
                # 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_qj73">
    <listOfUnitDefinitions>
      <unitDefinition id="id_g1v9">
        <listOfUnits>
          <unit kind="metre" exponent="1" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_8kuv">
        <listOfUnits>
          <unit kind="metre" exponent="2" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_3e18">
        <listOfUnits>
          <unit kind="litre" exponent="1" scale="0" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_qdo9">
        <listOfUnits>
          <unit kind="second" exponent="1" scale="-3" multiplier="60"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_vrub">
        <listOfUnits>
          <unit kind="mole" exponent="1" scale="-6" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_hiwg">
        <listOfUnits>
          <unit kind="second" exponent="-1" scale="-3" multiplier="60"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_62jg">
        <listOfUnits>
          <unit kind="mole" exponent="1" scale="-6" multiplier="1"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_4eku">
        <listOfUnits>
          <unit kind="mole" exponent="-1" scale="-6" multiplier="1"/>
          <unit kind="second" exponent="-1" scale="-3" multiplier="60"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_zyq4">
        <listOfUnits>
          <unit kind="mole" exponent="1" scale="-6" multiplier="1"/>
          <unit kind="second" exponent="-1" scale="-3" multiplier="60"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_pr6u" spatialDimensions="3" size="1" constant="true"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_g7mj" compartment="id_pr6u" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_l2xx" compartment="id_pr6u" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_sgod" compartment="id_pr6u" initialConcentration="2" boundaryCondition="false" constant="false"/>
      <species id="id_jj65" compartment="id_pr6u" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_t6k9" compartment="id_pr6u" initialConcentration="0.08" boundaryCondition="false" constant="false"/>
      <species id="id_3r8d" compartment="id_pr6u" initialConcentration="0" boundaryCondition="false" constant="false"/>
      <species id="id_npcr" compartment="id_pr6u" initialConcentration="6" boundaryCondition="false" constant="false"/>
      <species id="id_0qoe" compartment="id_pr6u" initialConcentration="0" 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 has 8 species: id_g7mj, id_l2xx, id_sgod, id_jj65, id_t6k9, id_3r8d, id_npcr, id_0qoe.
Their initial concentrations are 0, 0, 2, 0, 0.08, 0, 6, 0 respectively.
There are no reactions in the model.
My goal is to discover the missing reactions.

First, I will run an "observe" experiment to see the baseline behavior of the system. This will show how the species concentrations change over time with the given initial conditions. This data will be crucial for forming initial hypotheses about the 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 × 9 columns. 

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

Time   id_g7mj  id_l2xx  id_sgod  id_jj65  id_t6k9  id_3r8d  id_npcr  id_0qoe
0         0        0 2.00e+00        0 8.00e-02        0 6.00e+00        0
...
2.00e+00  2.78e-03 7.75e-05 2.00e+00 1.09e-05 8.00e-02 1.87e-05 6.00e+00 5.26e-04
...
4.00e+00  4.41e-02 1.36e-03 1.99e+00 1.73e-04 8.00e-02 4.39e-04 5.95e+00 8.34e-03
...
6.00e+00  6.51e-01 2.01e-02 1.85e+00 2.45e-03 8.00e-02 6.92e-03 5.21e+00 1.17e-01
...
8.00e+00  4.56e+00 1.66e-01 1.16e+00 1.32e-02 8.00e-02 7.74e-02 6.90e-01 5.83e-01
...
1.00e+01  5.18e+00 3.08e-01 8.61e-01 1.19e-02 8.00e-02 3.09e-01 6.53e-04 5.12e-01
...
1.20e+01  5.29e+00 3.16e-01 6.69e-01 9.40e-03 8.00e-02 6.02e-01 5.44e-04 4.06e-01
...
1.40e+01  5.42e+00 2.80e-01 5.17e-01 7.43e-03 8.00e-02 8.78e-01 6.09e-04 3.22e-01
...
1.60e+01  5.54e+00 2.33e-01 3.99e-01 5.85e-03 8.00e-02 1.11e+00 7.26e-04 2.54e-01
...
1.80e+01  5.65e+00 1.88e-01 3.07e-01 4.58e-03 8.00e-02 1.31e+00 8.91e-04 1.99e-01
...
2.00e+01  5.74e+00 1.50e-01 2.36e-01 3.58e-03 8.00e-02 1.46e+00 1.11e-03 1.56e-01
...
2.20e+01  5.81e+00 1.18e-01 1.82e-01 2.79e-03 8.00e-02 1.59e+00 1.39e-03 1.21e-01
...
2.40e+01  5.87e+00 9.26e-02 1.40e-01 2.17e-03 8.00e-02 1.68e+00 1.75e-03 9.44e-02
...
2.60e+01  5.92e+00 7.23e-02 1.08e-01 1.68e-03 8.00e-02 1.76e+00 2.20e-03 7.33e-02
...
2.80e+01  5.95e+00 5.63e-02 8.33e-02 1.31e-03 8.00e-02 1.82e+00 2.77e-03 5.70e-02
...
3.00e+01  5.99e+00 4.38e-02 6.44e-02 1.02e-03 8.00e-02 1.86e+00 3.47e-03 4.43e-02
...
3.20e+01  6.01e+00 3.41e-02 5.00e-02 7.91e-04 8.00e-02 1.90e+00 4.32e-03 3.46e-02
...
3.40e+01  6.03e+00 2.66e-02 3.90e-02 6.19e-04 8.00e-02 1.93e+00 5.35e-03 2.70e-02
...
3.60e+01  6.05e+00 2.08e-02 3.06e-02 4.87e-04 8.00e-02 1.95e+00 6.58e-03 2.13e-02
...
3.80e+01  6.06e+00 1.63e-02 2.42e-02 3.85e-04 8.00e-02 1.96e+00 8.01e-03 1.68e-02
...
4.00e+01  6.07e+00 1.29e-02 1.93e-02 3.07e-04 8.00e-02 1.98e+00 9.67e-03 1.34e-02
...
4.20e+01  6.08e+00 1.03e-02 1.56e-02 2.48e-04 8.00e-02 1.99e+00 1.15e-02 1.08e-02
...
4.40e+01  6.09e+00 8.25e-03 1.27e-02 2.02e-04 8.00e-02 2.00e+00 1.36e-02 8.85e-03
...
4.60e+01  6.10e+00 6.71e-03 1.05e-02 1.67e-04 8.00e-02 2.00e+00 1.59e-02 7.33e-03
...
4.80e+01  6.10e+00 5.53e-03 8.84e-03 1.41e-04 8.00e-02 2.01e+00 1.84e-02 6.16e-03
...
5.00e+01  6.11e+00 4.63e-03 7.57e-03 1.20e-04 8.00e-02 2.01e+00 2.11e-02 5.27e-03
...
5.20e+01  6.12e+00 3.94e-03 6.60e-03 1.05e-04 8.00e-02 2.02e+00 2.39e-02 4.60e-03
...
5.40e+01  6.12e+00 3.41e-03 5.86e-03 9.28e-05 8.00e-02 2.02e+00 2.68e-02 4.08e-03
...
5.60e+01  6.12e+00 3.01e-03 5.29e-03 8.38e-05 8.00e-02 2.02e+00 2.98e-02 3.68e-03
...
5.80e+01  6.13e+00 2.70e-03 4.86e-03 7.69e-05 8.00e-02 2.03e+00 3.29e-02 3.38e-03
...
6.00e+01  6.13e+00 2.47e-03 4.53e-03 7.16e-05 8.00e-02 2.03e+00 3.59e-02 3.15e-03
...
6.20e+01  6.13e+00 2.29e-03 4.28e-03 6.76e-05 8.00e-02 2.03e+00 3.90e-02 2.97e-03
...
6.40e+01  6.14e+00 2.15e-03 4.08e-03 6.45e-05 8.00e-02 2.03e+00 4.20e-02 2.84e-03
...
6.60e+01  6.14e+00 2.05e-03 3.94e-03 6.21e-05 8.00e-02 2.04e+00 4.50e-02 2.74e-03
...
6.80e+01  6.15e+00 1.97e-03 3.82e-03 6.03e-05 8.00e-02 2.04e+00 4.79e-02 2.66e-03
...
7.00e+01  6.15e+00 1.91e-03 3.74e-03 5.90e-05 8.00e-02 2.04e+00 5.07e-02 2.60e-03
...
7.20e+01  6.15e+00 1.86e-03 3.67e-03 5.79e-05 8.00e-02 2.04e+00 5.34e-02 2.55e-03
...
7.40e+01  6.16e+00 1.83e-03 3.62e-03 5.72e-05 8.00e-02 2.04e+00 5.60e-02 2.52e-03
...
7.60e+01  6.16e+00 1.80e-03 3.58e-03 5.66e-05 8.00e-02 2.04e+00 5.85e-02 2.49e-03
...
7.80e+01  6.16e+00 1.78e-03 3.55e-03 5.61e-05 8.00e-02 2.05e+00 6.09e-02 2.47e-03
...
8.00e+01  6.17e+00 1.77e-03 3.53e-03 5.57e-05 8.00e-02 2.05e+00 6.32e-02 2.46e-03
...
8.20e+01  6.17e+00 1.75e-03 3.51e-03 5.55e-05 8.00e-02 2.05e+00 6.54e-02 2.45e-03
...
8.40e+01  6.18e+00 1.74e-03 3.49e-03 5.53e-05 8.00e-02 2.05e+00 6.74e-02 2.44e-03
...
8.60e+01  6.18e+00 1.74e-03 3.48e-03 5.51e-05 8.00e-02 2.05e+00 6.94e-02 2.43e-03
...
8.80e+01  6.19e+00 1.73e-03 3.47e-03 5.50e-05 8.00e-02 2.05e+00 7.12e-02 2.43e-03
...
9.00e+01  6.19e+00 1.73e-03 3.46e-03 5.49e-05 8.00e-02 2.06e+00 7.30e-02 2.42e-03
...
9.20e+01  6.19e+00 1.73e-03 3.46e-03 5.49e-05 8.00e-02 2.06e+00 7.46e-02 2.42e-03
...
9.40e+01  6.20e+00 1.72e-03 3.45e-03 5.48e-05 8.00e-02 2.06e+00 7.62e-02 2.42e-03
...
9.60e+01  6.20e+00 1.72e-03 3.45e-03 5.48e-05 8.00e-02 2.06e+00 7.77e-02 2.41e-03
...
1.00e+02  6.21e+00 1.72e-03 3.44e-03 5.47e-05 8.00e-02 2.06e+00 8.04e-02 2.41e-03

## 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 from `iteration_0` shows that `id_sgod` and `id_npcr` are consumed, while `id_g7mj` and `id_3r8d` are produced. The species `id_t6k9` remains constant, suggesting it might be a catalyst. The species `id_l2xx`, `id_jj65`, and `id_0qoe` behave as intermediates, as their concentrations first rise and then fall.

Based on the stoichiometry of consumption and production (approximately 1 `id_sgod` + 3 `id_npcr` -> 3 `id_g7mj` + 1 `id_3r8d`), and the peak times of the intermediates (`id_jj65` < `id_0qoe` < `id_l2xx`), I hypothesize the following reaction pathway:

1.  **R1:** `id_sgod + id_npcr -> id_jj65` (catalyzed by `id_t6k9`)
2.  **R2:** `id_jj65 + id_npcr -> id_0qoe` (catalyzed by `id_t6k9`)
3.  **R3:** `id_0qoe + id_npcr -> id_l2xx` (catalyzed by `id_t6k9`)
4.  **R4:** `id_l2xx -> 3 id_g7mj + 1 id_3r8d` (catalyzed by `id_t6k9`)

This pathway consumes 1 `id_sgod` and 3 `id_npcr` in total, and produces 3 `id_g7mj` and 1 `id_3r8d`, matching the observed overall stoichiometry. `id_t6k9` acts as a catalyst in each step.

I will now implement this model in SBML. I will use mass-action kinetics for each reaction, with `id_t6k9` included in the rate law as a catalyst. I will set all rate constants (`k1`, `k2`, `k3`, `k4`) to an initial value of 1.0 for simulation. Then, I will simulate this model and compare its output to the experimental data.

Since plotting libraries like `matplotlib` are not explicitly listed as available for direct output, I will print the head and tail of the simulation data and key statistics for comparison. I will also save the simulation data to `shared_variables` for potential future analysis if needed.

## Action

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

def add_reaction_with_catalyst(model, reaction_id, reactants, products, catalyst_id, parameter_id, parameter_value):
    """
    Adds a reaction to the model with specified reactants, products, catalyst, and mass-action kinetics.
    Reactants and products are dictionaries of species_id: stoichiometry.
    """
    reaction = model.createReaction()
    reaction.setId(reaction_id)
    reaction.setReversible(False)
    reaction.setFast(False)

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

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

    if catalyst_id:
        modifier = reaction.createModifier()
        modifier.setSpecies(catalyst_id)

    # Kinetic Law
    kinetic_law = reaction.createKineticLaw()
    
    # Add parameter for the rate constant
    parameter = kinetic_law.createParameter()
    parameter.setId(parameter_id)
    parameter.setValue(parameter_value)
    parameter.setUnits("dimensionless") # Or appropriate units, simplified for now

    # Create math formula for mass action
    # rate = k * [Reactant1]^stoich1 * [Reactant2]^stoich2 * ... * [Catalyst]
    math_ast = libsbml.parseL3Formula(parameter_id) # k
    
    for species_id in reactants.keys():
        term = libsbml.parseL3Formula(species_id)
        math_ast = libsbml.ASTNode(libsbml.AST_TIMES)
        math_ast.addChild(libsbml.parseL3Formula(parameter_id)) # k will be the first child after this loop
        math_ast.addChild(term) # Add reactant
        # For simplicity, assuming elementary reaction kinetics where stoichiometry matches order
        # For this problem, let's assume order 1 for each reactant in the rate law for now
        # This means rate = k * R1 * R2 * Cat

    # Rebuild math_ast to be k * R1 * R2 * ... * Cat
    # Start with the parameter
    formula_terms = [parameter_id]
    
    # Add all reactant species IDs
    formula_terms.extend(reactants.keys())
    
    # Add catalyst species ID
    if catalyst_id:
        formula_terms.append(catalyst_id)
    
    # Build the formula string: k * S1 * S2 * ...
    formula_str = " * ".join(formula_terms)
    
    math_ast = libsbml.parseL3Formula(formula_str)
    kinetic_law.setMath(math_ast)
    
    return reaction

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

# Define catalyst
catalyst = "id_t6k9"

# Define rate constants (initial guesses)
k1_val = 1.0
k2_val = 1.0
k3_val = 1.0
k4_val = 1.0

# Add parameters to the model globally (so they can be changed later if needed)
# This is good practice, but for the kineticLaw.createParameter(), it's local to the law.
# For now, local parameters are fine. If we need to make them global:
def create_global_parameter(model, p_id, p_value, p_units="dimensionless"):
    if model.getParameter(p_id) is None:
        p = model.createParameter()
        p.setId(p_id)
        p.setValue(p_value)
        p.setUnits(p_units)
        p.setConstant(True) # Rate constants are typically constant

create_global_parameter(model, "k1", k1_val)
create_global_parameter(model, "k2", k2_val)
create_global_parameter(model, "k3", k3_val)
create_global_parameter(model, "k4", k4_val)


# Reaction 1: id_sgod + id_npcr -> id_jj65 (catalyzed by id_t6k9)
# Rate = k1 * id_sgod * id_npcr * id_t6k9
r1_reactants = {"id_sgod": 1, "id_npcr": 1}
r1_products = {"id_jj65": 1}
add_reaction_with_catalyst(model, "R1", r1_reactants, r1_products, catalyst, "k1", k1_val)

# Reaction 2: id_jj65 + id_npcr -> id_0qoe (catalyzed by id_t6k9)
# Rate = k2 * id_jj65 * id_npcr * id_t6k9
r2_reactants = {"id_jj65": 1, "id_npcr": 1}
r2_products = {"id_0qoe": 1}
add_reaction_with_catalyst(model, "R2", r2_reactants, r2_products, catalyst, "k2", k2_val)

# Reaction 3: id_0qoe + id_npcr -> id_l2xx (catalyzed by id_t6k9)
# Rate = k3 * id_0qoe * id_npcr * id_t6k9
r3_reactants = {"id_0qoe": 1, "id_npcr": 1}
r3_products = {"id_l2xx": 1}
add_reaction_with_catalyst(model, "R3", r3_reactants, r3_products, catalyst, "k3", k3_val)

# Reaction 4: id_l2xx -> 3 id_g7mj + 1 id_3r8d (catalyzed by id_t6k9)
# Rate = k4 * id_l2xx * id_t6k9
r4_reactants = {"id_l2xx": 1}
r4_products = {"id_g7mj": 3, "id_3r8d": 1}
add_reaction_with_catalyst(model, "R4", r4_reactants, r4_products, catalyst, "k4", k4_val)


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

# Save the updated SBML string for the simulation function
shared_variables.add("current_sbml_model", updated_sbml_string)

# Simulate the model
# The simulate function is globally available.
sim_data = simulate(updated_sbml_string)
shared_variables.add("iteration_1_sim_data", sim_data)

# Print some info for comparison
print("Experimental Data (iteration_0):")
exp_data_iter0 = experiment_history['iteration_0']
print(exp_data_iter0.head())
print(exp_data_iter0.tail())
# Print key points from experimental data for comparison
print("\nExperimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])


print("\nSimulation Data with k=1.0 for all reactions:")
print(sim_data.head())
print(sim_data.tail())
print("\nSimulation Data Summary (End Time T=100):")
print(sim_data.iloc[-1])


# Basic comparison of final values
exp_final = exp_data_iter0.iloc[-1]
sim_final = sim_data.iloc[-1]

comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final})
comparison['Difference'] = comparison['Experimental'] - comparison['Simulated']
comparison['RelativeDifference (%)'] = (comparison['Difference'] / comparison['Experimental']).abs() * 100
# Handle cases where experimental is zero
comparison['RelativeDifference (%)'] = comparison['RelativeDifference (%)'].replace([np.inf, -np.inf], 100) 


print("\nComparison of Final Values (T=100):")
print(comparison)

# Store the current model as the best guess so far
shared_variables.add("best_sbml_model_so_far", updated_sbml_string)

# The next step would be to analyze these results and refine the rate constants or model structure.
# For now, this action submits the code to perform the simulation with the new model.
```
# Observation

## Code Stdout
Experimental Data (iteration_0):
    id_g7mj       id_l2xx   id_sgod       id_jj65  id_t6k9       id_3r8d   id_npcr   id_0qoe  Time
0  0.000000  0.000000e+00  2.000000  0.000000e+00     0.08  0.000000e+00  6.000000  0.000000   0.0
1  0.000056  1.240825e-08  2.000009  3.113027e-08     0.08  1.228962e-10  6.000021  0.000004   0.1
2  0.000108  1.334073e-07  2.000013  1.544314e-07     0.08  2.811383e-09  6.000041  0.000012   0.2
3  0.000159  4.748432e-07  2.000014  3.444165e-07     0.08  1.580647e-08  6.000061  0.000022   0.3
4  0.000212  1.097640e-06  2.000015  5.708382e-07     0.08  5.082848e-08  6.000077  0.000032   0.4
       id_g7mj   id_l2xx   id_sgod   id_jj65  id_t6k9   id_3r8d   id_npcr   id_0qoe   Time
996   6.212795  0.001719  0.003439  0.000055     0.08  2.063031  0.080102  0.002412   99.6
997   6.213044  0.001719  0.003439  0.000055     0.08  2.063110  0.080166  0.002412   99.7
998   6.213293  0.001719  0.003439  0.000055     0.08  2.063189  0.080230  0.002412   99.8
999   6.213543  0.001719  0.003439  0.000055     0.08  2.063268  0.080293  0.002412   99.9
1000  6.213792  0.001719  0.003438  0.000055     0.08  2.063347  0.080357  0.002412  100.0

Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with k=1.0 for all reactions:
        id_g7mj   id_l2xx   id_sgod   id_jj65  id_t6k9       id_3r8d   id_npcr   id_0qoe  Time
0  0.000000e+00  0.000000  2.000000  0.000000     0.08  0.000000e+00  6.000000  0.000000   0.0
1  2.105291e-07  0.000035  1.906996  0.090807     0.08  7.017638e-08  5.904764  0.002162   0.1
2  3.208260e-06  0.000261  1.819691  0.171925     0.08  1.069420e-06  5.811046  0.008122   0.2
3  1.547687e-05  0.000829  1.737676  0.244315     0.08  5.158955e-06  5.718832  0.017175   0.3
4  4.663540e-05  0.001851  1.660571  0.308842     0.08  1.554513e-05  5.628118  0.028720   0.4
       id_g7mj   id_l2xx   id_sgod   id_jj65  id_t6k9   id_3r8d   id_npcr   id_0qoe   Time
996   5.528511  0.024766  0.005435  0.032110     0.08  1.842837  0.175376  0.094852   99.6
997   5.529105  0.024701  0.005427  0.032072     0.08  1.843035  0.175190  0.094764   99.7
998   5.529697  0.024637  0.005420  0.032035     0.08  1.843232  0.175005  0.094677   99.8
999   5.530288  0.024572  0.005412  0.031998     0.08  1.843429  0.174820  0.094589   99.9
1000  5.530877  0.024508  0.005405  0.031960     0.08  1.843626  0.174636  0.094501  100.0

Simulation Data Summary (End Time T=100):
id_g7mj      5.530877
id_l2xx      0.024508
id_sgod      0.005405
id_jj65      0.031960
id_t6k9      0.080000
id_3r8d      1.843626
id_npcr      0.174636
id_0qoe      0.094501
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100):
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.530877    0.682916               10.990319
id_l2xx      0.001719    0.024508   -0.022789             1325.892564
id_sgod      0.003438    0.005405   -0.001966               57.179902
id_jj65      0.000055    0.031960   -0.031906            58316.427890
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.843626    0.219721               10.648781
id_npcr      0.080357    0.174636   -0.094279              117.326364
id_0qoe      0.002412    0.094501   -0.092089             3817.528387
Time       100.000000  100.000000    0.000000                0.000000

## 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. (current_sbml_model, iteration_1_sim_data, best_sbml_model_so_far)

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


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



# Iteration 2
## Thoughts

The simulation results with all `k=1.0` show that the model captures the general trends (consumption of `id_sgod`, `id_npcr`; production of `id_g7mj`, `id_3r8d`; intermediate behavior of `id_l2xx`, `id_jj65`, `id_0qoe`). However, the quantitative match is poor, especially for the intermediates `id_l2xx`, `id_jj65`, and `id_0qoe`, which have very high relative differences. `id_npcr` is also consumed too slowly in the simulation compared to the experiment. The final products `id_g7mj` and `id_3r8d` are lower in the simulation.

This suggests that the reaction rates are not well-balanced.
-   `id_jj65` and `id_0qoe` are much higher in simulation than experiment. This means R1 might be too fast relative to R2, or R2 is too slow relative to R3, or R3 is too slow relative to R4. Or, R2 and R3 are generally too slow.
-   `id_l2xx` is also much higher in simulation. This means R3 might be too fast relative to R4, or R4 is too slow.
-   `id_sgod` is consumed slightly faster in simulation (simulated `id_sgod` is 0.0054 vs experimental 0.0034 at T=100).
-   `id_npcr` is consumed much slower in simulation (simulated `id_npcr` is 0.174 vs experimental 0.080 at T=100). This is a significant discrepancy and indicates that the reactions consuming `id_npcr` (R1, R2, R3) are, on average, too slow, or their dependence on `id_npcr` is not strong enough.
-   Final products `id_g7mj` and `id_3r8d` are lower in simulation, which is consistent with `id_npcr` (a reactant) being consumed too slowly and/or the final production step R4 being too slow.

Let's analyze the consumption of `id_npcr`. It is consumed in R1, R2, and R3.
The intermediates `id_jj65`, `id_0qoe`, `id_l2xx` accumulate too much. This means their consumption rates (R2, R3, R4 respectively) are too slow compared to their production rates (R1, R2, R3 respectively).

To reduce intermediate accumulation and speed up `id_npcr` consumption:
1.  Increase `k2`, `k3`, and `k4`.
2.  `k1` might need adjustment too. If `id_sgod` is consumed a bit too fast, `k1` might be slightly too high.

Let's try to adjust the rate constants.
-   Since `id_jj65`, `id_0qoe`, `id_l2xx` are orders of magnitude higher in simulation, their consumption rates (R2, R3, R4) need to be significantly faster.
-   `id_npcr` consumption is slow. R1, R2, R3 consume `id_npcr`.

Consider the ratios:
- Exp `id_jj65` (end) ~5.5e-5, Sim ~3.2e-2. Ratio ~580.
- Exp `id_0qoe` (end) ~2.4e-3, Sim ~9.5e-2. Ratio ~39.
- Exp `id_l2xx` (end) ~1.7e-3, Sim ~2.5e-2. Ratio ~14.

This suggests `k2`, `k3`, `k4` need to be increased. `k4` (consumes `id_l2xx`) needs a moderate increase. `k3` (consumes `id_0qoe`) needs a larger increase. `k2` (consumes `id_jj65`) needs the largest increase.

Let's try:
-   `k1`: Keep at 1.0 for now, or slightly decrease if `id_sgod` is still consumed too fast.
-   `k2`: Increase significantly, e.g., `k2 = 100.0` (to reduce `id_jj65`).
-   `k3`: Increase significantly, e.g., `k3 = 50.0` (to reduce `id_0qoe`).
-   `k4`: Increase, e.g., `k4 = 20.0` (to reduce `id_l2xx` and increase product formation).

These are rough guesses. Parameter optimization is a complex task. I will make these changes and simulate again.

I will modify the existing SBML string from `shared_variables.access("current_sbml_model")` by changing the parameter values.

## Action

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

# Retrieve the current SBML model
sbml_string_to_modify = shared_variables.access("current_sbml_model")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants
new_k1_val = 0.5 # Slightly decrease k1 as id_sgod was consumed a bit too fast
new_k2_val = 100.0
new_k3_val = 50.0
new_k4_val = 20.0

# Update parameters in the model
# The parameters were defined locally within kinetic laws.
# We need to find them within each reaction's kinetic law.

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                # If parameter was global and referenced, this would be different
                # For now, assuming local parameters k1, k2, k3, k4 in each kinetic law
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
        else:
            print(f"Warning: KineticLaw not found for {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

# Also update global parameters if they were created (they were, for good practice)
# but the kinetic laws used local copies. If kinetic laws were changed to use global params,
# this would be the primary way.
def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)


# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml_string_iter2 = writer.writeSBMLToString(sbml_doc)

# Save the updated SBML string
shared_variables.add("current_sbml_model_iter2", updated_sbml_string_iter2)

# Simulate the model
sim_data_iter2 = simulate(updated_sbml_string_iter2)
shared_variables.add("iteration_2_sim_data", sim_data_iter2)

# Print some info for comparison
print("Experimental Data (iteration_0):")
exp_data_iter0 = experiment_history['iteration_0']
print(exp_data_iter0.tail())
print("\nExperimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print("\nSimulation Data with new k values (k1=0.5, k2=100, k3=50, k4=20):")
print(sim_data_iter2.tail())
print("\nSimulation Data Summary (End Time T=100):")
print(sim_data_iter2.iloc[-1])

# Comparison of final values
exp_final = exp_data_iter0.iloc[-1]
sim_final_iter2 = sim_data_iter2.iloc[-1]

comparison_iter2 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter2})
comparison_iter2['Difference'] = comparison_iter2['Experimental'] - comparison_iter2['Simulated']
comparison_iter2['RelativeDifference (%)'] = (comparison_iter2['Difference'].abs() / comparison_iter2['Experimental']) * 100
comparison_iter2['RelativeDifference (%)'] = comparison_iter2['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0) # Handle zero/NaN division

print("\nComparison of Final Values (T=100) - Iteration 2:")
print(comparison_iter2)

# Check if this model is better than the previous one
# For simplicity, let's sum the absolute relative differences for species (excluding Time)
prev_sim_data = shared_variables.access("iteration_1_sim_data")
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter2.loc[comparison_iter2.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter2)
else:
    print("Current model is not an improvement over the k=1 model. Reverting best_sbml_model_so_far or keeping previous.")
    # No change to best_sbml_model_so_far if it's worse
    # For this exercise, we'll update it anyway to see the effect of changes.
    # In a real scenario, one might revert.
    # shared_variables.add("best_sbml_model_so_far", shared_variables.access("current_sbml_model")) # if reverting

```
# Observation

## Code Stdout
Experimental Data (iteration_0):
       id_g7mj   id_l2xx   id_sgod   id_jj65  id_t6k9   id_3r8d   id_npcr   id_0qoe   Time
996   6.212795  0.001719  0.003439  0.000055     0.08  2.063031  0.080102  0.002412   99.6
997   6.213044  0.001719  0.003439  0.000055     0.08  2.063110  0.080166  0.002412   99.7
998   6.213293  0.001719  0.003439  0.000055     0.08  2.063189  0.080230  0.002412   99.8
999   6.213543  0.001719  0.003439  0.000055     0.08  2.063268  0.080293  0.002412   99.9
1000  6.213792  0.001719  0.003438  0.000055     0.08  2.063347  0.080357  0.002412  100.0

Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=0.5, k2=100, k3=50, k4=20):
       id_g7mj   id_l2xx   id_sgod   id_jj65  id_t6k9   id_3r8d   id_npcr   id_0qoe   Time
996   5.755507  0.000494  0.079793  0.000401     0.08  1.918502  0.240990  0.000810   99.6
997   5.755744  0.000493  0.079716  0.000401     0.08  1.918581  0.240758  0.000809   99.7
998   5.755980  0.000492  0.079639  0.000400     0.08  1.918660  0.240526  0.000808   99.8
999   5.756216  0.000491  0.079563  0.000400     0.08  1.918739  0.240295  0.000808   99.9
1000  5.756452  0.000490  0.079486  0.000399     0.08  1.918817  0.240064  0.000807  100.0

Simulation Data Summary (End Time T=100):
id_g7mj      5.756452
id_l2xx      0.000490
id_sgod      0.079486
id_jj65      0.000399
id_t6k9      0.080000
id_3r8d      1.918817
id_npcr      0.240064
id_0qoe      0.000807
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 2:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.756452    0.457340                7.360085
id_l2xx      0.001719    0.000490    0.001229               71.479518
id_sgod      0.003438    0.079486   -0.076048             2211.688833
id_jj65      0.000055    0.000399   -0.000345              630.063319
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.918817    0.144530                7.004618
id_npcr      0.080357    0.240064   -0.159708              198.748789
id_0qoe      0.002412    0.000807    0.001605               66.549173
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous): 63655.99420800154
Sum of absolute relative differences (current): 3192.8943360218955
Current model is an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data)

### 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 new set of parameters (k1=0.5, k2=100, k3=50, k4=20) resulted in a significant improvement, as the sum of relative differences dropped drastically.

Let's analyze the current discrepancies:
-   **`id_g7mj`** (Product): Simulated 5.75 vs Exp 6.21 (7.3% low). Better, but still low.
-   **`id_l2xx`** (Intermediate): Simulated 4.9e-4 vs Exp 1.7e-3 (71% low). Previously it was too high, now it's too low. This means `k4` (consumes `id_l2xx`) might be too high relative to `k3` (produces `id_l2xx`), or `k3` is too low.
-   **`id_sgod`** (Reactant): Simulated 0.079 vs Exp 0.0034 (2211% high). This is a major issue. `id_sgod` is barely consumed in the simulation. This means `k1` (0.5) is far too low.
-   **`id_jj65`** (Intermediate): Simulated 3.99e-4 vs Exp 5.5e-5 (630% high). Still too high. This means `k2` (consumes `id_jj65`) is still too low relative to `k1` (produces `id_jj65`).
-   **`id_t6k9`** (Catalyst): Perfect match, as expected.
-   **`id_3r8d`** (Product): Simulated 1.91 vs Exp 2.06 (7.0% low). Similar to `id_g7mj`, low.
-   **`id_npcr`** (Reactant): Simulated 0.240 vs Exp 0.080 (198% high). Still consumed too slowly. This means `k1`, `k2`, `k3` (which consume `id_npcr`) are collectively too low.
-   **`id_0qoe`** (Intermediate): Simulated 8.07e-4 vs Exp 2.41e-3 (66% low). Previously too high, now too low. This means `k3` (consumes `id_0qoe`) might be too high relative to `k2` (produces `id_0qoe`), or `k2` is too low.

Primary issues:
1.  `id_sgod` is not being consumed. `k1` needs to be much higher.
2.  `id_npcr` is not being consumed enough. `k1`, `k2`, `k3` need to be higher.
3.  `id_jj65` is still too high. `k2` needs to be higher relative to the new `k1`.

Let's reconsider `k1`. The previous value was 1.0, and `id_sgod` was 0.0054 (Exp 0.0034) - slightly too fast. Now with `k1=0.5`, `id_sgod` is 0.079. This is a very strong sensitivity or an error in my reasoning.
The rate law for R1 is `k1 * id_sgod * id_npcr * id_t6k9`.
Initial `id_sgod` = 2, `id_npcr` = 6, `id_t6k9` = 0.08.
Initial rate of R1 (k1=1): `1 * 2 * 6 * 0.08 = 0.96`.
Initial rate of R1 (k1=0.5): `0.5 * 2 * 6 * 0.08 = 0.48`.
This change in initial rate doesn't seem like it would cause `id_sgod` to barely be consumed. There might be something else.

Let's look at the time courses.
Experimental `id_sgod` goes from 2 to 0.0034.
Simulated (k=1) `id_sgod` goes from 2 to 0.0054.
Simulated (k1=0.5, others high) `id_sgod` goes from 2 to 0.079.

The problem is that if `k2`, `k3`, `k4` are very high, the intermediates `id_jj65`, `id_0qoe`, `id_l2xx` are kept very low.
If `id_jj65` is low, R2 (`id_jj65 + id_npcr -> id_0qoe`) slows down.
If `id_0qoe` is low, R3 (`id_0qoe + id_npcr -> id_l2xx`) slows down.
If `id_l2xx` is low, R4 (`id_l2xx -> products`) slows down.

The issue with `id_sgod` (and `id_npcr`) consumption being too low in the last simulation, despite increasing downstream rates, suggests that `k1` is indeed the bottleneck for the *overall pathway flux*.
My previous adjustment of `k1` from 1.0 to 0.5 was in the wrong direction if the goal was to increase overall flux and consumption of initial reactants.

Let's try to increase `k1` significantly to drive the consumption of `id_sgod` and `id_npcr`.
If `k1` is increased, `id_jj65` production will increase. So `k2` will also need to be proportionally high to keep `id_jj65` at the correct level. The same logic applies to `k3` and `k4`.

Proposed changes:
-   **`k1`**: Increase significantly. Let's try `k1 = 10.0`. (Was 0.5, originally 1.0). This should increase `id_sgod` and `id_npcr` consumption.
-   **`id_jj65`** was high (630%). If `k1` increases by 20x (0.5 to 10), `id_jj65` production will increase. `k2` was 100. To compensate for increased `k1` and further reduce `id_jj65`, `k2` needs to be much higher. Let's try `k2 = k1 * (current_k2/old_k1_approx) * factor_to_reduce_jj65 = 10 * (100/0.5) * 6 = 10 * 200 * 6 = 12000`. This is a very large value. Let's be more conservative: if `id_jj65` is `X` times too high, and `k1` increases `Y` times, then `k2_new = k2_old * X * Y`. `k2_new = 100 * 6.3 * (10/0.5) = 100 * 6.3 * 20 = 12600`. This seems too aggressive.
    Let's simplify: `id_jj65` is proportional to `k1/k2`. We want to reduce `id_jj65` by a factor of ~6.3. We are increasing `k1` by a factor of 20 (from 0.5 to 10). So, `k2` needs to increase by `20 * 6.3 = 126` times its current value. `k2_new = 100 * 126 = 12600`.
    This suggests the system is very stiff. Let's try a more moderate increase for `k2` first, e.g., `k2 = 2000`.
-   **`id_0qoe`** was low (66%). `id_0qoe` is prop. to `k2/k3` (given `id_jj65` is its source). We want to increase `id_0qoe` by `1/0.34 = ~3` times. `k2` is increasing by `2000/100 = 20` times. `k1` increased by `10/0.5 = 20` times.
    If `k2` increases significantly, `id_0qoe` production increases. `k3` was 50. If `id_0qoe` is too low, we need to decrease its consumption relative to its production. So `k3` should decrease relative to `k2`, or `k2` should increase more than `k3`.
    Let `k3_new = k3_old * (k2_new/k2_old) / (target_increase_factor_0qoe) = 50 * (2000/100) / (1/0.66) = 50 * 20 / 1.5 = 1000 / 1.5 = ~660`.
-   **`id_l2xx`** was low (71%). `id_l2xx` is prop. to `k3/k4`. We want to increase `id_l2xx` by `1/0.29 = ~3.4` times. `k3` is increasing from 50 to ~660 (factor of 13.2).
    Let `k4_new = k4_old * (k3_new/k3_old) / (target_increase_factor_l2xx) = 20 * (660/50) / (1/0.71) = 20 * 13.2 / 1.4 = 264 / 1.4 = ~188`.

This chained reasoning is getting complex. Let's simplify the strategy:
1.  Increase `k1` substantially to fix `id_sgod` and `id_npcr` consumption. Target: `k1 = 10.0`.
2.  Adjust `k2` to bring `id_jj65` down. `id_jj65` is ~6x too high. `k1` increased 20x (0.5->10). So `k2` needs to increase by `6 * 20 = 120x`. `k2 = 100 * 120 = 12000`.
3.  Adjust `k3` to bring `id_0qoe` up. `id_0qoe` is ~0.34x of target. `k2` increased 120x (100->12000). So `k3` needs to increase by `120 / (1/0.66) = 120 * 0.66 = 79.2x`. `k3 = 50 * 79.2 = 3960`.
4.  Adjust `k4` to bring `id_l2xx` up. `id_l2xx` is ~0.29x of target. `k3` increased ~79x (50->3960). So `k4` needs to increase by `79 / (1/0.71) = 79 * 0.71 = 56x`. `k4 = 20 * 56 = 1120`.

New proposed values:
-   `k1 = 10.0`
-   `k2 = 12000.0`
-   `k3 = 4000.0` (rounded)
-   `k4 = 1100.0` (rounded)

These values are very high, which might lead to numerical stiffness issues for the simulator. However, the previous changes showed that large changes in k values are needed.

Let's check `id_npcr` consumption. It's consumed by R1, R2, R3. Increasing all these k values should help.
The products `id_g7mj` and `id_3r8d` were low. Increasing overall flux via `k1` and ensuring downstream reactions `k2, k3, k4` are fast enough should increase product formation.

One concern: `id_sgod` in the previous simulation (k1=0.5) was 0.079486, while initial was 2.0. This means only (2.0 - 0.079486)/2.0 = 96% of `id_sgod` was consumed. This is actually a lot.
Experimental `id_sgod` is 0.003438. So (2.0 - 0.003438)/2.0 = 99.8% consumed.
The issue was that the *remaining* `id_sgod` (0.079) was much higher than the experimental remaining `id_sgod` (0.0034). So `id_sgod` consumption was indeed insufficient. My "2211% high" referred to the remaining amount, which is correct.

Let's try these new, much larger k values.

## Action

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

# Retrieve the SBML model from the previous successful iteration
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far") # This was updated in iter 2
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants
new_k1_val = 10.0
new_k2_val = 12000.0
new_k3_val = 4000.0
new_k4_val = 1100.0

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
        else:
            print(f"Warning: KineticLaw not found for {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

# Update global parameters as well (if they were used, good practice)
def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

# Write the updated SBML model to a string
writer = libsbml.SBMLWriter()
updated_sbml_string_iter3 = writer.writeSBMLToString(sbml_doc)

# Save the updated SBML string
shared_variables.add("current_sbml_model_iter3", updated_sbml_string_iter3)

# Simulate the model
sim_data_iter3 = simulate(updated_sbml_string_iter3)
shared_variables.add("iteration_3_sim_data", sim_data_iter3)

# Print some info for comparison
print("Experimental Data (iteration_0):")
exp_data_iter0 = experiment_history['iteration_0']
print(exp_data_iter0.tail()) # Show tail for final values
print("\nExperimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter3.tail()) # Show tail for final values
print("\nSimulation Data Summary (End Time T=100):")
print(sim_data_iter3.iloc[-1])

# Comparison of final values
exp_final = exp_data_iter0.iloc[-1]
sim_final_iter3 = sim_data_iter3.iloc[-1]

comparison_iter3 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter3})
comparison_iter3['Difference'] = comparison_iter3['Experimental'] - comparison_iter3['Simulated']
comparison_iter3['RelativeDifference (%)'] = (comparison_iter3['Difference'].abs() / comparison_iter3['Experimental']) * 100
# Handle cases where experimental is zero or very small, or sim is zero
comparison_iter3['RelativeDifference (%)'] = comparison_iter3['RelativeDifference (%)'].replace([np.inf, -np.inf], 100.0) # Cap at 100% if exp is zero
comparison_iter3.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter3[exp_final == 0]) / 1.0 * 100 # Avoid division by zero if exp is 0
comparison_iter3 = comparison_iter3.fillna(0) # If both are 0, diff is 0

print("\nComparison of Final Values (T=100) - Iteration 3:")
print(comparison_iter3)

# Check if this model is better than the previous one
prev_sim_data = shared_variables.access("iteration_2_sim_data") # from iter 2
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)


sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter3.loc[comparison_iter3.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 2): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 3): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 3) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter3)
else:
    print("Current model (Iter 3) is NOT an improvement.")
    # best_sbml_model_so_far remains the one from iter 2
```
# Observation

## Code Stdout
Experimental Data (iteration_0):
       id_g7mj   id_l2xx   id_sgod   id_jj65  id_t6k9   id_3r8d   id_npcr   id_0qoe   Time
996   6.212795  0.001719  0.003439  0.000055     0.08  2.063031  0.080102  0.002412   99.6
997   6.213044  0.001719  0.003439  0.000055     0.08  2.063110  0.080166  0.002412   99.7
998   6.213293  0.001719  0.003439  0.000055     0.08  2.063189  0.080230  0.002412   99.8
999   6.213543  0.001719  0.003439  0.000055     0.08  2.063268  0.080293  0.002412   99.9
1000  6.213792  0.001719  0.003438  0.000055     0.08  2.063347  0.080357  0.002412  100.0

Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=10.0, k2=12000.0, k3=4000.0, k4=1100.0):
       id_g7mj       id_l2xx   id_sgod   id_jj65  id_t6k9   id_3r8d   id_npcr  id_0qoe   Time
996   5.987450  4.763428e-07  0.004169  0.000003     0.08  1.995817  0.012524  0.00001   99.6
997   5.987463  4.753896e-07  0.004165  0.000003     0.08  1.995821  0.012512  0.00001   99.7
998   5.987475  4.744393e-07  0.004161  0.000003     0.08  1.995825  0.012499  0.00001   99.8
999   5.987488  4.734918e-07  0.004156  0.000003     0.08  1.995829  0.012487  0.00001   99.9
1000  5.987500  4.725472e-07  0.004152  0.000003     0.08  1.995833  0.012474  0.00001  100.0

Simulation Data Summary (End Time T=100):
id_g7mj    5.987500e+00
id_l2xx    4.725472e-07
id_sgod    4.152239e-03
id_jj65    3.463085e-06
id_t6k9    8.000000e-02
id_3r8d    1.995833e+00
id_npcr    1.247406e-02
id_0qoe    1.041529e-05
Time       1.000000e+02
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 3:
         Experimental     Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792  5.987500e+00    0.226292                3.641769
id_l2xx      0.001719  4.725472e-07    0.001718               99.972507
id_sgod      0.003438  4.152239e-03   -0.000714               20.759165
id_jj65      0.000055  3.463085e-06    0.000051               93.670271
id_t6k9      0.080000  8.000000e-02    0.000000                0.000000
id_3r8d      2.063347  1.995833e+00    0.067513                3.272035
id_npcr      0.080357  1.247406e-02    0.067883               84.476619
id_0qoe      0.002412  1.041529e-05    0.002402               99.568237
Time       100.000000  1.000000e+02    0.000000                0.000000

Sum of absolute relative differences (previous iter 2): 3192.8943360218955
Sum of absolute relative differences (current iter 3): 405.36060260163003
Current model (Iter 3) is an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data)

### 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 model from Iteration 3 (k1=10, k2=12000, k3=4000, k4=1100) is a significant improvement, with the sum of relative differences dropping from ~3192 to ~405.

Let's analyze the current discrepancies:
-   **`id_g7mj`** (Product): Simulated 5.987 vs Exp 6.213 (3.6% low). Much better.
-   **`id_l2xx`** (Intermediate): Simulated 4.7e-7 vs Exp 1.7e-3 (99.97% low). Now extremely low. This means `k4` is far too high relative to `k3`, or `k3` is too low.
-   **`id_sgod`** (Reactant): Simulated 0.00415 vs Exp 0.00343 (20.7% high). This is pretty good. `k1` is in the right ballpark.
-   **`id_jj65`** (Intermediate): Simulated 3.46e-6 vs Exp 5.5e-5 (93.6% low). Now too low. This means `k2` is too high relative to `k1`.
-   **`id_t6k9`** (Catalyst): Perfect.
-   **`id_3r8d`** (Product): Simulated 1.995 vs Exp 2.063 (3.27% low). Much better, similar to `id_g7mj`.
-   **`id_npcr`** (Reactant): Simulated 0.01247 vs Exp 0.08035 (84.4% low). `id_npcr` is now consumed *too much*. This means the combined effect of `k1, k2, k3` is too strong.
-   **`id_0qoe`** (Intermediate): Simulated 1.04e-5 vs Exp 2.41e-3 (99.5% low). Now extremely low. This means `k3` is too high relative to `k2`.

Summary of issues:
1.  Intermediates `id_l2xx`, `id_jj65`, `id_0qoe` are all far too low. This implies their consumption rates (`k4`, `k2`, `k3` respectively) are too high relative to their production rates.
2.  `id_npcr` is consumed too much. This is consistent with `k1, k2, k3` being too high.
3.  Products `id_g7mj`, `id_3r8d` are slightly low, which could be due to `id_npcr` being overly depleted, limiting the reactions, or `k4` being slightly off.
4.  `id_sgod` is reasonably close.

The fact that all intermediates are too low suggests that `k2`, `k3`, and `k4` are generally too high compared to `k1`.
`id_npcr` being too low also suggests `k1`, `k2`, `k3` are too high.

Let's adjust based on these observations:
-   **`k1`** (10.0): `id_sgod` is 20% high (simulated 0.00415 vs exp 0.00343). This means `id_sgod` is consumed slightly *less* than desired. So `k1` might need a small increase. Or, the issue is downstream. Given `id_npcr` is too low, increasing `k1` might exacerbate that. Let's keep `k1=10.0` for now and focus on `k2, k3, k4`.

-   **`id_jj65`**: Exp/Sim ratio = 5.5e-5 / 3.46e-6 = ~15.9. So `id_jj65` needs to increase by ~16x.
    `id_jj65` is roughly prop. to `k1/k2`. To increase `id_jj65` by 16x (with `k1` constant), `k2` needs to decrease by 16x.
    Old `k2 = 12000`. New `k2 = 12000 / 16 = 750`.

-   **`id_0qoe`**: Exp/Sim ratio = 2.41e-3 / 1.04e-5 = ~231.7. So `id_0qoe` needs to increase by ~232x.
    `id_0qoe` is roughly prop. to `k2/k3` (assuming `id_jj65` reaches its new level).
    To increase `id_0qoe` by 232x, if `k2` changes from 12000 to 750 (decreases by 16x), then `k3` needs to decrease by `16 * 232 = 3712` times.
    Old `k3 = 4000`. New `k3 = 4000 / ( (Exp/Sim_0qoe) / (Old_k2/New_k2) ) = 4000 / (232 / (12000/750)) = 4000 / (232 / 16) = 4000 / 14.5 = ~275`.

-   **`id_l2xx`**: Exp/Sim ratio = 1.7e-3 / 4.7e-7 = ~3617. So `id_l2xx` needs to increase by ~3617x.
    `id_l2xx` is roughly prop. to `k3/k4`.
    To increase `id_l2xx` by 3617x, if `k3` changes from 4000 to 275 (decreases by ~14.5x), then `k4` needs to decrease by `14.5 * 3617` times. This is too much.
    Let's use the formula: `New_kX = Old_kX * (Sim_Intermediate / Exp_Intermediate) * (Prod_Rate_Factor / Cons_Rate_Factor)`
    For `k2`: `k2_new = k2_old * (Sim_jj65 / Exp_jj65) = 12000 * (3.46e-6 / 5.5e-5) = 12000 * 0.063 = 756`. Let's use `k2 = 750`.
    For `k3`: `k3_new = k3_old * (Sim_0qoe / Exp_0qoe) * (New_k2/Old_k2) = 4000 * (1.04e-5 / 2.41e-3) * (750/12000) = 4000 * 0.0043 * 0.0625 = 17.2 * 0.0625 = ~1.075`. This value is extremely small. The logic of proportional scaling might be breaking down or my calculation is off.

Let's re-evaluate. The intermediates are too low, meaning `k2, k3, k4` are too high relative to their upstream production.
`id_npcr` is too low (consumed too much). This means `k1, k2, k3` are, on average, too high.

This contradicts the previous thought that `k2,k3,k4` are too high relative to production.
If `id_npcr` is consumed too much, it means the sum of fluxes through R1, R2, R3 is too high.
If intermediates are too low, it means R2, R3, R4 are too fast *relative to R1, R2, R3 respectively*.

Let's try to reduce `k1, k2, k3` to address `id_npcr` overconsumption.
`id_npcr` (sim 0.012 vs exp 0.080). Exp/Sim = 0.080 / 0.012 = ~6.5. So `id_npcr` needs to be 6.5x higher. This means the overall rate of `id_npcr` consumption needs to decrease by a factor of ~6.5.
The reactions consuming `id_npcr` are R1, R2, R3. Let's try reducing `k1, k2, k3` by a common factor.
However, `id_sgod` (affected by `k1`) is already good (sim 0.00415 vs exp 0.00343). If we reduce `k1`, `id_sgod` consumption will worsen (less consumed).
This implies that the *distribution* of `id_npcr` consumption among R1, R2, R3 is problematic, or the stoichiometry of `id_npcr` in the model is different from reality (but we assume the model structure is correct for now).

Let's assume `k1` is mostly correct because `id_sgod` is close.
`id_npcr` is consumed in R1, R2, R3.
Flux through R1 is `F1 = k1 * sgod * npcr * t6k9`.
Flux through R2 is `F2 = k2 * jj65 * npcr * t6k9`.
Flux through R3 is `F3 = k3 * 0qoe * npcr * t6k9`.
Total `id_npcr` consumption rate = `F1 + F2 + F3`.

Since `id_jj65` and `id_0qoe` are very low, `F2` and `F3` might be small despite large `k2, k3`.
This means `F1` might be the dominant consumer of `id_npcr`.
If `k1` is correct for `id_sgod`, but `id_npcr` is over-consumed, this is puzzling.

Let's re-target intermediate levels first by adjusting `k2, k3, k4` relative to their current values, keeping `k1` fixed for a moment.
-   `id_jj65`: Needs to increase ~16x. `k2` should decrease ~16x. `k2 = 12000 / 16 = 750`.
-   `id_0qoe`: Needs to increase ~232x. `id_0qoe` ~ `(k1/k2) * (k2/k3) = k1/k3`. (This is simplified, assuming steady state for `id_jj65`).
    If `k1` is constant, and `id_0qoe` needs to increase 232x, then `k3` should decrease 232x.
    Old `k3 = 4000`. New `k3 = 4000 / 232 = ~17.2`.
-   `id_l2xx`: Needs to increase ~3617x. `id_l2xx` ~ `(k1/k3) * (k3/k4) = k1/k4`. (Simplified, assuming steady state for `id_0qoe`).
    If `k1` is constant, and `id_l2xx` needs to increase 3617x, then `k4` should decrease 3617x.
    Old `k4 = 1100`. New `k4 = 1100 / 3617 = ~0.3`.

Proposed values based on this:
-   `k1 = 10.0` (no change yet)
-   `k2 = 750` (was 12000)
-   `k3 = 17` (was 4000)
-   `k4 = 0.3` (was 1100)

These are drastic reductions for `k3` and `k4`. This will slow down the pathway significantly after R1.
This might cause `id_npcr` to be consumed less, which is desired.
It will also likely reduce the final product formation (`id_g7mj`, `id_3r8d`), which are currently only slightly low. This could be a problem.

Let's consider the `id_npcr` issue more carefully.
Simulated `id_npcr` is 0.012, Exp is 0.08. So, simulated `id_npcr` is too low.
This means the reactions R1, R2, R3 consume `id_npcr` too quickly or too much.
The total `id_npcr` consumed is `(Initial_npcr - Final_npcr)`.
Sim: `6 - 0.012 = 5.988`.
Exp: `6 - 0.080 = 5.92`.
The simulation consumes slightly *more* `id_npcr` than the experiment (5.988 vs 5.92). This difference is small (about 1%).
The main issue is that the *rate* of consumption might be too high initially, depleting `id_npcr` too fast, leading to lower final concentrations of intermediates and products if they depend on `id_npcr`.

The products `id_g7mj` and `id_3r8d` are 3-4% low.
If we decrease `k2, k3, k4` as proposed, product formation will likely decrease further.

This suggests a more complex interplay.
Perhaps the initial estimate for `k1` (based on `id_sgod`) is okay, but the subsequent rates `k2, k3, k4` need to be balanced to achieve the correct intermediate levels *and* allow enough flux for product formation, while also ensuring `id_npcr` is not over-consumed.

Let's try the proposed `k` values: `k1=10, k2=750, k3=17, k4=0.3`.
This set of parameters aims to raise the levels of intermediates.
The very low `k4=0.3` will likely make product formation very slow.
The experimental `id_l2xx` is 0.0017. If `k4` is very small, `id_l2xx` might accumulate too much.

Let's reconsider the scaling for `k3` and `k4`.
`id_jj65` (target increase 16x) => `k2_new = k2_old / 16 = 12000 / 16 = 750`.
`id_0qoe` (target increase 232x). `[0qoe] ~ k2_eff / k3_eff`. If `k2_eff` (effective production rate for `0qoe`) decreases by 16x (due to `k2` decreasing), then to get `0qoe` to increase 232x, `k3` needs to decrease by `16 * 232 = 3712` times.
`k3_new = k3_old / 3712 = 4000 / 3712 = ~1.07`.
`id_l2xx` (target increase 3617x). `[l2xx] ~ k3_eff / k4_eff`. If `k3_eff` decreases by 3712x, then to get `l2xx` to increase 3617x, `k4` needs to decrease by `3712 * 3617` times. This is definitely wrong.

The simple `[Intermediate] ~ k_prod / k_cons` assumes the upstream species is constant. This is not true here.
Let's use a more direct approach:
If `id_jj65` is 1/16 of target, we need to reduce its consumption rate by a factor of 16, so `k2_new = k2_old / 16 = 750`.
If `id_0qoe` is 1/232 of target, we need to reduce its consumption rate `k3` by a factor of 232. `k3_new = k3_old / 232 = 4000 / 232 = ~17.2`.
If `id_l2xx` is 1/3617 of target, we need to reduce its consumption rate `k4` by a factor of 3617. `k4_new = k4_old / 3617 = 1100 / 3617 = ~0.304`.

These are the values I first derived: `k1=10, k2=750, k3=17.2, k4=0.304`.
Let's try these.
The main concern is that product formation will be very low with such a small `k4`.
Experimental `id_g7mj` is 6.2. `id_3r8d` is 2.06.
The rate of R4 is `k4 * id_l2xx * id_t6k9`.
If `k4` is 0.3, and `id_l2xx` reaches its target of 0.0017, then R4 rate is `0.3 * 0.0017 * 0.08 = 0.0000408`. This is extremely slow.
The total amount of `id_g7mj` to be produced is ~6. Over 100s, average rate needed is `6/100 = 0.06`.
So, this `k4` is far too small.

This implies that the problem is not just the relative values of `k`, but perhaps their absolute magnitudes or the model structure itself. However, we must assume the structure is correct.

If `id_l2xx` is too low, it means `k4` is too high OR `k3` is too low (not producing enough `id_l2xx`).
If `id_0qoe` is too low, it means `k3` is too high OR `k2` is too low.
If `id_jj65` is too low, it means `k2` is too high OR `k1` is too low.

This is a chain:
- `id_jj65` low (sim/exp = 0.063) => `k2` is too high relative to `k1`.
- `id_0qoe` low (sim/exp = 0.0043) => `k3` is too high relative to `k2`.
- `id_l2xx` low (sim/exp = 0.00027) => `k4` is too high relative to `k3`.

Let's adjust `k2, k3, k4` downwards sequentially.
`k1 = 10.0` (current best for `id_sgod`).
`k2_new = k2_old * (Sim_jj65/Exp_jj65) = 12000 * 0.063 = 756`. Let's use `k2 = 750`.
Now, assuming `k1` and this new `k2` are set, `id_jj65` should be closer to target.
Next, `id_0qoe`. Its level depends on production from `id_jj65` (via `k2`) and consumption (via `k3`).
If `k2` was reduced by `12000/750 = 16x`. The flux into `id_0qoe` is reduced.
The previous `id_0qoe` was `1/232` of target.
We need `id_0qoe` to increase 232x.
`[0qoe] ~ Flux_from_jj65 / k3`. `Flux_from_jj65` is now `~1/16` of what it was (due to lower `jj65` if `k2` was not changed, but `k2` was changed to target `jj65`).
This is getting confusing. Let's use the ratios directly on `k` values.
`k1 = 10`
`k2` needs to be smaller. `k2_new = k2_old * (sim_jj65/exp_jj65) = 12000 * (3.46e-6 / 5.5e-5) = 755`. Set `k2 = 750`.
`k3` needs to be smaller. `k3_new = k3_old * (sim_0qoe/exp_0qoe) = 4000 * (1.04e-5 / 0.002412) = 17.2`. Set `k3 = 17`.
`k4` needs to be smaller. `k4_new = k4_old * (sim_l2xx/exp_l2xx) = 1100 * (4.72e-7 / 0.001719) = 0.30`. Set `k4 = 0.3`.

These are the values `k1=10, k2=750, k3=17, k4=0.3`.
The problem of low product formation with `k4=0.3` is real.
The final products `id_g7mj` and `id_3r8d` were only 3-4% low. If `k4` is reduced from 1100 to 0.3 (by a factor of ~3600), product formation will plummet.

This suggests that the issue with intermediates being low is not that their individual consumption parameters (`k2,k3,k4`) are too high in an absolute sense for the final flux, but that they are too high *relative to the actual concentrations of the intermediates themselves*.
The simulation ran with `k1=10, k2=12000, k3=4000, k4=1100`.
The intermediates were low. This means that `k2` was too efficient at consuming `id_jj65` (given `k1`'s production), `k3` too efficient for `id_0qoe`, `k4` for `id_l2xx`.

What if `id_npcr` being too low (0.012 vs 0.08) is the key?
If `id_npcr` is artificially low in the simulation towards the end, it will slow down R1, R2, R3.
R1: `k1 * id_sgod * id_npcr * id_t6k9`
R2: `k2 * id_jj65 * id_npcr * id_t6k9`
R3: `k3 * id_0qoe * id_npcr * id_t6k9`
If `id_npcr` is lower than it should be, these reaction rates will be lower.
This would mean less `id_jj65` produced by R1, less `id_0qoe` by R2, less `id_l2xx` by R3.
This would lead to low intermediates, which is what we see.
And it would lead to low products, which we also see (slightly).

So, the primary goal should be to get `id_npcr` correct.
`id_npcr` is consumed too much (final sim 0.012 vs exp 0.080).
This means the sum of rates `k1*sgod*npcr*cat + k2*jj65*npcr*cat + k3*0qoe*npcr*cat` is too high over the time course.
Since `id_sgod` (reactant for R1) is okay, `k1` is likely in the right range.
The terms `k2*jj65` and `k3*0qoe` contribute to `id_npcr` consumption.
Even though `jj65` and `0qoe` are low, `k2` and `k3` are very high (12000, 4000).
So `k2*jj65 = 12000 * 3.46e-6 = 0.04152`
`k3*0qoe = 4000 * 1.04e-5 = 0.0416`
These effective rate contributions (excluding `npcr` and `cat`) are small.
Compare to `k1*sgod` (at end): `10 * 0.00415 = 0.0415`.
So all three reactions have similar "effective" rate constants multiplying `id_npcr * id_t6k9` towards the end of the simulation.

To reduce `id_npcr` consumption: we need to reduce `k1`, `k2`, and/or `k3`.
If we reduce `k1`, `id_sgod` will be less consumed (currently sim `id_sgod` 0.00415 vs exp 0.00343 - sim is 20% higher, meaning less consumed than exp). So `k1` should ideally be *increased* slightly to match `id_sgod` better. This contradicts the need to reduce `id_npcr` consumption.

This is a tricky situation.
What if the stoichiometry of `id_npcr` consumption is different in one of the reactions?
E.g. if R1 consumed 2 `id_npcr` instead of 1? But we are not supposed to change stoichiometry of species in reactions, only add reactions or change parameters. The current stoichiometry is 1 `id_npcr` per R1, R2, R3.

Let's try a moderate, across-the-board reduction of `k1, k2, k3` to address `id_npcr` over-consumption, and then fine-tune.
`id_npcr` final sim/exp = 0.01247 / 0.080357 = 0.155. So actual `id_npcr` is much lower.
Total `id_npcr` consumed: Sim: 5.9875. Exp: 5.9196. Sim consumes 1.1% more `id_npcr`.
This small difference in total consumption leads to a large relative difference in remaining `id_npcr` because remaining amount is small.

Perhaps the rates `k1, k2, k3` are too high *early* in the reaction, depleting `id_npcr` too fast.
Let's try to reduce `k1, k2, k3` by a factor.
If `id_npcr` (final) needs to increase from 0.012 to 0.08 (factor of 6.5), this is difficult to achieve by small parameter changes.

Let's reconsider the intermediate levels. They are very sensitive.
`k1=10, k2=12000, k3=4000, k4=1100`
`id_jj65` needs 16x increase.
`id_0qoe` needs 232x increase.
`id_l2xx` needs 3617x increase.

This implies `k2` is too large by ~16x relative to `k1`.
`k3` is too large by ~232x relative to effective `k2` flux.
`k4` is too large by ~3617x relative to effective `k3` flux.

Let's try to adjust `k2, k3, k4` downwards significantly, but not as extremely as `k4=0.3`.
The goal is to raise intermediates without killing product formation.
And to slightly reduce `id_npcr` consumption.

New strategy:
1.  `k1`: `id_sgod` sim 0.00415 vs exp 0.00343. Sim is 20% higher (less consumption). To increase consumption, `k1` should increase. Let `k1 = 10 * 1.2 = 12`.
2.  `k2`: `id_jj65` needs 16x increase. `k2` should decrease relative to `k1`.
    New `k1` is 1.2x old `k1`. So `k2` should be `k2_old / (16 / 1.2) = 12000 / 13.33 = 900`.
    Let `k2 = 900`.
3.  `k3`: `id_0qoe` needs 232x increase. `k3` should decrease relative to `k2`.
    New `k2` is `900/12000 = 0.075x` old `k2`. So `k3` should be `k3_old / (232 * 0.075) = 4000 / 17.4 = 230`.
    Let `k3 = 230`.
4.  `k4`: `id_l2xx` needs 3617x increase. `k4` should decrease relative to `k3`.
    New `k3` is `230/4000 = 0.0575x` old `k3`. So `k4` should be `k4_old / (3617 * 0.0575) = 1100 / 208 = 5.28`.
    Let `k4 = 5`.

Proposed parameters:
`k1 = 12`
`k2 = 900`
`k3 = 230`
`k4 = 5`

This set of parameters:
- Increases `k1` slightly (for `id_sgod`).
- Decreases `k2, k3, k4` significantly to raise intermediate levels.
- The reduction in `k1, k2, k3` overall might help with `id_npcr` overconsumption.
  Old sum of `k`s (weighted by nothing): 10+12000+4000 = 16010.
  New sum: 12+900+230 = 1142. This is a large reduction, which should reduce `id_npcr` consumption.
- `k4=5` is much more reasonable for product formation than `k4=0.3`.
  Rate R4 ~ `5 * (target id_l2xx=0.0017) * 0.08 = 5 * 0.000136 = 0.00068`. Still low compared to 0.06 average.
  This suggests that even if `id_l2xx` reaches its target, `k4=5` might be too low for the products.
  The products are currently only 3-4% low. A drastic reduction in `k4` (from 1100 to 5) will make them much lower.

This iterative adjustment is hard because of the coupled nature.
The fact that products are nearly correct with `k4=1100` (and very low intermediates) means that `k4` is likely in the right order of magnitude, IF the intermediates were at their correct levels.
If `id_l2xx` (sim 4.7e-7) was actually at exp level (1.7e-3), then flux through R4 would be `1100 * 1.7e-3 * 0.08 = 1100 * 1.36e-4 = 0.1496`. This is a high flux, likely leading to fast product formation.
Current product formation rate (average) with `k4=1100` and `id_l2xx` at `4.7e-7`: `1100 * 4.7e-7 * 0.08 = 1100 * 3.76e-8 = 4.1e-5`. This is low.
The simulation must have higher `id_l2xx` transiently to produce the amount of product it does.

Let's focus on `id_npcr` and `id_sgod` first, then intermediates, then products.
`id_sgod`: sim 0.00415, exp 0.00343. Needs more consumption. `k1` up. `k1 = 12`.
`id_npcr`: sim 0.012, exp 0.080. Needs much less consumption. `k1,k2,k3` down.
This is the core conflict. `k1` affects both.

If `k1` increases, `id_sgod` consumption increases (good). `id_npcr` consumption via R1 increases (bad).
If `k2, k3` decrease, `id_npcr` consumption via R2, R3 decreases (good). Intermediates `id_jj65, id_0qoe` increase (good).

Let's try:
- `k1 = 12` (for `id_sgod`)
- To counteract `id_npcr` overconsumption from increased `k1`, `k2` and `k3` must decrease more substantially.
- `k2_new = k2_old * (Sim_jj65/Exp_jj65) / (New_k1/Old_k1) = 12000 * 0.063 / 1.2 = 756 / 1.2 = 630`.
- `k3_new = k3_old * (Sim_0qoe/Exp_0qoe) / (New_k2_factor)`. `New_k2_factor` is `630/12000 = 0.0525`.
  `k3_new = 4000 * 0.0043 / 0.0525 = 17.2 / 0.0525 = 327`. (This is higher than before, which is odd).

Let's use the previous set of "target ratios" for `k` values, but try to scale them globally to fix `id_npcr`.
Previous ratios that gave low intermediates: `k1=10, k2=12000, k3=4000, k4=1100`.
Ratios: `k2/k1 = 1200`, `k3/k2 = 1/3`, `k4/k3 = 11/40 = 0.275`.
We need to reduce overall `id_npcr` consumption. Let's scale down `k1, k2, k3` by a factor `f < 1`.
`id_npcr` consumed: Sim: 5.9875. Exp: 5.9196. Difference is 0.0679.
This is tricky. The *final amount* of `id_npcr` is sensitive.

What if the model is missing a reaction that *produces* `id_npcr` or consumes one of its consumers less efficiently? This is outside the scope of just finding rate constants.

Let's try to make less drastic changes to `k2, k3, k4` than the 16x, 232x, 3617x factors suggested.
The system is very stiff.
`k1=10, k2=12000, k3=4000, k4=1100` (Iter 3 model)
- `id_jj65` low by 16x. Try reducing `k2` by, say, 4x, not 16x. `k2 = 3000`.
- `id_0qoe` low by 232x. Try reducing `k3` by, say, 10x, not 232x. `k3 = 400`.
- `id_l2xx` low by 3617x. Try reducing `k4` by, say, 20x, not 3617x. `k4 = 55`.

New trial parameters:
- `k1 = 10` (keep as is for now, `id_sgod` is close)
- `k2 = 3000` (was 12000)
- `k3 = 400` (was 4000)
- `k4 = 55` (was 1100)

This should:
- Raise `id_jj65` (due to lower `k2`).
- Raise `id_0qoe` (due to lower `k3` and potentially higher `id_jj65`).
- Raise `id_l2xx` (due to lower `k4` and potentially higher `id_0qoe`).
- Reduce `id_npcr` consumption (due to lower `k2, k3`).
- Reduce product formation (due to lower `k4`). This might make products too low.

This is a more heuristic approach due to the difficulty in precise scaling.

## Action

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

# Retrieve the SBML model from the previous successful iteration (Iter 3)
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants from Iteration 4 thoughts
new_k1_val = 10.0  # Keep k1 from iter 3 for now
new_k2_val = 3000.0 # Was 12000
new_k3_val = 400.0  # Was 4000
new_k4_val = 55.0   # Was 1100

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
        else:
            print(f"Warning: KineticLaw not found for {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter4 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter4", updated_sbml_string_iter4)
sim_data_iter4 = simulate(updated_sbml_string_iter4)
shared_variables.add("iteration_4_sim_data", sim_data_iter4)

exp_data_iter0 = experiment_history['iteration_0']
print("Experimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter4.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter4 = sim_data_iter4.iloc[-1]

comparison_iter4 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter4})
comparison_iter4['Difference'] = comparison_iter4['Experimental'] - comparison_iter4['Simulated']
comparison_iter4['RelativeDifference (%)'] = (comparison_iter4['Difference'].abs() / comparison_iter4['Experimental']) * 100
comparison_iter4['RelativeDifference (%)'] = comparison_iter4['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter4.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter4[exp_final == 0]) / 1.0 * 100 # Avoid division by zero
comparison_iter4 = comparison_iter4.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 4:")
print(comparison_iter4)

prev_sim_data = shared_variables.access("iteration_3_sim_data") # from iter 3
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter4.loc[comparison_iter4.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 3): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 4): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 4) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter4)
else:
    print("Current model (Iter 4) is NOT an improvement.")
```
# Observation

## Code Stdout
Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=10.0, k2=3000.0, k3=400.0, k4=55.0):
id_g7mj      5.987271
id_l2xx      0.000010
id_sgod      0.004114
id_jj65      0.000014
id_t6k9      0.080000
id_3r8d      1.995757
id_npcr      0.012474
id_0qoe      0.000106
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 4:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.987271    0.226521                3.645452
id_l2xx      0.001719    0.000010    0.001709               99.438844
id_sgod      0.003438    0.004114   -0.000675               19.636749
id_jj65      0.000055    0.000014    0.000041               74.853376
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.995757    0.067590                3.275732
id_npcr      0.080357    0.012474    0.067882               84.476338
id_0qoe      0.002412    0.000106    0.002306               95.612819
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous iter 3): 405.36060260163003
Sum of absolute relative differences (current iter 4): 380.93930957127094
Current model (Iter 4) is an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data)

### 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 from Iteration 4 (k1=10, k2=3000, k3=400, k4=55) showed a small improvement, with the sum of relative differences decreasing from ~405 to ~381.

Let's analyze the current discrepancies:
-   **`id_g7mj`** (Product): Sim 5.987 vs Exp 6.213 (3.6% low). No significant change.
-   **`id_l2xx`** (Intermediate): Sim 1.0e-5 vs Exp 1.7e-3 (99.4% low). Still extremely low. Was 4.7e-7. So it increased slightly (from 0.00027 of target to 0.0058 of target), but still far off.
-   **`id_sgod`** (Reactant): Sim 0.00411 vs Exp 0.00343 (19.6% high). Slightly better (was 20.7% high).
-   **`id_jj65`** (Intermediate): Sim 1.4e-5 vs Exp 5.5e-5 (74.8% low). Was 3.46e-6 (93.6% low). This is a good improvement (from 0.063 of target to 0.252 of target). `k2` change was effective.
-   **`id_t6k9`** (Catalyst): Perfect.
-   **`id_3r8d`** (Product): Sim 1.995 vs Exp 2.063 (3.27% low). No significant change.
-   **`id_npcr`** (Reactant): Sim 0.01247 vs Exp 0.08035 (84.4% low). No change. This is still a major issue.
-   **`id_0qoe`** (Intermediate): Sim 1.06e-4 vs Exp 2.41e-3 (95.6% low). Was 1.04e-5 (99.5% low). This is a good improvement (from 0.0043 of target to 0.044 of target). `k3` change was effective.

Summary of progress and issues:
-   `id_jj65` and `id_0qoe` levels improved significantly by reducing `k2` and `k3`. They are still low, but much closer.
-   `id_l2xx` is still critically low.
-   `id_npcr` remains critically low (over-consumed).
-   `id_sgod` is reasonably close.
-   Products are slightly low.

Strategy:
1.  **`id_npcr`**: This is the most pressing global issue. It's consumed too much. Reactions R1, R2, R3 consume `id_npcr`.
    -   `k1` (10): `id_sgod` is 19.6% high (meaning `id_sgod` is not consumed enough). This suggests `k1` should be *increased* for `id_sgod`. But increasing `k1` will worsen `id_npcr` over-consumption. This conflict remains.
    -   `k2` (3000) and `k3` (400): Reducing these helped intermediates but didn't fix `id_npcr`.
    The total `id_npcr` consumed is still 5.9875 (sim) vs 5.9196 (exp). The simulation consumes ~1.1% more `id_npcr` in total. This small absolute difference leads to a large relative error in the small remaining amount.
    Perhaps the initial rate of `id_npcr` consumption is too high.
    If `k1` is the main driver of early `id_npcr` consumption (when `id_sgod` and `id_npcr` are high), then `k1` might be too large. But this conflicts with `id_sgod` data.

    Could it be that `id_t6k9` (catalyst) has a different role or is involved differently than assumed (e.g. saturation kinetics, or not involved in all steps)? The problem statement implies we only add reactions and find parameters, not change species roles fundamentally unless it's a new reaction. The current model has `id_t6k9` as a simple multiplier in mass-action for all reactions.

    Let's assume the current reaction structure is correct.
    To reduce `id_npcr` consumption without significantly worsening `id_sgod` (which needs *more* consumption):
    This implies that R2 and/or R3 might be consuming more `id_npcr` than they should, relative to R1's consumption.
    Or, R1 consumes `id_sgod` but `id_npcr` consumption in R1 is somehow less than 1:1 with `id_sgod` (not possible with current model structure).

    If `id_npcr` is too low at the end, it means the integrated consumption over time was too high.
    Let's try to reduce `k1, k2, k3` proportionally by a small factor to see if `id_npcr` can be raised without disrupting other species too much.
    Target: Raise final `id_npcr` from 0.01247 to ~0.04 (halfway to 0.08). This is a 3.2x increase.
    This would require a significant reduction in overall consumption rates.
    Let's try reducing `k1, k2, k3` by a factor, say 2.
    Old: `k1=10, k2=3000, k3=400`.
    New trial: `k1=5, k2=1500, k3=200`.
    This will hurt `id_sgod` consumption (it will be even less consumed).
    And it will lower intermediate production rates.

2.  **Intermediates**:
    -   `id_jj65`: Sim/Exp = 1.4e-5 / 5.5e-5 = 0.25. Needs ~4x increase.
        Current `k1=10, k2=3000`. Ratio `k1/k2 = 10/3000 = 0.0033`.
        If `k1` changes, `k2` must adapt.
    -   `id_0qoe`: Sim/Exp = 1.06e-4 / 2.41e-3 = 0.044. Needs ~22.7x increase.
        Current `k2=3000, k3=400`. Ratio `k2/k3 = 3000/400 = 7.5`.
    -   `id_l2xx`: Sim/Exp = 1.0e-5 / 1.7e-3 = 0.0058. Needs ~172x increase.
        Current `k3=400, k4=55`. Ratio `k3/k4 = 400/55 = 7.27`.

Let's try to address `id_npcr` first by a more targeted adjustment.
The problem might be that `k1` is too high relative to `k2` and `k3` in terms of `id_npcr` usage.
What if `k1` is slightly reduced, and `k2, k3` are reduced more significantly?
This would shift the balance of `id_npcr` consumption away from R1.

Revised plan:
-   **`k1`**: `id_sgod` needs more consumption (sim is 19.6% high). So `k1` should ideally increase.
    Let's try `k1 = 11` (was 10). This will slightly worsen `id_npcr`.
-   **`k2`**: `id_jj65` needs ~4x increase. `[jj65] ~ k1/k2`.
    `k2_new = k1_new / ( ([jj65]_exp/[jj65]_sim_old) * (k1_old/k2_old) )`
    `k2_new = k1_new * (k2_old/k1_old) * ([jj65]_sim_old/[jj65]_exp)`
    `k2_new = 11 * (3000/10) * 0.25 = 11 * 300 * 0.25 = 11 * 75 = 825`.
    Let `k2 = 825`. (Was 3000). This is a significant reduction, good for `id_npcr`.
-   **`k3`**: `id_0qoe` needs ~22.7x increase. `[0qoe] ~ k2/k3`.
    `k3_new = k2_new * ([0qoe]_sim_old/[0qoe]_exp) * (k3_old/k2_old)`
    `k3_new = 825 * 0.044 * (400/3000) = 825 * 0.044 * 0.1333 = 36.3 * 0.1333 = ~4.8`.
    This `k3` is very small. Let's try `k3 = 10`. (Was 400). This is a very large reduction, good for `id_npcr`.
-   **`k4`**: `id_l2xx` needs ~172x increase. `[l2xx] ~ k3/k4`.
    `k4_new = k3_new * ([l2xx]_sim_old/[l2xx]_exp) * (k4_old/k3_old)`
    `k4_new = 10 * 0.0058 * (55/400) = 10 * 0.0058 * 0.1375 = 0.058 * 0.1375 = ~0.008`.
    This `k4` is extremely small. Products will die.
    The products are only 3% low. `k4` cannot be reduced this much from 55.
    This indicates that the upstream intermediate `id_0qoe` (and `id_jj65`) are not going to reach their target levels with these `k` values if `k4` has to remain relatively high.

The scaling `[Intermediate] ~ k_upstream / k_downstream` is too simplistic.
Let's use the previous approach: if `id_X` is `N` times too low, reduce `k_consumes_X` by `N` times, and adjust for changes in upstream `k`.

New parameters based on Iter 4 results:
`k1_prev=10, k2_prev=3000, k3_prev=400, k4_prev=55`
Sim/Exp ratios for intermediates:
`jj65_ratio = 0.25` (needs 4x increase)
`0qoe_ratio = 0.044` (needs 22.7x increase)
`l2xx_ratio = 0.0058` (needs 172x increase)

1.  `k1`: Target `id_sgod` (sim 0.00411 vs exp 0.00343, sim is 1.2x exp). `k1` should increase by ~1.2x.
    `k1_new = 10 * 1.2 = 12`.
    This change (12/10 = 1.2x) will affect `id_jj65` production.

2.  `k2`: To get `id_jj65` up by 4x, `k2` should decrease by `4 / (k1_new/k1_prev)`
    `k2_new = k2_prev / (4 / 1.2) = 3000 / 3.33 = 900`.
    Let `k2 = 900`. (Change factor `k2_new/k2_prev = 900/3000 = 0.3x`).

3.  `k3`: To get `id_0qoe` up by 22.7x, `k3` should decrease by `22.7 / (k2_new/k2_prev)`
    `k3_new = k3_prev / (22.7 / 0.3) = 400 / 75.6 = 5.29`.
    Let `k3 = 5`. (Change factor `k3_new/k3_prev = 5/400 = 0.0125x`).

4.  `k4`: To get `id_l2xx` up by 172x, `k4` should decrease by `172 / (k3_new/k3_prev)`
    `k4_new = k4_prev / (172 / 0.0125) = 55 / 13760`. This is extremely small.
    This means `k4` must be very small if the upstream `k` values are changed this drastically.
    This will kill product formation. Products are only 3% low. `k4` cannot change this much.

This implies that `k4` is relatively correct, and the problem is that `id_l2xx` is not being produced enough (i.e., `k3` is too high, or `k2` is too high, or `k1` is too low for the whole chain).

If `k4=55` is about right for products, then `id_l2xx` needs to be at a level such that `55 * [l2xx] * 0.08` gives the right flux.
Target flux for `id_g7mj` is `~6 / 100 = 0.06`. Stoichiometry is 3 `id_g7mj` from 1 `id_l2xx`.
So flux for `id_l2xx` consumption is `0.06 / 3 = 0.02`.
`k4 * [l2xx] * id_t6k9 = 0.02`
`55 * [l2xx] * 0.08 = 0.02`
`4.4 * [l2xx] = 0.02`
`[l2xx] = 0.02 / 4.4 = 0.0045`.
The experimental `id_l2xx` is `0.0017`. So my target `[l2xx]` based on product flux (0.0045) is higher than experimental. This means `k4=55` might be a bit too low if `[l2xx]` is to be 0.0017.
Or, `k4` should be higher: `k4 = 0.02 / (0.0017 * 0.08) = 0.02 / 0.000136 = ~147`.
The previous `k4` was 1100, which was clearly too high for the intermediates.
The current `k4=55` resulted in products being 3% low. If `k4` was 147, products might be higher.

Let's assume `k4` should be around 50-150.
If `k4 = 100` (guess). Then target `[l2xx]` is `0.02 / (100 * 0.08) = 0.02 / 8 = 0.0025`. (Exp is 0.0017). This is plausible.

Now, work backwards with `k4=100` and target `[l2xx]=0.0017`.
- `k4 = 100`.
- `id_l2xx` needs to be 0.0017. Sim is 1.0e-5. Needs 170x increase.
  `[l2xx] ~ Flux_from_0qoe / k4`.
  To get `id_l2xx` up 170x, with `k4` going from 55 to 100 (1.8x increase), flux from `id_0qoe` needs to increase by `170 * 1.8 = 306x`.
  Flux from `id_0qoe` is `k3 * [0qoe] * npcr * t6k9`.
  This means `k3 * [0qoe]` needs to increase 306x.
  `id_0qoe` (sim 1.06e-4) needs to reach its target (exp 2.41e-3) - a 22.7x increase.
  So `k3` needs to change by `306 / 22.7 = 13.4x` from its role in producing current `id_0qoe`.
  This means `k3_new` should be `k3_old (400) / 13.4 = ~30`.
  Let `k3 = 30`. (Was 400).
- `id_0qoe` needs to be 0.00241. Sim is 1.06e-4. Needs 22.7x increase.
  `[0qoe] ~ Flux_from_jj65 / k3`.
  To get `id_0qoe` up 22.7x, with `k3` going from 400 to 30 (13.3x decrease), flux from `id_jj65` needs to increase by `22.7 / 13.3 = 1.7x`.
  This means `k2 * [jj65]` needs to increase 1.7x.
  `id_jj65` (sim 1.4e-5) needs to reach its target (exp 5.5e-5) - a 4x increase.
  So `k2` needs to change by `1.7 / 4 = 0.425x` from its role in producing current `id_jj65`.
  This means `k2_new` should be `k2_old (3000) * 0.425 = 1275`.
  Let `k2 = 1275`. (Was 3000).
- `id_jj65` needs to be 5.5e-5. Sim is 1.4e-5. Needs 4x increase.
  `[jj65] ~ Flux_from_sgod / k2`.
  To get `id_jj65` up 4x, with `k2` going from 3000 to 1275 (2.35x decrease), flux from `id_sgod` (i.e. `k1*[sgod]`) needs to increase by `4 / 2.35 = 1.7x`.
  `id_sgod` (sim 0.00411) needs to reach its target (exp 0.00343) - a 0.83x change (sim is 1.2x exp, so target is 1/1.2 = 0.83 of sim).
  So `k1` needs to change by `1.7 * 0.83 = 1.4x`.
  `k1_new = k1_old (10) * 1.4 = 14`.
  Let `k1 = 14`.

Proposed parameters:
`k1 = 14`
`k2 = 1275`
`k3 = 30`
`k4 = 100`

Check `id_npcr`:
Old `k1,k2,k3` were `10, 3000, 400`.
New `k1,k2,k3` are `14, 1275, 30`.
`k1` increased (bad for `id_npcr`). `k2` decreased (good). `k3` decreased significantly (good).
Overall, this might reduce `id_npcr` consumption.

This set of parameters is derived by working backward from a desired `k4` and product flux, and propagating the requirements upstream.

## Action

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

# Retrieve the SBML model from the previous successful iteration (Iter 4)
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants from Iteration 5 thoughts
new_k1_val = 14.0
new_k2_val = 1275.0
new_k3_val = 30.0
new_k4_val = 100.0

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter5 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter5", updated_sbml_string_iter5)
sim_data_iter5 = simulate(updated_sbml_string_iter5)
shared_variables.add("iteration_5_sim_data", sim_data_iter5)

exp_data_iter0 = experiment_history['iteration_0']
print("Experimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter5.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter5 = sim_data_iter5.iloc[-1]

comparison_iter5 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter5})
comparison_iter5['Difference'] = comparison_iter5['Experimental'] - comparison_iter5['Simulated']
comparison_iter5['RelativeDifference (%)'] = (comparison_iter5['Difference'].abs() / comparison_iter5['Experimental']) * 100
comparison_iter5['RelativeDifference (%)'] = comparison_iter5['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter5.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter5[exp_final == 0]) / 1.0 * 100 # Avoid division by zero
comparison_iter5 = comparison_iter5.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 5:")
print(comparison_iter5)

prev_sim_data = shared_variables.access("iteration_4_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter5.loc[comparison_iter5.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 4): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 5): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 5) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter5)
else:
    print("Current model (Iter 5) is NOT an improvement.")
```
# Observation

## Code Stdout
Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=14.0, k2=1275.0, k3=30.0, k4=100.0):
id_g7mj      5.986988
id_l2xx      0.000005
id_sgod      0.002285
id_jj65      0.000025
id_t6k9      0.080000
id_3r8d      1.995663
id_npcr      0.008928
id_0qoe      0.002021
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 5:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.986988    0.226804                3.650010
id_l2xx      0.001719    0.000005    0.001713               99.684260
id_sgod      0.003438    0.002285    0.001153               33.532917
id_jj65      0.000055    0.000025    0.000029               53.623056
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.995663    0.067684                3.280307
id_npcr      0.080357    0.008928    0.071428               88.889393
id_0qoe      0.002412    0.002021    0.000391               16.217255
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous iter 4): 380.93930957127094
Sum of absolute relative differences (current iter 5): 298.8771988946437
Current model (Iter 5) is an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data)

### 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 model from Iteration 5 (k1=14, k2=1275, k3=30, k4=100) showed a good improvement, with the sum of relative differences decreasing from ~381 to ~299.

Let's analyze the current discrepancies:
-   **`id_g7mj`** (Product): Sim 5.987 vs Exp 6.213 (3.65% low). Stable, still slightly low.
-   **`id_l2xx`** (Intermediate): Sim 5.0e-6 vs Exp 1.7e-3 (99.68% low). Still extremely low. Decreased from 1.0e-5. This is bad.
-   **`id_sgod`** (Reactant): Sim 0.002285 vs Exp 0.003438 (33.5% low). `id_sgod` is now consumed *too much*. `k1=14` was too high.
-   **`id_jj65`** (Intermediate): Sim 2.5e-5 vs Exp 5.5e-5 (53.6% low). Improved from 74.8% low. Sim/Exp = 0.46. Needs ~2.2x increase.
-   **`id_t6k9`** (Catalyst): Perfect.
-   **`id_3r8d`** (Product): Sim 1.995 vs Exp 2.063 (3.28% low). Stable, still slightly low.
-   **`id_npcr`** (Reactant): Sim 0.0089 vs Exp 0.0803 (88.8% low). Still critically low, very little change.
-   **`id_0qoe`** (Intermediate): Sim 0.00202 vs Exp 0.00241 (16.2% low). Massive improvement! Was 95.6% low. Sim/Exp = 0.83. Needs ~1.2x increase. This is very good.

Summary of progress and issues:
-   `id_0qoe` is now very close! This is a breakthrough. The `k3=30` value seems to be in the right ballpark relative to `k2`.
-   `id_jj65` improved, but still needs to be higher.
-   `id_l2xx` became worse, still critically low. This means `k4=100` is too high relative to the flux from `id_0qoe` (via `k3`).
-   `id_sgod` is now over-consumed. `k1=14` was too high.
-   `id_npcr` remains critically low (over-consumed). This is the biggest problem.
-   Products are consistently slightly low.

Strategy:
The fact that `id_0qoe` is now well-predicted suggests that the ratio `k2/k3` and their absolute values (or at least `k3` relative to the flux it receives) are getting much better.
`k1=14, k2=1275, k3=30, k4=100`

1.  **`id_sgod`**: Sim 0.002285 vs Exp 0.003438. Exp/Sim = 1.5. `id_sgod` needs to be 1.5x higher (less consumption). So `k1` needs to decrease by factor of 1.5.
    `k1_new = 14 / 1.5 = 9.33`. Let `k1 = 9.5`. (Was 14).

2.  **`id_npcr`**: Still the major issue. Sim 0.0089 vs Exp 0.0803. Needs ~9x increase.
    Reducing `k1` from 14 to 9.5 will help `id_npcr` (less consumption via R1).
    The other consumers are R2 and R3. `k2=1275, k3=30`. These are already much lower than in early iterations.
    If `id_npcr` is still far too low after adjusting `k1`, then `k2` and `k3` might need further reduction, or there's a fundamental issue with `id_npcr` dynamics not captured.

3.  **`id_jj65`**: Sim 2.5e-5 vs Exp 5.5e-5. Exp/Sim = 2.2. Needs 2.2x increase.
    `[jj65] ~ k1/k2`.
    `k1` changes from 14 to 9.5 (factor 9.5/14 = 0.678).
    `k2_new = k2_old * ( (k1_new/k1_old) / (target_jj65_increase_factor) ) = 1275 * (0.678 / 2.2) = 1275 * 0.308 = 393`.
    Let `k2 = 400`. (Was 1275). This reduction will also help `id_npcr`.

4.  **`id_0qoe`**: Sim 0.00202 vs Exp 0.00241. Exp/Sim = 1.19. Needs ~1.2x increase. (This is already very good).
    `[0qoe] ~ k2/k3`.
    `k2` changes from 1275 to 400 (factor 400/1275 = 0.313).
    `k3_new = k3_old * ( (k2_new/k2_old) / (target_0qoe_increase_factor) ) = 30 * (0.313 / 1.19) = 30 * 0.263 = 7.89`.
    Let `k3 = 8`. (Was 30). This reduction will also help `id_npcr`.

5.  **`id_l2xx`**: Sim 5.0e-6 vs Exp 1.7e-3. Exp/Sim = 340. Needs 340x increase.
    `[l2xx] ~ k3/k4`.
    `k3` changes from 30 to 8 (factor 8/30 = 0.267).
    `k4_new = k4_old * ( (k3_new/k3_old) / (target_l2xx_increase_factor) ) = 100 * (0.267 / 340) = 100 * 0.000785 = 0.0785`.
    This `k4` is extremely small. Products will be far too low.
    This implies that `k4=100` was not the problem for `id_l2xx` being low; rather, `id_l2xx` was not produced enough (flux from `k3` was too low).
    If `id_0qoe` is now targeted correctly (needs 1.2x increase), and `k3` is adjusted to achieve this, then the flux into `id_l2xx` should be more accurate.
    If `k3=8` and `id_0qoe` is at its target `0.00241`, then flux into `id_l2xx` is `8 * 0.00241 * npcr * t6k9`.
    We need `id_l2xx` to be `0.0017`.
    If `k4` remains `100`, then `[l2xx] = (k3 * [0qoe]_target) / k4 = (8 * 0.00241) / 100 = 0.01928 / 100 = 0.0001928`.
    This is still `0.0001928 / 0.0017 = ~1/9` of the target `id_l2xx`. So `id_l2xx` would still be too low.
    This means `k4` must be lower than 100 if `k3` is 8 and `id_0qoe` is correct.
    `k4_new = k3_new * ([0qoe]_target / [l2xx]_target) = 8 * (0.00241 / 0.0017) = 8 * 1.417 = 11.34`.
    Let `k4 = 11`. (Was 100).

6.  **Products**: `id_g7mj`, `id_3r8d` are ~3% low.
    If `k4` changes from 100 to 11 (factor of 0.11), products will decrease significantly. This is a problem.
    The only way products can be maintained is if `k4` is not reduced so much, meaning `id_l2xx` must be higher than `0.0001928`.
    Or, the target `id_l2xx` of `0.0017` is correct, and `k4=11` is correct for that, but then the product calculation above was flawed.
    Product flux: `k4 * [l2xx]_target * id_t6k9 = 11 * 0.0017 * 0.08 = 11 * 0.000136 = 0.001496`.
    Target product flux (for `id_l2xx` consumption) was `0.02`.
    So `k4=11` gives a flux that is `0.001496 / 0.02 = ~1/13` of what's needed for products.
    This means the system cannot simultaneously satisfy the experimental `id_l2xx` level AND the product formation rate with this reaction structure and simple mass-action kinetics, if my reasoning for target flux is correct.

Let's pause the product concern and focus on getting all reactants/intermediates right. If they are right, products should follow, or `k4` is the final tuning knob.
The large required increase for `id_l2xx` (340x) means `k4` must decrease substantially from 100, or `k3` must be much higher than 8.
If `k3=8` and `id_0qoe` is correct, then `id_l2xx` will be `k3/k4 * [0qoe]`.
To get `id_l2xx` up by 340x (from 5e-6 to 1.7e-3), and `k3` changed by `8/30=0.267x`.
`k4_new = k4_old * (k3_factor / l2xx_target_factor) = 100 * (0.267 / 340) = 0.0785`.
This value for `k4` is consistently coming up very small.

What if `id_npcr` is the primary reason intermediates are low?
If `id_npcr` is artificially low in the simulation (0.0089 vs 0.08), then all reactions R1, R2, R3 are slower than they should be.
R1: `k1 * sgod * npcr * t6k9`
R2: `k2 * jj65 * npcr * t6k9`
R3: `k3 * 0qoe * npcr * t6k9`
If `npcr` (sim) is `0.0089/0.0803 = 0.11` of `npcr` (exp) at the end.
This means all rates are `~0.11x` of what they would be if `npcr` was at experimental levels.
This would lead to lower downstream species.

The most critical step is to fix `id_npcr`.
Proposed `k1=9.5, k2=400, k3=8`.
Let's see how these affect `id_npcr` first.
`k1` down from 14 to 9.5 (helps `id_npcr`)
`k2` down from 1275 to 400 (helps `id_npcr`)
`k3` down from 30 to 8 (helps `id_npcr`)
All these changes should significantly increase final `id_npcr`.

Then, let's keep `k4=11` as calculated for `id_l2xx` target, and see what happens to products.
It's possible the system reaches a state where `id_npcr` is higher, allowing intermediates to also be higher, and then `k4=11` might be sufficient.

Revised parameters:
`k1 = 9.5`
`k2 = 400`
`k3 = 8`
`k4 = 11`

## Action

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

# Retrieve the SBML model from the previous successful iteration (Iter 5)
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants from Iteration 6 thoughts
new_k1_val = 9.5
new_k2_val = 400.0
new_k3_val = 8.0
new_k4_val = 11.0

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter6 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter6", updated_sbml_string_iter6)
sim_data_iter6 = simulate(updated_sbml_string_iter6)
shared_variables.add("iteration_6_sim_data", sim_data_iter6)

exp_data_iter0 = experiment_history['iteration_0']
print("Experimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter6.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter6 = sim_data_iter6.iloc[-1]

comparison_iter6 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter6})
comparison_iter6['Difference'] = comparison_iter6['Experimental'] - comparison_iter6['Simulated']
comparison_iter6['RelativeDifference (%)'] = (comparison_iter6['Difference'].abs() / comparison_iter6['Experimental']) * 100
comparison_iter6['RelativeDifference (%)'] = comparison_iter6['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter6.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter6[exp_final == 0]) / 1.0 * 100 # Avoid division by zero
comparison_iter6 = comparison_iter6.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 6:")
print(comparison_iter6)

prev_sim_data = shared_variables.access("iteration_5_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter6.loc[comparison_iter6.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 5): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 6): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 6) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter6)
else:
    print("Current model (Iter 6) is NOT an improvement.")
```
# Observation

## Code Stdout
Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=9.5, k2=400.0, k3=8.0, k4=11.0):
id_g7mj      5.955862
id_l2xx      0.000166
id_sgod      0.000887
id_jj65      0.000022
id_t6k9      0.080000
id_3r8d      1.985287
id_npcr      0.016342
id_0qoe      0.013639
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 6:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.955862    0.257931                4.150936
id_l2xx      0.001719    0.000166    0.001553               90.350386
id_sgod      0.003438    0.000887    0.002552               74.216660
id_jj65      0.000055    0.000022    0.000033               60.579007
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.985287    0.078060                3.783155
id_npcr      0.080357    0.016342    0.064015               79.663663
id_0qoe      0.002412    0.013639   -0.011227              465.392059
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous iter 5): 298.8771988946437
Sum of absolute relative differences (current iter 6): 778.1358656661309
Current model (Iter 6) is NOT an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data, current_sbml_model_iter6, iteration_6_sim_data)

### 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 model from Iteration 6 (k1=9.5, k2=400, k3=8, k4=11) was NOT an improvement. The sum of relative differences increased from ~299 to ~778.
The main regression was `id_0qoe`, which went from 16% low to 465% high. This means `k3=8` was far too low relative to `k2=400`.
Also, `id_sgod` became much more over-consumed (74% low vs 33% low).
`id_npcr` improved slightly (79% low vs 88% low), but is still a major issue.
`id_l2xx` improved (90% low vs 99% low), but still very low.

The "best_sbml_model_so_far" is still the one from Iteration 5:
`k1=14, k2=1275, k3=30, k4=100`
Results for Iteration 5 model:
-   `id_g7mj`: 3.65% low
-   `id_l2xx`: 99.68% low (Sim 5e-6, Exp 1.7e-3) -> Needs 340x increase
-   `id_sgod`: 33.5% low (Sim 0.002285, Exp 0.003438) -> Needs Exp/Sim = 1.5x increase (less consumption)
-   `id_jj65`: 53.6% low (Sim 2.5e-5, Exp 5.5e-5) -> Needs Exp/Sim = 2.2x increase
-   `id_npcr`: 88.8% low (Sim 0.0089, Exp 0.0803) -> Needs Exp/Sim = 9x increase
-   `id_0qoe`: 16.2% low (Sim 0.00202, Exp 0.00241) -> Needs Exp/Sim = 1.19x increase (This is good!)

Let's revert to Iteration 5 parameters as the baseline and make careful adjustments.
`k1=14, k2=1275, k3=30, k4=100`

Priority:
1.  **`id_npcr`**: Needs 9x increase. This requires reducing consumption from R1, R2, R3.
2.  **`id_sgod`**: Needs 1.5x increase (less consumption). This requires reducing `k1`.
3.  **`id_l2xx`**: Needs 340x increase. Requires `k4` to decrease significantly OR flux from `k3` to increase.
4.  **`id_jj65`**: Needs 2.2x increase.
5.  **`id_0qoe`**: Needs 1.2x increase (already good).

Plan:
-   **`k1`**: To increase `id_sgod` by 1.5x (less consumption), `k1` should decrease by 1.5x.
    `k1_new = 14 / 1.5 = 9.33`. Let `k1 = 9.5` (as tried in Iter 6, but other params were different).
    This change (9.5/14 = 0.678x) will help `id_npcr`.

-   **`k2`**: `id_jj65` needs 2.2x increase. `[jj65] ~ k1/k2`.
    `k1` changed by 0.678x.
    `k2_new = k2_old * ( (k1_new/k1_old) / jj65_increase_factor ) = 1275 * (0.678 / 2.2) = 1275 * 0.308 = 393`.
    Let `k2 = 400` (as tried in Iter 6). This change (400/1275 = 0.313x) will significantly help `id_npcr`.

-   **`k3`**: `id_0qoe` needs 1.2x increase. `[0qoe] ~ k2/k3`.
    `k2` changed by 0.313x.
    `k3_new = k3_old * ( (k2_new/k2_old) / 0qoe_increase_factor ) = 30 * (0.313 / 1.19) = 30 * 0.263 = 7.89`.
    This was `k3=8` in Iter 6, which made `id_0qoe` shoot up (465% high).
    The Iter 5 `id_0qoe` was 16% low. The Iter 6 `id_0qoe` was 465% high.
    This means `k3=30` (Iter 5) was slightly too high (for `id_0qoe`), and `k3=8` (Iter 6) was far too low.
    The target for `id_0qoe` is good. We want `k3` such that `k2_new/k3_new` is similar to `k2_old/k3_old` adjusted by 1.19.
    `k2_old/k3_old = 1275/30 = 42.5`.
    `k2_new = 400`.
    We want `400/k3_new` to be `42.5 * 1.19 = 50.575`.
    `k3_new = 400 / 50.575 = 7.90`.
    So `k3=8` was indeed the calculated value. The overshoot of `id_0qoe` in Iter 6 must be due to other factors, perhaps the `id_npcr` level changing dynamics or the `id_jj65` level not hitting its exact sub-target.
    Given `id_0qoe` was good with `k3=30` (only 16% low), and `k2` is decreasing significantly (from 1275 to 400), `k3` must also decrease to maintain `id_0qoe`.
    If `k2` decreases by `400/1275 = 0.313x`, and we want `id_0qoe` to increase by 1.19x, then `k3` should decrease by `0.313 / 1.19 = 0.263x`.
    `k3_new = 30 * 0.263 = 7.89`.
    Let's try `k3 = 10` instead of 8, to be a bit more conservative given the overshoot in Iter 6. This is a substantial reduction from 30 and will help `id_npcr`.

-   **`k4`**: `id_l2xx` needs 340x increase. `[l2xx] ~ k3/k4`.
    `k3` changes from 30 to 10 (factor 10/30 = 0.333x).
    `k4_new = k4_old * ( (k3_new/k3_old) / l2xx_increase_factor ) = 100 * (0.333 / 340) = 100 * 0.000979 = 0.0979`.
    This is still extremely small for `k4`. Products will be very low.
    The Iter 5 `k4=100` gave products that were only 3% low, while `id_l2xx` was 99% low.
    This implies `k4=100` is too efficient for `id_l2xx` (keeps it low), but the flux it *does* generate (from the tiny amount of `id_l2xx`) is almost enough for the products.
    This is the persistent contradiction.
    If `id_l2xx` were at its target `0.0017`, then `k4` should be `k4 = (k3_new * [0qoe]_target) / [l2xx]_target = 10 * (0.00241 / 0.0017) = 10 * 1.417 = 14.17`.
    Let `k4 = 15`. (Was 100). This is a significant reduction.

Parameters for this iteration:
`k1 = 9.5` (was 14)
`k2 = 400` (was 1275)
`k3 = 10` (was 30)
`k4 = 15` (was 100)

Expected impact:
-   `id_sgod`: Should improve (less consumption).
-   `id_npcr`: Should improve significantly due to reductions in `k1, k2, k3`. This is the main hope.
-   `id_jj65`: Should improve.
-   `id_0qoe`: `k3=10` is a bit higher than the calculated `k3=8`. Might be slightly lower than target but better than Iter 6.
-   `id_l2xx`: `k4=15` is calculated based on target `id_l2xx`. Should improve drastically.
-   Products: `k4` reduced from 100 to 15. Products likely to be lower. This is a risk.

The key is whether the improvement in `id_npcr` (if it occurs) will positively affect the entire system dynamics, allowing intermediates to rise more naturally.

## Action

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

# SBML model from Iteration 5 is the current best
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
# This should be the model string from iteration 5, as iteration 6 was worse.
# Let's explicitly re-access iteration 5's model string if "best_sbml_model_so_far" was overwritten by iter 6 by mistake in logic.
# However, the logic was "if sum_rel_diff_curr < sum_rel_diff_prev: update", so it should be correct.

sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants from Iteration 7 thoughts
new_k1_val = 9.5
new_k2_val = 400.0
new_k3_val = 10.0  # Iter 5 was 30, Iter 6 (bad) was 8. Trying 10.
new_k4_val = 15.0  # Iter 5 was 100, Iter 6 (bad) was 11. Trying 15.

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
        else:
            print(f"Warning: KineticLaw not found for {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter7 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter7", updated_sbml_string_iter7)
sim_data_iter7 = simulate(updated_sbml_string_iter7)
shared_variables.add("iteration_7_sim_data", sim_data_iter7)

exp_data_iter0 = experiment_history['iteration_0']
print("Experimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter7.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter7 = sim_data_iter7.iloc[-1]

comparison_iter7 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter7})
comparison_iter7['Difference'] = comparison_iter7['Experimental'] - comparison_iter7['Simulated']
comparison_iter7['RelativeDifference (%)'] = (comparison_iter7['Difference'].abs() / comparison_iter7['Experimental']) * 100
comparison_iter7['RelativeDifference (%)'] = comparison_iter7['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter7.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter7[exp_final == 0]) / 1.0 * 100 
comparison_iter7 = comparison_iter7.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 7:")
print(comparison_iter7)

# Compare with Iteration 5 data as that was the previous best
prev_sim_data = shared_variables.access("iteration_5_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter7.loc[comparison_iter7.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 5): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 7): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 7) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter7)
else:
    print("Current model (Iter 7) is NOT an improvement.")
```
# Observation

## Code Stdout
Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=9.5, k2=400.0, k3=10.0, k4=15.0):
id_g7mj      5.965954
id_l2xx      0.000094
id_sgod      0.001584
id_jj65      0.000039
id_t6k9      0.080000
id_3r8d      1.988651
id_npcr      0.014461
id_0qoe      0.009632
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 7:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.965954    0.247838                3.988514
id_l2xx      0.001719    0.000094    0.001624               94.505992
id_sgod      0.003438    0.001584    0.001854               53.929554
id_jj65      0.000055    0.000039    0.000016               29.561578
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.988651    0.074695                3.620110
id_npcr      0.080357    0.014461    0.065896               82.004063
id_0qoe      0.002412    0.009632   -0.007219              299.271625
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous iter 5): 298.8771988946437
Sum of absolute relative differences (current iter 7): 566.8814373462786
Current model (Iter 7) is NOT an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data, current_sbml_model_iter6, iteration_6_sim_data, current_sbml_model_iter7, iteration_7_sim_data)

### 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

Iteration 7 (k1=9.5, k2=400, k3=10, k4=15) was NOT an improvement. Sum of errors increased from ~299 (Iter 5) to ~567.
The main regression was `id_0qoe` (299% high, was 16% low). This means `k3=10` was too low relative to `k2=400`.
`id_sgod` also got worse (53% low, was 33% low). `k1=9.5` over-consumed `id_sgod` even more than `k1=14`. This is counter-intuitive as lower k1 should mean less consumption. This suggests complex feedback or `id_npcr` levels affecting R1. If `id_npcr` became higher (it did slightly: 0.014 vs 0.0089), it could drive R1 more despite lower `k1`.
`id_npcr` (82% low) is still very bad.
`id_jj65` improved (29% low, was 53% low).
`id_l2xx` improved (94% low, was 99% low), but still very low.

The "best_sbml_model_so_far" is still from Iteration 5:
`k1=14, k2=1275, k3=30, k4=100`
Results for Iteration 5 model:
-   `id_g7mj`: 3.65% low
-   `id_l2xx`: 99.68% low (Sim 5e-6, Exp 1.7e-3) -> Needs 340x increase
-   `id_sgod`: 33.5% low (Sim 0.002285, Exp 0.003438) -> Needs Exp/Sim = 1.5x increase (less consumption)
-   `id_jj65`: 53.6% low (Sim 2.5e-5, Exp 5.5e-5) -> Needs Exp/Sim = 2.2x increase
-   `id_npcr`: 88.8% low (Sim 0.0089, Exp 0.0803) -> Needs Exp/Sim = 9x increase
-   `id_0qoe`: 16.2% low (Sim 0.00202, Exp 0.00241) -> Needs Exp/Sim = 1.19x increase (Good!)

Let's re-strategize from Iteration 5 parameters.
The fact that `id_0qoe` is close with `k3=30` (relative to `k2=1275`) is a strong anchor.

Priorities:
1.  **`id_npcr`**: Needs 9x increase. This is paramount. Requires reducing overall consumption by R1, R2, R3.
2.  **`id_sgod`**: Needs 1.5x increase (less consumption). Requires reducing `k1`.
3.  **`id_jj65`**: Needs 2.2x increase.
4.  **`id_l2xx`**: Needs 340x increase.

Plan based on Iteration 5 (`k1=14, k2=1275, k3=30, k4=100`):

-   **`k1`**: `id_sgod` needs to be 1.5x higher (less consumption). So `k1` should decrease by 1.5x.
    `k1_new = 14 / 1.5 = 9.33`. Let `k1 = 9.5`. (This change helps `id_npcr`).
    (Factor `k1_new/k1_old = 9.5/14 = 0.678x`).

-   **`k2`**: `id_jj65` needs 2.2x increase. `[jj65] ~ k1/k2`.
    `k1` changed by 0.678x.
    `k2_new = k2_old * ( (k1_new/k1_old) / jj65_increase_factor ) = 1275 * (0.678 / 2.2) = 1275 * 0.308 = 393`.
    Let `k2 = 400`. (This change helps `id_npcr`).
    (Factor `k2_new/k2_old = 400/1275 = 0.313x`).

-   **`k3`**: `id_0qoe` needs 1.19x increase. `[0qoe] ~ k2/k3`.
    `k2` changed by 0.313x.
    `k3_new = k3_old * ( (k2_new/k2_old) / 0qoe_increase_factor ) = 30 * (0.313 / 1.19) = 30 * 0.263 = 7.89`.
    In Iter 7, `k1=9.5, k2=400, k3=10` led to `id_0qoe` being 299% high.
    The previous `k3=30` (with `k1=14, k2=1275`) gave `id_0qoe` 16% low.
    The ratio `k2/k3` in Iter 5 was `1275/30 = 42.5`.
    The new `k2` is `400`. To get `id_0qoe` to increase by 1.19x, the new ratio `k2_new/k3_new` should be `42.5 * 1.19 = 50.575`.
    So, `k3_new = k2_new / 50.575 = 400 / 50.575 = 7.90`.
    This calculation consistently points to `k3` around 8-10.
    The overshoot of `id_0qoe` in Iter 7 (with `k3=10`) suggests that the actual `id_npcr` level significantly impacts the effective rates. If `id_npcr` becomes higher, R3 might run faster than expected.
    Let's try `k3 = 15`. This is between 8 (calculated) and 30 (Iter 5). This is a moderate reduction from 30, should help `id_npcr`.
    (Factor `k3_new/k3_old = 15/30 = 0.5x`).

-   **`k4`**: `id_l2xx` needs 340x increase. `[l2xx] ~ k3/k4`.
    `k3` changed by 0.5x (from 30 to 15).
    `k4_new = k4_old * ( (k3_new/k3_old) / l2xx_increase_factor ) = 100 * (0.5 / 340) = 100 * 0.00147 = 0.147`.
    This is still extremely small.
    Let's use the logic: `k4_new = k3_new * ([0qoe]_target / [l2xx]_target)`.
    `k4_new = 15 * (0.00241 / 0.0017) = 15 * 1.417 = 21.26`.
    Let `k4 = 20`. (Was 100). This is a significant reduction.

Parameters for this iteration:
`k1 = 9.5`
`k2 = 400`
`k3 = 15`
`k4 = 20`

Expected impact:
-   `id_sgod`: `k1` reduced, should be less consumed.
-   `id_npcr`: `k1, k2, k3` all reduced from Iter 5 values. Should significantly increase final `id_npcr`.
-   `id_jj65`: `k1/k2` ratio `9.5/400 = 0.02375`. Iter 5 `k1/k2 = 14/1275 = 0.0109`. Ratio increased by `2.17x`. Should match `id_jj65` target increase of 2.2x.
-   `id_0qoe`: `k2/k3` ratio `400/15 = 26.67`. Iter 5 `k2/k3 = 1275/30 = 42.5`. Ratio decreased by `26.67/42.5 = 0.627x`. Target `id_0qoe` increase was 1.19x. This means `id_0qoe` might become too low.
    Recalculate `k3` based on `id_0qoe` target: `k3_new = k2_new / ( (k2_old/k3_old) * 1.19 ) = 400 / (42.5 * 1.19) = 400 / 50.575 = 7.9`.
    So `k3=15` is likely too high if `k2=400`. `id_0qoe` will be lower than target.
    Let's stick to `k3=15` for now to avoid the extreme overshoot seen with `k3=10` in Iter 7, and see. If `id_npcr` is higher, it might boost R3.
-   `id_l2xx`: `k3/k4` ratio `15/20 = 0.75`. Iter 5 `k3/k4 = 30/100 = 0.3`. Ratio increased by `0.75/0.3 = 2.5x`. Target `id_l2xx` increase was 340x. This is not enough. `id_l2xx` will still be very low.
    The calculation `k4_new = k3_new * ([0qoe]_target / [l2xx]_target)` is more direct for `id_l2xx`.
    If `k3=15`, then `k4_new = 15 * (0.00241/0.0017) = 21.26`. So `k4=20` is consistent with this.
    The problem is that `[0qoe]` itself might not reach its target if `k3=15` is too high.

The most important change is to see if `id_npcr` improves. If `id_npcr` gets closer to 0.08, then the effective rates of R1, R2, R3 will change, and intermediate levels might behave differently.

Let's try:
`k1 = 9.5`
`k2 = 400`
`k3 = 15` (Compromise for `id_0qoe`)
`k4 = 20` (Calculated for `id_l2xx` based on `k3=15` and target intermediates)

This set of parameters represents significant reductions in all rate constants compared to Iteration 5, which should substantially reduce `id_npcr` consumption.

## Action

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

# SBML model from Iteration 5 is the current best
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants from Iteration 8 thoughts
new_k1_val = 9.5
new_k2_val = 400.0
new_k3_val = 15.0
new_k4_val = 20.0

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
        else:
            print(f"Warning: KineticLaw not found for {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter8 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter8", updated_sbml_string_iter8)
sim_data_iter8 = simulate(updated_sbml_string_iter8)
shared_variables.add("iteration_8_sim_data", sim_data_iter8)

exp_data_iter0 = experiment_history['iteration_0']
print("Experimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter8.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter8 = sim_data_iter8.iloc[-1]

comparison_iter8 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter8})
comparison_iter8['Difference'] = comparison_iter8['Experimental'] - comparison_iter8['Simulated']
comparison_iter8['RelativeDifference (%)'] = (comparison_iter8['Difference'].abs() / comparison_iter8['Experimental']) * 100
comparison_iter8['RelativeDifference (%)'] = comparison_iter8['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter8.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter8[exp_final == 0]) / 1.0 * 100 
comparison_iter8 = comparison_iter8.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 8:")
print(comparison_iter8)

# Compare with Iteration 5 data as that was the previous best
prev_sim_data = shared_variables.access("iteration_5_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter8.loc[comparison_iter8.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 5): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 8): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 8) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter8)
else:
    print("Current model (Iter 8) is NOT an improvement.")
```
# Observation

## Code Stdout
Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=9.5, k2=400.0, k3=15.0, k4=20.0):
id_g7mj      5.976888
id_l2xx      0.000049
id_sgod      0.002780
id_jj65      0.000068
id_t6k9      0.080000
id_3r8d      1.992296
id_npcr      0.013283
id_0qoe      0.004808
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 8:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.976888    0.236904                3.812553
id_l2xx      0.001719    0.000049    0.001670               97.177786
id_sgod      0.003438    0.002780    0.000659               19.151235
id_jj65      0.000055    0.000068   -0.000013               23.611591
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.992296    0.071051                3.443473
id_npcr      0.080357    0.013283    0.067074               83.469961
id_0qoe      0.002412    0.004808   -0.002396               99.309299
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous iter 5): 298.8771988946437
Sum of absolute relative differences (current iter 8): 329.9758980636659
Current model (Iter 8) is NOT an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data, current_sbml_model_iter6, iteration_6_sim_data, current_sbml_model_iter7, iteration_7_sim_data, current_sbml_model_iter8, iteration_8_sim_data)

### 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

Iteration 8 (k1=9.5, k2=400, k3=15, k4=20) was NOT an improvement. Sum of errors increased from ~299 (Iter 5) to ~330.
Key changes from Iter 5 to Iter 8:
-   `id_sgod`: Sim 0.00278 vs Exp 0.00343 (19% low). Iter 5 was 33% low. This is an improvement (closer to target, less over-consumption). `k1=9.5` is better than `k1=14`.
-   `id_jj65`: Sim 6.8e-5 vs Exp 5.5e-5 (23% high). Iter 5 was 53% low. `id_jj65` overshot. `k2=400` was too low.
-   `id_0qoe`: Sim 0.0048 vs Exp 0.0024 (99% high). Iter 5 was 16% low. `id_0qoe` overshot significantly. `k3=15` was too low.
-   `id_l2xx`: Sim 4.9e-5 vs Exp 1.7e-3 (97% low). Iter 5 was 99% low. Slight improvement, but still very bad.
-   `id_npcr`: Sim 0.013 vs Exp 0.08 (83% low). Iter 5 was 88% low. Slight improvement, but still very bad.
-   Products: Stable, slightly low.

The "best_sbml_model_so_far" is still from Iteration 5:
`k1=14, k2=1275, k3=30, k4=100`
Results for Iteration 5 model:
-   `id_g7mj`: 3.65% low
-   `id_l2xx`: 99.68% low (Sim 5e-6, Exp 1.7e-3) -> Needs 340x increase
-   `id_sgod`: 33.5% low (Sim 0.002285, Exp 0.003438) -> Needs Exp/Sim = 1.5x increase (less consumption)
-   `id_jj65`: 53.6% low (Sim 2.5e-5, Exp 5.5e-5) -> Needs Exp/Sim = 2.2x increase
-   `id_npcr`: 88.8% low (Sim 0.0089, Exp 0.0803) -> Needs Exp/Sim = 9x increase
-   `id_0qoe`: 16.2% low (Sim 0.00202, Exp 0.00241) -> Needs Exp/Sim = 1.19x increase (Good!)

It seems the large reduction in `k2` and `k3` in Iter 8 (to 400 and 15) caused intermediates `id_jj65` and `id_0qoe` to overshoot their targets when `k1` was also reduced. This indicates a strong coupling and sensitivity.
The improvement in `id_sgod` (with `k1=9.5`) and `id_npcr` (slight) suggests that reducing `k1` is a correct direction.

Let's refine from Iter 5, focusing on `k1` and then carefully adjusting `k2, k3, k4`.

1.  **`k1`**: Iter 5 `id_sgod` needs 1.5x increase (less consumption). `k1_new = 14 / 1.5 = 9.33`.
    Let `k1 = 9.5`. (Factor `k1_new/k1_old = 9.5/14 = 0.678x`).

2.  **`k2`**: Iter 5 `id_jj65` needs 2.2x increase. `[jj65] ~ k1/k2`.
    `k1` changed by 0.678x.
    `k2_new = k2_old (1275) * ( (k1_new/k1_old) / jj65_increase_factor ) = 1275 * (0.678 / 2.2) = 1275 * 0.308 = 393`.
    In Iter 8, `k1=9.5, k2=400` made `id_jj65` 23% high. Target was 2.2x increase from Iter 5's 53% low.
    Iter 5 `id_jj65` sim/exp = 0.464. Target sim/exp = 1.
    Iter 8 `id_jj65` sim/exp = 1.23.
    So `k2=400` (with `k1=9.5`) was a bit too low (making `id_jj65` too high).
    We want `k2_new = k2_iter8 * (current_jj65_sim_exp_ratio_iter8 / target_jj65_sim_exp_ratio) = 400 * (1.23 / 1.0) = 492`.
    Let `k2 = 500`. (Iter 5 was 1275). (Factor `k2_new/k2_old_Iter5 = 500/1275 = 0.392x`).

3.  **`k3`**: Iter 5 `id_0qoe` needs 1.19x increase. `[0qoe] ~ k2/k3`.
    `k2` (from Iter 5) changed by 0.392x.
    `k3_new = k3_old (30) * ( (k2_new_factor_from_Iter5) / 0qoe_increase_factor ) = 30 * (0.392 / 1.19) = 30 * 0.329 = 9.87`.
    In Iter 8, `k1=9.5, k2=400, k3=15` made `id_0qoe` 99% high.
    Iter 8 `id_0qoe` sim/exp = 1.99. Target sim/exp = 1.
    `k3_new_from_iter8 = k3_iter8 * (current_0qoe_sim_exp_ratio_iter8 / target_0qoe_sim_exp_ratio) = 15 * (1.99 / 1.0) = 29.85`.
    This suggests `k3` should be around 30 if `k2` is 400-500 and `k1` is 9.5.
    This brings `k3` back to its Iter 5 value.
    Let `k3 = 25`. (Iter 5 was 30). (Factor `k3_new/k3_old_Iter5 = 25/30 = 0.833x`).

4.  **`k4`**: Iter 5 `id_l2xx` needs 340x increase. `[l2xx] ~ k3/k4`.
    `k3` (from Iter 5) changed by 0.833x.
    `k4_new = k4_old (100) * ( (k3_new_factor_from_Iter5) / l2xx_increase_factor ) = 100 * (0.833 / 340) = 100 * 0.00245 = 0.245`.
    Still extremely small.
    Let's use `k4_new = k3_new * ([0qoe]_target / [l2xx]_target)`.
    `k4_new = 25 * (0.00241 / 0.0017) = 25 * 1.417 = 35.4`.
    Let `k4 = 35`. (Iter 5 was 100).

Parameters for this iteration:
`k1 = 9.5`
`k2 = 500`
`k3 = 25`
`k4 = 35`

Expected impact:
-   `id_sgod`: `k1=9.5` should give good `id_sgod` levels (Iter 8 `id_sgod` was 19% low with `k1=9.5`).
-   `id_npcr`: `k1` reduced from 14. `k2` reduced from 1275 to 500. `k3` reduced from 30 to 25. `k4` reduced from 100 to 35. All these reductions should help `id_npcr` significantly.
-   `id_jj65`: `k1/k2 = 9.5/500 = 0.019`. Iter 5 `k1/k2 = 0.0109`. Ratio increased 1.74x. Target was 2.2x. Should be better, possibly a bit low.
-   `id_0qoe`: `k2/k3 = 500/25 = 20`. Iter 5 `k2/k3 = 42.5`. Ratio decreased `20/42.5 = 0.47x`. Target was 1.19x increase. So `id_0qoe` will likely be too low.
    Recalculate `k3` for `id_0qoe`: `k3_new = k2_new / ( (k2_old_Iter5/k3_old_Iter5) * 1.19 ) = 500 / (42.5 * 1.19) = 500 / 50.575 = 9.88`.
    So `k3` should be ~10.
    If `k3=10`, then `k4 = 10 * 1.417 = 14.17`.
    This is the set from Iter 7 (`k1=9.5, k2=400, k3=10, k4=15` - `k2` was 400 not 500) which was bad for `id_0qoe`.

The system is highly coupled. The assumption that intermediate ratios `k_upstream/k_downstream` dictate levels is only approximate.
The `id_npcr` level is crucial. If it rises, it speeds up R1, R2, R3.

Let's try to be less aggressive with `k2` and `k3` reduction from Iter 5 values, while `k1` is reduced.
Iter 5: `k1=14, k2=1275, k3=30, k4=100`. `id_0qoe` is good.
Target: `k1=9.5`.
If `k1` reduces by `0.678x`.
To keep `id_jj65` roughly the same relative to its new production rate (i.e. if it was X% of max, it stays X% of new max), `k2` should also reduce by `0.678x`.
`k2_new = 1275 * 0.678 = 864`. Let `k2 = 850`.
To keep `id_0qoe` roughly the same relative to its new production rate, `k3` should also reduce by `0.678x` (if `k2` also scaled by that).
`k3_new = 30 * (850/1275) = 30 * 0.666 = 20`. Let `k3 = 20`.
Now, `id_jj65` was 53% low, needs 2.2x increase. `id_0qoe` was 16% low, needs 1.19x increase.
These scaling factors (0.678x) don't account for improving the fit.

Let's use the `k` values from Iter 5 as a good starting point for ratios, and scale them down to help `id_npcr`, then fine tune.
`k1=14, k2=1275, k3=30`. Ratios: `k2/k1 ~ 90`, `k3/k2 ~ 0.0235`.
If `k1_new = 9.5`.
`k2_new = 9.5 * 90 = 855`. Let `k2 = 850`.
`k3_new = 850 * 0.0235 = 19.975`. Let `k3 = 20`.
This maintains the relative speeds of sequential reactions from Iter 5, but scales down overall rates due to lower `k1`.
This should help `id_npcr` and `id_sgod`.
`id_jj65` and `id_0qoe` should maintain their previous (Iter 5) percentage errors if this scaling works perfectly.
`id_jj65` (53% low) and `id_0qoe` (16% low).

Now for `k4`. `id_l2xx` needs 340x increase from Iter 5.
`k4_new = k3_new * ([0qoe]_target_from_Iter5_scaled / [l2xx]_target)`.
`[0qoe]_target_from_Iter5_scaled` would be `0.00202 * (1/0.678)` if `id_npcr` doesn't change. This is complex.
Let's use the simpler `k4_new = k3_new * ([0qoe]_exp / [l2xx]_exp) = 20 * (0.00241 / 0.0017) = 20 * 1.417 = 28.34`.
Let `k4 = 28`.

New parameters:
`k1 = 9.5`
`k2 = 850`
`k3 = 20`
`k4 = 28`

This set scales down `k1,k2,k3` from Iter 5 values by roughly the same factor (`~0.67x`), which should improve `id_npcr` and `id_sgod` while attempting to maintain the good `id_0qoe` balance and improve `id_jj65`. `k4` is adjusted for `id_l2xx`.

## Action

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

# SBML model from Iteration 5 is the current best
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants from Iteration 9 thoughts
new_k1_val = 9.5
new_k2_val = 850.0
new_k3_val = 20.0
new_k4_val = 28.0

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
        else:
            print(f"Warning: KineticLaw not found for {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter9 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter9", updated_sbml_string_iter9)
sim_data_iter9 = simulate(updated_sbml_string_iter9)
shared_variables.add("iteration_9_sim_data", sim_data_iter9)

exp_data_iter0 = experiment_history['iteration_0']
print("Experimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter9.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter9 = sim_data_iter9.iloc[-1]

comparison_iter9 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter9})
comparison_iter9['Difference'] = comparison_iter9['Experimental'] - comparison_iter9['Simulated']
comparison_iter9['RelativeDifference (%)'] = (comparison_iter9['Difference'].abs() / comparison_iter9['Experimental']) * 100
comparison_iter9['RelativeDifference (%)'] = comparison_iter9['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter9.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter9[exp_final == 0]) / 1.0 * 100 
comparison_iter9 = comparison_iter9.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 9:")
print(comparison_iter9)

# Compare with Iteration 5 data as that was the previous best
prev_sim_data = shared_variables.access("iteration_5_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter9.loc[comparison_iter9.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 5): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 9): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 9) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter9)
else:
    print("Current model (Iter 9) is NOT an improvement.")
```
# Observation

## Code Stdout
Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=9.5, k2=850.0, k3=20.0, k4=28.0):
id_g7mj      5.980606
id_l2xx      0.000029
id_sgod      0.003342
id_jj65      0.000038
id_t6k9      0.080000
id_3r8d      1.993535
id_npcr      0.013158
id_0qoe      0.003056
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 9:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.980606    0.233187                3.752727
id_l2xx      0.001719    0.000029    0.001690               98.313949
id_sgod      0.003438    0.003342    0.000096                2.792449
id_jj65      0.000055    0.000038    0.000017               30.948978
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.993535    0.069812                3.383418
id_npcr      0.080357    0.013158    0.067198               83.624884
id_0qoe      0.002412    0.003056   -0.000643               26.670716
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous iter 5): 298.8771988946437
Sum of absolute relative differences (current iter 9): 249.48712165767859
Current model (Iter 9) is an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data, current_sbml_model_iter6, iteration_6_sim_data, current_sbml_model_iter7, iteration_7_sim_data, current_sbml_model_iter8, iteration_8_sim_data, current_sbml_model_iter9, iteration_9_sim_data)

### 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

Iteration 9 (k1=9.5, k2=850, k3=20, k4=28) was an improvement! Sum of errors decreased from ~299 (Iter 5) to ~249.

Current model (Iter 9): `k1=9.5, k2=850, k3=20, k4=28`
Results:
-   `id_g7mj`: 3.75% low (Stable)
-   `id_l2xx`: 98.3% low (Sim 2.9e-5, Exp 1.7e-3) -> Needs Exp/Sim = 59x increase. (Was 340x, so big improvement but still very low)
-   `id_sgod`: 2.8% high (Sim 0.003342, Exp 0.003438) -> Excellent! `k1=9.5` is very good.
-   `id_jj65`: 30.9% low (Sim 3.8e-5, Exp 5.5e-5) -> Needs Exp/Sim = 1.45x increase. (Was 53% low, good improvement)
-   `id_npcr`: 83.6% low (Sim 0.013158, Exp 0.080357) -> Needs Exp/Sim = 6.1x increase. (Was 88% low, slight improvement, but still very bad).
-   `id_0qoe`: 26.6% high (Sim 0.003056, Exp 0.002412) -> Was 16% low. Overshot a bit.
-   Products (`id_3r8d`): 3.38% low (Stable)

Priorities:
1.  **`id_npcr`**: Still the biggest issue. Needs 6.1x increase.
2.  **`id_l2xx`**: Still very low. Needs 59x increase.
3.  **`id_jj65`**: Needs 1.45x increase.
4.  **`id_0qoe`**: Needs to decrease by `1 / (1+0.266) = 1/1.266 = 0.79x`. (Decrease by ~21%).

Plan based on Iteration 9 (`k1=9.5, k2=850, k3=20, k4=28`):

-   **`k1`**: `id_sgod` is excellent (2.8% high). Keep `k1 = 9.5`.

-   **`k2`**: `id_jj65` needs 1.45x increase. `[jj65] ~ k1/k2`. `k1` is constant.
    `k2_new = k2_old / 1.45 = 850 / 1.45 = 586`.
    Let `k2 = 580`. (Was 850). This reduction helps `id_npcr`.
    (Factor `k2_new/k2_old = 580/850 = 0.682x`).

-   **`k3`**: `id_0qoe` needs 0.79x decrease (it's 26.6% high). `[0qoe] ~ k2/k3`.
    `k2` changed by 0.682x.
    `k3_new = k3_old * ( (k2_new/k2_old) / 0qoe_decrease_factor ) = 20 * (0.682 / 0.79) = 20 * 0.863 = 17.26`.
    Let `k3 = 17`. (Was 20). This slight reduction might not help `id_npcr` much but aims for `id_0qoe`.
    (Factor `k3_new/k3_old = 17/20 = 0.85x`).

-   **`k4`**: `id_l2xx` needs 59x increase. `[l2xx] ~ k3/k4`.
    `k3` changed by 0.85x.
    `k4_new = k4_old * ( (k3_new/k3_old) / l2xx_increase_factor ) = 28 * (0.85 / 59) = 28 * 0.0144 = 0.40`.
    This is again extremely small.
    Using `k4_new = k3_new * ([0qoe]_target / [l2xx]_target)`:
    `k4_new = 17 * (0.002412 / 0.001719) = 17 * 1.403 = 23.85`.
    Let `k4 = 24`. (Was 28). This is a small change.

Parameters for this iteration:
`k1 = 9.5`
`k2 = 580`
`k3 = 17`
`k4 = 24`

Expected impact:
-   `id_sgod`: Should remain excellent.
-   `id_npcr`: `k2` reduced significantly (850 to 580). `k3` reduced slightly (20 to 17). `k4` reduced slightly (28 to 24). `k1` constant. Should improve `id_npcr`.
-   `id_jj65`: `k1/k2 = 9.5/580 = 0.0163`. Iter 9 `k1/k2 = 9.5/850 = 0.0111`. Ratio increased `0.0163/0.0111 = 1.46x`. Target was 1.45x. Should be very good.
-   `id_0qoe`: `k2/k3 = 580/17 = 34.1`. Iter 9 `k2/k3 = 850/20 = 42.5`. Ratio decreased `34.1/42.5 = 0.802x`. Target was 0.79x decrease. Should be very good.
-   `id_l2xx`: `k3/k4 = 17/24 = 0.708`. Iter 9 `k3/k4 = 20/28 = 0.714`. Ratio is very similar. `id_l2xx` will likely remain very low. The calculation `k4_new = k3_new * ([0qoe]_target / [l2xx]_target)` seems to be the most robust way to target `id_l2xx` if upstream intermediates are correct. The previous `k4=28` was based on `k3=20`. Now `k3=17`, so `k4=24` is consistent.
-   Products: `k4` changed from 28 to 24. Small change, products likely stable.

The main hope is that `id_npcr` improves substantially. If `id_npcr` gets much closer to its experimental value, the effective reaction rates might change enough to bring `id_l2xx` up without an extremely small `k4`.
If `id_npcr` is still very low, then the model might be missing a mechanism related to `id_npcr` or the parameter estimation is hitting a wall.

One more check on `id_l2xx` and `k4`:
If `id_l2xx` needs a 59x increase from sim value `2.9e-5` to `1.7e-3`.
And `k3/k4` ratio is currently `17/24 = 0.708`.
If `k3` is correct at 17 (producing correct `id_0qoe`), then `[l2xx] ~ 17/k4`.
To get `id_l2xx` to `0.0017`, `k4` should be `17 * [0qoe]_actual / [l2xx]_target`.
Assuming `[0qoe]_actual` will be close to `0.002412`.
`k4 = 17 * 0.002412 / 0.001719 = 17 * 1.403 = 23.85`. So `k4=24` is consistent.
The issue is that even with this `k4`, `id_l2xx` is predicted to be low if the upstream flux (determined by `k3*[0qoe]`) isn't high enough.
The current sim `id_l2xx` is `2.9e-5`. `k3/k4` was `20/28 = 0.714`.
New `k3/k4` is `17/24 = 0.708`. This ratio barely changed. So `id_l2xx` will likely not improve much.

This means `id_l2xx` is primarily limited by the flux from R3 (`k3 * id_0qoe * id_npcr * id_t6k9`).
If `id_0qoe` is correct, and `id_npcr` is low, then this flux is low.
If `id_npcr` increases, this flux increases, and `id_l2xx` should increase.
This highlights the importance of fixing `id_npcr`.

## Action

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

# SBML model from Iteration 9 is the current best
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants from Iteration 10 thoughts
new_k1_val = 9.5   # Keep from Iter 9
new_k2_val = 580.0  # Was 850 in Iter 9
new_k3_val = 17.0  # Was 20 in Iter 9
new_k4_val = 24.0  # Was 28 in Iter 9

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
        else:
            print(f"Warning: KineticLaw not found for {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter10 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter10", updated_sbml_string_iter10)
sim_data_iter10 = simulate(updated_sbml_string_iter10)
shared_variables.add("iteration_10_sim_data", sim_data_iter10)

exp_data_iter0 = experiment_history['iteration_0']
print("Experimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter10.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter10 = sim_data_iter10.iloc[-1]

comparison_iter10 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter10})
comparison_iter10['Difference'] = comparison_iter10['Experimental'] - comparison_iter10['Simulated']
comparison_iter10['RelativeDifference (%)'] = (comparison_iter10['Difference'].abs() / comparison_iter10['Experimental']) * 100
comparison_iter10['RelativeDifference (%)'] = comparison_iter10['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter10.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter10[exp_final == 0]) / 1.0 * 100 
comparison_iter10 = comparison_iter10.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 10:")
print(comparison_iter10)

# Compare with Iteration 9 data as that was the previous best
prev_sim_data = shared_variables.access("iteration_9_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter10.loc[comparison_iter10.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 9): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 10): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 10) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter10)
else:
    print("Current model (Iter 10) is NOT an improvement.")
```
# Observation

## Code Stdout
Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=9.5, k2=580.0, k3=17.0, k4=24.0):
id_g7mj      5.978801
id_l2xx      0.000037
id_sgod      0.003061
id_jj65      0.000051
id_t6k9      0.080000
id_3r8d      1.992934
id_npcr      0.013202
id_0qoe      0.003918
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 10:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.978801    0.234991                3.781763
id_l2xx      0.001719    0.000037    0.001682               97.846082
id_sgod      0.003438    0.003061    0.000378               10.985662
id_jj65      0.000055    0.000051    0.000004                6.843704
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.992934    0.070413                3.412566
id_npcr      0.080357    0.013202    0.067155               83.571220
id_0qoe      0.002412    0.003918   -0.001505               62.400059
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous iter 9): 249.48712165767859
Sum of absolute relative differences (current iter 10): 268.8410559526922
Current model (Iter 10) is NOT an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data, current_sbml_model_iter6, iteration_6_sim_data, current_sbml_model_iter7, iteration_7_sim_data, current_sbml_model_iter8, iteration_8_sim_data, current_sbml_model_iter9, iteration_9_sim_data, current_sbml_model_iter10, iteration_10_sim_data)

### 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

Iteration 10 (k1=9.5, k2=580, k3=17, k4=24) was NOT an improvement. Sum of errors increased from ~249 (Iter 9) to ~269.
The "best_sbml_model_so_far" is from Iteration 9:
`k1=9.5, k2=850, k3=20, k4=28`

Results for Iteration 9 model:
-   `id_g7mj`: 3.75% low
-   `id_l2xx`: 98.3% low (Sim 2.9e-5, Exp 1.7e-3) -> Needs Exp/Sim = 59x increase.
-   `id_sgod`: 2.8% high (Sim 0.003342, Exp 0.003438) -> Excellent!
-   `id_jj65`: 30.9% low (Sim 3.8e-5, Exp 5.5e-5) -> Needs Exp/Sim = 1.45x increase.
-   `id_npcr`: 83.6% low (Sim 0.013158, Exp 0.080357) -> Needs Exp/Sim = 6.1x increase. (Still very bad).
-   `id_0qoe`: 26.6% high (Sim 0.003056, Exp 0.002412) -> Needs 0.79x decrease.
-   Products (`id_3r8d`): 3.38% low

Changes from Iter 9 to Iter 10 and their effects:
-   `k1`: 9.5 (no change). `id_sgod` in Iter 10 was 10.9% high (worse than 2.8% high in Iter 9). This is likely due to `id_npcr` being slightly higher in Iter 10 (0.01320 vs 0.01315), driving R1 a bit more.
-   `k2`: 850 -> 580. `id_jj65` in Iter 10 was 6.8% low (target was 1.45x increase from 30.9% low). This is excellent for `id_jj65`.
-   `k3`: 20 -> 17. `id_0qoe` in Iter 10 was 62.4% high (target was 0.79x decrease from 26.6% high). `k3=17` was too low, causing `id_0qoe` to be even higher.
-   `k4`: 28 -> 24. `id_l2xx` in Iter 10 was 97.8% low (vs 98.3% low). Negligible change, still terrible.
-   `id_npcr`: 0.013158 -> 0.013202. Negligible change, still terrible.

The key failure in Iter 10 was `id_0qoe` becoming much worse. This was due to `k3` being too low (17) relative to the new `k2` (580).
The `id_jj65` targeting was successful with `k2=580`.

Let's refine from Iter 9 (`k1=9.5, k2=850, k3=20, k4=28`), but use the successful `k2` for `id_jj65`.

1.  **`k1`**: `id_sgod` is excellent (2.8% high with `k1=9.5`). Keep `k1 = 9.5`.

2.  **`k2`**: `k2=580` (from Iter 10 logic) made `id_jj65` 6.8% low. This is very good.
    Let `k2 = 580`. (Iter 9 was 850). (Factor `k2_new/k2_old_Iter9 = 580/850 = 0.682x`).

3.  **`k3`**: Iter 9 `id_0qoe` was 26.6% high (needs 0.79x decrease). `[0qoe] ~ k2/k3`.
    `k2` (from Iter 9) changed by 0.682x.
    `k3_new = k3_old_Iter9 * ( (k2_new/k2_old_Iter9) / 0qoe_decrease_factor ) = 20 * (0.682 / 0.79) = 20 * 0.863 = 17.26`.
    Iter 10 used `k3=17` and `id_0qoe` became 62.4% high. This means `k3=17` was too low.
    The ratio `k2/k3` in Iter 9 was `850/20 = 42.5`. `id_0qoe` was 26.6% high. Target ratio should be `42.5 * 0.79 = 33.575`.
    New `k2 = 580`. So `k3_new = 580 / 33.575 = 17.27`.
    This calculation still points to `k3 ~ 17-18`.
    The failure of `k3=17` in Iter 10 (making `id_0qoe` 62% high) when `id_jj65` was good suggests that `id_npcr` levels might be influencing this.
    If `id_0qoe` was 26.6% high with `k2/k3 = 42.5` (Iter 9), and we want it to be perfect, we need to increase `k3` relative to `k2`.
    Target `k2/k3` should be `42.5 * 0.79 = 33.575`.
    With `k2_new = 580`, `k3_new = 580 / 33.575 = 17.27`.
    Let's try `k3 = 18`. (Iter 9 was 20). This is a small change.

4.  **`k4`**: Iter 9 `id_l2xx` needs 59x increase. `[l2xx] ~ k3/k4`.
    `k3` changes from 20 (Iter 9) to 18. (Factor `18/20 = 0.9x`).
    `k4_new = k4_old_Iter9 * ( (k3_new/k3_old_Iter9) / l2xx_increase_factor ) = 28 * (0.9 / 59) = 28 * 0.0152 = 0.42`.
    Still extremely small.
    Using `k4_new = k3_new * ([0qoe]_target / [l2xx]_target)`:
    `k4_new = 18 * (0.002412 / 0.001719) = 18 * 1.403 = 25.25`.
    Let `k4 = 25`. (Iter 9 was 28).

Parameters for this iteration:
`k1 = 9.5`
`k2 = 580`
`k3 = 18`
`k4 = 25`

Expected impact:
-   `id_sgod`: Should remain excellent.
-   `id_npcr`: `k2` reduced (850->580). `k3` reduced (20->18). `k4` reduced (28->25). Should improve `id_npcr`.
-   `id_jj65`: `k2=580` should give good `id_jj65`.
-   `id_0qoe`: `k2/k3 = 580/18 = 32.22`. Target ratio was 33.575. This is very close. `id_0qoe` should be excellent.
-   `id_l2xx`: `k3/k4 = 18/25 = 0.72`. Iter 9 was `20/28 = 0.714`. Very similar. `id_l2xx` will likely remain very low.
-   Products: `k4` (28->25) small change. Products likely stable.

The main problem remains `id_npcr` and consequently `id_l2xx`.
If `id_npcr` does not improve significantly with these scaled-down `k2, k3, k4` values, then the issue is more fundamental.
The total consumption of `id_npcr` is `(Initial - Final)`.
Exp: `6 - 0.080357 = 5.919643`.
Iter 9 Sim: `6 - 0.013158 = 5.986842`. (Sim consumes 0.067 more `id_npcr`).
This is only a 1.1% overconsumption of total `id_npcr`.
The problem is that this small absolute overconsumption leads to a huge relative error in the *remaining* `id_npcr`.

Perhaps the reactions are too fast overall, depleting `id_npcr` too quickly, even if the total amount consumed is almost correct.
If all `k` values (`k1,k2,k3,k4`) were scaled down by a common factor, say 2x, this would slow everything down.
`id_sgod` is good with `k1=9.5`. If `k1` is halved, `id_sgod` will be under-consumed.
This suggests that `k1` is somewhat pinned, but `k2,k3` (which also consume `id_npcr`) might be too high relative to `k1` for the `id_npcr` dynamics, even if their ratios `k1/k2` and `k2/k3` are good for intermediates `id_jj65` and `id_0qoe`.

If `id_npcr` is the bottleneck for `id_l2xx` production, then `id_l2xx` will only rise if `id_npcr` rises.
Let's proceed with the current set, focusing on getting `id_jj65` and `id_0qoe` correct, and hoping `id_npcr` improves.

## Action

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

# SBML model from Iteration 9 is the current best
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants from Iteration 11 thoughts
new_k1_val = 9.5
new_k2_val = 580.0
new_k3_val = 18.0 # Was 17 in failed Iter 10, 20 in Iter 9. Target ratio k2/k3 = 33.5 -> k3 = 580/33.5 = 17.3
new_k4_val = 25.0 # k4 = k3 * (0qoe_exp/l2xx_exp) = 18 * 1.403 = 25.25

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
        else:
            print(f"Warning: KineticLaw not found for {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter11 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter11", updated_sbml_string_iter11)
sim_data_iter11 = simulate(updated_sbml_string_iter11)
shared_variables.add("iteration_11_sim_data", sim_data_iter11)

exp_data_iter0 = experiment_history['iteration_0']
print("Experimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter11.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter11 = sim_data_iter11.iloc[-1]

comparison_iter11 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter11})
comparison_iter11['Difference'] = comparison_iter11['Experimental'] - comparison_iter11['Simulated']
comparison_iter11['RelativeDifference (%)'] = (comparison_iter11['Difference'].abs() / comparison_iter11['Experimental']) * 100
comparison_iter11['RelativeDifference (%)'] = comparison_iter11['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter11.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter11[exp_final == 0]) / 1.0 * 100 
comparison_iter11 = comparison_iter11.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 11:")
print(comparison_iter11)

# Compare with Iteration 9 data as that was the previous best
prev_sim_data = shared_variables.access("iteration_9_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter11.loc[comparison_iter11.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 9): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 11): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 11) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter11)
else:
    print("Current model (Iter 11) is NOT an improvement.")
```
# Observation

## Code Stdout
Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=9.5, k2=580.0, k3=18.0, k4=25.0):
id_g7mj      5.979496
id_l2xx      0.000034
id_sgod      0.003164
id_jj65      0.000053
id_t6k9      0.080000
id_3r8d      1.993165
id_npcr      0.013181
id_0qoe      0.003584
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 11:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.979496    0.234297                3.770590
id_l2xx      0.001719    0.000034    0.001684               98.001103
id_sgod      0.003438    0.003164    0.000274                7.981383
id_jj65      0.000055    0.000053    0.000002                3.699649
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.993165    0.070182                3.401350
id_npcr      0.080357    0.013181    0.067175               83.596658
id_0qoe      0.002412    0.003584   -0.001171               48.563216
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous iter 9): 249.48712165767859
Sum of absolute relative differences (current iter 11): 249.01394836712433
Current model (Iter 11) is an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data, current_sbml_model_iter6, iteration_6_sim_data, current_sbml_model_iter7, iteration_7_sim_data, current_sbml_model_iter8, iteration_8_sim_data, current_sbml_model_iter9, iteration_9_sim_data, current_sbml_model_iter10, iteration_10_sim_data, current_sbml_model_iter11, iteration_11_sim_data)

### 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

Iteration 11 (k1=9.5, k2=580, k3=18, k4=25) was a tiny improvement! Sum of errors decreased from ~249.48 (Iter 9) to ~249.01. This is progress, however small.

Current model (Iter 11): `k1=9.5, k2=580, k3=18, k4=25`
Results:
-   `id_g7mj`: 3.77% low (Stable)
-   `id_l2xx`: 98.0% low (Sim 3.4e-5, Exp 1.7e-3) -> Needs Exp/Sim = 50x increase. (Slight improvement from 59x)
-   `id_sgod`: 7.98% high (Sim 0.003164, Exp 0.003438) -> Was 2.8% high. Slightly worse, but still good.
-   `id_jj65`: 3.7% low (Sim 5.3e-5, Exp 5.5e-5) -> Excellent! Was 30.9% low.
-   `id_npcr`: 83.6% low (Sim 0.013181, Exp 0.080357) -> Needs Exp/Sim = 6.1x increase. (No change, still very bad).
-   `id_0qoe`: 48.5% high (Sim 0.003584, Exp 0.002412) -> Was 26.6% high. Got worse. `k3=18` was too low relative to `k2=580`.
-   Products (`id_3r8d`): 3.4% low (Stable)

Key takeaways:
-   `id_jj65` is now excellent with `k1=9.5, k2=580`. This `k1/k2` ratio is good.
-   `id_sgod` is good with `k1=9.5`.
-   `id_0qoe` overshot with `k3=18`. It was better (26.6% high) with `k3=20` (Iter 9, with `k2=850`).
-   `id_npcr` and `id_l2xx` are still the major problems.

Plan based on Iter 11 (`k1=9.5, k2=580, k3=18, k4=25`):

1.  **`k1`**: Keep `k1 = 9.5`. (`id_sgod` is good).
2.  **`k2`**: Keep `k2 = 580`. (`id_jj65` is excellent).

3.  **`k3`**: `id_0qoe` is 48.5% high (needs `1/(1+0.485) = 0.673x` decrease). `[0qoe] ~ k2/k3`. `k2` is constant (580).
    `k3_new = k3_old / 0qoe_decrease_factor = 18 / 0.673 = 26.74`.
    In Iter 9, `k1=9.5, k2=850, k3=20` gave `id_0qoe` 26.6% high.
    The ratio `k2/k3` in Iter 11 is `580/18 = 32.22`. `id_0qoe` is 48.5% high. Target ratio should be `32.22 * 0.673 = 21.68`.
    So `k3_new = k2_new / 21.68 = 580 / 21.68 = 26.75`.
    Let `k3 = 27`. (Iter 11 was 18, Iter 9 was 20). This increases `k3`.

4.  **`k4`**: `id_l2xx` needs 50x increase. `[l2xx] ~ k3/k4`.
    `k3` changes from 18 to 27. (Factor `27/18 = 1.5x`).
    `k4_new = k4_old * ( (k3_new/k3_old) / l2xx_increase_factor ) = 25 * (1.5 / 50) = 25 * 0.03 = 0.75`.
    Still extremely small.
    Using `k4_new = k3_new * ([0qoe]_target / [l2xx]_target)`:
    `k4_new = 27 * (0.002412 / 0.001719) = 27 * 1.403 = 37.88`.
    Let `k4 = 38`. (Iter 11 was 25). This increases `k4`.

Parameters for this iteration:
`k1 = 9.5`
`k2 = 580`
`k3 = 27`
`k4 = 38`

Expected impact:
-   `id_sgod`, `id_jj65`: Should remain excellent.
-   `id_npcr`: `k3` increased (18->27), `k4` increased (25->38). `k1,k2` constant. Increased `k3` will consume more `id_npcr`, which is bad. This is a risk.
-   `id_0qoe`: `k2/k3 = 580/27 = 21.48`. Target ratio was 21.68. This is extremely close. `id_0qoe` should be excellent.
-   `id_l2xx`: `k3/k4 = 27/38 = 0.71`. Iter 11 was `18/25 = 0.72`. Very similar. `id_l2xx` will likely remain very low.
-   Products: `k4` increased (25->38). Products might increase slightly, which is good.

The main concern is `id_npcr`. Increasing `k3` will worsen it.
However, getting `id_0qoe` correct is also important.
If `id_npcr` continues to be the problem, it means the relative consumption by R1, R2, R3 is not balanced correctly for `id_npcr`, or the overall rates are too high.

Since `id_sgod`, `id_jj65`, and hopefully now `id_0qoe` are well-parameterized by `k1, k2, k3`, the remaining issues are `id_npcr` and `id_l2xx`.
These two are linked: if `id_npcr` is low, R3 is slow, so `id_l2xx` is low.
If `id_npcr` could be magically fixed to 0.08, then `id_l2xx` would be `(k3 * [0qoe] * 0.08 * 0.08) / (k4 * 0.08 * 0.08) = k3/k4 * [0qoe]`.
This is the same dependency.

The fact that `id_npcr` is consistently low suggests that the sum of fluxes `F1+F2+F3` is too high throughout the simulation.
Current `k1, k2, k3` values are `9.5, 580, 27`. These are much lower than initial guesses or early successful iterations (e.g. Iter 3: `10, 12000, 4000`).
This implies that the system is sensitive, and `id_npcr` is a key constraint.

If this iteration doesn't significantly improve `id_npcr` (it likely won't, due to increased `k3`), then the next step might be to try a global scaling down of `k1, k2, k3` while trying to maintain their ratios, or specifically target `id_npcr` by reducing the largest contributor if identifiable.

Let's proceed with the current parameters. The sum of errors is very low, so we are close on many species.

## Action

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

# SBML model from Iteration 11 is the current best
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants from Iteration 12 thoughts
new_k1_val = 9.5
new_k2_val = 580.0
new_k3_val = 27.0 
new_k4_val = 38.0

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
        else:
            print(f"Warning: KineticLaw not found for {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter12 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter12", updated_sbml_string_iter12)
sim_data_iter12 = simulate(updated_sbml_string_iter12)
shared_variables.add("iteration_12_sim_data", sim_data_iter12)

exp_data_iter0 = experiment_history['iteration_0']
print("Experimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter12.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter12 = sim_data_iter12.iloc[-1]

comparison_iter12 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter12})
comparison_iter12['Difference'] = comparison_iter12['Experimental'] - comparison_iter12['Simulated']
comparison_iter12['RelativeDifference (%)'] = (comparison_iter12['Difference'].abs() / comparison_iter12['Experimental']) * 100
comparison_iter12['RelativeDifference (%)'] = comparison_iter12['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter12.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter12[exp_final == 0]) / 1.0 * 100 
comparison_iter12 = comparison_iter12.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 12:")
print(comparison_iter12)

# Compare with Iteration 11 data as that was the previous best
prev_sim_data = shared_variables.access("iteration_11_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter12.loc[comparison_iter12.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 11): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 12): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 12) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter12)
else:
    print("Current model (Iter 12) is NOT an improvement.")
```
# Observation

## Code Stdout
Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=9.5, k2=580.0, k3=27.0, k4=38.0):
id_g7mj      5.982698
id_l2xx      0.000019
id_sgod      0.003665
id_jj65      0.000061
id_t6k9      0.080000
id_3r8d      1.994233
id_npcr      0.013139
id_0qoe      0.002022
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 12:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.982698    0.231094                3.719046
id_l2xx      0.001719    0.000019    0.001700               98.894228
id_sgod      0.003438    0.003665   -0.000226                6.578940
id_jj65      0.000055    0.000061   -0.000006               11.538176
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.994233    0.069114                3.349608
id_npcr      0.080357    0.013139    0.067218               83.649717
id_0qoe      0.002412    0.002022    0.000390               16.158114
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous iter 11): 249.01394836712433
Sum of absolute relative differences (current iter 12): 223.88782895248812
Current model (Iter 12) is an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data, current_sbml_model_iter6, iteration_6_sim_data, current_sbml_model_iter7, iteration_7_sim_data, current_sbml_model_iter8, iteration_8_sim_data, current_sbml_model_iter9, iteration_9_sim_data, current_sbml_model_iter10, iteration_10_sim_data, current_sbml_model_iter11, iteration_11_sim_data, current_sbml_model_iter12, iteration_12_sim_data)

### 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

Iteration 12 (k1=9.5, k2=580, k3=27, k4=38) was an improvement! Sum of errors decreased from ~249.01 (Iter 11) to ~223.88. This is good continued progress.

Current model (Iter 12): `k1=9.5, k2=580, k3=27, k4=38`
Results:
-   `id_g7mj`: 3.7% low (Stable)
-   `id_l2xx`: 98.9% low (Sim 1.9e-5, Exp 1.7e-3) -> Needs Exp/Sim = 90x increase. (Worsened slightly from 50x)
-   `id_sgod`: 6.5% high (Sim 0.003665, Exp 0.003438) -> Was 7.98% high. Slight improvement, still good.
-   `id_jj65`: 11.5% high (Sim 6.1e-5, Exp 5.5e-5) -> Was 3.7% low. Overshot slightly.
-   `id_npcr`: 83.6% low (Sim 0.013139, Exp 0.080357) -> Needs Exp/Sim = 6.1x increase. (No change, still very bad).
-   `id_0qoe`: 16.1% low (Sim 0.002022, Exp 0.002412) -> Was 48.5% high. Excellent! `k3=27` is very good.
-   Products (`id_3r8d`): 3.3% low (Stable)

Key takeaways:
-   `id_sgod` (`k1=9.5`) and `id_0qoe` (`k2=580, k3=27`) are now excellent.
-   `id_jj65` overshot slightly (11.5% high). `k2=580` is a bit too low.
-   `id_npcr` and `id_l2xx` are still the major problems. `id_npcr` has not improved.

Plan based on Iter 12 (`k1=9.5, k2=580, k3=27, k4=38`):

1.  **`k1`**: Keep `k1 = 9.5`. (`id_sgod` is good).
2.  **`k3`**: Keep `k3 = 27`. (`id_0qoe` is excellent).

3.  **`k2`**: `id_jj65` is 11.5% high (needs `1/(1+0.115) = 0.896x` decrease). `[jj65] ~ k1/k2`. `k1` is constant.
    `k2_new = k2_old / 0.896 = 580 / 0.896 = 647.3`.
    Let `k2 = 640`. (Iter 12 was 580). This increases `k2`.

4.  **`k4`**: `id_l2xx` needs 90x increase. `[l2xx] ~ k3/k4`. `k3` is constant (27).
    `k4_new = k4_old / l2xx_increase_factor = 38 / 90 = 0.42`. Still extremely small.
    Using `k4_new = k3_new * ([0qoe]_target / [l2xx]_target)`:
    `k4_new = 27 * (0.002412 / 0.001719) = 27 * 1.403 = 37.88`.
    This calculation suggests `k4` should be around 38, which it is.
    This means that with `k3=27` and `id_0qoe` at its target, `k4=38` *should* give the correct `id_l2xx`.
    The reason `id_l2xx` is so low must be because `id_0qoe` is not actually at its target *throughout the simulation* or, more likely, `id_npcr` is limiting R3.
    If `id_npcr` is very low, R3 (`k3 * id_0qoe * id_npcr * id_t6k9`) will be slow, thus producing very little `id_l2xx`.
    So, `id_l2xx` cannot be fixed without fixing `id_npcr`.

Parameters for this iteration, focusing on `k2` and then `id_npcr`:
`k1 = 9.5`
`k2 = 640`
`k3 = 27`
`k4 = 38` (Keep from previous, as it's theoretically correct if upstream is fine)

Expected impact:
-   `id_sgod`, `id_0qoe`: Should remain excellent.
-   `id_jj65`: `k1/k2 = 9.5/640 = 0.0148`. Iter 12 `k1/k2 = 9.5/580 = 0.0163`. Ratio decreased `0.0148/0.0163 = 0.907x`. Target was 0.896x decrease. `id_jj65` should be excellent.
-   `id_npcr`: `k2` increased (580->640). This will consume *more* `id_npcr`, which is bad. This is a major risk.
-   `id_l2xx`: Unlikely to change much if `id_npcr` remains low.
-   Products: Stable.

The increase in `k2` to fix `id_jj65` will worsen `id_npcr`. This is a problem.
This suggests that the `k1/k2` ratio is good for `id_jj65`, and `k2/k3` for `id_0qoe`, but the absolute magnitudes of `k1,k2,k3` are too high for `id_npcr`.

If `id_sgod`, `id_jj65`, `id_0qoe` are all good, this means the ratios `k1/k2` and `k2/k3` are good.
Let current values be `k1o=9.5, k2o=640, k3o=27`.
The problem is `id_npcr` (needs 6.1x increase, meaning consumption needs to decrease).
And `id_l2xx` (needs 90x increase, meaning `k3/k4` ratio needs to be much higher, or `k4` much lower).

Let's try scaling `k1, k2, k3` down by a common factor to address `id_npcr`.
If `id_npcr` needs to increase by 6.1x, the consumption rate needs to decrease significantly.
A factor of 2 reduction in `k1,k2,k3`:
`k1_new = 9.5 / 2 = 4.75`
`k2_new = 640 / 2 = 320`
`k3_new = 27 / 2 = 13.5`
This should:
-   Help `id_npcr` significantly.
-   Keep `id_jj65` and `id_0qoe` relative levels good (since `k1/k2` and `k2/k3` ratios are preserved).
-   `id_sgod` will become under-consumed (since `k1` is halved). This is a trade-off.

Now for `k4`. `id_l2xx` needs 90x increase.
`k4_new = k3_new * ([0qoe]_exp / [l2xx]_exp) = 13.5 * 1.403 = 18.94`.
Let `k4 = 19`.

New parameters with scaling:
`k1 = 4.75`
`k2 = 320`
`k3 = 13.5`
`k4 = 19`

This is a more drastic attempt to fix `id_npcr`.
The main negative consequence will be `id_sgod` becoming too high (under-consumed).
But if `id_npcr` gets fixed, the whole system might behave more predictably.

## Action

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

# SBML model from Iteration 12 is the current best
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants from Iteration 13 thoughts (scaling down k1,k2,k3)
new_k1_val = 4.75
new_k2_val = 320.0 
new_k3_val = 13.5
new_k4_val = 19.0

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
        else:
            print(f"Warning: KineticLaw not found for {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter13 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter13", updated_sbml_string_iter13)
sim_data_iter13 = simulate(updated_sbml_string_iter13)
shared_variables.add("iteration_13_sim_data", sim_data_iter13)

exp_data_iter0 = experiment_history['iteration_0']
print("Experimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter13.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter13 = sim_data_iter13.iloc[-1]

comparison_iter13 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter13})
comparison_iter13['Difference'] = comparison_iter13['Experimental'] - comparison_iter13['Simulated']
comparison_iter13['RelativeDifference (%)'] = (comparison_iter13['Difference'].abs() / comparison_iter13['Experimental']) * 100
comparison_iter13['RelativeDifference (%)'] = comparison_iter13['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter13.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter13[exp_final == 0]) / 1.0 * 100 
comparison_iter13 = comparison_iter13.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 13:")
print(comparison_iter13)

# Compare with Iteration 12 data as that was the previous best
prev_sim_data = shared_variables.access("iteration_12_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter13.loc[comparison_iter13.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 12): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 13): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 13) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter13)
else:
    print("Current model (Iter 13) is NOT an improvement.")
```
# Observation

## Code Stdout
Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=4.75, k2=320.0, k3=13.5, k4=19.0):
id_g7mj      5.965348
id_l2xx      0.000076
id_sgod      0.007327
id_jj65      0.000110
id_t6k9      0.080000
id_3r8d      1.988449
id_npcr      0.026238
id_0qoe      0.004037
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 13:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.965348    0.248444                3.998266
id_l2xx      0.001719    0.000076    0.001643               95.562434
id_sgod      0.003438    0.007327   -0.003888              113.083118
id_jj65      0.000055    0.000110   -0.000056              101.775188
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.988449    0.074897                3.629900
id_npcr      0.080357    0.026238    0.054118               67.347776
id_0qoe      0.002412    0.004037   -0.001625               67.359693
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous iter 12): 223.88782895248812
Sum of absolute relative differences (current iter 13): 452.75637561647
Current model (Iter 13) is NOT an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data, current_sbml_model_iter6, iteration_6_sim_data, current_sbml_model_iter7, iteration_7_sim_data, current_sbml_model_iter8, iteration_8_sim_data, current_sbml_model_iter9, iteration_9_sim_data, current_sbml_model_iter10, iteration_10_sim_data, current_sbml_model_iter11, iteration_11_sim_data, current_sbml_model_iter12, iteration_12_sim_data, current_sbml_model_iter13, iteration_13_sim_data)

### 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

Iteration 13 (scaling down k1,k2,k3 by 2x: `k1=4.75, k2=320, k3=13.5, k4=19`) was NOT an improvement. Sum of errors increased from ~224 (Iter 12) to ~452.
The "best_sbml_model_so_far" is from Iteration 12:
`k1=9.5, k2=580, k3=27, k4=38`

Results for Iteration 12 model:
-   `id_g7mj`: 3.7% low
-   `id_l2xx`: 98.9% low (Sim 1.9e-5, Exp 1.7e-3) -> Needs Exp/Sim = 90x increase.
-   `id_sgod`: 6.5% high (Sim 0.003665, Exp 0.003438) -> Good.
-   `id_jj65`: 11.5% high (Sim 6.1e-5, Exp 5.5e-5) -> Good.
-   `id_npcr`: 83.6% low (Sim 0.013139, Exp 0.080357) -> Needs Exp/Sim = 6.1x increase. (Still very bad).
-   `id_0qoe`: 16.1% low (Sim 0.002022, Exp 0.002412) -> Good.
-   Products (`id_3r8d`): 3.3% low

Changes from Iter 12 to Iter 13 and their effects:
-   `k1`: 9.5 -> 4.75. `id_sgod` in Iter 13 was 113% high (Sim 0.0073 vs Exp 0.0034). Much worse. `k1=4.75` is too low.
-   `k2`: 580 -> 320. `id_jj65` in Iter 13 was 101% high (Sim 1.1e-4 vs Exp 5.5e-5). Much worse.
-   `k3`: 27 -> 13.5. `id_0qoe` in Iter 13 was 67% high (Sim 0.0040 vs Exp 0.0024). Much worse.
-   `k4`: 38 -> 19. `id_l2xx` in Iter 13 was 95% low. Still terrible.
-   `id_npcr`: 0.013139 -> 0.026238. This was the only significant improvement (67% low vs 83% low). `id_npcr` doubled, but still 3x too low.

The scaling down approach failed because it ruined the already good fits for `id_sgod`, `id_jj65`, `id_0qoe`.
The improvement in `id_npcr` confirms that reducing the overall rates of R1, R2, R3 helps `id_npcr`.
However, the ratios `k1/k2` and `k2/k3` are finely tuned for `id_jj65` and `id_0qoe` with the higher `k` values.

We need to reduce `id_npcr` consumption without disturbing `id_sgod`, `id_jj65`, `id_0qoe` too much.
The current best parameters `k1=9.5, k2=580, k3=27` give good `id_sgod`, `id_jj65` (slightly high), `id_0qoe` (slightly low).
`id_npcr` is consumed by R1, R2, R3.
Fluxes (approx, using target conc for intermediates, and sim `id_npcr`):
`F1 ~ k1*sgod*npcr*cat = 9.5 * 0.0034 * 0.013 * 0.08 = 3.3e-5`
`F2 ~ k2*jj65*npcr*cat = 580 * 5.5e-5 * 0.013 * 0.08 = 3.3e-5`
`F3 ~ k3*0qoe*npcr*cat = 27 * 0.0024 * 0.013 * 0.08 = 6.7e-5`
It seems F3 is the largest consumer of `id_npcr` under these (final time, low `id_npcr`) conditions.
However, earlier in the reaction, when `id_sgod` is high, F1 would be dominant. When `id_jj65` is high, F2 would be.

The problem is that `id_npcr` is depleted too much *over the entire time course*.
If we reduce `k1, k2, k3` by a smaller common factor than 2x? Say 1.5x?
`k1_new = 9.5 / 1.5 = 6.33`
`k2_new = 580 / 1.5 = 386`
`k3_new = 27 / 1.5 = 18`
This would make `id_sgod` worse (more under-consumed). `id_jj65` and `id_0qoe` would retain their current error percentages relative to the new flux.

Let's adjust from Iter 12 parameters (`k1=9.5, k2=580, k3=27, k4=38`):
-   `id_jj65` is 11.5% high. Needs `k2` to increase slightly. `k2_new = 580 * 1.115 = 646`. Let `k2 = 640`. (This was done in the thoughts for Iter 13, but then scaled).
-   With `k2=640`, `id_0qoe` (16.1% low with `k2=580, k3=27`) needs to be adjusted.
    Old ratio `k2/k3 = 580/27 = 21.48`. Target ratio for `id_0qoe` to be perfect: `21.48 / (1-0.161) = 21.48 / 0.839 = 25.6`.
    `k3_new = k2_new / 25.6 = 640 / 25.6 = 25`.
So, `k1=9.5, k2=640, k3=25`.
These values for `k1,k2,k3` should give excellent `id_sgod, id_jj65, id_0qoe`.
`k4` was 38. `k4_new = k3_new * ([0qoe]_exp/[l2xx]_exp) = 25 * 1.403 = 35`.
Let `k4 = 35`.

Parameters:
`k1 = 9.5`
`k2 = 640`
`k3 = 25`
`k4 = 35`

This set primarily fine-tunes `k2` and `k3` from Iter 12 to perfect `id_jj65` and `id_0qoe`.
`k2` increased from 580 to 640 (bad for `id_npcr`).
`k3` decreased from 27 to 25 (good for `id_npcr`).
Net effect on `id_npcr` might be small, possibly slightly worse.
`id_l2xx` will still be very low.

At this point, if `id_npcr` and `id_l2xx` do not improve, it's highly indicative that the model structure or kinetic forms are insufficient for these species, or there's a very specific global rate issue.
The problem states "discover the missing reactions". So far, I've assumed the reaction structure from my initial hypothesis is correct and only tuned parameters.
The initial hypothesis was:
1.  R1: `id_sgod + id_npcr -> id_jj65` (cat `id_t6k9`)
2.  R2: `id_jj65 + id_npcr -> id_0qoe` (cat `id_t6k9`)
3.  R3: `id_0qoe + id_npcr -> id_l2xx` (cat `id_t6k9`)
4.  R4: `id_l2xx -> 3 id_g7mj + 1 id_3r8d` (cat `id_t6k9`)

This consumes 3 `id_npcr` for 1 `id_sgod`.
Exp `id_sgod` consumed: `2 - 0.003438 = 1.996562`.
Exp `id_npcr` consumed: `6 - 0.080357 = 5.919643`.
Ratio `id_npcr`_consumed / `id_sgod`_consumed = `5.919643 / 1.996562 = 2.965`.
This is very close to 3:1, supporting the stoichiometry of `id_npcr` consumption.

If `id_npcr` is consistently too low at the end, it means the *rate* of its consumption is too high, integrated over time.
The current parameter set (`k1=9.5, k2=640, k3=25, k4=35`) is my best attempt to fit `id_sgod, id_jj65, id_0qoe`.
Let's see this result. If `id_npcr` is still bad, I need to consider a different strategy for `id_npcr`.

Perhaps an experiment is needed if parameters can't resolve this.
For example, changing initial `id_npcr` or `id_sgod` could reveal more about their consumption kinetics.
However, I should try to optimize parameters first.

The sum of errors is already quite low (~223). `id_npcr` (83% error) and `id_l2xx` (98% error) contribute most to this.
If these two were perfect, error would be `223 - 83 - 98 = 42`. This would be excellent.

Consider the possibility that `id_t6k9` is not a simple catalyst but is consumed and regenerated, or its concentration affects rates non-linearly. But this is beyond simple parameter changes for existing reactions.

Let's run with `k1=9.5, k2=640, k3=25, k4=35`.

## Action

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

# SBML model from Iteration 12 is the current best
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants from Iteration 14 thoughts
new_k1_val = 9.5
new_k2_val = 640.0 
new_k3_val = 25.0
new_k4_val = 35.0

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
        else:
            print(f"Warning: KineticLaw not found for {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter14 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter14", updated_sbml_string_iter14)
sim_data_iter14 = simulate(updated_sbml_string_iter14)
shared_variables.add("iteration_14_sim_data", sim_data_iter14)

exp_data_iter0 = experiment_history['iteration_0']
print("Experimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter14.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter14 = sim_data_iter14.iloc[-1]

comparison_iter14 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter14})
comparison_iter14['Difference'] = comparison_iter14['Experimental'] - comparison_iter14['Simulated']
comparison_iter14['RelativeDifference (%)'] = (comparison_iter14['Difference'].abs() / comparison_iter14['Experimental']) * 100
comparison_iter14['RelativeDifference (%)'] = comparison_iter14['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter14.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter14[exp_final == 0]) / 1.0 * 100 
comparison_iter14 = comparison_iter14.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 14:")
print(comparison_iter14)

# Compare with Iteration 12 data as that was the previous best
prev_sim_data = shared_variables.access("iteration_12_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter14.loc[comparison_iter14.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 12): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 14): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 14) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter14)
else:
    print("Current model (Iter 14) is NOT an improvement.")
```
# Observation

## Code Stdout
Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=9.5, k2=640.0, k3=25.0, k4=35.0):
id_g7mj      5.982265
id_l2xx      0.000021
id_sgod      0.003598
id_jj65      0.000054
id_t6k9      0.080000
id_3r8d      1.994088
id_npcr      0.013141
id_0qoe      0.002238
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 14:
         Experimental   Simulated    Difference  RelativeDifference (%)
id_g7mj      6.213792    5.982265  2.315276e-01                3.726028
id_l2xx      0.001719    0.000021  1.697619e-03               98.768781
id_sgod      0.003438    0.003598 -1.595889e-04                4.641308
id_jj65      0.000055    0.000054  4.983479e-07                0.910866
id_t6k9      0.080000    0.080000  0.000000e+00                0.000000
id_3r8d      2.063347    1.994088  6.925864e-02                3.356617
id_npcr      0.080357    0.013141  6.721565e-02               83.646722
id_0qoe      0.002412    0.002238  1.738744e-04                7.207909
Time       100.000000  100.000000  0.000000e+00                0.000000

Sum of absolute relative differences (previous iter 12): 223.88782895248812
Sum of absolute relative differences (current iter 14): 202.25822980340192
Current model (Iter 14) is an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data, current_sbml_model_iter6, iteration_6_sim_data, current_sbml_model_iter7, iteration_7_sim_data, current_sbml_model_iter8, iteration_8_sim_data, current_sbml_model_iter9, iteration_9_sim_data, current_sbml_model_iter10, iteration_10_sim_data, current_sbml_model_iter11, iteration_11_sim_data, current_sbml_model_iter12, iteration_12_sim_data, current_sbml_model_iter13, iteration_13_sim_data, current_sbml_model_iter14, iteration_14_sim_data)

### 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

Iteration 14 (k1=9.5, k2=640, k3=25, k4=35) was an improvement! Sum of errors decreased from ~223.88 (Iter 12) to ~202.26. This is excellent.

Current model (Iter 14): `k1=9.5, k2=640, k3=25, k4=35`
Results:
-   `id_g7mj`: 3.7% low (Stable)
-   `id_l2xx`: 98.7% low (Sim 2.1e-5, Exp 1.7e-3) -> Needs Exp/Sim = 80x increase. (Still terrible)
-   `id_sgod`: 4.6% high (Sim 0.003598, Exp 0.003438) -> Excellent.
-   `id_jj65`: 0.9% low (Sim 5.4e-5, Exp 5.5e-5) -> Excellent!
-   `id_npcr`: 83.6% low (Sim 0.013141, Exp 0.080357) -> Needs Exp/Sim = 6.1x increase. (No change, still very bad).
-   `id_0qoe`: 7.2% low (Sim 0.002238, Exp 0.002412) -> Excellent!
-   Products (`id_3r8d`): 3.3% low (Stable)

Key takeaways:
-   `id_sgod`, `id_jj65`, `id_0qoe` are now excellent. This means `k1=9.5`, `k2=640`, `k3=25` and their ratios are very well tuned for these species.
-   `id_npcr` and `id_l2xx` are still the major problems. `id_npcr` has not improved. `id_l2xx` is critically dependent on `id_npcr` (via R3 flux) and `k4`.

The fact that `id_sgod, id_jj65, id_0qoe` are well-fit while `id_npcr` is massively off suggests that the consumption of `id_npcr` relative to `id_sgod` (and subsequent intermediates) is too high in the model.
The overall stoichiometry `1 id_sgod` to `3 id_npcr` seems correct from experimental data.
The model implements this: R1 consumes 1 `id_npcr`, R2 consumes 1 `id_npcr`, R3 consumes 1 `id_npcr`.

If `k1, k2, k3` are now "correct" for the fluxes of `id_sgod -> id_jj65 -> id_0qoe`, then the only way to reduce `id_npcr` consumption without altering these fluxes is if `id_npcr`'s role in the rate laws is different.
E.g., if one of the reactions had a lower order dependency on `id_npcr`. But we assume mass-action.

The problem might be that the *balance* of `id_npcr` consumption across R1, R2, R3 is such that it's depleted too quickly.
Or, the overall magnitude of `k1, k2, k3` is too high, leading to fast initial depletion of `id_npcr`.

Let's try a targeted reduction of `k1, k2, k3` by a common factor, aiming to improve `id_npcr`.
`id_npcr` needs a 6.1x increase in its final concentration. This means its consumption rate needs to decrease significantly.
Let's try reducing `k1, k2, k3` by a factor of `sqrt(6.1) ~ 2.5`. This is a guess that the effect on final concentration might be non-linear. A 2.5x reduction in rates might lead to a significant increase in final `id_npcr`.

Current `k1=9.5, k2=640, k3=25`.
`k1_new = 9.5 / 2.5 = 3.8`
`k2_new = 640 / 2.5 = 256`
`k3_new = 25 / 2.5 = 10`

This will:
-   Preserve `k1/k2` and `k2/k3` ratios, so `id_jj65` and `id_0qoe` should remain well-fitted *relative to the flux they receive*.
-   `id_sgod` will be significantly under-consumed (since `k1` is much lower). This is a known trade-off for this attempt.
-   `id_npcr` should improve significantly.

Now for `k4`. `id_l2xx` needs ~80x increase.
`k4_new = k3_new * ([0qoe]_exp / [l2xx]_exp) = 10 * 1.403 = 14.03`.
Let `k4 = 14`. (Iter 14 was 35).

Parameters for this iteration:
`k1 = 3.8`
`k2 = 256`
`k3 = 10`
`k4 = 14`

This is a bold move to fix `id_npcr`. It will likely make `id_sgod` worse, but if `id_npcr` improves substantially, it might reveal a better overall balance.
If `id_npcr` gets much better, and `id_l2xx` also improves due to higher `id_npcr` boosting R3, then we can fine-tune `k1` (for `id_sgod`) and `k4` (for products and `id_l2xx` final level).

The sum of errors is ~202. `id_npcr` contributes ~83 and `id_l2xx` ~98. If these are fixed, the error would be very low. This justifies a strong attempt to fix them, even at temporary cost to `id_sgod`.

## Action

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

# SBML model from Iteration 14 is the current best
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants from Iteration 15 thoughts
new_k1_val = 3.8
new_k2_val = 256.0 
new_k3_val = 10.0
new_k4_val = 14.0

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
        else:
            print(f"Warning: KineticLaw not found for {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter15 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter15", updated_sbml_string_iter15)
sim_data_iter15 = simulate(updated_sbml_string_iter15)
shared_variables.add("iteration_15_sim_data", sim_data_iter15)

exp_data_iter0 = experiment_history['iteration_0']
print("Experimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter15.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter15 = sim_data_iter15.iloc[-1]

comparison_iter15 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter15})
comparison_iter15['Difference'] = comparison_iter15['Experimental'] - comparison_iter15['Simulated']
comparison_iter15['RelativeDifference (%)'] = (comparison_iter15['Difference'].abs() / comparison_iter15['Experimental']) * 100
comparison_iter15['RelativeDifference (%)'] = comparison_iter15['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter15.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter15[exp_final == 0]) / 1.0 * 100 
comparison_iter15 = comparison_iter15.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 15:")
print(comparison_iter15)

# Compare with Iteration 14 data as that was the previous best
prev_sim_data = shared_variables.access("iteration_14_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter15.loc[comparison_iter15.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 14): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 15): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 15) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter15)
else:
    print("Current model (Iter 15) is NOT an improvement.")
```
# Observation

## Code Stdout
Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=3.8, k2=256.0, k3=10.0, k4=14.0):
id_g7mj      5.955508
id_l2xx      0.000133
id_sgod      0.008978
id_jj65      0.000135
id_t6k9      0.080000
id_3r8d      1.985169
id_npcr      0.032788
id_0qoe      0.005584
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 15:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.955508    0.258284                4.156622
id_l2xx      0.001719    0.000133    0.001586               92.251500
id_sgod      0.003438    0.008978   -0.005539              161.095304
id_jj65      0.000055    0.000135   -0.000081              147.241710
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.985169    0.078177                3.788863
id_npcr      0.080357    0.032788    0.047569               59.197015
id_0qoe      0.002412    0.005584   -0.003172              131.502622
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous iter 14): 202.25822980340192
Sum of absolute relative differences (current iter 15): 599.2336353412727
Current model (Iter 15) is NOT an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data, current_sbml_model_iter6, iteration_6_sim_data, current_sbml_model_iter7, iteration_7_sim_data, current_sbml_model_iter8, iteration_8_sim_data, current_sbml_model_iter9, iteration_9_sim_data, current_sbml_model_iter10, iteration_10_sim_data, current_sbml_model_iter11, iteration_11_sim_data, current_sbml_model_iter12, iteration_12_sim_data, current_sbml_model_iter13, iteration_13_sim_data, current_sbml_model_iter14, iteration_14_sim_data, current_sbml_model_iter15, iteration_15_sim_data)

### 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

Iteration 15 (scaling down k1,k2,k3 by 2.5x: `k1=3.8, k2=256, k3=10, k4=14`) was NOT an improvement. Sum of errors increased from ~202 (Iter 14) to ~599.
The "best_sbml_model_so_far" is from Iteration 14:
`k1=9.5, k2=640, k3=25, k4=35`

Results for Iteration 14 model:
-   `id_g7mj`: 3.7% low
-   `id_l2xx`: 98.7% low (Sim 2.1e-5, Exp 1.7e-3) -> Needs Exp/Sim = 80x increase.
-   `id_sgod`: 4.6% high (Sim 0.003598, Exp 0.003438) -> Excellent.
-   `id_jj65`: 0.9% low (Sim 5.4e-5, Exp 5.5e-5) -> Excellent!
-   `id_npcr`: 83.6% low (Sim 0.013141, Exp 0.080357) -> Needs Exp/Sim = 6.1x increase. (Still very bad).
-   `id_0qoe`: 7.2% low (Sim 0.002238, Exp 0.002412) -> Excellent!
-   Products (`id_3r8d`): 3.3% low

Changes from Iter 14 to Iter 15 and their effects:
-   `k1`: 9.5 -> 3.8. `id_sgod` in Iter 15 was 161% high (Sim 0.0089 vs Exp 0.0034). Much worse.
-   `k2`: 640 -> 256. `id_jj65` in Iter 15 was 147% high (Sim 1.35e-4 vs Exp 5.5e-5). Much worse.
-   `k3`: 25 -> 10. `id_0qoe` in Iter 15 was 131% high (Sim 0.0055 vs Exp 0.0024). Much worse.
-   `k4`: 35 -> 14. `id_l2xx` in Iter 15 was 92% low (Sim 1.33e-4 vs Exp 1.7e-3). Improved from 98% low, but still terrible.
-   `id_npcr`: 0.013141 -> 0.032788. This was a significant improvement (59% low vs 83% low). `id_npcr` more than doubled.

The scaling down approach (by 2.5x) improved `id_npcr` and `id_l2xx` somewhat, but at a huge cost to `id_sgod, id_jj65, id_0qoe`.
This confirms that `id_npcr` benefits from lower overall rates of R1,R2,R3.
The ratios `k1/k2` and `k2/k3` from Iter 14 are good for `id_jj65` and `id_0qoe` *when `k1,k2,k3` are at those higher magnitudes*. When scaled down, the system behaves differently, likely due to `id_npcr` levels.

We need to find a balance. The Iter 14 parameters (`k1=9.5, k2=640, k3=25, k4=35`) are good for most species except `id_npcr` and `id_l2xx`.
The Iter 15 scaling improved `id_npcr` from 83% low to 59% low (target is 0% low). This is a factor of `(1-0.59)/(1-0.83) = 0.41/0.17 = 2.4x` improvement in closeness to target.
The scaling factor for `k` values was 2.5x.

Let's try a more moderate scaling down from Iter 14 parameters.
If a 2.5x reduction in `k1,k2,k3` improved `id_npcr` from 6.1x too low to `0.0803/0.0327 = 2.45x` too low.
This is not a linear relationship.

Let's try scaling Iter 14's `k1, k2, k3` by a factor `f`.
`id_npcr_sim_iter14 = 0.013141`. `id_npcr_exp = 0.080357`. Ratio `exp/sim = 6.11`.
`id_npcr_sim_iter15 = 0.032788`. Ratio `exp/sim = 2.45`.
Scaling factor `s = 2.5`. `k_new = k_old / s`.
The improvement in `id_npcr` (exp/sim ratio) went from 6.11 to 2.45. `6.11/2.45 = 2.49`. This is very close to `s`.
So, to get `id_npcr` exp/sim ratio from 2.45 to 1 (perfect), we might need to scale `k1,k2,k3` (from Iter 15 values) down by another factor of 2.45.
This would mean an overall scaling from Iter 14 by `2.5 * 2.45 = 6.125x`.
This would make `k1 = 9.5 / 6.125 = 1.55`. This is likely too low and will destroy `id_sgod` fit.

Let's try a smaller scaling factor from Iter 14 values, say 1.5x or 1.75x instead of 2.5x.
Target: `id_npcr` needs to go from 0.013 to 0.08 (6.1x increase).
A 2.5x scaling of `k`s gave `id_npcr` from 0.013 to 0.032 (2.5x increase).
So, if `id_npcr_final ~ C / (sum of effective k's)`, then `k_new = k_old / factor` should give `id_npcr_new ~ id_npcr_old * factor`.
To get `id_npcr` to increase by 6.1x, we might need to scale `k1,k2,k3` down by 6.1x. This is too much.

The relationship is clearly not simple.
Let's try to find a sweet spot for `id_npcr` by adjusting the scaling factor `s`.
Iter 14 (`s=1`): `id_npcr`=0.0131 (83.6% low)
Iter 15 (`s=2.5`): `id_npcr`=0.0328 (59.2% low)
We want `id_npcr`=0.0803.
Let `y = id_npcr_sim`. We have `(1, 0.0131)` and `(2.5, 0.0328)`.
This is not enough points for a good fit.

Let's try scaling Iter 14's `k1,k2,k3` by a factor `s=1.75`.
`k1_new = 9.5 / 1.75 = 5.43`. Let `k1 = 5.4`.
`k2_new = 640 / 1.75 = 365.7`. Let `k2 = 365`.
`k3_new = 25 / 1.75 = 14.28`. Let `k3 = 14`.

This should keep `id_jj65` and `id_0qoe` relative fits okay.
`id_sgod` will be worse (target `k1=9.5`).
`id_npcr` should be between 0.0131 and 0.0328. Hopefully around `0.0131 * 1.75 = 0.023` (if linear, which it isn't perfectly). This is still far from 0.08.

Now for `k4`. `id_l2xx` needs ~80x increase from Iter 14's `2.1e-5`.
`k4_new = k3_new * ([0qoe]_exp / [l2xx]_exp) = 14 * 1.403 = 19.64`.
Let `k4 = 20`. (Iter 14 was 35).

Parameters for this iteration:
`k1 = 5.4`
`k2 = 365`
`k3 = 14`
`k4 = 20`

This is another attempt to balance `id_npcr` improvement with maintaining other fits.
The main risk is `id_sgod` becoming too high (under-consumed).
And `id_jj65`, `id_0qoe` might deviate more than expected due to `id_npcr` changes.

If `id_npcr` remains the primary issue, and `id_l2xx` by extension, it might be that the model cannot capture the `id_npcr` dynamics correctly with simple mass-action kinetics for R1, R2, R3 if `id_t6k9` is just a catalyst.
Perhaps one of the reactions involving `id_npcr` has a different kinetic law (e.g. Michaelis-Menten with respect to `id_npcr`, or inhibition). However, we are only allowed to add reactions or change parameters.

Let's assume the current reaction set is fixed.
The goal is to find the best parameter set.
The current best model (Iter 14) has a sum of errors of 202. This is already quite good.
The largest errors are `id_npcr` (83.6%) and `id_l2xx` (98.7%).
If I submit Iter 14 model, these two will be major penalties.

What if I try to directly target `id_npcr`?
To get `id_npcr` from 0.0131 to 0.0803 (a 6.1x increase), I need to reduce the effective overall rate of `id_npcr` consumption.
The scaling factor `s=2.5` for `k1,k2,k3` resulted in `id_npcr` increasing by `0.0328/0.0131 = 2.5x`.
This suggests `id_npcr_final` is roughly proportional to `1/s` or `s` if `s` is rate multiplier.
So if `k_new = k_old / s_factor`, then `id_npcr_new ~ id_npcr_old * s_factor`.
To get `id_npcr_new = id_npcr_old * 6.1`, we need `s_factor = 6.1`.
This means `k1_new = 9.5/6.1 = 1.55`, `k2_new = 640/6.1 = 105`, `k3_new = 25/6.1 = 4.1`.
This will completely destroy `id_sgod, id_jj65, id_0qoe` fits.

The current approach of iterative refinement of `k1,k2,k3,k4` based on individual species targets seems to have hit a local minimum where `id_sgod,jj65,0qoe` are good, but `npcr,l2xx` are bad.
The scaling attempt (Iter 15) showed `npcr` can be improved at cost to others.

Let's try the moderate scaling: `s=1.75`.
`k1 = 5.4, k2 = 365, k3 = 14, k4 = 20`.

## Action

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

# SBML model from Iteration 14 is the current best
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# New proposed rate constants from Iteration 16 thoughts
new_k1_val = 5.4
new_k2_val = 365.0 
new_k3_val = 14.0
new_k4_val = 20.0

def update_reaction_parameter(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")
        else:
            print(f"Warning: KineticLaw not found for {reaction_id}")
    else:
        print(f"Warning: Reaction {reaction_id} not found")

update_reaction_parameter(model, "R1", "k1", new_k1_val)
update_reaction_parameter(model, "R2", "k2", new_k2_val)
update_reaction_parameter(model, "R3", "k3", new_k3_val)
update_reaction_parameter(model, "R4", "k4", new_k4_val)

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else:
        print(f"Warning: Global parameter {p_id} not found.")

update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter16 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter16", updated_sbml_string_iter16)
sim_data_iter16 = simulate(updated_sbml_string_iter16)
shared_variables.add("iteration_16_sim_data", sim_data_iter16)

exp_data_iter0 = experiment_history['iteration_0']
print("Experimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter16.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter16 = sim_data_iter16.iloc[-1]

comparison_iter16 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter16})
comparison_iter16['Difference'] = comparison_iter16['Experimental'] - comparison_iter16['Simulated']
comparison_iter16['RelativeDifference (%)'] = (comparison_iter16['Difference'].abs() / comparison_iter16['Experimental']) * 100
comparison_iter16['RelativeDifference (%)'] = comparison_iter16['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter16.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter16[exp_final == 0]) / 1.0 * 100 
comparison_iter16 = comparison_iter16.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 16:")
print(comparison_iter16)

# Compare with Iteration 14 data as that was the previous best
prev_sim_data = shared_variables.access("iteration_14_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter16.loc[comparison_iter16.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 14): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 16): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 16) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter16)
else:
    print("Current model (Iter 16) is NOT an improvement.")
```
# Observation

## Code Stdout
Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=5.4, k2=365.0, k3=14.0, k4=20.0):
id_g7mj      5.968584
id_l2xx      0.000066
id_sgod      0.006298
id_jj65      0.000095
id_t6k9      0.080000
id_3r8d      1.989528
id_npcr      0.023097
id_0qoe      0.004014
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 16:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.968584    0.245208                3.946194
id_l2xx      0.001719    0.000066    0.001653               96.176541
id_sgod      0.003438    0.006298   -0.002860               83.168127
id_jj65      0.000055    0.000095   -0.000040               72.865322
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.989528    0.073819                3.577628
id_npcr      0.080357    0.023097    0.057259               71.256647
id_0qoe      0.002412    0.004014   -0.001601               66.382667
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous iter 14): 202.25822980340192
Sum of absolute relative differences (current iter 16): 397.37312597271864
Current model (Iter 16) is NOT an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data, current_sbml_model_iter6, iteration_6_sim_data, current_sbml_model_iter7, iteration_7_sim_data, current_sbml_model_iter8, iteration_8_sim_data, current_sbml_model_iter9, iteration_9_sim_data, current_sbml_model_iter10, iteration_10_sim_data, current_sbml_model_iter11, iteration_11_sim_data, current_sbml_model_iter12, iteration_12_sim_data, current_sbml_model_iter13, iteration_13_sim_data, current_sbml_model_iter14, iteration_14_sim_data, current_sbml_model_iter15, iteration_15_sim_data, current_sbml_model_iter16, iteration_16_sim_data)

### 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

Iteration 16 (scaling down k1,k2,k3 by 1.75x: `k1=5.4, k2=365, k3=14, k4=20`) was NOT an improvement. Sum of errors increased from ~202 (Iter 14) to ~397.
The "best_sbml_model_so_far" is from Iteration 14:
`k1=9.5, k2=640, k3=25, k4=35`

Results for Iteration 14 model (best so far):
-   `id_g7mj`: 3.7% low
-   `id_l2xx`: 98.7% low (Sim 2.1e-5, Exp 1.7e-3) -> Needs Exp/Sim = 80x increase.
-   `id_sgod`: 4.6% high (Sim 0.003598, Exp 0.003438) -> Excellent.
-   `id_jj65`: 0.9% low (Sim 5.4e-5, Exp 5.5e-5) -> Excellent!
-   `id_npcr`: 83.6% low (Sim 0.013141, Exp 0.080357) -> Needs Exp/Sim = 6.1x increase. (Still very bad).
-   `id_0qoe`: 7.2% low (Sim 0.002238, Exp 0.002412) -> Excellent!
-   Products (`id_3r8d`): 3.3% low

The scaling approach to fix `id_npcr` is too disruptive to the already well-fitted species.
The model (Iter 14) fits `id_sgod, id_jj65, id_0qoe` and products very well.
The only remaining significant errors are `id_npcr` (too low) and `id_l2xx` (too low).

These two are linked. If `id_npcr` is low, R3 (`id_0qoe + id_npcr -> id_l2xx`) will be slow, leading to low `id_l2xx`.
The parameters `k1, k2, k3` are tuned for the observed behavior of `id_sgod, id_jj65, id_0qoe`.
If these `k` values are "correct" for these species' transformations, then the `id_npcr` issue might stem from:
1.  The model consuming `id_npcr` too efficiently overall, even if individual step rates (for sgod, jj65, 0qoe) seem right.
2.  A missing reaction that produces `id_npcr` or a reaction that consumes `id_npcr` less than 1 per step. (Not allowed to change stoichiometry of existing reactions, but can add new ones).
3.  The kinetic law for `id_npcr` consumption is not simple mass-action as modelled.

Given the constraints (only add reactions or change parameters), and assuming the current 4-reaction pathway is largely correct for the transformation of `id_sgod` to products:
If `id_npcr` is consumed too much, and we cannot easily reduce `k1,k2,k3` without ruining other fits, what else can be done?

Could there be a reaction that regenerates `id_npcr` from one of the products or intermediates? This seems unlikely for a typical metabolic pathway unless it's a cycle.
Or a reaction that consumes `id_sgod` *without* consuming `id_npcr`? This would mean less `id_npcr` is needed for the observed `id_sgod` consumption, potentially leaving more `id_npcr`.
E.g., `id_sgod -> id_jj65` (R1b, no `id_npcr`).
This would mean R1 is actually two reactions: R1a (`sgod+npcr->jj65`) and R1b (`sgod->jj65`).
This would reduce `id_npcr` demand for a given `id_sgod` consumption.

However, the observed stoichiometry (3 `id_npcr` per `id_sgod`) strongly supports the current pathway structure where each of the first three steps consumes one `id_npcr`. Modifying this fundamental aspect by adding a reaction that bypasses `id_npcr` consumption for one of these steps would contradict this stoichiometric observation.

Let's reconsider `id_l2xx`. It needs an 80x increase.
`k4=35` is in the model. `[l2xx] ~ k3/k4 * [0qoe] * (influence of npcr)`.
If `id_0qoe` is at its target (0.002412), and `id_npcr` was at its target (0.080357), then flux R3 would be `k3 * 0.002412 * 0.080357 * 0.08`.
`k3=25`. Flux R3 ~ `25 * 0.002412 * 0.080357 * 0.08 = 25 * 1.55e-5 = 3.87e-4`.
This flux produces `id_l2xx`.
Consumption of `id_l2xx` is R4: `k4 * [l2xx] * 0.08`.
At steady state for `id_l2xx` (approx): `Production = Consumption`.
`3.87e-4 = k4 * [l2xx] * 0.08`.
`[l2xx] = 3.87e-4 / (k4 * 0.08)`.
If `k4=35`, then `[l2xx] = 3.87e-4 / (35 * 0.08) = 3.87e-4 / 2.8 = 0.000138`.
The experimental `id_l2xx` is `0.001719`.
So, even if `id_npcr` was at its target, the predicted `id_l2xx` (0.000138) is still `0.000138 / 0.001719 = 1/12.4` of the experimental value.
This means `k4` needs to be `~12.4x` smaller than 35, i.e., `k4 ~ 35/12.4 = 2.8`.
This calculation assumed `id_npcr` was at its target. Currently, `id_npcr` is much lower, so R3 flux is even lower, making `id_l2xx` even lower.

This suggests `k4` needs to be very small, around 3.
If `k4=3`, then products will be formed much slower. Current products are only 3-4% low with `k4=35`.
This is the fundamental contradiction that keeps appearing for `id_l2xx` and `k4`.

What if `id_t6k9` is not involved in R4?
R4: `id_l2xx -> 3 id_g7mj + 1 id_3r8d`. Rate = `k4 * [l2xx]`.
If so, `k4` would need to be larger to achieve same flux.
Current R4 rate: `k4_eff * [l2xx]` where `k4_eff = k4 * [id_t6k9] = 35 * 0.08 = 2.8`.
If `id_t6k9` is not in R4, then new `k4` would be `2.8`.
This is the same value derived above if `id_npcr` was fixed.
So, removing `id_t6k9` from R4 and setting `k4=2.8` might give the correct `id_l2xx` level *if R3 produces enough `id_l2xx`*.
And it would give the same product formation rate as `k4=35` with `id_t6k9`.

Let's try modifying R4: remove `id_t6k9` as catalyst, and set `k4` appropriately.
The current `k4=35` (with `id_t6k9=0.08`) gives an effective first-order rate for `id_l2xx` consumption of `35*0.08 = 2.8`.
If R4 is `id_l2xx -> P` with rate `k4_new * [l2xx]`. We want `k4_new = 2.8`.
This change would mean `id_t6k9` is a catalyst for R1, R2, R3 but not R4.
This is a structural model change.

Let's try this:
1. Modify R4 to not include `id_t6k9`.
2. Set `k1=9.5, k2=640, k3=25` (from Iter 14, good for sgod, jj65, 0qoe).
3. Set `k4_new_R4 = 2.8`.

This might fix `id_l2xx` levels if R3 produces enough.
It doesn't directly address `id_npcr`. But if `id_l2xx` is no longer artificially suppressed by a high effective `k4`, the system dynamics might change.

How to modify R4 in SBML:
The kinetic law for R4 is `k4 * id_l2xx * id_t6k9`.
Change to `k4_R4_no_cat * id_l2xx`.
The parameter `k4_R4_no_cat` would be the new `k4`.
The existing `k4` parameter in the model is currently 35.
If I change the formula, I need a new parameter value.
Let the parameter in the kinetic law still be called "k4", but its value will be 2.8.
And remove `id_t6k9` from the formula and as a modifier.

This is a significant hypothesis change.

## Action

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

# SBML model from Iteration 14 is the current best
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far")
sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# Parameters from Iter 14 that were good for sgod, jj65, 0qoe
# k1=9.5, k2=640, k3=25
# Old k4 was 35 (with catalyst id_t6k9=0.08, so effective k4_eff = 35*0.08 = 2.8)
# New k4 for R4 (no catalyst) will be 2.8.

new_k1_val = 9.5
new_k2_val = 640.0 
new_k3_val = 25.0
new_k4_val_for_R4_no_cat = 2.8 # This is the new rate constant for R4

# Update k1, k2, k3 parameters
def update_reaction_parameter_value(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")

update_reaction_parameter_value(model, "R1", "k1", new_k1_val)
update_reaction_parameter_value(model, "R2", "k2", new_k2_val)
update_reaction_parameter_value(model, "R3", "k3", new_k3_val)

# Modify Reaction R4
reaction_R4 = model.getReaction("R4")
if reaction_R4:
    # Remove catalyst id_t6k9 as a modifier if it exists
    num_modifiers = reaction_R4.getNumModifiers()
    modifier_to_remove = None
    for i in range(num_modifiers):
        modifier = reaction_R4.getModifier(i)
        if modifier.getSpecies() == "id_t6k9":
            modifier_to_remove = modifier # Store it to remove outside loop
            break 
    if modifier_to_remove:
        reaction_R4.removeModifier(modifier_to_remove.getSpecies()) # Pass species ID
        print("Removed id_t6k9 as modifier from R4.")

    kinetic_law_R4 = reaction_R4.getKineticLaw()
    if kinetic_law_R4:
        # Update k4 parameter value
        param_k4 = kinetic_law_R4.getParameter("k4")
        if param_k4:
            param_k4.setValue(new_k4_val_for_R4_no_cat)
            print(f"Set k4 in R4 to {new_k4_val_for_R4_no_cat}.")
        else:
            # If k4 param doesn't exist, create it (should exist from previous setup)
            param = kinetic_law_R4.createParameter()
            param.setId("k4")
            param.setValue(new_k4_val_for_R4_no_cat)
            print(f"Created and set k4 in R4 to {new_k4_val_for_R4_no_cat}.")

        # Update Math formula for R4: k4 * id_l2xx
        new_math_formula_R4 = "k4 * id_l2xx"
        math_ast_R4 = libsbml.parseL3Formula(new_math_formula_R4)
        kinetic_law_R4.setMath(math_ast_R4)
        print("Updated R4 kinetic law to k4 * id_l2xx.")
else:
    print("Error: Reaction R4 not found.")

# Update global parameters as well (though local ones in kinetic laws are used by simulator)
def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    else: # If it doesn't exist, create it
        p = model.createParameter()
        p.setId(p_id)
        p.setValue(p_value)
        p.setConstant(True)


update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val_for_R4_no_cat) # k4 global now refers to this new value

writer = libsbml.SBMLWriter()
updated_sbml_string_iter17 = writer.writeSBMLToString(sbml_doc)

# Check for errors in the generated SBML
# print("Modified SBML for Iter 17:\n", updated_sbml_string_iter17) # For debugging

shared_variables.add("current_sbml_model_iter17", updated_sbml_string_iter17)
sim_data_iter17 = simulate(updated_sbml_string_iter17)
shared_variables.add("iteration_17_sim_data", sim_data_iter17)

exp_data_iter0 = experiment_history['iteration_0']
print("\nExperimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values and modified R4 (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4_R4={new_k4_val_for_R4_no_cat}):")
print(sim_data_iter17.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter17 = sim_data_iter17.iloc[-1]

comparison_iter17 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter17})
comparison_iter17['Difference'] = comparison_iter17['Experimental'] - comparison_iter17['Simulated']
comparison_iter17['RelativeDifference (%)'] = (comparison_iter17['Difference'].abs() / comparison_iter17['Experimental']) * 100
comparison_iter17['RelativeDifference (%)'] = comparison_iter17['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter17.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter17[exp_final == 0]) / 1.0 * 100 
comparison_iter17 = comparison_iter17.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 17:")
print(comparison_iter17)

# Compare with Iteration 14 data as that was the previous best
prev_sim_data = shared_variables.access("iteration_14_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter17.loc[comparison_iter17.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 14): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 17): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 17) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter17)
else:
    print("Current model (Iter 17) is NOT an improvement.")
```
# Observation

## Code Stdout
Removed id_t6k9 as modifier from R4.
Set k4 in R4 to 2.8.
Updated R4 kinetic law to k4 * id_l2xx.

Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values and modified R4 (k1=9.5, k2=640.0, k3=25.0, k4_R4=2.8):
id_g7mj      5.982265
id_l2xx      0.000021
id_sgod      0.003598
id_jj65      0.000054
id_t6k9      0.080000
id_3r8d      1.994088
id_npcr      0.013141
id_0qoe      0.002238
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 17:
         Experimental   Simulated    Difference  RelativeDifference (%)
id_g7mj      6.213792    5.982265  2.315276e-01                3.726027
id_l2xx      0.001719    0.000021  1.697620e-03               98.768787
id_sgod      0.003438    0.003598 -1.595815e-04                4.641093
id_jj65      0.000055    0.000054  4.984535e-07                0.911059
id_t6k9      0.080000    0.080000  0.000000e+00                0.000000
id_3r8d      2.063347    1.994088  6.925863e-02                3.356616
id_npcr      0.080357    0.013141  6.721568e-02               83.646755
id_0qoe      0.002412    0.002238  1.738790e-04                7.208099
Time       100.000000  100.000000  0.000000e+00                0.000000

Sum of absolute relative differences (previous iter 14): 202.25822980340192
Sum of absolute relative differences (current iter 17): 202.2584375148818
Current model (Iter 17) is NOT an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data, current_sbml_model_iter6, iteration_6_sim_data, current_sbml_model_iter7, iteration_7_sim_data, current_sbml_model_iter8, iteration_8_sim_data, current_sbml_model_iter9, iteration_9_sim_data, current_sbml_model_iter10, iteration_10_sim_data, current_sbml_model_iter11, iteration_11_sim_data, current_sbml_model_iter12, iteration_12_sim_data, current_sbml_model_iter13, iteration_13_sim_data, current_sbml_model_iter14, iteration_14_sim_data, current_sbml_model_iter15, iteration_15_sim_data, current_sbml_model_iter16, iteration_16_sim_data, current_sbml_model_iter17, iteration_17_sim_data)

### 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

Iteration 17 (modifying R4 to remove catalyst `id_t6k9`, `k1=9.5, k2=640, k3=25, k4_R4_no_cat=2.8`) was NOT an improvement. The sum of errors was virtually identical to Iteration 14. The simulation output was also identical. This means my SBML modification for R4 did not have the intended effect, or the simulator handled it in a way that defaulted to the previous behavior, or the change was truly neutral.

Let's re-verify the SBML modification logic.
The kinetic law for R4 was `k4 * id_l2xx * id_t6k9`.
The new law should be `k4 * id_l2xx`.
The parameter `k4` in the model (global or local to R4) should be set to `2.8`.
The species `id_t6k9` should be removed as a `modifierSpecies` for R4.

Looking at the output: "Removed id_t6k9 as modifier from R4." and "Set k4 in R4 to 2.8." and "Updated R4 kinetic law to k4 * id_l2xx."
This all seems correct.
The fact that the simulation results are identical to Iteration 14 (where R4 was `k4_val=35 * id_l2xx * id_t6k9`) is puzzling.
`35 * id_t6k9 (0.08) = 2.8`. So the effective rate constant for `id_l2xx` consumption *is* the same.
This means the change was correctly implemented and mathematically equivalent *if `id_t6k9` is constant at 0.08*.
The species `id_t6k9` is indeed constant (initial 0.08, boundaryCondition=false, constant=false, but no reactions consume/produce it in my model). So its concentration effectively acts as part of the rate constant.

So, the structural change to R4 (removing `id_t6k9` as catalyst and adjusting `k4` value) had no net effect on the simulation because `id_t6k9` was constant anyway.
This means `id_l2xx` remains extremely low because the flux into it from R3 is too low, primarily due to low `id_npcr`.

The "best_sbml_model_so_far" is from Iteration 14:
`k1=9.5, k2=640, k3=25, k4=35` (R4 includes `id_t6k9` catalyst).
Error sum ~202.
`id_npcr`: 83.6% low (Sim 0.013141, Exp 0.080357) -> Needs Exp/Sim = 6.1x increase.
`id_l2xx`: 98.7% low (Sim 2.1e-5, Exp 1.7e-3) -> Needs Exp/Sim = 80x increase.

We are stuck on `id_npcr`.
The previous attempt to scale down `k1,k2,k3` (Iter 15, 16) improved `id_npcr` but ruined other fits.
Iter 15 (2.5x scaling): `id_npcr` went from 83.6% low to 59.2% low. (Sim from 0.013 to 0.032)
Iter 16 (1.75x scaling): `id_npcr` went from 83.6% low to 71.2% low. (Sim from 0.013 to 0.023)

This suggests a relationship: `id_npcr_final ~ C * (1/scaling_factor_for_ks)`.
Or `id_npcr_final / id_npcr_final_base = s_base / s_new`.
Let `s` be the scaling factor for `k1,k2,k3` (where `s=1` is Iter 14 values).
`s=1: id_npcr = 0.0131`
`s=1.75: id_npcr = 0.0231` (Ratio `0.0231/0.0131 = 1.76`, close to `s`)
`s=2.5: id_npcr = 0.0328` (Ratio `0.0328/0.0131 = 2.50`, very close to `s`)
So, `id_npcr_final_sim (s) = id_npcr_final_sim (s=1) * s`.
We want `id_npcr_final_sim = 0.080357`.
So, `s = 0.080357 / 0.013141 = 6.115`.
This means we need to scale down `k1,k2,k3` from Iter 14 values by a factor of 6.115.
`k1_new = 9.5 / 6.115 = 1.553`
`k2_new = 640 / 6.115 = 104.66`
`k3_new = 25 / 6.115 = 4.088`

This scaling will make `id_sgod, id_jj65, id_0qoe` much worse, as seen in Iter 15.
However, if `id_npcr` is correct, the system dynamics might be very different.
The rate laws are `k * A * B * npcr * cat`. If `npcr` is now 6x higher, the reactions will be 6x faster for the same `A, B, cat`.
This means the `k` values need to be 6x smaller to achieve the same flux for `A->B` if `npcr` was at its target.
The current `k1,k2,k3` (Iter 14) are tuned for low `id_npcr`.
If `id_npcr` becomes high, these `k` values will be too large.

This implies that the `k` values derived for `id_sgod, id_jj65, id_0qoe` (Iter 14) are effectively `k' = k / [npcr_factor]`, where `npcr_factor` reflects how much lower `npcr` is than its "true" effective level.
This is circular.

Let's assume the Iter 14 parameters (`k1=9.5, k2=640, k3=25`) correctly define the *relative* rates needed for `id_sgod, id_jj65, id_0qoe` if `id_npcr` were not limiting.
If `id_npcr` is actually 6x higher than in the simulation, then to get the same fluxes for `id_sgod, id_jj65, id_0qoe` transformations, the `k` values should be 6x lower.
This is exactly the scaling factor `s=6.115` derived above.

So, the parameters would be:
`k1 = 1.55`
`k2 = 105`
`k3 = 4.1`

Now for `k4`. `id_l2xx` needs ~80x increase from Iter 14's `2.1e-5`.
`k4_new = k3_new * ([0qoe]_exp / [l2xx]_exp) = 4.1 * 1.403 = 5.75`.
Let `k4 = 5.8`. (Iter 14 was 35).

Parameters for this iteration (drastic scaling):
`k1 = 1.55`
`k2 = 105`
`k3 = 4.1`
`k4 = 5.8`

This is a high-risk, high-reward attempt. It prioritizes fixing `id_npcr` by assuming the current `k1,k2,k3` are effectively inflated due to low `id_npcr` in the simulation.
If this works for `id_npcr`, then `id_sgod, id_jj65, id_0qoe` should ideally also be good because their relative `k` values (and thus `k/npcr` effective rates) are maintained.
`id_l2xx` is targeted with the new `k3` and `k4`.
Products will likely be low due to very low `k4`.

I have few iterations left. This is a necessary gamble.

## Action

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

# SBML model from Iteration 14 is the current best.
# Iter 17 was identical to Iter 14 in results, so best_sbml_model_so_far is still effectively Iter 14's model string.
sbml_string_to_modify = shared_variables.access("best_sbml_model_so_far") 
# Ensure it's the original Iter 14 model (R4 with catalyst)
# If Iter 17 model (R4 no cat) was stored as best, results would be same, but for clarity:
# We need to check what 'best_sbml_model_so_far' points to.
# The logic "if sum_rel_diff_curr < sum_rel_diff_prev: update" means Iter 14 model string is indeed the one.

sbml_doc = libsbml.readSBMLFromString(sbml_string_to_modify)
model = sbml_doc.getModel()

# Check R4 structure from "best_sbml_model_so_far" to be sure
# reaction_R4_check = model.getReaction("R4")
# print(f"R4 in best_sbml_model_so_far has {reaction_R4_check.getNumModifiers()} modifiers.")
# kinetic_law_R4_check = reaction_R4_check.getKineticLaw()
# print(f"R4 math: {libsbml.formulaToL3String(kinetic_law_R4_check.getMath())}")
# This check would confirm if it's Iter 14 (1 modifier, k4*l2xx*t6k9) or Iter 17 (0 modifiers, k4*l2xx)

# New proposed rate constants from Iteration 18 thoughts (drastic scaling)
# Based on Iter 14 values: k1=9.5, k2=640, k3=25, k4=35
scaling_factor = 6.115

new_k1_val = 9.5 / scaling_factor
new_k2_val = 640.0 / scaling_factor
new_k3_val = 25.0 / scaling_factor
# k4 is re-derived: k4 = k3_new * (0qoe_exp/l2xx_exp)
# 0qoe_exp/l2xx_exp = 0.002412 / 0.001719 = 1.40314
new_k4_val = new_k3_val * 1.40314 

print(f"Calculated new_k1_val: {new_k1_val}")
print(f"Calculated new_k2_val: {new_k2_val}")
print(f"Calculated new_k3_val: {new_k3_val}")
print(f"Calculated new_k4_val: {new_k4_val}")

# Use rounded/practical values
new_k1_val = 1.55
new_k2_val = 105.0 
new_k3_val = 4.1
new_k4_val = 5.8 # 4.1 * 1.40314 = 5.75

def update_reaction_parameter_value(model, reaction_id, parameter_id, new_value):
    reaction = model.getReaction(reaction_id)
    if reaction:
        kinetic_law = reaction.getKineticLaw()
        if kinetic_law:
            param = kinetic_law.getParameter(parameter_id)
            if param:
                param.setValue(new_value)
            else:
                print(f"Warning: Parameter {parameter_id} not found in KineticLaw of {reaction_id}")

update_reaction_parameter_value(model, "R1", "k1", new_k1_val)
update_reaction_parameter_value(model, "R2", "k2", new_k2_val)
update_reaction_parameter_value(model, "R3", "k3", new_k3_val)
update_reaction_parameter_value(model, "R4", "k4", new_k4_val) # This k4 is for R4 with catalyst

def update_global_parameter(model, p_id, p_value):
    param = model.getParameter(p_id)
    if param:
        param.setValue(p_value)
    # Create if not exists, for robustness, though they should exist
    else:
        p = model.createParameter(); p.setId(p_id); p.setConstant(True)
        param = p
    param.setValue(p_value)


update_global_parameter(model, "k1", new_k1_val)
update_global_parameter(model, "k2", new_k2_val)
update_global_parameter(model, "k3", new_k3_val)
update_global_parameter(model, "k4", new_k4_val)

writer = libsbml.SBMLWriter()
updated_sbml_string_iter18 = writer.writeSBMLToString(sbml_doc)

shared_variables.add("current_sbml_model_iter18", updated_sbml_string_iter18)
sim_data_iter18 = simulate(updated_sbml_string_iter18)
shared_variables.add("iteration_18_sim_data", sim_data_iter18)

exp_data_iter0 = experiment_history['iteration_0']
print("\nExperimental Data Summary (End Time T=100):")
print(exp_data_iter0.iloc[-1])

print(f"\nSimulation Data with new k values (k1={new_k1_val}, k2={new_k2_val}, k3={new_k3_val}, k4={new_k4_val}):")
print(sim_data_iter18.iloc[-1])

exp_final = exp_data_iter0.iloc[-1]
sim_final_iter18 = sim_data_iter18.iloc[-1]

comparison_iter18 = pd.DataFrame({'Experimental': exp_final, 'Simulated': sim_final_iter18})
comparison_iter18['Difference'] = comparison_iter18['Experimental'] - comparison_iter18['Simulated']
comparison_iter18['RelativeDifference (%)'] = (comparison_iter18['Difference'].abs() / comparison_iter18['Experimental']) * 100
comparison_iter18['RelativeDifference (%)'] = comparison_iter18['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
comparison_iter18.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(sim_final_iter18[exp_final == 0]) / 1.0 * 100 
comparison_iter18 = comparison_iter18.fillna(0)

print("\nComparison of Final Values (T=100) - Iteration 18:")
print(comparison_iter18)

# Compare with Iteration 14 data as that was the previous best
prev_sim_data = shared_variables.access("iteration_14_sim_data") 
prev_sim_final = prev_sim_data.iloc[-1]
prev_comparison = pd.DataFrame({'Experimental': exp_final, 'Simulated': prev_sim_final})
prev_comparison['Difference'] = prev_comparison['Experimental'] - prev_comparison['Simulated']
prev_comparison['RelativeDifference (%)'] = (prev_comparison['Difference'].abs() / prev_comparison['Experimental']) * 100
prev_comparison['RelativeDifference (%)'] = prev_comparison['RelativeDifference (%)'].replace([np.inf, -np.inf, np.nan], 100.0)
prev_comparison.loc[exp_final == 0, 'RelativeDifference (%)'] = np.abs(prev_sim_final[exp_final == 0]) / 1.0 * 100
prev_comparison = prev_comparison.fillna(0)

sum_rel_diff_prev = prev_comparison.loc[prev_comparison.index != 'Time', 'RelativeDifference (%)'].sum()
sum_rel_diff_curr = comparison_iter18.loc[comparison_iter18.index != 'Time', 'RelativeDifference (%)'].sum()

print(f"\nSum of absolute relative differences (previous iter 14): {sum_rel_diff_prev}")
print(f"Sum of absolute relative differences (current iter 18): {sum_rel_diff_curr}")

if sum_rel_diff_curr < sum_rel_diff_prev:
    print("Current model (Iter 18) is an improvement.")
    shared_variables.add("best_sbml_model_so_far", updated_sbml_string_iter18)
else:
    print("Current model (Iter 18) is NOT an improvement.")
```
# Observation

## Code Stdout
Calculated new_k1_val: 1.553556827473426
Calculated new_k2_val: 104.66067048242027
Calculated new_k3_val: 4.088307440719542
Calculated new_k4_val: 5.736467702371218

Experimental Data Summary (End Time T=100):
id_g7mj      6.213792
id_l2xx      0.001719
id_sgod      0.003438
id_jj65      0.000055
id_t6k9      0.080000
id_3r8d      2.063347
id_npcr      0.080357
id_0qoe      0.002412
Time       100.000000
Name: 1000, dtype: float64

Simulation Data with new k values (k1=1.55, k2=105.0, k3=4.1, k4=5.8):
id_g7mj      5.890232
id_l2xx      0.000800
id_sgod      0.021936
id_jj65      0.000329
id_t6k9      0.080000
id_3r8d      1.963411
id_npcr      0.079990
id_0qoe      0.013525
Time       100.000000
Name: 1000, dtype: float64

Comparison of Final Values (T=100) - Iteration 18:
         Experimental   Simulated  Difference  RelativeDifference (%)
id_g7mj      6.213792    5.890232    0.323561                5.207135
id_l2xx      0.001719    0.000800    0.000919               53.470128
id_sgod      0.003438    0.021936   -0.018497              537.960526
id_jj65      0.000055    0.000329   -0.000274              500.729810
id_t6k9      0.080000    0.080000    0.000000                0.000000
id_3r8d      2.063347    1.963411    0.099936                4.843407
id_npcr      0.080357    0.079990    0.000366                0.455901
id_0qoe      0.002412    0.013525   -0.011113              460.678897
Time       100.000000  100.000000    0.000000                0.000000

Sum of absolute relative differences (previous iter 14): 202.25822980340192
Sum of absolute relative differences (current iter 18): 1563.3458042510006
Current model (Iter 18) is NOT an improvement.

## 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, iteration_1_sim_data, best_sbml_model_so_far, current_sbml_model_iter2, iteration_2_sim_data, current_sbml_model_iter3, iteration_3_sim_data, current_sbml_model_iter4, iteration_4_sim_data, current_sbml_model_iter5, iteration_5_sim_data, current_sbml_model_iter6, iteration_6_sim_data, current_sbml_model_iter7, iteration_7_sim_data, current_sbml_model_iter8, iteration_8_sim_data, current_sbml_model_iter9, iteration_9_sim_data, current_sbml_model_iter10, iteration_10_sim_data, current_sbml_model_iter11, iteration_11_sim_data, current_sbml_model_iter12, iteration_12_sim_data, current_sbml_model_iter13, iteration_13_sim_data, current_sbml_model_iter14, iteration_14_sim_data, current_sbml_model_iter15, iteration_15_sim_data, current_sbml_model_iter16, iteration_16_sim_data, current_sbml_model_iter17, iteration_17_sim_data, current_sbml_model_iter18, iteration_18_sim_data)

### 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

Iteration 18 (drastic scaling: `k1=1.55, k2=105, k3=4.1, k4=5.8`) was NOT an improvement. Sum of errors increased massively from ~202 (Iter 14) to ~1563.
However, there was a HUGE success:
-   **`id_npcr`**: Sim 0.07999 vs Exp 0.080357 (0.45% low) -> PERFECT!

This is a major breakthrough. The scaling factor of 6.115 for `k1,k2,k3` (from Iter 14 values) correctly predicted the `id_npcr` final concentration.
This confirms the hypothesis: `id_npcr_final_sim (s) = id_npcr_final_sim (s=1) * s`, where `s` is the factor by which `k1,k2,k3` are divided.

The problem now is that `id_sgod, id_jj65, id_0qoe` are terrible with these low `k` values:
-   `id_sgod`: 537% high (Sim 0.0219 vs Exp 0.0034). `k1=1.55` is far too low.
-   `id_jj65`: 500% high (Sim 3.29e-4 vs Exp 5.5e-5). `k1/k2` ratio is preserved, but absolute levels are wrong.
-   `id_0qoe`: 460% high (Sim 0.0135 vs Exp 0.0024). `k2/k3` ratio is preserved.

And `id_l2xx` also improved significantly:
-   `id_l2xx`: 53.4% low (Sim 8.0e-4 vs Exp 1.7e-3). Was 98.7% low. Needs Exp/Sim = 2.1x increase.

This means that if `id_npcr` is at its correct (higher) level, the reactions R1, R2, R3 run much faster than with low `id_npcr`.
The `k` values `k1=1.55, k2=105, k3=4.1` are too low to match `id_sgod, id_jj65, id_0qoe` data *when `id_npcr` is high*.

This implies the original `k` values from Iter 14 (`k1=9.5, k2=640, k3=25`) were tuned for a scenario where `id_npcr` was artificially low in the simulation.
Now that `id_npcr` is correct with `k1=1.55, k2=105, k3=4.1`, these `k` values are too small to drive the transformations of `id_sgod, id_jj65, id_0qoe` at the observed rates.

We need `k` values that are:
1.  Small enough (like `k1=1.55, k2=105, k3=4.1`) so that `id_npcr` is not over-consumed.
2.  Large enough so that `id_sgod, id_jj65, id_0qoe` are consumed/produced correctly *given that `id_npcr` is now at its higher, correct level*.

This seems like a contradiction if the rate law is `k * A * B * npcr * cat`.
If `npcr` is higher, then for the same flux `A->B`, `k` must be lower.
The Iter 18 `k` values are low, `npcr` is high. But `sgod, jj65, 0qoe` are now accumulating (flux `A->B` is too slow).
This means the `k` values `1.55, 105, 4.1` are *still too low* even with high `npcr`.

Let's use Iter 18 as a new baseline because `id_npcr` is perfect.
`k1=1.55, k2=105, k3=4.1, k4=5.8`
-   `id_sgod`: Sim 0.0219 vs Exp 0.0034 (Exp/Sim = 0.155). Needs 0.155x (massive reduction, i.e. more consumption). `k1` needs to increase by `1/0.155 = 6.45x`.
    `k1_new = 1.55 * 6.45 = 10.0`.
-   `id_jj65`: Sim 3.29e-4 vs Exp 5.5e-5 (Exp/Sim = 0.167). Needs 0.167x. `[jj65] ~ k1/k2`.
    `k1` increases by 6.45x.
    `k2_new = k2_old * ( (k1_new/k1_old) / jj65_target_factor_from_sim ) = 105 * (6.45 / (1/0.167)) = 105 * (6.45 / 5.98) = 105 * 1.078 = 113`.
-   `id_0qoe`: Sim 0.0135 vs Exp 0.0024 (Exp/Sim = 0.177). Needs 0.177x. `[0qoe] ~ k2/k3`.
    `k2` changes by `113/105 = 1.076x`.
    `k3_new = k3_old * ( (k2_new/k2_old) / 0qoe_target_factor_from_sim ) = 4.1 * (1.076 / (1/0.177)) = 4.1 * (1.076 / 5.65) = 4.1 * 0.19 = 0.779`.
    This `k3` is very small.

This is essentially re-deriving the Iter 14 parameters, but starting from a state where `id_npcr` is correct.
Iter 14: `k1=9.5, k2=640, k3=25`.
If `k1` needs to be `~10` (from `id_sgod` above).
If `k1/k2` ratio from Iter 14 is good (`9.5/640 = 0.01484`). Then `k2 = 10 / 0.01484 = 673`.
If `k2/k3` ratio from Iter 14 is good (`640/25 = 25.6`). Then `k3 = 673 / 25.6 = 26.3`.

So, the parameters `k1=9.5 (or 10), k2=640 (or 673), k3=25 (or 26.3)` seem to be what's needed for `sgod, jj65, 0qoe` transformations.
BUT, these parameters lead to `id_npcr` being very low (Iter 14 result).
And parameters `k1=1.55, k2=105, k3=4.1` lead to `id_npcr` being correct, but `sgod, jj65, 0qoe` transformations being far too slow.

This is a fundamental conflict with the current model structure and mass-action kinetics.
The model cannot simultaneously satisfy:
a) Correct `id_npcr` final level.
b) Correct rates of transformation for `id_sgod, id_jj65, id_0qoe`.

If I have to choose, fitting the intermediate transformations is usually prioritized, and then `id_npcr` might be a consequence.
The Iter 14 model (`k1=9.5, k2=640, k3=25, k4=35`) has sum of errors 202.
This is the best achieved so far.
The main remaining errors are `id_npcr` (83%) and `id_l2xx` (98%).

Perhaps `id_l2xx` can be improved without breaking other things.
Iter 14: `id_l2xx` needs 80x increase. `k4=35`.
`k4_new = k3_val * ([0qoe]_exp/[l2xx]_exp) = 25 * 1.403 = 35.07`. This was already used.
The calculation for `k4` assumes `id_0qoe` is at its experimental value AND `id_npcr` is at a level that allows R3 to proceed to make enough `id_l2xx`.
Since `id_npcr` is low, R3 is slow, so `id_l2xx` is low.
If `k4` is reduced to compensate for low `id_l2xx` production, products will suffer.

Given I have only 2 iterations left, I should probably submit the best model found so far, which is Iteration 14.
The prompt says "discovering the true underlying mechanisms rather than overfitting to observed data is crucial."
The current model (Iter 14) fits most species well, but fails on `id_npcr` and `id_l2xx`. This suggests a mechanistic issue with `id_npcr` consumption or `id_l2xx` production/consumption that simple parameter tuning of these 4 reactions cannot resolve.

If I were to propose a "missing reaction", it might be one that affects `id_npcr` levels without disrupting the main pathway, or one that affects `id_l2xx` production more directly.
Example: What if `id_npcr` is also produced by some other source, or one of the reactions R1,R2,R3 is reversible?
Reversibility could allow `id_npcr` to be less depleted if products accumulate.

However, the task is to "discover the biological mechanisms missing from your model by designing experiments and analyzing results. You must ultimately express your findings as a complete SBML model".
I have not designed new experiments. I have only used the initial "observe".
The initial model was empty. I added 4 reactions.

If I cannot improve `id_npcr` and `id_l2xx` significantly in one more iteration, I will submit Iter 14 model.
Let's try one more attempt to improve `id_npcr` and `id_l2xx` from Iter 14, even if it slightly worsens others.
The Iter 15 scaling (2.5x) improved `id_npcr` (59% low) and `id_l2xx` (92% low).
Iter 14: `k1=9.5, k2=640, k3=25, k4=35`. `npcr` 83% low, `l2xx` 98% low.
Iter 15 params: `k1=3.8, k2=256, k3=10, k4=14`.
`sgod` error: Iter 14 (4.6% H), Iter 15 (161% H)
`jj65` error: Iter 14 (0.9% L), Iter 15 (147% H)
`0qoe` error: Iter 14 (7.2% L), Iter 15 (131% H)

The improvement in `id_npcr` and `id_l2xx` in Iter 15 came at too high a cost.
Is there an intermediate scaling factor that provides a better compromise?
Scaling factor `s`. `k_new = k_iter14 / s`.
`s=1`: Iter 14. SumErr=202. `npcr_err=83.6`, `l2xx_err=98.7`. `sgod_err=4.6`, `jj65_err=0.9`, `0qoe_err=7.2`.
`s=1.75`: Iter 16. SumErr=397. `npcr_err=71.2`, `l2xx_err=96.1`. `sgod_err=83.1`, `jj65_err=72.8`, `0qoe_err=66.3`.
`s=2.5`: Iter 15. SumErr=599. `npcr_err=59.2`, `l2xx_err=92.2`. `sgod_err=161`, `jj65_err=147`, `0qoe_err=131`.

As `s` increases (k's decrease):
- `npcr_err` decreases (good)
- `l2xx_err` decreases (good)
- `sgod_err` increases (bad)
- `jj65_err` increases (bad)
- `0qoe_err` increases (bad)
The sum of errors increases because the degradation of `sgod,jj65,0qoe` fits outweighs improvements in `npcr,l2xx`.

This means the Iter 14 model is likely the best achievable with this structure by parameter tuning.
The remaining errors for `id_npcr` and `id_l2xx` are large and persistent.
This strongly points to a missing mechanism or incorrect kinetic assumption related to these species.
Since I cannot change kinetic laws (e.g. to Michaelis-Menten for `id_npcr`) and adding a new reaction that fundamentally alters `id_npcr` balance (like production from an unknown source, or consumption by a different path) is speculative without more data.

I will make one final attempt to slightly adjust `k4` in the Iter 14 model to see if `id_l2xx` can be nudged without breaking product balance, but this is unlikely to fix the 80x discrepancy.
Iter 14: `k1=9.5, k2=640, k3=25, k4=35`. `id_l2xx` needs 80x increase.
If `k4` is reduced, `id_l2xx` will increase. Products will decrease.
Products are 3-4% low. They can tolerate a small decrease.
If `k4` is halved: `k4 = 17.5`.
This would make `id_l2xx` roughly double (still 40x too low).
Products would roughly halve their rate (error would go from 3-4% to ~50% low). This is not good.

The model from Iteration 14 is likely the best I can achieve.
I will use this last iteration to prepare the submission of this model.

## Action

### Submit
```python
import libsbml
import pandas as pd
import numpy as np

# The best model found so far is from Iteration 14
final_sbml = shared_variables.access("best_sbml_model_so_far")
# This variable should point to the SBML string of the Iteration 14 model.
# Let's double check the parameters in it for sanity, if possible, or just trust the process.

# The parameters for Iteration 14 model were:
# k1=9.5, k2=640, k3=25, k4=35
# R4 includes id_t6k9 as catalyst.

# No further modifications, submitting the best model found.
print("Submitting the model from Iteration 14.")
print("Parameters: k1=9.5, k2=640, k3=25, k4=35 (R4 with id_t6k9 catalyst)")

# The variable `final_sbml` must be defined for submission.
# `shared_variables.access("best_sbml_model_so_far")` already provides this.
```
