
                # Interation 0

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


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

                <?xml version="1.0" encoding="UTF-8"?>
<sbml xmlns="http://www.sbml.org/sbml/level2/version4" level="2" version="4">
  <model id="id_3fi6">
    <listOfUnitDefinitions>
      <unitDefinition id="id_tb6x">
        <listOfUnits>
          <unit kind="metre" exponent="1" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_jsj5">
        <listOfUnits>
          <unit kind="metre" exponent="2" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_zwbl">
        <listOfUnits>
          <unit kind="litre" exponent="1" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_e3oh">
        <listOfUnits>
          <unit kind="second" exponent="1" scale="0" multiplier="86400"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_u7s4">
        <listOfUnits>
          <unit kind="mole" exponent="1" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_zt8a" spatialDimensions="3" size="1" constant="true"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_1a2z" compartment="id_zt8a" initialConcentration="1" boundaryCondition="false" constant="false"/>
      <species id="id_khqo" compartment="id_zt8a" initialConcentration="1" boundaryCondition="false" constant="false"/>
      <species id="id_6o57" compartment="id_zt8a" initialConcentration="5" boundaryCondition="false" constant="false"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

                Format your response according to the instructions in the system message.
                
## Thoughts
The initial SBML model defines three species: `id_1a2z`, `id_khqo`, and `id_6o57`, with initial concentrations 1, 1, and 5 respectively. There are no reactions defined in the model.

My first step is to understand the baseline behavior of the system. I will request an "observe" experiment to see how the concentrations of these species change over time under default conditions. This data will be crucial for forming hypotheses about the underlying reactions.

After obtaining the experimental data, I will compare it to a simulation of the current (empty) model. Since the current model has no reactions, the species concentrations should remain constant. Any deviation from this in the experimental data will indicate the presence of reactions.

## Action

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

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

Total size: 1001 rows × 4 columns. 

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

Time   id_1a2z  id_khqo  id_6o57
0  1.00e+00 1.00e+00 5.00e+00
...
6.00e-01  4.34e-01 1.51e+00 3.22e+00
...
1.20e+00  3.18e-01 2.26e+00 2.22e+00
...
1.80e+00  3.28e-01 3.14e+00 1.65e+00
...
2.40e+00  4.32e-01 3.97e+00 1.34e+00
...
3.00e+00  6.59e-01 4.43e+00 1.16e+00
...
3.60e+00  1.03e+00 4.07e+00 1.06e+00
...
4.20e+00  1.41e+00 2.94e+00 1.01e+00
...
4.80e+00  1.60e+00 1.77e+00 9.74e-01
...
5.40e+00  1.59e+00 1.01e+00 9.57e-01
...
6.00e+00  1.48e+00 6.01e-01 9.47e-01
...
6.60e+00  1.34e+00 3.86e-01 9.41e-01
...
7.20e+00  1.20e+00 2.68e-01 9.38e-01
...
7.80e+00  1.08e+00 2.01e-01 9.36e-01
...
8.40e+00  9.82e-01 1.60e-01 9.35e-01
...
9.00e+00  8.95e-01 1.35e-01 9.35e-01
...
9.60e+00  8.21e-01 1.20e-01 9.34e-01
...
1.02e+01  7.57e-01 1.10e-01 9.34e-01
...
1.08e+01  7.01e-01 1.05e-01 9.34e-01
...
1.14e+01  6.53e-01 1.04e-01 9.34e-01
...
1.20e+01  6.12e-01 1.05e-01 9.34e-01
...
1.26e+01  5.75e-01 1.08e-01 9.34e-01
...
1.32e+01  5.43e-01 1.14e-01 9.34e-01
...
1.38e+01  5.15e-01 1.23e-01 9.34e-01
...
1.44e+01  4.90e-01 1.34e-01 9.34e-01
...
1.50e+01  4.69e-01 1.48e-01 9.34e-01
...
1.56e+01  4.50e-01 1.66e-01 9.34e-01
...
1.62e+01  4.34e-01 1.87e-01 9.34e-01
...
1.68e+01  4.21e-01 2.14e-01 9.34e-01
...
1.74e+01  4.10e-01 2.45e-01 9.34e-01
...
1.80e+01  4.02e-01 2.83e-01 9.34e-01
...
1.86e+01  3.97e-01 3.28e-01 9.34e-01
...
1.92e+01  3.94e-01 3.81e-01 9.34e-01
...
1.98e+01  3.95e-01 4.44e-01 9.34e-01
...
2.04e+01  3.99e-01 5.15e-01 9.34e-01
...
2.10e+01  4.07e-01 5.96e-01 9.34e-01
...
2.16e+01  4.20e-01 6.85e-01 9.34e-01
...
2.22e+01  4.38e-01 7.80e-01 9.34e-01
...
2.28e+01  4.62e-01 8.78e-01 9.34e-01
...
2.34e+01  4.92e-01 9.73e-01 9.34e-01
...
2.40e+01  5.29e-01 1.06e+00 9.34e-01
...
2.46e+01  5.72e-01 1.12e+00 9.34e-01
...
2.52e+01  6.20e-01 1.16e+00 9.34e-01
...
2.58e+01  6.70e-01 1.16e+00 9.34e-01
...
2.64e+01  7.19e-01 1.13e+00 9.34e-01
...
2.70e+01  7.63e-01 1.07e+00 9.34e-01
...
2.76e+01  7.99e-01 9.91e-01 9.34e-01
...
2.82e+01  8.24e-01 9.00e-01 9.34e-01
...
2.88e+01  8.37e-01 8.09e-01 9.34e-01
...
3.00e+01  8.33e-01 6.48e-01 9.34e-01

## Reminder

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



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

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


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



# Iteration 1
## Thoughts

The experimental data shows complex dynamics for all three species. `id_6o57` decreases and stabilizes. `id_khqo` increases, then decreases, then slightly increases again. `id_1a2z` decreases, then increases, then decreases again. This suggests a system of interconnected reactions, likely reversible, to explain the non-monotonic behaviors and stabilization above zero.

Based on the initial analysis, I hypothesize the following set of reversible reactions:
1.  `id_6o57 <=> id_khqo`
    *   `R1_fwd: id_6o57 -> id_khqo` (rate constant `k1f`)
    *   `R1_rev: id_khqo -> id_6o57` (rate constant `k1r`)
2.  `id_1a2z <=> id_khqo`
    *   `R2_fwd: id_1a2z -> id_khqo` (rate constant `k2f`)
    *   `R2_rev: id_khqo -> id_1a2z` (rate constant `k2r`)

This model structure can potentially explain:
- The decrease of `id_6o57` and its stabilization (due to `R1_fwd` and `R1_rev`).
- The initial decrease of `id_1a2z` (due to `R2_fwd`).
- The initial increase of `id_khqo` (due to `R1_fwd` and `R2_fwd`).
- The subsequent changes as the system moves towards equilibrium, with reverse reactions becoming significant.

I will now:
1.  Plot the experimental data for a clear visual.
2.  Add these four reactions to the `input_sbml_string` using `libsbml`. I will assign placeholder values (e.g., 0.1) for the kinetic parameters for now.
3.  Simulate this new model.
4.  Plot the simulation results alongside the experimental data for a qualitative comparison. This will help assess if the model structure is plausible before attempting to fit parameters.

## Action

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

# --- Part 1: Plot experimental data ---
exp_data = experiment_history['iteration_0']

plt.figure(figsize=(12, 7))
plt.plot(exp_data['Time'], exp_data['id_1a2z'], label='id_1a2z (Exp)', linestyle='--')
plt.plot(exp_data['Time'], exp_data['id_khqo'], label='id_khqo (Exp)', linestyle='--')
plt.plot(exp_data['Time'], exp_data['id_6o57'], label='id_6o57 (Exp)', linestyle='--')
plt.xlabel('Time')
plt.ylabel('Concentration')
plt.title('Experimental Data (iteration_0)')
plt.legend()
plt.grid(True)
# plt.show() # Cannot use plt.show() in this environment
plt.savefig("experimental_data_plot.png")
print("Experimental data plot saved as experimental_data_plot.png")
# Store the plot figure object if needed later, though saving is usually sufficient
# shared_variables.add("experimental_plot_fig_iter1", plt.gcf())


# --- Part 2: Add reactions to the SBML model ---
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Helper function to create a reaction
def create_reaction(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)

    for species_id, stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(species_id)
        reactant.setStoichiometry(stoich)
        reactant.setConstant(False) # Required in SBML Level 3, but good practice

    for species_id, stoich in products:
        product = reaction.createProduct()
        product.setSpecies(species_id)
        product.setStoichiometry(stoich)
        product.setConstant(False) # Required in SBML Level 3, but good practice

    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    
    math_ast = libsbml.parseL3Formula(f"{k_id} * {' * '.join([r[0] for r in reactants]) if reactants else '1'}")
    kinetic_law.setMath(math_ast)
    return reaction

# Define parameters (placeholder values)
k1f_val = 0.1
k1r_val = 0.05 # Made it different from k1f
k2f_val = 0.1
k2r_val = 0.05 # Made it different from k2f

# Reaction 1: id_6o57 -> id_khqo (k1f)
create_reaction(model, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")

# Reaction 2: id_khqo -> id_6o57 (k1r)
create_reaction(model, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")

# Reaction 3: id_1a2z -> id_khqo (k2f)
create_reaction(model, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")

# Reaction 4: id_khqo -> id_1a2z (k2r)
create_reaction(model, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

# Write the updated SBML to a string
writer = libsbml.SBMLWriter()
updated_sbml_str = writer.writeSBMLToString(sbml_doc)
shared_variables.add("current_sbml_model_iter1", updated_sbml_str)
print("\nUpdated SBML model with 4 reactions created.")
# print(updated_sbml_str) # Optional: print the SBML string if not too long


# --- Part 3: Simulate the new model ---
# The simulate function is provided by the environment
sim_data = simulate(updated_sbml_str)
shared_variables.add("simulation_results_iter1", sim_data)
print("\nSimulation of the updated model completed.")
print("Simulated data head:")
print(sim_data.head())


# --- Part 4: Plot simulation results alongside experimental data ---
plt.figure(figsize=(12, 7))

# Experimental data
plt.plot(exp_data['Time'], exp_data['id_1a2z'], label='id_1a2z (Exp)', linestyle='--', color='blue')
plt.plot(exp_data['Time'], exp_data['id_khqo'], label='id_khqo (Exp)', linestyle='--', color='orange')
plt.plot(exp_data['Time'], exp_data['id_6o57'], label='id_6o57 (Exp)', linestyle='--', color='green')

# Simulated data
plt.plot(sim_data['Time'], sim_data['id_1a2z'], label='id_1a2z (Sim)', color='blue')
plt.plot(sim_data['Time'], sim_data['id_khqo'], label='id_khqo (Sim)', color='orange')
plt.plot(sim_data['Time'], sim_data['id_6o57'], label='id_6o57 (Sim)', color='green')

plt.xlabel('Time')
plt.ylabel('Concentration')
plt.title('Comparison of Experimental Data and Initial Simulation')
plt.legend()
plt.grid(True)
# plt.show()
plt.savefig("comparison_plot_iter1.png")
print("\nComparison plot saved as comparison_plot_iter1.png")
# shared_variables.add("comparison_plot_fig_iter1", plt.gcf())

```
# 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 `matplotlib.pyplot` which is not an allowed library. I need to remove the plotting code. I will focus on creating the SBML model with the hypothesized reactions and then simulating it. I can analyze the simulation results numerically by printing the head and tail of the dataframe, and comparing them to the experimental data.

The core logic of adding reactions using `libsbml` and simulating the model should still be valid.

Revised plan:
1.  Remove all `matplotlib.pyplot` related code.
2.  Add the four hypothesized reactions (`id_6o57 <=> id_khqo` and `id_1a2z <=> id_khqo`) to the `input_sbml_string` using `libsbml` with placeholder kinetic parameters (e.g., 0.1 for forward, 0.05 for reverse).
3.  Simulate this new model.
4.  Print the head and tail of the simulation results and compare them qualitatively with the experimental data (which I can access from `experiment_history['iteration_0']`).

This will allow me to assess if the model structure is plausible even without direct plotting.

## Action

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

# Access experimental data for comparison
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) head:")
print(exp_data.head())
print("\nExperimental data (iteration_0) tail:")
print(exp_data.tail())

# --- Part 1: Add reactions to the SBML model ---
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Helper function to create a reaction
def create_reaction(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False) # Each direction is a separate reaction
    reaction.setFast(False)

    # Add reactants
    for species_id, stoich in reactants:
        reactant_ref = reaction.createReactant()
        reactant_ref.setSpecies(species_id)
        reactant_ref.setStoichiometry(stoich)
        reactant_ref.setConstant(False) # Required in SBML Level 3

    # Add products
    for species_id, stoich in products:
        product_ref = reaction.createProduct()
        product_ref.setSpecies(species_id)
        product_ref.setStoichiometry(stoich)
        product_ref.setConstant(False) # Required in SBML Level 3

    # Create kinetic law
    kinetic_law = reaction.createKineticLaw()
    
    # Add parameter for the rate constant
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    
    # Construct the math formula for mass action kinetics
    # e.g., k_id * S1 * S2 for S1 + S2 -> P
    # or k_id * S1 for S1 -> P
    # or k_id for 0 -> P (source reaction)
    reactant_species_ids = [r[0] for r in reactants]
    if not reactant_species_ids: # Source reaction (e.g., -> S)
        formula = f"{k_id}"
    else:
        formula = f"{k_id} * {' * '.join(reactant_species_ids)}"
    
    math_ast = libsbml.parseL3Formula(formula)
    if math_ast is None:
        print(f"Error parsing formula for {reaction_id}: {formula}")
        # Potentially raise an error or handle it
    kinetic_law.setMath(math_ast)
    
    return reaction

# Define parameters (placeholder values)
k1f_val = 0.1  # id_6o57 -> id_khqo
k1r_val = 0.05 # id_khqo -> id_6o57
k2f_val = 0.1  # id_1a2z -> id_khqo
k2r_val = 0.05 # id_khqo -> id_1a2z

# Reaction 1: id_6o57 -> id_khqo (k1f)
create_reaction(model, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")

# Reaction 2: id_khqo -> id_6o57 (k1r)
create_reaction(model, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")

# Reaction 3: id_1a2z -> id_khqo (k2f)
create_reaction(model, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")

# Reaction 4: id_khqo -> id_1a2z (k2r)
create_reaction(model, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

# Write the updated SBML to a string
writer = libsbml.SBMLWriter()
updated_sbml_str = writer.writeSBMLToString(sbml_doc)
shared_variables.add("current_sbml_model_iter2", updated_sbml_str)
print("\nUpdated SBML model with 4 reactions created.")
# print(updated_sbml_str) # Optional: print the SBML string if not too long


# --- Part 2: Simulate the new model ---
# The simulate function is provided by the environment
sim_data = simulate(updated_sbml_str)
shared_variables.add("simulation_results_iter2", sim_data)
print("\nSimulation of the updated model completed.")
print("Simulated data head:")
print(sim_data.head())
print("\nSimulated data tail:")
print(sim_data.tail())

# --- Qualitative comparison based on printed values ---
# Experimental data at T=0: id_1a2z=1.0, id_khqo=1.0, id_6o57=5.0
# Experimental data at T=30: id_1a2z=0.833, id_khqo=0.648, id_6o57=0.934

# Simulated data at T=0: (should match initial conditions)
# Simulated data at T=30: (will be printed)

# Based on the simulation output, I will assess if the trends are roughly in the right direction.
# For example:
# - Does id_6o57 decrease?
# - Does id_1a2z decrease initially?
# - Does id_khqo show some increase then decrease? (This might be hard to tell without plotting or more points)
# - Do concentrations stabilize or go to zero?

```
# Observation

## Code Stdout
Experimental data (iteration_0) head:
    id_1a2z   id_khqo   id_6o57  Time
0  1.000000  1.000000  5.000000  0.00
1  0.942983  1.017325  4.884438  0.03
2  0.891098  1.035826  4.772159  0.06
3  0.843793  1.055427  4.663072  0.09
4  0.800585  1.076063  4.557085  0.12

Experimental data (iteration_0) tail:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model with 4 reactions created.

Simulation of the updated model completed.
Simulated data head:
    id_1a2z   id_khqo   id_6o57  Time
0  1.000000  1.000000  5.000000  0.00
1  0.998514  1.014954  4.986533  0.03
2  0.997054  1.029819  4.973127  0.06
3  0.995621  1.044596  4.959783  0.09
4  0.994214  1.059285  4.946501  0.12

Simulated data tail:
       id_1a2z   id_khqo   id_6o57   Time
996   1.652399  3.493647  1.853954  29.88
997   1.652682  3.493685  1.853633  29.91
998   1.652964  3.493722  1.853313  29.94
999   1.653246  3.493760  1.852994  29.97
1000  1.653526  3.493797  1.852677  30.00

## 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_iter2, simulation_results_iter2)

### 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 simulation results with the initial guess parameters (`k1f=0.1, k1r=0.05, k2f=0.1, k2r=0.05`) show some discrepancies compared to the experimental data.

**Experimental Data (at T=30):**
*   `id_1a2z`: 0.833
*   `id_khqo`: 0.648
*   `id_6o57`: 0.934

**Simulated Data (at T=30):**
*   `id_1a2z`: 1.654
*   `id_khqo`: 3.494
*   `id_6o57`: 1.853

**Qualitative Comparison:**

*   **`id_6o57`**:
    *   Experimental: Decreases from 5.0 to 0.934.
    *   Simulated: Decreases from 5.0 to 1.853. The direction is correct, but the simulated value is too high. This suggests that the net consumption of `id_6o57` (driven by `R1_fwd: id_6o57 -> id_khqo`) might be too slow, or its reformation (by `R1_rev: id_khqo -> id_6o57`) is too fast relative to its consumption.
*   **`id_1a2z`**:
    *   Experimental: Decreases from 1.0 to 0.833 (after some initial fluctuations not visible in head/tail).
    *   Simulated: Increases from 1.0 to 1.654. This is the opposite of the overall trend. This implies that the net production of `id_1a2z` (driven by `R2_rev: id_khqo -> id_1a2z`) is too high, or its consumption (by `R2_fwd: id_1a2z -> id_khqo`) is too low.
*   **`id_khqo`**:
    *   Experimental: Ends at 0.648 (after initial increase and then decrease).
    *   Simulated: Increases from 1.0 to 3.494. The simulated value is much higher. This is consistent with `id_6o57` and `id_1a2z` observations: `id_khqo` is being overproduced or under-consumed in the simulation.

**Hypothesis Refinement & Parameter Adjustment Strategy:**

The current model structure (`id_6o57 <=> id_khqo` and `id_1a2z <=> id_khqo`) seems plausible as it connects all species. The issue likely lies in the rate constants.

To better match the experimental data:
1.  **`id_6o57` is too high:**
    *   Increase `k1f` (rate of `id_6o57 -> id_khqo`)
    *   Decrease `k1r` (rate of `id_khqo -> id_6o57`)
2.  **`id_1a2z` is too high (and should decrease):**
    *   Increase `k2f` (rate of `id_1a2z -> id_khqo`)
    *   Decrease `k2r` (rate of `id_khqo -> id_1a2z`)
3.  **`id_khqo` is too high:**
    *   This should be addressed by the adjustments above. If `id_khqo` is consumed more (by increasing `k1r` and `k2r`) and produced less (by decreasing `k1f` and `k2f`), its concentration should decrease. However, my reasoning for `id_6o57` and `id_1a2z` suggests the opposite for these k values.

Let's re-evaluate.
If `id_1a2z` (sim) is 1.654 vs (exp) 0.833, it means `id_1a2z` is being produced too much or consumed too little.
Reaction producing `id_1a2z`: `R2_rev: id_khqo -> id_1a2z` (rate `k2r`).
Reaction consuming `id_1a2z`: `R2_fwd: id_1a2z -> id_khqo` (rate `k2f`).
So, we need to decrease `k2r` or increase `k2f`.

If `id_6o57` (sim) is 1.853 vs (exp) 0.934, it means `id_6o57` is being produced too much or consumed too little.
Reaction producing `id_6o57`: `R1_rev: id_khqo -> id_6o57` (rate `k1r`).
Reaction consuming `id_6o57`: `R1_fwd: id_6o57 -> id_khqo` (rate `k1f`).
So, we need to decrease `k1r` or increase `k1f`.

If `id_khqo` (sim) is 3.494 vs (exp) 0.648, it means `id_khqo` is being produced too much or consumed too little.
Reactions producing `id_khqo`: `R1_fwd` (from `id_6o57`) and `R2_fwd` (from `id_1a2z`).
Reactions consuming `id_khqo`: `R1_rev` (to `id_6o57`) and `R2_rev` (to `id_1a2z`).
To decrease `id_khqo`:
    *   Decrease `k1f` and/or `k2f`.
    *   Increase `k1r` and/or `k2r`.

This creates a conflict.
Let's look at the initial phase:
Exp: `id_1a2z` decreases (0.94 at T=0.03), `id_khqo` increases (1.017 at T=0.03), `id_6o57` decreases (4.88 at T=0.03).
Sim: `id_1a2z` decreases (0.998), `id_khqo` increases (1.014), `id_6o57` decreases (4.98).
The initial trends are qualitatively similar, but the magnitudes are off.

The experimental data shows `id_1a2z` and `id_6o57` are consumed, and `id_khqo` is produced initially.
`id_6o57 -> id_khqo` (R1_fwd)
`id_1a2z -> id_khqo` (R2_fwd)

At equilibrium:
`id_1a2z` is lower than initial.
`id_6o57` is much lower than initial.
`id_khqo` is lower than initial.

This suggests that the equilibrium might favor `id_1a2z` and `id_6o57` over `id_khqo` more than the current parameters allow, or that `id_khqo` is an intermediate that is then consumed.
However, the problem states "You do not need to add new species."

Let's try to adjust parameters to push the equilibrium values closer.
To decrease final `id_1a2z`: increase `k2f` relative to `k2r`.
To decrease final `id_6o57`: increase `k1f` relative to `k1r`.
To decrease final `id_khqo`:
    - If `id_khqo` is mainly produced by `id_6o57` and `id_1a2z`, and then converts back, we need the "back" reactions (`k1r`, `k2r`) to be stronger relative to "forward" reactions (`k1f`, `k2f`) *at equilibrium*.

Let's try a new set of parameters:
- To get `id_1a2z` down: Increase `k2f`, decrease `k2r`. Let's try `k2f = 0.3`, `k2r = 0.02`. (Ratio 15)
- To get `id_6o57` down: Increase `k1f`, decrease `k1r`. Let's try `k1f = 0.5`, `k1r = 0.02`. (Ratio 25)

Previous parameters:
k1f_val = 0.1
k1r_val = 0.05
k2f_val = 0.1
k2r_val = 0.05

New trial parameters:
k1f_val_new = 0.5  # Increased significantly (id_6o57 -> id_khqo)
k1r_val_new = 0.02 # Decreased (id_khqo -> id_6o57)
k2f_val_new = 0.3  # Increased significantly (id_1a2z -> id_khqo)
k2r_val_new = 0.02 # Decreased (id_khqo -> id_1a2z)

This should:
- Drive `id_6o57` lower.
- Drive `id_1a2z` lower.
- Potentially increase `id_khqo` even more initially, but the reverse reactions are now weaker, which might not be what we want for the final state of `id_khqo`.

The experimental `id_khqo` ends up lower than its initial value (1.0 -> 0.648).
This means that overall, `id_khqo` is consumed.
The reactions `id_6o57 -> id_khqo` and `id_1a2z -> id_khqo` produce `id_khqo`.
The reactions `id_khqo -> id_6o57` and `id_khqo -> id_1a2z` consume `id_khqo`.
For `id_khqo` to decrease overall, the consumption rates must dominate its production rates at equilibrium.
This means `k1r * [id_khqo] + k2r * [id_khqo]` should be significant.

Let's reconsider the equilibrium state:
`d[id_1a2z]/dt = k2r * [id_khqo] - k2f * [id_1a2z] = 0  => k2r * [id_khqo] = k2f * [id_1a2z]`
`d[id_6o57]/dt = k1r * [id_khqo] - k1f * [id_6o57] = 0  => k1r * [id_khqo] = k1f * [id_6o57]`
`d[id_khqo]/dt = k1f * [id_6o57] + k2f * [id_1a2z] - (k1r + k2r) * [id_khqo] = 0`

From experimental equilibrium (approx T=30):
`[id_1a2z]_eq = 0.833`
`[id_khqo]_eq = 0.648`
`[id_6o57]_eq = 0.934`

So, `k2r/k2f = [id_1a2z]_eq / [id_khqo]_eq = 0.833 / 0.648 = 1.28`
And `k1r/k1f = [id_6o57]_eq / [id_khqo]_eq = 0.934 / 0.648 = 1.44`

This suggests `k2r > k2f` and `k1r > k1f`. This is the opposite of my previous parameter choices.
Let's try parameters based on these ratios.
Let `k2f = 0.1`. Then `k2r = 0.1 * 1.28 = 0.128`.
Let `k1f = 0.1`. Then `k1r = 0.1 * 1.44 = 0.144`.

New trial parameters set 2:
k1f_val = 0.1
k1r_val = 0.144
k2f_val = 0.1
k2r_val = 0.128

Let's simulate with these. The absolute magnitudes might be off, affecting the dynamics, but the equilibrium should be closer.

The initial decrease in `id_1a2z` and `id_6o57` means `k1f` and `k2f` must be active.
The initial increase in `id_khqo` also supports this.
The later decrease in `id_khqo` means `k1r` and `k2r` become dominant later.

Let's try to make the forward rates a bit higher to get the initial consumption, and then the reverse rates as calculated.
Perhaps the overall reaction speed needs to be scaled.

Let's try:
k1f = 0.2 (double the base for `k1r/k1f` ratio)
k1r = 0.2 * 1.44 = 0.288
k2f = 0.2 (double the base for `k2r/k2f` ratio)
k2r = 0.2 * 1.28 = 0.256

This set of parameters respects the equilibrium ratios while allowing for faster initial reaction rates.

Let's try this set:
k1f_val = 0.2
k1r_val = 0.288
k2f_val = 0.2
k2r_val = 0.256

I will use these new parameters and re-simulate.

One more thought: the problem states "all species are observable". This is good.
The non-monotonic behavior of `id_khqo` (increases then decreases) and `id_1a2z` (decreases then increases then decreases) is key.
My current model `A <=> B <=> C` (where `A=id_1a2z`, `B=id_khqo`, `C=id_6o57`) can produce such behavior.
`id_1a2z <=> id_khqo`
`id_6o57 <=> id_khqo`

This is equivalent to:
`id_1a2z --k2f--> id_khqo`
`id_khqo --k2r--> id_1a2z`
`id_6o57 --k1f--> id_khqo`
`id_khqo --k1r--> id_6o57`

This structure seems correct. The challenge is finding the parameters.
The parameter estimation from equilibrium ratios is a good starting point.

Let's proceed with the parameters derived from equilibrium ratios, scaled up slightly.
k1f_val = 0.2
k1r_val = 0.288
k2f_val = 0.2
k2r_val = 0.256

I will update the model with these new kinetic constants and simulate again.

## Action

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

# Access experimental data for comparison
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) head:")
print(exp_data.head())
print("\nExperimental data (iteration_0) tail:")
print(exp_data.tail())

# --- Part 1: Load the previous SBML model string ---
# The model structure is assumed to be correct from iter2, only parameters change.
# If shared_variables doesn't have it, I'd need to rebuild.
# For now, I'll rebuild it to be safe and explicit with new parameters.

sbml_doc_new = libsbml.readSBMLFromString(input_sbml_string) # Start from original empty model
model_new = sbml_doc_new.getModel()

# Helper function to create a reaction (copied from iter2 for completeness)
def create_reaction(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)

    for species_id, stoich in reactants:
        reactant_ref = reaction.createReactant()
        reactant_ref.setSpecies(species_id)
        reactant_ref.setStoichiometry(stoich)
        reactant_ref.setConstant(False)

    for species_id, stoich in products:
        product_ref = reaction.createProduct()
        product_ref.setSpecies(species_id)
        product_ref.setStoichiometry(stoich)
        product_ref.setConstant(False)

    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    
    reactant_species_ids = [r[0] for r in reactants]
    if not reactant_species_ids:
        formula = f"{k_id}"
    else:
        formula = f"{k_id} * {' * '.join(reactant_species_ids)}"
    
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)
    return reaction

# New trial parameters based on equilibrium ratios
k1f_val_new = 0.2    # id_6o57 -> id_khqo
k1r_val_new = 0.288  # id_khqo -> id_6o57
k2f_val_new = 0.2    # id_1a2z -> id_khqo
k2r_val_new = 0.256  # id_khqo -> id_1a2z

# Reaction 1: id_6o57 -> id_khqo (k1f)
create_reaction(model_new, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val_new, "k1f")

# Reaction 2: id_khqo -> id_6o57 (k1r)
create_reaction(model_new, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val_new, "k1r")

# Reaction 3: id_1a2z -> id_khqo (k2f)
create_reaction(model_new, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val_new, "k2f")

# Reaction 4: id_khqo -> id_1a2z (k2r)
create_reaction(model_new, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val_new, "k2r")

# Write the updated SBML to a string
writer = libsbml.SBMLWriter()
updated_sbml_str_iter3 = writer.writeSBMLToString(sbml_doc_new)
shared_variables.add("current_sbml_model_iter3", updated_sbml_str_iter3)
print("\nUpdated SBML model with new parameters.")

# --- Part 2: Simulate the new model ---
sim_data_iter3 = simulate(updated_sbml_str_iter3)
shared_variables.add("simulation_results_iter3", sim_data_iter3)
print("\nSimulation of the updated model (iter3) completed.")
print("Simulated data (iter3) head:")
print(sim_data_iter3.head())
print("\nSimulated data (iter3) tail:")
print(sim_data_iter3.tail())

# Compare with experimental tail:
# Exp: id_1a2z=0.833, id_khqo=0.648, id_6o57=0.934
# Sim (iter3) tail will be printed.

```
# Observation

## Code Stdout
Experimental data (iteration_0) head:
    id_1a2z   id_khqo   id_6o57  Time
0  1.000000  1.000000  5.000000  0.00
1  0.942983  1.017325  4.884438  0.03
2  0.891098  1.035826  4.772159  0.06
3  0.843793  1.055427  4.663072  0.09
4  0.800585  1.076063  4.557085  0.12

Experimental data (iteration_0) tail:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model with new parameters.

Simulation of the updated model (iter3) completed.
Simulated data (iter3) head:
    id_1a2z   id_khqo   id_6o57  Time
0  1.000000  1.000000  5.000000  0.00
1  1.001750  1.019460  4.978790  0.03
2  1.003637  1.038493  4.957870  0.06
3  1.005656  1.057106  4.937238  0.09
4  1.007804  1.075309  4.916887  0.12

Simulated data (iter3) tail:
       id_1a2z  id_khqo   id_6o57   Time
996   2.403970  1.88172  2.714310  29.88
997   2.403998  1.88172  2.714282  29.91
998   2.404025  1.88172  2.714254  29.94
999   2.404053  1.88172  2.714227  29.97
1000  2.404080  1.88172  2.714200  30.00

## 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_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3)

### 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 results with parameters derived from equilibrium ratios (`k1f=0.2, k1r=0.288, k2f=0.2, k2r=0.256`) are still not matching the experimental data well.

**Experimental Data (at T=30):**
*   `id_1a2z`: 0.833
*   `id_khqo`: 0.648
*   `id_6o57`: 0.934

**Simulated Data (iter3, at T=30):**
*   `id_1a2z`: 2.404
*   `id_khqo`: 1.882
*   `id_6o57`: 2.714

**Qualitative Comparison:**

*   **`id_1a2z`**:
    *   Experimental: Ends at 0.833. Initial trend: 1.0 -> 0.94 (decrease).
    *   Simulated (iter3): Ends at 2.404. Initial trend: 1.0 -> 1.00175 (slight increase). This is a major issue. The model should show `id_1a2z` decreasing initially.
*   **`id_khqo`**:
    *   Experimental: Ends at 0.648. Initial trend: 1.0 -> 1.017 (increase).
    *   Simulated (iter3): Ends at 1.882. Initial trend: 1.0 -> 1.019 (increase). Initial trend is okay, but final value is too high.
*   **`id_6o57`**:
    *   Experimental: Ends at 0.934. Initial trend: 5.0 -> 4.88 (decrease).
    *   Simulated (iter3): Ends at 2.714. Initial trend: 5.0 -> 4.97 (decrease). Initial trend is okay, but final value is too high.

**Problem Analysis:**

1.  **Initial decrease of `id_1a2z` is not captured:**
    *   Experimental `id_1a2z` at T=0.03 is 0.942983 (initial is 1.0).
    *   Simulated `id_1a2z` at T=0.03 is 1.001750.
    *   The net rate of change for `id_1a2z` is `k2r * [id_khqo] - k2f * [id_1a2z]`.
    *   At T=0: `[id_1a2z]=1, [id_khqo]=1`. So, `d[id_1a2z]/dt = k2r * 1 - k2f * 1 = k2r - k2f`.
    *   For `id_1a2z` to decrease, `k2f` must be greater than `k2r`.
    *   My current parameters: `k2f = 0.2`, `k2r = 0.256`. Here `k2r > k2f`, so `id_1a2z` increases, which is wrong.
    *   This contradicts the equilibrium calculation `k2r/k2f = 1.28`. This implies that the system might not be a simple reversible reaction reaching equilibrium, or my interpretation of equilibrium is too simplistic for the dynamic data.

2.  **Final concentrations are too high for all species (except `id_1a2z` which is also wrong direction).**

Let's reconsider the initial dynamics.
*   `id_1a2z` decreases: `k2f * [id_1a2z]_0 > k2r * [id_khqo]_0`. Since `[id_1a2z]_0 = [id_khqo]_0 = 1`, this means `k2f > k2r`.
*   `id_6o57` decreases: `k1f * [id_6o57]_0 > k1r * [id_khqo]_0`. `k1f * 5 > k1r * 1`. So `5*k1f > k1r`.
*   `id_khqo` increases: `(k1f * [id_6o57]_0 + k2f * [id_1a2z]_0) > (k1r * [id_khqo]_0 + k2r * [id_khqo]_0)`.
    `(5*k1f + k2f) > (k1r + k2r)`.

Let's try to satisfy these initial conditions and then see where the equilibrium lands.
Set `k2f > k2r`. Let `k2f = 0.3`, `k2r = 0.1`. (Ratio `k2f/k2r = 3`)
Set `5*k1f > k1r`. Let `k1f = 0.1`. Then `0.5 > k1r`. Let `k1r = 0.05`. (Ratio `k1f/k1r = 2`, and `5*0.1 > 0.05` is true).

Check the third condition:
`(5*0.1 + 0.3) > (0.05 + 0.1)`
`0.5 + 0.3 > 0.15`
`0.8 > 0.15`. This is true. So `id_khqo` should increase initially.

New trial parameters (Set 3 - "Initial Dynamics Driven"):
*   `k1f = 0.1`
*   `k1r = 0.05`
*   `k2f = 0.3`
*   `k2r = 0.1`

These parameters are similar to my very first guess, but with `k2f` significantly larger than `k2r`.
My first guess was: `k1f=0.1, k1r=0.05, k2f=0.1, k2r=0.05`.
The main change is boosting `k2f` from 0.1 to 0.3.

Let's see what these parameters do to the equilibrium.
`[id_1a2z]_eq / [id_khqo]_eq = k2r/k2f = 0.1/0.3 = 1/3`. So `[id_khqo]_eq = 3 * [id_1a2z]_eq`.
`[id_6o57]_eq / [id_khqo]_eq = k1r/k1f = 0.05/0.1 = 1/2`. So `[id_khqo]_eq = 2 * [id_6o57]_eq`.

This implies `3 * [id_1a2z]_eq = 2 * [id_6o57]_eq`.
Experimental equilibrium:
`[id_1a2z]_eq = 0.833`
`[id_khqo]_eq = 0.648`
`[id_6o57]_eq = 0.934`

Experimental ratios:
`[id_khqo]_eq / [id_1a2z]_eq = 0.648 / 0.833 = 0.778` (Simulated would be 3) - Mismatch
`[id_khqo]_eq / [id_6o57]_eq = 0.648 / 0.934 = 0.694` (Simulated would be 2) - Mismatch

The parameters derived from initial dynamics lead to equilibrium ratios that are very different from experimental ones. This suggests that the model might be missing something or the parameter fitting is non-trivial.

The problem states "discovering the true underlying mechanisms rather than overfitting to observed data is crucial."
The current mechanism is:
`id_1a2z <=> id_khqo`
`id_6o57 <=> id_khqo`

This is a common motif. What if the stoichiometry is different? The problem says "You do not need to add new species." It doesn't explicitly forbid changing stoichiometry of existing reactions if I were to define them. However, I've assumed 1:1 stoichiometry for all reactions.

Let's look at the overall changes:
`id_1a2z`: 1.0 -> 0.833 (net loss of 0.167)
`id_khqo`: 1.0 -> 0.648 (net loss of 0.352)
`id_6o57`: 5.0 -> 0.934 (net loss of 4.066)

This is strange. All species show a net loss from initial to final (T=30). This cannot happen in a closed system with only interconversions.
Total initial concentration = 1 + 1 + 5 = 7
Total final concentration (experimental) = 0.833 + 0.648 + 0.934 = 2.415

This implies there must be one or more reactions that consume these species and convert them into something that is *not* tracked, or is a boundary species (sink).
However, the problem states "all species are observable" and "You do not need to add new species."
This could mean:
1.  One of the species is a boundary species that acts as a sink. The SBML definition has `boundaryCondition="false"` for all.
2.  There's a degradation reaction for one or more species, e.g., `X -> null`.
3.  The compartment size is changing (unlikely for this type of problem).

If there's a global "decay" or "output" from the system, that would explain the net loss of total moles.
Let's assume there's a degradation pathway for `id_khqo` as it's central.
`id_khqo -> (sink)` with rate `k_deg * [id_khqo]`

If this is the case, the model would be:
1.  `id_1a2z <=> id_khqo` (k2f, k2r)
2.  `id_6o57 <=> id_khqo` (k1f, k1r)
3.  `id_khqo -> ø` (k_deg)

Let's test this hypothesis. This is a new mechanism.
If this is true, then at steady state (if it reaches one):
`d[id_1a2z]/dt = k2r * [id_khqo] - k2f * [id_1a2z] = 0`
`d[id_6o57]/dt = k1r * [id_khqo] - k1f * [id_6o57] = 0`
`d[id_khqo]/dt = k1f * [id_6o57] + k2f * [id_1a2z] - (k1r + k2r + k_deg) * [id_khqo] = 0`

The equilibrium ratios `[id_1a2z]_eq / [id_khqo]_eq = k2r/k2f` and `[id_6o57]_eq / [id_khqo]_eq = k1r/k1f` would still hold.
So the parameters `k1f=0.2, k1r=0.288, k2f=0.2, k2r=0.256` (from iter3) should give the correct ratios for `id_1a2z` and `id_6o57` relative to `id_khqo` *if* the system was closed.
The fact that all are lower suggests `k_deg` is significant.

Let's use the parameters from Iteration 3 (which gave correct ratios but wrong absolute levels):
k1f = 0.2
k1r = 0.288
k2f = 0.2
k2r = 0.256

And add a degradation reaction for `id_khqo`: `id_khqo -> ø` with rate `k_deg`.
How to estimate `k_deg`?
From the third equilibrium equation:
`k_deg * [id_khqo]_eq = k1f * [id_6o57]_eq + k2f * [id_1a2z]_eq - (k1r + k2r) * [id_khqo]_eq`
Using experimental equilibrium values:
`[id_1a2z]_eq = 0.833`
`[id_khqo]_eq = 0.648`
`[id_6o57]_eq = 0.934`

`k_deg * 0.648 = 0.2 * 0.934 + 0.2 * 0.833 - (0.288 + 0.256) * 0.648`
`k_deg * 0.648 = 0.1868 + 0.1666 - (0.544) * 0.648`
`k_deg * 0.648 = 0.3534 - 0.352352`
`k_deg * 0.648 = 0.001048`
`k_deg = 0.001048 / 0.648 = 0.001617`

This `k_deg` seems very small. It might not be enough to cause the large drop in total concentration.
The sum of initial concentrations is 7. The sum of final concentrations is 2.415. A drop of 4.585.
The time is 30 units. Average rate of loss is 4.585 / 30 = 0.15 per time unit.
If `id_khqo` is the only one degrading, and its average concentration is, say, 1.0, then `k_deg` would be around 0.15.

Let's try a more substantial `k_deg`.
The issue with the previous simulation (iter3) was that concentrations were too high:
Sim: `id_1a2z=2.4, id_khqo=1.88, id_6o57=2.71`
Exp: `id_1a2z=0.83, id_khqo=0.65, id_6o57=0.93`
All simulated values are roughly 3 times higher than experimental.
If `(k1r + k2r + k_deg)` is about 3 times `(k1r + k2r)`, then `k_deg` should be about `2 * (k1r + k2r)`.
`k1r + k2r = 0.288 + 0.256 = 0.544`.
So, `k_deg` could be around `2 * 0.544 = 1.088`. This is a large rate constant.

Let's try an intermediate `k_deg`, say `k_deg = 0.2`.
This is a significant change in the model structure.

Revised model:
1.  `id_6o57 -> id_khqo` (k1f = 0.2)
2.  `id_khqo -> id_6o57` (k1r = 0.288)
3.  `id_1a2z -> id_khqo` (k2f = 0.2)
4.  `id_khqo -> id_1a2z` (k2r = 0.256)
5.  `id_khqo -> ø` (k_deg = 0.2)  (New reaction)

The initial dynamics for `id_1a2z` (increase in sim vs decrease in exp) is still a concern.
The parameters `k2f=0.2, k2r=0.256` mean `k2r > k2f`, so `id_1a2z` will initially increase if `[id_khqo]` and `[id_1a2z]` are similar. This is what happened in iter3 sim.
Experimental data: `id_1a2z` decreases from 1.0 to 0.94. This requires `k2f > k2r`.

This means the equilibrium ratio calculation `k2r/k2f = [id_1a2z]_eq / [id_khqo]_eq` might be misleading if the system isn't truly at equilibrium or if other reactions are pulling it.
If `id_khqo -> ø` is active, then the system is not closed, and the simple equilibrium ratio for `id_1a2z <=> id_khqo` might not hold if `id_khqo` is constantly being removed.

Let's use parameters that satisfy initial dynamics:
*   `k2f > k2r` for `id_1a2z` to decrease. Let `k2f = 0.3, k2r = 0.1`.
*   `5*k1f > k1r` for `id_6o57` to decrease. Let `k1f = 0.1, k1r = 0.05`.
*   `(5*k1f + k2f) > (k1r + k2r + k_deg)` for `id_khqo` to increase initially.
    `(5*0.1 + 0.3) > (0.05 + 0.1 + k_deg)`
    `0.8 > 0.15 + k_deg`
    `0.65 > k_deg`.

So, `k_deg` must be less than 0.65 for `id_khqo` to increase initially.
Let's try `k_deg = 0.1`.

New parameters (Set 4 - "Degradation Model with Initial Dynamics"):
*   `k1f = 0.1` (id_6o57 -> id_khqo)
*   `k1r = 0.05` (id_khqo -> id_6o57)
*   `k2f = 0.3` (id_1a2z -> id_khqo)
*   `k2r = 0.1` (id_khqo -> id_1a2z)
*   `k_deg = 0.1` (id_khqo -> ø)

This set of parameters:
- Should make `id_1a2z` decrease initially (`k2f > k2r`).
- Should make `id_6o57` decrease initially (`5*k1f > k1r`).
- Should make `id_khqo` increase initially (`0.8 > 0.15 + 0.1 => 0.8 > 0.25`, true).
- Includes degradation to account for overall mass loss.

This is a new hypothesis for the model structure.

A reaction `S -> ø` is represented in SBML by having `S` as a reactant but no products.

Let's implement this.

## Action

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

# Access experimental data for comparison
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) head:")
print(exp_data.head())
print("\nExperimental data (iteration_0) tail:")
print(exp_data.tail())

# --- Part 1: Build the new SBML model with a degradation reaction ---
sbml_doc_new_model = libsbml.readSBMLFromString(input_sbml_string) # Start from original empty model
model = sbml_doc_new_model.getModel()

# Helper function to create a reaction
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)

    for species_id, stoich in reactants:
        reactant_ref = reaction.createReactant()
        reactant_ref.setSpecies(species_id)
        reactant_ref.setStoichiometry(stoich)
        reactant_ref.setConstant(False)

    for species_id, stoich in products: # Can be empty for degradation
        product_ref = reaction.createProduct()
        product_ref.setSpecies(species_id)
        product_ref.setStoichiometry(stoich)
        product_ref.setConstant(False)

    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    
    reactant_species_ids = [r[0] for r in reactants]
    if not reactant_species_ids: # Should not happen for these reactions
        formula = f"{k_id}"
    else:
        formula = f"{k_id} * {' * '.join(reactant_species_ids)}"
    
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)
    return reaction

# Parameters (Set 4 - "Degradation Model with Initial Dynamics")
k1f_val = 0.1    # id_6o57 -> id_khqo
k1r_val = 0.05   # id_khqo -> id_6o57
k2f_val = 0.3    # id_1a2z -> id_khqo
k2r_val = 0.1    # id_khqo -> id_1a2z
k_deg_val = 0.1  # id_khqo -> ø

# Reaction 1: id_6o57 -> id_khqo
create_reaction_mod(model, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")

# Reaction 2: id_khqo -> id_6o57
create_reaction_mod(model, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")

# Reaction 3: id_1a2z -> id_khqo
create_reaction_mod(model, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")

# Reaction 4: id_khqo -> id_1a2z
create_reaction_mod(model, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

# Reaction 5: id_khqo -> ø (Degradation)
# For a degradation reaction S -> ø, there are no products listed.
reaction_deg = model.createReaction()
reaction_deg.setId("R_deg_khqo")
reaction_deg.setReversible(False)
reaction_deg.setFast(False)
reactant_deg = reaction_deg.createReactant()
reactant_deg.setSpecies("id_khqo")
reactant_deg.setStoichiometry(1)
reactant_deg.setConstant(False)
# No products for S -> ø

kinetic_law_deg = reaction_deg.createKineticLaw()
param_deg = kinetic_law_deg.createParameter()
param_deg.setId("k_deg")
param_deg.setValue(k_deg_val)
param_deg.setConstant(True)
math_ast_deg = libsbml.parseL3Formula("k_deg * id_khqo")
kinetic_law_deg.setMath(math_ast_deg)


# Write the updated SBML to a string
writer = libsbml.SBMLWriter()
updated_sbml_str_iter4 = writer.writeSBMLToString(sbml_doc_new_model)
shared_variables.add("current_sbml_model_iter4", updated_sbml_str_iter4)
print("\nUpdated SBML model with 5 reactions (including degradation).")

# --- Part 2: Simulate the new model ---
sim_data_iter4 = simulate(updated_sbml_str_iter4)
shared_variables.add("simulation_results_iter4", sim_data_iter4)
print("\nSimulation of the updated model (iter4) completed.")
print("Simulated data (iter4) head:")
print(sim_data_iter4.head())
print("\nSimulated data (iter4) tail:")
print(sim_data_iter4.tail())

# Compare with experimental tail:
# Exp: id_1a2z=0.833, id_khqo=0.648, id_6o57=0.934
# Sim (iter4) tail will be printed.
# Expected initial trends:
# id_1a2z: decrease (1.0 -> ?)
# id_khqo: increase (1.0 -> ?)
# id_6o57: decrease (5.0 -> ?)
```
# Observation

## Code Stdout
Experimental data (iteration_0) head:
    id_1a2z   id_khqo   id_6o57  Time
0  1.000000  1.000000  5.000000  0.00
1  0.942983  1.017325  4.884438  0.03
2  0.891098  1.035826  4.772159  0.06
3  0.843793  1.055427  4.663072  0.09
4  0.800585  1.076063  4.557085  0.12

Experimental data (iteration_0) tail:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model with 5 reactions (including degradation).

Simulation of the updated model (iter4) completed.
Simulated data (iter4) head:
    id_1a2z   id_khqo   id_6o57  Time
0  1.000000  1.000000  5.000000  0.00
1  0.994052  1.016390  4.986533  0.03
2  0.988205  1.032566  4.973130  0.06
3  0.982459  1.048530  4.959792  0.09
4  0.976811  1.064284  4.946517  0.12

Simulated data (iter4) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.371182  0.963729  0.892636  29.88
997   0.370733  0.962521  0.891405  29.91
998   0.370284  0.961313  0.890176  29.94
999   0.369835  0.960107  0.888948  29.97
1000  0.369387  0.958902  0.887722  30.00

## 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_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4)

### 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 model with degradation of `id_khqo` and parameters chosen to match initial dynamics (`k1f=0.1, k1r=0.05, k2f=0.3, k2r=0.1, k_deg=0.1`) shows promising improvements.

**Experimental Data (T=0.12 and T=30):**
*   T=0.12: `id_1a2z=0.800`, `id_khqo=1.076`, `id_6o57=4.557`
*   T=30: `id_1a2z=0.833`, `id_khqo=0.648`, `id_6o57=0.934`

**Simulated Data (iter4, T=0.12 and T=30):**
*   T=0.12: `id_1a2z=0.977`, `id_khqo=1.064`, `id_6o57=4.947`
*   T=30: `id_1a2z=0.369`, `id_khqo=0.959`, `id_6o57=0.888`

**Comparison of Initial Trends (e.g., at T=0.12):**

*   **`id_1a2z`**:
    *   Exp: 1.0 -> 0.800 (decrease)
    *   Sim: 1.0 -> 0.977 (decrease). Correct direction. Magnitude of decrease is less than experimental. (Exp drops by 0.2, Sim drops by 0.023).
*   **`id_khqo`**:
    *   Exp: 1.0 -> 1.076 (increase)
    *   Sim: 1.0 -> 1.064 (increase). Correct direction and magnitude is reasonably close.
*   **`id_6o57`**:
    *   Exp: 5.0 -> 4.557 (decrease)
    *   Sim: 5.0 -> 4.947 (decrease). Correct direction. Magnitude of decrease is much less than experimental. (Exp drops by ~0.44, Sim drops by ~0.053).

**Comparison of Final Values (T=30):**

*   **`id_1a2z`**:
    *   Exp: 0.833
    *   Sim: 0.369. Simulated is too low.
*   **`id_khqo`**:
    *   Exp: 0.648
    *   Sim: 0.959. Simulated is too high.
*   **`id_6o57`**:
    *   Exp: 0.934
    *   Sim: 0.888. Simulated is reasonably close. This is good.

**Analysis and Parameter Adjustment Strategy:**

The introduction of `id_khqo` degradation seems to be a correct step in capturing the overall mass loss. The initial trends are now mostly correct in direction.

1.  **`id_1a2z` dynamics:**
    *   Initial decrease is too slow: `k2f * [id_1a2z] - k2r * [id_khqo]`. To make it decrease faster, increase `k2f` or decrease `k2r`. Current: `k2f=0.3, k2r=0.1`.
    *   Final value is too low (0.369 vs 0.833): This means at equilibrium, either `id_1a2z` is consumed too much by `R2_fwd` or produced too little by `R2_rev`. The ratio `k2r/k2f` determines the `[id_1a2z]/[id_khqo]` ratio at pseudo-equilibrium for this pair.
        Current `k2r/k2f = 0.1/0.3 = 1/3`. So `[id_1a2z] ~ 1/3 [id_khqo]`.
        Exp: `[id_1a2z]_eq / [id_khqo]_eq = 0.833 / 0.648 = 1.28`.
        To increase this ratio, we need to increase `k2r` relative to `k2f`. This conflicts with the need for faster initial decrease of `id_1a2z` if we only scale them.

2.  **`id_6o57` dynamics:**
    *   Initial decrease is too slow: `k1f * [id_6o57] - k1r * [id_khqo]`. To make it decrease faster, increase `k1f` or decrease `k1r`. Current: `k1f=0.1, k1r=0.05`.
    *   Final value is good (0.888 vs 0.934). This suggests the ratio `k1r/k1f` is reasonable.
        Current `k1r/k1f = 0.05/0.1 = 1/2`. So `[id_6o57] ~ 1/2 [id_khqo]`.
        Exp: `[id_6o57]_eq / [id_khqo]_eq = 0.934 / 0.648 = 1.44`.
        The simulated ratio `1/2 * [id_khqo]` (e.g. `0.5 * 0.959 = 0.4795`) is lower than the simulated `id_6o57` (0.888). This is because the system is not at simple equilibrium due to `k_deg`.
        The experimental ratio (1.44) is higher than the current `k1r/k1f` implies. To get `[id_6o57]` higher relative to `[id_khqo]`, we need to increase `k1r` relative to `k1f`.

3.  **`id_khqo` dynamics:**
    *   Initial increase is good.
    *   Final value is too high (0.959 vs 0.648). This suggests `id_khqo` is either produced too much or not removed enough (by `R1_rev`, `R2_rev`, or `R_deg`).
        To decrease final `[id_khqo]`:
        *   Decrease production: decrease `k1f`, `k2f`.
        *   Increase consumption: increase `k1r`, `k2r`, `k_deg`.

**Refined Parameter Tuning Strategy:**

*   **Focus on `id_6o57` first:**
    *   Initial drop of `id_6o57` needs to be much faster. Increase `k1f`. Let's try `k1f = 0.5` (5x increase).
    *   To maintain the `id_6o57` final value (which was good), if we increase `k1f`, we might need to adjust `k1r` or other parameters. The ratio `k1r/k1f` influences `[id_6o57]/[id_khqo]`. Exp ratio is 1.44. If `k1f=0.5`, then `k1r` should be `0.5 * 1.44 = 0.72`. This is a very high `k1r`.
    *   Let's try increasing `k1f` significantly, e.g., `k1f = 0.4`. Keep `k1r = 0.05` for now and see. This will make `id_6o57` drop faster and lower.
    *   Previous `k1f=0.1, k1r=0.05`. New trial: `k1f=0.4, k1r=0.2` (maintaining ratio 1/2, but faster).
        Exp ratio `k1r/k1f` should be ~1.44. So if `k1f=0.4`, then `k1r = 0.4 * 1.44 = 0.576`.
        Let's try `k1f = 0.2` (double previous) and `k1r = 0.05 * (1.44 / (0.05/0.1)) = 0.05 * (1.44/0.5) = 0.05 * 2.88 = 0.144`.
        So, `k1f=0.2, k1r=0.144`. (Ratio `k1r/k1f = 0.72`). This is different from target 1.44.
        Let's use the target ratio: `k1r = 1.44 * k1f`.
        If `k1f = 0.2`, then `k1r = 1.44 * 0.2 = 0.288`. (These are params from iter3 for this pair).

*   **Address `id_1a2z`:**
    *   Initial drop needs to be faster. Increase `k2f`. Current `k2f=0.3`.
    *   Final `[id_1a2z]` needs to be higher. This means `k2r/k2f` ratio needs to be larger. Exp ratio `k2r/k2f` is ~1.28.
    *   If `k2f` is increased for initial dynamics, `k2r` must also increase significantly to maintain the ratio for the final state.
    *   Let `k2f = 0.5`. Then `k2r = 1.28 * 0.5 = 0.64`.
    *   These are much larger than before.

*   **Adjust `k_deg` for `id_khqo` final level:**
    *   If `k1f, k2f` increase, `id_khqo` production increases. If `k1r, k2r` increase, `id_khqo` consumption by reverse reactions increases.
    *   The net effect on `id_khqo` needs to be managed by `k_deg`.

Let's try a new set of parameters (Set 5):
Target Ratios:
`k1r/k1f = 1.44`
`k2r/k2f = 1.28`

To speed up initial consumption of `id_6o57` (needs `k1f` to be effective against initial `[id_6o57]=5`):
Let `k1f = 0.2`. Then `k1r = 1.44 * 0.2 = 0.288`. (These were used in iter3, where `id_6o57` final was 2.7, too high. So this `k1f` might still be too low, or `k1r` too high for the degradation model).

To speed up initial consumption of `id_1a2z` (needs `k2f > k2r` initially, but `k2r/k2f = 1.28` for final state):
This is the fundamental conflict. `k2f > k2r` for initial drop, but `k2r > k2f` for final ratio.
This implies that the assumption `[id_1a2z]_eq / [id_khqo]_eq = k2r/k2f` might be too simple when `k_deg` is present and significant.
The degradation of `id_khqo` pulls `[id_khqo]` down.
`d[id_1a2z]/dt = k2r * [id_khqo] - k2f * [id_1a2z]`
If `[id_khqo]` is kept low by degradation, then to maintain `[id_1a2z]` at a higher level, `k2r` might not need to be that much larger than `k2f`.

Let's prioritize initial dynamics:
`k2f > k2r`. Let `k2f = 0.4`, `k2r = 0.2`. (Ratio `k2r/k2f = 0.5`). This will make `id_1a2z` drop initially.
`5*k1f > k1r`. Let `k1f = 0.2`. We need `1.0 > k1r`. Let `k1r = 0.1`. (Ratio `k1r/k1f = 0.5`).

New parameters (Set 5 - "Faster Initial Dynamics, Adjusted Ratios"):
*   `k1f = 0.2`
*   `k1r = 0.1` (Ratio 0.5. Exp target ~1.44. This will make `id_6o57` lower than `id_khqo` if this ratio dominates)
*   `k2f = 0.4`
*   `k2r = 0.2` (Ratio 0.5. Exp target ~1.28. This will make `id_1a2z` lower than `id_khqo` if this ratio dominates)
*   `k_deg`: We need to adjust this.
    Previous `k_deg = 0.1`.
    With these new rates, `id_khqo` production from `id_1a2z` is `k2f*[id_1a2z] = 0.4*1 = 0.4`.
    Production from `id_6o57` is `k1f*[id_6o57] = 0.2*5 = 1.0`. Total initial production flux = 1.4.
    Initial consumption flux (excluding degradation) = `k1r*[id_khqo] + k2r*[id_khqo] = (0.1+0.2)*1 = 0.3`.
    So, `id_khqo` will increase rapidly.
    `d[id_khqo]/dt = (k1f [S3] + k2f [S1]) - (k1r + k2r + k_deg)[S2]`
    At T=30 (Exp): `[S1]=0.833, [S2]=0.648, [S3]=0.934`.
    Flux in = `0.2*0.934 + 0.4*0.833 = 0.1868 + 0.3332 = 0.52`
    Flux out (non-deg) = `(0.1+0.2)*0.648 = 0.3*0.648 = 0.1944`
    So, `k_deg * 0.648` must be `0.52 - 0.1944 = 0.3256`.
    `k_deg = 0.3256 / 0.648 = 0.502`. This is much higher than before.

Let's try `k_deg = 0.5`.

Parameters (Set 5):
*   `k1f = 0.2`
*   `k1r = 0.1`
*   `k2f = 0.4`
*   `k2r = 0.2`
*   `k_deg = 0.5`

Check initial `id_khqo` increase: `(5*k1f + k2f) > (k1r + k2r + k_deg)`
`(5*0.2 + 0.4) > (0.1 + 0.2 + 0.5)`
`1.0 + 0.4 > 0.3 + 0.5`
`1.4 > 0.8`. True. So `id_khqo` should increase initially.

This set of parameters aims for:
1.  Faster initial consumption of `id_1a2z` and `id_6o57`.
2.  A `k_deg` value calculated based on target equilibrium and other rates.
3.  The ratios `k1r/k1f` and `k2r/k2f` are set to 0.5, which might make final `id_1a2z` and `id_6o57` too low relative to `id_khqo`. However, the strong `k_deg` might alter these relationships significantly.

It's an iterative process. Let's see what this set does.

## Action

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

# Access experimental data for comparison
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())

# --- Part 1: Build the SBML model with new parameters ---
sbml_doc_iter5 = libsbml.readSBMLFromString(input_sbml_string)
model_iter5 = sbml_doc_iter5.getModel()

# Helper function (copied for completeness)
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 5)
k1f_val = 0.2    # id_6o57 -> id_khqo
k1r_val = 0.1    # id_khqo -> id_6o57
k2f_val = 0.4    # id_1a2z -> id_khqo
k2r_val = 0.2    # id_khqo -> id_1a2z
k_deg_val = 0.5  # id_khqo -> ø

# Reaction 1: id_6o57 -> id_khqo
create_reaction_mod(model_iter5, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
# Reaction 2: id_khqo -> id_6o57
create_reaction_mod(model_iter5, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
# Reaction 3: id_1a2z -> id_khqo
create_reaction_mod(model_iter5, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
# Reaction 4: id_khqo -> id_1a2z
create_reaction_mod(model_iter5, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

# Reaction 5: id_khqo -> ø (Degradation)
reaction_deg = model_iter5.createReaction()
reaction_deg.setId("R_deg_khqo")
reaction_deg.setReversible(False)
reaction_deg.setFast(False)
reactant_deg = reaction_deg.createReactant()
reactant_deg.setSpecies("id_khqo")
reactant_deg.setStoichiometry(1)
reactant_deg.setConstant(False)
kinetic_law_deg = reaction_deg.createKineticLaw()
param_deg = kinetic_law_deg.createParameter()
param_deg.setId("k_deg")
param_deg.setValue(k_deg_val)
param_deg.setConstant(True)
math_ast_deg = libsbml.parseL3Formula("k_deg * id_khqo")
kinetic_law_deg.setMath(math_ast_deg)

writer = libsbml.SBMLWriter()
updated_sbml_str_iter5 = writer.writeSBMLToString(sbml_doc_iter5)
shared_variables.add("current_sbml_model_iter5", updated_sbml_str_iter5)
print("\nUpdated SBML model (iter5) with 5 reactions and new parameters.")

# --- Part 2: Simulate the new model ---
sim_data_iter5 = simulate(updated_sbml_str_iter5)
shared_variables.add("simulation_results_iter5", sim_data_iter5)
print("\nSimulation of the updated model (iter5) completed.")
print("Simulated data (iter5) head:")
print(sim_data_iter5.head())
print("\nSimulated data (iter5) tail:")
print(sim_data_iter5.tail())

# Compare with experimental tail:
# Exp: id_1a2z=0.833, id_khqo=0.648, id_6o57=0.934
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model (iter5) with 5 reactions and new parameters.

Simulation of the updated model (iter5) completed.
Simulated data (iter5) head:
    id_1a2z   id_khqo   id_6o57  Time
0  1.000000  1.000000  5.000000  0.00
1  0.994090  1.017668  4.973108  0.03
2  0.988352  1.034693  4.946428  0.06
3  0.982783  1.051090  4.919958  0.09
4  0.977375  1.066876  4.893694  0.12

Simulated data (iter5) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.026479  0.034254  0.059751  29.88
997   0.026367  0.034108  0.059496  29.91
998   0.026256  0.033963  0.059242  29.94
999   0.026145  0.033819  0.058989  29.97
1000  0.026034  0.033675  0.058737  30.00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5)

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


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



# Iteration 6
## Thoughts

The simulation results with parameters from Set 5 (`k1f=0.2, k1r=0.1, k2f=0.4, k2r=0.2, k_deg=0.5`) show that the concentrations of all species have become far too low at T=30.

**Experimental Data (T=30):**
*   `id_1a2z`: 0.833
*   `id_khqo`: 0.648
*   `id_6o57`: 0.934

**Simulated Data (iter5, T=30):**
*   `id_1a2z`: 0.026
*   `id_khqo`: 0.034
*   `id_6o57`: 0.059

**Comparison of Initial Trends (e.g., at T=0.12):**
*   Exp: `id_1a2z=0.800`, `id_khqo=1.076`, `id_6o57=4.557`
*   Sim: `id_1a2z=0.977`, `id_khqo=1.067`, `id_6o57=4.894`
    *   `id_1a2z`: Sim decrease (0.023) is much smaller than Exp decrease (0.2).
    *   `id_khqo`: Sim increase matches Exp increase well.
    *   `id_6o57`: Sim decrease (0.106) is smaller than Exp decrease (0.443).

**Analysis:**

1.  **Final concentrations are drastically too low:** This clearly indicates that `k_deg = 0.5` is too high. The system is losing mass too quickly.
2.  **Initial decrease of `id_1a2z` and `id_6o57` is still too slow:**
    *   For `id_1a2z`: `k2f=0.4` might still not be aggressive enough, or `k2r=0.2` is too strong in reverse initially.
    *   For `id_6o57`: `k1f=0.2` is not strong enough given `[id_6o57]_0 = 5`.

**Revised Parameter Tuning Strategy:**

*   **Reduce `k_deg` significantly.** The previous `k_deg=0.1` (from iter4) resulted in `id_khqo` being too high (0.959 vs 0.648). So the optimal `k_deg` is likely between 0.1 and 0.5, probably closer to 0.1 or slightly higher. Let's try `k_deg = 0.15`.

*   **Increase `k1f` and `k2f` for faster initial consumption, and adjust reverse rates.**
    *   **`id_6o57` (`S3`):** Initial concentration is 5. `d[S3]/dt = k1r[S2] - k1f[S3]`. To get a fast drop, `k1f` needs to be substantial.
        Let's try `k1f = 0.4`. (Was 0.2).
        Target experimental ratio `[S3]/[S2] = 0.934/0.648 = 1.44`.
        If we assume `k1r[S2] - k1f[S3] ~ 0` at steady state (ignoring that `S2` is also fed by `S1` and degrades), then `k1r/k1f ~ [S3]/[S2] = 1.44`.
        So, `k1r = 1.44 * k1f = 1.44 * 0.4 = 0.576`. This `k1r` is very high.
        Let's try to keep `k1r` smaller. If `k1f=0.4` and `k1r=0.1` (as in Set 5 attempt but with higher k1f), the ratio `k1r/k1f = 0.1/0.4 = 0.25`. This would drive `S3` very low compared to `S2`.
        The previous simulation (iter4) had `k1f=0.1, k1r=0.05`. Final `S3=0.888, S2=0.959`. Ratio `S3/S2 = 0.92`. This was close to the experimental ratio of 1.44, but `S2` was too high.
        Let's try `k1f = 0.3`. And `k1r = 0.15` (to keep ratio 0.5 for now, will likely need adjustment).

    *   **`id_1a2z` (`S1`):** Initial concentration is 1. `d[S1]/dt = k2r[S2] - k2f[S1]`.
        Let's try `k2f = 0.6`. (Was 0.4).
        Target experimental ratio `[S1]/[S2] = 0.833/0.648 = 1.28`.
        So, `k2r/k2f ~ 1.28 => k2r = 1.28 * k2f = 1.28 * 0.6 = 0.768`. This `k2r` is also very high.
        If `k2f=0.6` and `k2r=0.2` (as in Set 5 attempt but with higher k2f), ratio `k2r/k2f = 0.2/0.6 = 1/3 = 0.33`. This would drive `S1` low compared to `S2`.
        Previous simulation (iter4) had `k2f=0.3, k2r=0.1`. Final `S1=0.369, S2=0.959`. Ratio `S1/S2 = 0.38`. This was far from exp ratio 1.28. `S1` was too low.
        To get `S1` higher relative to `S2`, we need `k2r/k2f` to be higher.
        Let's try `k2f = 0.5`. And `k2r = 0.3` (Ratio `k2r/k2f = 0.3/0.5 = 0.6`).

Parameters (Set 6):
*   `k_deg = 0.15` (Reduced from 0.5, slightly up from 0.1)

*   `k1f = 0.3` (Increased from 0.2, to speed up S3 consumption)
*   `k1r = 0.15` (Increased from 0.1, maintaining ratio k1r/k1f = 0.5. Target exp ratio S3/S2 is 1.44)

*   `k2f = 0.5` (Increased from 0.4, to speed up S1 consumption)
*   `k2r = 0.3` (Increased from 0.2, ratio k2r/k2f = 0.6. Target exp ratio S1/S2 is 1.28)

Let's check initial `id_khqo` increase condition: `(5*k1f + k2f) > (k1r + k2r + k_deg)`
`(5*0.3 + 0.5) > (0.15 + 0.3 + 0.15)`
`(1.5 + 0.5) > (0.6)`
`2.0 > 0.6`. True. So `id_khqo` should increase initially.

The ratios `k1r/k1f = 0.5` and `k2r/k2f = 0.6` are still below the target experimental ratios (1.44 and 1.28). This means `S3` and `S1` might end up lower than `S2` compared to experimental data, if these reversible reactions were the only factors. However, `k_deg` affects `S2` levels directly.

The goal is to get the final values in the ballpark first by adjusting `k_deg` and overall reaction speeds, then fine-tune ratios.
The previous `k_deg=0.1` (iter4) gave:
S1=0.369 (exp 0.833) - too low
S2=0.959 (exp 0.648) - too high
S3=0.888 (exp 0.934) - close

If `k_deg` is increased from 0.1 to 0.15, `S2` should decrease. This is good.
This decrease in `S2` will also affect `S1` and `S3`.
If `S2` decreases, then `S1 = (k2r/k2f) * S2` will also decrease, making it even lower. This is bad.
And `S3 = (k1r/k1f) * S2` will also decrease.

This suggests that the ratios `k2r/k2f` and `k1r/k1f` need to be increased towards their experimental targets.
Let's use the target ratios more directly with the new `k2f` and `k1f`.

Revised Parameters (Set 6b):
*   `k_deg = 0.15`

*   `k1f = 0.3`
*   `k1r = k1f * 1.44 = 0.3 * 1.44 = 0.432` (Uses experimental S3/S2 ratio)

*   `k2f = 0.5`
*   `k2r = k2f * 1.28 = 0.5 * 1.28 = 0.64` (Uses experimental S1/S2 ratio)

Check initial `id_khqo` increase: `(5*k1f + k2f) > (k1r + k2r + k_deg)`
`(5*0.3 + 0.5) > (0.432 + 0.64 + 0.15)`
`(1.5 + 0.5) > (1.072 + 0.15)`
`2.0 > 1.222`. True. `id_khqo` should still increase initially.

These `k1r` and `k2r` values are now quite high. This might make the reverse reactions very fast, potentially slowing down the net initial consumption of S1 and S3 if S2 builds up quickly.
Initial `d[S1]/dt = k2r[S2] - k2f[S1] = 0.64*1 - 0.5*1 = 0.14`. This means S1 will *increase* initially. This is wrong.
Experimental S1 decreases. So `k2f > k2r` must hold, at least initially when S1 and S2 are at their starting concentrations.

The conflict remains: initial dynamics require `k2f > k2r`, but apparent final equilibrium ratios suggest `k2r/k2f > 1`.
This could mean:
1.  The system is not actually reaching a simple steady state for the reversible parts due to the continuous drain by `k_deg`.
2.  The model is still missing a crucial element or interaction.
3.  The time course is complex, and S1 might dip then recover somewhat to its final value. (Exp data: S1 at T=0 is 1, T=0.12 is 0.8, T=30 is 0.833. It does dip and slightly recover).

Let's stick to `k2f > k2r` for the initial S1 drop.
Let `k2f = 0.5`, `k2r = 0.4`. (Ratio `k2r/k2f = 0.4/0.5 = 0.8`). This is closer to exp 1.28 than 0.6 was.
Initial `d[S1]/dt = 0.4*1 - 0.5*1 = -0.1`. S1 decreases. Good.

For S3: `k1f > k1r` (or `5*k1f > k1r` more accurately).
Let `k1f = 0.3`. Let `k1r = 0.2`. (Ratio `k1r/k1f = 0.2/0.3 = 0.67`). Exp S3/S2 is 1.44.
Initial `d[S3]/dt = k1r[S2] - k1f[S3] = 0.2*1 - 0.3*5 = 0.2 - 1.5 = -1.3`. S3 decreases. Good.

Parameters (Set 6c - "Manual Tuning Iteration"):
*   `k_deg = 0.25` (Trying a slightly higher k_deg than 0.15, as S2 was too high in iter4 with k_deg=0.1)

*   `k1f = 0.3`
*   `k1r = 0.2` (Ratio 0.67. Exp S3/S2=1.44)

*   `k2f = 0.5`
*   `k2r = 0.4` (Ratio 0.8. Exp S1/S2=1.28)

Check initial `id_khqo` increase: `(5*k1f + k2f) > (k1r + k2r + k_deg)`
`(5*0.3 + 0.5) > (0.2 + 0.4 + 0.25)`
`(1.5 + 0.5) > (0.6 + 0.25)`
`2.0 > 0.85`. True.

This set prioritizes:
- Initial decrease of S1 and S3.
- Initial increase of S2.
- A `k_deg` that hopefully brings S2 into the right range.
- `k1r/k1f` and `k2r/k2f` ratios are still below experimental apparent ratios, meaning S1 and S3 might be lower than target relative to S2.

Let's try this. The key is that `k_deg` might be the dominant factor setting the scale, and the reversible reactions then establish ratios around that.

## Action

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

# Access experimental data for comparison
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())
print("\nExperimental data (iteration_0) at T=0.12 for initial trend check:")
print(exp_data[exp_data['Time'] == 0.12])


# --- Part 1: Build the SBML model with new parameters (Set 6c) ---
sbml_doc_iter6 = libsbml.readSBMLFromString(input_sbml_string)
model_iter6 = sbml_doc_iter6.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 6c)
k1f_val = 0.3    # id_6o57 -> id_khqo
k1r_val = 0.2    # id_khqo -> id_6o57
k2f_val = 0.5    # id_1a2z -> id_khqo
k2r_val = 0.4    # id_khqo -> id_1a2z
k_deg_val = 0.25 # id_khqo -> ø

# Reactions
create_reaction_mod(model_iter6, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
create_reaction_mod(model_iter6, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
create_reaction_mod(model_iter6, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
create_reaction_mod(model_iter6, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

reaction_deg = model_iter6.createReaction()
reaction_deg.setId("R_deg_khqo")
reaction_deg.setReversible(False)
reaction_deg.setFast(False)
reactant_deg = reaction_deg.createReactant()
reactant_deg.setSpecies("id_khqo")
reactant_deg.setStoichiometry(1)
reactant_deg.setConstant(False)
kinetic_law_deg = reaction_deg.createKineticLaw()
param_deg = kinetic_law_deg.createParameter()
param_deg.setId("k_deg")
param_deg.setValue(k_deg_val)
param_deg.setConstant(True)
math_ast_deg = libsbml.parseL3Formula("k_deg * id_khqo")
kinetic_law_deg.setMath(math_ast_deg)

writer = libsbml.SBMLWriter()
updated_sbml_str_iter6 = writer.writeSBMLToString(sbml_doc_iter6)
shared_variables.add("current_sbml_model_iter6", updated_sbml_str_iter6)
print("\nUpdated SBML model (iter6) with 5 reactions and new parameters (Set 6c).")

# --- Part 2: Simulate the new model ---
sim_data_iter6 = simulate(updated_sbml_str_iter6)
shared_variables.add("simulation_results_iter6", sim_data_iter6)
print("\nSimulation of the updated model (iter6) completed.")
print("Simulated data (iter6) head:")
print(sim_data_iter6.head())
print("\nSimulated data (iter6) at T=0.12 for initial trend check:")
# Find the row closest to T=0.12 if not exact
time_point = 0.12
closest_time_row = sim_data_iter6.iloc[(sim_data_iter6['Time']-time_point).abs().argsort()[:1]]
print(closest_time_row)
print("\nSimulated data (iter6) tail:")
print(sim_data_iter6.tail())

# Compare with experimental tail:
# Exp: id_1a2z=0.833, id_khqo=0.648, id_6o57=0.934
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Experimental data (iteration_0) at T=0.12 for initial trend check:
    id_1a2z   id_khqo   id_6o57  Time
4  0.800585  1.076063  4.557085  0.12

Updated SBML model (iter6) with 5 reactions and new parameters (Set 6c).

Simulation of the updated model (iter6) completed.
Simulated data (iter6) head:
    id_1a2z   id_khqo   id_6o57  Time
0  1.000000  1.000000  5.000000  0.00
1  0.997226  1.033868  4.961278  0.03
2  0.994889  1.066507  4.923100  0.06
3  0.992967  1.097956  4.885455  0.09
4  0.991443  1.128254  4.848332  0.12

Simulated data (iter6) at T=0.12 for initial trend check:
    id_1a2z   id_khqo   id_6o57  Time
4  0.991443  1.128254  4.848332  0.12

Simulated data (iter6) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.195179  0.201965  0.188948  29.88
997   0.194676  0.201443  0.188460  29.91
998   0.194174  0.200924  0.187973  29.94
999   0.193673  0.200405  0.187487  29.97
1000  0.193173  0.199888  0.187003  30.00

## 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_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6)

### 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 results with parameters from Set 6c (`k1f=0.3, k1r=0.2, k2f=0.5, k2r=0.4, k_deg=0.25`) are getting closer in some aspects but still off.

**Experimental Data:**
*   T=0.12: `id_1a2z=0.800`, `id_khqo=1.076`, `id_6o57=4.557`
*   T=30: `id_1a2z=0.833`, `id_khqo=0.648`, `id_6o57=0.934`

**Simulated Data (iter6, Set 6c):**
*   T=0.12: `id_1a2z=0.991`, `id_khqo=1.128`, `id_6o57=4.848`
*   T=30: `id_1a2z=0.193`, `id_khqo=0.200`, `id_6o57=0.187`

**Analysis:**

1.  **Initial Trends (T=0.12):**
    *   `id_1a2z`: Exp drop = 0.2 (1.0 -> 0.8). Sim drop = 0.009 (1.0 -> 0.991). Initial consumption of `id_1a2z` is far too slow. `k2f` needs to be much larger relative to `k2r` for the initial phase, or `k2f` itself needs to be larger.
    *   `id_khqo`: Exp increase to 1.076. Sim increase to 1.128. This is reasonably good.
    *   `id_6o57`: Exp drop = 0.443 (5.0 -> 4.557). Sim drop = 0.152 (5.0 -> 4.848). Initial consumption of `id_6o57` is too slow. `k1f` needs to be larger.

2.  **Final Concentrations (T=30):**
    *   All simulated final concentrations are too low.
        *   `id_1a2z`: 0.193 (Exp 0.833)
        *   `id_khqo`: 0.200 (Exp 0.648)
        *   `id_6o57`: 0.187 (Exp 0.934)
    *   This suggests `k_deg = 0.25` is still too high, or the production/recycling via reverse reactions is too weak.

**Revised Parameter Tuning Strategy:**

*   **Reduce `k_deg`:** Since all final values are too low, `k_deg` is a primary suspect. It was 0.1 in iter4 (S2 too high), 0.5 in iter5 (all too low), 0.25 in iter6 (all too low). The sweet spot is likely lower than 0.25. Let's try `k_deg = 0.1` again, or perhaps `0.08`.
    If `k_deg` from iter4 (`0.1`) gave `S2=0.959` (Exp 0.648), and `k_deg=0.25` (iter6) gave `S2=0.200`, then `k_deg` has a strong effect.
    Target `S2` is ~0.65. Iter4 `S2` was `0.96`. Iter6 `S2` was `0.20`.
    A linear interpolation for `k_deg` to get `S2=0.65`:
    `(0.65 - 0.20) / (0.96 - 0.20) = (k_deg_target - 0.25) / (0.1 - 0.25)`
    `0.45 / 0.76 = (k_deg_target - 0.25) / (-0.15)`
    `0.592 = (k_deg_target - 0.25) / (-0.15)`
    `0.592 * (-0.15) = k_deg_target - 0.25`
    `-0.0888 = k_deg_target - 0.25`
    `k_deg_target = 0.25 - 0.0888 = 0.1612`.
    Let's try `k_deg = 0.16`.

*   **Increase `k1f` and `k2f` significantly for faster initial consumption.**
    *   **`id_6o57` (`S3`):** `k1f` was 0.3. Initial drop was too slow. Let's try `k1f = 0.7`.
        Keep `k1r` such that `k1r/k1f` aims for the experimental ratio `[S3]/[S2] = 1.44`.
        `k1r = 1.44 * k1f = 1.44 * 0.7 = 1.008`. This is a very high reverse rate.

    *   **`id_1a2z` (`S1`):** `k2f` was 0.5. Initial drop was far too slow. Let's try `k2f = 1.5` (a big jump).
        Keep `k2r` such that `k2r/k2f` aims for the experimental ratio `[S1]/[S2] = 1.28`.
        `k2r = 1.28 * k2f = 1.28 * 1.5 = 1.92`. Also a very high reverse rate.

    The problem with using final equilibrium ratios for `k_rev/k_fwd` is that it might conflict with initial dynamics if `k_fwd` and `k_rev` are both large.
    For `S1` to decrease initially: `k2f * [S1]_0 > k2r * [S2]_0`.
    With `[S1]_0=1, [S2]_0=1`: `k2f > k2r`.
    But our ratio calculation gives `k2r = 1.28 * k2f`, so `k2r > k2f`. This is the persistent conflict.

    This implies that the system does not simply settle to `(k_rev/k_fwd) * S2`. The `k_deg` term means `S2` is actively drained, so `S1` and `S3` might be higher relative to `S2` than these simple ratios suggest, because the "source" reactions (`S1->S2`, `S3->S2`) are constantly working against the drain on `S2`.

    Let's re-evaluate. The non-monotonic behavior of `S1` (id_1a2z) is:
    1.0 (initial) -> 0.80 (T=0.12, dip) -> ... -> 0.318 (T=1.2, deeper dip) -> ... -> 1.6 (T=4.8, peak) -> ... -> 0.833 (T=30, final).
    This is complex! A simple `S1 <=> S2` + `S2 drain` might not capture this.
    The peak at T=4.8 where `S1` is 1.6 (higher than initial) is particularly interesting.
    This means `S1` is produced significantly at some point. The only reaction producing `S1` is `S2 -> S1` (rate `k2r`).
    For `S1` to go above its initial value, `k2r * [S2]` must be greater than `k2f * [S1]` when `S1` is around 1.0-1.6 and `S2` is whatever its value is at that time.

    The experimental data for `id_khqo` (S2) is:
    1.0 (initial) -> 1.076 (T=0.12) -> ... -> 2.26 (T=1.2, peak for S2?) -> ... -> 0.648 (T=30, final).
    So `S2` also has a peak.

    This complex oscillatory/multi-phasic behavior might hint at something more than simple mass-action kinetics or a missing regulatory step. However, we are constrained to adding reactions with existing species.

    Perhaps the high intermediate values of `S2` drive the production of `S1` (via `k2r`) causing `S1` to overshoot its initial value, before everything settles down due to `k_deg`.

    Let's try to get the initial drops faster and the final values closer with `k_deg = 0.16`.
    To get `S1` to drop fast: `k2f` must be large, and `k2r` must be smaller than `k2f` (at T=0).
    Let `k2f = 1.0`. Let `k2r = 0.5`. (So `k2f > k2r`). Ratio `k2r/k2f = 0.5`. (Exp target 1.28).
    To get `S3` to drop fast: `k1f` must be large.
    Let `k1f = 0.5`. Let `k1r = 0.25`. (So `5*k1f > k1r` is `2.5 > 0.25`). Ratio `k1r/k1f = 0.5`. (Exp target 1.44).

Parameters (Set 7 - "Aggressive Initial, Moderate k_deg, Low Ratios"):
*   `k_deg = 0.16`

*   `k1f = 0.5` (S3 -> S2)
*   `k1r = 0.25` (S2 -> S3) Ratio 0.5

*   `k2f = 1.0` (S1 -> S2)
*   `k2r = 0.5` (S2 -> S1) Ratio 0.5

Check initial `id_khqo` increase: `(5*k1f + k2f) > (k1r + k2r + k_deg)`
`(5*0.5 + 1.0) > (0.25 + 0.5 + 0.16)`
`(2.5 + 1.0) > (0.75 + 0.16)`
`3.5 > 0.91`. True. `S2` should increase strongly.

This set has:
- Faster forward rates `k1f, k2f`.
- `k_fwd > k_rev` for both pairs initially.
- Reverse/Forward ratios are 0.5, which is lower than experimental targets (1.44, 1.28). This might make S1 and S3 too low compared to S2 at the end. But the goal is to see if `k_deg=0.16` brings S2 to the right ballpark, and if the faster initial rates work.

The fact that `S1` experimentally goes 1.0 -> 0.8 -> 1.6 -> 0.833 is very challenging for this simple model structure.
The rise of `S1` to 1.6 means that `k2r * [S2]` must dominate `k2f * [S1]` during that phase.
If `S2` peaks around 2.26 (at T=1.2) and `S1` is, say, 0.5 at that time:
`k2r * 2.26` vs `k2f * 0.5`.
If `k2f=1.0, k2r=0.5`: `0.5 * 2.26 = 1.13` vs `1.0 * 0.5 = 0.5`. So `S1` would indeed increase.
This suggests that the chosen `k2f, k2r` might allow for such behavior if `S2` peaks appropriately.

## Action

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

# Access experimental data for comparison
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())
print("\nExperimental data (iteration_0) at T=0.12 for initial trend check:")
print(exp_data[exp_data['Time'] == 0.12])
print("\nExperimental data (iteration_0) at T=1.2 for S2 peak check:")
print(exp_data[exp_data['Time'] == 1.2])
print("\nExperimental data (iteration_0) at T=4.8 for S1 peak check:")
print(exp_data[exp_data['Time'] == 4.8])


# --- Part 1: Build the SBML model with new parameters (Set 7) ---
sbml_doc_iter7 = libsbml.readSBMLFromString(input_sbml_string)
model_iter7 = sbml_doc_iter7.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 7)
k1f_val = 0.5    # S3 (id_6o57) -> S2 (id_khqo)
k1r_val = 0.25   # S2 -> S3
k2f_val = 1.0    # S1 (id_1a2z) -> S2
k2r_val = 0.5    # S2 -> S1
k_deg_val = 0.16 # S2 -> ø

# Reactions
create_reaction_mod(model_iter7, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
create_reaction_mod(model_iter7, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
create_reaction_mod(model_iter7, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
create_reaction_mod(model_iter7, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

reaction_deg = model_iter7.createReaction()
reaction_deg.setId("R_deg_khqo")
reaction_deg.setReversible(False)
reaction_deg.setFast(False)
reactant_deg = reaction_deg.createReactant()
reactant_deg.setSpecies("id_khqo")
reactant_deg.setStoichiometry(1)
reactant_deg.setConstant(False)
kinetic_law_deg = reaction_deg.createKineticLaw()
param_deg = kinetic_law_deg.createParameter()
param_deg.setId("k_deg")
param_deg.setValue(k_deg_val)
param_deg.setConstant(True)
math_ast_deg = libsbml.parseL3Formula("k_deg * id_khqo")
kinetic_law_deg.setMath(math_ast_deg)

writer = libsbml.SBMLWriter()
updated_sbml_str_iter7 = writer.writeSBMLToString(sbml_doc_iter7)
shared_variables.add("current_sbml_model_iter7", updated_sbml_str_iter7)
print("\nUpdated SBML model (iter7) with 5 reactions and new parameters (Set 7).")

# --- Part 2: Simulate the new model ---
sim_data_iter7 = simulate(updated_sbml_str_iter7)
shared_variables.add("simulation_results_iter7", sim_data_iter7)
print("\nSimulation of the updated model (iter7) completed.")

print("\nSimulated data (iter7) at T=0.12:")
time_point = 0.12
closest_time_row_sim_012 = sim_data_iter7.iloc[(sim_data_iter7['Time']-time_point).abs().argsort()[:1]]
print(closest_time_row_sim_012)

print("\nSimulated data (iter7) at T=1.2:")
time_point = 1.2
closest_time_row_sim_12 = sim_data_iter7.iloc[(sim_data_iter7['Time']-time_point).abs().argsort()[:1]]
print(closest_time_row_sim_12)

print("\nSimulated data (iter7) at T=4.8:")
time_point = 4.8
closest_time_row_sim_48 = sim_data_iter7.iloc[(sim_data_iter7['Time']-time_point).abs().argsort()[:1]]
print(closest_time_row_sim_48)

print("\nSimulated data (iter7) tail:")
print(sim_data_iter7.tail())
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Experimental data (iteration_0) at T=0.12 for initial trend check:
    id_1a2z   id_khqo   id_6o57  Time
4  0.800585  1.076063  4.557085  0.12

Experimental data (iteration_0) at T=1.2 for S2 peak check:
     id_1a2z  id_khqo  id_6o57  Time
40  0.317717  2.26247  2.21713   1.2

Experimental data (iteration_0) at T=4.8 for S1 peak check:
     id_1a2z   id_khqo   id_6o57  Time
160  1.59978  1.771463  0.974262   4.8

Updated SBML model (iter7) with 5 reactions and new parameters (Set 7).

Simulation of the updated model (iter7) completed.

Simulated data (iter7) at T=0.12:
    id_1a2z   id_khqo  id_6o57  Time
4  0.951888  1.283863  4.74224  0.12

Simulated data (iter7) at T=1.2:
     id_1a2z   id_khqo   id_6o57  Time
40  1.016033  2.423864  3.191746   1.2

Simulated data (iter7) at T=4.8:
      id_1a2z   id_khqo   id_6o57  Time
160  1.231245  2.372246  1.571886   4.8

Simulated data (iter7) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.200235  0.370375  0.217945  29.88
997   0.199784  0.369541  0.217454  29.91
998   0.199334  0.368708  0.216964  29.94
999   0.198885  0.367878  0.216475  29.97
1000  0.198437  0.367050  0.215988  30.00

## 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)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6, current_sbml_model_iter7, simulation_results_iter7)

### 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 simulation results with parameters from Set 7 (`k1f=0.5, k1r=0.25, k2f=1.0, k2r=0.5, k_deg=0.16`) show some improvements in capturing peaks but still have issues with initial drops and final values.

**Experimental Data:**
*   T=0.12: `S1=0.800`, `S2=1.076`, `S3=4.557`
*   T=1.2: `S1=0.318`, `S2=2.262`, `S3=2.217` (S2 peak around here)
*   T=4.8: `S1=1.600`, `S2=1.771`, `S3=0.974` (S1 peak around here)
*   T=30: `S1=0.833`, `S2=0.648`, `S3=0.934`

**Simulated Data (iter7, Set 7):**
*   T=0.12: `S1=0.952`, `S2=1.284`, `S3=4.742`
*   T=1.2: `S1=1.016`, `S2=2.424`, `S3=3.192`
*   T=4.8: `S1=1.231`, `S2=2.372`, `S3=1.572`
*   T=30: `S1=0.198`, `S2=0.367`, `S3=0.216`

**Analysis:**

1.  **Initial Trends (T=0.12):**
    *   `S1 (id_1a2z)`: Exp drop = 0.2 (1.0 -> 0.8). Sim drop = 0.048 (1.0 -> 0.952). Still too slow. `k2f` needs to be even more dominant over `k2r` initially or `k2f` larger.
    *   `S2 (id_khqo)`: Exp increase to 1.076. Sim increase to 1.284. Sim S2 is a bit high/fast.
    *   `S3 (id_6o57)`: Exp drop = 0.443 (5.0 -> 4.557). Sim drop = 0.258 (5.0 -> 4.742). Still too slow. `k1f` needs to be larger.

2.  **Intermediate Peaks:**
    *   `S2` peak: Exp ~2.26 at T=1.2. Sim ~2.42 at T=1.2. This is quite good in terms of magnitude and timing!
    *   `S1` behavior around T=1.2: Exp `S1=0.318`. Sim `S1=1.016`. Simulated `S1` does not dip low enough. It should be consumed more heavily by `k2f` before `S2` peaks and `k2r` drives it back up.
    *   `S1` peak: Exp ~1.6 at T=4.8. Sim `S1=1.231` at T=4.8. Simulated `S1` does show a rise after the initial phase (it was 0.952 at T=0.12, then 1.016 at T=1.2, then 1.231 at T=4.8), but the peak is too low and possibly too late/broad. The rise is driven by `k2r * S2`.

3.  **Final Concentrations (T=30):**
    *   All simulated final concentrations are too low again.
        *   `S1`: 0.198 (Exp 0.833)
        *   `S2`: 0.367 (Exp 0.648)
        *   `S3`: 0.216 (Exp 0.934)
    *   This suggests `k_deg = 0.16` is still too high. The interpolation was based on different `k` values for other reactions.

**Revised Parameter Tuning Strategy:**

*   **Reduce `k_deg` further.** Iter4 (`k_deg=0.1`) gave `S1=0.369, S2=0.959, S3=0.888`. `S2` was too high, `S1` too low, `S3` good.
    Iter7 (`k_deg=0.16`) gave `S1=0.198, S2=0.367, S3=0.216`. All too low.
    The optimal `k_deg` is likely between 0.1 and 0.16. Let's try `k_deg = 0.08`. This is a substantial reduction. This should raise all final concentrations.

*   **Aggressively increase `k2f` for initial `S1` drop, and `k1f` for `S3` drop.**
    *   **`S1 (id_1a2z)`:**
        *   Initial drop: `k2f` needs to be much larger. Let `k2f = 2.5`.
        *   To allow `S1` to dip low and then recover to ~1.6, `k2r` needs to be effective when `S2` is high.
        *   The ratio `k2r/k2f` influences where `S1` might try to settle relative to `S2` if `k_deg` was zero. Exp `S1/S2` at T=30 is 1.28.
        *   Let `k2r = k2f * 0.3 = 2.5 * 0.3 = 0.75`. This keeps `k2f > k2r` for the initial drop. Ratio `k2r/k2f = 0.3`. This is low compared to 1.28, which might make final `S1` too low if `S2` is correct. But the dynamics are complex.

    *   **`S3 (id_6o57)`:**
        *   Initial drop: `k1f` needs to be larger. Let `k1f = 1.0`.
        *   Exp `S3/S2` at T=30 is 1.44.
        *   Let `k1r = k1f * 0.3 = 1.0 * 0.3 = 0.3`. Ratio `k1r/k1f = 0.3`. Low compared to 1.44.

    The choice of `k_rev/k_fwd = 0.3` is arbitrary, aiming to keep reverse rates lower than forward rates to ensure initial consumption, but allowing some recovery.

Parameters (Set 8 - "Very Aggressive Initial, Lower k_deg, Low Ratios"):
*   `k_deg = 0.08` (Reduced from 0.16)

*   `k1f = 1.0` (S3 -> S2) (Was 0.5)
*   `k1r = 0.3` (S2 -> S3) (Ratio 0.3) (Was 0.25)

*   `k2f = 2.5` (S1 -> S2) (Was 1.0)
*   `k2r = 0.75` (S2 -> S1) (Ratio 0.3) (Was 0.5)

Check initial `id_khqo` (S2) increase: `(5*k1f + k2f) > (k1r + k2r + k_deg)`
`(5*1.0 + 2.5) > (0.3 + 0.75 + 0.08)`
`(5.0 + 2.5) > (1.05 + 0.08)`
`7.5 > 1.13`. True. `S2` should increase very strongly. This might make `S2` peak too high/fast.

The strategy is to get the initial deep plunge of S1 by making `k2f` very large. Then, when S2 peaks (hopefully due to the large influx from S1 and S3), `k2r` (also now larger) can drive S1 back up. The lower `k_deg` should help final values.

The low `k_rev/k_fwd` ratios (0.3) might mean that S1 and S3 will be too low compared to S2 at the end.
Experimental final ratios: `S1/S2 = 0.833/0.648 = 1.28`. `S3/S2 = 0.934/0.648 = 1.44`.
My chosen ratios are much smaller. This is a gamble on dynamic effects.

If this doesn't work, I might need to reconsider the model structure. The complex S1 dynamics are the hardest to capture.
Could there be a reaction like `S2 + S2 -> S1` or some other non-linearity? The problem says "You do not need to add new species", which usually implies sticking to simpler reaction orders unless data strongly forces it.

Let's test Set 8.

## Action

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

# Access experimental data for comparison
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())
print("\nExperimental data (iteration_0) at T=0.12:")
print(exp_data[exp_data['Time'] == 0.12])
print("\nExperimental data (iteration_0) at T=1.2:")
print(exp_data[exp_data['Time'] == 1.2])
print("\nExperimental data (iteration_0) at T=4.8:")
print(exp_data[exp_data['Time'] == 4.8])

# --- Part 1: Build the SBML model with new parameters (Set 8) ---
sbml_doc_iter8 = libsbml.readSBMLFromString(input_sbml_string)
model_iter8 = sbml_doc_iter8.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 8)
k1f_val = 1.0    # S3 (id_6o57) -> S2 (id_khqo)
k1r_val = 0.3    # S2 -> S3
k2f_val = 2.5    # S1 (id_1a2z) -> S2
k2r_val = 0.75   # S2 -> S1
k_deg_val = 0.08 # S2 -> ø

# Reactions
create_reaction_mod(model_iter8, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
create_reaction_mod(model_iter8, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
create_reaction_mod(model_iter8, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
create_reaction_mod(model_iter8, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

reaction_deg = model_iter8.createReaction()
reaction_deg.setId("R_deg_khqo")
reaction_deg.setReversible(False)
reaction_deg.setFast(False)
reactant_deg = reaction_deg.createReactant()
reactant_deg.setSpecies("id_khqo")
reactant_deg.setStoichiometry(1)
reactant_deg.setConstant(False)
kinetic_law_deg = reaction_deg.createKineticLaw()
param_deg = kinetic_law_deg.createParameter()
param_deg.setId("k_deg")
param_deg.setValue(k_deg_val)
param_deg.setConstant(True)
math_ast_deg = libsbml.parseL3Formula("k_deg * id_khqo")
kinetic_law_deg.setMath(math_ast_deg)

writer = libsbml.SBMLWriter()
updated_sbml_str_iter8 = writer.writeSBMLToString(sbml_doc_iter8)
shared_variables.add("current_sbml_model_iter8", updated_sbml_str_iter8)
print("\nUpdated SBML model (iter8) with 5 reactions and new parameters (Set 8).")

# --- Part 2: Simulate the new model ---
sim_data_iter8 = simulate(updated_sbml_str_iter8)
shared_variables.add("simulation_results_iter8", sim_data_iter8)
print("\nSimulation of the updated model (iter8) completed.")

print("\nSimulated data (iter8) at T=0.12:")
time_point = 0.12
closest_time_row_sim_012 = sim_data_iter8.iloc[(sim_data_iter8['Time']-time_point).abs().argsort()[:1]]
print(closest_time_row_sim_012)

print("\nSimulated data (iter8) at T=1.2:")
time_point = 1.2
closest_time_row_sim_12 = sim_data_iter8.iloc[(sim_data_iter8['Time']-time_point).abs().argsort()[:1]]
print(closest_time_row_sim_12)

print("\nSimulated data (iter8) at T=4.8:")
time_point = 4.8
closest_time_row_sim_48 = sim_data_iter8.iloc[(sim_data_iter8['Time']-time_point).abs().argsort()[:1]]
print(closest_time_row_sim_48)

print("\nSimulated data (iter8) tail:")
print(sim_data_iter8.tail())
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Experimental data (iteration_0) at T=0.12:
    id_1a2z   id_khqo   id_6o57  Time
4  0.800585  1.076063  4.557085  0.12

Experimental data (iteration_0) at T=1.2:
     id_1a2z  id_khqo  id_6o57  Time
40  0.317717  2.26247  2.21713   1.2

Experimental data (iteration_0) at T=4.8:
     id_1a2z   id_khqo   id_6o57  Time
160  1.59978  1.771463  0.974262   4.8

Updated SBML model (iter8) with 5 reactions and new parameters (Set 8).

Simulation of the updated model (iter8) completed.

Simulated data (iter8) at T=0.12:
    id_1a2z   id_khqo   id_6o57  Time
4  0.846779  1.659797  4.480499  0.12

Simulated data (iter8) at T=1.2:
     id_1a2z   id_khqo   id_6o57  Time
40  0.980383  3.609635  2.140328   1.2

Simulated data (iter8) at T=4.8:
     id_1a2z   id_khqo   id_6o57  Time
160  1.06512  3.486756  1.113573   4.8

Simulated data (iter8) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.310280  1.013857  0.319941  29.88
997   0.309821  1.012358  0.319468  29.91
998   0.309363  1.010860  0.318995  29.94
999   0.308905  1.009365  0.318524  29.97
1000  0.308449  1.007873  0.318053  30.00

## 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)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6, current_sbml_model_iter7, simulation_results_iter7, current_sbml_model_iter8, simulation_results_iter8)

### 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 simulation results with parameters from Set 8 (`k1f=1.0, k1r=0.3, k2f=2.5, k2r=0.75, k_deg=0.08`) are showing some interesting dynamics, but still not quite there.

**Experimental Data:**
*   T=0.12: `S1=0.800`, `S2=1.076`, `S3=4.557`
*   T=1.2: `S1=0.318`, `S2=2.262`, `S3=2.217`
*   T=4.8: `S1=1.600`, `S2=1.771`, `S3=0.974`
*   T=30: `S1=0.833`, `S2=0.648`, `S3=0.934`

**Simulated Data (iter8, Set 8):**
*   T=0.12: `S1=0.847`, `S2=1.660`, `S3=4.480`
*   T=1.2: `S1=0.980`, `S2=3.610`, `S3=2.140`
*   T=4.8: `S1=1.065`, `S2=3.487`, `S3=1.114`
*   T=30: `S1=0.308`, `S2=1.008`, `S3=0.318`

**Analysis:**

1.  **Initial Trends (T=0.12):**
    *   `S1 (id_1a2z)`: Exp drop = 0.2 (to 0.800). Sim drop = 0.153 (to 0.847). This is much better! The initial drop is now significant.
    *   `S2 (id_khqo)`: Exp increase to 1.076. Sim increase to 1.660. Sim S2 is now too high/fast initially. This is due to the very large `k1f` and `k2f`.
    *   `S3 (id_6o57)`: Exp drop = 0.443 (to 4.557). Sim drop = 0.520 (to 4.480). This is also much better!

2.  **Intermediate Peaks & Dips:**
    *   `S1` dip at T=1.2: Exp `S1=0.318`. Sim `S1=0.980`. The simulated `S1` does not dip nearly low enough. It seems `k2f` is not sustained enough or `k2r*S2` kicks in too early/strongly.
    *   `S2` peak at T=1.2: Exp `S2=2.262`. Sim `S2=3.610`. Simulated `S2` peak is too high. This is likely due to the very aggressive `k1f` and `k2f`.
    *   `S1` peak at T=4.8: Exp `S1=1.600`. Sim `S1=1.065`. Simulated `S1` does rise after its initial value (0.847 -> 0.980 -> 1.065), but the peak is far too low.
    *   `S3` at T=1.2: Exp `S3=2.217`. Sim `S3=2.140`. This is surprisingly close!

3.  **Final Concentrations (T=30):**
    *   `S1`: 0.308 (Exp 0.833) - Too low.
    *   `S2`: 1.008 (Exp 0.648) - Too high.
    *   `S3`: 0.318 (Exp 0.934) - Too low.
    *   The `k_deg=0.08` seems to have made `S2` too high at the end, and consequently `S1` and `S3` are also not matching their targets (though their lowness is also due to their `k_rev/k_fwd` ratios).

**Revised Parameter Tuning Strategy:**

*   **`k_deg`:** `k_deg=0.08` made final `S2` too high (1.008 vs 0.648). `k_deg=0.16` (iter7) made final `S2` too low (0.367 vs 0.648). The target `k_deg` is between 0.08 and 0.16. Let's try `k_deg = 0.12`. (Interpolating again: `(0.648-0.367)/(1.008-0.367) = (k_target-0.16)/(0.08-0.16)` => `0.281/0.641 = (k_target-0.16)/(-0.08)` => `0.438 * -0.08 = k_target-0.16` => `-0.035 = k_target-0.16` => `k_target = 0.125`. So `0.12` or `0.13` seems reasonable). Let's use `k_deg = 0.12`.

*   **Initial `S2` overshoot:** `S2` peak is too high (3.61 vs 2.26). This is from `k1f` and `k2f` being too large.
    *   Reduce `k1f` and `k2f` slightly from Set 8.
    *   Set 8: `k1f=1.0, k2f=2.5`.
    *   Let's try `k1f = 0.8` and `k2f = 2.0`.

*   **`S1` dynamics (dip and peak):**
    *   The dip of `S1` to 0.318 was not achieved. `S1` only went to ~0.847. This means `k2f` needs to be even more dominant initially, or `S2` needs to stay lower initially so `k2r*S2` is small.
    *   The peak of `S1` to 1.6 was not achieved (sim peak ~1.065). This needs stronger `k2r*S2` when `S2` is high.
    *   This suggests `k2f` should be very high, and `k2r` should also be substantial but less than `k2f`.
    *   Current `k2f=2.0, k2r = k2f*0.3 = 0.6`. (Ratio 0.3).
    *   Experimental final `S1/S2 = 1.28`. If `S2` final is ~0.65, then `S1` final should be `1.28*0.65 = 0.832`.
    *   If `k2r/k2f` is set to 1.28, then `k2r = 1.28 * k2f`. This would mean `k2r > k2f`, violating initial S1 drop.

*   **`S3` dynamics:**
    *   Initial drop of `S3` was good with `k1f=1.0`. `k1f=0.8` might make it slightly slower but could help S2 peak.
    *   `k1r = k1f*0.3 = 0.8*0.3 = 0.24`. (Ratio 0.3).
    *   Experimental final `S3/S2 = 1.44`. If `S2` final is ~0.65, then `S3` final should be `1.44*0.65 = 0.936`.

The ratios `k_rev/k_fwd` are critical for final distributions if `k_deg` is small or the system is near equilibrium for reversible parts.
Let's try to use the target experimental ratios for `k_rev/k_fwd` and see if the dynamics can still work out with a carefully chosen `k_deg`.
This means `k2r > k2f` and `k1r > k1f`. This will prevent initial S1/S3 drop if S1,S2,S3 start at similar levels.
However, S3 starts very high (5.0). So `k1f*S3_0` can still be much larger than `k1r*S2_0`.
`k1f*5 > k1r*1`. If `k1r/k1f = 1.44`, then `k1r = 1.44*k1f`. So `5*k1f > 1.44*k1f*1`, which is `5 > 1.44`. True. So S3 can still drop.

For S1: `k2f*S1_0` vs `k2r*S2_0`. `k2f*1` vs `k2r*1`. If `k2r/k2f = 1.28`, then `k2r = 1.28*k2f`.
So `k2f` vs `1.28*k2f`. This means `d[S1]/dt` will be negative only if `k2f < 1.28 k2f` which is true, but it means `d[S1]/dt = (1.28 k2f) * S2_0 - k2f * S1_0 = k2f * (1.28 S2_0 - S1_0)`.
If `S1_0=1, S2_0=1`, then `d[S1]/dt = k2f * (1.28 - 1) = 0.28 * k2f > 0`. So S1 will *increase* initially. This is the persistent problem.

This implies that the model `S1 <=> S2 -> ø` and `S3 <=> S2` with mass action cannot capture the S1 initial drop *and* its later rise above initial *and* its final value relative to S2 using these target ratios.

What if the initial drop of S1 is due to a different, faster reaction that gets inactivated or substrate-limited? Not possible with current constraints.

Is it possible that one of the species (e.g. S1) also degrades directly?
`S1 -> ø` (k_deg_S1)
This would help S1 drop initially and stay lower.
If S1 also degrades, then `d[S1]/dt = k2r*S2 - k2f*S1 - k_deg_S1*S1`.
For S1 to drop initially: `k2f*S1_0 + k_deg_S1*S1_0 > k2r*S2_0`.
`(k2f + k_deg_S1) > k2r`. This is easier to satisfy.

Let's try adding a small degradation term for S1. This is a model structure change.
The problem states "all species are observable" and "You do not need to add new species." It doesn't explicitly forbid adding more reactions like degradation for existing species. The observation of net loss of total moles already pushed for `S2 -> ø`.

Hypothesis: S1 also degrades. `S1 -> ø` with rate `k_d1 * S1`.
Parameters (Set 9 - "S1 degradation, target ratios for reversible"):
*   `k_deg_S2 = 0.12` (for S2, formerly k_deg)

*   `k1f = 0.8` (S3 -> S2)
*   `k1r = k1f * 1.44 = 0.8 * 1.44 = 1.152` (S2 -> S3, using exp. S3/S2 ratio)

*   `k2f = 1.0` (S1 -> S2) (Reduced from 2.0 to make S2 peak less extreme)
*   `k2r = k2f * 1.28 = 1.0 * 1.28 = 1.28` (S2 -> S1, using exp. S1/S2 ratio)

*   `k_d1 = ?` (S1 -> ø)
    Initial `d[S1]/dt = k2r*S2_0 - k2f*S1_0 - k_d1*S1_0 = 1.28*1 - 1.0*1 - k_d1*1 = 0.28 - k_d1`.
    For S1 to drop, `0.28 - k_d1 < 0 => k_d1 > 0.28`. Let `k_d1 = 0.4`.

Check S2 initial increase: `(5*k1f + k2f) > (k1r + k2r + k_deg_S2)`
`(5*0.8 + 1.0) > (1.152 + 1.28 + 0.12)`
`(4.0 + 1.0) > (2.432 + 0.12)`
`5.0 > 2.552`. True. S2 should increase.

This model now has 6 reactions.
This might allow S1 to drop initially (due to `k2f + k_d1`) and then rise (if `k2r*S2` becomes large) and then settle.

## Action

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

# Access experimental data
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())
# ... (print other specific time points if needed for checking)

# --- Part 1: Build the SBML model with S1 degradation (Set 9) ---
sbml_doc_iter9 = libsbml.readSBMLFromString(input_sbml_string)
model_iter9 = sbml_doc_iter9.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    # ... (same helper function as before)
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 9)
k1f_val = 0.8     # S3 (id_6o57) -> S2 (id_khqo)
k1r_val = 1.152   # S2 -> S3 (k1f * 1.44)
k2f_val = 1.0     # S1 (id_1a2z) -> S2
k2r_val = 1.28    # S2 -> S1 (k2f * 1.28)
k_deg_S2_val = 0.12 # S2 -> ø (formerly k_deg)
k_d1_val = 0.4    # S1 -> ø (new degradation for S1)

# Reactions
# S3 <-> S2
create_reaction_mod(model_iter9, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
create_reaction_mod(model_iter9, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
# S1 <-> S2
create_reaction_mod(model_iter9, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
create_reaction_mod(model_iter9, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

# S2 degradation
reaction_deg_S2 = model_iter9.createReaction()
reaction_deg_S2.setId("R_deg_S2")
reaction_deg_S2.setReversible(False)
reactant_deg_S2 = reaction_deg_S2.createReactant(); reactant_deg_S2.setSpecies("id_khqo"); reactant_deg_S2.setStoichiometry(1)
kl_S2 = reaction_deg_S2.createKineticLaw(); param_S2 = kl_S2.createParameter(); param_S2.setId("k_deg_S2"); param_S2.setValue(k_deg_S2_val)
kl_S2.setMath(libsbml.parseL3Formula("k_deg_S2 * id_khqo"))

# S1 degradation (New)
reaction_deg_S1 = model_iter9.createReaction()
reaction_deg_S1.setId("R_deg_S1")
reaction_deg_S1.setReversible(False)
reactant_deg_S1 = reaction_deg_S1.createReactant(); reactant_deg_S1.setSpecies("id_1a2z"); reactant_deg_S1.setStoichiometry(1)
kl_S1 = reaction_deg_S1.createKineticLaw(); param_S1 = kl_S1.createParameter(); param_S1.setId("k_d1"); param_S1.setValue(k_d1_val)
kl_S1.setMath(libsbml.parseL3Formula("k_d1 * id_1a2z"))


writer = libsbml.SBMLWriter()
updated_sbml_str_iter9 = writer.writeSBMLToString(sbml_doc_iter9)
shared_variables.add("current_sbml_model_iter9", updated_sbml_str_iter9)
print("\nUpdated SBML model (iter9) with 6 reactions (S1 and S2 degradation).")

# --- Part 2: Simulate the new model ---
sim_data_iter9 = simulate(updated_sbml_str_iter9)
shared_variables.add("simulation_results_iter9", sim_data_iter9)
print("\nSimulation of the updated model (iter9) completed.")

# Print relevant time points for comparison
print("\nSimulated data (iter9) at T=0.12:")
print(sim_data_iter9.iloc[(sim_data_iter9['Time']-0.12).abs().argsort()[:1]])
print("\nSimulated data (iter9) at T=1.2:")
print(sim_data_iter9.iloc[(sim_data_iter9['Time']-1.2).abs().argsort()[:1]])
print("\nSimulated data (iter9) at T=4.8:")
print(sim_data_iter9.iloc[(sim_data_iter9['Time']-4.8).abs().argsort()[:1]])
print("\nSimulated data (iter9) tail:")
print(sim_data_iter9.tail())

```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model (iter9) with 6 reactions (S1 and S2 degradation).

Simulation of the updated model (iter9) completed.

Simulated data (iter9) at T=0.12:
    id_1a2z   id_khqo   id_6o57  Time
4  1.005326  1.239178  4.691267  0.12

Simulated data (iter9) at T=1.2:
     id_1a2z   id_khqo   id_6o57  Time
40  1.344533  1.596601  3.280472   1.2

Simulated data (iter9) at T=4.8:
      id_1a2z   id_khqo   id_6o57  Time
160  1.032233  1.021471  1.791449   4.8

Simulated data (iter9) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.031080  0.030596  0.053399  29.88
997   0.030950  0.030468  0.053176  29.91
998   0.030820  0.030340  0.052953  29.94
999   0.030691  0.030213  0.052731  29.97
1000  0.030563  0.030087  0.052510  30.00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6, current_sbml_model_iter7, simulation_results_iter7, current_sbml_model_iter8, simulation_results_iter8, current_sbml_model_iter9, simulation_results_iter9)

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


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



# Iteration 10
## Thoughts

The simulation results with Set 9 parameters (added S1 degradation, `k_d1=0.4`, `k_deg_S2=0.12`, and reversible rates based on target ratios) are not good.

**Experimental Data:**
*   T=0.12: `S1=0.800`, `S2=1.076`, `S3=4.557`
*   T=1.2: `S1=0.318`, `S2=2.262`, `S3=2.217`
*   T=4.8: `S1=1.600`, `S2=1.771`, `S3=0.974`
*   T=30: `S1=0.833`, `S2=0.648`, `S3=0.934`

**Simulated Data (iter9, Set 9):**
*   T=0.12: `S1=1.005`, `S2=1.239`, `S3=4.691`
*   T=1.2: `S1=1.345`, `S2=1.597`, `S3=3.280`
*   T=4.8: `S1=1.032`, `S2=1.021`, `S3=1.791`
*   T=30: `S1=0.031`, `S2=0.030`, `S3=0.053`

**Analysis:**

1.  **Initial `S1` drop NOT achieved:** `S1` actually *increased* initially (1.0 -> 1.005).
    My calculation for `k_d1` was: `d[S1]/dt = k2r*S2_0 - k2f*S1_0 - k_d1*S1_0 = 1.28*1 - 1.0*1 - k_d1*1 = 0.28 - k_d1`.
    I set `k_d1 = 0.4`, so `d[S1]/dt` should have been `0.28 - 0.4 = -0.12`.
    The simulation shows an increase. This is puzzling.
    Ah, the `create_reaction_mod` helper function was not updated in the thought block, but I assume the code used the correct one. Let me double check the kinetic law for S1 degradation: `k_d1 * id_1a2z`. This is correct.
    Perhaps the time step of the simulation or interplay with S2 (which increases) makes the average rate positive over the first 0.03s interval.
    The key is that `k2r > k2f` was used. This inherently makes S1 want to increase if S2 is present. The degradation `k_d1` has to fight both the net production from `S2 -> S1` and the consumption by `S1 -> S2`.
    Net change for S1 from reversible reactions: `k2r*S2 - k2f*S1`. At T=0, this is `(1.28-1.0)*1 = 0.28`.
    So, `d[S1]/dt = 0.28 - k_d1*S1`. For `d[S1]/dt < 0`, `k_d1*S1 > 0.28`. With `S1=1`, `k_d1 > 0.28`. My choice `k_d1=0.4` should have worked.
    The simulation output `S1=1.005326` at T=0.12 is very slightly above 1.0 after many steps. This suggests the initial rate might be negative but S2 rises fast, and `k2r*S2` quickly overcomes `(k2f+k_d1)*S1`.

2.  **`S1` dip and peak NOT captured:** `S1` never dips below initial, and its "peak" (1.345) is not impressive.
3.  **`S2` peak too low and early:** Exp peak ~2.26. Sim peak ~1.6.
4.  **Final concentrations are extremely low:** `k_deg_S2=0.12` and `k_d1=0.4` are clearly too much degradation overall.

**Backtracking and Simplification:**
The model with S1 degradation and trying to force final ratios for reversible reactions made things worse. The complexity of S1's trajectory (dip, rise above initial, then settle) is the biggest challenge.

Let's go back to the 5-reaction model (only S2 degrades).
Model: `S1 <=> S2`, `S3 <=> S2`, `S2 -> ø`.

The key features to capture:
*   Initial S1 drop (1.0 -> 0.8)
*   Initial S3 drop (5.0 -> 4.5)
*   Initial S2 rise (1.0 -> 1.07)
*   S2 peak around 2.26 (T=1.2)
*   S1 deep dip to 0.318 (T=1.2)
*   S1 rise to 1.6 (T=4.8)
*   Final state (T=30): S1=0.833, S2=0.648, S3=0.934

Set 8 was (`k1f=1.0, k1r=0.3, k2f=2.5, k2r=0.75, k_deg=0.08`):
*   T=0.12: `S1=0.847` (good drop!), `S2=1.660` (too high), `S3=4.480` (good drop!)
*   T=1.2: `S1=0.980` (no deep dip), `S2=3.610` (peak too high), `S3=2.140` (good!)
*   T=4.8: `S1=1.065` (no real peak to 1.6), `S2=3.487` (still too high), `S3=1.114` (bit high)
*   T=30: `S1=0.308` (too low), `S2=1.008` (too high), `S3=0.318` (too low)

Problems with Set 8:
*   S2 initial rise and peak too high. (Reduce `k1f, k2f`).
*   S1 doesn't dip low enough (needs stronger net consumption initially).
*   S1 doesn't peak high enough (needs stronger net production later).
*   Final S2 too high (increase `k_deg`).
*   Final S1, S3 too low (adjust `k_rev/k_fwd` ratios, or related to S2 being off).

Let's try to moderate Set 8:
*   **`k_deg`**: Target final S2=0.648. Set 8 had S2=1.008 with `k_deg=0.08`. Set 7 had S2=0.367 with `k_deg=0.16`.
    Interpolating for `k_deg` to get S2=0.648:
    `(0.648-0.367)/(1.008-0.367) = (k_target-0.16)/(0.08-0.16)`
    `0.281/0.641 = (k_target-0.16)/(-0.08)`
    `0.438 * -0.08 = k_target-0.16` => `-0.035 = k_target-0.16` => `k_target = 0.125`.
    Let's use `k_deg = 0.13`.

*   **Reduce S2 peak (was 3.61, target 2.26):** Reduce inflow rates `k1f, k2f`.
    Set 8: `k1f=1.0, k2f=2.5`.
    Let `k1f = 0.6` (was 1.0).
    Let `k2f = 1.5` (was 2.5).

*   **`S1` dynamics:**
    *   Initial drop: `k2f=1.5`. `k2r` should be smaller. Let `k2r = 0.5` (as in Set 7). `k2f > k2r`.
    *   Deep dip for S1: This requires `k2f * S1` to be large when `S1` is still somewhat high, and `k2r * S2` to be smaller during this phase.
    *   Later S1 peak: Needs `k2r * S2` to be large when `S2` is high. `k2r=0.5` might be okay if `S2` peaks well.

*   **`S3` dynamics:**
    *   Initial drop: `k1f=0.6`. `k1r` should be smaller. Let `k1r = 0.2` (similar to Set 6c `k1r=0.2, k1f=0.3`). `5*k1f > k1r` => `3.0 > 0.2`.

Parameters (Set 10 - "Moderated Set 8, new k_deg"):
*   `k_deg = 0.13`

*   `k1f = 0.6` (S3 -> S2)
*   `k1r = 0.2` (S2 -> S3) (Ratio `k1r/k1f = 0.2/0.6 = 0.33`)

*   `k2f = 1.5` (S1 -> S2)
*   `k2r = 0.5` (S2 -> S1) (Ratio `k2r/k2f = 0.5/1.5 = 0.33`)

Check S2 initial increase: `(5*k1f + k2f) > (k1r + k2r + k_deg)`
`(5*0.6 + 1.5) > (0.2 + 0.5 + 0.13)`
`(3.0 + 1.5) > (0.7 + 0.13)`
`4.5 > 0.83`. True. S2 should increase.

The `k_rev/k_fwd` ratios are 0.33.
Exp final ratios: `S1/S2 = 1.28`, `S3/S2 = 1.44`.
This means final S1 and S3 will likely be too low if S2 is correct.
If S2 final is ~0.65:
Sim S1 final ~ `0.33 * 0.65 = 0.21` (Exp 0.833) - Bad
Sim S3 final ~ `0.33 * 0.65 = 0.21` (Exp 0.934) - Bad

This indicates that the `k_rev/k_fwd` ratios *must* be higher, closer to the experimental final ratios.
The problem is achieving the initial S1 drop if `k2r > k2f`.

What if the initial S1 drop is extremely fast and transient, and the model can't capture it with the given time resolution of data? The first data point after T=0 is T=0.03.
`S1(0)=1, S1(0.03)=0.94, S1(0.06)=0.89, S1(0.09)=0.84, S1(0.12)=0.80`. The drop is smooth.

Could it be that `id_1a2z` (S1) is consumed in forming `id_6o57` (S3)? Or vice-versa?
E.g. `S1 -> S3` or `S1 + X -> S3`.
Or `S1 -> S2` and `S2 -> S3` (sequential), and `S3` also feeds back to `S2` or `S1`?
Current model: `S1 -> S2 <- S3`. And `S1 <- S2 -> S3`.

If the true mechanism is significantly different, parameter tuning will hit a wall.
The S1 profile (dip, big rise, settle) is very indicative of more complex regulation, like feedback or sequential reactions where an intermediate builds up and then drives a later reaction.

Let's try one more iteration with the 5-reaction model, focusing on getting the S2 peak and final S2 correct, and accepting that S1/S3 final ratios might be off if their `k_rev/k_fwd` are set low for dynamics.

Parameters (Set 10b - Adjusting Set 8 values slightly, aiming for S2 profile):
*   `k_deg = 0.13` (from 0.08 in Set 8, should lower final S2)

*   `k1f = 0.8` (from 1.0 in Set 8, to lower S2 peak slightly)
*   `k1r = 0.25` (from 0.3 in Set 8, ratio `0.25/0.8 = 0.31`)

*   `k2f = 2.0` (from 2.5 in Set 8, to lower S2 peak slightly)
*   `k2r = 0.6` (from 0.75 in Set 8, ratio `0.6/2.0 = 0.3`)

Check S2 initial increase: `(5*k1f + k2f) > (k1r + k2r + k_deg)`
`(5*0.8 + 2.0) > (0.25 + 0.6 + 0.13)`
`(4.0 + 2.0) > (0.85 + 0.13)`
`6.0 > 0.98`. True. S2 should increase strongly.

This is a slight moderation of Set 8's forward rates, and an increase in `k_deg`.
The goal is to lower the S2 peak (was 3.61, target 2.26) and lower final S2 (was 1.008, target 0.648).

## Action

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

# Access experimental data
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())
# ... (print other specific time points if needed for checking)

# --- Part 1: Build the SBML model (Set 10b) ---
# This uses the 5-reaction model (S2 degradation only)
sbml_doc_iter10 = libsbml.readSBMLFromString(input_sbml_string)
model_iter10 = sbml_doc_iter10.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 10b)
k1f_val = 0.8    # S3 (id_6o57) -> S2 (id_khqo)
k1r_val = 0.25   # S2 -> S3
k2f_val = 2.0    # S1 (id_1a2z) -> S2
k2r_val = 0.6    # S2 -> S1
k_deg_val = 0.13 # S2 -> ø (this is the k_deg for S2)

# Reactions
create_reaction_mod(model_iter10, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
create_reaction_mod(model_iter10, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
create_reaction_mod(model_iter10, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
create_reaction_mod(model_iter10, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

reaction_deg_S2 = model_iter10.createReaction()
reaction_deg_S2.setId("R_deg_S2") # Changed from R_deg_khqo for consistency if I add other degs
reaction_deg_S2.setReversible(False)
reactant_deg_S2 = reaction_deg_S2.createReactant(); reactant_deg_S2.setSpecies("id_khqo"); reactant_deg_S2.setStoichiometry(1)
kl_S2 = reaction_deg_S2.createKineticLaw(); param_S2 = kl_S2.createParameter(); param_S2.setId("k_deg_S2"); param_S2.setValue(k_deg_val) # k_deg_val is k_deg_S2
kl_S2.setMath(libsbml.parseL3Formula("k_deg_S2 * id_khqo"))


writer = libsbml.SBMLWriter()
updated_sbml_str_iter10 = writer.writeSBMLToString(sbml_doc_iter10)
shared_variables.add("current_sbml_model_iter10", updated_sbml_str_iter10)
print("\nUpdated SBML model (iter10) with 5 reactions (Set 10b).")

# --- Part 2: Simulate the new model ---
sim_data_iter10 = simulate(updated_sbml_str_iter10)
shared_variables.add("simulation_results_iter10", sim_data_iter10)
print("\nSimulation of the updated model (iter10) completed.")

# Print relevant time points for comparison
print("\nSimulated data (iter10) at T=0.12:")
print(sim_data_iter10.iloc[(sim_data_iter10['Time']-0.12).abs().argsort()[:1]])
print("\nSimulated data (iter10) at T=1.2:")
print(sim_data_iter10.iloc[(sim_data_iter10['Time']-1.2).abs().argsort()[:1]])
print("\nSimulated data (iter10) at T=4.8:")
print(sim_data_iter10.iloc[(sim_data_iter10['Time']-4.8).abs().argsort()[:1]])
print("\nSimulated data (iter10) tail:")
print(sim_data_iter10.tail())
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model (iter10) with 5 reactions (Set 10b).

Simulation of the updated model (iter10) completed.

Simulated data (iter10) at T=0.12:
    id_1a2z   id_khqo   id_6o57  Time
4  0.869062  1.532038  4.578976  0.12

Simulated data (iter10) at T=1.2:
     id_1a2z   id_khqo  id_6o57  Time
40  0.881708  3.284242  2.43654   1.2

Simulated data (iter10) at T=4.8:
      id_1a2z   id_khqo  id_6o57  Time
160  0.938591  3.024699  1.08645   4.8

Simulated data (iter10) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.133217  0.426656  0.147811  29.88
997   0.132904  0.425654  0.147464  29.91
998   0.132592  0.424654  0.147118  29.94
999   0.132281  0.423657  0.146772  29.97
1000  0.131970  0.422662  0.146427  30.00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6, current_sbml_model_iter7, simulation_results_iter7, current_sbml_model_iter8, simulation_results_iter8, current_sbml_model_iter9, simulation_results_iter9, current_sbml_model_iter10, simulation_results_iter10)

### 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 previous iteration (Set 10b) showed that `k_deg_S2 = 0.13` resulted in final concentrations that were too low for all species, particularly S2 (0.423 vs exp 0.648). The S2 peak was also too high (3.284 vs exp 2.262). The complex S1 dynamics (initial drop, deep dip, high peak) remain elusive.

My strategy for Set 11 is to:
1.  Adjust `k_deg_S2` to better match the final S2 concentration. Based on interpolation, `k_deg_S2 = 0.11` is a good candidate.
2.  Reduce the S2 peak by lowering the influx rates `k1f` and `k2f`.
3.  Maintain `k2f > k2r` to ensure an initial drop for S1, and similarly for S3 with `5*k1f > k1r`.
4.  Keep the `k_rev/k_fwd` ratios relatively low for now. This will likely result in low final S1 and S3 concentrations if S2 is correct, but the primary goal is to see if the S2 profile can be matched, which might then allow the S1 dynamic features (dip/peak) to emerge.

**Parameters (Set 11):**
*   `k_deg_S2 = 0.11` (Target final S2 ~0.648)

*   `k1f = 0.6` (Reduced from 0.8 in Set 10b, to lower S2 peak)
*   `k1r = 0.25` (Kept from Set 10b. Ratio `k1r/k1f = 0.25/0.6 approx 0.417`)

*   `k2f = 1.5` (Reduced from 2.0 in Set 10b, to lower S2 peak)
*   `k2r = 0.6` (Kept from Set 10b. Ratio `k2r/k2f = 0.6/1.5 = 0.4`)

**Rationale Check:**
*   Initial S1 drop: `d[S1]/dt = k2r*S2_0 - k2f*S1_0 = 0.6*1 - 1.5*1 = -0.9`. S1 should drop sharply.
*   Initial S3 drop: `d[S3]/dt = k1r*S2_0 - k1f*S3_0 = 0.25*1 - 0.6*5 = 0.25 - 3.0 = -2.75`. S3 should drop sharply.
*   Initial S2 rise: `(5*k1f + k2f) > (k1r + k2r + k_deg_S2)`
    `(5*0.6 + 1.5) > (0.25 + 0.6 + 0.11)`
    `(3.0 + 1.5) > (0.85 + 0.11)`
    `4.5 > 0.96`. True. S2 should increase.

This set has significantly faster initial consumption rates for S1 and S3 compared to Set 10b, and lower overall production rates for S2. This should lead to a lower S2 peak and faster initial drops for S1 and S3. The adjusted `k_deg_S2` aims for a better final S2. The S1 dip and subsequent rise to a peak are still the main features to watch.

## Action

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

# Access experimental data
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())
print("\nExperimental data (iteration_0) at T=0.12:")
print(exp_data[exp_data['Time'] == 0.12])
print("\nExperimental data (iteration_0) at T=1.2:")
print(exp_data[exp_data['Time'] == 1.2])
print("\nExperimental data (iteration_0) at T=4.8:")
print(exp_data[exp_data['Time'] == 4.8])

# --- Part 1: Build the SBML model (Set 11) ---
# This uses the 5-reaction model (S2 degradation only)
sbml_doc_iter11 = libsbml.readSBMLFromString(input_sbml_string)
model_iter11 = sbml_doc_iter11.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 11)
k1f_val = 0.6    # S3 (id_6o57) -> S2 (id_khqo)
k1r_val = 0.25   # S2 -> S3
k2f_val = 1.5    # S1 (id_1a2z) -> S2
k2r_val = 0.6    # S2 -> S1
k_deg_S2_val = 0.11 # S2 -> ø 

# Reactions
create_reaction_mod(model_iter11, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
create_reaction_mod(model_iter11, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
create_reaction_mod(model_iter11, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
create_reaction_mod(model_iter11, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

reaction_deg_S2 = model_iter11.createReaction()
reaction_deg_S2.setId("R_deg_S2") 
reaction_deg_S2.setReversible(False)
reactant_deg_S2 = reaction_deg_S2.createReactant(); reactant_deg_S2.setSpecies("id_khqo"); reactant_deg_S2.setStoichiometry(1)
kl_S2 = reaction_deg_S2.createKineticLaw(); param_S2 = kl_S2.createParameter(); param_S2.setId("k_deg_S2"); param_S2.setValue(k_deg_S2_val)
kl_S2.setMath(libsbml.parseL3Formula("k_deg_S2 * id_khqo"))


writer = libsbml.SBMLWriter()
updated_sbml_str_iter11 = writer.writeSBMLToString(sbml_doc_iter11)
shared_variables.add("current_sbml_model_iter11", updated_sbml_str_iter11)
print("\nUpdated SBML model (iter11) with 5 reactions (Set 11).")

# --- Part 2: Simulate the new model ---
sim_data_iter11 = simulate(updated_sbml_str_iter11)
shared_variables.add("simulation_results_iter11", sim_data_iter11)
print("\nSimulation of the updated model (iter11) completed.")

# Print relevant time points for comparison
print("\nSimulated data (iter11) at T=0.12:")
print(sim_data_iter11.iloc[(sim_data_iter11['Time']-0.12).abs().argsort()[:1]])
print("\nSimulated data (iter11) at T=1.2:")
print(sim_data_iter11.iloc[(sim_data_iter11['Time']-1.2).abs().argsort()[:1]])
print("\nSimulated data (iter11) at T=4.8:")
print(sim_data_iter11.iloc[(sim_data_iter11['Time']-4.8).abs().argsort()[:1]])
print("\nSimulated data (iter11) tail:")
print(sim_data_iter11.tail())
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Experimental data (iteration_0) at T=0.12:
    id_1a2z   id_khqo   id_6o57  Time
4  0.800585  1.076063  4.557085  0.12

Experimental data (iteration_0) at T=1.2:
     id_1a2z  id_khqo  id_6o57  Time
40  0.317717  2.26247  2.21713   1.2

Experimental data (iteration_0) at T=4.8:
     id_1a2z   id_khqo   id_6o57  Time
160  1.59978  1.771463  0.974262   4.8

Updated SBML model (iter11) with 5 reactions (Set 11).

Simulation of the updated model (iter11) completed.

Simulated data (iter11) at T=0.12:
    id_1a2z   id_khqo   id_6o57  Time
4  0.914579  1.382214  4.687395  0.12

Simulated data (iter11) at T=1.2:
     id_1a2z   id_khqo   id_6o57  Time
40  0.972056  2.816562  2.922658   1.2

Simulated data (iter11) at T=4.8:
      id_1a2z   id_khqo  id_6o57  Time
160  1.184988  2.892891  1.44145   4.8

Simulated data (iter11) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.281930  0.677303  0.312740  29.88
997   0.281435  0.676114  0.312190  29.91
998   0.280941  0.674927  0.311642  29.94
999   0.280448  0.673742  0.311095  29.97
1000  0.279955  0.672559  0.310549  30.00

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 9/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6, current_sbml_model_iter7, simulation_results_iter7, current_sbml_model_iter8, simulation_results_iter8, current_sbml_model_iter9, simulation_results_iter9, current_sbml_model_iter10, simulation_results_iter10, current_sbml_model_iter11, simulation_results_iter11)

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


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



# Iteration 12
## Thoughts

The simulation results with Set 11 (`k1f=0.6, k1r=0.25, k2f=1.5, k2r=0.6, k_deg_S2=0.11`) are getting closer for some aspects, particularly the final S2 value.

**Experimental Data:**
*   T=0.12: `S1=0.800`, `S2=1.076`, `S3=4.557`
*   T=1.2: `S1=0.318`, `S2=2.262`, `S3=2.217`
*   T=4.8: `S1=1.600`, `S2=1.771`, `S3=0.974`
*   T=30: `S1=0.833`, `S2=0.648`, `S3=0.934`

**Simulated Data (iter11, Set 11):**
*   T=0.12: `S1=0.915`, `S2=1.382`, `S3=4.687`
*   T=1.2: `S1=0.972`, `S2=2.817`, `S3=2.923`
*   T=4.8: `S1=1.185`, `S2=2.893`, `S3=1.441`
*   T=30: `S1=0.280`, `S2=0.673`, `S3=0.311`

**Analysis:**

1.  **Final Concentrations (T=30):**
    *   `S2 (id_khqo)`: Sim=0.673. Exp=0.648. This is very good! `k_deg_S2 = 0.11` seems to be a good value.
    *   `S1 (id_1a2z)`: Sim=0.280. Exp=0.833. Too low.
    *   `S3 (id_6o57)`: Sim=0.311. Exp=0.934. Too low.
    *   The low S1 and S3 final values are expected because their `k_rev/k_fwd` ratios (0.4 and 0.417 respectively) are much lower than the experimental target ratios (S1/S2=1.28, S3/S2=1.44).

2.  **Initial Trends (T=0.12):**
    *   `S1`: Exp drop to 0.800. Sim drop to 0.915. Initial drop is not sharp enough. `k2f` needs to be even more dominant or larger.
    *   `S2`: Exp rise to 1.076. Sim rise to 1.382. Sim S2 rises a bit too fast/high initially.
    *   `S3`: Exp drop to 4.557. Sim drop to 4.687. Initial drop not sharp enough. `k1f` needs to be larger.

3.  **Intermediate Dynamics:**
    *   `S1` dip at T=1.2: Exp=0.318. Sim=0.972. No significant dip captured.
    *   `S2` peak at T=1.2: Exp=2.262. Sim=2.817. Sim peak is too high and S2 stays high for too long (at T=4.8, Sim S2=2.893 while Exp S2=1.771).
    *   `S1` peak at T=4.8: Exp=1.600. Sim=1.185. Sim S1 does rise from its T=0.12 value, but the peak is too low.

**Revised Parameter Tuning Strategy:**

The final S2 concentration is good. Now, the main goals are:
1.  Achieve correct final S1 and S3 concentrations by adjusting `k1r` and `k2r` to match target `k_rev/k_fwd` ratios based on experimental final values.
    *   Target `k2r/k2f = S1_final/S2_final = 0.833/0.648 = 1.286`
    *   Target `k1r/k1f = S3_final/S2_final = 0.934/0.648 = 1.441`
2.  Address the initial S1 drop. If we set `k2r/k2f = 1.286`, then `k2r > k2f`. This will make S1 *increase* initially if S1 and S2 start at 1. This is the fundamental conflict.
    The only way for S1 to drop initially if `k2r > k2f` is if `S2_0` is significantly lower than `S1_0` such that `k2f*S1_0 > k2r*S2_0`. But they both start at 1.0.
    This strongly suggests that the 5-reaction model might be insufficient for the S1 dynamics.

However, I must try to optimize within the current 5-reaction structure first.
What if the initial S1 drop is extremely rapid, and by T=0.03 (first data point), S2 has already risen enough to make `k2r*S2 > k2f*S1` if `k2r/k2f` is high?
Let's assume the target `k_rev/k_fwd` ratios are correct for the final state.

Parameters (Set 12 - "Target Ratios, Adjusted k_fwd for dynamics"):
*   `k_deg_S2 = 0.11` (Keep, as final S2 was good)

*   `k1f`: Need to adjust for S2 peak and S3 initial drop. Set 11 `k1f=0.6` gave S2 peak=2.8 (too high), S3 drop to 4.68 (not enough).
    Let's try `k1f = 0.7`.
*   `k1r = k1f * 1.441 = 0.7 * 1.441 = 1.0087`.

*   `k2f`: Need to adjust for S2 peak and S1 initial dynamics. Set 11 `k2f=1.5` gave S2 peak=2.8 (too high), S1 drop to 0.915 (not enough).
    Let's try `k2f = 1.0`. (This is lower, which will reduce S2 peak, but might worsen S1 initial drop).
*   `k2r = k2f * 1.286 = 1.0 * 1.286 = 1.286`.

With these, initial `d[S1]/dt = k2r*S2_0 - k2f*S1_0 = 1.286*1 - 1.0*1 = 0.286`. S1 will increase. This is not matching the initial data.

This is a critical point. The model structure `S1 <=> S2`, `S3 <=> S2`, `S2 -> ø` with mass-action kinetics cannot simultaneously satisfy:
a) S1 initial concentration decrease (requires effective `k2f > k2r` at T=0).
b) S1 final concentration being `1.286 * S2_final` (requires effective `k2r/k2f = 1.286`).

This implies a missing mechanism or a more complex rate law for the S1 reactions.
Possibilities:
1.  S1 degradation (tried in iter9, didn't quite work with those params, and made final values too low).
2.  A transient activation of S1 consumption or inhibition of S1 production.
3.  A different network topology. For example, `S3 -> S1 -> S2 -> ø`.

Given the prompt "discovering the true underlying mechanisms rather than overfitting", if a simple parameter set for the current 5-reaction model cannot explain major qualitative features (like S1 initial drop AND its final ratio), the model is likely wrong.

Let's try one more set of parameters for the 5-reaction model, prioritizing the S2 profile and final values, and see how badly S1 behaves.
If S1 is still very off, I will have to propose a structural change.

Parameters (Set 12b - Focus on S2 profile and final values, using target k_rev/k_fwd ratios):
*   `k_deg_S2 = 0.11`

*   `k1f = 0.5` (To reduce S2 peak from 2.8 towards 2.26)
*   `k1r = k1f * 1.441 = 0.5 * 1.441 = 0.7205`

*   `k2f = 0.8` (To reduce S2 peak. This `k2f` is now smaller than `k2r` if we use target ratio)
*   `k2r = k2f * 1.286 = 0.8 * 1.286 = 1.0288`

Initial `d[S1]/dt = k2r*1 - k2f*1 = 1.0288 - 0.8 = 0.2288`. S1 increases.
Initial `d[S3]/dt = k1r*1 - k1f*5 = 0.7205 - 0.5*5 = 0.7205 - 2.5 = -1.7795`. S3 decreases. (Good)
Initial S2 rise: `(5*k1f + k2f) > (k1r + k2r + k_deg_S2)`
`(5*0.5 + 0.8) > (0.7205 + 1.0288 + 0.11)`
`(2.5 + 0.8) > (1.7493 + 0.11)`
`3.3 > 1.8593`. True. S2 increases.

This set will get final S1, S2, S3 ratios correct if it reaches steady state. S3 initial drop is fine. S1 initial drop will be wrong. Let's see the overall dynamics.

## Action

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

# Access experimental data
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())
# ... (print other specific time points if needed for checking)

# --- Part 1: Build the SBML model (Set 12b) ---
# This uses the 5-reaction model (S2 degradation only)
sbml_doc_iter12 = libsbml.readSBMLFromString(input_sbml_string)
model_iter12 = sbml_doc_iter12.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 12b)
k1f_val = 0.5     # S3 (id_6o57) -> S2 (id_khqo)
k1r_val = 0.7205  # S2 -> S3 (k1f * 1.441)
k2f_val = 0.8     # S1 (id_1a2z) -> S2
k2r_val = 1.0288  # S2 -> S1 (k2f * 1.286)
k_deg_S2_val = 0.11 # S2 -> ø 

# Reactions
create_reaction_mod(model_iter12, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
create_reaction_mod(model_iter12, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
create_reaction_mod(model_iter12, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
create_reaction_mod(model_iter12, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

reaction_deg_S2 = model_iter12.createReaction()
reaction_deg_S2.setId("R_deg_S2") 
reaction_deg_S2.setReversible(False)
reactant_deg_S2 = reaction_deg_S2.createReactant(); reactant_deg_S2.setSpecies("id_khqo"); reactant_deg_S2.setStoichiometry(1)
kl_S2 = reaction_deg_S2.createKineticLaw(); param_S2 = kl_S2.createParameter(); param_S2.setId("k_deg_S2"); param_S2.setValue(k_deg_S2_val)
kl_S2.setMath(libsbml.parseL3Formula("k_deg_S2 * id_khqo"))


writer = libsbml.SBMLWriter()
updated_sbml_str_iter12 = writer.writeSBMLToString(sbml_doc_iter12)
shared_variables.add("current_sbml_model_iter12", updated_sbml_str_iter12)
print("\nUpdated SBML model (iter12) with 5 reactions (Set 12b).")

# --- Part 2: Simulate the new model ---
sim_data_iter12 = simulate(updated_sbml_str_iter12)
shared_variables.add("simulation_results_iter12", sim_data_iter12)
print("\nSimulation of the updated model (iter12) completed.")

# Print relevant time points for comparison
print("\nSimulated data (iter12) at T=0.12:")
print(sim_data_iter12.iloc[(sim_data_iter12['Time']-0.12).abs().argsort()[:1]])
print("\nSimulated data (iter12) at T=1.2:")
print(sim_data_iter12.iloc[(sim_data_iter12['Time']-1.2).abs().argsort()[:1]])
print("\nSimulated data (iter12) at T=4.8:")
print(sim_data_iter12.iloc[(sim_data_iter12['Time']-4.8).abs().argsort()[:1]])
print("\nSimulated data (iter12) tail:")
print(sim_data_iter12.tail())
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model (iter12) with 5 reactions (Set 12b).

Simulation of the updated model (iter12) completed.

Simulated data (iter12) at T=0.12:
    id_1a2z   id_khqo   id_6o57  Time
4  1.035605  1.150732  4.799422  0.12

Simulated data (iter12) at T=1.2:
     id_1a2z   id_khqo   id_6o57  Time
40  1.537879  1.594446  3.680877   1.2

Simulated data (iter12) at T=4.8:
      id_1a2z  id_khqo  id_6o57  Time
160  2.040081  1.58233  2.54934   4.8

Simulated data (iter12) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   1.043693  0.782682  1.195983  29.88
997   1.042801  0.782014  1.194961  29.91
998   1.041911  0.781346  1.193941  29.94
999   1.041021  0.780678  1.192921  29.97
1000  1.040131  0.780011  1.191902  30.00

## 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)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6, current_sbml_model_iter7, simulation_results_iter7, current_sbml_model_iter8, simulation_results_iter8, current_sbml_model_iter9, simulation_results_iter9, current_sbml_model_iter10, simulation_results_iter10, current_sbml_model_iter11, simulation_results_iter11, current_sbml_model_iter12, simulation_results_iter12)

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


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



# Iteration 13
## Thoughts

The simulation results with Set 12b (`k1f=0.5, k1r=0.7205, k2f=0.8, k2r=1.0288, k_deg_S2=0.11`) show that using target final ratios for `k_rev/k_fwd` indeed leads to S1 increasing initially, which is incorrect.

**Experimental Data (Final T=30):**
*   `S1=0.833`, `S2=0.648`, `S3=0.934`

**Simulated Data (iter12, Set 12b, Final T=30):**
*   `S1=1.040`, `S2=0.780`, `S3=1.192`

**Analysis of Final Values (Set 12b):**
*   `S2 (id_khqo)`: Sim=0.780. Exp=0.648. Sim is a bit high. `k_deg_S2=0.11` is perhaps slightly too low.
*   `S1 (id_1a2z)`: Sim=1.040. Exp=0.833. Sim is high. Ratio Sim S1/S2 = 1.040/0.780 = 1.33. Exp S1/S2 = 1.286. Close.
*   `S3 (id_6o57)`: Sim=1.192. Exp=0.934. Sim is high. Ratio Sim S3/S2 = 1.192/0.780 = 1.53. Exp S3/S2 = 1.441. Close.
The final *ratios* are reasonably well captured, but the absolute level of S2 is off, which then throws off S1 and S3 absolute levels.

**Analysis of Dynamics (Set 12b):**
*   Initial S1: Sim `S1(0.12)=1.035`. Exp `S1(0.12)=0.800`. S1 increases as predicted, which is wrong.
*   S2 peak: Sim `S2(1.2)=1.59`. Exp `S2(1.2)=2.26`. Sim S2 peak is too low and too early/flat.
*   S1 dip: Not observed in sim.
*   S1 peak: Sim `S1(4.8)=2.04`. Exp `S1(4.8)=1.60`. Sim S1 peak is too high and likely shaped differently.

**Conclusion on 5-Reaction Model:**
The 5-reaction model (`S1 <=> S2`, `S3 <=> S2`, `S2 -> ø`) with simple mass-action kinetics is struggling significantly to capture the complex dynamics of S1 (initial drop, then deep dip, then rise above initial, then settle) while also matching the S2 peak and final concentrations. The conflict between parameters needed for initial S1 drop versus those for final S1/S2 ratio is fundamental.

**Proposing a Model Structure Change:**
The behavior of S1 suggests it might be an intermediate that is rapidly consumed and then later produced.
Consider a sequential model: `S3 -> S2 -> S1`.
And S2 is also fed by S1 (reversible `S1 <=> S2`).
And S1 is the species that ultimately degrades, or S2 degrades.
The net loss of mass implies at least one degradation. The previous `S2 -> ø` seemed reasonable for overall mass balance.

Let's try a new structure:
1.  `id_6o57 -> id_1a2z` (R1: S3 -> S1, rate k1)  *This is a major change*
2.  `id_1a2z -> id_khqo` (R2: S1 -> S2, rate k2f)
3.  `id_khqo -> id_1a2z` (R3: S2 -> S1, rate k2r)
4.  `id_khqo -> ø`      (R4: S2 -> ø, rate kd)

In this model:
*   S3 is an initial source that feeds S1.
*   S1 is an intermediate. It's produced from S3 and S2 (via k2r), and consumed to form S2 (via k2f).
*   S2 is produced from S1 and consumed by degradation and conversion back to S1.

This structure could potentially explain:
*   Initial S3 drop (consumption by R1).
*   Initial S1 behavior: If `k2f*S1 > k1*S3 + k2r*S2` initially, S1 could drop. Or if S1 starts at 1 and S3 at 5, `k1*S3` could make S1 rise initially. This needs careful thought.
    At T=0: `dS1/dt = k1*S3_0 - k2f*S1_0 + k2r*S2_0 = k1*5 - k2f*1 + k2r*1`.
    For S1 to drop, `k2f > 5*k1 + k2r`. This requires a very large `k2f`.
*   S1 dip and rise: S1 is consumed by `S1->S2`. If S2 builds up, `S2->S1` could replenish S1.
*   S2 peak: S2 builds up from S1.
*   Overall degradation via S2.

Let's try to set parameters for this new model.
This is a significant departure.

Parameters for New Model (Set 13 - "Sequential S3->S1->S2"):
*   `kd (S2 -> ø)`: Let's use `0.11` as it gave good final S2 levels previously (though that was for a different model structure's balance).

*   `k1 (S3 -> S1)`: This reaction consumes S3. S3 drops from 5 to ~1.
    Let `k1 = 0.2`. (This means initial flux from S3 is `0.2*5 = 1.0`).

*   `k2f (S1 -> S2)` and `k2r (S2 -> S1)`: These govern S1/S2 interconversion.
    Exp S1 final = 0.833, S2 final = 0.648. Ratio S1/S2 = 1.286.
    So, at steady state for S1/S2 (ignoring S3 feed and S2 degradation for a moment), `k2r/k2f = 1.286`.
    Let `k2f = 1.0`. Then `k2r = 1.286`.
    Now check initial S1 drop: `dS1/dt = k1*5 - k2f*1 + k2r*1 = 0.2*5 - 1.0*1 + 1.286*1 = 1.0 - 1.0 + 1.286 = 1.286`.
    S1 will *increase* very rapidly. This structure does not give an initial S1 drop easily.

The initial S1 drop is the hardest feature.
What if S1 is consumed by *two* pathways initially?
`S1 -> S2` and `S1 -> S_something_else_or_degrades_fast_then_stops`.

Let's reconsider the previous 5-reaction model but be very aggressive with `k2f` and ensure `k2r` is small enough for the initial S1 drop, and then hope the S2 peak is large enough to drive S1 back up significantly via `k2r`. The final S1/S2 ratio will likely be wrong with this approach.

Revert to 5-reaction model: `S1<=>S2`, `S3<=>S2`, `S2->ø`.
Parameters (Set 13b - "Aggressive S1 drop, S2 profile focus"):
*   `k_deg_S2 = 0.11` (Target final S2 ~0.65)

*   `k2f = 3.0` (Very high, for S1 initial drop)
*   `k2r = 0.5` (Much smaller than k2f. Ratio `k2r/k2f = 0.5/3.0 = 0.167`. This will make final S1 very low if S2 is 0.65, S1 ~ 0.1. Exp S1=0.833)
    Initial `d[S1]/dt = k2r*1 - k2f*1 = 0.5 - 3.0 = -2.5`. Strong S1 drop.

*   `k1f`: To control S2 peak (target ~2.26) and S3 drop.
    Set 11: `k1f=0.6, k2f=1.5` gave S2 peak 2.817.
    Now `k2f=3.0` (double). This will push S2 up more. So `k1f` should be smaller.
    Let `k1f = 0.3`.
*   `k1r = 0.15` (Ratio `k1r/k1f = 0.15/0.3 = 0.5`. Final S3 will be `0.5 * S2_final = 0.5 * 0.65 = 0.325`. Exp S3=0.934. Too low).

Check S2 initial increase: `(5*k1f + k2f) > (k1r + k2r + k_deg_S2)`
`(5*0.3 + 3.0) > (0.15 + 0.5 + 0.11)`
`(1.5 + 3.0) > (0.65 + 0.11)`
`4.5 > 0.76`. True. S2 increases.

This set prioritizes:
1.  Final S2 level (via `k_deg_S2`).
2.  Strong initial S1 drop (high `k2f`, low `k2r`).
3.  Moderate S2 peak (by adjusting `k1f` relative to the high `k2f`).
It sacrifices final S1 and S3 levels due to low `k_rev/k_fwd` ratios.
The hope is to see if the S1 dip and subsequent rise can be qualitatively captured.

## Action

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

# Access experimental data
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())
# ... (print other specific time points if needed for checking)

# --- Part 1: Build the SBML model (Set 13b) ---
# This uses the 5-reaction model (S2 degradation only)
sbml_doc_iter13 = libsbml.readSBMLFromString(input_sbml_string)
model_iter13 = sbml_doc_iter13.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 13b)
k1f_val = 0.3     # S3 (id_6o57) -> S2 (id_khqo)
k1r_val = 0.15    # S2 -> S3
k2f_val = 3.0     # S1 (id_1a2z) -> S2
k2r_val = 0.5     # S2 -> S1
k_deg_S2_val = 0.11 # S2 -> ø 

# Reactions
create_reaction_mod(model_iter13, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
create_reaction_mod(model_iter13, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
create_reaction_mod(model_iter13, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
create_reaction_mod(model_iter13, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

reaction_deg_S2 = model_iter13.createReaction()
reaction_deg_S2.setId("R_deg_S2") 
reaction_deg_S2.setReversible(False)
reactant_deg_S2 = reaction_deg_S2.createReactant(); reactant_deg_S2.setSpecies("id_khqo"); reactant_deg_S2.setStoichiometry(1)
kl_S2 = reaction_deg_S2.createKineticLaw(); param_S2 = kl_S2.createParameter(); param_S2.setId("k_deg_S2"); param_S2.setValue(k_deg_S2_val)
kl_S2.setMath(libsbml.parseL3Formula("k_deg_S2 * id_khqo"))


writer = libsbml.SBMLWriter()
updated_sbml_str_iter13 = writer.writeSBMLToString(sbml_doc_iter13)
shared_variables.add("current_sbml_model_iter13", updated_sbml_str_iter13)
print("\nUpdated SBML model (iter13) with 5 reactions (Set 13b).")

# --- Part 2: Simulate the new model ---
sim_data_iter13 = simulate(updated_sbml_str_iter13)
shared_variables.add("simulation_results_iter13", sim_data_iter13)
print("\nSimulation of the updated model (iter13) completed.")

# Print relevant time points for comparison
print("\nSimulated data (iter13) at T=0.12:")
print(sim_data_iter13.iloc[(sim_data_iter13['Time']-0.12).abs().argsort()[:1]])
print("\nSimulated data (iter13) at T=1.2 (S1 dip, S2 peak):")
print(sim_data_iter13.iloc[(sim_data_iter13['Time']-1.2).abs().argsort()[:1]])
print("\nSimulated data (iter13) at T=4.8 (S1 peak):")
print(sim_data_iter13.iloc[(sim_data_iter13['Time']-4.8).abs().argsort()[:1]])
print("\nSimulated data (iter13) tail:")
print(sim_data_iter13.tail())
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model (iter13) with 5 reactions (Set 13b).

Simulation of the updated model (iter13) completed.

Simulated data (iter13) at T=0.12:
    id_1a2z   id_khqo   id_6o57  Time
4  0.758766  1.380924  4.844456  0.12

Simulated data (iter13) at T=1.2 (S1 dip, S2 peak):
     id_1a2z   id_khqo   id_6o57  Time
40  0.405402  2.524823  3.801559   1.2

Simulated data (iter13) at T=4.8 (S1 peak):
      id_1a2z  id_khqo  id_6o57  Time
160  0.483631  2.88449  2.23784   4.8

Simulated data (iter13) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.115691  0.679993  0.427088  29.88
997   0.115479  0.678747  0.426305  29.91
998   0.115267  0.677502  0.425523  29.94
999   0.115056  0.676260  0.424743  29.97
1000  0.114845  0.675020  0.423964  30.00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6, current_sbml_model_iter7, simulation_results_iter7, current_sbml_model_iter8, simulation_results_iter8, current_sbml_model_iter9, simulation_results_iter9, current_sbml_model_iter10, simulation_results_iter10, current_sbml_model_iter11, simulation_results_iter11, current_sbml_model_iter12, simulation_results_iter12, current_sbml_model_iter13, simulation_results_iter13)

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


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



# Iteration 14
## Thoughts

The simulation results with Set 13b (`k1f=0.3, k1r=0.15, k2f=3.0, k2r=0.5, k_deg_S2=0.11`) are showing some very promising dynamic features for S1!

**Experimental Data:**
*   T=0.12: `S1=0.800`, `S2=1.076`, `S3=4.557`
*   T=1.2 (S1 dip, S2 peak): `S1=0.318`, `S2=2.262`, `S3=2.217`
*   T=4.8 (S1 peak): `S1=1.600`, `S2=1.771`, `S3=0.974`
*   T=30 (Final): `S1=0.833`, `S2=0.648`, `S3=0.934`

**Simulated Data (iter13, Set 13b):**
*   T=0.12: `S1=0.759`, `S2=1.381`, `S3=4.844`
    *   S1 drop: Exp to 0.800. Sim to 0.759. Excellent initial drop!
    *   S2 rise: Exp to 1.076. Sim to 1.381. Sim S2 a bit high.
    *   S3 drop: Exp to 4.557. Sim to 4.844. Sim S3 drop is a bit slow. (k1f=0.3 might be too low for initial S3 drop given S3_0=5).
*   T=1.2 (S1 dip, S2 peak): `S1=0.405`, `S2=2.525`, `S3=3.802`
    *   S1 dip: Exp to 0.318. Sim to 0.405. This is the first time a significant dip is observed! Magnitude is close.
    *   S2 peak: Exp to 2.262. Sim to 2.525. Magnitude is close! Timing seems right.
    *   S3: Exp=2.217. Sim=3.802. Sim S3 is too high here (meaning S3 not consumed fast enough by k1f).
*   T=4.8 (S1 peak): `S1=0.484`, `S2=2.884`, `S3=2.238`
    *   S1 peak: Exp to 1.600. Sim only "recovers" to 0.484. No significant rise above initial or even back to initial. The S1 rise is missing. This is likely because `k2r=0.5` is too small to make `k2r*S2` overcome `k2f*S1` when S1 is low and S2 is high.
    *   S2: Exp=1.771. Sim=2.884. Sim S2 is too high and stays high too long.
    *   S3: Exp=0.974. Sim=2.238. Sim S3 is too high.
*   T=30 (Final): `S1=0.115`, `S2=0.675`, `S3=0.424`
    *   S2: Sim=0.675. Exp=0.648. Excellent! `k_deg_S2=0.11` is good.
    *   S1: Sim=0.115. Exp=0.833. Far too low. (Expected due to low `k2r/k2f` ratio).
    *   S3: Sim=0.424. Exp=0.934. Far too low. (Expected due to low `k1r/k1f` ratio).

**Key Successes of Set 13b:**
*   Correct final S2.
*   Excellent S1 initial drop.
*   Good S1 dip around T=1.2 (qualitatively and somewhat quantitatively).
*   Good S2 peak magnitude and timing.

**Key Failures of Set 13b:**
*   S1 does not rise to a peak of ~1.6 after the dip. It stays low.
*   Final S1 and S3 are far too low.
*   S3 initial drop is a bit slow, and S3 remains too high during mid-phase.
*   S2 stays too high for too long after its peak.

**Revised Parameter Tuning Strategy (Set 14):**

1.  **Keep `k_deg_S2 = 0.11`**. Final S2 is good.
2.  **S1 rise after dip:** For S1 to rise significantly when S2 is high (e.g. S2 ~ 2.5), `k2r * S2` must become much larger than `k2f * S1` (when S1 is low, e.g. 0.4).
    Current: `k2f=3.0, k2r=0.5`. If `S1=0.4, S2=2.5`: `k2r*S2 = 0.5*2.5 = 1.25`. `k2f*S1 = 3.0*0.4 = 1.2`.
    `dS1/dt ~ 1.25 - 1.2 = 0.05`. This is a very slow rise.
    To get a strong rise, `k2r` needs to be much larger.
    Let's try increasing `k2r` significantly. E.g., `k2r = 1.5`.
    This will affect the initial S1 drop: `d[S1]/dt = k2r*1 - k2f*1 = 1.5 - 3.0 = -1.5`. Still a strong drop.
    This will also affect final S1: `k2r/k2f = 1.5/3.0 = 0.5`. If S2_final=0.675, S1_final ~ `0.5 * 0.675 = 0.3375`. Still too low (Exp 0.833), but better than 0.115.

3.  **S3 dynamics:**
    *   Initial drop of S3 was slow (`k1f=0.3`). S3 stayed too high. Increase `k1f`. Let `k1f = 0.6` (as in Set 11).
    *   Final S3 needs to be higher. `k1r` needs to increase relative to `k1f`.
        Target `k1r/k1f = S3_final/S2_final = 1.441`.
        If `k1f=0.6`, then `k1r = 0.6 * 1.441 = 0.8646`.
    *   Check S3 initial drop: `d[S3]/dt = k1r*1 - k1f*5 = 0.8646*1 - 0.6*5 = 0.8646 - 3.0 = -2.1354`. Strong drop.

4.  **Final S1 level:**
    *   Target `k2r/k2f = S1_final/S2_final = 1.286`.
    *   If `k2f=3.0` (kept for initial drop), then `k2r = 3.0 * 1.286 = 3.858`. This is a very large `k2r`.
    *   Initial S1 drop with this: `d[S1]/dt = k2r*1 - k2f*1 = 3.858 - 3.0 = 0.858`. S1 would *increase* initially. This is the problem again.

It seems I cannot satisfy both the initial S1 drop (requiring `k2f > k2r`) and the final S1/S2 ratio (requiring `k2r/k2f > 1`) with this model.

However, the S1 dip to ~0.3-0.4 was achieved with `k2f=3.0, k2r=0.5`. The subsequent rise was missing.
The rise depends on `k2r * S2_peak`. If `S2_peak ~ 2.5`, then `k2r * 2.5` needs to be large.
If `k2r=0.5`, `k2r*S2_peak = 1.25`.
If `k2r=1.5` (as proposed above), `k2r*S2_peak = 1.5 * 2.5 = 3.75`. This should make S1 rise much more strongly.

Let's try parameters focusing on the S1 dip and subsequent rise, and S2 profile.
Parameters (Set 14):
*   `k_deg_S2 = 0.11`

*   `k1f = 0.6` (Increased from 0.3 for faster S3 consumption & better S2 shape)
*   `k1r = 0.25` (Kept from Set 11. Ratio `0.25/0.6 ~ 0.417`. Final S3 will be low).

*   `k2f = 3.0` (Kept for strong S1 initial drop and dip)
*   `k2r = 1.5` (Increased significantly from 0.5 to promote S1 rise after dip)
    Ratio `k2r/k2f = 1.5/3.0 = 0.5`. Final S1 will be `0.5 * S2_final = 0.5 * 0.675 = 0.3375`. Still low, but the dynamic shape of S1 is a higher priority now.

Check S2 initial increase: `(5*k1f + k2f) > (k1r + k2r + k_deg_S2)`
`(5*0.6 + 3.0) > (0.25 + 1.5 + 0.11)`
`(3.0 + 3.0) > (1.75 + 0.11)`
`6.0 > 1.86`. True. S2 increases. S2 peak might be high due to large influx.

This set attempts to get the S1 rise after the dip. It will likely still fail on final S1 and S3 levels.
If this shows a good S1 peak, then the next step would be to adjust `k1r` and `k2r` (and possibly `k1f, k2f` slightly) to fix final levels, hoping not to destroy the dynamics.

## Action

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

# Access experimental data
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())
# ... (print other specific time points if needed for checking)

# --- Part 1: Build the SBML model (Set 14) ---
# This uses the 5-reaction model (S2 degradation only)
sbml_doc_iter14 = libsbml.readSBMLFromString(input_sbml_string)
model_iter14 = sbml_doc_iter14.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 14)
k1f_val = 0.6     # S3 (id_6o57) -> S2 (id_khqo)
k1r_val = 0.25    # S2 -> S3
k2f_val = 3.0     # S1 (id_1a2z) -> S2
k2r_val = 1.5     # S2 -> S1  (Increased from 0.5)
k_deg_S2_val = 0.11 # S2 -> ø 

# Reactions
create_reaction_mod(model_iter14, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
create_reaction_mod(model_iter14, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
create_reaction_mod(model_iter14, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
create_reaction_mod(model_iter14, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

reaction_deg_S2 = model_iter14.createReaction()
reaction_deg_S2.setId("R_deg_S2") 
reaction_deg_S2.setReversible(False)
reactant_deg_S2 = reaction_deg_S2.createReactant(); reactant_deg_S2.setSpecies("id_khqo"); reactant_deg_S2.setStoichiometry(1)
kl_S2 = reaction_deg_S2.createKineticLaw(); param_S2 = kl_S2.createParameter(); param_S2.setId("k_deg_S2"); param_S2.setValue(k_deg_S2_val)
kl_S2.setMath(libsbml.parseL3Formula("k_deg_S2 * id_khqo"))


writer = libsbml.SBMLWriter()
updated_sbml_str_iter14 = writer.writeSBMLToString(sbml_doc_iter14)
shared_variables.add("current_sbml_model_iter14", updated_sbml_str_iter14)
print("\nUpdated SBML model (iter14) with 5 reactions (Set 14).")

# --- Part 2: Simulate the new model ---
sim_data_iter14 = simulate(updated_sbml_str_iter14)
shared_variables.add("simulation_results_iter14", sim_data_iter14)
print("\nSimulation of the updated model (iter14) completed.")

# Print relevant time points for comparison
print("\nSimulated data (iter14) at T=0.12:")
print(sim_data_iter14.iloc[(sim_data_iter14['Time']-0.12).abs().argsort()[:1]])
print("\nSimulated data (iter14) at T=1.2 (S1 dip, S2 peak):")
print(sim_data_iter14.iloc[(sim_data_iter14['Time']-1.2).abs().argsort()[:1]])
print("\nSimulated data (iter14) at T=4.8 (S1 peak):")
print(sim_data_iter14.iloc[(sim_data_iter14['Time']-4.8).abs().argsort()[:1]])
print("\nSimulated data (iter14) tail:")
print(sim_data_iter14.tail())
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model (iter14) with 5 reactions (Set 14).

Simulation of the updated model (iter14) completed.

Simulated data (iter14) at T=0.12:
    id_1a2z   id_khqo   id_6o57  Time
4  0.883801  1.412097  4.688011  0.12

Simulated data (iter14) at T=1.2 (S1 dip, S2 peak):
    id_1a2z   id_khqo   id_6o57  Time
40  1.20163  2.622181  2.899595   1.2

Simulated data (iter14) at T=4.8 (S1 peak):
      id_1a2z   id_khqo   id_6o57  Time
160  1.412219  2.789106  1.389778   4.8

Simulated data (iter14) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.356855  0.700419  0.321805  29.88
997   0.356257  0.699246  0.321266  29.91
998   0.355661  0.698075  0.320728  29.94
999   0.355065  0.696906  0.320191  29.97
1000  0.354470  0.695739  0.319655  30.00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6, current_sbml_model_iter7, simulation_results_iter7, current_sbml_model_iter8, simulation_results_iter8, current_sbml_model_iter9, simulation_results_iter9, current_sbml_model_iter10, simulation_results_iter10, current_sbml_model_iter11, simulation_results_iter11, current_sbml_model_iter12, simulation_results_iter12, current_sbml_model_iter13, simulation_results_iter13, current_sbml_model_iter14, simulation_results_iter14)

### 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 results with Set 14 (`k1f=0.6, k1r=0.25, k2f=3.0, k2r=1.5, k_deg_S2=0.11`) are showing progress on the S1 dynamic shape, but still issues.

**Experimental Data:**
*   T=0.12: `S1=0.800`, `S2=1.076`, `S3=4.557`
*   T=1.2 (S1 dip, S2 peak): `S1=0.318`, `S2=2.262`, `S3=2.217`
*   T=4.8 (S1 peak): `S1=1.600`, `S2=1.771`, `S3=0.974`
*   T=30 (Final): `S1=0.833`, `S2=0.648`, `S3=0.934`

**Simulated Data (iter14, Set 14):**
*   T=0.12: `S1=0.884`, `S2=1.412`, `S3=4.688`
    *   S1 drop: Exp to 0.800. Sim to 0.884. Initial drop is present but not quite as deep/fast as exp. (Set 13b S1=0.759 was better). `k2f=3.0, k2r=1.5` means initial `dS1/dt = 1.5 - 3.0 = -1.5`. This should be a strong drop.
    *   S2 rise: Exp to 1.076. Sim to 1.412. Sim S2 a bit high.
    *   S3 drop: Exp to 4.557. Sim to 4.688. Sim S3 drop is a bit slow.
*   T=1.2 (S1 dip, S2 peak): `S1=1.202`, `S2=2.622`, `S3=2.900`
    *   S1 dip: Exp to 0.318. Sim `S1=1.202`. No dip below initial observed. S1 is already rising. The increase in `k2r` to 1.5 (from 0.5 in Set 13b) prevented the dip.
    *   S2 peak: Exp to 2.262. Sim to 2.622. Magnitude is reasonably close, timing seems okay.
    *   S3: Exp=2.217. Sim=2.900. Sim S3 is too high.
*   T=4.8 (S1 peak): `S1=1.412`, `S2=2.789`, `S3=1.390`
    *   S1 peak: Exp to 1.600. Sim to 1.412. The magnitude is getting closer! This is good.
    *   S2: Exp=1.771. Sim=2.789. Sim S2 is too high and stays high too long.
    *   S3: Exp=0.974. Sim=1.390. Sim S3 is too high.
*   T=30 (Final): `S1=0.354`, `S2=0.696`, `S3=0.320`
    *   S2: Sim=0.696. Exp=0.648. Good, `k_deg_S2=0.11` is robust.
    *   S1: Sim=0.354. Exp=0.833. Too low. (Ratio `k2r/k2f = 1.5/3.0 = 0.5`. Target 1.286).
    *   S3: Sim=0.320. Exp=0.934. Too low. (Ratio `k1r/k1f = 0.25/0.6 = 0.417`. Target 1.441).

**Key Successes of Set 14:**
*   Correct final S2.
*   S1 initial drop is present (though not as deep as Set 13b).
*   S1 shows a rise to a peak of ~1.41, which is the first time it's gone significantly above its initial value post-drop. This is a major qualitative improvement.
*   S2 peak magnitude and timing are reasonable.

**Key Failures of Set 14:**
*   S1 dip to ~0.3 is lost. The increase in `k2r` (to get the later S1 peak) made S1 recover too quickly.
*   Final S1 and S3 are far too low.
*   S3 initial drop is still a bit slow, and S3 remains too high during mid-phase.
*   S2 stays too high for too long after its peak.

**Revised Parameter Tuning Strategy (Set 15):**
This is about fine-tuning now to balance the S1 dip, S1 peak, and final concentrations.
The S1 dip requires `k2f*S1 > k2r*S2` when S1 is low.
The S1 peak requires `k2r*S2 > k2f*S1` when S2 is high.

1.  **Keep `k_deg_S2 = 0.11`**.
2.  **S1 dip vs S1 peak:**
    *   Set 13b (`k2f=3.0, k2r=0.5`) gave S1 dip (0.405) but no peak (max 0.48).
    *   Set 14 (`k2f=3.0, k2r=1.5`) gave no S1 dip (min 0.88) but S1 peak (1.41).
    *   The optimal `k2r` is between 0.5 and 1.5. Let's try `k2r = 1.0`.
    *   Keep `k2f = 3.0`. Initial `dS1/dt = 1.0 - 3.0 = -2.0`. Strong drop.
    *   Ratio `k2r/k2f = 1.0/3.0 = 0.333`. Final S1 will be `0.333 * S2_final = 0.333 * 0.696 = 0.232`. Still very low.

3.  **S3 dynamics and final S3 level:**
    *   S3 initial drop needs to be faster, S3 mid-phase too high. Increase `k1f`.
    *   Let `k1f = 0.8` (from 0.6).
    *   To get final S3 correct: `k1r = k1f * (S3_exp_final / S2_exp_final) = 0.8 * 1.441 = 1.1528`.
    *   Initial `dS3/dt = k1r*1 - k1f*5 = 1.1528 - 0.8*5 = 1.1528 - 4.0 = -2.8472`. Strong drop.

4.  **Final S1 level:**
    *   With `k2f=3.0, k2r=1.0`, final S1 will be too low.
    *   To get final S1 correct, `k2r` would need to be `k2f * 1.286 = 3.0 * 1.286 = 3.858`. This would prevent the initial drop.
    *   This reinforces the idea that the 5-reaction model cannot meet all criteria.

**Compromise for Set 15:**
Prioritize:
*   Final S2.
*   S1 initial drop.
*   S1 dip (qualitatively).
*   S1 peak (qualitatively, aiming for >1.0).
*   S2 peak magnitude/timing.
*   Then, try to get final S1/S3 as good as possible without breaking above.

Parameters (Set 15):
*   `k_deg_S2 = 0.11`

*   `k1f = 0.7` (Slightly increased from Set 14's 0.6, for S3 drop and S2 shape)
*   `k1r = 0.4` (Increased from Set 14's 0.25, to raise final S3. Ratio `0.4/0.7 = 0.57`. Target 1.44. Final S3 will be `0.57 * 0.696 = 0.39`. Still low).

*   `k2f = 2.5` (Slightly reduced from Set 14's 3.0, to help S1 dip by not consuming it *too* fast, and reduce S2 peak a bit)
*   `k2r = 1.2` (Compromise between 0.5 for dip and 1.5 for peak. Ratio `1.2/2.5 = 0.48`. Final S1 will be `0.48 * 0.696 = 0.33`. Still low).

Initial `d[S1]/dt = 1.2 - 2.5 = -1.3`. (Drop)
Initial `d[S3]/dt = 0.4 - 0.7*5 = 0.4 - 3.5 = -3.1`. (Drop)
Check S2 initial increase: `(5*k1f + k2f) > (k1r + k2r + k_deg_S2)`
`(5*0.7 + 2.5) > (0.4 + 1.2 + 0.11)`
`(3.5 + 2.5) > (1.6 + 0.11)`
`6.0 > 1.71`. True.

This is a careful balancing act. The goal is to find a parameter set that gets most features qualitatively right, even if quantitative match for final S1/S3 is off. This would be the best this model structure can do.

## Action

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

# Access experimental data
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())
# ... (print other specific time points if needed for checking)

# --- Part 1: Build the SBML model (Set 15) ---
# This uses the 5-reaction model (S2 degradation only)
sbml_doc_iter15 = libsbml.readSBMLFromString(input_sbml_string)
model_iter15 = sbml_doc_iter15.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 15)
k1f_val = 0.7     # S3 (id_6o57) -> S2 (id_khqo)
k1r_val = 0.4     # S2 -> S3
k2f_val = 2.5     # S1 (id_1a2z) -> S2
k2r_val = 1.2     # S2 -> S1
k_deg_S2_val = 0.11 # S2 -> ø 

# Reactions
create_reaction_mod(model_iter15, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
create_reaction_mod(model_iter15, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
create_reaction_mod(model_iter15, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
create_reaction_mod(model_iter15, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

reaction_deg_S2 = model_iter15.createReaction()
reaction_deg_S2.setId("R_deg_S2") 
reaction_deg_S2.setReversible(False)
reactant_deg_S2 = reaction_deg_S2.createReactant(); reactant_deg_S2.setSpecies("id_khqo"); reactant_deg_S2.setStoichiometry(1)
kl_S2 = reaction_deg_S2.createKineticLaw(); param_S2 = kl_S2.createParameter(); param_S2.setId("k_deg_S2"); param_S2.setValue(k_deg_S2_val)
kl_S2.setMath(libsbml.parseL3Formula("k_deg_S2 * id_khqo"))


writer = libsbml.SBMLWriter()
updated_sbml_str_iter15 = writer.writeSBMLToString(sbml_doc_iter15)
shared_variables.add("current_sbml_model_iter15", updated_sbml_str_iter15)
print("\nUpdated SBML model (iter15) with 5 reactions (Set 15).")

# --- Part 2: Simulate the new model ---
sim_data_iter15 = simulate(updated_sbml_str_iter15)
shared_variables.add("simulation_results_iter15", sim_data_iter15)
print("\nSimulation of the updated model (iter15) completed.")

# Print relevant time points for comparison
print("\nSimulated data (iter15) at T=0.12:")
print(sim_data_iter15.iloc[(sim_data_iter15['Time']-0.12).abs().argsort()[:1]])
print("\nSimulated data (iter15) at T=1.2 (S1 dip, S2 peak):")
print(sim_data_iter15.iloc[(sim_data_iter15['Time']-1.2).abs().argsort()[:1]])
print("\nSimulated data (iter15) at T=4.8 (S1 peak):")
print(sim_data_iter15.iloc[(sim_data_iter15['Time']-4.8).abs().argsort()[:1]])
print("\nSimulated data (iter15) tail:")
print(sim_data_iter15.tail())
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model (iter15) with 5 reactions (Set 15).

Simulation of the updated model (iter15) completed.

Simulated data (iter15) at T=0.12:
    id_1a2z   id_khqo   id_6o57  Time
4  0.895158  1.434694  4.653915  0.12

Simulated data (iter15) at T=1.2 (S1 dip, S2 peak):
     id_1a2z   id_khqo   id_6o57  Time
40  1.162299  2.664273  2.889316   1.2

Simulated data (iter15) at T=4.8 (S1 peak):
      id_1a2z   id_khqo   id_6o57  Time
160  1.292665  2.647328  1.676368   4.8

Simulated data (iter15) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.352989  0.720042  0.444600  29.88
997   0.352437  0.718915  0.443905  29.91
998   0.351885  0.717790  0.443210  29.94
999   0.351335  0.716667  0.442517  29.97
1000  0.350785  0.715546  0.441824  30.00

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6, current_sbml_model_iter7, simulation_results_iter7, current_sbml_model_iter8, simulation_results_iter8, current_sbml_model_iter9, simulation_results_iter9, current_sbml_model_iter10, simulation_results_iter10, current_sbml_model_iter11, simulation_results_iter11, current_sbml_model_iter12, simulation_results_iter12, current_sbml_model_iter13, simulation_results_iter13, current_sbml_model_iter14, simulation_results_iter14, current_sbml_model_iter15, simulation_results_iter15)

### 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 results with Set 15 (`k1f=0.7, k1r=0.4, k2f=2.5, k2r=1.2, k_deg_S2=0.11`) are a reasonable compromise for the 5-reaction model, capturing some key dynamic features but failing on others, especially final concentrations of S1 and S3, and the S1 dip.

**Experimental Data:**
*   T=0.12: `S1=0.800`, `S2=1.076`, `S3=4.557`
*   T=1.2 (S1 dip, S2 peak): `S1=0.318`, `S2=2.262`, `S3=2.217`
*   T=4.8 (S1 peak): `S1=1.600`, `S2=1.771`, `S3=0.974`
*   T=30 (Final): `S1=0.833`, `S2=0.648`, `S3=0.934`

**Simulated Data (iter15, Set 15):**
*   T=0.12: `S1=0.895`, `S2=1.435`, `S3=4.654`
    *   S1 drop: Exp to 0.800. Sim to 0.895. Present, but not deep enough.
    *   S2 rise: Exp to 1.076. Sim to 1.435. Sim S2 a bit high.
    *   S3 drop: Exp to 4.557. Sim to 4.654. Sim S3 drop a bit slow.
*   T=1.2 (S1 dip, S2 peak): `S1=1.162`, `S2=2.664`, `S3=2.889`
    *   S1 dip: Exp to 0.318. Sim `S1=1.162`. No dip below initial observed.
    *   S2 peak: Exp to 2.262. Sim to 2.664. Magnitude is reasonably close.
    *   S3: Exp=2.217. Sim=2.889. Sim S3 is too high.
*   T=4.8 (S1 peak): `S1=1.293`, `S2=2.647`, `S3=1.676`
    *   S1 peak: Exp to 1.600. Sim to 1.293. Sim S1 rises, but peak is too low.
    *   S2: Exp=1.771. Sim=2.647. Sim S2 is too high / stays high too long.
    *   S3: Exp=0.974. Sim=1.676. Sim S3 is too high.
*   T=30 (Final): `S1=0.351`, `S2=0.716`, `S3=0.442`
    *   S2: Sim=0.716. Exp=0.648. A bit high, but `k_deg_S2=0.11` is in the right ballpark.
    *   S1: Sim=0.351. Exp=0.833. Too low.
    *   S3: Sim=0.442. Exp=0.934. Too low.

**Conclusion on 5-Reaction Model:**
This model structure (`S1 <=> S2`, `S3 <=> S2`, `S2 -> ø`) with mass-action kinetics, despite extensive tuning, cannot simultaneously capture:
1.  The deep initial dip of S1 to ~0.3.
2.  The subsequent strong rise of S1 to a peak of ~1.6.
3.  The correct final concentrations/ratios for S1 and S3 relative to S2.

The conflict arises because parameters that allow the S1 dip (very high `k2f`, low `k2r`) prevent the later S1 rise and lead to incorrect final S1 levels. Parameters that allow the S1 rise (higher `k2r`) prevent the initial dip.

**Time to Propose a New Model Structure - The True Mechanism is Likely Different.**
The complex S1 profile (initial consumption, then production leading to overshoot, then settling) is highly suggestive of a mechanism where S1 is part of a more elaborate pathway, possibly involving an intermediate that accumulates and then drives S1 production, or a feedback mechanism.

Given the constraint "You do not need to add new species", I must use S1, S2, S3.
Consider a branched pathway or a cycle.

What if S3 is converted to an intermediate (let's say S2 acts as this intermediate or is closely linked), and this intermediate then produces S1?
Model Idea:
1.  `S3 -> S2` (k1f) (S3 consumption, S2 production)
2.  `S2 -> S1` (k2_S2_to_S1) (S2 consumption, S1 production - this is key for S1 rise)
3.  `S1 -> S2` (k2_S1_to_S2) (S1 consumption, S2 production - for S1 initial drop and dip)
4.  `S1 -> ø` (kd_S1) (S1 degradation - to help with S1 initial drop and overall mass balance)
5.  `S2 -> ø` (kd_S2) (S2 degradation - for overall mass balance and S2 profile)
This model has S1 and S2 degrading. It also has `S1 <=> S2` effectively. S3 is an upstream source for S2.

Let's analyze this new structure:
`dS3/dt = -k1f * S3`
`dS2/dt = k1f * S3 + k2_S1_to_S2 * S1 - k2_S2_to_S1 * S2 - kd_S2 * S2`
`dS1/dt = k2_S2_to_S1 * S2 - k2_S1_to_S2 * S1 - kd_S1 * S1`

Initial conditions: S1=1, S2=1, S3=5.
*   S3 will always decrease. (Matches data)
*   Initial S1 drop: `dS1/dt = k2_S2_to_S1 * 1 - (k2_S1_to_S2 + kd_S1) * 1`.
    Requires `(k2_S1_to_S2 + kd_S1) > k2_S2_to_S1`.
*   S1 rise after dip: If S2 peaks high, `k2_S2_to_S1 * S2_peak` could overcome consumption terms.
*   S2 dynamics: Fed by S3 and S1, consumed by conversion to S1 and degradation.

This structure seems more plausible for the S1 overshoot.
Let's try to parameterize this. This is a significant model change.

Parameters (Set 16 - New Model Structure):
*   `k1f (S3->S2)`: S3 drops from 5 to ~1. Let `k1f = 0.15` (average lifetime of S3 ~ 1/0.15 ~ 6-7 time units, reasonable for a 30-unit simulation).
*   `kd_S2 (S2->ø)`: Final S2 is ~0.65. Let `kd_S2 = 0.2` (trial value).
*   `kd_S1 (S1->ø)`: Final S1 is ~0.83. Let `kd_S1 = 0.1` (trial value).

*   `k2_S1_to_S2 (S1->S2)` and `k2_S2_to_S1 (S2->S1)`:
    *   For initial S1 drop: `(k2_S1_to_S2 + kd_S1) > k2_S2_to_S1`.
        `(k2_S1_to_S2 + 0.1) > k2_S2_to_S1`.
    *   For S1 dip to ~0.3 and S2 peak to ~2.2: This needs high `k2_S1_to_S2`.
        Let `k2_S1_to_S2 = 2.0`.
    *   Then `(2.0 + 0.1) > k2_S2_to_S1 => 2.1 > k2_S2_to_S1`.
    *   For S1 to rise to ~1.6 driven by S2 peak of ~2.2: `k2_S2_to_S1 * 2.2` must be large.
        Let `k2_S2_to_S1 = 1.0`. Then `2.1 > 1.0` is true (initial S1 drop).
        When S1=0.3, S2=2.2: `dS1/dt = 1.0*2.2 - (2.0+0.1)*0.3 = 2.2 - 2.1*0.3 = 2.2 - 0.63 = 1.57`. Strong rise. This looks promising!

    *   Final state: `S1_final ~ 0.83`, `S2_final ~ 0.65`.
        `dS1/dt = 0 => k2_S2_to_S1 * S2_f = (k2_S1_to_S2 + kd_S1) * S1_f`
        `1.0 * 0.65 = (2.0 + 0.1) * 0.83`
        `0.65 = 2.1 * 0.83 = 1.743`. This is not balanced. `S1_f` would be `0.65/2.1 = 0.31`. Too low.
        This means `k2_S2_to_S1` needs to be higher relative to `(k2_S1_to_S2 + kd_S1)`.
        Let `R = (k2_S1_to_S2 + kd_S1) / k2_S2_to_S1`. We want `S1_f/S2_f = 1/R = 1.286`. So `R = 1/1.286 = 0.778`.
        `(k2_S1_to_S2 + kd_S1) / k2_S2_to_S1 = 0.778`.
        If `kd_S1 = 0.1`. Let `k2_S2_to_S1 = 1.5`.
        Then `k2_S1_to_S2 + 0.1 = 0.778 * 1.5 = 1.167`.
        `k2_S1_to_S2 = 1.067`.
        Check initial S1 drop: `(k2_S1_to_S2 + kd_S1) > k2_S2_to_S1` => `(1.067 + 0.1) > 1.5` => `1.167 > 1.5`. False. S1 would increase.

This shows the difficulty. The requirements for dynamics (initial drop, later rise) and final steady-state ratios are hard to meet simultaneously.

Let's prioritize dynamics.
Set 16b (New Model, Dynamics Focus):
*   `k1f (S3->S2) = 0.2` (Controls S3 decay and S2 feed)
*   `kd_S2 (S2->ø) = 0.25` (Adjust for S2 final level, S2 peak was ~2.2-2.8)
*   `kd_S1 (S1->ø) = 0.3` (For S1 initial drop, and final level)

*   `k2_S1_to_S2 (S1->S2) = 2.5` (Strong S1 consumption for dip)
*   `k2_S2_to_S1 (S2->S1) = 1.5` (Strong S1 production from S2 peak for S1 rise)

    Initial S1 drop: `(k2_S1_to_S2 + kd_S1) > k2_S2_to_S1`
    `(2.5 + 0.3) > 1.5` => `2.8 > 1.5`. True. S1 should drop.
    `dS1/dt(0) = 1.5*1 - (2.5+0.3)*1 = 1.5 - 2.8 = -1.3`.

    S1 rise from dip (S1=0.3, S2=2.2):
    `dS1/dt = 1.5*2.2 - (2.5+0.3)*0.3 = 3.3 - 2.8*0.3 = 3.3 - 0.84 = 2.46`. Strong rise.

    Final S1/S2 ratio from reversible part: `S1/S2 = k2_S2_to_S1 / k2_S1_to_S2 = 1.5 / 2.5 = 0.6`.
    If `kd_S1` is also active, `S1_f/S2_f = k2_S2_to_S1 / (k2_S1_to_S2 + kd_S1) = 1.5 / (2.5 + 0.3) = 1.5 / 2.8 = 0.53`.
    If S2_final is ~0.65, S1_final ~ `0.53 * 0.65 = 0.34`. Still too low.

This new model structure is a hypothesis. It might be the "true underlying mechanism".
The reactions are:
1. `id_6o57 -> id_khqo` (k1f)
2. `id_1a2z -> id_khqo` (k_S1_to_S2)
3. `id_khqo -> id_1a2z` (k_S2_to_S1)
4. `id_1a2z -> ø` (kd_S1)
5. `id_khqo -> ø` (kd_S2)
This is 5 reactions, not 6 as I wrote earlier. It's a re-interpretation of the roles.
S3 (id_6o57) is an input to S2 (id_khqo). S1 (id_1a2z) and S2 interconvert, and both S1 and S2 degrade.

## Action

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

# Access experimental data
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())

# --- Part 1: Build the SBML model (Set 16b - New Structure) ---
sbml_doc_iter16 = libsbml.readSBMLFromString(input_sbml_string) # Start fresh
model_iter16 = sbml_doc_iter16.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    if products: # Allow no products for degradation
        for p_spec_id, p_stoich in products:
            product = reaction.createProduct()
            product.setSpecies(p_spec_id)
            product.setStoichiometry(p_stoich)
            product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    # Formula assumes mass action based on reactants
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 16b - New Structure)
# Species: S1=id_1a2z, S2=id_khqo, S3=id_6o57
k_S3_to_S2_val = 0.2     # Reaction 1: S3 -> S2 (k1f in thoughts)
k_S1_to_S2_val = 2.5     # Reaction 2: S1 -> S2
k_S2_to_S1_val = 1.5     # Reaction 3: S2 -> S1
kd_S1_val = 0.3          # Reaction 4: S1 -> ø
kd_S2_val = 0.25         # Reaction 5: S2 -> ø

# Reaction 1: id_6o57 -> id_khqo
create_reaction_mod(model_iter16, "R_S3_to_S2", [("id_6o57", 1)], [("id_khqo", 1)], k_S3_to_S2_val, "k_S3_to_S2")
# Reaction 2: id_1a2z -> id_khqo
create_reaction_mod(model_iter16, "R_S1_to_S2", [("id_1a2z", 1)], [("id_khqo", 1)], k_S1_to_S2_val, "k_S1_to_S2")
# Reaction 3: id_khqo -> id_1a2z
create_reaction_mod(model_iter16, "R_S2_to_S1", [("id_khqo", 1)], [("id_1a2z", 1)], k_S2_to_S1_val, "k_S2_to_S1")
# Reaction 4: id_1a2z -> ø
create_reaction_mod(model_iter16, "R_deg_S1", [("id_1a2z", 1)], None, kd_S1_val, "kd_S1")
# Reaction 5: id_khqo -> ø
create_reaction_mod(model_iter16, "R_deg_S2", [("id_khqo", 1)], None, kd_S2_val, "kd_S2")


writer = libsbml.SBMLWriter()
updated_sbml_str_iter16 = writer.writeSBMLToString(sbml_doc_iter16)
shared_variables.add("current_sbml_model_iter16", updated_sbml_str_iter16)
print("\nUpdated SBML model (iter16) with NEW 5-reaction structure (Set 16b).")

# --- Part 2: Simulate the new model ---
sim_data_iter16 = simulate(updated_sbml_str_iter16)
shared_variables.add("simulation_results_iter16", sim_data_iter16)
print("\nSimulation of the updated model (iter16) completed.")

# Print relevant time points for comparison
print("\nSimulated data (iter16) at T=0.12:")
print(sim_data_iter16.iloc[(sim_data_iter16['Time']-0.12).abs().argsort()[:1]])
print("\nSimulated data (iter16) at T=1.2 (S1 dip, S2 peak):")
print(sim_data_iter16.iloc[(sim_data_iter16['Time']-1.2).abs().argsort()[:1]])
print("\nSimulated data (iter16) at T=4.8 (S1 peak):")
print(sim_data_iter16.iloc[(sim_data_iter16['Time']-4.8).abs().argsort()[:1]])
print("\nSimulated data (iter16) tail:")
print(sim_data_iter16.tail())
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model (iter16) with NEW 5-reaction structure (Set 16b).

Simulation of the updated model (iter16) completed.

Simulated data (iter16) at T=0.12:
   id_1a2z   id_khqo   id_6o57  Time
4  0.88216  1.170008  4.881429  0.12

Simulated data (iter16) at T=1.2 (S1 dip, S2 peak):
     id_1a2z   id_khqo   id_6o57  Time
40  0.806977  1.549114  3.933139   1.2

Simulated data (iter16) at T=4.8 (S1 peak):
      id_1a2z   id_khqo   id_6o57  Time
160  0.754947  1.367858  1.914464   4.8

Simulated data (iter16) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.012063  0.020980  0.012695  29.88
997   0.011994  0.020860  0.012619  29.91
998   0.011926  0.020740  0.012543  29.94
999   0.011857  0.020622  0.012468  29.97
1000  0.011790  0.020503  0.012394  30.00

## 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)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6, current_sbml_model_iter7, simulation_results_iter7, current_sbml_model_iter8, simulation_results_iter8, current_sbml_model_iter9, simulation_results_iter9, current_sbml_model_iter10, simulation_results_iter10, current_sbml_model_iter11, simulation_results_iter11, current_sbml_model_iter12, simulation_results_iter12, current_sbml_model_iter13, simulation_results_iter13, current_sbml_model_iter14, simulation_results_iter14, current_sbml_model_iter15, simulation_results_iter15, current_sbml_model_iter16, simulation_results_iter16)

### 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 new model structure from Set 16b (`S3->S2`, `S1<=>S2`, `S1->0`, `S2->0`) did not perform well.
Final concentrations are extremely low, and the S1 dynamics (dip, peak) are not captured correctly. S1 does drop initially (to 0.88 at T=0.12, then to 0.80 at T=1.2), but this is not the deep dip to 0.3. It doesn't rise above initial. S2 peak is too low (1.5 vs 2.2).

This suggests the new structure, or at least this parameterization of it, is not better. The previous 5-reaction model (`S1<=>S2`, `S3<=>S2`, `S2->0`) was closer to capturing some of the complex dynamics, especially with Set 13b/14.

Let's revert to the 5-reaction model from Iteration 13/14/15.
Model:
1.  `id_6o57 -> id_khqo` (k1f: S3 -> S2)
2.  `id_khqo -> id_6o57` (k1r: S2 -> S3)
3.  `id_1a2z -> id_khqo` (k2f: S1 -> S2)
4.  `id_khqo -> id_1a2z` (k2r: S2 -> S1)
5.  `id_khqo -> ø`      (k_deg_S2: S2 -> ø)

Set 13b (`k1f=0.3, k1r=0.15, k2f=3.0, k2r=0.5, k_deg_S2=0.11`) gave:
*   T=0.12: `S1=0.759` (Good drop!), `S2=1.381` (bit high), `S3=4.844` (drop slow)
*   T=1.2: `S1=0.405` (Good dip!), `S2=2.525` (Good peak!), `S3=3.802` (too high)
*   T=4.8: `S1=0.484` (No rise to peak), `S2=2.884` (too high), `S3=2.238` (too high)
*   T=30: `S1=0.115` (too low), `S2=0.675` (Good!), `S3=0.424` (too low)

Set 14 (`k1f=0.6, k1r=0.25, k2f=3.0, k2r=1.5, k_deg_S2=0.11`) gave:
*   T=0.12: `S1=0.884` (drop not deep), `S2=1.412` (bit high), `S3=4.688` (drop slow)
*   T=1.2: `S1=1.202` (no dip), `S2=2.622` (Good peak!), `S3=2.900` (bit high)
*   T=4.8: `S1=1.412` (Good peak!), `S2=2.789` (too high), `S3=1.390` (bit high)
*   T=30: `S1=0.354` (too low), `S2=0.696` (Good!), `S3=0.320` (too low)

Set 13b was good for S1 dip and S2 peak. Set 14 was good for S1 peak (rise after initial phase).
The main issue is balancing the S1 dip (needs low `k2r`) and S1 peak (needs high `k2r`).
And then fixing final S1 and S3 concentrations (which need specific `k_rev/k_fwd` ratios).

Let's try to combine aspects:
Use `k2f` from Set 13b for the strong initial S1 processing.
Use a `k2r` that is a compromise, perhaps closer to Set 14's to get some S1 rise.
Adjust `k1f` to control S3 consumption and S2 peak height.
Adjust `k1r` and `k2r` (again) to try and improve final concentrations without losing all dynamics.

This is very challenging. The model might be at its limit.
If I have to submit, I'd pick the model that gets the most *qualitative* features correct, even if quantitative agreement is imperfect. The S1 dip and subsequent rise to a peak are very distinctive.

Let's try to refine Set 14, as it produced the S1 peak.
Problem: S1 initial drop was not deep enough (0.884 vs 0.800 exp, and no deep dip to 0.3).
This was with `k2f=3.0, k2r=1.5`. Initial `dS1/dt = -1.5`.
Set 13b had `k2f=3.0, k2r=0.5`. Initial `dS1/dt = -2.5`. This gave the dip.

What if `k2r` is not constant? E.g. `S2` activates `k2r`? (Michaelis-Menten for S2 in `S2->S1`?)
This is adding complexity beyond simple mass-action for the rate constants. The problem doesn't forbid changing rate laws, only adding species.

If I stick to mass-action:
To get the S1 dip AND the S1 peak, S2 must peak very high when S1 is low, and `k2r` must be significant.
Set 13b: S1 dip to 0.405, S2 peak 2.525. `k2r=0.5`. `k2r*S2_peak = 1.26`. `k2f*S1_dip = 3.0*0.405 = 1.215`.
So `dS1/dt` at dip was `1.26 - 1.215 = 0.045`. A very slow rise. This is why S1 didn't peak well.

To make S1 rise more from the dip: increase `k2r`.
Let's take Set 13b as a base, and only increase `k2r`.
Set 13b: `k1f=0.3, k1r=0.15, k2f=3.0, k2r=0.5, k_deg_S2=0.11`.
New Set 17 (based on 13b, increasing `k2r`):
*   `k_deg_S2 = 0.11`
*   `k1f = 0.3`
*   `k1r = 0.15` (Final S3 will be low: `(0.15/0.3)*0.67 = 0.33`. Exp 0.934)
*   `k2f = 3.0`
*   `k2r = 1.0` (Increased from 0.5. Set 14 had 1.5. This is a mid-point).
    Initial `dS1/dt = 1.0 - 3.0 = -2.0`. (Strong drop).
    Ratio `k2r/k2f = 1.0/3.0 = 0.333`. Final S1 will be low: `0.333 * 0.67 = 0.22`. (Exp 0.833).

    At S1 dip (assume S1~0.4, S2_peak~2.5 from Set 13b):
    `dS1/dt = k2r*S2_peak - k2f*S1_dip = 1.0*2.5 - 3.0*0.4 = 2.5 - 1.2 = 1.3`. This is a much stronger rise.

This set might give the S1 dip AND a subsequent rise. Final S1/S3 will be off.
S2 peak might be affected by the change in `k2r` as it influences S1 levels, which feed S2.

Let's try this. This is about getting the shape of S1 right.

## Action

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

# Access experimental data
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())

# --- Part 1: Build the SBML model (Set 17) ---
# Based on Set 13b, increasing k2r
sbml_doc_iter17 = libsbml.readSBMLFromString(input_sbml_string)
model_iter17 = sbml_doc_iter17.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 17)
k1f_val = 0.3     # S3 (id_6o57) -> S2 (id_khqo)
k1r_val = 0.15    # S2 -> S3
k2f_val = 3.0     # S1 (id_1a2z) -> S2
k2r_val = 1.0     # S2 -> S1 (Increased from 0.5 in Set 13b)
k_deg_S2_val = 0.11 # S2 -> ø 

# Reactions
create_reaction_mod(model_iter17, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
create_reaction_mod(model_iter17, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
create_reaction_mod(model_iter17, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
create_reaction_mod(model_iter17, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

reaction_deg_S2 = model_iter17.createReaction()
reaction_deg_S2.setId("R_deg_S2") 
reaction_deg_S2.setReversible(False)
reactant_deg_S2 = reaction_deg_S2.createReactant(); reactant_deg_S2.setSpecies("id_khqo"); reactant_deg_S2.setStoichiometry(1)
kl_S2 = reaction_deg_S2.createKineticLaw(); param_S2 = kl_S2.createParameter(); param_S2.setId("k_deg_S2"); param_S2.setValue(k_deg_S2_val)
kl_S2.setMath(libsbml.parseL3Formula("k_deg_S2 * id_khqo"))


writer = libsbml.SBMLWriter()
updated_sbml_str_iter17 = writer.writeSBMLToString(sbml_doc_iter17)
shared_variables.add("current_sbml_model_iter17", updated_sbml_str_iter17)
print("\nUpdated SBML model (iter17) with 5 reactions (Set 17).")

# --- Part 2: Simulate the new model ---
sim_data_iter17 = simulate(updated_sbml_str_iter17)
shared_variables.add("simulation_results_iter17", sim_data_iter17)
print("\nSimulation of the updated model (iter17) completed.")

# Print relevant time points for comparison
print("\nSimulated data (iter17) at T=0.12:")
print(sim_data_iter17.iloc[(sim_data_iter17['Time']-0.12).abs().argsort()[:1]])
print("\nSimulated data (iter17) at T=1.2 (S1 dip, S2 peak):")
print(sim_data_iter17.iloc[(sim_data_iter17['Time']-1.2).abs().argsort()[:1]])
print("\nSimulated data (iter17) at T=4.8 (S1 peak):")
print(sim_data_iter17.iloc[(sim_data_iter17['Time']-4.8).abs().argsort()[:1]])
print("\nSimulated data (iter17) tail:")
print(sim_data_iter17.tail())
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model (iter17) with 5 reactions (Set 17).

Simulation of the updated model (iter17) completed.

Simulated data (iter17) at T=0.12:
   id_1a2z   id_khqo   id_6o57  Time
4  0.81675  1.323842  4.843938  0.12

Simulated data (iter17) at T=1.2 (S1 dip, S2 peak):
     id_1a2z   id_khqo  id_6o57  Time
40  0.709903  2.271064  3.77398   1.2

Simulated data (iter17) at T=4.8 (S1 peak):
      id_1a2z  id_khqo  id_6o57  Time
160  0.896046  2.67961  2.14989   4.8

Simulated data (iter17) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.245704  0.723289  0.445135  29.88
997   0.245290  0.722069  0.444384  29.91
998   0.244876  0.720851  0.443635  29.94
999   0.244463  0.719636  0.442886  29.97
1000  0.244051  0.718422  0.442139  30.00

## 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)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6, current_sbml_model_iter7, simulation_results_iter7, current_sbml_model_iter8, simulation_results_iter8, current_sbml_model_iter9, simulation_results_iter9, current_sbml_model_iter10, simulation_results_iter10, current_sbml_model_iter11, simulation_results_iter11, current_sbml_model_iter12, simulation_results_iter12, current_sbml_model_iter13, simulation_results_iter13, current_sbml_model_iter14, simulation_results_iter14, current_sbml_model_iter15, simulation_results_iter15, current_sbml_model_iter16, simulation_results_iter16, current_sbml_model_iter17, simulation_results_iter17)

### 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

Set 17 (`k1f=0.3, k1r=0.15, k2f=3.0, k2r=1.0, k_deg_S2=0.11`) showed good progress.

**Experimental Data:**
*   T=0.12: `S1=0.800`, `S2=1.076`, `S3=4.557`
*   T=1.2 (S1 dip, S2 peak): `S1=0.318`, `S2=2.262`, `S3=2.217`
*   T=4.8 (S1 peak): `S1=1.600`, `S2=1.771`, `S3=0.974`
*   T=30 (Final): `S1=0.833`, `S2=0.648`, `S3=0.934`

**Simulated Data (iter17, Set 17):**
*   T=0.12: `S1=0.817`, `S2=1.324`, `S3=4.844`
    *   S1 drop: Exp to 0.800. Sim to 0.817. Very good initial drop!
    *   S2 rise: Exp to 1.076. Sim to 1.324. Sim S2 a bit high.
    *   S3 drop: Exp to 4.557. Sim to 4.844. Sim S3 drop is slow.
*   T=1.2 (S1 dip, S2 peak): `S1=0.709`, `S2=2.271`, `S3=3.774`
    *   S1 dip: Exp to 0.318. Sim to 0.709. A dip is present below the T=0.12 value, but not nearly as deep as experimental.
    *   S2 peak: Exp to 2.262. Sim to 2.271. Excellent S2 peak magnitude and timing!
    *   S3: Exp=2.217. Sim=3.774. Sim S3 is too high.
*   T=4.8 (S1 peak): `S1=0.896`, `S2=2.680`, `S3=2.150`
    *   S1 peak: Exp to 1.600. Sim to 0.896. S1 rises after its dip, but the peak is far too low.
    *   S2: Exp=1.771. Sim=2.680. Sim S2 is too high / stays high too long.
    *   S3: Exp=0.974. Sim=2.150. Sim S3 is too high.
*   T=30 (Final): `S1=0.244`, `S2=0.718`, `S3=0.442`
    *   S2: Sim=0.718. Exp=0.648. Good (slightly high). `k_deg_S2=0.11` is good.
    *   S1: Sim=0.244. Exp=0.833. Too low.
    *   S3: Sim=0.442. Exp=0.934. Too low.

**Key Successes of Set 17:**
*   Excellent S2 peak.
*   Good final S2.
*   Good S1 initial drop.
*   S1 shows a dip then a rise, qualitatively matching the complex shape.

**Key Failures of Set 17:**
*   S1 dip is not deep enough (0.7 vs 0.3).
*   S1 peak after dip is far too low (0.9 vs 1.6).
*   Final S1 and S3 are too low.
*   S3 initial drop is slow, and S3 stays too high in mid-phase.
*   S2 stays too high for too long after its peak.

**Revised Parameter Tuning Strategy (Set 18):**
This is likely the final tuning attempt for this 5-reaction model. The goal is to improve the S1 dip depth and peak height, and the S3 profile, while trying to maintain the good S2 peak and final S2. Final S1/S3 levels will likely remain a compromise.

1.  **Keep `k_deg_S2 = 0.11`**.
2.  **S1 dip depth:** To make S1 dip deeper, `k2f*S1` needs to dominate `k2r*S2` more strongly when S1 is around 0.7-0.8 and S2 is rising.
    Set 17: `k2f=3.0, k2r=1.0`.
    Perhaps `k2f` is slightly too low, or `k2r` is slightly too high for the *dip phase*.
    However, `k2r=1.0` was chosen to help the *peak phase*.
    If `k2f` is increased, S2 peak might get too high.
    Let's keep `k2f=3.0`. To deepen the dip, `k2r` would need to be smaller initially, but larger later. This points to the limitation of constant rate coefficients.

3.  **S1 peak height:** To make S1 peak higher (target 1.6), `k2r*S2_peak` needs to be much larger.
    S2_peak is ~2.3. If S1 is at its dip (say 0.4-0.7), `k2f*S1` is `3.0 * (0.4 to 0.7) = 1.2 to 2.1`.
    We need `k2r*2.3` to be significantly larger than this.
    If `k2r=1.0` (Set 17), `k2r*2.3 = 2.3`. `2.3` vs `1.2-2.1`. This gives some rise.
    If `k2r=1.5` (Set 14, which had S1 peak 1.41 but no dip), `k2r*2.3 = 3.45`.
    Let's try `k2r = 1.8`. This is a large increase.
    Initial `dS1/dt = 1.8 - 3.0 = -1.2`. Still a good drop.
    Ratio `k2r/k2f = 1.8/3.0 = 0.6`. Final S1 will be `0.6 * S2_final = 0.6 * 0.7 = 0.42`. Still low.

4.  **S3 profile:** S3 initial drop slow, S3 too high mid-phase.
    Increase `k1f`. Set 17 `k1f=0.3`. Let `k1f = 0.5`. (Set 14 had 0.6).
    This will increase S2 production, potentially making S2 peak higher and S2 stay high longer.
    Keep `k1r = 0.15` (from Set 17). Ratio `0.15/0.5 = 0.3`. Final S3 will be very low.
    This is a trade-off: better S3 dynamics vs worse final S3.

5.  **S2 staying too high after peak:** If `k1f` is increased, S2 might stay even higher. The `k_deg_S2` is the main way to bring it down. If S2 is persistently too high after peak, `k_deg_S2` might need a slight increase, or consumption of S2 via `k1r` and `k2r` needs to be more effective.

Parameters (Set 18 - "Final Attempt at S1 Shape"):
*   `k_deg_S2 = 0.11`

*   `k1f = 0.5` (Increased from 0.3, for S3 dynamics)
*   `k1r = 0.15` (Kept. Final S3 will be very low)

*   `k2f = 3.0` (Kept for S1 initial drop)
*   `k2r = 1.8` (Increased significantly from 1.0 for S1 peak)

Check S2 initial increase: `(5*k1f + k2f) > (k1r + k2r + k_deg_S2)`
`(5*0.5 + 3.0) > (0.15 + 1.8 + 0.11)`
`(2.5 + 3.0) > (1.95 + 0.11)`
`5.5 > 2.06`. True. S2 increases. S2 peak might be higher than Set 17 due to higher `k1f` and `k2r` (which pulls S1 up, reducing S1->S2 flux later).

This is my best attempt to get the S1 dip-then-peak shape, accepting poor final S1/S3.
If this doesn't work well enough, the 5-reaction model is fundamentally limited for this dataset.
Given only a few iterations left, this will likely be the model I submit if it's the best compromise.

## Action

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

# Access experimental data
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())

# --- Part 1: Build the SBML model (Set 18) ---
sbml_doc_iter18 = libsbml.readSBMLFromString(input_sbml_string)
model_iter18 = sbml_doc_iter18.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 18)
k1f_val = 0.5     # S3 (id_6o57) -> S2 (id_khqo)
k1r_val = 0.15    # S2 -> S3
k2f_val = 3.0     # S1 (id_1a2z) -> S2
k2r_val = 1.8     # S2 -> S1 (Increased from 1.0 in Set 17)
k_deg_S2_val = 0.11 # S2 -> ø 

# Reactions
create_reaction_mod(model_iter18, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
create_reaction_mod(model_iter18, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
create_reaction_mod(model_iter18, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
create_reaction_mod(model_iter18, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

reaction_deg_S2 = model_iter18.createReaction()
reaction_deg_S2.setId("R_deg_S2") 
reaction_deg_S2.setReversible(False)
reactant_deg_S2 = reaction_deg_S2.createReactant(); reactant_deg_S2.setSpecies("id_khqo"); reactant_deg_S2.setStoichiometry(1)
kl_S2 = reaction_deg_S2.createKineticLaw(); param_S2 = kl_S2.createParameter(); param_S2.setId("k_deg_S2"); param_S2.setValue(k_deg_S2_val)
kl_S2.setMath(libsbml.parseL3Formula("k_deg_S2 * id_khqo"))


writer = libsbml.SBMLWriter()
final_sbml_candidate = writer.writeSBMLToString(sbml_doc_iter18) # Store this as a candidate
shared_variables.add("final_sbml_candidate_iter18", final_sbml_candidate) 
# If this is the last iteration before submission, I will use this variable.
# For now, just simulating.
print("\nUpdated SBML model (iter18) with 5 reactions (Set 18).")

# --- Part 2: Simulate the new model ---
sim_data_iter18 = simulate(final_sbml_candidate) # Use the candidate string
shared_variables.add("simulation_results_iter18", sim_data_iter18)
print("\nSimulation of the updated model (iter18) completed.")

# Print relevant time points for comparison
print("\nSimulated data (iter18) at T=0.12:")
print(sim_data_iter18.iloc[(sim_data_iter18['Time']-0.12).abs().argsort()[:1]])
print("\nSimulated data (iter18) at T=1.2 (S1 dip, S2 peak):")
print(sim_data_iter18.iloc[(sim_data_iter18['Time']-1.2).abs().argsort()[:1]])
print("\nSimulated data (iter18) at T=4.8 (S1 peak):")
print(sim_data_iter18.iloc[(sim_data_iter18['Time']-4.8).abs().argsort()[:1]])
print("\nSimulated data (iter18) tail:")
print(sim_data_iter18.tail())

# Decision for next step:
# If this set (18) is the best compromise on dynamics, especially S1 shape,
# I will consider submitting it, acknowledging the limitations on final S1/S3 levels.
# Or, if there's a clear way to improve final S1/S3 without losing the S1 dynamics,
# I'll try that in the next iteration.
# For example, slightly increasing k1r and k2r, if the S1 peak is now TOO high or S1 dip not deep enough.
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model (iter18) with 5 reactions (Set 18).

Simulation of the updated model (iter18) completed.

Simulated data (iter18) at T=0.12:
    id_1a2z   id_khqo   id_6o57  Time
4  0.913828  1.341084  4.729493  0.12

Simulated data (iter18) at T=1.2 (S1 dip, S2 peak):
    id_1a2z  id_khqo   id_6o57  Time
40  1.31905    2.413  3.013388   1.2

Simulated data (iter18) at T=4.8 (S1 peak):
     id_1a2z   id_khqo   id_6o57  Time
160  1.68016  2.777935  1.196513   4.8

Simulated data (iter18) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.432732  0.707656  0.239299  29.88
997   0.432000  0.706459  0.238894  29.91
998   0.431269  0.705264  0.238490  29.94
999   0.430540  0.704072  0.238087  29.97
1000  0.429812  0.702881  0.237684  30.00

## 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)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6, current_sbml_model_iter7, simulation_results_iter7, current_sbml_model_iter8, simulation_results_iter8, current_sbml_model_iter9, simulation_results_iter9, current_sbml_model_iter10, simulation_results_iter10, current_sbml_model_iter11, simulation_results_iter11, current_sbml_model_iter12, simulation_results_iter12, current_sbml_model_iter13, simulation_results_iter13, current_sbml_model_iter14, simulation_results_iter14, current_sbml_model_iter15, simulation_results_iter15, current_sbml_model_iter16, simulation_results_iter16, current_sbml_model_iter17, simulation_results_iter17, final_sbml_candidate_iter18, simulation_results_iter18)

### 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

Set 18 (`k1f=0.5, k1r=0.15, k2f=3.0, k2r=1.8, k_deg_S2=0.11`) is the best so far in capturing the S1 peak.

**Experimental Data:**
*   T=0.12: `S1=0.800`, `S2=1.076`, `S3=4.557`
*   T=1.2 (S1 dip, S2 peak): `S1=0.318`, `S2=2.262`, `S3=2.217`
*   T=4.8 (S1 peak): `S1=1.600`, `S2=1.771`, `S3=0.974`
*   T=30 (Final): `S1=0.833`, `S2=0.648`, `S3=0.934`

**Simulated Data (iter18, Set 18):**
*   T=0.12: `S1=0.914`, `S2=1.341`, `S3=4.729`
    *   S1 drop: Exp to 0.800. Sim to 0.914. Initial drop is present but not deep enough. (Set 17 S1=0.817 was better). This is because `k2r=1.8` is fighting `k2f=3.0` more strongly (`dS1/dt = 1.8-3.0 = -1.2`). Set 17 had `k2r=1.0` (`dS1/dt = 1.0-3.0 = -2.0`).
*   T=1.2 (S1 dip, S2 peak): `S1=1.319`, `S2=2.413`, `S3=3.013`
    *   S1 dip: Exp to 0.318. Sim `S1=1.319`. No dip below initial observed. The S1 dip is completely lost with `k2r=1.8`.
    *   S2 peak: Exp to 2.262. Sim to 2.413. Good S2 peak magnitude!
    *   S3: Exp=2.217. Sim=3.013. Sim S3 is too high.
*   T=4.8 (S1 peak): `S1=1.680`, `S2=2.778`, `S3=1.197`
    *   S1 peak: Exp to 1.600. Sim to 1.680. Excellent S1 peak magnitude! This is a major success.
    *   S2: Exp=1.771. Sim=2.778. Sim S2 is too high / stays high too long.
    *   S3: Exp=0.974. Sim=1.197. Sim S3 is a bit high but much better than before.
*   T=30 (Final): `S1=0.430`, `S2=0.703`, `S3=0.238`
    *   S2: Sim=0.703. Exp=0.648. Good (slightly high).
    *   S1: Sim=0.430. Exp=0.833. Too low. (Ratio `k2r/k2f = 1.8/3.0 = 0.6`. Target 1.286).
    *   S3: Sim=0.238. Exp=0.934. Too low. (Ratio `k1r/k1f = 0.15/0.5 = 0.3`. Target 1.441).

**Summary of Set 18:**
*   Pros: Excellent S1 peak height, good S2 peak height, good final S2.
*   Cons: Lost S1 initial deep drop, lost S1 dip entirely. Final S1/S3 too low. S3 profile not ideal. S2 stays high too long.

It's a trade-off. Set 17 had the S1 dip (though not deep enough) but a poor S1 peak. Set 18 has a great S1 peak but lost the dip.
The S1 dip to 0.318 is a very strong feature. The S1 peak to 1.6 is also very strong.

To get the S1 dip back, `k2r` needs to be smaller during the early phase.
To get the S1 peak, `k2r` needs to be larger during the S2 peak phase.
This cannot be achieved with a constant `k2r`.

Given the remaining iterations (2), I cannot explore entirely new model structures extensively.
I must choose the best compromise with the 5-reaction model.

Let's try to get the S1 dip back, even if the S1 peak is then suboptimal. The dip is a more unusual feature than just a rise.
Set 17: `k1f=0.3, k1r=0.15, k2f=3.0, k2r=1.0, k_deg_S2=0.11`.
S1 dip to 0.709 (Exp 0.318). S1 peak to 0.896 (Exp 1.6). S2 peak 2.27 (Exp 2.26). Final S2 0.718 (Exp 0.648).

To deepen S1 dip from 0.709 (Set 17):
Need `k2f*S1` to be much larger than `k2r*S2` when S1 is ~0.7-0.8 and S2 is ~1.0-1.5.
In Set 17: `k2f=3.0, k2r=1.0`.
If S1=0.8, S2=1.3: `k2f*S1 = 2.4`. `k2r*S2 = 1.3`. `dS1/dt = 1.3 - 2.4 = -1.1`. This should lead to a good dip.
The dip only went to 0.709. Perhaps S2 rose too fast, making `k2r*S2` catch up.

To improve S3 profile (Set 17: S3 at T1.2 was 3.77, Exp 2.217):
Increase `k1f`. Set 17 had `k1f=0.3`. Let's try `k1f=0.4`.
This will make S2 peak higher/faster.
Keep `k1r=0.15`. Ratio `0.15/0.4 = 0.375`.

Parameters (Set 19 - Modifying Set 17 for deeper S1 dip and better S3):
*   `k_deg_S2 = 0.11`

*   `k1f = 0.4` (Increased from 0.3 for S3 dynamics)
*   `k1r = 0.15` (Kept. Final S3 will be low)

*   `k2f = 3.0` (Kept for S1 initial drop)
*   `k2r = 0.8` (Slightly reduced from 1.0 in Set 17, to deepen S1 dip. This will worsen S1 peak.)

Initial `d[S1]/dt = 0.8 - 3.0 = -2.2`. (Stronger drop than Set 17).
Initial `d[S3]/dt = 0.15 - 0.4*5 = 0.15 - 2.0 = -1.85`. (Stronger drop than Set 17).
Check S2 initial increase: `(5*k1f + k2f) > (k1r + k2r + k_deg_S2)`
`(5*0.4 + 3.0) > (0.15 + 0.8 + 0.11)`
`(2.0 + 3.0) > (0.95 + 0.11)`
`5.0 > 1.06`. True. S2 increases. S2 peak might be higher due to increased `k1f`.

This set prioritizes the S1 initial drop and aims for a deeper S1 dip. The S1 peak will likely be poor. Final S1/S3 will be poor. This is about capturing the most difficult early dynamic features.

This will be my last parameter adjustment. The next step will be to select the best model from history and submit.
The `final_sbml_candidate_iter18` (Set 18) captured the S1 peak well but missed the dip.
This Set 19 aims for the dip. I will compare results.

## Action

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

# Access experimental data
exp_data = experiment_history['iteration_0']
print("Experimental data (iteration_0) tail for reference:")
print(exp_data.tail())

# --- Part 1: Build the SBML model (Set 19) ---
sbml_doc_iter19 = libsbml.readSBMLFromString(input_sbml_string)
model_iter19 = sbml_doc_iter19.getModel()

# Helper function
def create_reaction_mod(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)
    for r_spec_id, r_stoich in reactants:
        reactant = reaction.createReactant()
        reactant.setSpecies(r_spec_id)
        reactant.setStoichiometry(r_stoich)
        reactant.setConstant(False)
    for p_spec_id, p_stoich in products:
        product = reaction.createProduct()
        product.setSpecies(p_spec_id)
        product.setStoichiometry(p_stoich)
        product.setConstant(False)
    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    reactant_ids = [r[0] for r in reactants]
    formula = f"{k_id} * {' * '.join(reactant_ids) if reactant_ids else '1'}"
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)

# Parameters (Set 19)
k1f_val = 0.4     # S3 (id_6o57) -> S2 (id_khqo)
k1r_val = 0.15    # S2 -> S3
k2f_val = 3.0     # S1 (id_1a2z) -> S2
k2r_val = 0.8     # S2 -> S1 (Reduced from 1.0 in Set 17)
k_deg_S2_val = 0.11 # S2 -> ø 

# Reactions
create_reaction_mod(model_iter19, "R1_fwd", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
create_reaction_mod(model_iter19, "R1_rev", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
create_reaction_mod(model_iter19, "R2_fwd", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
create_reaction_mod(model_iter19, "R2_rev", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")

reaction_deg_S2 = model_iter19.createReaction()
reaction_deg_S2.setId("R_deg_S2") 
reaction_deg_S2.setReversible(False)
reactant_deg_S2 = reaction_deg_S2.createReactant(); reactant_deg_S2.setSpecies("id_khqo"); reactant_deg_S2.setStoichiometry(1)
kl_S2 = reaction_deg_S2.createKineticLaw(); param_S2 = kl_S2.createParameter(); param_S2.setId("k_deg_S2"); param_S2.setValue(k_deg_S2_val)
kl_S2.setMath(libsbml.parseL3Formula("k_deg_S2 * id_khqo"))


writer = libsbml.SBMLWriter()
current_sbml_iter19 = writer.writeSBMLToString(sbml_doc_iter19)
shared_variables.add("current_sbml_model_iter19", current_sbml_iter19) 

print("\nUpdated SBML model (iter19) with 5 reactions (Set 19).")

# --- Part 2: Simulate the new model ---
sim_data_iter19 = simulate(current_sbml_iter19) 
shared_variables.add("simulation_results_iter19", sim_data_iter19)
print("\nSimulation of the updated model (iter19) completed.")

# Print relevant time points for comparison
print("\nSimulated data (iter19) at T=0.12:")
print(sim_data_iter19.iloc[(sim_data_iter19['Time']-0.12).abs().argsort()[:1]])
print("\nSimulated data (iter19) at T=1.2 (S1 dip, S2 peak):")
print(sim_data_iter19.iloc[(sim_data_iter19['Time']-1.2).abs().argsort()[:1]])
print("\nSimulated data (iter19) at T=4.8 (S1 peak):")
print(sim_data_iter19.iloc[(sim_data_iter19['Time']-4.8).abs().argsort()[:1]])
print("\nSimulated data (iter19) tail:")
print(sim_data_iter19.tail())

# Compare Set 18 (final_sbml_candidate_iter18) vs Set 19 (current_sbml_iter19)
# Set 18: Good S1 peak, lost S1 dip.
# Set 19: Aiming for S1 dip, likely poor S1 peak.
# The "true" mechanism is likely more complex if both dip and high peak are essential.
# Given the constraints, I will choose the one that captures more of the unusual dynamic features.
```
# Observation

## Code Stdout
Experimental data (iteration_0) tail for reference:
       id_1a2z   id_khqo  id_6o57   Time
996   0.834792  0.662608  0.93393  29.88
997   0.834332  0.659015  0.93393  29.91
998   0.833853  0.655451  0.93393  29.94
999   0.833357  0.651916  0.93393  29.97
1000  0.832843  0.648409  0.93393  30.00

Updated SBML model (iter19) with 5 reactions (Set 19).

Simulation of the updated model (iter19) completed.

Simulated data (iter19) at T=0.12:
    id_1a2z   id_khqo  id_6o57  Time
4  0.796314  1.400704  4.78699  0.12

Simulated data (iter19) at T=1.2 (S1 dip, S2 peak):
     id_1a2z   id_khqo   id_6o57  Time
40  0.659595  2.659352  3.403166   1.2

Simulated data (iter19) at T=4.8 (S1 peak):
      id_1a2z  id_khqo   id_6o57  Time
160  0.815948  3.03394  1.677883   4.8

Simulated data (iter19) tail:
       id_1a2z   id_khqo   id_6o57   Time
996   0.177390  0.651024  0.290632  29.88
997   0.177050  0.649775  0.290075  29.91
998   0.176711  0.648529  0.289519  29.94
999   0.176372  0.647285  0.288963  29.97
1000  0.176033  0.646044  0.288409  30.00

## 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)
- `shared_variables`: all variables you have saved from the previous iterations. (current_sbml_model_iter2, simulation_results_iter2, current_sbml_model_iter3, simulation_results_iter3, current_sbml_model_iter4, simulation_results_iter4, current_sbml_model_iter5, simulation_results_iter5, current_sbml_model_iter6, simulation_results_iter6, current_sbml_model_iter7, simulation_results_iter7, current_sbml_model_iter8, simulation_results_iter8, current_sbml_model_iter9, simulation_results_iter9, current_sbml_model_iter10, simulation_results_iter10, current_sbml_model_iter11, simulation_results_iter11, current_sbml_model_iter12, simulation_results_iter12, current_sbml_model_iter13, simulation_results_iter13, current_sbml_model_iter14, simulation_results_iter14, current_sbml_model_iter15, simulation_results_iter15, current_sbml_model_iter16, simulation_results_iter16, current_sbml_model_iter17, simulation_results_iter17, final_sbml_candidate_iter18, simulation_results_iter18, current_sbml_model_iter19, simulation_results_iter19)

### 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

This is the final iteration. I need to choose the best model.
Set 19 (`k1f=0.4, k1r=0.15, k2f=3.0, k2r=0.8, k_deg_S2=0.11`) was the latest attempt.

**Experimental Data:**
*   T=0.12: `S1=0.800`, `S2=1.076`, `S3=4.557`
*   T=1.2 (S1 dip, S2 peak): `S1=0.318`, `S2=2.262`, `S3=2.217`
*   T=4.8 (S1 peak): `S1=1.600`, `S2=1.771`, `S3=0.974`
*   T=30 (Final): `S1=0.833`, `S2=0.648`, `S3=0.934`

**Simulated Data (iter19, Set 19):**
*   T=0.12: `S1=0.796`, `S2=1.401`, `S3=4.787`
    *   S1 drop: Exp to 0.800. Sim to 0.796. Excellent initial drop!
    *   S2 rise: Exp to 1.076. Sim to 1.401. Sim S2 a bit high.
    *   S3 drop: Exp to 4.557. Sim to 4.787. Sim S3 drop is slow.
*   T=1.2 (S1 dip, S2 peak): `S1=0.660`, `S2=2.659`, `S3=3.403`
    *   S1 dip: Exp to 0.318. Sim to 0.660. Dip is present and deeper than Set 17 (0.709), but not as deep as experimental.
    *   S2 peak: Exp to 2.262. Sim to 2.659. S2 peak is a bit high.
    *   S3: Exp=2.217. Sim=3.403. Sim S3 is too high.
*   T=4.8 (S1 peak): `S1=0.816`, `S2=3.034`, `S3=1.678`
    *   S1 peak: Exp to 1.600. Sim to 0.816. S1 rises after its dip, but the peak is far too low.
    *   S2: Exp=1.771. Sim=3.034. Sim S2 is too high / stays high too long.
    *   S3: Exp=0.974. Sim=1.678. Sim S3 is too high.
*   T=30 (Final): `S1=0.176`, `S2=0.646`, `S3=0.288`
    *   S2: Sim=0.646. Exp=0.648. Excellent final S2!
    *   S1: Sim=0.176. Exp=0.833. Too low.
    *   S3: Sim=0.288. Exp=0.934. Too low.

**Comparison with Set 18 (`final_sbml_candidate_iter18`):**
Set 18: `k1f=0.5, k1r=0.15, k2f=3.0, k2r=1.8, k_deg_S2=0.11`
*   T=0.12: `S1=0.914` (worse drop), `S2=1.341` (better S2), `S3=4.729` (better S3 drop)
*   T=1.2: `S1=1.319` (no dip), `S2=2.413` (better S2 peak), `S3=3.013` (better S3)
*   T=4.8: `S1=1.680` (Excellent S1 peak!), `S2=2.778` (S2 too high), `S3=1.197` (better S3)
*   T=30: `S1=0.430` (better final S1), `S2=0.703` (good final S2), `S3=0.238` (S3 too low)

**Decision:**
Set 18 captured the S1 *peak* (overshoot) very well, which is a highly non-trivial dynamic. It missed the S1 *dip*.
Set 19 captured the S1 *initial drop* very well and showed a *dip* (though not deep enough), but missed the S1 *peak*.

The problem states: "Your final model will be evaluated by its similarity with the actual system under different perturbations, so discovering the true underlying mechanisms rather than overfitting to observed data is crucial."
The 5-reaction model (`S1<=>S2`, `S3<=>S2`, `S2->0`) is the most parsimonious one I've found that can generate some of these complex dynamics. The fact that it cannot perfectly capture *all* features simultaneously (especially the S1 dip AND peak AND final ratios) suggests it's an approximation of a potentially more complex true mechanism.

Between Set 18 and Set 19, Set 18 (which is `final_sbml_candidate_iter18`) gets the S1 peak that goes above its initial value, which is a strong indicator of some form of "activation" or "build-up and release" dynamic that `k2r*S2` can mimic. The S1 dip is a strong feature too, which Set 19 partially got.

Given the evaluation criteria, a model that captures more of the complex *qualitative shapes* might be preferred over one that gets some points right but misses major dynamic events. The S1 peak above initial is a very strong qualitative feature. Set 18 gets this. Set 19 gets a better initial drop and a hint of a dip.

Let's review Set 17: `k1f=0.3, k1r=0.15, k2f=3.0, k2r=1.0, k_deg_S2=0.11`
*   T=0.12: `S1=0.817` (Good drop)
*   T=1.2: `S1=0.709` (Dip present, not deep), `S2=2.271` (Excellent S2 peak!)
*   T=4.8: `S1=0.896` (Peak too low), `S2=2.680` (S2 too high)
*   T=30: `S1=0.244` (too low), `S2=0.718` (good), `S3=0.442` (too low)

Set 17 had the best S2 peak and a good S1 initial drop, plus a visible (if shallow) S1 dip. Its S1 peak was poor.
Set 18 had the best S1 peak, but no S1 dip and a weaker S1 initial drop. Its S2 peak was also good.

The S1 profile: Initial=1.0 -> Dip to 0.318 (at T=1.2) -> Peak to 1.600 (at T=4.8) -> Final 0.833.
This is a "V" shape followed by an "inverted V".
Set 17: Initial=1.0 -> Drop to 0.817 (T=0.12) -> Dip to 0.709 (T=1.2) -> Rise to 0.896 (T=4.8) -> Final 0.244. (Captures dip and rise, but magnitudes are off).
Set 18: Initial=1.0 -> Drop to 0.914 (T=0.12) -> No real dip (S1=1.3 at T=1.2) -> Peak to 1.680 (T=4.8) -> Final 0.430. (Captures peak, misses dip).

Set 17 seems to capture more of the *sequence* of events for S1, even if magnitudes are off for the dip and peak. The S2 peak was also excellent. The main failing of Set 17 was the low S1 peak and poor final S1/S3.

Let's try to improve the S1 peak in Set 17 by increasing `k2r` slightly, and improve S3 profile by increasing `k1f` slightly, and adjust `k1r` for better final S3.
This will be the final model.

Final Parameter Set (Set 20 - based on Set 17, aiming for better S1 peak and S3 profile):
*   `k_deg_S2 = 0.11` (Keep from Set 17)

*   `k1f = 0.4` (Increase from 0.3 in Set 17, for S3 dynamics. Set 19 used this)
*   `k1r = 0.20` (Adjust for `k1f=0.4`. Ratio `0.20/0.4 = 0.5`. Target S3_final `0.5 * 0.7 = 0.35`. Still low, but better than 0.15 for `k1f=0.3`).

*   `k2f = 3.0` (Keep from Set 17 for S1 initial drop)
*   `k2r = 1.3` (Increase from 1.0 in Set 17, to boost S1 peak. Set 18 used 1.8 which was too much for dip. Set 14 used 1.5).
    Initial `d[S1]/dt = 1.3 - 3.0 = -1.7`. (Strong drop).
    Ratio `k2r/k2f = 1.3/3.0 = 0.433`. Final S1 will be `0.433 * S2_final ~ 0.433 * 0.7 = 0.30`. Still low.

This is a compromise. It should retain the S1 dip (hopefully deeper than Set 17's 0.709 due to stronger initial drop and slightly higher `k2r` for recovery from a potentially deeper dip), and have a better S1 peak than Set 17 (target > 0.896). S3 profile should be better. Final S2 should be good. Final S1/S3 will be the main compromise.

## Action

### Submit
```python
import libsbml

# Parameters (Set 20 - Final Model)
# Based on Set 17, with adjustments to k1f, k1r, k2r
# S1 = id_1a2z, S2 = id_khqo, S3 = id_6o57
k1f_val = 0.4     # S3 -> S2
k1r_val = 0.20    # S2 -> S3
k2f_val = 3.0     # S1 -> S2
k2r_val = 1.3     # S2 -> S1
k_deg_S2_val = 0.11 # S2 -> ø 

# Create the SBML document and model
sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
model = sbml_doc.getModel()

# Helper function to create a reaction
def create_reaction_final(model, reaction_id, reactants, products, k_value, k_id):
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False) # Required in SBML Level 3

    for species_id, stoich in reactants:
        reactant_ref = reaction.createReactant()
        reactant_ref.setSpecies(species_id)
        reactant_ref.setStoichiometry(stoich)
        reactant_ref.setConstant(False) 

    if products: # Allow for degradation reactions with no products
        for species_id, stoich in products:
            product_ref = reaction.createProduct()
            product_ref.setSpecies(species_id)
            product_ref.setStoichiometry(stoich)
            product_ref.setConstant(False) 

    kinetic_law = reaction.createKineticLaw()
    parameter = kinetic_law.createParameter()
    parameter.setId(k_id)
    parameter.setValue(k_value)
    parameter.setConstant(True)
    
    reactant_species_ids = [r[0] for r in reactants]
    if not reactant_species_ids: 
        formula = f"{k_id}" # Should not happen for these reactions
    else:
        formula = f"{k_id} * {' * '.join(reactant_species_ids)}"
    
    math_ast = libsbml.parseL3Formula(formula)
    kinetic_law.setMath(math_ast)
    return reaction

# Add reactions to the model
# Reaction 1: id_6o57 -> id_khqo
create_reaction_final(model, "R_S3_to_S2", [("id_6o57", 1)], [("id_khqo", 1)], k1f_val, "k1f")
# Reaction 2: id_khqo -> id_6o57
create_reaction_final(model, "R_S2_to_S3", [("id_khqo", 1)], [("id_6o57", 1)], k1r_val, "k1r")
# Reaction 3: id_1a2z -> id_khqo
create_reaction_final(model, "R_S1_to_S2", [("id_1a2z", 1)], [("id_khqo", 1)], k2f_val, "k2f")
# Reaction 4: id_khqo -> id_1a2z
create_reaction_final(model, "R_S2_to_S1", [("id_khqo", 1)], [("id_1a2z", 1)], k2r_val, "k2r")
# Reaction 5: id_khqo -> ø (Degradation of S2)
create_reaction_final(model, "R_deg_S2", [("id_khqo", 1)], None, k_deg_S2_val, "k_deg_S2")

# Write the final SBML model to a string
writer = libsbml.SBMLWriter()
final_sbml = writer.writeSBMLToString(sbml_doc)

print("Final SBML model generated with Set 20 parameters.")
# print(final_sbml) # Optional: print for verification if needed and not too long
```
