
                # 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_augn">
    <listOfUnitDefinitions>
      <unitDefinition id="id_ct29">
        <listOfUnits>
          <unit kind="mole" scale="-6"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_1qha">
        <listOfUnits>
          <unit kind="mole" scale="-6"/>
          <unit kind="litre" exponent="-1"/>
          <unit kind="second" exponent="-1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_b4q2">
        <listOfUnits>
          <unit kind="second" exponent="-1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_cvjw">
        <listOfUnits>
          <unit kind="mole" scale="-6"/>
          <unit kind="litre" exponent="-1"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_39qx" size="1"/>
      <compartment id="id_k1wm" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_fzx2" compartment="id_39qx" initialConcentration="0.15"/>
      <species id="id_zldk" compartment="id_k1wm" initialConcentration="1.6"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

                Format your response according to the instructions in the system message.
                
## Thoughts
The first step is to understand the baseline behavior of the system. The initial SBML model contains two species, `id_fzx2` and `id_zldk`, in separate compartments, but no reactions. I need to run an observation experiment to see if the concentrations of these species change over time. If they do, it indicates that there are reactions occurring in the true system that are missing from the model.

## 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 × 3 columns. 

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

Time   id_fzx2  id_zldk
0  1.50e-01 1.60e+00
...
2.00e-01  2.38e-01 1.72e+00
...
4.00e-01  2.52e-01 1.85e+00
...
6.00e-01  2.65e-01 1.96e+00
...
8.00e-01  2.80e-01 2.04e+00
...
1.00e+00  2.98e-01 2.09e+00
...
1.20e+00  3.21e-01 2.09e+00
...
1.40e+00  3.83e-01 1.98e+00
...
1.60e+00  5.24e-01 8.69e-01
...
1.80e+00  2.12e-01 1.29e+00
...
2.00e+00  2.22e-01 1.48e+00
...
2.20e+00  2.34e-01 1.66e+00
...
2.40e+00  2.47e-01 1.80e+00
...
2.60e+00  2.60e-01 1.92e+00
...
2.80e+00  2.74e-01 2.01e+00
...
3.00e+00  2.90e-01 2.07e+00
...
3.20e+00  3.11e-01 2.09e+00
...
3.40e+00  3.45e-01 2.05e+00
...
3.60e+00  1.11e+00 6.68e-01
...
3.80e+00  2.17e-01 1.20e+00
...
4.00e+00  2.18e-01 1.41e+00
...
4.20e+00  2.29e-01 1.59e+00
...
4.40e+00  2.42e-01 1.75e+00
...
4.60e+00  2.54e-01 1.88e+00
...
4.80e+00  2.68e-01 1.98e+00
...
5.00e+00  2.84e-01 2.05e+00
...
5.20e+00  3.02e-01 2.09e+00
...
5.40e+00  3.28e-01 2.08e+00
...
5.60e+00  4.64e-01 1.86e+00
...
5.80e+00  3.06e-01 1.05e+00
...
6.00e+00  2.13e-01 1.33e+00
...
6.20e+00  2.25e-01 1.52e+00
...
6.40e+00  2.37e-01 1.69e+00
...
6.60e+00  2.49e-01 1.83e+00
...
6.80e+00  2.63e-01 1.94e+00
...
7.00e+00  2.77e-01 2.03e+00
...
7.20e+00  2.94e-01 2.08e+00
...
7.40e+00  3.16e-01 2.09e+00
...
7.60e+00  3.61e-01 2.02e+00
...
7.80e+00  7.84e-01 7.26e-01
...
8.00e+00  2.12e-01 1.25e+00
...
8.20e+00  2.20e-01 1.45e+00
...
8.40e+00  2.32e-01 1.63e+00
...
8.60e+00  2.44e-01 1.78e+00
...
8.80e+00  2.57e-01 1.90e+00
...
9.00e+00  2.71e-01 2.00e+00
...
9.20e+00  2.87e-01 2.07e+00
...
9.40e+00  3.06e-01 2.09e+00
...
9.60e+00  3.36e-01 2.06e+00
...
1.00e+01  2.34e-01 1.15e+00

## 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
The observation experiment clearly shows dynamic changes in the concentrations of both species, `id_fzx2` and `id_zldk`. This confirms that reactions are occurring in the system that are not present in the initial model. The concentration profiles show complex behavior, possibly indicating a feedback loop or multiple reactions.

To better understand the relationship between the species and the nature of the reactions, I will plot the time series data. This visualization should help identify potential correlations or patterns that suggest specific reaction mechanisms.

## Action

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

# Access the experiment data
exp_data = experiment_history['iteration_0']

# Plot the time series data
plt.figure(figsize=(10, 6))
plt.plot(exp_data['Time'], exp_data['id_fzx2'], label='id_fzx2')
plt.plot(exp_data['Time'], exp_data['id_zldk'], label='id_zldk')
plt.xlabel('Time')
plt.ylabel('Concentration')
plt.title('Time Series Data from Observation Experiment')
plt.legend()
plt.grid(True)
plt.show()

# Print the first few rows of the data to confirm access
print(exp_data.head())
```
# Observation

## Code Stderror
 Unauthorized modules matplotlib detected. Only these modules are allowed: numpy, pandas, libsbml, math, scipy, jax, sklearn, io, traceback.

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 19/20



### 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 2
## Thoughts
My apologies, I used an unauthorized library (`matplotlib`). I need to analyze the data without plotting directly in the code execution environment. I can still examine the data numerically to understand the relationship between the species.

Looking at the subset of the data provided in the previous response, I see that the concentrations of both species fluctuate over time. There seems to be some inverse relationship or oscillation. When `id_fzx2` increases, `id_zldk` seems to decrease, and vice versa, although the pattern is not perfectly synchronized and shows some complex dynamics.

This suggests a reaction where one species is converted to the other, or where one species influences the rate of change of the other. Given the oscillations and the fact that both concentrations change significantly, a simple unidirectional reaction (A -> B) or independent production/degradation is unlikely to fully explain the behavior. A reversible reaction (A <=> B) or a system with feedback could produce such oscillations.

Let's consider a simple reversible reaction: `id_fzx2 <=> id_zldk`. This would involve `id_fzx2` being converted to `id_zldk` and `id_zldk` being converted back to `id_fzx2`. I will add these two reactions to the model and see if the simulated behavior resembles the observed data. I will start with simple mass action kinetics and default rate constants (e.g., 1.0) as a starting point.

## Action

### Code
```python
import libsbml

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

# Check if reactions already exist to avoid adding duplicates in case of re-running
if not model.getReaction("reaction_fzx2_to_zldk"):
    # Create reaction: id_fzx2 -> id_zldk
    reaction1 = model.createReaction()
    reaction1.setId("reaction_fzx2_to_zldk")
    reaction1.setReversible(False) # Start with irreversible, will add reverse later
    reaction1.setFast(False)

    reactant1 = reaction1.createReactant()
    reactant1.setSpecies("id_fzx2")
    reactant1.setStoichiometry(1.0)
    reactant1.setConstant(False)

    product1 = reaction1.createProduct()
    product1.setSpecies("id_zldk")
    product1.setStoichiometry(1.0)
    product1.setConstant(False)

    # Add a rate law (Mass Action)
    kinetics1 = reaction1.createKineticLaw()
    kinetics1.setMath(libsbml.parseL3Formula("k1 * id_fzx2"))
    # Add parameter k1
    p1 = model.createParameter()
    p1.setId("k1")
    p1.setValue(0.5) # Starting with an arbitrary value

if not model.getReaction("reaction_zldk_to_fzx2"):
    # Create reaction: id_zldk -> id_fzx2
    reaction2 = model.createReaction()
    reaction2.setId("reaction_zldk_to_fzx2")
    reaction2.setReversible(False)
    reaction2.setFast(False)

    reactant2 = reaction2.createReactant()
    reactant2.setSpecies("id_zldk")
    reactant2.setStoichiometry(1.0)
    reactant2.setConstant(False)

    product2 = reaction2.createProduct()
    product2.setSpecies("id_fzx2")
    product2.setStoichiometry(1.0)
    product2.setConstant(False)

    # Add a rate law (Mass Action)
    kinetics2 = reaction2.createKineticLaw()
    kinetics2.setMath(libsbml.parseL3Formula("k2 * id_zldk"))
    # Add parameter k2
    p2 = model.createParameter()
    p2.setId("k2")
    p2.setValue(0.3) # Starting with an arbitrary value


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

# Simulate the updated model
sim_data = simulate(updated_sbml)

# Print the head of the simulated data for comparison
print("Simulated Data Head:")
print(sim_data.head())

# Print the head of the experimental data for comparison
print("\nExperimental Data Head (iteration_0):")
print(experiment_history['iteration_0'].head())

# Store the updated SBML for potential future use
shared_variables.add("current_sbml_model", updated_sbml)
```
# Observation

## Code Stdout
Simulated Data Head:
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.154034  1.595966  0.01
2  0.158035  1.591965  0.02
3  0.162005  1.587995  0.03
4  0.165944  1.584056  0.04

Experimental Data Head (iteration_0):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.167854  1.598189  0.01
2  0.181754  1.598753  0.02
3  0.192594  1.601146  0.03
4  0.201091  1.604921  0.04

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

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


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



# Iteration 3
## Thoughts
The simulated data from the model with simple reversible reactions (`id_fzx2 <=> id_zldk`) and mass action kinetics does not match the experimental data. The simulated concentrations change monotonically towards a steady state, while the experimental data shows oscillations and more complex dynamics. This indicates that the simple reversible reaction model is insufficient.

The observed oscillations suggest a system with some form of positive or negative feedback, or perhaps a more complex reaction network involving autocatalysis or interaction with other implicit species (though the problem states no new species need to be added).

Let's re-examine the experimental data. `id_fzx2` concentration increases initially, then decreases sharply, then increases again, showing a clear oscillatory pattern. `id_zldk` shows a somewhat inverse pattern, but also with complex changes. The sharp drops in `id_fzx2` and subsequent increases in `id_zldk` (around Time 1.6, 3.6, 5.6, 7.8) are particularly interesting and suggest a rapid conversion or consumption of `id_fzx2` that might be triggered when `id_fzx2` reaches a certain level, or when `id_zldk` is at a certain level.

A common motif for oscillations in biological systems is a predator-prey type interaction or a system with activation/inhibition. Since we only have two species, perhaps one species catalyzes or inhibits the reaction involving the other.

Consider the possibility that `id_fzx2` is converted to `id_zldk`, and this conversion rate is somehow dependent on the concentration of `id_zldk` or `id_fzx2` itself in a non-linear way. Or perhaps `id_zldk` is converted to `id_fzx2` with a similar dependency.

Let's try a different approach. Instead of simple mass action, let's consider if one species catalyzes the conversion of the other. For example, `id_zldk` could catalyze the conversion of `id_fzx2` to `id_zldk`. This would be a reaction like `id_fzx2 -> id_zldk` with a rate law dependent on `id_zldk`. Or, `id_fzx2` could catalyze the conversion of `id_zldk` to `id_fzx2`.

Let's try adding a reaction where `id_fzx2` is converted to `id_zldk`, and the rate depends on both `id_fzx2` and `id_zldk`. A simple form could be `k * id_fzx2 * id_zldk`. This represents a bimolecular reaction or a catalyzed reaction.

Let's remove the previous simple reversible reactions and add a single reaction: `id_fzx2 -> id_zldk` with rate `k * id_fzx2 * id_zldk`.

## Action

### Code
```python
import libsbml

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

# Remove existing reactions if any were added in previous steps
while model.getNumReactions() > 0:
    model.removeReaction(0)

# Create a new reaction: id_fzx2 -> id_zldk, catalyzed by id_zldk (or bimolecular)
reaction = model.createReaction()
reaction.setId("reaction_fzx2_to_zldk_catalyzed")
reaction.setReversible(False)
reaction.setFast(False)

reactant = reaction.createReactant()
reactant.setSpecies("id_fzx2")
reactant.setStoichiometry(1.0)
reactant.setConstant(False)

product = reaction.createProduct()
product.setSpecies("id_zldk")
product.setStoichiometry(1.0)
product.setConstant(False)

# Add a rate law (Mass Action with both species)
kinetics = reaction.createKineticLaw()
kinetics.setMath(libsbml.parseL3Formula("k * id_fzx2 * id_zldk"))

# Add parameter k
p = model.createParameter()
p.setId("k")
p.setValue(0.1) # Starting with an arbitrary value

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

# Simulate the updated model
sim_data = simulate(updated_sbml)

# Print the head of the simulated data for comparison
print("Simulated Data Head:")
print(sim_data.head())

# Print the head of the experimental data for comparison
print("\nExperimental Data Head (iteration_0):")
print(experiment_history['iteration_0'].head())

# Store the updated SBML
shared_variables.add("current_sbml_model", updated_sbml)
```
# Observation

## Code Stdout
Simulated Data Head:
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.149760  1.600240  0.01
2  0.149521  1.600479  0.02
3  0.149282  1.600718  0.03
4  0.149043  1.600957  0.04

Experimental Data Head (iteration_0):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.167854  1.598189  0.01
2  0.181754  1.598753  0.02
3  0.192594  1.601146  0.03
4  0.201091  1.604921  0.04

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

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


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



# Iteration 4
## Thoughts
The simulation with the reaction `id_fzx2 -> id_zldk` with rate `k * id_fzx2 * id_zldk` also does not reproduce the observed oscillations. The simulated concentrations show a slow, monotonic change, which is very different from the experimental data. This suggests that a simple conversion from `id_fzx2` to `id_zldk` with this rate law is not the correct mechanism.

The experimental data shows that `id_fzx2` increases initially, then drops sharply, while `id_zldk` decreases initially, then increases. This pattern repeats. The sharp drop in `id_fzx2` and increase in `id_zldk` suggests a reaction that consumes `id_fzx2` and produces `id_zldk`. The fact that this happens periodically suggests that the rate of this reaction might be dependent on the concentrations in a way that creates a limit cycle or oscillatory behavior.

Let's consider the possibility of a system similar to the Lotka-Volterra model, which describes predator-prey interactions and produces oscillations. In a simplified form with two species, this often involves reactions like:
1. Prey growth (e.g., `id_fzx2` production): This would require a source for `id_fzx2`. Since we cannot add new species, perhaps `id_fzx2` is produced from a constant boundary species or has a constant production rate. However, the initial model doesn't have any boundary species or parameters for constant production. Let's assume for now that production is not the primary missing mechanism, as the initial concentration is non-zero and the oscillations involve consumption and production relative to each other.
2. Prey consumption by predator (e.g., `id_fzx2` consumed by `id_zldk`): `id_fzx2 + id_zldk -> 2 * id_zldk` (predator increases) or `id_fzx2 + id_zldk -> id_zldk + X` where X is consumed or removed. A simpler form is `id_fzx2 -> X` with rate dependent on `id_zldk`, or `id_fzx2 + id_zldk -> products`.
3. Predator death/removal (e.g., `id_zldk` degradation): `id_zldk -> Y`.

Given the observed data, where `id_fzx2` drops and `id_zldk` increases, a reaction where `id_fzx2` is converted to `id_zldk` seems plausible. Let's revisit the reaction `id_fzx2 -> id_zldk`. What kind of rate law could cause oscillations?

Consider a scenario where `id_fzx2` is converted to `id_zldk`, and the rate of this conversion is *activated* by `id_zldk`. This is a form of positive feedback on the production of `id_zldk`. A rate law like `k * id_fzx2 * id_zldk` (which I just tried) is a simple form of this. However, it didn't oscillate. Perhaps the rate law needs to be non-linear, like Michaelis-Menten or Hill kinetics, or perhaps there's another reaction involved.

Let's consider the reverse reaction as well: `id_zldk -> id_fzx2`. If this reaction also exists, the system is reversible.

What if there are two reactions:
1. `id_fzx2 -> id_zldk` (Rate depends on something)
2. `id_zldk -> id_fzx2` (Rate depends on something else)

Let's look at the data again. `id_fzx2` increases, then crashes. `id_zldk` decreases, then increases. This looks like `id_fzx2` is the "prey" and `id_zldk` is the "predator".
- `id_fzx2` grows (or is produced) - but we don't have a source. Let's assume it's produced from an implicit source or has a constant influx, even though we can't model that directly with the given constraints. Or maybe the "growth" is actually the reverse reaction `id_zldk -> id_fzx2`.
- `id_fzx2` is consumed by `id_zldk`: `id_fzx2 + id_zldk -> id_zldk` (or `id_fzx2 -> id_zldk` with rate proportional to `id_zldk`).
- `id_zldk` decays: `id_zldk -> X` (consumed or removed).

Let's try modeling this Lotka-Volterra-like system using the two species we have:
Reaction 1: `id_fzx2 -> id_zldk` (Consumption of `id_fzx2` by `id_zldk`, producing more `id_zldk`). Rate: `k1 * id_fzx2 * id_zldk`.
Reaction 2: `id_zldk -> id_fzx2` (Conversion of `id_zldk` back to `id_fzx2`, representing `id_zldk` "decay" and regeneration of `id_fzx2`). Rate: `k2 * id_zldk`.

Let's implement these two reactions and simulate.

## Action

### Code
```python
import libsbml

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

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

# Reaction 1: id_fzx2 -> id_zldk (rate k1 * id_fzx2 * id_zldk)
reaction1 = model.createReaction()
reaction1.setId("reaction_fzx2_consumption")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_fzx2")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)

product1 = reaction1.createProduct()
product1.setSpecies("id_zldk")
product1.setStoichiometry(1.0) # Assuming 1:1 conversion for now
product1.setConstant(False)

kinetics1 = reaction1.createKineticLaw()
kinetics1.setMath(libsbml.parseL3Formula("k1 * id_fzx2 * id_zldk"))

p1 = model.createParameter()
p1.setId("k1")
p1.setValue(0.1) # Arbitrary initial value

# Reaction 2: id_zldk -> id_fzx2 (rate k2 * id_zldk)
reaction2 = model.createReaction()
reaction2.setId("reaction_zldk_decay")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_zldk")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)

product2 = reaction2.createProduct()
product2.setSpecies("id_fzx2")
product2.setStoichiometry(1.0) # Assuming 1:1 conversion for now
product2.setConstant(False)

kinetics2 = reaction2.createKineticLaw()
kinetics2.setMath(libsbml.parseL3Formula("k2 * id_zldk"))

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(0.1) # Arbitrary initial value


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

# Simulate the updated model
sim_data = simulate(updated_sbml)

# Print the head of the simulated data for comparison
print("Simulated Data Head:")
print(sim_data.head())

# Print the head of the experimental data for comparison
print("\nExperimental Data Head (iteration_0):")
print(experiment_history['iteration_0'].head())

# Store the updated SBML
shared_variables.add("current_sbml_model", updated_sbml)
```
# Observation

## Code Stdout
Simulated Data Head:
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.151358  1.598642  0.01
2  0.152713  1.597287  0.02
3  0.154065  1.595935  0.03
4  0.155413  1.594587  0.04

Experimental Data Head (iteration_0):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.167854  1.598189  0.01
2  0.181754  1.598753  0.02
3  0.192594  1.601146  0.03
4  0.201091  1.604921  0.04

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

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


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



# Iteration 5
## Thoughts
The simulation results from the Lotka-Volterra-like model (`id_fzx2 -> id_zldk` with rate `k1 * id_fzx2 * id_zldk` and `id_zldk -> id_fzx2` with rate `k2 * id_zldk`) still do not match the experimental data. The simulated concentrations show a slow, non-oscillatory change, unlike the pronounced oscillations observed.

My current model structure is:
Reaction 1: `id_fzx2` -> `id_zldk` (rate `k1 * id_fzx2 * id_zldk`)
Reaction 2: `id_zldk` -> `id_fzx2` (rate `k2 * id_zldk`)

Let's reconsider the stoichiometry and rate laws. In a typical Lotka-Volterra model:
- Prey growth: `X -> 2X` (rate `alpha * X`) or `Source -> X` (rate `alpha * X`)
- Predator consumes prey: `X + Y -> 2Y` (rate `beta * X * Y`)
- Predator decay: `Y -> Sink` (rate `gamma * Y`)

Mapping this to our species:
- `id_fzx2` (Prey), `id_zldk` (Predator)
- `id_fzx2` growth: This is the missing piece if we strictly follow LV. The data shows `id_fzx2` increasing when `id_zldk` is low. This could be interpreted as `id_fzx2` having a growth phase. Since we can't add a source, maybe the reverse reaction `id_zldk -> id_fzx2` acts as the "growth" for `id_fzx2`?
- `id_fzx2` consumed by `id_zldk`: `id_fzx2 + id_zldk -> id_zldk` (rate `k1 * id_fzx2 * id_zldk`). This means `id_fzx2` is consumed, and `id_zldk` is produced. The net change is -1 for `id_fzx2` and +1 for `id_zldk`. This matches my Reaction 1 stoichiometry.
- `id_zldk` decay: `id_zldk -> id_fzx2` (rate `k2 * id_zldk`). This means `id_zldk` is consumed, and `id_fzx2` is produced. The net change is -1 for `id_zldk` and +1 for `id_fzx2`. This matches my Reaction 2 stoichiometry.

So the current model structure seems consistent with a variation of Lotka-Volterra where the "prey growth" comes from predator decay.

Let's check the rate laws again.
Reaction 1: `id_fzx2 -> id_zldk` with rate `k1 * id_fzx2 * id_zldk`. This consumes `id_fzx2` and produces `id_zldk`.
Reaction 2: `id_zldk -> id_fzx2` with rate `k2 * id_zldk`. This consumes `id_zldk` and produces `id_fzx2`.

The differential equations for this system would be:
d[id_fzx2]/dt = - k1 * [id_fzx2] * [id_zldk] + k2 * [id_zldk]
d[id_zldk]/dt = + k1 * [id_fzx2] * [id_zldk] - k2 * [id_zldk]

This system *can* produce oscillations, but the parameter values are crucial. My initial guess of k1=0.1 and k2=0.1 might be far off.

Let's try to find parameters that might lead to oscillations. Oscillations in Lotka-Volterra-like systems typically occur when the parameters are in a certain range relative to the initial conditions.

Instead of guessing parameters, let's consider if the reaction stoichiometry or rate laws are fundamentally wrong.

What if the conversion is not 1:1? For example, `id_fzx2 -> 2 * id_zldk` or `2 * id_fzx2 -> id_zldk`. The data doesn't give stoichiometry directly.

Let's look at the initial phase of the experiment again. `id_fzx2` increases, `id_zldk` decreases slightly. This initial increase in `id_fzx2` is not explained by the current model unless `k2 * id_zldk` is initially larger than `k1 * id_fzx2 * id_zldk`.

What if there is a reaction that *only* produces `id_fzx2`? Or *only* consumes `id_zldk`?
- Production of `id_fzx2`: `Source -> id_fzx2`. Not possible without adding species.
- Consumption of `id_zldk`: `id_zldk -> Sink`. Not possible without adding species.

Could the oscillations be driven by a single reaction with a complex rate law? For example, `id_fzx2 -> id_zldk` with a rate law that has a threshold or saturation effect?

Let's consider the possibility that the reaction `id_fzx2 -> id_zldk` is activated by `id_fzx2` itself (autocatalysis) or inhibited by `id_zldk`.

Let's try a different model structure based on common oscillatory systems like the Brusselator or Oregonator, although those typically involve more species or intermediates. With only two species, the options are limited.

Could there be a reaction that consumes both species? `id_fzx2 + id_zldk -> products`. This would decrease both concentrations. The data doesn't show both decreasing simultaneously for a prolonged period.

Let's go back to the idea of `id_fzx2` being converted to `id_zldk` and vice versa, but with potentially different rate laws or stoichiometries.

Maybe the initial increase in `id_fzx2` is due to a reaction `id_zldk -> id_fzx2`, and the subsequent crash is due to a reaction `id_fzx2 -> id_zldk` that becomes dominant as `id_fzx2` increases.

Let's try the following reactions:
Reaction 1: `id_zldk -> id_fzx2` (Rate `k1 * id_zldk`) - This produces `id_fzx2` and consumes `id_zldk`.
Reaction 2: `id_fzx2 -> id_zldk` (Rate `k2 * id_fzx2^n` or `k2 * id_fzx2 * id_zldk^m` or similar non-linear rate) - This consumes `id_fzx2` and produces `id_zldk`.

Let's try Reaction 1: `id_zldk -> id_fzx2` (rate `k1 * id_zldk`) and Reaction 2: `id_fzx2 -> id_zldk` (rate `k2 * id_fzx2`). This is just the simple reversible reaction again, which didn't work.

Let's try Reaction 1: `id_zldk -> id_fzx2` (rate `k1 * id_zldk`) and Reaction 2: `id_fzx2 -> id_zldk` (rate `k2 * id_fzx2 * id_zldk`). This is the same as the previous attempt, just swapping the "decay" and "consumption" roles. The equations would be:
d[id_fzx2]/dt = + k1 * [id_zldk] - k2 * [id_fzx2] * [id_zldk]
d[id_zldk]/dt = - k1 * [id_zldk] + k2 * [id_fzx2] * [id_zldk]
This is essentially the same system as before, just with signs flipped and parameters potentially different. It should still be able to oscillate. The issue might be the parameter values.

Let's try to find parameters that make this system oscillate. For the system:
dx/dt = alpha * y - beta * x * y
dy/dt = beta * x * y - gamma * y
Oscillations occur around the fixed point (gamma/beta, alpha/beta). The period depends on the parameters.

In our case:
d[id_fzx2]/dt = k1 * [id_zldk] - k2 * [id_fzx2] * [id_zldk]
d[id_zldk]/dt = k2 * [id_fzx2] * [id_zldk] - k1 * [id_zldk]

Fixed point: k1 * [id_zldk] - k2 * [id_fzx2] * [id_zldk] = 0 => [id_zldk] * (k1 - k2 * [id_fzx2]) = 0. So [id_zldk] = 0 or [id_fzx2] = k1/k2.
k2 * [id_fzx2] * [id_zldk] - k1 * [id_zldk] = 0 => [id_zldk] * (k2 * [id_fzx2] - k1) = 0. So [id_zldk] = 0 or [id_fzx2] = k1/k2.
The non-trivial fixed point is ([id_fzx2], [id_zldk]) = (k1/k2, 0). This doesn't look right for oscillations where both species coexist.

Let's re-check the standard Lotka-Volterra equations and mapping.
Prey (X): dX/dt = alpha*X - beta*X*Y
Predator (Y): dY/dt = delta*X*Y - gamma*Y

Mapping: X = id_fzx2, Y = id_zldk
dX/dt = alpha * id_fzx2 - beta * id_fzx2 * id_zldk
dY/dt = delta * id_fzx2 * id_zldk - gamma * id_zldk

Reaction 1 (Prey growth): `id_fzx2 -> 2 * id_fzx2` (rate `alpha * id_fzx2`). This adds `id_fzx2`.
Reaction 2 (Predator consumes prey): `id_fzx2 + id_zldk -> 2 * id_zldk` (rate `beta * id_fzx2 * id_zldk`). This consumes `id_fzx2` and produces `id_zldk`.
Reaction 3 (Predator decay): `id_zldk -> Sink` (rate `gamma * id_zldk`). This consumes `id_zldk`.

Can I represent these reactions using only `id_fzx2` and `id_zldk` and no new species or boundary species?
Reaction 1: `id_fzx2 -> 2 * id_fzx2` is equivalent to a net production of `id_fzx2` with rate `alpha * id_fzx2`. This cannot be represented as a simple reaction between `id_fzx2` and `id_zldk`.
Reaction 2: `id_fzx2 + id_zldk -> 2 * id_zldk`. This consumes `id_fzx2` and produces `id_zldk`. Net change: -1 `id_fzx2`, +1 `id_zldk`. Rate `k1 * id_fzx2 * id_zldk`.
Reaction 3: `id_zldk -> Sink`. This consumes `id_zldk`. Net change: -1 `id_zldk`. Rate `k2 * id_zldk`.

So, a possible model structure using only `id_fzx2` and `id_zldk` that resembles Lotka-Volterra would need a reaction that *produces* `id_fzx2` without consuming `id_zldk`, and a reaction that *consumes* `id_zldk` without producing `id_fzx2`.

Let's try:
Reaction 1: `id_zldk -> id_fzx2` (rate `k1 * id_zldk`). This produces `id_fzx2` and consumes `id_zldk`. This doesn't fit the "prey growth" idea perfectly as it consumes the predator.
Reaction 2: `id_fzx2 -> id_zldk` (rate `k2 * id_fzx2 * id_zldk`). This consumes `id_fzx2` and produces `id_zldk`. This fits the "predator consumes prey" idea.

Let's reconsider the initial increase in `id_fzx2` and decrease in `id_zldk`. This suggests a net conversion from `id_zldk` to `id_fzx2` initially. This would be favored by the reaction `id_zldk -> id_fzx2`.

The subsequent crash of `id_fzx2` and increase of `id_zldk` suggests a net conversion from `id_fzx2` to `id_zldk`. This would be favored by the reaction `id_fzx2 -> id_zldk`.

Let's try the two reactions again:
Reaction 1: `id_zldk -> id_fzx2` (rate `k1 * id_zldk`)
Reaction 2: `id_fzx2 -> id_zldk` (rate `k2 * id_fzx2 * id_zldk`)

The differential equations are:
d[id_fzx2]/dt = + k1 * [id_zldk] - k2 * [id_fzx2] * [id_zldk]
d[id_zldk]/dt = - k1 * [id_zldk] + k2 * [id_fzx2] * [id_zldk]

This system *can* oscillate. The fixed point is (k1/k2, 0). This still doesn't look like a stable oscillation point where both species coexist.

Let's try swapping the rate laws:
Reaction 1: `id_zldk -> id_fzx2` (rate `k1 * id_zldk * id_fzx2`)
Reaction 2: `id_fzx2 -> id_zldk` (rate `k2 * id_fzx2`)

d[id_fzx2]/dt = + k1 * [id_zldk] * [id_fzx2] - k2 * [id_fzx2]
d[id_zldk]/dt = - k1 * [id_zldk] * [id_fzx2] + k2 * [id_fzx2]

Fixed point:
k1 * [id_zldk] * [id_fzx2] - k2 * [id_fzx2] = 0 => [id_fzx2] * (k1 * [id_zldk] - k2) = 0. So [id_fzx2] = 0 or [id_zldk] = k2/k1.
- k1 * [id_zldk] * [id_fzx2] + k2 * [id_fzx2] = 0 => [id_fzx2] * (-k1 * [id_zldk] + k2) = 0. So [id_fzx2] = 0 or [id_zldk] = k2/k1.
The non-trivial fixed point is ([id_fzx2], [id_zldk]) = (0, k2/k1). This also doesn't look right.

Let's go back to the first Lotka-Volterra mapping attempt:
Reaction 1: `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * id_zldk`) - Consumes `id_fzx2`, produces `id_zldk`.
Reaction 2: `id_zldk -> id_fzx2` (rate `k2 * id_zldk`) - Consumes `id_zldk`, produces `id_fzx2`.

d[id_fzx2]/dt = - k1 * [id_fzx2] * [id_zldk] + k2 * [id_zldk]
d[id_zldk]/dt = + k1 * [id_fzx2] * [id_zldk] - k2 * [id_zldk]

Fixed point:
- k1 * [id_fzx2] * [id_zldk] + k2 * [id_zldk] = 0 => [id_zldk] * (-k1 * [id_fzx2] + k2) = 0. So [id_zldk] = 0 or [id_fzx2] = k2/k1.
+ k1 * [id_fzx2] * [id_zldk] - k2 * [id_zldk] = 0 => [id_zldk] * (k1 * [id_fzx2] - k2) = 0. So [id_zldk] = 0 or [id_fzx2] = k2/k1.
The non-trivial fixed point is ([id_fzx2], [id_zldk]) = (k2/k1, 0). Still not a coexistence fixed point.

My interpretation of mapping Lotka-Volterra to these two species might be incorrect, or the system is not a simple LV.

Let's look at the data again. The sharp drops in `id_fzx2` and increases in `id_zldk` are key features. This looks like a rapid conversion of `id_fzx2` to `id_zldk`. The rate of this conversion seems to increase as `id_fzx2` increases, and perhaps also as `id_zldk` increases (positive feedback).

What about a single reversible reaction with non-linear kinetics?
`id_fzx2 <=> id_zldk`
Forward rate: `k_f * rate_f([id_fzx2], [id_zldk])`
Reverse rate: `k_r * rate_r([id_fzx2], [id_zldk])`

Let's try the forward reaction `id_fzx2 -> id_zldk` with rate `k1 * id_fzx2 * id_zldk` again, as it seems to capture the consumption of `id_fzx2` and production of `id_zldk` dependent on both.
And the reverse reaction `id_zldk -> id_fzx2` with rate `k2 * id_zldk`. This represents `id_zldk` "decaying" back into `id_fzx2`.

This is the exact model I just simulated. The issue is likely the parameter values. Oscillations in this system require specific parameter ranges.

Let's try to find parameters that might cause oscillations. I need to simulate with different `k1` and `k2` values. Since I can't easily do a parameter scan here, I'll try some values that might push the system towards oscillation. Higher `k1` relative to `k2` might make the forward reaction more dominant, leading to faster consumption of `id_fzx2` when both are present.

Let's try increasing `k1` and decreasing `k2`.

## Action

### Code
```python
import libsbml

# Load the model from shared variables
sbml_string = shared_variables.access("current_sbml_model")
sbml_doc = libsbml.readSBMLFromString(sbml_string)
model = sbml_doc.getModel()

# Update parameter values
p1 = model.getParameter("k1")
if p1:
    p1.setValue(0.5) # Increase k1

p2 = model.getParameter("k2")
if p2:
    p2.setValue(0.05) # Decrease k2

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

# Simulate the updated model
sim_data = simulate(updated_sbml)

# Print the head of the simulated data for comparison
print("Simulated Data Head (New Params):")
print(sim_data.head())

# Print the head of the experimental data for comparison
print("\nExperimental Data Head (iteration_0):")
print(experiment_history['iteration_0'].head())

# Store the updated SBML
shared_variables.add("current_sbml_model", updated_sbml)
```
# Observation

## Code Stdout
Simulated Data Head (New Params):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.149602  1.600398  0.01
2  0.149206  1.600794  0.02
3  0.148814  1.601186  0.03
4  0.148425  1.601575  0.04

Experimental Data Head (iteration_0):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.167854  1.598189  0.01
2  0.181754  1.598753  0.02
3  0.192594  1.601146  0.03
4  0.201091  1.604921  0.04

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

### 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
Changing the parameters `k1` and `k2` in the model with reactions `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * id_zldk`) and `id_zldk -> id_fzx2` (rate `k2 * id_zldk`) still did not produce oscillations. The simulated data continues to show monotonic changes, albeit with slightly different rates. This suggests that either the chosen reaction mechanisms are incorrect, or the parameter values required for oscillation are very specific and I'm not finding them by simple guessing.

Let's reconsider the reaction mechanisms. The sharp, periodic drops in `id_fzx2` and corresponding increases in `id_zldk` are the most striking features of the experimental data. This looks like a switch-like behavior or a rapid conversion that is triggered under certain conditions.

What if the conversion of `id_fzx2` to `id_zldk` is not simply proportional to `id_fzx2` and `id_zldk`, but follows a more complex rate law? For example, a rate law that is very low below a certain threshold of `id_fzx2` or `id_zldk`, and then increases sharply. Hill functions are often used to model such cooperative or switch-like behavior.

Let's try the reaction `id_fzx2 -> id_zldk` with a rate law that is activated by `id_fzx2` itself (autocatalysis) or by `id_zldk`.

Consider the reaction `id_fzx2 -> id_zldk` with a rate law like `k * id_fzx2 * (id_fzx2^n / (K^n + id_fzx2^n))` (autocatalysis via Hill function) or `k * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))` (activation by `id_zldk`).

Let's try the latter: `id_fzx2 -> id_zldk` with rate `k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))`. This means the conversion of `id_fzx2` to `id_zldk` is catalyzed or activated by `id_zldk` in a sigmoidal manner.

We still need a reaction that produces `id_fzx2` or consumes `id_zldk` to complete the cycle and allow for oscillations. The initial increase in `id_fzx2` suggests production of `id_fzx2`. Let's keep the reaction `id_zldk -> id_fzx2` with rate `k2 * id_zldk` as the source of `id_fzx2` and consumer of `id_zldk`.

So the proposed model is:
Reaction 1: `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))`)
Reaction 2: `id_zldk -> id_fzx2` (rate `k2 * id_zldk`)

This system has parameters `k1`, `k2`, `K`, and `n`. `n` is the Hill coefficient, typically an integer >= 1. Let's start with n=2 (cooperativity). `K` is the half-saturation constant.

Let's implement this model. I'll need to add parameters `K` and `n` (or just `K` and use a fixed `n`). SBML requires parameters to be defined.

## Action

### Code
```python
import libsbml

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

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

# Remove existing parameters (k1, k2 from previous attempts)
while model.getNumParameters() > 0:
    model.removeParameter(0)

# Reaction 1: id_fzx2 -> id_zldk (rate k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n)))
reaction1 = model.createReaction()
reaction1.setId("reaction_fzx2_to_zldk_activated")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_fzx2")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)

product1 = reaction1.createProduct()
product1.setSpecies("id_zldk")
product1.setStoichiometry(1.0)
product1.setConstant(False)

kinetics1 = reaction1.createKineticLaw()
# Need to define parameters k1, K, n
p_k1 = model.createParameter()
p_k1.setId("k1")
p_k1.setValue(1.0) # Arbitrary initial value

p_K = model.createParameter()
p_K.setId("K")
p_K.setValue(1.0) # Arbitrary initial value

p_n = model.createParameter()
p_n.setId("n")
p_n.setValue(2.0) # Hill coefficient, starting with 2
p_n.setConstant(True) # Hill coefficient is usually a fixed value

# Rate law formula: k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))
formula1 = "k1 * id_fzx2 * (pow(id_zldk, n) / (pow(K, n) + pow(id_zldk, n)))"
kinetics1.setMath(libsbml.parseL3Formula(formula1))


# Reaction 2: id_zldk -> id_fzx2 (rate k2 * id_zldk)
reaction2 = model.createReaction()
reaction2.setId("reaction_zldk_to_fzx2_decay")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_zldk")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)

product2 = reaction2.createProduct()
product2.setSpecies("id_fzx2")
product2.setStoichiometry(1.0)
product2.setConstant(False)

kinetics2 = reaction2.createKineticLaw()
# Need to define parameter k2
p_k2 = model.createParameter()
p_k2.setId("k2")
p_k2.setValue(0.1) # Arbitrary initial value

formula2 = "k2 * id_zldk"
kinetics2.setMath(libsbml.parseL3Formula(formula2))


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

# Simulate the updated model
sim_data = simulate(updated_sbml)

# Print the head of the simulated data for comparison
print("Simulated Data Head (Hill Kinetics):")
print(sim_data.head())

# Print the head of the experimental data for comparison
print("\nExperimental Data Head (iteration_0):")
print(experiment_history['iteration_0'].head())

# Store the updated SBML
shared_variables.add("current_sbml_model", updated_sbml)
```
# Observation

## Code Stdout
Simulated Data Head (Hill Kinetics):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.150519  1.599481  0.01
2  0.151034  1.598966  0.02
3  0.151546  1.598454  0.03
4  0.152053  1.597947  0.04

Experimental Data Head (iteration_0):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.167854  1.598189  0.01
2  0.181754  1.598753  0.02
3  0.192594  1.601146  0.03
4  0.201091  1.604921  0.04

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

### 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 simulation with the Hill kinetics model (`id_fzx2 -> id_zldk` with rate `k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))` and `id_zldk -> id_fzx2` with rate `k2 * id_zldk`) still does not produce oscillations with the initial parameter guesses (k1=1.0, K=1.0, n=2.0, k2=0.1). The simulated concentrations show a slow, monotonic change.

This type of system *can* oscillate, but it is highly dependent on the parameter values. Finding the right parameters by manual guessing is inefficient and unlikely to succeed within the remaining iterations.

I need a way to explore the parameter space or gain more information about the system's behavior under different conditions. Perturbing the system by changing initial concentrations can provide valuable clues about the underlying mechanisms and help constrain the possible parameter values or even rule out model structures.

Let's try changing the initial concentration of one of the species and observe the system's response. I will increase the initial concentration of `id_fzx2` significantly and see how the oscillations are affected. This might tell me if the period or amplitude of oscillations changes, or if the system behaves differently when starting further from the apparent steady state.

I will set the initial concentration of `id_fzx2` to a higher value, say 0.5 (default is 0.15), while keeping `id_zldk` at its default (1.6).

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_fzx2": 0.5
    }
}
```
# Observation

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

Total size: 1001 rows × 3 columns. 

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

Time   id_fzx2  id_zldk
0  5.00e-01 1.60e+00
...
2.00e-01  2.67e-01 1.10e+00
...
4.00e-01  2.14e-01 1.35e+00
...
6.00e-01  2.26e-01 1.54e+00
...
8.00e-01  2.38e-01 1.70e+00
...
1.00e+00  2.50e-01 1.84e+00
...
1.20e+00  2.64e-01 1.95e+00
...
1.40e+00  2.79e-01 2.04e+00
...
1.60e+00  2.96e-01 2.08e+00
...
1.80e+00  3.18e-01 2.09e+00
...
2.00e+00  3.70e-01 2.00e+00
...
2.20e+00  6.55e-01 7.86e-01
...
2.40e+00  2.12e-01 1.27e+00
...
2.60e+00  2.21e-01 1.47e+00
...
2.80e+00  2.33e-01 1.64e+00
...
3.00e+00  2.45e-01 1.79e+00
...
3.20e+00  2.59e-01 1.91e+00
...
3.40e+00  2.73e-01 2.01e+00
...
3.60e+00  2.89e-01 2.07e+00
...
3.80e+00  3.08e-01 2.09e+00
...
4.00e+00  3.40e-01 2.06e+00
...
4.20e+00  1.26e+00 6.79e-01
...
4.40e+00  2.23e-01 1.18e+00
...
4.60e+00  2.17e-01 1.39e+00
...
4.80e+00  2.28e-01 1.58e+00
...
5.00e+00  2.40e-01 1.73e+00
...
5.20e+00  2.53e-01 1.87e+00
...
5.40e+00  2.67e-01 1.97e+00
...
5.60e+00  2.82e-01 2.05e+00
...
5.80e+00  3.00e-01 2.09e+00
...
6.00e+00  3.25e-01 2.08e+00
...
6.20e+00  4.15e-01 1.93e+00
...
6.40e+00  3.74e-01 9.87e-01
...
6.60e+00  2.13e-01 1.31e+00
...
6.80e+00  2.24e-01 1.51e+00
...
7.00e+00  2.36e-01 1.68e+00
...
7.20e+00  2.48e-01 1.82e+00
...
7.40e+00  2.61e-01 1.94e+00
...
7.60e+00  2.76e-01 2.02e+00
...
7.80e+00  2.93e-01 2.08e+00
...
8.00e+00  3.14e-01 2.09e+00
...
8.20e+00  3.53e-01 2.03e+00
...
8.40e+00  9.16e-01 6.89e-01
...
8.60e+00  2.13e-01 1.23e+00
...
8.80e+00  2.19e-01 1.43e+00
...
9.00e+00  2.31e-01 1.61e+00
...
9.20e+00  2.43e-01 1.77e+00
...
9.40e+00  2.56e-01 1.89e+00
...
9.60e+00  2.70e-01 1.99e+00
...
1.00e+01  3.05e-01 2.09e+00

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 13/20



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

### 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 experiment with the increased initial concentration of `id_fzx2` (Experiment ID: iteration_7) still shows oscillations, similar in character to the initial observation (iteration_0). This confirms that the oscillatory behavior is robust to changes in initial conditions, which is characteristic of limit cycle oscillations.

Comparing the data from `iteration_0` (initial `id_fzx2` = 0.15) and `iteration_7` (initial `id_fzx2` = 0.5):
- The initial state is different, as expected.
- Both experiments show oscillations.
- The period and amplitude of the oscillations appear somewhat similar after the initial transient phase, although a precise comparison would require plotting or numerical analysis.

The fact that the system returns to a similar oscillatory pattern regardless of the starting point (within the tested range) supports the idea of a limit cycle attractor.

My current model structure with Hill kinetics (`id_fzx2 -> id_zldk` activated by `id_zldk`, and `id_zldk -> id_fzx2` decay) is a plausible candidate for generating limit cycle oscillations. The failure to simulate oscillations is likely due to incorrect parameter values (`k1`, `k2`, `K`, `n`).

Since manual parameter tuning is difficult, and I cannot use plotting to visually compare the simulated and experimental data, I need a more systematic approach or more informative experiments.

Another type of perturbation is changing the initial concentration of `id_zldk`. Let's try increasing the initial concentration of `id_zldk` and see the effect. This might reveal different aspects of the system's dynamics.

I will set the initial concentration of `id_zldk` to a higher value, say 2.5 (default is 1.6), while keeping `id_fzx2` at its default (0.15).

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_zldk": 2.5
    }
}
```
# Observation

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

Total size: 1001 rows × 3 columns. 

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

Time   id_fzx2  id_zldk
0  1.50e-01 2.50e+00
...
2.00e-01  6.54e-01 2.03e+00
...
4.00e-01  3.28e-01 1.03e+00
...
6.00e-01  2.13e-01 1.33e+00
...
8.00e-01  2.24e-01 1.52e+00
...
1.00e+00  2.36e-01 1.68e+00
...
1.20e+00  2.49e-01 1.83e+00
...
1.40e+00  2.62e-01 1.94e+00
...
1.60e+00  2.77e-01 2.03e+00
...
1.80e+00  2.94e-01 2.08e+00
...
2.00e+00  3.15e-01 2.09e+00
...
2.20e+00  3.58e-01 2.02e+00
...
2.40e+00  8.34e-01 7.10e-01
...
2.60e+00  2.12e-01 1.24e+00
...
2.80e+00  2.20e-01 1.45e+00
...
3.00e+00  2.32e-01 1.62e+00
...
3.20e+00  2.44e-01 1.77e+00
...
3.40e+00  2.57e-01 1.90e+00
...
3.60e+00  2.71e-01 2.00e+00
...
3.80e+00  2.87e-01 2.06e+00
...
4.00e+00  3.06e-01 2.09e+00
...
4.20e+00  3.35e-01 2.07e+00
...
4.40e+00  1.25e+00 9.25e-01
...
4.60e+00  2.40e-01 1.14e+00
...
4.80e+00  2.15e-01 1.37e+00
...
5.00e+00  2.27e-01 1.56e+00
...
5.20e+00  2.39e-01 1.72e+00
...
5.40e+00  2.52e-01 1.85e+00
...
5.60e+00  2.65e-01 1.96e+00
...
5.80e+00  2.80e-01 2.04e+00
...
6.00e+00  2.98e-01 2.09e+00
...
6.20e+00  3.21e-01 2.09e+00
...
6.40e+00  3.84e-01 1.98e+00
...
6.60e+00  5.17e-01 8.74e-01
...
6.80e+00  2.12e-01 1.29e+00
...
7.00e+00  2.22e-01 1.49e+00
...
7.20e+00  2.34e-01 1.66e+00
...
7.40e+00  2.47e-01 1.80e+00
...
7.60e+00  2.60e-01 1.92e+00
...
7.80e+00  2.74e-01 2.01e+00
...
8.00e+00  2.90e-01 2.07e+00
...
8.20e+00  3.11e-01 2.09e+00
...
8.40e+00  3.45e-01 2.05e+00
...
8.60e+00  1.10e+00 6.68e-01
...
8.80e+00  2.17e-01 1.20e+00
...
9.00e+00  2.18e-01 1.41e+00
...
9.20e+00  2.29e-01 1.59e+00
...
9.40e+00  2.42e-01 1.75e+00
...
9.60e+00  2.55e-01 1.88e+00
...
1.00e+01  2.84e-01 2.05e+00

## 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_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model)

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


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



# Iteration 9
## Thoughts
The experiment with increased initial `id_zldk` (iteration_8) also shows oscillations, similar to the previous experiments. This further supports the hypothesis of a limit cycle attractor. The system seems to quickly converge to the oscillatory behavior regardless of the initial state (within the tested range).

Comparing the three experiments (iteration_0, iteration_7, iteration_8), the qualitative behavior (oscillations) is consistent. The period and amplitude appear similar after the initial transient. This suggests that the core oscillatory mechanism is robust.

My current model structure:
Reaction 1: `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))`)
Reaction 2: `id_zldk -> id_fzx2` (rate `k2 * id_zldk`)

This structure represents `id_fzx2` being converted to `id_zldk` in a process activated by `id_zldk` (positive feedback on `id_zldk` production/removal of `id_fzx2`), and `id_zldk` converting back to `id_fzx2` (decay of `id_zldk` and production of `id_fzx2`). This type of feedback loop is known to generate oscillations.

The fact that my simulations haven't produced oscillations yet strongly suggests that the parameter values I've chosen are incorrect. Finding the right parameters is crucial.

Since I cannot perform parameter fitting or visualization directly, I need to rely on the simulation function and the experimental data. I can try to manually adjust parameters and simulate, comparing the output to the experimental data numerically (e.g., comparing peak times, amplitudes, or just the general shape of the curves). However, this is very inefficient.

Is there any other reaction mechanism that could produce such oscillations with only two species?
- Predator-prey (Lotka-Volterra): Requires prey growth and predator decay. My current model has predator decay (`id_zldk -> id_fzx2`) and predator-consuming-prey (`id_fzx2 -> id_zldk` activated by `id_zldk`). The "prey growth" is implicitly handled by the predator decay reaction producing prey.
- Activator-inhibitor systems: Often involve one species activating its own production and inhibiting the production of another, or similar feedback loops.

Let's consider the possibility that the Hill function is on the other reaction, or the activation is by `id_fzx2`.

Option A (current):
R1: `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * Hill(id_zldk)`)
R2: `id_zldk -> id_fzx2` (rate `k2 * id_zldk`)

Option B:
R1: `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2`)
R2: `id_zldk -> id_fzx2` (rate `k2 * id_zldk * Hill(id_fzx2)`) - `id_zldk` conversion to `id_fzx2` activated by `id_fzx2`.

Option C:
R1: `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * Hill(id_fzx2)`) - Autocatalysis of `id_fzx2` conversion.
R2: `id_zldk -> id_fzx2` (rate `k2 * id_zldk`)

Option D:
R1: `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2`)
R2: `id_zldk -> id_fzx2` (rate `k2 * id_zldk * Hill(id_zldk)`) - Autocatalysis of `id_zldk` conversion.

Let's re-examine the data visually (mentally, based on the printed subsets). `id_fzx2` increases, then crashes. The crash happens when `id_fzx2` is relatively high and `id_zldk` is also relatively high (e.g., around Time 1.6, 3.6, 5.6, 7.8 in iteration_0). This supports the idea that the conversion of `id_fzx2` to `id_zldk` is dependent on both species, and perhaps strongly activated when both are high. This aligns with Reaction 1 in Option A or Reaction 2 in the Lotka-Volterra mapping (`id_fzx2 + id_zldk -> ...`).

The increase in `id_fzx2` happens when `id_zldk` is decreasing and `id_fzx2` is low. This suggests a reaction that produces `id_fzx2` and consumes `id_zldk`, and its rate might be proportional to `id_zldk` (as in Reaction 2 of Option A).

So, Option A still seems the most plausible structure:
R1: `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))`)
R2: `id_zldk -> id_fzx2` (rate `k2 * id_zldk`)

I need to find parameters that make this system oscillate and match the experimental data. I will try adjusting the parameters again, focusing on values that might promote the switch-like behavior of the Hill function. A higher `k1` makes the activated conversion faster. A lower `K` means the activation happens at lower concentrations of `id_zldk`. A higher `n` makes the switch sharper. `k2` affects the rate of the reverse reaction and the "recovery" phase.

Let's try increasing `k1` and decreasing `K`. I'll keep `n=2` for now.

## Action

### Code
```python
import libsbml

# Load the model from shared variables
sbml_string = shared_variables.access("current_sbml_model")
sbml_doc = libsbml.readSBMLFromString(sbml_string)
model = sbml_doc.getModel()

# Update parameter values
p_k1 = model.getParameter("k1")
if p_k1:
    p_k1.setValue(5.0) # Increase k1

p_K = model.getParameter("K")
if p_K:
    p_K.setValue(0.5) # Decrease K

p_k2 = model.getParameter("k2")
if p_k2:
    p_k2.setValue(0.1) # Keep k2 the same for now

p_n = model.getParameter("n")
if p_n:
     p_n.setValue(2.0) # Keep n the same for now


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

# Simulate the updated model
sim_data = simulate(updated_sbml)

# Print the head of the simulated data for comparison
print("Simulated Data Head (Adjusted Hill Params):")
print(sim_data.head())

# Print the head of the experimental data for comparison
print("\nExperimental Data Head (iteration_0):")
print(experiment_history['iteration_0'].head())

# Store the updated SBML
shared_variables.add("current_sbml_model", updated_sbml)
```
# Observation

## Code Stdout
Simulated Data Head (Adjusted Hill Params):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.144885  1.605115  0.01
2  0.140000  1.610000  0.02
3  0.135333  1.614667  0.03
4  0.130877  1.619123  0.04

Experimental Data Head (iteration_0):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.167854  1.598189  0.01
2  0.181754  1.598753  0.02
3  0.192594  1.601146  0.03
4  0.201091  1.604921  0.04

## 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_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model)

### 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
Adjusting the parameters (`k1=5.0`, `K=0.5`, `k2=0.1`, `n=2.0`) in the Hill kinetics model still did not produce oscillations. The simulated data shows a monotonic decrease in `id_fzx2` and increase in `id_zldk` initially, which is the opposite of the experimental data's initial trend.

This suggests that either:
1. The model structure is still incorrect.
2. The parameter values are still far from the oscillatory regime.
3. The Hill coefficient `n` needs to be higher for a sharper switch.

Let's reconsider the model structure. The initial experimental data shows `id_fzx2` increasing and `id_zldk` decreasing. My current model's Reaction 2 (`id_zldk -> id_fzx2` with rate `k2 * id_zldk`) does produce `id_fzx2` and consume `id_zldk`, which aligns with this initial phase. However, the overall dynamics are not matched.

What if the stoichiometry is not 1:1? For example, `id_zldk -> 2 * id_fzx2` or `id_fzx2 -> 0.5 * id_zldk`. The problem statement says I don't need to add new species, but it doesn't explicitly forbid non-integer stoichiometry. However, non-integer stoichiometry can sometimes be a way to implicitly represent more complex mechanisms or pools. Let's assume integer stoichiometry for now unless there's strong evidence otherwise.

Let's revisit the possibility of a simple reversible reaction `id_fzx2 <=> id_zldk` but with different kinetics. What if the forward rate (`id_fzx2 -> id_zldk`) is activated by `id_fzx2` (autocatalysis)?
R1: `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * Hill(id_fzx2)`)
R2: `id_zldk -> id_fzx2` (rate `k2 * id_zldk`)

Let's try this model structure.

## Action

### Code
```python
import libsbml

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

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

# Remove existing parameters
while model.getNumParameters() > 0:
    model.removeParameter(0)

# Reaction 1: id_fzx2 -> id_zldk (rate k1 * id_fzx2 * (id_fzx2^n / (K^n + id_fzx2^n))) - Autocatalysis
reaction1 = model.createReaction()
reaction1.setId("reaction_fzx2_to_zldk_autocatalyzed")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_fzx2")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)

product1 = reaction1.createProduct()
product1.setSpecies("id_zldk")
product1.setStoichiometry(1.0)
product1.setConstant(False)

kinetics1 = reaction1.createKineticLaw()
# Need to define parameters k1, K, n
p_k1 = model.createParameter()
p_k1.setId("k1")
p_k1.setValue(1.0) # Arbitrary initial value

p_K = model.createParameter()
p_K.setId("K")
p_K.setValue(0.2) # Arbitrary initial value, near initial id_fzx2 concentration

p_n = model.createParameter()
p_n.setId("n")
p_n.setValue(3.0) # Try a higher Hill coefficient
p_n.setConstant(True)

# Rate law formula: k1 * id_fzx2 * (id_fzx2^n / (K^n + id_fzx2^n))
formula1 = "k1 * id_fzx2 * (pow(id_fzx2, n) / (pow(K, n) + pow(id_fzx2, n)))"
kinetics1.setMath(libsbml.parseL3Formula(formula1))


# Reaction 2: id_zldk -> id_fzx2 (rate k2 * id_zldk)
reaction2 = model.createReaction()
reaction2.setId("reaction_zldk_to_fzx2_decay")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_zldk")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)

product2 = reaction2.createProduct()
product2.setSpecies("id_fzx2")
product2.setStoichiometry(1.0)
product2.setConstant(False)

kinetics2 = reaction2.createKineticLaw()
# Need to define parameter k2
p_k2 = model.createParameter()
p_k2.setId("k2")
p_k2.setValue(0.1) # Arbitrary initial value

formula2 = "k2 * id_zldk"
kinetics2.setMath(libsbml.parseL3Formula(formula2))


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

# Simulate the updated model
sim_data = simulate(updated_sbml)

# Print the head of the simulated data for comparison
print("Simulated Data Head (Autocatalysis Hill Kinetics):")
print(sim_data.head())

# Print the head of the experimental data for comparison
print("\nExperimental Data Head (iteration_0):")
print(experiment_history['iteration_0'].head())

# Store the updated SBML
shared_variables.add("current_sbml_model", updated_sbml)
```
# Observation

## Code Stdout
Simulated Data Head (Autocatalysis Hill Kinetics):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.151149  1.598851  0.01
2  0.152286  1.597714  0.02
3  0.153411  1.596589  0.03
4  0.154525  1.595475  0.04

Experimental Data Head (iteration_0):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.167854  1.598189  0.01
2  0.181754  1.598753  0.02
3  0.192594  1.601146  0.03
4  0.201091  1.604921  0.04

## 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_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model)

### 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 simulation with the autocatalytic Hill kinetics model (`id_fzx2 -> id_zldk` activated by `id_fzx2`, and `id_zldk -> id_fzx2` decay) also failed to produce oscillations with the chosen parameters (`k1=1.0`, `K=0.2`, `n=3.0`, `k2=0.1`). The simulated data shows a slow, monotonic change, similar to previous attempts.

It's becoming clear that finding the correct parameters for these non-linear oscillatory systems by manual trial and error is extremely difficult without visualization or parameter fitting tools.

I have tried two main model structures that are known to produce oscillations with two species:
1. `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * id_zldk`) and `id_zldk -> id_fzx2` (rate `k2 * id_zldk`) - A variation of Lotka-Volterra.
2. `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * Hill(id_zldk)`) and `id_zldk -> id_fzx2` (rate `k2 * id_zldk`) - Conversion activated by product.
3. `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * Hill(id_fzx2)`) and `id_zldk -> id_fzx2` (rate `k2 * id_zldk`) - Conversion activated by reactant (autocatalysis).

None of these have produced oscillations with my arbitrary parameter choices.

Let's reconsider the experimental data and the sharp transitions. The rapid drop in `id_fzx2` and rise in `id_zldk` suggests a fast reaction that is triggered. This could be represented by a reaction with a high maximum rate and a strong dependence on the concentrations.

What if the system involves a reversible reaction, but one direction is strongly activated?
`id_fzx2 <=> id_zldk`
Forward: `id_fzx2 -> id_zldk`
Reverse: `id_zldk -> id_fzx2`

Let's try the reversible reaction with mass action kinetics again, but consider the possibility that the parameters need to be very specific.
R1: `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2`)
R2: `id_zldk -> id_fzx2` (rate `k2 * id_zldk`)

This simple reversible reaction does not produce limit cycle oscillations; it approaches a stable steady state. So this structure is likely wrong.

Let's go back to the structures that *can* oscillate. The Lotka-Volterra-like structure (`id_fzx2 -> id_zldk` rate `k1*fzx2*zldk`, `id_zldk -> id_fzx2` rate `k2*zldk`) is a strong candidate. The issue is the parameters.

Let's try one more parameter adjustment for the Lotka-Volterra-like model (from Iteration 4/5).
Model:
Reaction 1: `id_fzx2` -> `id_zldk` (rate `k1 * id_fzx2 * id_zldk`)
Reaction 2: `id_zldk` -> `id_fzx2` (rate `k2 * id_zldk`)

Let's try increasing `k1` significantly and keeping `k2` relatively low. This would make the conversion of `id_fzx2` to `id_zldk` very sensitive to the presence of both species, potentially driving oscillations.

## Action

### Code
```python
import libsbml

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

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

# Remove existing parameters
while model.getNumParameters() > 0:
    model.removeParameter(0)

# Reaction 1: id_fzx2 -> id_zldk (rate k1 * id_fzx2 * id_zldk)
reaction1 = model.createReaction()
reaction1.setId("reaction_fzx2_consumption")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_fzx2")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)

product1 = reaction1.createProduct()
product1.setSpecies("id_zldk")
product1.setStoichiometry(1.0)
product1.setConstant(False)

kinetics1 = reaction1.createKineticLaw()
kinetics1.setMath(libsbml.parseL3Formula("k1 * id_fzx2 * id_zldk"))

p1 = model.createParameter()
p1.setId("k1")
p1.setValue(5.0) # Try a higher value

# Reaction 2: id_zldk -> id_fzx2 (rate k2 * id_zldk)
reaction2 = model.createReaction()
reaction2.setId("reaction_zldk_decay")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_zldk")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)

product2 = reaction2.createProduct()
product2.setSpecies("id_fzx2")
product2.setStoichiometry(1.0)
product2.setConstant(False)

kinetics2 = reaction2.createKineticLaw()
kinetics2.setMath(libsbml.parseL3Formula("k2 * id_zldk"))

p2 = model.createParameter()
p2.setId("k2")
p2.setValue(0.2) # Keep relatively low


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

# Simulate the updated model
sim_data = simulate(updated_sbml)

# Print the head of the simulated data for comparison
print("Simulated Data Head (LV-like, Adjusted Params):")
print(sim_data.head())

# Print the head of the experimental data for comparison
print("\nExperimental Data Head (iteration_0):")
print(experiment_history['iteration_0'].head())

# Store the updated SBML
shared_variables.add("current_sbml_model", updated_sbml)
```
# Observation

## Code Stdout
Simulated Data Head (LV-like, Adjusted Params):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.141521  1.608479  0.01
2  0.133657  1.616343  0.02
3  0.126369  1.623631  0.03
4  0.119621  1.630379  0.04

Experimental Data Head (iteration_0):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.167854  1.598189  0.01
2  0.181754  1.598753  0.02
3  0.192594  1.601146  0.03
4  0.201091  1.604921  0.04

## 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_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model)

### 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
Another attempt with the Lotka-Volterra-like model (`id_fzx2 -> id_zldk` rate `k1*fzx2*zldk`, `id_zldk -> id_fzx2` rate `k2*zldk`) and adjusted parameters (`k1=5.0`, `k2=0.2`) still did not produce oscillations. The simulated data shows a monotonic change, decreasing `id_fzx2` and increasing `id_zldk` initially.

I have now tried the most common two-species oscillatory motifs (Lotka-Volterra variation, and feedback with Hill kinetics) and have been unable to find parameters that produce oscillations matching the experimental data.

Given the limited number of iterations left and the difficulty of parameter tuning without visualization or fitting, I need to consider if I am missing a fundamental aspect of the mechanism or if the parameters are simply in a very narrow range.

Let's look closely at the experimental data again, particularly the sharp transitions. The concentration of `id_fzx2` builds up, then rapidly drops. The concentration of `id_zldk` decreases initially, then increases, following the drop in `id_fzx2`. This suggests that when `id_fzx2` reaches a certain level (or perhaps when `id_zldk` is low), a process that consumes `id_fzx2` and produces `id_zldk` is strongly activated.

The Hill kinetics model with activation by `id_zldk` (Option A from Iteration 9) seems conceptually aligned with this:
R1: `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))`) - Conversion activated by `id_zldk`.
R2: `id_zldk -> id_fzx2` (rate `k2 * id_zldk`) - Decay of `id_zldk` producing `id_fzx2`.

Let's think about the parameter roles in this model:
- `k1`: Maximum rate of the activated conversion. Higher `k1` means faster conversion when activated.
- `K`: The concentration of `id_zldk` at which the rate of R1 is half-maximal. Lower `K` means activation happens at lower `id_zldk`.
- `n`: Hill coefficient, determines the steepness of the activation curve. Higher `n` means a sharper switch.
- `k2`: Rate constant for the decay of `id_zldk` and production of `id_fzx2`. Higher `k2` means faster recovery of `id_fzx2`.

For oscillations to occur, there needs to be a balance between the rates. The system needs to build up `id_fzx2` (driven by R2 when `id_zldk` is present), then rapidly convert it to `id_zldk` (driven by R1 when `id_zldk` reaches a sufficient level), then `id_zldk` needs to decay (R2) allowing `id_fzx2` to build up again.

Let's try adjusting parameters in the Hill kinetics model again, focusing on making the activation strong and the decay rate reasonable. I'll increase `k1` and `n`, and try a `K` value that is within the range of observed `id_zldk` concentrations where the switch seems to occur.

Looking at the data, the sharp drop in `id_fzx2` seems to happen when `id_zldk` is above ~1.5-1.8. Let's try setting `K` around this value. Let's also increase `n` to make the switch sharper.

## Action

### Code
```python
import libsbml

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

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

# Remove existing parameters
while model.getNumParameters() > 0:
    model.removeParameter(0)

# Reaction 1: id_fzx2 -> id_zldk (rate k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))) - Activation by id_zldk
reaction1 = model.createReaction()
reaction1.setId("reaction_fzx2_to_zldk_activated")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_fzx2")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)

product1 = reaction1.createProduct()
product1.setSpecies("id_zldk")
product1.setStoichiometry(1.0)
product1.setConstant(False)

kinetics1 = reaction1.createKineticLaw()
# Define parameters k1, K, n
p_k1 = model.createParameter()
p_k1.setId("k1")
p_k1.setValue(10.0) # Increase k1

p_K = model.createParameter()
p_K.setId("K")
p_K.setValue(1.5) # Set K around observed switch point

p_n = model.createParameter()
p_n.setId("n")
p_n.setValue(4.0) # Increase Hill coefficient for sharper switch
p_n.setConstant(True)

# Rate law formula: k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))
formula1 = "k1 * id_fzx2 * (pow(id_zldk, n) / (pow(K, n) + pow(id_zldk, n)))"
kinetics1.setMath(libsbml.parseL3Formula(formula1))


# Reaction 2: id_zldk -> id_fzx2 (rate k2 * id_zldk) - Decay of id_zldk
reaction2 = model.createReaction()
reaction2.setId("reaction_zldk_to_fzx2_decay")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_zldk")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)

product2 = reaction2.createProduct()
product2.setSpecies("id_fzx2")
product2.setStoichiometry(1.0)
product2.setConstant(False)

kinetics2 = reaction2.createKineticLaw()
# Define parameter k2
p_k2 = model.createParameter()
p_k2.setId("k2")
p_k2.setValue(0.2) # Adjust k2 slightly


formula2 = "k2 * id_zldk"
kinetics2.setMath(libsbml.parseL3Formula(formula2))


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

# Simulate the updated model
sim_data = simulate(updated_sbml)

# Print the head of the simulated data for comparison
print("Simulated Data Head (Hill Kinetics, Adjusted Params):")
print(sim_data.head())

# Print the head of the experimental data for comparison
print("\nExperimental Data Head (iteration_0):")
print(experiment_history['iteration_0'].head())

# Store the updated SBML
shared_variables.add("current_sbml_model", updated_sbml)
```
# Observation

## Code Stdout
Simulated Data Head (Hill Kinetics, Adjusted Params):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.144865  1.605135  0.01
2  0.139980  1.610020  0.02
3  0.135335  1.614665  0.03
4  0.130922  1.619078  0.04

Experimental Data Head (iteration_0):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.167854  1.598189  0.01
2  0.181754  1.598753  0.02
3  0.192594  1.601146  0.03
4  0.201091  1.604921  0.04

## 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_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model)

### 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
Despite adjusting parameters in the Hill kinetics model (`id_fzx2 -> id_zldk` activated by `id_zldk`, and `id_zldk -> id_fzx2` decay), I am still not observing oscillations in the simulated data. The initial trend in the simulation (decreasing `id_fzx2`, increasing `id_zldk`) is the opposite of the experimental data (increasing `id_fzx2`, decreasing `id_zldk`).

This persistent mismatch in the initial trend suggests that the model structure might still be incorrect, specifically regarding which reaction is dominant at low concentrations or how `id_fzx2` is initially increasing.

Let's reconsider the initial phase of the experimental data (iteration_0): `id_fzx2` increases from 0.15, and `id_zldk` decreases from 1.6. This implies a net reaction that consumes `id_zldk` and produces `id_fzx2`. My current model has `id_zldk -> id_fzx2` (rate `k2 * id_zldk`) which does this. It also has `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * Hill(id_zldk)`). For `id_fzx2` to increase initially, the rate of `id_zldk -> id_fzx2` must be greater than the rate of `id_fzx2 -> id_zldk`.

Rate of R2 = `k2 * 1.6`
Rate of R1 = `k1 * 0.15 * (1.6^n / (K^n + 1.6^n))`

With `k1=10`, `K=1.5`, `n=4`, `k2=0.2`:
Rate of R2 = `0.2 * 1.6 = 0.32`
Rate of R1 = `10 * 0.15 * (1.6^4 / (1.5^4 + 1.6^4)) = 1.5 * (6.55 / (5.06 + 6.55)) = 1.5 * (6.55 / 11.61) ≈ 1.5 * 0.56 ≈ 0.84`

In this case, Rate of R1 (0.84) is greater than Rate of R2 (0.32), leading to a net decrease in `id_fzx2` and increase in `id_zldk` initially, which contradicts the data.

To match the initial trend, I need Rate of R2 > Rate of R1 at the initial conditions.
`k2 * 1.6 > k1 * 0.15 * (1.6^n / (K^n + 1.6^n))`

This means I need a higher `k2` relative to `k1`, or a `K` value that makes the Hill term very small at `id_zldk = 1.6`. A `K` value significantly higher than 1.6 would make the Hill term small.

Let's try increasing `k2` and potentially adjusting `K` again.

Let's try `k2 = 1.0` and keep `k1=10`, `n=4`. Let's try a higher `K` as well, say `K=3.0`.

## Action

### Code
```python
import libsbml

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

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

# Remove existing parameters
while model.getNumParameters() > 0:
    model.removeParameter(0)

# Reaction 1: id_fzx2 -> id_zldk (rate k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))) - Activation by id_zldk
reaction1 = model.createReaction()
reaction1.setId("reaction_fzx2_to_zldk_activated")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_fzx2")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)

product1 = reaction1.createProduct()
product1.setSpecies("id_zldk")
product1.setStoichiometry(1.0)
product1.setConstant(False)

kinetics1 = reaction1.createKineticLaw()
# Define parameters k1, K, n
p_k1 = model.createParameter()
p_k1.setId("k1")
p_k1.setValue(10.0) # Keep k1 high

p_K = model.createParameter()
p_K.setId("K")
p_K.setValue(3.0) # Increase K

p_n = model.createParameter()
p_n.setId("n")
p_n.setValue(4.0) # Keep n high
p_n.setConstant(True)

# Rate law formula: k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))
formula1 = "k1 * id_fzx2 * (pow(id_zldk, n) / (pow(K, n) + pow(id_zldk, n)))"
kinetics1.setMath(libsbml.parseL3Formula(formula1))


# Reaction 2: id_zldk -> id_fzx2 (rate k2 * id_zldk) - Decay of id_zldk
reaction2 = model.createReaction()
reaction2.setId("reaction_zldk_to_fzx2_decay")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_zldk")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)

product2 = reaction2.createProduct()
product2.setSpecies("id_fzx2")
product2.setStoichiometry(1.0)
product2.setConstant(False)

kinetics2 = reaction2.createKineticLaw()
# Define parameter k2
p_k2 = model.createParameter()
p_k2.setId("k2")
p_k2.setValue(1.0) # Increase k2


formula2 = "k2 * id_zldk"
kinetics2.setMath(libsbml.parseL3Formula(formula2))


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

# Simulate the updated model
sim_data = simulate(updated_sbml)

# Print the head of the simulated data for comparison
print("Simulated Data Head (Hill Kinetics, Adjusted Params 2):")
print(sim_data.head())

# Print the head of the experimental data for comparison
print("\nExperimental Data Head (iteration_0):")
print(experiment_history['iteration_0'].head())

# Store the updated SBML
shared_variables.add("current_sbml_model", updated_sbml)
```
# Observation

## Code Stdout
Simulated Data Head (Hill Kinetics, Adjusted Params 2):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.164768  1.585232  0.01
2  0.179325  1.570675  0.02
3  0.193678  1.556322  0.03
4  0.207838  1.542162  0.04

Experimental Data Head (iteration_0):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.167854  1.598189  0.01
2  0.181754  1.598753  0.02
3  0.192594  1.601146  0.03
4  0.201091  1.604921  0.04

## 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_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model)

### 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
Success! The simulation with the Hill kinetics model (`id_fzx2 -> id_zldk` activated by `id_zldk`, and `id_zldk -> id_fzx2` decay) and the adjusted parameters (`k1=10.0`, `K=3.0`, `n=4.0`, `k2=1.0`) finally shows an initial trend that matches the experimental data: `id_fzx2` increases and `id_zldk` decreases.

Let's look beyond the head of the data. Does it oscillate? I need to examine the full simulated data. Since I can't plot, I'll look for changes in direction in the concentration values over time.

I will access the full simulated data and check if the concentrations reverse their initial trend and show oscillatory behavior.

## Action

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

# Access the simulated data from the last run
sim_data = simulate(shared_variables.access("current_sbml_model"))

# Print the first 20 rows to see if the trend reverses
print("Simulated Data (first 20 rows):")
print(sim_data.head(20))

# Check for changes in direction (simple check: look for non-monotonic behavior)
# Check id_fzx2: does it increase then decrease?
fzx2_diff = sim_data['id_fzx2'].diff()
print("\nid_fzx2 concentration changes (first 20):")
print(fzx2_diff.head(20))

# Check id_zldk: does it decrease then increase?
zldk_diff = sim_data['id_zldk'].diff()
print("\nid_zldk concentration changes (first 20):")
print(zldk_diff.head(20))

# Check for a later point in time to see if oscillations occur
print("\nSimulated Data (around time 1.5 - 2.5):")
print(sim_data[(sim_data['Time'] >= 1.5) & (sim_data['Time'] <= 2.5)])

print("\nExperimental Data (around time 1.5 - 2.5, iteration_0):")
print(experiment_history['iteration_0'][(experiment_history['iteration_0']['Time'] >= 1.5) & (experiment_history['iteration_0']['Time'] <= 2.5)])
```
# Observation

## Code Stdout
Simulated Data (first 20 rows):
     id_fzx2   id_zldk  Time
0   0.150000  1.600000  0.00
1   0.164768  1.585232  0.01
2   0.179325  1.570675  0.02
3   0.193678  1.556322  0.03
4   0.207838  1.542162  0.04
5   0.221811  1.528189  0.05
6   0.235605  1.514395  0.06
7   0.249228  1.500772  0.07
8   0.262685  1.487315  0.08
9   0.275983  1.474017  0.09
10  0.289127  1.460873  0.10
11  0.302123  1.447877  0.11
12  0.314976  1.435024  0.12
13  0.327691  1.422309  0.13
14  0.340272  1.409728  0.14
15  0.352723  1.397277  0.15
16  0.365048  1.384952  0.16
17  0.377251  1.372749  0.17
18  0.389335  1.360665  0.18
19  0.401304  1.348696  0.19

id_fzx2 concentration changes (first 20):
0          NaN
1     0.014768
2     0.014557
3     0.014354
4     0.014159
5     0.013973
6     0.013794
7     0.013622
8     0.013457
9     0.013298
10    0.013144
11    0.012996
12    0.012853
13    0.012715
14    0.012581
15    0.012451
16    0.012325
17    0.012203
18    0.012084
19    0.011969
Name: id_fzx2, dtype: float64

id_zldk concentration changes (first 20):
0          NaN
1    -0.014768
2    -0.014557
3    -0.014354
4    -0.014159
5    -0.013973
6    -0.013794
7    -0.013622
8    -0.013457
9    -0.013298
10   -0.013144
11   -0.012996
12   -0.012853
13   -0.012715
14   -0.012581
15   -0.012451
16   -0.012325
17   -0.012203
18   -0.012084
19   -0.011969
Name: id_zldk, dtype: float64

Simulated Data (around time 1.5 - 2.5):
      id_fzx2   id_zldk  Time
150  1.357313  0.392687  1.50
151  1.361182  0.388818  1.51
152  1.365013  0.384987  1.52
153  1.368808  0.381192  1.53
154  1.372566  0.377434  1.54
..        ...       ...   ...
246  1.599130  0.150870  2.46
247  1.600630  0.149370  2.47
248  1.602116  0.147884  2.48
249  1.603586  0.146414  2.49
250  1.605042  0.144958  2.50

[101 rows x 3 columns]

Experimental Data (around time 1.5 - 2.5, iteration_0):
      id_fzx2   id_zldk  Time
150  1.282021  0.686775  1.50
151  1.205269  0.671041  1.51
152  1.123887  0.667939  1.52
153  1.044068  0.671353  1.53
154  0.966850  0.680020  1.54
..        ...       ...   ...
246  0.250418  1.841003  2.46
247  0.251069  1.847251  2.47
248  0.251721  1.853432  2.48
249  0.252376  1.859546  2.49
250  0.253033  1.865592  2.50

[101 rows x 3 columns]

## 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_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model)

### 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 simulation with the latest parameters (`k1=10.0`, `K=3.0`, `n=4.0`, `k2=1.0`) for the Hill kinetics model (`id_fzx2 -> id_zldk` activated by `id_zldk`, and `id_zldk -> id_fzx2` decay) successfully reproduces the initial trend of increasing `id_fzx2` and decreasing `id_zldk`.

However, looking at the data around time 1.5-2.5, the simulated data shows `id_fzx2` continuing to increase and `id_zldk` continuing to decrease, albeit at a slower rate. It does not show the sharp reversal and oscillatory behavior seen in the experimental data around the same time points (where `id_fzx2` crashes and `id_zldk` increases).

This means the model structure is likely correct, but the parameters are still not in the range that produces limit cycle oscillations with the correct period and amplitude. The system is currently approaching a stable steady state instead of oscillating.

I need to adjust the parameters further to push the system into the oscillatory regime and match the observed dynamics. The current parameters make the `id_zldk -> id_fzx2` reaction too dominant or the `id_fzx2 -> id_zldk` reaction not strong enough or not activated sharply enough at the right concentrations to cause the reversal.

Let's revisit the parameters:
- `k1`: Rate of activated conversion `id_fzx2 -> id_zldk`. Needs to be high enough to cause a rapid drop in `id_fzx2`.
- `K`: Half-saturation constant for `id_zldk` activation. Determines where the switch happens. The experimental data suggests the switch happens when `id_zldk` is around 1.5-1.8. My current `K=3.0` might be too high, meaning the activation is weak at `id_zldk=1.6`.
- `n`: Hill coefficient. Higher `n` makes the switch sharper. `n=4` is reasonably sharp.
- `k2`: Rate of `id_zldk -> id_fzx2`. This drives the initial increase in `id_fzx2` and decrease in `id_zldk`. If `k2` is too high relative to `k1` and the Hill term, the system might just settle to a steady state where `id_fzx2` is high and `id_zldk` is low.

Let's try decreasing `K` back towards the observed switch point and potentially increasing `k1` further. I'll keep `n=4` and `k2=1.0` for now.

Let's try `K=1.8` (closer to the observed switch) and `k1=20.0`.

## Action

### Code
```python
import libsbml

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

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

# Remove existing parameters
while model.getNumParameters() > 0:
    model.removeParameter(0)

# Reaction 1: id_fzx2 -> id_zldk (rate k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))) - Activation by id_zldk
reaction1 = model.createReaction()
reaction1.setId("reaction_fzx2_to_zldk_activated")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_fzx2")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)

product1 = reaction1.createProduct()
product1.setSpecies("id_zldk")
product1.setStoichiometry(1.0)
product1.setConstant(False)

kinetics1 = reaction1.createKineticLaw()
# Define parameters k1, K, n
p_k1 = model.createParameter()
p_k1.setId("k1")
p_k1.setValue(20.0) # Increase k1 further

p_K = model.createParameter()
p_K.setId("K")
p_K.setValue(1.8) # Decrease K, closer to observed switch

p_n = model.createParameter()
p_n.setId("n")
p_n.setValue(4.0) # Keep n high
p_n.setConstant(True)

# Rate law formula: k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))
formula1 = "k1 * id_fzx2 * (pow(id_zldk, n) / (pow(K, n) + pow(id_zldk, n)))"
kinetics1.setMath(libsbml.parseL3Formula(formula1))


# Reaction 2: id_zldk -> id_fzx2 (rate k2 * id_zldk) - Decay of id_zldk
reaction2 = model.createReaction()
reaction2.setId("reaction_zldk_to_fzx2_decay")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_zldk")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)

product2 = reaction2.createProduct()
product2.setSpecies("id_fzx2")
product2.setStoichiometry(1.0)
product2.setConstant(False)

kinetics2 = reaction2.createKineticLaw()
# Define parameter k2
p_k2 = model.createParameter()
p_k2.setId("k2")
p_k2.setValue(1.0) # Keep k2


formula2 = "k2 * id_zldk"
kinetics2.setMath(libsbml.parseL3Formula(formula2))


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

# Simulate the updated model
sim_data = simulate(updated_sbml)

# Print the head of the simulated data for comparison
print("Simulated Data Head (Hill Kinetics, Adjusted Params 3):")
print(sim_data.head())

# Print the head of the experimental data for comparison
print("\nExperimental Data Head (iteration_0):")
print(experiment_history['iteration_0'].head())

# Store the updated SBML
shared_variables.add("current_sbml_model", updated_sbml)
```
# Observation

## Code Stdout
Simulated Data Head (Hill Kinetics, Adjusted Params 3):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.154319  1.595681  0.01
2  0.158355  1.591645  0.02
3  0.162127  1.587873  0.03
4  0.165658  1.584342  0.04

Experimental Data Head (iteration_0):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.167854  1.598189  0.01
2  0.181754  1.598753  0.02
3  0.192594  1.601146  0.03
4  0.201091  1.604921  0.04

## 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_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model)

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


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



# Iteration 16
## Thoughts
The simulation with the latest parameters (`k1=20.0`, `K=1.8`, `n=4.0`, `k2=1.0`) for the Hill kinetics model still shows the initial trend of increasing `id_fzx2` and decreasing `id_zldk`, which matches the experimental data's initial phase. However, I need to check if it actually oscillates over a longer time frame.

Let's examine the simulated data at later time points again to see if the concentrations reverse direction and exhibit oscillatory behavior.

## Action

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

# Access the simulated data from the last run
sim_data = simulate(shared_variables.access("current_sbml_model"))

# Print data around the time points where oscillations are expected based on experimental data
print("\nSimulated Data (around time 1.5 - 2.5):")
print(sim_data[(sim_data['Time'] >= 1.5) & (sim_data['Time'] <= 2.5)])

print("\nExperimental Data (around time 1.5 - 2.5, iteration_0):")
print(experiment_history['iteration_0'][(experiment_history['iteration_0']['Time'] >= 1.5) & (experiment_history['iteration_0']['Time'] <= 2.5)])

print("\nSimulated Data (around time 3.5 - 4.5):")
print(sim_data[(sim_data['Time'] >= 3.5) & (sim_data['Time'] <= 4.5)])

print("\nExperimental Data (around time 3.5 - 4.5, iteration_0):")
print(experiment_history['iteration_0'][(experiment_history['iteration_0']['Time'] >= 3.5) & (experiment_history['iteration_0']['Time'] <= 4.5)])
```
# Observation

## Code Stdout

Simulated Data (around time 1.5 - 2.5):
      id_fzx2   id_zldk  Time
150  0.223980  1.526020  1.50
151  0.223981  1.526019  1.51
152  0.223983  1.526017  1.52
153  0.223984  1.526016  1.53
154  0.223985  1.526015  1.54
..        ...       ...   ...
246  0.224007  1.525993  2.46
247  0.224007  1.525993  2.47
248  0.224007  1.525993  2.48
249  0.224007  1.525993  2.49
250  0.224007  1.525993  2.50

[101 rows x 3 columns]

Experimental Data (around time 1.5 - 2.5, iteration_0):
      id_fzx2   id_zldk  Time
150  1.282021  0.686775  1.50
151  1.205269  0.671041  1.51
152  1.123887  0.667939  1.52
153  1.044068  0.671353  1.53
154  0.966850  0.680020  1.54
..        ...       ...   ...
246  0.250418  1.841003  2.46
247  0.251069  1.847251  2.47
248  0.251721  1.853432  2.48
249  0.252376  1.859546  2.49
250  0.253033  1.865592  2.50

[101 rows x 3 columns]

Simulated Data (around time 3.5 - 4.5):
      id_fzx2   id_zldk  Time
350  0.224007  1.525993  3.50
351  0.224007  1.525993  3.51
352  0.224007  1.525993  3.52
353  0.224007  1.525993  3.53
354  0.224007  1.525993  3.54
..        ...       ...   ...
446  0.224007  1.525993  4.46
447  0.224007  1.525993  4.47
448  0.224007  1.525993  4.48
449  0.224007  1.525993  4.49
450  0.224007  1.525993  4.50

[101 rows x 3 columns]

Experimental Data (around time 3.5 - 4.5, iteration_0):
      id_fzx2   id_zldk  Time
350  0.408564  1.934993  3.50
351  0.427827  1.905943  3.51
352  0.457474  1.864123  3.52
353  0.510141  1.795339  3.53
354  0.630453  1.650939  3.54
..        ...       ...   ...
446  0.245385  1.789679  4.46
447  0.246020  1.796447  4.47
448  0.246657  1.803149  4.48
449  0.247296  1.809785  4.49
450  0.247936  1.816356  4.50

[101 rows x 3 columns]

## 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_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model)

### 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 simulation results from the Hill kinetics model with parameters `k1=20.0`, `K=1.8`, `n=4.0`, `k2=1.0` show that the system quickly settles to a stable steady state around `id_fzx2` ≈ 0.224 and `id_zldk` ≈ 1.526. It does not exhibit the oscillations seen in the experimental data.

While the initial trend matches, the parameters are not in the oscillatory regime. I have limited iterations left and manual parameter tuning is proving ineffective.

Let's reconsider the model structure one last time. The sharp, periodic drops in `id_fzx2` and rises in `id_zldk` are the defining features. This strongly suggests a reaction that consumes `id_fzx2` and produces `id_zldk`, and this reaction is highly sensitive to the concentrations, acting like a switch. The Hill kinetics model with activation by `id_zldk` (or `id_fzx2`) is designed to capture this.

Given that this model structure is theoretically capable of producing limit cycles, the problem must lie in the parameter values. Without better tools for parameter estimation or visualization, I am struggling to find the correct values.

However, I have observed the system's behavior under three different initial conditions (iteration_0, iteration_7, iteration_8). All show similar oscillations after a transient. This robustness is a strong indicator of a limit cycle.

Let's assume the Hill kinetics model structure is correct:
Reaction 1: `id_fzx2 -> id_zldk` (rate `k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))`)
Reaction 2: `id_zldk -> id_fzx2` (rate `k2 * id_zldk`)

I need to find parameters (`k1`, `k2`, `K`, `n`) that make this model oscillate and roughly match the period and amplitude of the experimental data.

Let's try one more set of parameter adjustments, aiming for values that might push it towards oscillation based on general knowledge of these systems. Oscillations often occur when the feedback is strong and the decay/recovery rates are balanced appropriately.

Let's try increasing `k1` further, decreasing `k2` slightly, keeping `n` high, and adjusting `K` again.

Let's try `k1=50.0`, `k2=0.5`, `K=1.0`, `n=4.0`. This increases the maximum rate of the activated reaction, decreases the decay rate of `id_zldk`, and sets the activation threshold `K` lower.

## Action

### Code
```python
import libsbml

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

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

# Remove existing parameters
while model.getNumParameters() > 0:
    model.removeParameter(0)

# Reaction 1: id_fzx2 -> id_zldk (rate k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))) - Activation by id_zldk
reaction1 = model.createReaction()
reaction1.setId("reaction_fzx2_to_zldk_activated")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_fzx2")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)

product1 = reaction1.createProduct()
product1.setSpecies("id_zldk")
product1.setStoichiometry(1.0)
product1.setConstant(False)

kinetics1 = reaction1.createKineticLaw()
# Define parameters k1, K, n
p_k1 = model.createParameter()
p_k1.setId("k1")
p_k1.setValue(50.0) # Increase k1 significantly

p_K = model.createParameter()
p_K.setId("K")
p_K.setValue(1.0) # Adjust K

p_n = model.createParameter()
p_n.setId("n")
p_n.setValue(4.0) # Keep n high
p_n.setConstant(True)

# Rate law formula: k1 * id_fzx2 * (pow(id_zldk, n) / (pow(K, n) + pow(id_zldk, n)))
formula1 = "k1 * id_fzx2 * (pow(id_zldk, n) / (pow(K, n) + pow(id_zldk, n)))"
kinetics1.setMath(libsbml.parseL3Formula(formula1))


# Reaction 2: id_zldk -> id_fzx2 (rate k2 * id_zldk) - Decay of id_zldk
reaction2 = model.createReaction()
reaction2.setId("reaction_zldk_to_fzx2_decay")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_zldk")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)

product2 = reaction2.createProduct()
product2.setSpecies("id_fzx2")
product2.setStoichiometry(1.0)
product2.setConstant(False)

kinetics2 = reaction2.createKineticLaw()
# Define parameter k2
p_k2 = model.createParameter()
p_k2.setId("k2")
p_k2.setValue(0.5) # Decrease k2


formula2 = "k2 * id_zldk"
kinetics2.setMath(libsbml.parseL3Formula(formula2))


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

# Simulate the updated model
sim_data = simulate(updated_sbml)

# Print the head of the simulated data for comparison
print("Simulated Data Head (Hill Kinetics, Adjusted Params 4):")
print(sim_data.head())

# Print the head of the experimental data for comparison
print("\nExperimental Data Head (iteration_0):")
print(experiment_history['iteration_0'].head())

# Store the updated SBML
shared_variables.add("current_sbml_model", updated_sbml)
```
# Observation

## Code Stdout
Simulated Data Head (Hill Kinetics, Adjusted Params 4):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.103456  1.646544  0.01
2  0.073209  1.676791  0.02
3  0.053721  1.696279  0.03
4  0.041229  1.708771  0.04

Experimental Data Head (iteration_0):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.167854  1.598189  0.01
2  0.181754  1.598753  0.02
3  0.192594  1.601146  0.03
4  0.201091  1.604921  0.04

## 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_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model)

### 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
The simulation with the latest parameters (`k1=50.0`, `K=1.0`, `n=4.0`, `k2=0.5`) for the Hill kinetics model shows an initial trend where `id_fzx2` decreases and `id_zldk` increases. This is the opposite of the experimental data's initial trend. This indicates that the rate of Reaction 1 (`id_fzx2 -> id_zldk`) is too high relative to Reaction 2 (`id_zldk -> id_fzx2`) at the initial conditions.

Rate of R1 = `k1 * 0.15 * (1.6^n / (K^n + 1.6^n))`
Rate of R2 = `k2 * 1.6`

With `k1=50`, `K=1.0`, `n=4`, `k2=0.5`:
Rate of R1 = `50 * 0.15 * (1.6^4 / (1.0^4 + 1.6^4)) = 7.5 * (6.55 / (1 + 6.55)) = 7.5 * (6.55 / 7.55) ≈ 7.5 * 0.867 ≈ 6.5`
Rate of R2 = `0.5 * 1.6 = 0.8`

Rate of R1 (6.5) is much greater than Rate of R2 (0.8), causing the initial decrease in `id_fzx2`.

To match the initial trend, I need Rate of R2 > Rate of R1 at the initial conditions.
`k2 * 1.6 > k1 * 0.15 * (1.6^n / (K^n + 1.6^n))`

This requires increasing `k2` relative to `k1`, or increasing `K` significantly so the Hill term is small at `id_zldk = 1.6`.

I am running out of iterations. I am confident that the Hill kinetics model structure (`id_fzx2 -> id_zldk` activated by `id_zldk`, and `id_zldk -> id_fzx2` decay) is the correct one, as it is a common motif for generating limit cycle oscillations and aligns with the observed sharp transitions and robust oscillations under different initial conditions. The challenge is finding the precise parameter values.

Given the constraints, I will make one final attempt to set parameters that balance the initial trend and hopefully push the system into oscillation. I need `k2` to be high enough to drive the initial `id_fzx2` increase, and `k1` and `K` to be set such that the activated reaction becomes dominant later, causing the crash.

Let's try `k2=1.5`, `k1=20.0`, `K=2.0`, `n=4.0`. This increases `k2` and adjusts `K` to be slightly higher than the initial `id_zldk`.

## Action

### Code
```python
import libsbml

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

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

# Remove existing parameters
while model.getNumParameters() > 0:
    model.removeParameter(0)

# Reaction 1: id_fzx2 -> id_zldk (rate k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))) - Activation by id_zldk
reaction1 = model.createReaction()
reaction1.setId("reaction_fzx2_to_zldk_activated")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_fzx2")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)

product1 = reaction1.createProduct()
product1.setSpecies("id_zldk")
product1.setStoichiometry(1.0)
product1.setConstant(False)

kinetics1 = reaction1.createKineticLaw()
# Define parameters k1, K, n
p_k1 = model.createParameter()
p_k1.setId("k1")
p_k1.setValue(20.0) # Adjust k1

p_K = model.createParameter()
p_K.setId("K")
p_K.setValue(2.0) # Adjust K

p_n = model.createParameter()
p_n.setId("n")
p_n.setValue(4.0) # Keep n high
p_n.setConstant(True)

# Rate law formula: k1 * id_fzx2 * (pow(id_zldk, n) / (pow(K, n) + pow(id_zldk, n)))
formula1 = "k1 * id_fzx2 * (pow(id_zldk, n) / (pow(K, n) + pow(id_zldk, n)))"
kinetics1.setMath(libsbml.parseL3Formula(formula1))


# Reaction 2: id_zldk -> id_fzx2 (rate k2 * id_zldk) - Decay of id_zldk
reaction2 = model.createReaction()
reaction2.setId("reaction_zldk_to_fzx2_decay")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_zldk")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)

product2 = reaction2.createProduct()
product2.setSpecies("id_fzx2")
product2.setStoichiometry(1.0)
product2.setConstant(False)

kinetics2 = reaction2.createKineticLaw()
# Define parameter k2
p_k2 = model.createParameter()
p_k2.setId("k2")
p_k2.setValue(1.5) # Increase k2


formula2 = "k2 * id_zldk"
kinetics2.setMath(libsbml.parseL3Formula(formula2))


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

# Simulate the updated model
sim_data = simulate(updated_sbml)

# Print the head of the simulated data for comparison
print("Simulated Data Head (Hill Kinetics, Adjusted Params 5):")
print(sim_data.head())

# Print the head of the experimental data for comparison
print("\nExperimental Data Head (iteration_0):")
print(experiment_history['iteration_0'].head())

# Store the updated SBML
shared_variables.add("current_sbml_model", updated_sbml)
```
# Observation

## Code Stdout
Simulated Data Head (Hill Kinetics, Adjusted Params 5):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.164858  1.585142  0.01
2  0.178925  1.571075  0.02
3  0.192278  1.557722  0.03
4  0.204988  1.545012  0.04

Experimental Data Head (iteration_0):
    id_fzx2   id_zldk  Time
0  0.150000  1.600000  0.00
1  0.167854  1.598189  0.01
2  0.181754  1.598753  0.02
3  0.192594  1.601146  0.03
4  0.201091  1.604921  0.04

## 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_7, iteration_8)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model)

### 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 simulation with the latest parameters (`k1=20.0`, `K=2.0`, `n=4.0`, `k2=1.5`) for the Hill kinetics model shows an initial trend that matches the experimental data (increasing `id_fzx2`, decreasing `id_zldk`). This is promising.

With only two iterations left, I need to determine if this model with these parameters produces oscillations and if they are reasonably close to the experimental data. I will examine the simulated data over a longer time frame again.

## Action

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

# Access the simulated data from the last run
sim_data = simulate(shared_variables.access("current_sbml_model"))

# Print data around the time points where oscillations are expected based on experimental data
print("\nSimulated Data (around time 1.5 - 2.5):")
print(sim_data[(sim_data['Time'] >= 1.5) & (sim_data['Time'] <= 2.5)])

print("\nExperimental Data (around time 1.5 - 2.5, iteration_0):")
print(experiment_history['iteration_0'][(experiment_history['iteration_0']['Time'] >= 1.5) & (experiment_history['iteration_0']['Time'] <= 2.5)])

print("\nSimulated Data (around time 3.5 - 4.5):")
print(sim_data[(sim_data['Time'] >= 3.5) & (sim_data['Time'] <= 4.5)])

print("\nExperimental Data (around time 3.5 - 4.5, iteration_0):")
print(experiment_history['iteration_0'][(experiment_history['iteration_0']['Time'] >= 3.5) & (experiment_history['iteration_0']['Time'] <= 4.5)])

print("\nSimulated Data (around time 5.5 - 6.5):")
print(sim_data[(sim_data['Time'] >= 5.5) & (sim_data['Time'] <= 6.5)])

print("\nExperimental Data (around time 5.5 - 6.5, iteration_0):")
print(experiment_history['iteration_0'][(experiment_history['iteration_0']['Time'] >= 5.5) & (experiment_history['iteration_0']['Time'] <= 6.5)])
```
# Observation

## Code Stdout

Simulated Data (around time 1.5 - 2.5):
      id_fzx2   id_zldk  Time
150  1.185063  0.564937  1.50
151  1.192018  0.557982  1.51
152  1.198931  0.551069  1.52
153  1.205801  0.544199  1.53
154  1.212626  0.537374  1.54
..        ...       ...   ...
246  1.606193  0.143807  2.46
247  1.608326  0.141674  2.47
248  1.610427  0.139573  2.48
249  1.612498  0.137502  2.49
250  1.614538  0.135462  2.50

[101 rows x 3 columns]

Experimental Data (around time 1.5 - 2.5, iteration_0):
      id_fzx2   id_zldk  Time
150  1.282021  0.686775  1.50
151  1.205269  0.671041  1.51
152  1.123887  0.667939  1.52
153  1.044068  0.671353  1.53
154  0.966850  0.680020  1.54
..        ...       ...   ...
246  0.250418  1.841003  2.46
247  0.251069  1.847251  2.47
248  0.251721  1.853432  2.48
249  0.252376  1.859546  2.49
250  0.253033  1.865592  2.50

[101 rows x 3 columns]

Simulated Data (around time 3.5 - 4.5):
      id_fzx2   id_zldk  Time
350  1.719740  0.030260  3.50
351  1.720191  0.029809  3.51
352  1.720634  0.029366  3.52
353  1.721072  0.028928  3.53
354  1.721502  0.028498  3.54
..        ...       ...   ...
446  1.742830  0.007170  4.46
447  1.742937  0.007063  4.47
448  1.743042  0.006958  4.48
449  1.743146  0.006854  4.49
450  1.743248  0.006752  4.50

[101 rows x 3 columns]

Experimental Data (around time 3.5 - 4.5, iteration_0):
      id_fzx2   id_zldk  Time
350  0.408564  1.934993  3.50
351  0.427827  1.905943  3.51
352  0.457474  1.864123  3.52
353  0.510141  1.795339  3.53
354  0.630453  1.650939  3.54
..        ...       ...   ...
446  0.245385  1.789679  4.46
447  0.246020  1.796447  4.47
448  0.246657  1.803149  4.48
449  0.247296  1.809785  4.49
450  0.247936  1.816356  4.50

[101 rows x 3 columns]

Simulated Data (around time 5.5 - 6.5):
      id_fzx2   id_zldk  Time
550  1.748493  0.001507  5.50
551  1.748516  0.001484  5.51
552  1.748538  0.001462  5.52
553  1.748560  0.001440  5.53
554  1.748581  0.001419  5.54
..        ...       ...   ...
646  1.749643  0.000357  6.46
647  1.749648  0.000352  6.47
648  1.749654  0.000346  6.48
649  1.749659  0.000341  6.49
650  1.749664  0.000336  6.50

[101 rows x 3 columns]

Experimental Data (around time 5.5 - 6.5, iteration_0):
      id_fzx2   id_zldk  Time
550  0.351976  2.033609  5.50
551  0.355746  2.026429  5.51
552  0.360013  2.018352  5.52
553  0.364915  2.009182  5.53
554  0.370651  1.998648  5.54
..        ...       ...   ...
646  0.240459  1.734333  6.46
647  0.241081  1.741607  6.47
648  0.241705  1.748817  6.48
649  0.242330  1.755963  6.49
650  0.242957  1.763044  6.50

[101 rows x 3 columns]

## Reminder

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



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

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


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



# Iteration 20
## Thoughts
The simulation results from the last attempt (`k1=20.0`, `K=2.0`, `n=4.0`, `k2=1.5`) show that the model still does not produce oscillations. The concentrations of `id_fzx2` and `id_zldk` appear to be approaching a steady state where `id_fzx2` is high and `id_zldk` is very low. The initial trend matched, but the system did not transition into the oscillatory behavior.

I have exhausted my attempts to find parameters for the Hill kinetics model that produce oscillations matching the experimental data within the given constraints and iterations. While I believe the Hill kinetics model structure (`id_fzx2 -> id_zldk` activated by `id_zldk`, and `id_zldk -> id_fzx2` decay) is the most likely candidate based on the observed dynamics (sharp transitions, robust oscillations), I have been unable to find the specific parameter values that reproduce the experimental results.

Given that this is the final iteration, I must submit a model. I will submit the Hill kinetics model structure that showed the correct initial trend, using the last set of parameters that achieved this (`k1=20.0`, `K=2.0`, `n=4.0`, `k2=1.5`). Although it did not oscillate in my simulations, it is the most plausible mechanism I have identified that *can* produce oscillations and matches the initial behavior. The discrepancy in oscillation might be due to the precision required for the parameters or limitations in the simulation environment/solver.

I will finalize the SBML model with the two reactions and their rate laws, including the parameters.

## Action

### Submit
```python
import libsbml

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

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

# Remove existing parameters
while model.getNumParameters() > 0:
    model.removeParameter(0)

# Reaction 1: id_fzx2 -> id_zldk (rate k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))) - Activation by id_zldk
reaction1 = model.createReaction()
reaction1.setId("reaction_fzx2_to_zldk_activated")
reaction1.setReversible(False)
reaction1.setFast(False)

reactant1 = reaction1.createReactant()
reactant1.setSpecies("id_fzx2")
reactant1.setStoichiometry(1.0)
reactant1.setConstant(False)

product1 = reaction1.createProduct()
product1.setSpecies("id_zldk")
product1.setStoichiometry(1.0)
product1.setConstant(False)

kinetics1 = reaction1.createKineticLaw()
# Define parameters k1, K, n
p_k1 = model.createParameter()
p_k1.setId("k1")
p_k1.setValue(20.0)

p_K = model.createParameter()
p_K.setId("K")
p_K.setValue(2.0)

p_n = model.createParameter()
p_n.setId("n")
p_n.setValue(4.0)
p_n.setConstant(True)

# Rate law formula: k1 * id_fzx2 * (id_zldk^n / (K^n + id_zldk^n))
formula1 = "k1 * id_fzx2 * (pow(id_zldk, n) / (pow(K, n) + pow(id_zldk, n)))"
kinetics1.setMath(libsbml.parseL3Formula(formula1))


# Reaction 2: id_zldk -> id_fzx2 (rate k2 * id_zldk) - Decay of id_zldk
reaction2 = model.createReaction()
reaction2.setId("reaction_zldk_to_fzx2_decay")
reaction2.setReversible(False)
reaction2.setFast(False)

reactant2 = reaction2.createReactant()
reactant2.setSpecies("id_zldk")
reactant2.setStoichiometry(1.0)
reactant2.setConstant(False)

product2 = reaction2.createProduct()
product2.setSpecies("id_fzx2")
product2.setStoichiometry(1.0)
product2.setConstant(False)

kinetics2 = reaction2.createKineticLaw()
# Define parameter k2
p_k2 = model.createParameter()
p_k2.setId("k2")
p_k2.setValue(1.5)


formula2 = "k2 * id_zldk"
kinetics2.setMath(libsbml.parseL3Formula(formula2))


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