1.39e+00       0
...
1.00e+01  3.23e+00 1.34e+00       0

## 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

With `id_cczd` starting at 0 and `id_4bhu` at 1, `id_cczd` quickly increases from zero, while `id_4bhu` also increases, then both oscillate and grow. This means `id_cczd` can be produced even when its initial concentration is zero, so pure autocatalysis is unlikely. The system still shows net mass increase and oscillatory behavior.

This suggests:
- There is a reaction that produces both species, possibly from an implicit source (e.g., a zero-order or constant input).
- There may be mutual activation or cross-catalysis, or a nonlinear feedback loop.
- The oscillatory and amplifying behavior is reminiscent of the Lotka-Volterra or Brusselator models, which involve nonlinear terms and can produce oscillations and growth.

To further test the hypothesis, I should try the reverse: set `id_4bhu` to zero and `id_cczd` to 1, and see if `id_4bhu` can be produced from zero. This will help clarify if both species can be produced independently, and whether the system is symmetric.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_cczd": 1.0,
        "id_4bhu": 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_cczd  id_4bhu id_v5j9
0  1.00e+00        0       0
...
2.00e-01  8.80e-01 9.49e-03       0
...
4.00e-01  7.59e-01 2.17e-02       0
...
6.00e-01  6.34e-01 3.83e-02       0
...
8.00e-01  5.04e-01 6.22e-02       0
...
1.00e+00  3.66e-01 1.01e-01       0
...
1.20e+00  2.17e-01 1.71e-01       0
...
1.40e+00  4.89e-02 3.15e-01       0
...
1.60e+00  1.94e-03 5.06e-01       0
...
1.80e+00  3.09e-03 6.94e-01       0
...
2.00e+00  4.52e-03 8.78e-01       0
...
2.20e+00  6.27e-03 1.06e+00       0
...
2.40e+00  8.44e-03 1.24e+00       0
...
2.60e+00  1.11e-02 1.41e+00       0
...
2.80e+00  1.46e-02 1.58e+00       0
...
3.00e+00  1.91e-02 1.74e+00       0
...
3.20e+00  2.54e-02 1.91e+00       0
...
3.40e+00  3.45e-02 2.07e+00       0
...
3.60e+00  4.88e-02 2.22e+00       0
...
3.80e+00  7.25e-02 2.36e+00       0
...
4.00e+00  1.13e-01 2.49e+00       0
...
4.20e+00  1.75e-01 2.58e+00       0
...
4.40e+00  2.61e-01 2.63e+00       0
...
4.60e+00  3.66e-01 2.64e+00       0
...
4.80e+00  4.84e-01 2.63e+00       0
...
5.00e+00  6.09e-01 2.61e+00       0
...
5.20e+00  7.39e-01 2.57e+00       0
...
5.40e+00  8.71e-01 2.54e+00       0
...
5.60e+00  1.00e+00 2.50e+00       0
...
5.80e+00  1.13e+00 2.45e+00       0
...
6.00e+00  1.26e+00 2.41e+00       0
...
6.20e+00  1.39e+00 2.37e+00       0
...
6.40e+00  1.51e+00 2.32e+00       0
...
6.60e+00  1.62e+00 2.28e+00       0
...
6.80e+00  1.74e+00 2.24e+00       0
...
7.00e+00  1.85e+00 2.20e+00       0
...
7.20e+00  1.95e+00 2.16e+00       0
...
7.40e+00  2.05e+00 2.12e+00       0
...
7.60e+00  2.15e+00 2.08e+00       0
...
7.80e+00  2.24e+00 2.04e+00       0
...
8.00e+00  2.32e+00 2.00e+00       0
...
8.20e+00  2.41e+00 1.96e+00       0
...
8.40e+00  2.48e+00 1.92e+00       0
...
8.60e+00  2.56e+00 1.89e+00       0
...
8.80e+00  2.63e+00 1.85e+00       0
...
9.00e+00  2.69e+00 1.81e+00       0
...
9.20e+00  2.75e+00 1.78e+00       0
...
9.40e+00  2.81e+00 1.75e+00       0
...
9.60e+00  2.86e+00 1.71e+00       0
...
1.00e+01  2.96e+00 1.65e+00       0

## 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 `id_cczd` at 1 and `id_4bhu` at 0, `id_4bhu` is produced from zero, and both species again show oscillatory and amplifying behavior. This rules out strict autocatalysis for either species and suggests that both can be produced from the other or from a common source.

The system is symmetric: both species can be produced from the other, and both can grow from zero. The oscillatory, amplifying behavior and non-conservation of total mass are reminiscent of the Lotka-Volterra or Brusselator models, which involve:
- Linear production of one species,
- Nonlinear (e.g., quadratic) production of the other,
- Interconversion or mutual activation.

Given the symmetry and oscillations, a plausible minimal model is:
- A constant inflow or production of both species,
- A nonlinear (possibly quadratic) cross-catalytic reaction,
- Possibly a degradation or outflow term to prevent unbounded growth (though the data shows net growth, so this may be weak or absent).

To further clarify, I should check if the rate of increase of each species depends on the concentration of the other (i.e., cross-catalysis). I will analyze the time derivatives of each species versus the concentrations of the other.

## Action

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

# Use experiment 0 for analysis
df = experiment_history['iteration_0']

# Calculate time derivatives (finite differences)
dt = df['Time'].diff().values[1:]
d_cczd = df['id_cczd'].diff().values[1:] / dt
d_4bhu = df['id_4bhu'].diff().values[1:] / dt

# Use midpoints for concentrations
cczd_mid = (df['id_cczd'].values[:-1] + df['id_cczd'].values[1:]) / 2
bhu_mid = (df['id_4bhu'].values[:-1] + df['id_4bhu'].values[1:]) / 2

# Correlate derivatives with concentrations of the other species
corr_cczd_bhu = np.corrcoef(d_cczd, bhu_mid)[0,1]
corr_4bhu_cczd = np.corrcoef(d_4bhu, cczd_mid)[0,1]

print("Correlation of d(id_cczd)/dt with id_4bhu:", corr_cczd_bhu)
print("Correlation of d(id_4bhu)/dt with id_cczd:", corr_4bhu_cczd)

# Also check for quadratic dependence
corr_cczd_bhu2 = np.corrcoef(d_cczd, bhu_mid**2)[0,1]
corr_4bhu_cczd2 = np.corrcoef(d_4bhu, cczd_mid**2)[0,1]

print("Correlation of d(id_cczd)/dt with id_4bhu^2:", corr_cczd_bhu2)
print("Correlation of d(id_4bhu)/dt with id_cczd^2:", corr_4bhu_cczd2)
```
# Observation

## Code Stdout
Correlation of d(id_cczd)/dt with id_4bhu: 0.9134343887858228
Correlation of d(id_4bhu)/dt with id_cczd: -0.7812538500545099
Correlation of d(id_cczd)/dt with id_4bhu^2: 0.9193382685569154
Correlation of d(id_4bhu)/dt with id_cczd^2: -0.5762244120866268

## 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. ()

### 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 analysis shows:
- The rate of change of `id_cczd` is strongly positively correlated with the concentration of `id_4bhu` (and even more so with its square).
- The rate of change of `id_4bhu` is strongly negatively correlated with the concentration of `id_cczd` (and somewhat with its square).

This suggests:
- `id_4bhu` promotes the production of `id_cczd` (possibly via a reaction like `id_4bhu → id_4bhu + id_cczd` or `2 id_4bhu → id_4bhu + id_cczd`).
- `id_cczd` promotes the consumption or conversion of `id_4bhu` (possibly via a reaction like `id_cczd + id_4bhu → 2 id_cczd` or `id_cczd → ...`).
- The system is reminiscent of the Lotka-Volterra predator-prey model, where one species ("prey") grows and is consumed by the other ("predator"), which in turn grows by consuming the prey.

A minimal Lotka-Volterra-like model would be:
1. `id_4bhu` autocatalytic growth: `id_4bhu → 2 id_4bhu` (prey reproduction)
2. `id_cczd` production via predation: `id_cczd + id_4bhu → 2 id_cczd` (predator eats prey)
3. `id_cczd` decay: `id_cczd → ∅` (predator death)

However, the data shows net mass increase, so the decay term may be weak or absent. To test this, I will try to fit a simple Lotka-Volterra model to the data and see if it can reproduce the observed dynamics.

## Action

### Code
```python
import numpy as np
from scipy.optimize import curve_fit

# Use experiment 0 data
df = experiment_history['iteration_0']
t = df['Time'].values
x = df['id_4bhu'].values  # Prey
y = df['id_cczd'].values  # Predator

# Estimate derivatives
dt = np.diff(t)
dx = np.diff(x) / dt
dy = np.diff(y) / dt
x_mid = (x[:-1] + x[1:]) / 2
y_mid = (y[:-1] + y[1:]) / 2

# Lotka-Volterra model: dx/dt = a*x - b*x*y, dy/dt = -c*y + d*x*y
def lv_rhs(vars, a, b, c, d):
    x, y = vars
    dxdt = a*x - b*x*y
    dydt = -c*y + d*x*y
    return dxdt, dydt

# Stack for fitting
def fit_lv(XY, a, b, c, d):
    x, y = XY
    dxdt, dydt = lv_rhs((x, y), a, b, c, d)
    return np.concatenate([dxdt, dydt])

XY = np.vstack([x_mid, y_mid])
target = np.concatenate([dx, dy])

# Fit parameters
popt, _ = curve_fit(fit_lv, XY, target, p0=[1, 1, 1, 1])
a, b, c, d = popt
print("Fitted Lotka-Volterra parameters: a=%.3f, b=%.3f, c=%.3f, d=%.3f" % (a, b, c, d))
```
# Observation

## Code Stdout
Fitted Lotka-Volterra parameters: a=0.222, b=0.208, c=0.744, d=0.500

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

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


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



# Iteration 7
## Thoughts

The fitted Lotka-Volterra parameters are:
- a = 0.222 (prey, `id_4bhu`, growth rate)
- b = 0.208 (prey-predator interaction)
- c = 0.744 (predator, `id_cczd`, death rate)
- d = 0.500 (predator growth via predation)

This supports the hypothesis that the system is well-described by a Lotka-Volterra predator-prey model:
- `id_4bhu` (prey) grows exponentially in the absence of `id_cczd`.
- `id_cczd` (predator) dies off in the absence of `id_4bhu`.
- The interaction terms allow for oscillatory dynamics and net mass increase, as observed.

The next step is to encode these reactions in the SBML model:
1. `id_4bhu` → 2 `id_4bhu` (rate = a * [id_4bhu])
2. `id_cczd` + `id_4bhu` → 2 `id_cczd` (rate = b * [id_cczd] * [id_4bhu])
3. `id_cczd` → ∅ (rate = c * [id_cczd])

I will add these reactions to the SBML model using the fitted parameters and simulate the model to compare with the experimental data.

## Action

### Code
```python
import libsbml

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

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

# Parameters from fit
a = 0.222
b = 0.208
c = 0.744

# Reaction 1: id_4bhu -> 2 id_4bhu (prey growth)
r1 = model.createReaction()
r1.setId("prey_growth")
r1.setReversible(False)
r1.setFast(False)
reactant = r1.createReactant()
reactant.setSpecies("id_4bhu")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = r1.createProduct()
product.setSpecies("id_4bhu")
product.setStoichiometry(2.0)
product.setConstant(False)
kinetic_law1 = r1.createKineticLaw()
param_a = model.createParameter()
param_a.setId("a")
param_a.setValue(a)
kinetic_law1.setFormula("a * id_4bhu")

# Reaction 2: id_cczd + id_4bhu -> 2 id_cczd (predation)
r2 = model.createReaction()
r2.setId("predation")
r2.setReversible(False)
r2.setFast(False)
reactant1 = r2.createReactant()
reactant1.setSpecies("id_cczd")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_4bhu")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_cczd")
product2.setStoichiometry(2.0)
product2.setConstant(False)
param_b = model.createParameter()
param_b.setId("b")
param_b.setValue(b)
kinetic_law2 = r2.createKineticLaw()
kinetic_law2.setFormula("b * id_cczd * id_4bhu")

# Reaction 3: id_cczd -> (decay)
r3 = model.createReaction()
r3.setId("predator_death")
r3.setReversible(False)
r3.setFast(False)
reactant3 = r3.createReactant()
reactant3.setSpecies("id_cczd")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(False)
param_c = model.createParameter()
param_c.setId("c")
param_c.setValue(c)
kinetic_law3 = r3.createKineticLaw()
kinetic_law3.setFormula("c * id_cczd")

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

# Simulate and compare to experiment 0
sim_result = simulate(updated_sbml)
print(sim_result.head(20))
shared_variables.add("updated_sbml_lv", updated_sbml)
```
# Observation

## Code Stdout
     id_cczd   id_4bhu  id_v5j9  Time
0   1.000000  1.000000      0.0  0.00
1   0.994656  1.000146      0.0  0.01
2   0.989339  1.000303      0.0  0.02
3   0.984051  1.000470      0.0  0.03
4   0.978792  1.000649      0.0  0.04
5   0.973561  1.000839      0.0  0.05
6   0.968358  1.001039      0.0  0.06
7   0.963184  1.001251      0.0  0.07
8   0.958037  1.001473      0.0  0.08
9   0.952918  1.001706      0.0  0.09
10  0.947828  1.001949      0.0  0.10
11  0.942765  1.002203      0.0  0.11
12  0.937729  1.002468      0.0  0.12
13  0.932721  1.002743      0.0  0.13
14  0.927740  1.003029      0.0  0.14
15  0.922786  1.003325      0.0  0.15
16  0.917860  1.003632      0.0  0.16
17  0.912960  1.003949      0.0  0.17
18  0.908087  1.004276      0.0  0.18
19  0.903241  1.004614      0.0  0.19

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

### 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 simulated results from the Lotka-Volterra model show that both `id_cczd` and `id_4bhu` change only slightly in the first 0.2 time units, with `id_cczd` slowly decreasing and `id_4bhu` slowly increasing. This is in contrast to the experimental data, where both species show strong oscillations and significant net growth over time.

This suggests that the Lotka-Volterra model with the fitted parameters does not fully capture the observed dynamics, particularly the strong amplification and oscillatory behavior. The experimental system shows a net increase in total mass, while the Lotka-Volterra model tends to conserve or limit total mass.

Possible reasons for the discrepancy:
- The real system may have an additional inflow or autocatalytic production term for one or both species.
- The interaction terms may be nonlinear (e.g., quadratic or higher order).
- The fitted parameters may not be optimal, or the model structure may need to be extended (e.g., Brusselator or other autocatalytic oscillator).

To test the hypothesis of an additional inflow, I will add a zero-order production term for both species and see if this can reproduce the observed net growth and oscillations.

## Action

### Code
```python
import libsbml

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

# Add zero-order inflow for id_cczd
r_in_cczd = model.createReaction()
r_in_cczd.setId("inflow_cczd")
r_in_cczd.setReversible(False)
r_in_cczd.setFast(False)
prod_cczd = r_in_cczd.createProduct()
prod_cczd.setSpecies("id_cczd")
prod_cczd.setStoichiometry(1.0)
prod_cczd.setConstant(False)
param_in_cczd = model.createParameter()
param_in_cczd.setId("in_cczd")
param_in_cczd.setValue(0.1)
kinetic_law_in_cczd = r_in_cczd.createKineticLaw()
kinetic_law_in_cczd.setFormula("in_cczd")

# Add zero-order inflow for id_4bhu
r_in_4bhu = model.createReaction()
r_in_4bhu.setId("inflow_4bhu")
r_in_4bhu.setReversible(False)
r_in_4bhu.setFast(False)
prod_4bhu = r_in_4bhu.createProduct()
prod_4bhu.setSpecies("id_4bhu")
prod_4bhu.setStoichiometry(1.0)
prod_4bhu.setConstant(False)
param_in_4bhu = model.createParameter()
param_in_4bhu.setId("in_4bhu")
param_in_4bhu.setValue(0.1)
kinetic_law_in_4bhu = r_in_4bhu.createKineticLaw()
kinetic_law_in_4bhu.setFormula("in_4bhu")

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

# Simulate and compare to experiment 0
sim_result2 = simulate(updated_sbml2)
print(sim_result2.head(20))
shared_variables.add("updated_sbml_lv_inflow", updated_sbml2)
```
# Observation

## Code Stdout
     id_cczd   id_4bhu  id_v5j9  Time
0   1.000000  1.000000      0.0  0.00
1   0.995654  1.001145      0.0  0.01
2   0.991333  1.002299      0.0  0.02
3   0.987036  1.003462      0.0  0.03
4   0.982766  1.004634      0.0  0.04
5   0.978520  1.005815      0.0  0.05
6   0.974299  1.007005      0.0  0.06
7   0.970103  1.008205      0.0  0.07
8   0.965932  1.009413      0.0  0.08
9   0.961785  1.010630      0.0  0.09
10  0.957664  1.011856      0.0  0.10
11  0.953566  1.013092      0.0  0.11
12  0.949492  1.014336      0.0  0.12
13  0.945443  1.015589      0.0  0.13
14  0.941418  1.016850      0.0  0.14
15  0.937416  1.018121      0.0  0.15
16  0.933439  1.019400      0.0  0.16
17  0.929484  1.020688      0.0  0.17
18  0.925554  1.021985      0.0  0.18
19  0.921647  1.023291      0.0  0.19

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

### 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

Adding zero-order inflow terms for both species results in only a slight increase in the concentrations over time, and still does not reproduce the strong oscillations and net amplification seen in the experimental data. The simulated system remains relatively stable, with no large oscillations or rapid growth.

This suggests that the missing mechanism is not simply a constant inflow, but likely involves nonlinear autocatalytic or cross-catalytic reactions, as seen in the Brusselator or other chemical oscillators. In such models, a key feature is a nonlinear production term (e.g., quadratic or cubic in one or both species).

Given the strong positive correlation between d(id_cczd)/dt and id_4bhu^2, and the net amplification, a plausible next step is to add a quadratic autocatalytic production term for `id_cczd` (e.g., `2 id_4bhu → id_4bhu + id_cczd`) and/or for `id_4bhu`.

I will modify the model to include a quadratic autocatalytic production of `id_cczd` from `id_4bhu` and see if this can reproduce the observed oscillations and amplification.

## Action

### Code
```python
import libsbml

# Start from the original model to avoid reaction duplication
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Parameters (use previous fit for Lotka-Volterra, and guess for new term)
a = 0.222  # prey growth
b = 0.208  # predation
c = 0.744  # predator death
k = 0.5    # quadratic autocatalytic production (guess)

# Reaction 1: id_4bhu -> 2 id_4bhu (prey growth)
r1 = model.createReaction()
r1.setId("prey_growth")
r1.setReversible(False)
r1.setFast(False)
reactant = r1.createReactant()
reactant.setSpecies("id_4bhu")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = r1.createProduct()
product.setSpecies("id_4bhu")
product.setStoichiometry(2.0)
product.setConstant(False)
kinetic_law1 = r1.createKineticLaw()
param_a = model.createParameter()
param_a.setId("a")
param_a.setValue(a)
kinetic_law1.setFormula("a * id_4bhu")

# Reaction 2: id_cczd + id_4bhu -> 2 id_cczd (predation)
r2 = model.createReaction()
r2.setId("predation")
r2.setReversible(False)
r2.setFast(False)
reactant1 = r2.createReactant()
reactant1.setSpecies("id_cczd")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_4bhu")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_cczd")
product2.setStoichiometry(2.0)
product2.setConstant(False)
param_b = model.createParameter()
param_b.setId("b")
param_b.setValue(b)
kinetic_law2 = r2.createKineticLaw()
kinetic_law2.setFormula("b * id_cczd * id_4bhu")

# Reaction 3: id_cczd -> (decay)
r3 = model.createReaction()
r3.setId("predator_death")
r3.setReversible(False)
r3.setFast(False)
reactant3 = r3.createReactant()
reactant3.setSpecies("id_cczd")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(False)
param_c = model.createParameter()
param_c.setId("c")
param_c.setValue(c)
kinetic_law3 = r3.createKineticLaw()
kinetic_law3.setFormula("c * id_cczd")

# Reaction 4: 2 id_4bhu -> id_4bhu + id_cczd (quadratic autocatalysis)
r4 = model.createReaction()
r4.setId("quad_autocat")
r4.setReversible(False)
r4.setFast(False)
reactant4a = r4.createReactant()
reactant4a.setSpecies("id_4bhu")
reactant4a.setStoichiometry(2.0)
reactant4a.setConstant(False)
product4a = r4.createProduct()
product4a.setSpecies("id_4bhu")
product4a.setStoichiometry(1.0)
product4a.setConstant(False)
product4b = r4.createProduct()
product4b.setSpecies("id_cczd")
product4b.setStoichiometry(1.0)
product4b.setConstant(False)
param_k = model.createParameter()
param_k.setId("k")
param_k.setValue(k)
kinetic_law4 = r4.createKineticLaw()
kinetic_law4.setFormula("k * id_4bhu^2")

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

# Simulate and compare to experiment 0
sim_result3 = simulate(updated_sbml3)
print(sim_result3.head(20))
shared_variables.add("updated_sbml_quad", updated_sbml3)
```
# Observation

## Code Stdout
     id_cczd   id_4bhu  id_v5j9  Time
0   1.000000  1.000000      0.0  0.00
1   0.999611  0.995165      0.0  0.01
2   0.999167  0.990377      0.0  0.02
3   0.998669  0.985637      0.0  0.03
4   0.998118  0.980943      0.0  0.04
5   0.997514  0.976296      0.0  0.05
6   0.996859  0.971694      0.0  0.06
7   0.996154  0.967138      0.0  0.07
8   0.995399  0.962626      0.0  0.08
9   0.994596  0.958159      0.0  0.09
10  0.993746  0.953735      0.0  0.10
11  0.992849  0.949354      0.0  0.11
12  0.991906  0.945016      0.0  0.12
13  0.990919  0.940720      0.0  0.13
14  0.989889  0.936466      0.0  0.14
15  0.988816  0.932252      0.0  0.15
16  0.987701  0.928079      0.0  0.16
17  0.986545  0.923946      0.0  0.17
18  0.985350  0.919853      0.0  0.18
19  0.984115  0.915798      0.0  0.19

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

### 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 addition of a quadratic autocatalytic production term for `id_cczd` from `id_4bhu` still does not reproduce the strong oscillations and net amplification seen in the experimental data. Both species decrease over time, which is inconsistent with the experimental results.

This suggests that the system may require both nonlinear autocatalytic production and a nonlinear production term for `id_4bhu` (as in the Brusselator model), or that the cross-catalytic terms need to be adjusted. The Brusselator model, which is known for producing oscillations and amplification, includes:
- A constant inflow for `id_4bhu`
- A linear conversion of `id_4bhu` to `id_cczd`
- A nonlinear autocatalytic production of `id_4bhu` from both species
- A linear outflow for `id_cczd`

Given the symmetry and oscillatory behavior, I will try implementing a Brusselator-like model:
1. Inflow: ∅ → `id_4bhu`
2. Linear conversion: `id_4bhu` → `id_cczd`
3. Nonlinear autocatalysis: 2 `id_4bhu` + `id_cczd` → 3 `id_4bhu`
4. Outflow: `id_cczd` → ∅

I will use reasonable parameter guesses and simulate the model to see if it matches the experimental data.

## Action

### Code
```python
import libsbml

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

# Parameters for Brusselator-like model
A = 1.0  # inflow rate for id_4bhu
B = 2.5  # conversion rate id_4bhu -> id_cczd
C = 1.0  # nonlinear autocatalysis
D = 1.0  # outflow rate for id_cczd

# Reaction 1: inflow ∅ -> id_4bhu
r1 = model.createReaction()
r1.setId("inflow_4bhu")
r1.setReversible(False)
r1.setFast(False)
prod1 = r1.createProduct()
prod1.setSpecies("id_4bhu")
prod1.setStoichiometry(1.0)
prod1.setConstant(False)
param_A = model.createParameter()
param_A.setId("A")
param_A.setValue(A)
kinetic_law1 = r1.createKineticLaw()
kinetic_law1.setFormula("A")

# Reaction 2: id_4bhu -> id_cczd
r2 = model.createReaction()
r2.setId("bhu_to_cczd")
r2.setReversible(False)
r2.setFast(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_4bhu")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_cczd")
product2.setStoichiometry(1.0)
product2.setConstant(False)
param_B = model.createParameter()
param_B.setId("B")
param_B.setValue(B)
kinetic_law2 = r2.createKineticLaw()
kinetic_law2.setFormula("B * id_4bhu")

# Reaction 3: 2 id_4bhu + id_cczd -> 3 id_4bhu (nonlinear autocatalysis)
r3 = model.createReaction()
r3.setId("autocat_4bhu")
r3.setReversible(False)
r3.setFast(False)
reactant3a = r3.createReactant()
reactant3a.setSpecies("id_4bhu")
reactant3a.setStoichiometry(2.0)
reactant3a.setConstant(False)
reactant3b = r3.createReactant()
reactant3b.setSpecies("id_cczd")
reactant3b.setStoichiometry(1.0)
reactant3b.setConstant(False)
product3 = r3.createProduct()
product3.setSpecies("id_4bhu")
product3.setStoichiometry(3.0)
product3.setConstant(False)
param_C = model.createParameter()
param_C.setId("C")
param_C.setValue(C)
kinetic_law3 = r3.createKineticLaw()
kinetic_law3.setFormula("C * id_4bhu^2 * id_cczd")

# Reaction 4: id_cczd -> ∅ (outflow)
r4 = model.createReaction()
r4.setId("outflow_cczd")
r4.setReversible(False)
r4.setFast(False)
reactant4 = r4.createReactant()
reactant4.setSpecies("id_cczd")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(False)
param_D = model.createParameter()
param_D.setId("D")
param_D.setValue(D)
kinetic_law4 = r4.createKineticLaw()
kinetic_law4.setFormula("D * id_cczd")

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

# Simulate and compare to experiment 0
sim_result_bru = simulate(updated_sbml_bru)
print(sim_result_bru.head(20))
shared_variables.add("updated_sbml_bru", updated_sbml_bru)
```
# Observation

## Code Stdout
     id_cczd   id_4bhu  id_v5j9  Time
0   1.000000  1.000000      0.0  0.00
1   1.004937  0.995038      0.0  0.01
2   1.009754  0.990147      0.0  0.02
3   1.014453  0.985328      0.0  0.03
4   1.019037  0.980577      0.0  0.04
5   1.023508  0.975893      0.0  0.05
6   1.027870  0.971275      0.0  0.06
7   1.032124  0.966721      0.0  0.07
8   1.036274  0.962229      0.0  0.08
9   1.040322  0.957798      0.0  0.09
10  1.044271  0.953426      0.0  0.10
11  1.048123  0.949112      0.0  0.11
12  1.051881  0.944854      0.0  0.12
13  1.055546  0.940651      0.0  0.13
14  1.059122  0.936501      0.0  0.14
15  1.062611  0.932404      0.0  0.15
16  1.066014  0.928357      0.0  0.16
17  1.069334  0.924361      0.0  0.17
18  1.072572  0.920413      0.0  0.18
19  1.075730  0.916513      0.0  0.19

## 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)
- `shared_variables`: all variables you have saved from the previous iterations. (updated_sbml_lv, updated_sbml_lv_inflow, updated_sbml_quad, updated_sbml_bru)

### 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 Brusselator-like model with the chosen parameters still does not reproduce the strong oscillations and net amplification seen in the experimental data. Both species change only slightly in the first 0.2 time units, and there is no sign of the rapid growth or oscillatory behavior observed experimentally.

This suggests that the parameter values may need to be tuned, or that the model structure still needs adjustment. In the classic Brusselator, oscillations occur only for certain parameter regimes (e.g., when the inflow rate is sufficiently high relative to the other rates).

Given that the experimental data shows rapid amplification and oscillations, I should try increasing the inflow rate (`A`) and the nonlinear autocatalytic rate (`C`) to see if this produces the desired behavior.

## Action

### Code
```python
import libsbml

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

# Try higher inflow and autocatalytic rates
A = 2.0  # inflow rate for id_4bhu
B = 2.5  # conversion rate id_4bhu -> id_cczd
C = 3.0  # nonlinear autocatalysis (increased)
D = 1.0  # outflow rate for id_cczd

# Reaction 1: inflow ∅ -> id_4bhu
r1 = model.createReaction()
r1.setId("inflow_4bhu")
r1.setReversible(False)
r1.setFast(False)
prod1 = r1.createProduct()
prod1.setSpecies("id_4bhu")
prod1.setStoichiometry(1.0)
prod1.setConstant(False)
param_A = model.createParameter()
param_A.setId("A")
param_A.setValue(A)
kinetic_law1 = r1.createKineticLaw()
kinetic_law1.setFormula("A")

# Reaction 2: id_4bhu -> id_cczd
r2 = model.createReaction()
r2.setId("bhu_to_cczd")
r2.setReversible(False)
r2.setFast(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_4bhu")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_cczd")
product2.setStoichiometry(1.0)
product2.setConstant(False)
param_B = model.createParameter()
param_B.setId("B")
param_B.setValue(B)
kinetic_law2 = r2.createKineticLaw()
kinetic_law2.setFormula("B * id_4bhu")

# Reaction 3: 2 id_4bhu + id_cczd -> 3 id_4bhu (nonlinear autocatalysis)
r3 = model.createReaction()
r3.setId("autocat_4bhu")
r3.setReversible(False)
r3.setFast(False)
reactant3a = r3.createReactant()
reactant3a.setSpecies("id_4bhu")
reactant3a.setStoichiometry(2.0)
reactant3a.setConstant(False)
reactant3b = r3.createReactant()
reactant3b.setSpecies("id_cczd")
reactant3b.setStoichiometry(1.0)
reactant3b.setConstant(False)
product3 = r3.createProduct()
product3.setSpecies("id_4bhu")
product3.setStoichiometry(3.0)
product3.setConstant(False)
param_C = model.createParameter()
param_C.setId("C")
param_C.setValue(C)
kinetic_law3 = r3.createKineticLaw()
kinetic_law3.setFormula("C * id_4bhu^2 * id_cczd")

# Reaction 4: id_cczd -> ∅ (outflow)
r4 = model.createReaction()
r4.setId("outflow_cczd")
r4.setReversible(False)
r4.setFast(False)
reactant4 = r4.createReactant()
reactant4.setSpecies("id_cczd")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(False)
param_D = model.createParameter()
param_D.setId("D")
param_D.setValue(D)
kinetic_law4 = r4.createKineticLaw()
kinetic_law4.setFormula("D * id_cczd")

# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml_bru2 = writer.writeSBMLToString(sbml_doc)

# Simulate and compare to experiment 0
sim_result_bru2 = simulate(updated_sbml_bru2)
print(sim_result_bru2.head(20))
shared_variables.add("updated_sbml_bru2", updated_sbml_bru2)
```
# Observation

## Code Stdout
     id_cczd   id_4bhu  id_v5j9  Time
0   1.000000  1.000000      0.0  0.00
1   0.984862  1.025214      0.0  0.01
2   0.969456  1.050849      0.0  0.02
3   0.953788  1.076901      0.0  0.03
4   0.937865  1.103366      0.0  0.04
5   0.921699  1.130234      0.0  0.05
6   0.905305  1.157493      0.0  0.06
7   0.888699  1.185128      0.0  0.07
8   0.871903  1.213122      0.0  0.08
9   0.854937  1.241453      0.0  0.09
10  0.837828  1.270098      0.0  0.10
11  0.820605  1.299029      0.0  0.11
12  0.803295  1.328219      0.0  0.12
13  0.785934  1.357634      0.0  0.13
14  0.768555  1.387240      0.0  0.14
15  0.751195  1.417001      0.0  0.15
16  0.733894  1.446877      0.0  0.16
17  0.716691  1.476827      0.0  0.17
18  0.699627  1.506809      0.0  0.18
19  0.682743  1.536782      0.0  0.19

## 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)
- `shared_variables`: all variables you have saved from the previous iterations. (updated_sbml_lv, updated_sbml_lv_inflow, updated_sbml_quad, updated_sbml_bru, updated_sbml_bru2)

### 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

With the increased inflow (`A=2.0`) and nonlinear autocatalytic rate (`C=3.0`), the simulation now shows a rapid increase in `id_4bhu` and a decrease in `id_cczd` at first, which is more in line with the net amplification seen in the experimental data. However, the simulation still does not show the strong oscillations observed experimentally; instead, `id_4bhu` grows steadily while `id_cczd` decreases.

In the classic Brusselator, oscillations occur only for certain parameter regimes, typically when the inflow rate is high and the conversion/outflow rates are balanced. The lack of oscillations suggests that further parameter tuning is needed, or that the model structure needs a slight adjustment.

Given the experimental data shows both species oscillating and amplifying, I will:
- Further increase the inflow rate (`A`) and the nonlinear autocatalytic rate (`C`).
- Slightly decrease the outflow rate (`D`) to allow for more amplification.
- Increase the conversion rate (`B`) to see if this helps induce oscillations.

## Action

### Code
```python
import libsbml

# Start from the original model for a clean slate
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Try even higher inflow and autocatalytic rates, and adjust other parameters
A = 3.0  # inflow rate for id_4bhu
B = 4.0  # conversion rate id_4bhu -> id_cczd
C = 5.0  # nonlinear autocatalysis
D = 0.5  # outflow rate for id_cczd (reduced)

# Reaction 1: inflow ∅ -> id_4bhu
r1 = model.createReaction()
r1.setId("inflow_4bhu")
r1.setReversible(False)
r1.setFast(False)
prod1 = r1.createProduct()
prod1.setSpecies("id_4bhu")
prod1.setStoichiometry(1.0)
prod1.setConstant(False)
param_A = model.createParameter()
param_A.setId("A")
param_A.setValue(A)
kinetic_law1 = r1.createKineticLaw()
kinetic_law1.setFormula("A")

# Reaction 2: id_4bhu -> id_cczd
r2 = model.createReaction()
r2.setId("bhu_to_cczd")
r2.setReversible(False)
r2.setFast(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_4bhu")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_cczd")
product2.setStoichiometry(1.0)
product2.setConstant(False)
param_B = model.createParameter()
param_B.setId("B")
param_B.setValue(B)
kinetic_law2 = r2.createKineticLaw()
kinetic_law2.setFormula("B * id_4bhu")

# Reaction 3: 2 id_4bhu + id_cczd -> 3 id_4bhu (nonlinear autocatalysis)
r3 = model.createReaction()
r3.setId("autocat_4bhu")
r3.setReversible(False)
r3.setFast(False)
reactant3a = r3.createReactant()
reactant3a.setSpecies("id_4bhu")
reactant3a.setStoichiometry(2.0)
reactant3a.setConstant(False)
reactant3b = r3.createReactant()
reactant3b.setSpecies("id_cczd")
reactant3b.setStoichiometry(1.0)
reactant3b.setConstant(False)
product3 = r3.createProduct()
product3.setSpecies("id_4bhu")
product3.setStoichiometry(3.0)
product3.setConstant(False)
param_C = model.createParameter()
param_C.setId("C")
param_C.setValue(C)
kinetic_law3 = r3.createKineticLaw()
kinetic_law3.setFormula("C * id_4bhu^2 * id_cczd")

# Reaction 4: id_cczd -> ∅ (outflow)
r4 = model.createReaction()
r4.setId("outflow_cczd")
r4.setReversible(False)
r4.setFast(False)
reactant4 = r4.createReactant()
reactant4.setSpecies("id_cczd")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(False)
param_D = model.createParameter()
param_D.setId("D")
param_D.setValue(D)
kinetic_law4 = r4.createKineticLaw()
kinetic_law4.setFormula("D * id_cczd")

# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml_bru3 = writer.writeSBMLToString(sbml_doc)

# Simulate and compare to experiment 0
sim_result_bru3 = simulate(updated_sbml_bru3)
print(sim_result_bru3.head(20))
shared_variables.add("updated_sbml_bru3", updated_sbml_bru3)
```
# Observation

## Code Stdout
     id_cczd   id_4bhu  id_v5j9  Time
0   1.000000  1.000000      0.0  0.00
1   0.984203  1.040836      0.0  0.01
2   0.966788  1.083372      0.0  0.02
3   0.947728  1.127646      0.0  0.03
4   0.927015  1.173671      0.0  0.04
5   0.904669  1.221437      0.0  0.05
6   0.880741  1.270902      0.0  0.06
7   0.855316  1.321986      0.0  0.07
8   0.828520  1.374572      0.0  0.08
9   0.800518  1.428500      0.0  0.09
10  0.771519  1.483569      0.0  0.10
11  0.741769  1.539536      0.0  0.11
12  0.711550  1.596121      0.0  0.12
13  0.681172  1.653017      0.0  0.13
14  0.650959  1.709900      0.0  0.14
15  0.621236  1.766443      0.0  0.15
16  0.592316  1.822330      0.0  0.16
17  0.564485  1.877268      0.0  0.17
18  0.537993  1.931005      0.0  0.18
19  0.513036  1.983335      0.0  0.19

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_3, iteration_4)
- `shared_variables`: all variables you have saved from the previous iterations. (updated_sbml_lv, updated_sbml_lv_inflow, updated_sbml_quad, updated_sbml_bru, updated_sbml_bru2, updated_sbml_bru3)

### 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

With the latest parameter set, the simulation shows a much more rapid increase in `id_4bhu` and a decrease in `id_cczd`, which is closer to the net amplification seen in the experimental data. However, there are still no clear oscillations in the first 0.2 time units. In the experimental data, oscillations are visible over a longer time frame, so it is possible that oscillations may emerge later in the simulation.

To check for oscillations and compare the simulated dynamics to the experimental data, I should examine the full time course (not just the first 20 time points) and plot or analyze the trajectories for both species.

## Action

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

# Retrieve the latest simulation result and the experimental data
sim_result = simulate(shared_variables.access("updated_sbml_bru3"))
exp_result = experiment_history['iteration_0']

# Print summary statistics and a few rows from the end to check for oscillations/amplification
print("Simulated (end):\n", sim_result.tail(20))
print("Experimental (end):\n", exp_result.tail(20))

# Calculate and print the min/max for both species in the simulation
print("Simulated id_cczd min/max:", sim_result['id_cczd'].min(), sim_result['id_cczd'].max())
print("Simulated id_4bhu min/max:", sim_result['id_4bhu'].min(), sim_result['id_4bhu'].max())
```
# Observation

## Code Stdout
Simulated (end):
        id_cczd    id_4bhu  id_v5j9   Time
981   0.025828  30.972110      0.0   9.81
982   0.025803  31.002006      0.0   9.82
983   0.025778  31.031901      0.0   9.83
984   0.025753  31.061797      0.0   9.84
985   0.025728  31.091693      0.0   9.85
986   0.025703  31.121590      0.0   9.86
987   0.025679  31.151486      0.0   9.87
988   0.025654  31.181382      0.0   9.88
989   0.025630  31.211278      0.0   9.89
990   0.025605  31.241175      0.0   9.90
991   0.025581  31.271071      0.0   9.91
992   0.025556  31.300968      0.0   9.92
993   0.025532  31.330865      0.0   9.93
994   0.025507  31.360761      0.0   9.94
995   0.025483  31.390658      0.0   9.95
996   0.025459  31.420555      0.0   9.96
997   0.025435  31.450452      0.0   9.97
998   0.025411  31.480349      0.0   9.98
999   0.025386  31.510246      0.0   9.99
1000  0.025362  31.540143      0.0  10.00
Experimental (end):
        id_cczd   id_4bhu  id_v5j9   Time
981   2.181623  2.061247      0.0   9.81
982   2.186195  2.059275      0.0   9.82
983   2.190756  2.057306      0.0   9.83
984   2.195305  2.055337      0.0   9.84
985   2.199843  2.053371      0.0   9.85
986   2.204369  2.051406      0.0   9.86
987   2.208885  2.049442      0.0   9.87
988   2.213389  2.047481      0.0   9.88
989   2.217882  2.045521      0.0   9.89
990   2.222364  2.043562      0.0   9.90
991   2.226835  2.041605      0.0   9.91
992   2.231295  2.039650      0.0   9.92
993   2.235743  2.037696      0.0   9.93
994   2.240180  2.035744      0.0   9.94
995   2.244605  2.033794      0.0   9.95
996   2.249020  2.031845      0.0   9.96
997   2.253423  2.029897      0.0   9.97
998   2.257815  2.027952      0.0   9.98
999   2.262196  2.026008      0.0   9.99
1000  2.266566  2.024065      0.0  10.00
Simulated id_cczd min/max: 0.025362419749047495 1.0
Simulated id_4bhu min/max: 1.0 31.540143402285562

## 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)
- `shared_variables`: all variables you have saved from the previous iterations. (updated_sbml_lv, updated_sbml_lv_inflow, updated_sbml_quad, updated_sbml_bru, updated_sbml_bru2, updated_sbml_bru3)

### 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 simulation with the latest Brusselator-like model and high parameter values produces rapid, monotonic amplification of `id_4bhu` and depletion of `id_cczd`, but still does not reproduce the oscillatory behavior seen in the experimental data. In the experiment, both `id_cczd` and `id_4bhu` oscillate and amplify together, while in the simulation, `id_4bhu` grows unchecked and `id_cczd` is depleted.

Key differences:
- The experimental system shows both species increasing and oscillating, with their sum increasing over time.
- The simulated system shows one species (`id_4bhu`) dominating and the other (`id_cczd`) being depleted.

This suggests that the model is missing a mechanism that allows both species to be produced and to oscillate together. The Lotka-Volterra and Brusselator models are not sufficient. Given the strong positive correlation between d(id_cczd)/dt and id_4bhu^2, and the fact that both species can be produced from zero, a symmetric autocatalytic model may be more appropriate.

Hypothesis: Both species are produced autocatalytically from each other, e.g.:
- `2 id_4bhu → id_4bhu + id_cczd`
- `2 id_cczd → id_cczd + id_4bhu`
- Plus possible linear decay terms for both.

This would allow both species to amplify and oscillate together. I will implement this symmetric autocatalytic model and simulate it.

## Action

### Code
```python
import libsbml

# Start from the original model for a clean slate
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Parameters for symmetric autocatalysis
k1 = 1.0  # 2 id_4bhu -> id_4bhu + id_cczd
k2 = 1.0  # 2 id_cczd -> id_cczd + id_4bhu
d1 = 0.1  # id_4bhu decay
d2 = 0.1  # id_cczd decay

# Reaction 1: 2 id_4bhu -> id_4bhu + id_cczd
r1 = model.createReaction()
r1.setId("bhu_to_cczd_autocat")
r1.setReversible(False)
r1.setFast(False)
reactant1 = r1.createReactant()
reactant1.setSpecies("id_4bhu")
reactant1.setStoichiometry(2.0)
reactant1.setConstant(False)
product1a = r1.createProduct()
product1a.setSpecies("id_4bhu")
product1a.setStoichiometry(1.0)
product1a.setConstant(False)
product1b = r1.createProduct()
product1b.setSpecies("id_cczd")
product1b.setStoichiometry(1.0)
product1b.setConstant(False)
param_k1 = model.createParameter()
param_k1.setId("k1")
param_k1.setValue(k1)
kinetic_law1 = r1.createKineticLaw()
kinetic_law1.setFormula("k1 * id_4bhu^2")

# Reaction 2: 2 id_cczd -> id_cczd + id_4bhu
r2 = model.createReaction()
r2.setId("cczd_to_bhu_autocat")
r2.setReversible(False)
r2.setFast(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_cczd")
reactant2.setStoichiometry(2.0)
reactant2.setConstant(False)
product2a = r2.createProduct()
product2a.setSpecies("id_cczd")
product2a.setStoichiometry(1.0)
product2a.setConstant(False)
product2b = r2.createProduct()
product2b.setSpecies("id_4bhu")
product2b.setStoichiometry(1.0)
product2b.setConstant(False)
param_k2 = model.createParameter()
param_k2.setId("k2")
param_k2.setValue(k2)
kinetic_law2 = r2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_cczd^2")

# Reaction 3: id_4bhu -> ∅ (decay)
r3 = model.createReaction()
r3.setId("bhu_decay")
r3.setReversible(False)
r3.setFast(False)
reactant3 = r3.createReactant()
reactant3.setSpecies("id_4bhu")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(False)
param_d1 = model.createParameter()
param_d1.setId("d1")
param_d1.setValue(d1)
kinetic_law3 = r3.createKineticLaw()
kinetic_law3.setFormula("d1 * id_4bhu")

# Reaction 4: id_cczd -> ∅ (decay)
r4 = model.createReaction()
r4.setId("cczd_decay")
r4.setReversible(False)
r4.setFast(False)
reactant4 = r4.createReactant()
reactant4.setSpecies("id_cczd")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(False)
param_d2 = model.createParameter()
param_d2.setId("d2")
param_d2.setValue(d2)
kinetic_law4 = r4.createKineticLaw()
kinetic_law4.setFormula("d2 * id_cczd")

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

# Simulate and compare to experiment 0
sim_result_symm = simulate(updated_sbml_symm)
print(sim_result_symm.head(20))
shared_variables.add("updated_sbml_symm", updated_sbml_symm)
```
# Observation

## Code Stdout
     id_cczd   id_4bhu  id_v5j9  Time
0   1.000000  1.000000      0.0  0.00
1   0.999001  0.999001      0.0  0.01
2   0.998002  0.998002      0.0  0.02
3   0.997005  0.997005      0.0  0.03
4   0.996009  0.996009      0.0  0.04
5   0.995013  0.995013      0.0  0.05
6   0.994019  0.994019      0.0  0.06
7   0.993025  0.993025      0.0  0.07
8   0.992033  0.992033      0.0  0.08
9   0.991041  0.991041      0.0  0.09
10  0.990050  0.990050      0.0  0.10
11  0.989061  0.989061      0.0  0.11
12  0.988072  0.988072      0.0  0.12
13  0.987085  0.987085      0.0  0.13
14  0.986098  0.986098      0.0  0.14
15  0.985113  0.985113      0.0  0.15
16  0.984128  0.984128      0.0  0.16
17  0.983144  0.983144      0.0  0.17
18  0.982162  0.982162      0.0  0.18
19  0.981180  0.981180      0.0  0.19

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_3, iteration_4)
- `shared_variables`: all variables you have saved from the previous iterations. (updated_sbml_lv, updated_sbml_lv_inflow, updated_sbml_quad, updated_sbml_bru, updated_sbml_bru2, updated_sbml_bru3, updated_sbml_symm)

### 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 symmetric autocatalytic model with quadratic production and linear decay for both species results in both `id_cczd` and `id_4bhu` decreasing together, with no oscillations or amplification. This is inconsistent with the experimental data, where both species oscillate and amplify over time.

Key observations:
- The experimental system shows both species increasing and oscillating, with their sum increasing over time.
- All tested models so far (Lotka-Volterra, Brusselator, symmetric autocatalysis) fail to reproduce both the oscillations and the net amplification.
- The experimental data suggests a mechanism where both species can be produced from each other, and there is a net source of mass.

A possible missing element is a constant inflow for both species, in addition to the autocatalytic terms. This would allow for net amplification and, with the right balance, could produce oscillations.

I will add constant inflow terms for both species to the symmetric autocatalytic model and simulate the result.

## Action

### Code
```python
import libsbml

# Start from the original model for a clean slate
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Parameters for symmetric autocatalysis with inflow
k1 = 1.0  # 2 id_4bhu -> id_4bhu + id_cczd
k2 = 1.0  # 2 id_cczd -> id_cczd + id_4bhu
d1 = 0.1  # id_4bhu decay
d2 = 0.1  # id_cczd decay
in1 = 0.2 # inflow id_4bhu
in2 = 0.2 # inflow id_cczd

# Reaction 1: 2 id_4bhu -> id_4bhu + id_cczd
r1 = model.createReaction()
r1.setId("bhu_to_cczd_autocat")
r1.setReversible(False)
r1.setFast(False)
reactant1 = r1.createReactant()
reactant1.setSpecies("id_4bhu")
reactant1.setStoichiometry(2.0)
reactant1.setConstant(False)
product1a = r1.createProduct()
product1a.setSpecies("id_4bhu")
product1a.setStoichiometry(1.0)
product1a.setConstant(False)
product1b = r1.createProduct()
product1b.setSpecies("id_cczd")
product1b.setStoichiometry(1.0)
product1b.setConstant(False)
param_k1 = model.createParameter()
param_k1.setId("k1")
param_k1.setValue(k1)
kinetic_law1 = r1.createKineticLaw()
kinetic_law1.setFormula("k1 * id_4bhu^2")

# Reaction 2: 2 id_cczd -> id_cczd + id_4bhu
r2 = model.createReaction()
r2.setId("cczd_to_bhu_autocat")
r2.setReversible(False)
r2.setFast(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_cczd")
reactant2.setStoichiometry(2.0)
reactant2.setConstant(False)
product2a = r2.createProduct()
product2a.setSpecies("id_cczd")
product2a.setStoichiometry(1.0)
product2a.setConstant(False)
product2b = r2.createProduct()
product2b.setSpecies("id_4bhu")
product2b.setStoichiometry(1.0)
product2b.setConstant(False)
param_k2 = model.createParameter()
param_k2.setId("k2")
param_k2.setValue(k2)
kinetic_law2 = r2.createKineticLaw()
kinetic_law2.setFormula("k2 * id_cczd^2")

# Reaction 3: id_4bhu -> ∅ (decay)
r3 = model.createReaction()
r3.setId("bhu_decay")
r3.setReversible(False)
r3.setFast(False)
reactant3 = r3.createReactant()
reactant3.setSpecies("id_4bhu")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(False)
param_d1 = model.createParameter()
param_d1.setId("d1")
param_d1.setValue(d1)
kinetic_law3 = r3.createKineticLaw()
kinetic_law3.setFormula("d1 * id_4bhu")

# Reaction 4: id_cczd -> ∅ (decay)
r4 = model.createReaction()
r4.setId("cczd_decay")
r4.setReversible(False)
r4.setFast(False)
reactant4 = r4.createReactant()
reactant4.setSpecies("id_cczd")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(False)
param_d2 = model.createParameter()
param_d2.setId("d2")
param_d2.setValue(d2)
kinetic_law4 = r4.createKineticLaw()
kinetic_law4.setFormula("d2 * id_cczd")

# Reaction 5: inflow ∅ -> id_4bhu
r5 = model.createReaction()
r5.setId("inflow_bhu")
r5.setReversible(False)
r5.setFast(False)
prod5 = r5.createProduct()
prod5.setSpecies("id_4bhu")
prod5.setStoichiometry(1.0)
prod5.setConstant(False)
param_in1 = model.createParameter()
param_in1.setId("in1")
param_in1.setValue(in1)
kinetic_law5 = r5.createKineticLaw()
kinetic_law5.setFormula("in1")

# Reaction 6: inflow ∅ -> id_cczd
r6 = model.createReaction()
r6.setId("inflow_cczd")
r6.setReversible(False)
r6.setFast(False)
prod6 = r6.createProduct()
prod6.setSpecies("id_cczd")
prod6.setStoichiometry(1.0)
prod6.setConstant(False)
param_in2 = model.createParameter()
param_in2.setId("in2")
param_in2.setValue(in2)
kinetic_law6 = r6.createKineticLaw()
kinetic_law6.setFormula("in2")

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

# Simulate and compare to experiment 0
sim_result_symm_inflow = simulate(updated_sbml_symm_inflow)
print(sim_result_symm_inflow.head(20))
shared_variables.add("updated_sbml_symm_inflow", updated_sbml_symm_inflow)
```
# Observation

## Code Stdout
     id_cczd   id_4bhu  id_v5j9  Time
0   1.000000  1.000000      0.0  0.00
1   1.000999  1.000999      0.0  0.01
2   1.001998  1.001998      0.0  0.02
3   1.002995  1.002995      0.0  0.03
4   1.003991  1.003991      0.0  0.04
5   1.004987  1.004987      0.0  0.05
6   1.005981  1.005981      0.0  0.06
7   1.006975  1.006975      0.0  0.07
8   1.007967  1.007967      0.0  0.08
9   1.008959  1.008959      0.0  0.09
10  1.009950  1.009950      0.0  0.10
11  1.010939  1.010939      0.0  0.11
12  1.011928  1.011928      0.0  0.12
13  1.012915  1.012915      0.0  0.13
14  1.013902  1.013902      0.0  0.14
15  1.014887  1.014887      0.0  0.15
16  1.015872  1.015872      0.0  0.16
17  1.016856  1.016856      0.0  0.17
18  1.017838  1.017838      0.0  0.18
19  1.018820  1.018820      0.0  0.19

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_3, iteration_4)
- `shared_variables`: all variables you have saved from the previous iterations. (updated_sbml_lv, updated_sbml_lv_inflow, updated_sbml_quad, updated_sbml_bru, updated_sbml_bru2, updated_sbml_bru3, updated_sbml_symm, updated_sbml_symm_inflow)

### 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 constant inflow terms to the symmetric autocatalytic model results in both `id_cczd` and `id_4bhu` increasing together, but the increase is monotonic and linear, with no oscillations or amplification as seen in the experimental data. The model still does not capture the oscillatory dynamics.

The experimental data shows:
- Both species oscillate and amplify together.
- The sum of both species increases over time.
- The system is not symmetric: the oscillations are not perfectly in phase, and the rates of change are not identical.

Given the strong positive correlation between d(id_cczd)/dt and id_4bhu^2, and the negative correlation between d(id_4bhu)/dt and id_cczd, the system may be best described by a nonlinear cross-catalytic model, where:
- `id_4bhu` autocatalytically produces `id_cczd` (quadratic in `id_4bhu`)
- `id_cczd` linearly depletes `id_4bhu`
- Both species have inflow and outflow

This is similar to the Selkov model for glycolytic oscillations:
- inflow for `id_4bhu`
- `id_4bhu` → `id_cczd`
- `2 id_4bhu` + `id_cczd` → `3 id_4bhu`
- outflow for `id_cczd`

I will try a Selkov-like model with parameter tuning.

## Action

### Code
```python
import libsbml

# Start from the original model for a clean slate
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Selkov-like model parameters
A = 1.0   # inflow for id_4bhu
B = 2.0   # conversion id_4bhu -> id_cczd
C = 2.0   # autocatalytic production of id_4bhu
D = 0.5   # outflow for id_cczd

# Reaction 1: inflow ∅ -> id_4bhu
r1 = model.createReaction()
r1.setId("inflow_4bhu")
r1.setReversible(False)
r1.setFast(False)
prod1 = r1.createProduct()
prod1.setSpecies("id_4bhu")
prod1.setStoichiometry(1.0)
prod1.setConstant(False)
param_A = model.createParameter()
param_A.setId("A")
param_A.setValue(A)
kinetic_law1 = r1.createKineticLaw()
kinetic_law1.setFormula("A")

# Reaction 2: id_4bhu -> id_cczd
r2 = model.createReaction()
r2.setId("bhu_to_cczd")
r2.setReversible(False)
r2.setFast(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_4bhu")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_cczd")
product2.setStoichiometry(1.0)
product2.setConstant(False)
param_B = model.createParameter()
param_B.setId("B")
param_B.setValue(B)
kinetic_law2 = r2.createKineticLaw()
kinetic_law2.setFormula("B * id_4bhu")

# Reaction 3: 2 id_4bhu + id_cczd -> 3 id_4bhu (autocatalysis)
r3 = model.createReaction()
r3.setId("autocat_4bhu")
r3.setReversible(False)
r3.setFast(False)
reactant3a = r3.createReactant()
reactant3a.setSpecies("id_4bhu")
reactant3a.setStoichiometry(2.0)
reactant3a.setConstant(False)
reactant3b = r3.createReactant()
reactant3b.setSpecies("id_cczd")
reactant3b.setStoichiometry(1.0)
reactant3b.setConstant(False)
product3 = r3.createProduct()
product3.setSpecies("id_4bhu")
product3.setStoichiometry(3.0)
product3.setConstant(False)
param_C = model.createParameter()
param_C.setId("C")
param_C.setValue(C)
kinetic_law3 = r3.createKineticLaw()
kinetic_law3.setFormula("C * id_4bhu^2 * id_cczd")

# Reaction 4: id_cczd -> ∅ (outflow)
r4 = model.createReaction()
r4.setId("outflow_cczd")
r4.setReversible(False)
r4.setFast(False)
reactant4 = r4.createReactant()
reactant4.setSpecies("id_cczd")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(False)
param_D = model.createParameter()
param_D.setId("D")
param_D.setValue(D)
kinetic_law4 = r4.createKineticLaw()
kinetic_law4.setFormula("D * id_cczd")

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

# Simulate and compare to experiment 0
sim_result_selkov = simulate(updated_sbml_selkov)
print(sim_result_selkov.head(20))
shared_variables.add("updated_sbml_selkov", updated_sbml_selkov)
```
# Observation

## Code Stdout
     id_cczd   id_4bhu  id_v5j9  Time
0   1.000000  1.000000      0.0  0.00
1   0.994962  1.010051      0.0  0.01
2   0.989849  1.020202      0.0  0.02
3   0.984661  1.030453      0.0  0.03
4   0.979399  1.040806      0.0  0.04
5   0.974061  1.051260      0.0  0.05
6   0.968650  1.061815      0.0  0.06
7   0.963164  1.072471      0.0  0.07
8   0.957604  1.083229      0.0  0.08
9   0.951972  1.094087      0.0  0.09
10  0.946268  1.105046      0.0  0.10
11  0.940492  1.116105      0.0  0.11
12  0.934646  1.127264      0.0  0.12
13  0.928730  1.138521      0.0  0.13
14  0.922747  1.149876      0.0  0.14
15  0.916697  1.161327      0.0  0.15
16  0.910581  1.172875      0.0  0.16
17  0.904403  1.184516      0.0  0.17
18  0.898162  1.196250      0.0  0.18
19  0.891862  1.208075      0.0  0.19

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_3, iteration_4)
- `shared_variables`: all variables you have saved from the previous iterations. (updated_sbml_lv, updated_sbml_lv_inflow, updated_sbml_quad, updated_sbml_bru, updated_sbml_bru2, updated_sbml_bru3, updated_sbml_symm, updated_sbml_symm_inflow, updated_sbml_selkov)

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


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



# Iteration 17
## Thoughts

The Selkov-like model with the current parameters produces a slow, monotonic increase in `id_4bhu` and a decrease in `id_cczd`, with no oscillations or rapid amplification. This is still not matching the experimental data, which shows both species oscillating and amplifying together.

Oscillations in the Selkov model typically require a higher inflow rate and/or a higher nonlinear autocatalytic rate. The current parameter set may be too low to induce oscillations. I will increase the inflow (`A`) and the autocatalytic rate (`C`) to see if this produces the desired oscillatory and amplifying behavior.

## Action

### Code
```python
import libsbml

# Start from the original model for a clean slate
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Selkov-like model parameters (increased for oscillations)
A = 3.0   # inflow for id_4bhu
B = 2.0   # conversion id_4bhu -> id_cczd
C = 8.0   # autocatalytic production of id_4bhu (increased)
D = 0.5   # outflow for id_cczd

# Reaction 1: inflow ∅ -> id_4bhu
r1 = model.createReaction()
r1.setId("inflow_4bhu")
r1.setReversible(False)
r1.setFast(False)
prod1 = r1.createProduct()
prod1.setSpecies("id_4bhu")
prod1.setStoichiometry(1.0)
prod1.setConstant(False)
param_A = model.createParameter()
param_A.setId("A")
param_A.setValue(A)
kinetic_law1 = r1.createKineticLaw()
kinetic_law1.setFormula("A")

# Reaction 2: id_4bhu -> id_cczd
r2 = model.createReaction()
r2.setId("bhu_to_cczd")
r2.setReversible(False)
r2.setFast(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_4bhu")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_cczd")
product2.setStoichiometry(1.0)
product2.setConstant(False)
param_B = model.createParameter()
param_B.setId("B")
param_B.setValue(B)
kinetic_law2 = r2.createKineticLaw()
kinetic_law2.setFormula("B * id_4bhu")

# Reaction 3: 2 id_4bhu + id_cczd -> 3 id_4bhu (autocatalysis)
r3 = model.createReaction()
r3.setId("autocat_4bhu")
r3.setReversible(False)
r3.setFast(False)
reactant3a = r3.createReactant()
reactant3a.setSpecies("id_4bhu")
reactant3a.setStoichiometry(2.0)
reactant3a.setConstant(False)
reactant3b = r3.createReactant()
reactant3b.setSpecies("id_cczd")
reactant3b.setStoichiometry(1.0)
reactant3b.setConstant(False)
product3 = r3.createProduct()
product3.setSpecies("id_4bhu")
product3.setStoichiometry(3.0)
product3.setConstant(False)
param_C = model.createParameter()
param_C.setId("C")
param_C.setValue(C)
kinetic_law3 = r3.createKineticLaw()
kinetic_law3.setFormula("C * id_4bhu^2 * id_cczd")

# Reaction 4: id_cczd -> ∅ (outflow)
r4 = model.createReaction()
r4.setId("outflow_cczd")
r4.setReversible(False)
r4.setFast(False)
reactant4 = r4.createReactant()
reactant4.setSpecies("id_cczd")
reactant4.setStoichiometry(1.0)
reactant4.setConstant(False)
param_D = model.createParameter()
param_D.setId("D")
param_D.setValue(D)
kinetic_law4 = r4.createKineticLaw()
kinetic_law4.setFormula("D * id_cczd")

# Write the updated SBML
writer = libsbml.SBMLWriter()
updated_sbml_selkov2 = writer.writeSBMLToString(sbml_doc)

# Simulate and compare to experiment 0
sim_result_selkov2 = simulate(updated_sbml_selkov2)
print(sim_result_selkov2.head(20))
shared_variables.add("updated_sbml_selkov2", updated_sbml_selkov2)
```
# Observation

## Code Stdout
     id_cczd   id_4bhu  id_v5j9  Time
0   1.000000  1.000000      0.0  0.00
1   0.931509  1.093660      0.0  0.01
2   0.856407  1.194289      0.0  0.02
3   0.775758  1.300856      0.0  0.03
4   0.691384  1.411561      0.0  0.04
5   0.605856  1.523846      0.0  0.05
6   0.522255  1.634628      0.0  0.06
7   0.443758  1.740713      0.0  0.07
8   0.373089  1.839344      0.0  0.08
9   0.312075  1.928649      0.0  0.09
10  0.261442  2.007853      0.0  0.10
11  0.220892  2.077200      0.0  0.11
12  0.189394  2.137677      0.0  0.12
13  0.165524  2.190662      0.0  0.13
14  0.147772  2.237633      0.0  0.14
15  0.134730  2.279970      0.0  0.15
16  0.125204  2.318848      0.0  0.16
17  0.118234  2.355210      0.0  0.17
18  0.113084  2.389783      0.0  0.18
19  0.109208  2.423103      0.0  0.19

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_3, iteration_4)
- `shared_variables`: all variables you have saved from the previous iterations. (updated_sbml_lv, updated_sbml_lv_inflow, updated_sbml_quad, updated_sbml_bru, updated_sbml_bru2, updated_sbml_bru3, updated_sbml_symm, updated_sbml_symm_inflow, updated_sbml_selkov, updated_sbml_selkov2)

### 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

With the increased inflow and autocatalytic rates, the Selkov-like model now shows rapid amplification of `id_4bhu` and depletion of `id_cczd`, but still does not produce oscillations. Instead, `id_4bhu` grows unchecked while `id_cczd` is depleted, which is not consistent with the experimental data where both species oscillate and amplify together.

The experimental data suggests that both species are being produced and consumed in a way that allows for oscillations and net amplification. The closest match in the literature is the dual autocatalytic model with cross-catalysis and inflow for both species.

I will try a model with:
- Inflow for both species
- Cross-catalytic quadratic production: `id_4bhu` catalyzes `id_cczd` and vice versa
- Linear decay for both species

This should allow for both oscillations and amplification.

## Action

### Code
```python
import libsbml

# Start from the original model for a clean slate
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Parameters for cross-catalytic model
in1 = 1.0  # inflow id_4bhu
in2 = 1.0  # inflow id_cczd
k1 = 2.0   # id_4bhu^2 catalyzes id_cczd
k2 = 2.0   # id_cczd^2 catalyzes id_4bhu
d1 = 0.5   # id_4bhu decay
d2 = 0.5   # id_cczd decay

# Reaction 1: inflow ∅ -> id_4bhu
r1 = model.createReaction()
r1.setId("inflow_bhu")
r1.setReversible(False)
r1.setFast(False)
prod1 = r1.createProduct()
prod1.setSpecies("id_4bhu")
prod1.setStoichiometry(1.0)
prod1.setConstant(False)
param_in1 = model.createParameter()
param_in1.setId("in1")
param_in1.setValue(in1)
kinetic_law1 = r1.createKineticLaw()
kinetic_law1.setFormula("in1")

# Reaction 2: inflow ∅ -> id_cczd
r2 = model.createReaction()
r2.setId("inflow_cczd")
r2.setReversible(False)
r2.setFast(False)
prod2 = r2.createProduct()
prod2.setSpecies("id_cczd")
prod2.setStoichiometry(1.0)
prod2.setConstant(False)
param_in2 = model.createParameter()
param_in2.setId("in2")
param_in2.setValue(in2)
kinetic_law2 = r2.createKineticLaw()
kinetic_law2.setFormula("in2")

# Reaction 3: 2 id_4bhu -> id_4bhu + id_cczd (cross-catalysis)
r3 = model.createReaction()
r3.setId("bhu_to_cczd_crosscat")
r3.setReversible(False)
r3.setFast(False)
reactant3 = r3.createReactant()
reactant3.setSpecies("id_4bhu")
reactant3.setStoichiometry(2.0)
reactant3.setConstant(False)
product3a = r3.createProduct()
product3a.setSpecies("id_4bhu")
product3a.setStoichiometry(1.0)
product3a.setConstant(False)
product3b = r3.createProduct()
product3b.setSpecies("id_cczd")
product3b.setStoichiometry(1.0)
product3b.setConstant(False)
param_k1 = model.createParameter()
param_k1.setId("k1")
param_k1.setValue(k1)
kinetic_law3 = r3.createKineticLaw()
kinetic_law3.setFormula("k1 * id_4bhu^2")

# Reaction 4: 2 id_cczd -> id_cczd + id_4bhu (cross-catalysis)
r4 = model.createReaction()
r4.setId("cczd_to_bhu_crosscat")
r4.setReversible(False)
r4.setFast(False)
reactant4 = r4.createReactant()
reactant4.setSpecies("id_cczd")
reactant4.setStoichiometry(2.0)
reactant4.setConstant(False)
product4a = r4.createProduct()
product4a.setSpecies("id_cczd")
product4a.setStoichiometry(1.0)
product4a.setConstant(False)
product4b = r4.createProduct()
product4b.setSpecies("id_4bhu")
product4b.setStoichiometry(1.0)
product4b.setConstant(False)
param_k2 = model.createParameter()
param_k2.setId("k2")
param_k2.setValue(k2)
kinetic_law4 = r4.createKineticLaw()
kinetic_law4.setFormula("k2 * id_cczd^2")

# Reaction 5: id_4bhu -> ∅ (decay)
r5 = model.createReaction()
r5.setId("bhu_decay")
r5.setReversible(False)
r5.setFast(False)
reactant5 = r5.createReactant()
reactant5.setSpecies("id_4bhu")
reactant5.setStoichiometry(1.0)
reactant5.setConstant(False)
param_d1 = model.createParameter()
param_d1.setId("d1")
param_d1.setValue(d1)
kinetic_law5 = r5.createKineticLaw()
kinetic_law5.setFormula("d1 * id_4bhu")

# Reaction 6: id_cczd -> ∅ (decay)
r6 = model.createReaction()
r6.setId("cczd_decay")
r6.setReversible(False)
r6.setFast(False)
reactant6 = r6.createReactant()
reactant6.setSpecies("id_cczd")
reactant6.setStoichiometry(1.0)
reactant6.setConstant(False)
param_d2 = model.createParameter()
param_d2.setId("d2")
param_d2.setValue(d2)
kinetic_law6 = r6.createKineticLaw()
kinetic_law6.setFormula("d2 * id_cczd")

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

# Simulate and compare to experiment 0
sim_result_crosscat = simulate(updated_sbml_crosscat)
print(sim_result_crosscat.head(20))
shared_variables.add("updated_sbml_crosscat", updated_sbml_crosscat)
```
# Observation

## Code Stdout
     id_cczd   id_4bhu  id_v5j9  Time
0   1.000000  1.000000      0.0  0.00
1   1.004987  1.004987      0.0  0.01
2   1.009949  1.009949      0.0  0.02
3   1.014887  1.014887      0.0  0.03
4   1.019800  1.019800      0.0  0.04
5   1.024690  1.024690      0.0  0.05
6   1.029554  1.029554      0.0  0.06
7   1.034394  1.034394      0.0  0.07
8   1.039211  1.039211      0.0  0.08
9   1.044003  1.044003      0.0  0.09
10  1.048771  1.048771      0.0  0.10
11  1.053516  1.053516      0.0  0.11
12  1.058237  1.058237      0.0  0.12
13  1.062934  1.062934      0.0  0.13
14  1.067608  1.067608      0.0  0.14
15  1.072259  1.072259      0.0  0.15
16  1.076886  1.076886      0.0  0.16
17  1.081491  1.081491      0.0  0.17
18  1.086072  1.086072      0.0  0.18
19  1.090631  1.090631      0.0  0.19

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_1, iteration_3, iteration_4)
- `shared_variables`: all variables you have saved from the previous iterations. (updated_sbml_lv, updated_sbml_lv_inflow, updated_sbml_quad, updated_sbml_bru, updated_sbml_bru2, updated_sbml_bru3, updated_sbml_symm, updated_sbml_symm_inflow, updated_sbml_selkov, updated_sbml_selkov2, updated_sbml_crosscat)

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


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



# Iteration 19
## Thoughts

The cross-catalytic model with inflow and quadratic production for both species results in both `id_cczd` and `id_4bhu` increasing together, but the increase is monotonic and linear, with no oscillations or amplification as seen in the experimental data. The model still does not capture the oscillatory dynamics.

Given the persistent lack of oscillations, it is likely that the true system involves a nonlinear feedback loop with a delay or a more complex interaction, such as a predator-prey (Lotka-Volterra) or a Brusselator/Selkov model in a specific parameter regime. However, all reasonable variants have been tested, and none have produced oscillations.

Given the time and iteration constraints, the best match to the experimental data is the Lotka-Volterra model, which at least captures the predator-prey relationship and the possibility of oscillations with the right parameters. The original Lotka-Volterra fit produced strong correlations with the experimental data.

I will submit the Lotka-Volterra model as the final model, as it is the most mechanistically plausible and closest to the observed dynamics.

## Action

### Submit
```python
import libsbml

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

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

# Parameters from fit
a = 0.222
b = 0.208
c = 0.744

# Reaction 1: id_4bhu -> 2 id_4bhu (prey growth)
r1 = model.createReaction()
r1.setId("prey_growth")
r1.setReversible(False)
r1.setFast(False)
reactant = r1.createReactant()
reactant.setSpecies("id_4bhu")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)
product = r1.createProduct()
product.setSpecies("id_4bhu")
product.setStoichiometry(2.0)
product.setConstant(False)
kinetic_law1 = r1.createKineticLaw()
param_a = model.createParameter()
param_a.setId("a")
param_a.setValue(a)
kinetic_law1.setFormula("a * id_4bhu")

# Reaction 2: id_cczd + id_4bhu -> 2 id_cczd (predation)
r2 = model.createReaction()
r2.setId("predation")
r2.setReversible(False)
r2.setFast(False)
reactant1 = r2.createReactant()
reactant1.setSpecies("id_cczd")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)
reactant2 = r2.createReactant()
reactant2.setSpecies("id_4bhu")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)
product2 = r2.createProduct()
product2.setSpecies("id_cczd")
product2.setStoichiometry(2.0)
product2.setConstant(False)
param_b = model.createParameter()
param_b.setId("b")
param_b.setValue(b)
kinetic_law2 = r2.createKineticLaw()
kinetic_law2.setFormula("b * id_cczd * id_4bhu")

# Reaction 3: id_cczd -> (decay)
r3 = model.createReaction()
r3.setId("predator_death")
r3.setReversible(False)
r3.setFast(False)
reactant3 = r3.createReactant()
reactant3.setSpecies("id_cczd")
reactant3.setStoichiometry(1.0)
reactant3.setConstant(False)
param_c = model.createParameter()
param_c.setId("c")
param_c.setValue(c)
kinetic_law3 = r3.createKineticLaw()
kinetic_law3.setFormula("c * id_cczd")

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