
                # 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_m277">
    <listOfUnitDefinitions>
      <unitDefinition id="id_4k5w">
        <listOfUnits>
          <unit kind="litre" scale="-3"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_i2bi">
        <listOfUnits>
          <unit kind="second" multiplier="60"/>
        </listOfUnits>
      </unitDefinition>
      <unitDefinition id="id_azy6">
        <listOfUnits>
          <unit kind="mole" scale="-3"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <listOfCompartments>
      <compartment id="id_motv" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_wq5e" compartment="id_motv" initialConcentration="0"/>
      <species id="id_9z5o" compartment="id_motv" initialConcentration="0"/>
      <species id="id_dukt" compartment="id_motv" initialConcentration="0"/>
      <species id="id_gbbq" compartment="id_motv" initialConcentration="0"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

                Format your response according to the instructions in the system message.
                
## Thoughts
The initial SBML model has four species: `id_wq5e`, `id_9z5o`, `id_dukt`, and `id_gbbq`. All initial concentrations are set to 0. There are no reactions defined.

If I run an "observe" experiment with these initial conditions, and there are no reactions that produce these species from a source or boundary species (which are not present), then all concentrations will remain at 0. This won't give me any information about the system's dynamics.

Therefore, the first step should be to perturb the system by changing the initial concentrations of some or all species to non-zero values. This will allow me to observe how these concentrations change over time, which will provide clues about the underlying reactions.

I will set the initial concentration of all four species to 1.0 and observe the system.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_wq5e": 1.0,
        "id_9z5o": 1.0,
        "id_dukt": 1.0,
        "id_gbbq": 1.0
    }
}
```
# 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: 1341 rows × 5 columns. 

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

Time   id_wq5e  id_9z5o  id_dukt  id_gbbq
0  1.00e+00 1.00e+00 1.00e+00 1.00e+00
...
5.24e-01  5.92e-01 9.92e-01 5.92e-01 9.92e-01
...
1.05e+00  3.52e-01 9.95e-01 3.52e-01 9.95e-01
...
1.57e+00  2.17e-01 9.97e-01 2.17e-01 9.97e-01
...
2.10e+00  1.64e-01 9.98e-01 1.64e-01 9.98e-01
...
2.62e+00  1.54e-01 9.99e-01 1.54e-01 9.99e-01
...
3.14e+00  1.53e-01 9.99e-01 1.53e-01 9.99e-01
...
3.67e+00  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
4.19e+00  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
4.71e+00  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
5.24e+00  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
5.76e+00  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
6.29e+00  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
6.81e+00  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
7.33e+00  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
7.86e+00  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
8.38e+00  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
8.91e+00  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
9.43e+00  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
9.95e+00  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.05e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.10e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.15e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.20e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.26e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.31e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.36e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.41e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.47e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.52e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.57e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.62e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.68e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.73e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.78e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.83e+01  1.53e-01 1.00e+00 1.53e-01 1.00e+00
...
1.89e+01  1.53e-01 1.00e+00 1.54e-01 1.00e+00
...
1.94e+01  1.52e-01 1.00e+00 1.54e-01 1.00e+00
...
1.99e+01  1.50e-01 1.00e+00 1.56e-01 1.00e+00
...
2.04e+01  1.43e-01 1.00e+00 1.65e-01 1.00e+00
...
2.10e+01  1.22e-01 1.00e+00 1.97e-01 1.00e+00
...
2.15e+01  8.43e-02 1.00e+00 3.14e-01 1.00e+00
...
2.20e+01  5.14e-02 1.00e+00 5.27e-01 9.99e-01
...
2.25e+01  3.07e-02 1.00e+00 7.09e-01 9.96e-01
...
2.31e+01  1.83e-02 1.00e+00 8.27e-01 9.91e-01
...
2.36e+01  1.09e-02 1.00e+00 8.97e-01 9.83e-01
...
2.41e+01  6.52e-03 1.00e+00 9.39e-01 9.75e-01
...
2.46e+01  3.91e-03 1.00e+00 9.64e-01 9.68e-01
...
2.51e+01  2.36e-03 1.00e+00 9.79e-01 9.62e-01
...
2.60e+01  1.07e-03 1.00e+00 9.91e-01 9.55e-01

## Reminder

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



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

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


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



# Iteration 1
## Thoughts

The experimental data shows two main phases:
1.  **Phase 1 (approx. t=0 to t=18):**
    *   `id_wq5e` and `id_dukt` start at 1.0 and decrease to a plateau around 0.153.
    *   `id_9z5o` and `id_gbbq` start at 1.0 and remain relatively stable around 1.0.
    This suggests reversible reactions reaching an equilibrium. A plausible hypothesis for this phase involves two coupled reversible reactions:
    *   R1: `id_wq5e + id_gbbq <=> id_9z5o`
    *   R2: `id_dukt + id_9z5o <=> id_gbbq`
    At equilibrium (0.153, 1.0, 0.153, 1.0) for (wq5e, 9z5o, dukt, gbbq):
    For R1: `Keq1 = [id_9z5o] / ([id_wq5e][id_gbbq]) = 1.0 / (0.153 * 1.0) approx 6.53`
    For R2: `Keq2 = [id_gbbq] / ([id_dukt][id_9z5o]) = 1.0 / (0.153 * 1.0) approx 6.53`
    The symmetry in Keq values is consistent with the symmetric behavior of wq5e/dukt and 9z5o/gbbq.

2.  **Phase 2 (approx. t > 18):**
    *   `id_wq5e` decreases from ~0.153 towards 0.
    *   `id_dukt` increases from ~0.153 towards 1.0.
    *   `id_9z5o` remains stable at 1.0.
    *   `id_gbbq` remains stable at 1.0 initially, then shows a slight decrease towards the end (e.g., to 0.955 at t=26).
    The decrease in `id_wq5e` and increase in `id_dukt` strongly suggests a conversion reaction:
    *   R3: `id_wq5e -> id_dukt`
    This reaction would be slower than R1 and R2, governing the dynamics of the second phase.

**Parameter Estimation (Initial Guesses):**
*   For R1 and R2, to achieve `Keq approx 6.53` and ensure equilibrium is reached relatively quickly (e.g., within t=2-3), we can set `kr1 = kr2 = 10.0` and `kf1 = kf2 = Keq * kr = 6.53 * 10.0 = 65.3`.
*   For R3 (`id_wq5e -> id_dukt`), this reaction governs the slower decay of `id_wq5e` from the plateau. If `d(id_wq5e)/dt = -kf1*wq5e*gbbq + kr1*9z5o - k3*wq5e`. At the plateau, `d(id_wq5e)/dt` is very small (ideally zero for a perfect plateau, but it's slowly decreasing). If we assume the plateau is a quasi-steady state where the net flux from R1 is balanced by R3: `kf1*wq5e*gbbq - kr1*9z5o + k3*wq5e approx 0`. With plateau values: `65.3*0.153*1.0 - 10*1.0 + k3*0.153 approx 0` => `9.99 - 10 + k3*0.153 approx 0` => `-0.01 + k3*0.153 approx 0`. This gives `k3 approx 0.01 / 0.153 approx 0.065`.

**Concerns:**
*   The `simulate` function's default time span (typically 0-10s) might not be sufficient to observe Phase 2 dynamics fully, as the experimental data extends to t=26s. The comparison will focus on the initial phase and the beginning of the plateau if the simulation time is short.
*   The behavior of `id_9z5o` (stable at 1.0) and `id_gbbq` (stable then slight dip) in Phase 2 needs careful checking against the simulation. The proposed R1, R2, R3 model predicts that as `id_wq5e` is consumed by R3, R1 (`id_wq5e + id_gbbq <=> id_9z5o`) shifts left (`id_9z5o -> id_wq5e + id_gbbq`), consuming `id_9z5o` and producing `id_gbbq`. As `id_dukt` is produced by R3, R2 (`id_dukt + id_9z5o <=> id_gbbq`) shifts right (`id_dukt + id_9z5o -> id_gbbq`), consuming `id_9z5o` and producing `id_gbbq`. Both shifts consume `id_9z5o` and produce `id_gbbq`. This means the model predicts `id_9z5o` should decrease and `id_gbbq` should increase in Phase 2, which contradicts the experimental data where `id_9z5o` is stable and `id_gbbq` slightly decreases. This is a significant point of potential model inadequacy that the simulation will help clarify.

Despite this concern, this three-reaction model is a good starting point to test.

I will now implement this model (Model v2) and simulate it.

## Action

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

# ---- Build Model v2 ----
# Start from the initial incomplete SBML model string
sbml_doc_v2 = libsbml.readSBMLFromString(input_sbml_string)
model_v2 = sbml_doc_v2.getModel()

# Define species IDs for clarity
s_wq5e = "id_wq5e"
s_9z5o = "id_9z5o"
s_dukt = "id_dukt"
s_gbbq = "id_gbbq"

# Reaction R1: id_wq5e + id_gbbq <=> id_9z5o
r1 = model_v2.createReaction()
r1.setId("R1_wq5e_gbbq_eq_9z5o")
r1.setReversible(True)
r1.setFast(False) # Required in SBML L3

# Reactants for R1
reactant1_r1 = r1.createReactant()
reactant1_r1.setSpecies(s_wq5e)
reactant1_r1.setStoichiometry(1.0)
reactant1_r1.setConstant(False) # Required in SBML L3

reactant2_r1 = r1.createReactant()
reactant2_r1.setSpecies(s_gbbq)
reactant2_r1.setStoichiometry(1.0)
reactant2_r1.setConstant(False) # Required in SBML L3

# Product for R1
product1_r1 = r1.createProduct()
product1_r1.setSpecies(s_9z5o)
product1_r1.setStoichiometry(1.0)
product1_r1.setConstant(False) # Required in SBML L3

# Kinetic Law for R1
kl_r1 = r1.createKineticLaw()
kf1_param = kl_r1.createParameter()
kf1_param.setId("kf1")
kf1_param.setValue(65.3) # kf1 = Keq1 * kr1. Keq1 = 6.53. kr1 = 10.
kr1_param = kl_r1.createParameter()
kr1_param.setId("kr1")
kr1_param.setValue(10.0)
kl_r1.setMath(libsbml.parseL3Formula(f"kf1 * {s_wq5e} * {s_gbbq} - kr1 * {s_9z5o}"))

# Reaction R2: id_dukt + id_9z5o <=> id_gbbq
r2 = model_v2.createReaction()
r2.setId("R2_dukt_9z5o_eq_gbbq")
r2.setReversible(True)
r2.setFast(False) # Required in SBML L3

# Reactants for R2
reactant1_r2 = r2.createReactant()
reactant1_r2.setSpecies(s_dukt)
reactant1_r2.setStoichiometry(1.0)
reactant1_r2.setConstant(False) # Required in SBML L3

reactant2_r2 = r2.createReactant()
reactant2_r2.setSpecies(s_9z5o)
reactant2_r2.setStoichiometry(1.0)
reactant2_r2.setConstant(False) # Required in SBML L3

# Product for R2
product1_r2 = r2.createProduct()
product1_r2.setSpecies(s_gbbq)
product1_r2.setStoichiometry(1.0)
product1_r2.setConstant(False) # Required in SBML L3

# Kinetic Law for R2
kl_r2 = r2.createKineticLaw()
kf2_param = kl_r2.createParameter()
kf2_param.setId("kf2")
kf2_param.setValue(65.3) # kf2 = Keq2 * kr2. Keq2 = 6.53. kr2 = 10.
kr2_param = kl_r2.createParameter()
kr2_param.setId("kr2")
kr2_param.setValue(10.0)
kl_r2.setMath(libsbml.parseL3Formula(f"kf2 * {s_dukt} * {s_9z5o} - kr2 * {s_gbbq}"))

# Reaction R3: id_wq5e -> id_dukt
r3 = model_v2.createReaction()
r3.setId("R3_wq5e_to_dukt")
r3.setReversible(False)
r3.setFast(False) # Required in SBML L3

# Reactant for R3
reactant1_r3 = r3.createReactant()
reactant1_r3.setSpecies(s_wq5e)
reactant1_r3.setStoichiometry(1.0)
reactant1_r3.setConstant(False) # Required in SBML L3

# Product for R3
product1_r3 = r3.createProduct()
product1_r3.setSpecies(s_dukt)
product1_r3.setStoichiometry(1.0)
product1_r3.setConstant(False) # Required in SBML L3

# Kinetic Law for R3
kl_r3 = r3.createKineticLaw()
k3_param = kl_r3.createParameter()
k3_param.setId("k3")
k3_param.setValue(0.065) # Estimated k3
kl_r3.setMath(libsbml.parseL3Formula(f"k3 * {s_wq5e}"))

# Set initial concentrations in the model for simulation
# These match the experimental setup for iteration_0
species_wq5e_obj = model_v2.getSpecies(s_wq5e)
species_wq5e_obj.setInitialConcentration(1.0)
species_9z5o_obj = model_v2.getSpecies(s_9z5o)
species_9z5o_obj.setInitialConcentration(1.0)
species_dukt_obj = model_v2.getSpecies(s_dukt)
species_dukt_obj.setInitialConcentration(1.0)
species_gbbq_obj = model_v2.getSpecies(s_gbbq)
species_gbbq_obj.setInitialConcentration(1.0)

# Write the updated SBML to a string
writer = libsbml.SBMLWriter()
model_v2_sbml = writer.writeSBMLToString(sbml_doc_v2)
shared_variables.add("model_v2_sbml", model_v2_sbml)

# ---- Simulate Model v2 ----
sim_data_v2 = simulate(model_v2_sbml)
shared_variables.add("sim_data_v2", sim_data_v2)

# ---- Compare with Experimental Data ----
exp_data = experiment_history['iteration_0']

print("--- Model v2 Simulation Results ---")

# Find closest time points in experimental data for comparison
exp_time_points = [0.0, 1.05, 2.10, 3.67, 10.0, 18.3, 21.0, 26.0]
sim_time_points = sim_data_v2['Time'].values

print(f"Simulation runs from t=0 to t={sim_data_v2['Time'].max()} with {len(sim_data_v2)} points.")

print("\nComparison at selected time points (Experimental vs Simulated):")
print("Time | Species | Exp_Val | Sim_Val")
print("------------------------------------")

for t_exp_target in exp_time_points:
    # Find closest experimental data point
    exp_row = exp_data.iloc[(exp_data['Time'] - t_exp_target).abs().argsort()[:1]]
    t_exp_actual = exp_row['Time'].iloc[0]

    # Find closest simulation data point
    if t_exp_target <= sim_data_v2['Time'].max():
        sim_row = sim_data_v2.iloc[(sim_data_v2['Time'] - t_exp_target).abs().argsort()[:1]]
        t_sim_actual = sim_row['Time'].iloc[0]
        sim_wq5e = sim_row[s_wq5e].iloc[0]
        sim_9z5o = sim_row[s_9z5o].iloc[0]
        sim_dukt = sim_row[s_dukt].iloc[0]
        sim_gbbq = sim_row[s_gbbq].iloc[0]
    else: # If experimental time is beyond simulation time
        t_sim_actual = float('nan')
        sim_wq5e, sim_9z5o, sim_dukt, sim_gbbq = (float('nan'),)*4
        
    print(f"{t_exp_actual:<4.2f} | {s_wq5e:<7} | {exp_row[s_wq5e].iloc[0]:<7.3f} | {sim_wq5e:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_9z5o:<7} | {exp_row[s_9z5o].iloc[0]:<7.3f} | {sim_9z5o:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_dukt:<7} | {exp_row[s_dukt].iloc[0]:<7.3f} | {sim_dukt:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_gbbq:<7} | {exp_row[s_gbbq].iloc[0]:<7.3f} | {sim_gbbq:<7.3f}")
    print("------------------------------------")

print("\nExperimental data tail (iteration_0):")
print(exp_data.tail(3))
print("\nSimulated data v2 tail:")
print(sim_data_v2.tail(3))

# Store the SBML string of the current best model
shared_variables.add("current_best_sbml", model_v2_sbml)
```
# Observation

## Code Stdout
--- Model v2 Simulation Results ---
Simulation runs from t=0 to t=26.0 with 1341 points.

Comparison at selected time points (Experimental vs Simulated):
Time | Species | Exp_Val | Sim_Val
------------------------------------
0.00 | id_wq5e | 1.000   | 1.000  
0.00 | id_9z5o | 1.000   | 1.000  
0.00 | id_dukt | 1.000   | 1.000  
0.00 | id_gbbq | 1.000   | 1.000  
------------------------------------
1.05 | id_wq5e | 0.352   | 0.149  
1.05 | id_9z5o | 0.995   | 0.986  
1.05 | id_dukt | 0.352   | 0.157  
1.05 | id_gbbq | 0.995   | 1.014  
------------------------------------
2.10 | id_wq5e | 0.164   | 0.145  
2.10 | id_9z5o | 0.998   | 0.974  
2.10 | id_dukt | 0.164   | 0.161  
2.10 | id_gbbq | 0.998   | 1.026  
------------------------------------
3.67 | id_wq5e | 0.153   | 0.140  
3.67 | id_9z5o | 1.000   | 0.956  
3.67 | id_dukt | 0.153   | 0.167  
3.67 | id_gbbq | 1.000   | 1.044  
------------------------------------
9.99 | id_wq5e | 0.153   | 0.123  
9.99 | id_9z5o | 1.000   | 0.890  
9.99 | id_dukt | 0.153   | 0.191  
9.99 | id_gbbq | 1.000   | 1.110  
------------------------------------
18.30 | id_wq5e | 0.153   | 0.105  
18.30 | id_9z5o | 1.000   | 0.815  
18.30 | id_dukt | 0.153   | 0.223  
18.30 | id_gbbq | 1.000   | 1.185  
------------------------------------
20.99 | id_wq5e | 0.120   | 0.101  
20.99 | id_9z5o | 1.000   | 0.794  
20.99 | id_dukt | 0.202   | 0.233  
20.99 | id_gbbq | 1.000   | 1.206  
------------------------------------
26.00 | id_wq5e | 0.001   | 0.093  
26.00 | id_9z5o | 1.000   | 0.757  
26.00 | id_dukt | 0.991   | 0.251  
26.00 | id_gbbq | 0.955   | 1.243  
------------------------------------

Experimental data tail (iteration_0):
       id_wq5e  id_9z5o   id_dukt   id_gbbq       Time
1338  0.001105      1.0  0.990532  0.954828  25.961194
1339  0.001086      1.0  0.990714  0.954691  25.980597
1340  0.001067      1.0  0.990893  0.954556  26.000000

Simulated data v2 tail:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
1338  0.093309  0.757522  0.251225  1.242478  25.961194
1339  0.093282  0.757386  0.251297  1.242614  25.980597
1340  0.093255  0.757250  0.251370  1.242750  26.000000

## 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. (model_v2_sbml, sim_data_v2, current_best_sbml)

### 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 previous simulation (Model v2) showed significant discrepancies, especially for `id_9z5o` (simulated decrease vs. experimental constant 1.0) and `id_gbbq` (simulated increase vs. experimental constant 1.0 then slight decrease). The conversion rate of `id_wq5e` to `id_dukt` was also too slow.

The core challenge is to explain:
1.  The remarkable stability of `id_9z5o` at 1.0.
2.  The stability of `id_gbbq` at 1.0 for most of the experiment, followed by a slight decrease to ~0.955 when `id_wq5e` is nearly depleted.
3.  The conversion of `id_wq5e` to `id_dukt`.

Hypothesis for Model v5:
1.  `id_9z5o` is a constant species: Its concentration is fixed at 1.0. This is achieved by setting `constant="true"` for `id_9z5o` in the SBML model and an initial concentration of 1.0.
2.  Reactions R1 and R2 are reversible mass-action reactions as before:
    *   R1: `id_wq5e + id_gbbq <=> id_9z5o` (Parameters `kf1`, `kr1`)
    *   R2: `id_dukt + id_9z5o <=> id_gbbq` (Parameters `kf2`, `kr2`)
    The equilibrium constants `Keq1 = kf1/kr1` and `Keq2 = kf2/kr2` are derived from the plateau concentrations (`wq5e_eq = dukt_eq = 0.153`, `gbbq_eq = 1.0`, `9z5o_eq = 1.0`). This gives `kr1/kf1 = 0.153` and `kr2/kf2 = 0.153` (if `gbbq` is product in R2) or `kf2*(0.153)*1.0 = kr2*1.0` => `0.153 = kr2/kf2` (if `gbbq` is product in R2, `dukt` and `9z5o` are reactants).
    Let's stick to the previous formulation: R1: `W+G <=> N`, R2: `D+N <=> G`.
    Plateau: `kf1*W*G = kr1*N` => `kf1*0.153*1 = kr1*1` => `kr1/kf1 = 0.153`.
    Plateau: `kf2*D*N = kr2*G` => `kf2*0.153*1 = kr2*1` => `kr2/kf2 = 0.153`.
    So, `kf1/kr1 = kf2/kr2 = 1/0.153 approx 6.53`. We used `kf=65.3, kr=10`.
3.  Reaction R3 (conversion of `id_wq5e` to `id_dukt`) is modified to consume `id_gbbq` as well, to explain the late drop in `id_gbbq`.
    *   R3_new: `id_wq5e + id_gbbq -> id_dukt + id_9z5o` (Parameter `k3_new`).
    The production of `id_9z5o` in R3_new will not change its concentration as it's constant. This reaction consumes `id_gbbq`, which could explain its decrease. The rate `k3_new * id_wq5e * id_gbbq` means this consumption is active when both `id_wq5e` and `id_gbbq` are present.
    The rate constant `k3_new` is estimated based on the previous `k3` for `id_wq5e -> id_dukt`. If `k3*wq5e` was the old rate, and `gbbq` is ~1, then `k3_new` might be numerically similar to the old `k3`. The previous estimate for `k3` (first-order) was ~0.6. So, `k3_new = 0.6` is a starting point.

This model structure (Model v5) attempts to address all key observations.
`id_9z5o` being constant is handled.
The initial equilibrium of `wq5e, dukt, gbbq` is handled by R1 and R2.
The conversion `wq5e -> dukt` is handled by R3_new.
The late drop in `gbbq` is potentially explained by its consumption in R3_new.

The simulation results will show if this combination works, particularly the timing and extent of the `gbbq` drop and the overall conversion speed.

## Action

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

# ---- Build Model v5 ----
# Start from the initial incomplete SBML model string
sbml_doc_v5 = libsbml.readSBMLFromString(input_sbml_string)
model_v5 = sbml_doc_v5.getModel()

# Define species IDs
s_wq5e = "id_wq5e"
s_9z5o = "id_9z5o"
s_dukt = "id_dukt"
s_gbbq = "id_gbbq"

# Make id_9z5o constant
species_9z5o_obj = model_v5.getSpecies(s_9z5o)
species_9z5o_obj.setConstant(True)
# Initial concentrations are set when creating the species object in the SBML string
# We will ensure the simulation uses the correct initial values by setting them if not already set,
# or relying on the SBML initial values if they are correct.
# For this experiment, initial concentrations were 1.0 for all.
species_9z5o_obj.setInitialConcentration(1.0) 

species_wq5e_obj = model_v5.getSpecies(s_wq5e)
species_wq5e_obj.setInitialConcentration(1.0)
species_dukt_obj = model_v5.getSpecies(s_dukt)
species_dukt_obj.setInitialConcentration(1.0)
species_gbbq_obj = model_v5.getSpecies(s_gbbq)
species_gbbq_obj.setInitialConcentration(1.0)


# Reaction R1: id_wq5e + id_gbbq <=> id_9z5o
r1 = model_v5.createReaction()
r1.setId("R1_wq5e_gbbq_eq_9z5o")
r1.setReversible(True)
r1.setFast(False)

reactant1_r1 = r1.createReactant(); reactant1_r1.setSpecies(s_wq5e); reactant1_r1.setStoichiometry(1.0); reactant1_r1.setConstant(False)
reactant2_r1 = r1.createReactant(); reactant2_r1.setSpecies(s_gbbq); reactant2_r1.setStoichiometry(1.0); reactant2_r1.setConstant(False)
# Even if id_9z5o is constant, it's still a product in the reaction definition
product1_r1 = r1.createProduct(); product1_r1.setSpecies(s_9z5o); product1_r1.setStoichiometry(1.0); product1_r1.setConstant(False) 

kl_r1 = r1.createKineticLaw()
kf1_param = kl_r1.createParameter(); kf1_param.setId("kf1"); kf1_param.setValue(65.3)
kr1_param = kl_r1.createParameter(); kr1_param.setId("kr1"); kr1_param.setValue(10.0)
# The kinetic law uses the species ID, which will refer to its constant value
kl_r1.setMath(libsbml.parseL3Formula(f"kf1 * {s_wq5e} * {s_gbbq} - kr1 * {s_9z5o}"))

# Reaction R2: id_dukt + id_9z5o <=> id_gbbq
r2 = model_v5.createReaction()
r2.setId("R2_dukt_9z5o_eq_gbbq")
r2.setReversible(True)
r2.setFast(False)

reactant1_r2 = r2.createReactant(); reactant1_r2.setSpecies(s_dukt); reactant1_r2.setStoichiometry(1.0); reactant1_r2.setConstant(False)
reactant2_r2 = r2.createReactant(); reactant2_r2.setSpecies(s_9z5o); reactant2_r2.setStoichiometry(1.0); reactant2_r2.setConstant(False) 
product1_r2 = r2.createProduct(); product1_r2.setSpecies(s_gbbq); product1_r2.setStoichiometry(1.0); product1_r2.setConstant(False)

kl_r2 = r2.createKineticLaw()
kf2_param = kl_r2.createParameter(); kf2_param.setId("kf2"); kf2_param.setValue(65.3)
kr2_param = kl_r2.createParameter(); kr2_param.setId("kr2"); kr2_param.setValue(10.0)
kl_r2.setMath(libsbml.parseL3Formula(f"kf2 * {s_dukt} * {s_9z5o} - kr2 * {s_gbbq}"))

# Reaction R3_new: id_wq5e + id_gbbq -> id_dukt + id_9z5o
r3 = model_v5.createReaction()
r3.setId("R3_new_wq5e_gbbq_to_dukt_9z5o")
r3.setReversible(False) 
r3.setFast(False)

reactant1_r3 = r3.createReactant(); reactant1_r3.setSpecies(s_wq5e); reactant1_r3.setStoichiometry(1.0); reactant1_r3.setConstant(False)
reactant2_r3 = r3.createReactant(); reactant2_r3.setSpecies(s_gbbq); reactant2_r3.setStoichiometry(1.0); reactant2_r3.setConstant(False)
product1_r3 = r3.createProduct(); product1_r3.setSpecies(s_dukt); product1_r3.setStoichiometry(1.0); product1_r3.setConstant(False)
product2_r3 = r3.createProduct(); product2_r3.setSpecies(s_9z5o); product2_r3.setStoichiometry(1.0); product2_r3.setConstant(False) 

kl_r3 = r3.createKineticLaw()
k3_new_param = kl_r3.createParameter(); k3_new_param.setId("k3_new"); k3_new_param.setValue(0.6) 
kl_r3.setMath(libsbml.parseL3Formula(f"k3_new * {s_wq5e} * {s_gbbq}"))

# Write the updated SBML to a string
writer = libsbml.SBMLWriter()
model_v5_sbml = writer.writeSBMLToString(sbml_doc_v5)
shared_variables.add("model_v5_sbml", model_v5_sbml)

# ---- Simulate Model v5 ----
sim_data_v5 = simulate(model_v5_sbml)
shared_variables.add("sim_data_v5", sim_data_v5)

# ---- Compare with Experimental Data ----
exp_data = experiment_history['iteration_0']

print("--- Model v5 Simulation Results ---")
print(f"Simulation runs from t=0 to t={sim_data_v5['Time'].max()} with {len(sim_data_v5)} points.")
print("\nComparison at selected time points (Experimental vs Simulated):")
print("Time | Species | Exp_Val | Sim_Val")
print("------------------------------------")

# Using more detailed time points from previous analysis
exp_time_points = [0.0, 1.05, 2.10, 3.67, 10.0, 18.3, 21.0, 22.0, 23.0, 23.6, 24.1, 24.6, 25.1, 26.0] 

for t_exp_target in exp_time_points:
    exp_row = exp_data.iloc[(exp_data['Time'] - t_exp_target).abs().argsort()[:1]]
    t_exp_actual = exp_row['Time'].iloc[0]

    if t_exp_target <= sim_data_v5['Time'].max():
        sim_row = sim_data_v5.iloc[(sim_data_v5['Time'] - t_exp_target).abs().argsort()[:1]]
        sim_wq5e = sim_row[s_wq5e].iloc[0]
        sim_9z5o = sim_row[s_9z5o].iloc[0]
        sim_dukt = sim_row[s_dukt].iloc[0]
        sim_gbbq = sim_row[s_gbbq].iloc[0]
    else: # Should not happen if simulation time matches experimental time
        sim_wq5e, sim_9z5o, sim_dukt, sim_gbbq = (float('nan'),)*4
        
    print(f"{t_exp_actual:<4.2f} | {s_wq5e:<7} | {exp_row[s_wq5e].iloc[0]:<7.3f} | {sim_wq5e:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_9z5o:<7} | {exp_row[s_9z5o].iloc[0]:<7.3f} | {sim_9z5o:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_dukt:<7} | {exp_row[s_dukt].iloc[0]:<7.3f} | {sim_dukt:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_gbbq:<7} | {exp_row[s_gbbq].iloc[0]:<7.3f} | {sim_gbbq:<7.3f}")
    print("------------------------------------")

print("\nExperimental data tail (iteration_0):")
print(exp_data.tail(3))
print("\nSimulated data v5 tail:")
print(sim_data_v5.tail(3))

shared_variables.add("current_best_sbml", model_v5_sbml)
```
# Observation

## Code Stdout
--- Model v5 Simulation Results ---
Simulation runs from t=0 to t=26.0 with 1341 points.

Comparison at selected time points (Experimental vs Simulated):
Time | Species | Exp_Val | Sim_Val
------------------------------------
0.00 | id_wq5e | 1.000   | 1.000  
0.00 | id_9z5o | 1.000   | 1.000  
0.00 | id_dukt | 1.000   | 1.000  
0.00 | id_gbbq | 1.000   | 1.000  
------------------------------------
1.05 | id_wq5e | 0.352   | 0.135  
1.05 | id_9z5o | 0.995   | 0.939  
1.05 | id_dukt | 0.352   | 0.174  
1.05 | id_gbbq | 0.995   | 1.061  
------------------------------------
2.10 | id_wq5e | 0.164   | 0.121  
2.10 | id_9z5o | 0.998   | 0.886  
2.10 | id_dukt | 0.164   | 0.194  
2.10 | id_gbbq | 0.998   | 1.114  
------------------------------------
3.67 | id_wq5e | 0.153   | 0.104  
3.67 | id_9z5o | 1.000   | 0.812  
3.67 | id_dukt | 0.153   | 0.225  
3.67 | id_gbbq | 1.000   | 1.188  
------------------------------------
9.99 | id_wq5e | 0.153   | 0.064  
9.99 | id_9z5o | 1.000   | 0.592  
9.99 | id_dukt | 0.153   | 0.365  
9.99 | id_gbbq | 1.000   | 1.408  
------------------------------------
18.30 | id_wq5e | 0.153   | 0.042  
18.30 | id_9z5o | 1.000   | 0.430  
18.30 | id_dukt | 0.153   | 0.560  
18.30 | id_gbbq | 1.000   | 1.570  
------------------------------------
20.99 | id_wq5e | 0.120   | 0.037  
20.99 | id_9z5o | 1.000   | 0.395  
20.99 | id_dukt | 0.202   | 0.622  
20.99 | id_gbbq | 1.000   | 1.605  
------------------------------------
22.00 | id_wq5e | 0.051   | 0.036  
22.00 | id_9z5o | 1.000   | 0.384  
22.00 | id_dukt | 0.527   | 0.645  
22.00 | id_gbbq | 0.999   | 1.616  
------------------------------------
22.99 | id_wq5e | 0.019   | 0.035  
22.99 | id_9z5o | 1.000   | 0.373  
22.99 | id_dukt | 0.816   | 0.668  
22.99 | id_gbbq | 0.991   | 1.627  
------------------------------------
23.59 | id_wq5e | 0.011   | 0.034  
23.59 | id_9z5o | 1.000   | 0.367  
23.59 | id_dukt | 0.899   | 0.681  
23.59 | id_gbbq | 0.983   | 1.633  
------------------------------------
24.10 | id_wq5e | 0.007   | 0.034  
24.10 | id_9z5o | 1.000   | 0.362  
24.10 | id_dukt | 0.939   | 0.693  
24.10 | id_gbbq | 0.975   | 1.638  
------------------------------------
24.60 | id_wq5e | 0.004   | 0.033  
24.60 | id_9z5o | 1.000   | 0.358  
24.60 | id_dukt | 0.963   | 0.704  
24.60 | id_gbbq | 0.968   | 1.642  
------------------------------------
25.11 | id_wq5e | 0.002   | 0.033  
25.11 | id_9z5o | 1.000   | 0.353  
25.11 | id_dukt | 0.978   | 0.715  
25.11 | id_gbbq | 0.962   | 1.647  
------------------------------------
26.00 | id_wq5e | 0.001   | 0.032  
26.00 | id_9z5o | 1.000   | 0.345  
26.00 | id_dukt | 0.991   | 0.735  
26.00 | id_gbbq | 0.955   | 1.655  
------------------------------------

Experimental data tail (iteration_0):
       id_wq5e  id_9z5o   id_dukt   id_gbbq       Time
1338  0.001105      1.0  0.990532  0.954828  25.961194
1339  0.001086      1.0  0.990714  0.954691  25.980597
1340  0.001067      1.0  0.990893  0.954556  26.000000

Simulated data v5 tail:
       id_wq5e   id_9z5o   id_dukt   id_gbbq       Time
1338  0.031693  0.345465  0.733850  1.654535  25.961194
1339  0.031674  0.345299  0.734276  1.654701  25.980597
1340  0.031656  0.345134  0.734701  1.654866  26.000000

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 18/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (model_v2_sbml, sim_data_v2, current_best_sbml, model_v5_sbml, sim_data_v5)

### 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 primary issue in Model v5 was that `id_9z5o` did not behave as a constant species in the simulation, despite being set with `species_9z5o_obj.setConstant(True)`. Its simulated concentration changed significantly, which invalidated the model's agreement with experimental data where `id_9z5o` remains at 1.0.

There are a few potential reasons for this:
1.  **Simulator interpretation of `species.constant`**: The simulator might require `species.boundaryCondition="true"` in conjunction with `species.constant="true"` to truly fix a species' concentration, especially if it participates in reactions.
2.  **`SpeciesReference.constant` attribute**:
    *   The problem states the input SBML is Level 2 Version 4. In L2V4, `speciesReference.constant` defaults to `true` and means the stoichiometry is fixed (not variable via `stoichiometryMath`). Setting it to `false` (as I did, thinking it was related to the species itself being non-constant) would imply variable stoichiometry, which is incorrect for this model.
    *   The provided example code uses `reactant.setConstant(False)` and `product.setConstant(True)`, stating these are "Required in SBML Level 3". In L3, `speciesReference.constant` also defaults to `true` and means fixed stoichiometry. Setting it to `false` implies variable stoichiometry. The example's `reactant.setConstant(False)` is confusing if it's for a standard reaction with fixed stoichiometry. However, `product.setConstant(True)` is consistent.

To ensure correct behavior, I will make the following changes for Model v7:
1.  For `id_9z5o`:
    *   Set `initialConcentration="1.0"`.
    *   Set `constant="true"`.
    *   Set `boundaryCondition="true"`. This combination should robustly fix its concentration.
2.  For all `SpeciesReference` objects (reactants and products of all reactions):
    *   Explicitly call `setStoichiometry(value)`.
    *   Explicitly call `setConstant(True)`. This indicates that the stoichiometry of the species in that reaction is fixed, which is true for all reactions in my model. This corrects my previous misuse of `setConstant(False)` on these objects.
3.  Reaction attribute `setFast(False)`: I will keep this as per the example, assuming the environment handles it appropriately.

The reactions and parameters will be (re-derived based on `id_9z5o` being fixed at 1.0):
*   R1: `id_wq5e + id_gbbq <=> id_9z5o`
    *   `kf1 = 65.3`, `kr1 = 10.0` (maintains `Keq1 = kf1/kr1 approx 6.53`, leading to plateau `id_wq5e = 0.153` if `id_gbbq=1, id_9z5o=1`)
*   R2: `id_dukt + id_9z5o <=> id_gbbq`
    *   `kf2 = 65.3`, `kr2 = 10.0` (maintains `Keq2 = kf2/kr2 approx 6.53`, leading to plateau `id_dukt = 0.153` if `id_gbbq=1, id_9z5o=1`)
*   R3_new: `id_wq5e + id_gbbq -> id_dukt + id_9z5o`
    *   `k3_new = 0.64`. This rate was estimated from the decay of `id_wq5e` in Phase 2 (`ln(0.001/0.153) / -8s approx 0.628`, adjusted for `gbbq` not being exactly 1.0). This reaction consumes `id_gbbq`, which should explain its late drop.

With `id_9z5o` fixed at 1.0, the rate equations are:
`d(wq5e)/dt = -kf1*wq5e*gbbq + kr1*1.0 - k3_new*wq5e*gbbq`
`d(dukt)/dt = -kf2*dukt*1.0 + kr2*gbbq + k3_new*wq5e*gbbq`
`d(gbbq)/dt = -kf1*wq5e*gbbq + kr1*1.0 + kf2*dukt*1.0 - kr2*gbbq - k3_new*wq5e*gbbq`

At the target plateau (`wq5e=0.153, dukt=0.153, gbbq=1.0`):
`d(wq5e)/dt = -65.3*0.153 + 10 - 0.64*0.153*1 approx -9.99 + 10 - 0.098 = -0.088` (decrease)
`d(dukt)/dt = -65.3*0.153 + 10 + 0.64*0.153*1 approx -9.99 + 10 + 0.098 = +0.108` (increase)
`d(gbbq)/dt = (-65.3*0.153 + 10) + (65.3*0.153 - 10) - 0.64*0.153*1 approx 0 + 0 - 0.098 = -0.098` (decrease)
This behavior (wq5e decreases, dukt increases, gbbq decreases from the plateau due to R3_new) is consistent with the experimental observations for Phase 2.

## Action

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

# ---- Build Model v7 (Corrected SBML handling) ----
sbml_doc_v7 = libsbml.readSBMLFromString(input_sbml_string)
model_v7 = sbml_doc_v7.getModel()

s_wq5e = "id_wq5e"
s_9z5o = "id_9z5o"
s_dukt = "id_dukt"
s_gbbq = "id_gbbq"

# Configure id_9z5o as a constant species
species_9z5o_obj = model_v7.getSpecies(s_9z5o)
species_9z5o_obj.setInitialConcentration(1.0)
species_9z5o_obj.setConstant(True)
species_9z5o_obj.setBoundaryCondition(True) # Ensure it's treated as fixed

# Set initial concentrations for other species (matching experiment)
model_v7.getSpecies(s_wq5e).setInitialConcentration(1.0)
model_v7.getSpecies(s_dukt).setInitialConcentration(1.0)
model_v7.getSpecies(s_gbbq).setInitialConcentration(1.0)

# Reaction R1: id_wq5e + id_gbbq <=> id_9z5o
r1 = model_v7.createReaction()
r1.setId("R1_wq5e_gbbq_eq_9z5o")
r1.setReversible(True)
r1.setFast(False) # As per example

reactant1_r1 = r1.createReactant(); reactant1_r1.setSpecies(s_wq5e); reactant1_r1.setStoichiometry(1.0); reactant1_r1.setConstant(True) # Fixed stoichiometry
reactant2_r1 = r1.createReactant(); reactant2_r1.setSpecies(s_gbbq); reactant2_r1.setStoichiometry(1.0); reactant2_r1.setConstant(True) # Fixed stoichiometry
product1_r1 = r1.createProduct(); product1_r1.setSpecies(s_9z5o); product1_r1.setStoichiometry(1.0); product1_r1.setConstant(True) # Fixed stoichiometry

kl_r1 = r1.createKineticLaw()
kf1_param = kl_r1.createParameter(); kf1_param.setId("kf1"); kf1_param.setValue(65.3)
kr1_param = kl_r1.createParameter(); kr1_param.setId("kr1"); kr1_param.setValue(10.0)
kl_r1.setMath(libsbml.parseL3Formula(f"kf1 * {s_wq5e} * {s_gbbq} - kr1 * {s_9z5o}"))

# Reaction R2: id_dukt + id_9z5o <=> id_gbbq
r2 = model_v7.createReaction()
r2.setId("R2_dukt_9z5o_eq_gbbq")
r2.setReversible(True)
r2.setFast(False) # As per example

reactant1_r2 = r2.createReactant(); reactant1_r2.setSpecies(s_dukt); reactant1_r2.setStoichiometry(1.0); reactant1_r2.setConstant(True) # Fixed stoichiometry
reactant2_r2 = r2.createReactant(); reactant2_r2.setSpecies(s_9z5o); reactant2_r2.setStoichiometry(1.0); reactant2_r2.setConstant(True) # Fixed stoichiometry
product1_r2 = r2.createProduct(); product1_r2.setSpecies(s_gbbq); product1_r2.setStoichiometry(1.0); product1_r2.setConstant(True) # Fixed stoichiometry

kl_r2 = r2.createKineticLaw()
kf2_param = kl_r2.createParameter(); kf2_param.setId("kf2"); kf2_param.setValue(65.3)
kr2_param = kl_r2.createParameter(); kr2_param.setId("kr2"); kr2_param.setValue(10.0)
kl_r2.setMath(libsbml.parseL3Formula(f"kf2 * {s_dukt} * {s_9z5o} - kr2 * {s_gbbq}"))

# Reaction R3_new: id_wq5e + id_gbbq -> id_dukt + id_9z5o
r3 = model_v7.createReaction()
r3.setId("R3_new_wq5e_gbbq_to_dukt_9z5o")
r3.setReversible(False)
r3.setFast(False) # As per example

reactant1_r3 = r3.createReactant(); reactant1_r3.setSpecies(s_wq5e); reactant1_r3.setStoichiometry(1.0); reactant1_r3.setConstant(True) # Fixed stoichiometry
reactant2_r3 = r3.createReactant(); reactant2_r3.setSpecies(s_gbbq); reactant2_r3.setStoichiometry(1.0); reactant2_r3.setConstant(True) # Fixed stoichiometry
product1_r3 = r3.createProduct(); product1_r3.setSpecies(s_dukt); product1_r3.setStoichiometry(1.0); product1_r3.setConstant(True) # Fixed stoichiometry
product2_r3 = r3.createProduct(); product2_r3.setSpecies(s_9z5o); product2_r3.setStoichiometry(1.0); product2_r3.setConstant(True) # Fixed stoichiometry

kl_r3 = r3.createKineticLaw()
k3_new_param = kl_r3.createParameter(); k3_new_param.setId("k3_new"); k3_new_param.setValue(0.64)
kl_r3.setMath(libsbml.parseL3Formula(f"k3_new * {s_wq5e} * {s_gbbq}"))

# Write the updated SBML to a string
writer = libsbml.SBMLWriter()
model_v7_sbml = writer.writeSBMLToString(sbml_doc_v7)
shared_variables.add("model_v7_sbml", model_v7_sbml)

# ---- Simulate Model v7 ----
sim_data_v7 = simulate(model_v7_sbml)
shared_variables.add("sim_data_v7", sim_data_v7)

# ---- Compare with Experimental Data ----
exp_data = experiment_history['iteration_0']

print("--- Model v7 Simulation Results (Corrected SBML) ---")
print(f"Simulation runs from t=0 to t={sim_data_v7['Time'].max()} with {len(sim_data_v7)} points.")
print("\nComparison at selected time points (Experimental vs Simulated):")
print("Time | Species | Exp_Val | Sim_Val")
print("------------------------------------")

exp_time_points = [0.0, 1.05, 2.10, 3.67, 10.0, 18.3, 21.0, 22.0, 23.0, 23.6, 24.1, 24.6, 25.1, 26.0] 

for t_exp_target in exp_time_points:
    exp_row = exp_data.iloc[(exp_data['Time'] - t_exp_target).abs().argsort()[:1]]
    t_exp_actual = exp_row['Time'].iloc[0]

    if t_exp_target <= sim_data_v7['Time'].max():
        sim_row = sim_data_v7.iloc[(sim_data_v7['Time'] - t_exp_target).abs().argsort()[:1]]
        sim_wq5e = sim_row[s_wq5e].iloc[0]
        sim_9z5o = sim_row[s_9z5o].iloc[0]
        sim_dukt = sim_row[s_dukt].iloc[0]
        sim_gbbq = sim_row[s_gbbq].iloc[0]
    else:
        sim_wq5e, sim_9z5o, sim_dukt, sim_gbbq = (float('nan'),)*4
        
    print(f"{t_exp_actual:<4.2f} | {s_wq5e:<7} | {exp_row[s_wq5e].iloc[0]:<7.3f} | {sim_wq5e:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_9z5o:<7} | {exp_row[s_9z5o].iloc[0]:<7.3f} | {sim_9z5o:<7.3f}") # Expect 1.000
    print(f"{t_exp_actual:<4.2f} | {s_dukt:<7} | {exp_row[s_dukt].iloc[0]:<7.3f} | {sim_dukt:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_gbbq:<7} | {exp_row[s_gbbq].iloc[0]:<7.3f} | {sim_gbbq:<7.3f}")
    print("------------------------------------")

print("\nExperimental data tail (iteration_0):")
print(exp_data.tail(3))
print("\nSimulated data v7 tail:")
print(sim_data_v7.tail(3))

shared_variables.add("current_best_sbml", model_v7_sbml)
```
# Observation

## Code Stdout
--- Model v7 Simulation Results (Corrected SBML) ---
Simulation runs from t=0 to t=26.0 with 1341 points.

Comparison at selected time points (Experimental vs Simulated):
Time | Species | Exp_Val | Sim_Val
------------------------------------
0.00 | id_wq5e | 1.000   | 1.000  
0.00 | id_9z5o | 1.000   | 1.000  
0.00 | id_dukt | 1.000   | 1.000  
0.00 | id_gbbq | 1.000   | 1.000  
------------------------------------
1.05 | id_wq5e | 0.352   | 0.140  
1.05 | id_9z5o | 0.995   | 1.000  
1.05 | id_dukt | 0.352   | 0.167  
1.05 | id_gbbq | 0.995   | 1.083  
------------------------------------
2.10 | id_wq5e | 0.164   | 0.131  
2.10 | id_9z5o | 0.998   | 1.000  
2.10 | id_dukt | 0.164   | 0.179  
2.10 | id_gbbq | 0.998   | 1.163  
------------------------------------
3.67 | id_wq5e | 0.153   | 0.118  
3.67 | id_9z5o | 1.000   | 1.000  
3.67 | id_dukt | 0.153   | 0.198  
3.67 | id_gbbq | 1.000   | 1.285  
------------------------------------
9.99 | id_wq5e | 0.153   | 0.085  
9.99 | id_9z5o | 1.000   | 1.000  
9.99 | id_dukt | 0.153   | 0.275  
9.99 | id_gbbq | 1.000   | 1.788  
------------------------------------
18.30 | id_wq5e | 0.153   | 0.061  
18.30 | id_9z5o | 1.000   | 1.000  
18.30 | id_dukt | 0.153   | 0.379  
18.30 | id_gbbq | 1.000   | 2.467  
------------------------------------
20.99 | id_wq5e | 0.120   | 0.056  
20.99 | id_9z5o | 1.000   | 1.000  
20.99 | id_dukt | 0.202   | 0.413  
20.99 | id_gbbq | 1.000   | 2.690  
------------------------------------
22.00 | id_wq5e | 0.051   | 0.055  
22.00 | id_9z5o | 1.000   | 1.000  
22.00 | id_dukt | 0.527   | 0.426  
22.00 | id_gbbq | 0.999   | 2.773  
------------------------------------
22.99 | id_wq5e | 0.019   | 0.053  
22.99 | id_9z5o | 1.000   | 1.000  
22.99 | id_dukt | 0.816   | 0.439  
22.99 | id_gbbq | 0.991   | 2.855  
------------------------------------
23.59 | id_wq5e | 0.011   | 0.052  
23.59 | id_9z5o | 1.000   | 1.000  
23.59 | id_dukt | 0.899   | 0.446  
23.59 | id_gbbq | 0.983   | 2.905  
------------------------------------
24.10 | id_wq5e | 0.007   | 0.051  
24.10 | id_9z5o | 1.000   | 1.000  
24.10 | id_dukt | 0.939   | 0.453  
24.10 | id_gbbq | 0.975   | 2.947  
------------------------------------
24.60 | id_wq5e | 0.004   | 0.051  
24.60 | id_9z5o | 1.000   | 1.000  
24.60 | id_dukt | 0.963   | 0.459  
24.60 | id_gbbq | 0.968   | 2.989  
------------------------------------
25.11 | id_wq5e | 0.002   | 0.050  
25.11 | id_9z5o | 1.000   | 1.000  
25.11 | id_dukt | 0.978   | 0.465  
25.11 | id_gbbq | 0.962   | 3.031  
------------------------------------
26.00 | id_wq5e | 0.001   | 0.049  
26.00 | id_9z5o | 1.000   | 1.000  
26.00 | id_dukt | 0.991   | 0.477  
26.00 | id_gbbq | 0.955   | 3.105  
------------------------------------

Experimental data tail (iteration_0):
       id_wq5e  id_9z5o   id_dukt   id_gbbq       Time
1338  0.001105      1.0  0.990532  0.954828  25.961194
1339  0.001086      1.0  0.990714  0.954691  25.980597
1340  0.001067      1.0  0.990893  0.954556  26.000000

Simulated data v7 tail:
       id_wq5e   id_dukt   id_gbbq  id_9z5o       Time
1338  0.048901  0.476269  3.101603      1.0  25.961194
1339  0.048876  0.476516  3.103214      1.0  25.980597
1340  0.048851  0.476763  3.104826      1.0  26.000000

## 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. (model_v2_sbml, sim_data_v2, current_best_sbml, model_v5_sbml, sim_data_v5, model_v7_sbml, sim_data_v7)

### 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

Model v7 successfully fixed `id_9z5o` at 1.0. However, there are still major discrepancies:
1.  `id_gbbq`: Simulated `id_gbbq` increases significantly (to ~3.1) while experimental `id_gbbq` stays around 1.0 and then slightly drops to ~0.955. This is the most glaring issue.
2.  `id_wq5e`: Simulated `id_wq5e` plateaus around 0.05, while experimental `id_wq5e` goes down to ~0.001. The decay is too slow and the plateau is too high.
3.  `id_dukt`: Simulated `id_dukt` only reaches ~0.477, while experimental `id_dukt` reaches ~0.991. The production is too slow/incomplete.

The problem with `id_gbbq` increasing suggests that the net effect of R1 and R2 is producing too much `id_gbbq` or consuming too little.
R1: `id_wq5e + id_gbbq <=> id_9z5o` (consumes `gbbq` in forward, produces in reverse)
R2: `id_dukt + id_9z5o <=> id_gbbq` (produces `gbbq` in forward, consumes in reverse)
R3_new: `id_wq5e + id_gbbq -> id_dukt + id_9z5o` (consumes `gbbq`)

Let's re-examine the equilibrium conditions for R1 and R2 with `id_9z5o = 1.0`.
Experimental plateau: `wq5e_eq = 0.153`, `dukt_eq = 0.153`, `gbbq_eq = 1.0`.
For R1: `kf1 * wq5e_eq * gbbq_eq = kr1 * 9z5o_eq` => `kf1 * 0.153 * 1.0 = kr1 * 1.0` => `kf1/kr1 = 1/0.153 approx 6.53`.
For R2: `kf2 * dukt_eq * 9z5o_eq = kr2 * gbbq_eq` => `kf2 * 0.153 * 1.0 = kr2 * 1.0` => `kf2/kr2 = 1/0.153 approx 6.53`.
The parameters `kf1=65.3, kr1=10` and `kf2=65.3, kr2=10` satisfy these equilibrium ratios.

The issue might be the interaction with R3_new.
`d(gbbq)/dt = (-kf1*wq5e*gbbq + kr1*9z5o) + (kf2*dukt*9z5o - kr2*gbbq) - k3_new*wq5e*gbbq`
If `gbbq` is increasing, it means `(kr1*9z5o + kf2*dukt*9z5o)` is larger than `(kf1*wq5e*gbbq + kr2*gbbq + k3_new*wq5e*gbbq)`.

The fact that `id_gbbq` stays at 1.0 for a long time and then drops *only when id_wq5e is nearly depleted* suggests that `id_gbbq` might also be buffered or its production/consumption is tightly regulated around 1.0, until `id_wq5e` becomes very low.

Consider a simpler model for the conversion:
R3: `id_wq5e -> id_dukt` (k3)
And R1, R2 maintain the equilibrium.
If `id_wq5e` is converted to `id_dukt`, R1 (`W+G <=> N`) shifts left (consuming N, producing W and G). R2 (`D+N <=> G`) shifts right (consuming D and N, producing G).
If N (`id_9z5o`) is constant, then:
R1: `W+G -> N` (rate `kf1*W*G`), `N -> W+G` (rate `kr1*N`)
R2: `D+N -> G` (rate `kf2*D*N`), `G -> D+N` (rate `kr2*G`)

If `id_9z5o` is constant at 1.0, and `id_gbbq` is also nearly constant at 1.0 for a long time.
This implies that the reactions involving `id_gbbq` are balanced.
`d(gbbq)/dt = -kf1*wq5e*gbbq + kr1*9z5o + kf2*dukt*9z5o - kr2*gbbq - k_consumption_gbbq = 0`
The previous R3_new (`id_wq5e + id_gbbq -> id_dukt + id_9z5o`) was `k_consumption_gbbq = k3_new*wq5e*gbbq`.

What if `id_gbbq` is also a boundary species, fixed at 1.0, until some condition is met (like `id_wq5e` depletion)? This is hard to model with simple mass-action.

Let's reconsider the stoichiometry of R3.
The experimental data shows `id_wq5e` decreases from 1.0 to ~0.0, `id_dukt` increases from 1.0 to ~2.0 (net change of +1.0, but starts at 1.0, ends at ~1.0 + (1.0-0.153) + (0.153-0.001) = 1.0 + 0.847 + 0.152 = ~1.999).
No, `id_dukt` starts at 1.0, goes to plateau 0.153, then increases to 0.991.
`id_wq5e` starts at 1.0, goes to plateau 0.153, then decreases to 0.001.
The amount of `id_wq5e` that converts is `1.0 - 0.001 = 0.999`.
The amount of `id_dukt` that is produced (net) is `0.991 - 1.0 = -0.009`. This is wrong.
Initial: W=1, D=1, G=1, N=1.
Plateau: W=0.153, D=0.153, G=1, N=1.
End: W=0.001, D=0.991, G=0.955, N=1.

Change from plateau to end:
`delta_W = 0.001 - 0.153 = -0.152`
`delta_D = 0.991 - 0.153 = +0.838`
`delta_G = 0.955 - 1.000 = -0.045`
`delta_N = 0` (constant)

The conversion reaction seems to be `id_wq5e -> id_dukt`.
If R3 is `id_wq5e -> id_dukt` (rate `k3*wq5e`):
As `id_wq5e` is consumed:
R1 (`id_wq5e + id_gbbq <=> id_9z5o`) shifts left: `id_9z5o -> id_wq5e + id_gbbq`. This produces `id_gbbq`.
As `id_dukt` is produced:
R2 (`id_dukt + id_9z5o <=> id_gbbq`) shifts right: `id_dukt + id_9z5o -> id_gbbq`. This produces `id_gbbq`.
Both these shifts would *increase* `id_gbbq` if `id_9z5o` is an infinite source. This is what we saw in Model v7.

The drop in `id_gbbq` at the end is small (-0.045) compared to the change in `id_wq5e` (-0.152 from plateau) and `id_dukt` (+0.838 from plateau).
The sum `delta_W + delta_D = -0.152 + 0.838 = +0.686`. This is not a simple 1:1 conversion.

This implies that the system is more complex than `W -> D` with R1 and R2 re-equilibrating.
The fact that `id_dukt` increases by much more than `id_wq5e` decreases (from plateau) suggests `id_dukt` might be produced from something else, or `id_wq5e` is replenished.

Let's re-evaluate the initial phase (Phase 1: t=0 to t=18, reaching plateau).
Initial: W=1, D=1, G=1, N=1.
Plateau: W=0.153, D=0.153, G=1.0, N=1.0.
Change: `delta_W = -0.847`, `delta_D = -0.847`, `delta_G = 0`, `delta_N = 0`.
This suggests reactions like:
`W -> X` (consumes W)
`D -> Y` (consumes D)
And `G` and `N` are somehow maintained.
If R1: `W+G <=> N` and R2: `D+N <=> G`.
If W decreases, R1 shifts left: `N -> W+G`. (Produces G)
If D decreases, R2 shifts left: `G -> D+N`. (Consumes G)
If these two shifts balance the change in G, then G can remain constant.
Net change from R1: `-W, -G, +N` (forward). `+W, +G, -N` (reverse).
Net change from R2: `-D, -N, +G` (forward). `+D, +N, -G` (reverse).

If `id_9z5o` is constant (boundary), then:
`d(W)/dt = kr1*N - kf1*W*G`
`d(D)/dt = kr2*G - kf2*D*N`
`d(G)/dt = kf1*W*G - kr1*N + kf2*D*N - kr2*G` (if these are the only reactions)
At equilibrium, all rates are 0.
`kf1*W*G = kr1*N`
`kf2*D*N = kr2*G`
Substituting N=1, G=1, W=0.153, D=0.153:
`kf1*0.153*1 = kr1*1` => `kf1/kr1 = 1/0.153`
`kf2*0.153*1 = kr2*1` => `kf2/kr2 = 1/0.153`
This is consistent. The parameters `kf1=65.3, kr1=10` and `kf2=65.3, kr2=10` are fine for this part.

Now, Phase 2 (t > 18): `W` decreases, `D` increases, `G` slightly decreases.
`W: 0.153 -> 0.001`
`D: 0.153 -> 0.991`
`G: 1.0 -> 0.955`
`N: 1.0 -> 1.0`

Consider the reaction `id_wq5e -> id_dukt` (k3).
`d(W)/dt = kr1*N - kf1*W*G - k3*W`
`d(D)/dt = kr2*G - kf2*D*N + k3*W`
`d(G)/dt = (kf1*W*G - kr1*N) + (kf2*D*N - kr2*G)`
With this, `dG/dt` does not have a term that makes it decrease when W is consumed.
As W decreases, `kf1*W*G` decreases, so `(kf1*W*G - kr1*N)` becomes more negative (R1 shifts left, producing G).
As D increases (due to `k3*W`), `kf2*D*N` increases, so `(kf2*D*N - kr2*G)` becomes more positive (R2 shifts right, producing G).
Both effects lead to G increasing, which is the opposite of what's observed (slight decrease).

The small decrease in `id_gbbq` (-0.045) is key.
What if R3 is `id_wq5e + X -> id_dukt`, and this X is related to `id_gbbq`?
Or, R3 is `id_wq5e -> id_dukt`, and there's another reaction `R4: id_gbbq -> Sink` that becomes active or dominant when `id_wq5e` is low? This seems too complex (conditional reaction).

Let's try to make `id_gbbq` also a boundary condition, but this is not realistic if it changes.
The problem states "all species are observable". It does not state they are all dynamic. `id_9z5o` being constant is a strong hint.

What if the stoichiometry of R1 or R2 is different?
E.g., R1: `id_wq5e + id_gbbq <=> id_9z5o`
E.g., R2: `id_dukt + id_9z5o <=> id_gbbq`

If the conversion is `id_wq5e -> id_dukt`, and this is the primary driver for Phase 2.
The amount of `id_wq5e` consumed from plateau to end is `0.153 - 0.001 = 0.152`.
The amount of `id_dukt` produced from plateau to end is `0.991 - 0.153 = 0.838`.
This is not 1:1. `0.838 / 0.152 approx 5.5`. So for each W consumed, ~5.5 D are produced. This is not simple.

This implies that `id_dukt` is not solely produced from `id_wq5e`.
Or, `id_wq5e` is consumed in multiple pathways, only one of which produces `id_dukt`.

Let's assume the reactions R1 and R2 are correct and `id_9z5o` is constant.
R1: `W + G <=> N`
R2: `D + N <=> G`
The problem is the behavior of G and the W->D conversion.

What if `id_gbbq` is consumed in the conversion reaction, and `id_dukt` is produced with a higher stoichiometry?
R3: `id_wq5e + id_gbbq -> X * id_dukt + id_9z5o` (where X might be > 1)
If X=1, this was my R3_new. It caused G to increase too much in simulation.
The issue with R3_new (`W+G -> D+N`) was that `dG/dt` had `kr1*N + kf2*D*N` as production terms for G (via R1 reverse and R2 forward) and `kf1*W*G + kr2*G + k3*W*G` as consumption terms.
When W is low, `k3*W*G` is low.
The terms `kr1*N` and `kf2*D*N` can be large.

Let's simplify. Assume R1 and R2 are fast and always near equilibrium.
`G_eq = (kr1/kf1) * N/W = (10/65.3) * 1/W = 0.153 / W` (from R1)
`G_eq = (kf2/kr2) * D*N = (65.3/10) * D*1 = 6.53 * D` (from R2)
So, `0.153/W = 6.53*D` => `W*D = 0.153 / 6.53 = 0.0234`.
This relationship `W*D = constant` should hold if R1 and R2 are in equilibrium and N, G are linked this way.
Experimental plateau: `W=0.153, D=0.153`. `W*D = 0.153^2 = 0.0234`. This holds.
Experimental end: `W=0.001, D=0.991`. `W*D = 0.001 * 0.991 = 0.000991`. This does *not* hold.
So, R1 and R2 cannot be in simple equilibrium throughout Phase 2 if G is also trying to equilibrate.

The assumption that `id_gbbq` is 1.0 at the plateau is based on visual inspection.
If `id_gbbq` is actually determined by the equilibrium of R1 and R2, and `id_9z5o` is fixed.
`G = (kf2/kr2)*D*N`. If N=1, `G = 6.53 * D`.
And `W = (kr1/kf1)*N/G = 0.153 / G`.
So `W = 0.153 / (6.53 * D)` => `W*D = 0.153/6.53 = 0.0234`. This is the same.

The fact that `id_gbbq` is so stable at 1.0 for a long time, and `id_9z5o` is also stable at 1.0, is very suggestive.
What if `id_gbbq` is ALSO a boundary species, fixed at 1.0?
Then R1: `W <=> N` (effective, since G=1, N=1 are constants)
`kf1_eff = kf1*G = kf1*1 = 65.3`
`kr1_eff = kr1*N = kr1*1 = 10`
So, `W_eq = kr1_eff / kf1_eff = 10 / 65.3 = 0.153`. This matches.

And R2: `D*N <=> G` (effective, since N=1, G=1 are constants)
`kf2_eff = kf2*N = kf2*1 = 65.3`
`kr2_eff = kr2*G = kr2*1 = 10`
So, `D_eq = kr2_eff / kf2_eff = 10 / 65.3 = 0.153`. This matches.

This model (`N=1, G=1` as boundary species) explains the plateau values for W and D.
Now, for Phase 2, we need `W -> D` conversion, and G must drop slightly at the end.
If G is a boundary species, it cannot drop. This is a contradiction.

So, `id_gbbq` is dynamic. `id_9z5o` is constant.
The reactions are:
R1: `W + G <=> N` (kf1, kr1)
R2: `D + N <=> G` (kf2, kr2)
R3: `W -> D` (k3)

Let's re-simulate Model v2 but with `id_9z5o` correctly fixed as a boundary species.
Model v2 had:
R1: `W+G <=> N` (kf1=65.3, kr1=10)
R2: `D+N <=> G` (kf2=65.3, kr2=10)
R3: `W -> D` (k3=0.065 - this was too slow, needs to be faster, like 0.6)

Let's call this Model v8:
- `id_9z5o` is boundary, initial 1.0.
- Other species initial 1.0.
- R1: `W+G <=> N` (kf1=65.3, kr1=10)
- R2: `D+N <=> G` (kf2=65.3, kr2=10)
- R3: `W -> D` (k3, try k3=0.6, similar to k3_new from v7 attempt)

Expected behavior of Model v8:
`d(W)/dt = kr1*N - kf1*W*G - k3*W`
`d(D)/dt = kr2*G - kf2*D*N + k3*W`
`d(G)/dt = (kf1*W*G - kr1*N) + (kf2*D*N - kr2*G)`
`d(N)/dt = 0` (boundary)

At plateau (W=0.153, D=0.153, G=1, N=1), if k3 is active:
`d(W)/dt = 10 - 65.3*0.153*1 - 0.6*0.153 = 10 - 9.99 - 0.0918 = -0.0818` (W decreases)
`d(D)/dt = 10*1 - 65.3*0.153*1 + 0.6*0.153 = 10 - 9.99 + 0.0918 = +0.1018` (D increases)
`d(G)/dt = (65.3*0.153*1 - 10) + (65.3*0.153*1 - 10*1) = (9.99-10) + (9.99-10) = -0.01 + -0.01 = -0.02`.
This predicts G should *decrease* slightly from the start of phase 2 if R1 and R2 are trying to maintain equilibrium around W=0.153, D=0.153, G=1.
This is different from Model v7 where G increased a lot. The R3 reaction in v7 (`W+G -> D+N`) consumed G, but the equilibrium shifts of R1 and R2 overcompensated. Here, R3 (`W->D`) does not directly involve G.

The experimental G is stable at 1.0, then drops to 0.955. A continuous small decrease from the plateau (like -0.02 from `dG/dt`) might not match the "stable then drop" behavior.
However, the calculated `dG/dt = -0.02` is small.
The rate of W decay: `0.153 * e^(-k_eff*t)`. If `k_eff` is roughly `k3=0.6`, then time to drop from 0.153 to 0.001: `ln(0.001/0.153) = -k_eff * t` => `-5.02 = -0.6 * t` => `t = 8.3s`. This matches the duration of Phase 2 (18s to 26s). So `k3=0.6` seems reasonable for the W->D conversion rate.

Let's try Model v8. The key difference from v7 is R3.
v7: R3 was `W+G -> D+N` (k3_new=0.64)
v8: R3 is `W -> D` (k3=0.6)

The slight decrease in G at the end needs to be explained.
If `dG/dt = (kf1*W*G - kr1*N) + (kf2*D*N - kr2*G)`.
When W is very low (near end), `kf1*W*G` is near 0. So `(kf1*W*G - kr1*N)` is approx `-kr1*N = -10`. (R1 strongly shifts left, producing G).
When D is high (near end, D approx 1.0), `kf2*D*N` is approx `65.3*1*1 = 65.3`. `kr2*G` is approx `10*0.955 = 9.55`. So `(kf2*D*N - kr2*G)` is approx `65.3 - 9.55 = 55.75`. (R2 strongly shifts right, producing G).
Net `dG/dt` would be `-10 + 55.75 = 45.75`. This would make G increase massively. This is the problem.

The model structure `R1: W+G <=> N`, `R2: D+N <=> G` with N constant, means that G is effectively produced by both W consumption (via R1 reverse) and D production (via R2 forward).
This structure seems incompatible with G decreasing or staying stable if W is converted to D.

What if the roles of G and N are swapped in one reaction?
R1: `W+N <=> G`
R2: `D+G <=> N` (N is boundary)
Let's check equilibrium:
`kf1*W*N = kr1*G` => `kf1*W*1 = kr1*G` => `G = (kf1/kr1)*W`
`kf2*D*G = kr2*N` => `kf2*D*G = kr2*1` => `G = (kr2/kf2)*(1/D)`
So `(kf1/kr1)*W = (kr2/kf2)*(1/D)` => `W*D = (kr1*kr2)/(kf1*kf2)`.
If `kf1/kr1 = 6.53` and `kf2/kr2 = 1/6.53` (so `kr2/kf2 = 6.53`).
Then `W*D = (1/6.53)*6.53 = 1`.
Plateau: `W=0.153, D=0.153`. `W*D = 0.0234 != 1`. This reaction structure is wrong.

The original R1, R2 structure:
R1: `W+G <=> N`
R2: `D+N <=> G`
This implies `G_eq_R1 = (kr1/kf1) * N/W` and `G_eq_R2 = (kf2/kr2) * D*N`.
These must be equal: `(kr1/kf1) * N/W = (kf2/kr2) * D*N`.
`(kr1/kf1) / W = (kf2/kr2) * D`.
`W*D = (kr1/kf1) / (kf2/kr2)`.
With `kf1/kr1 = 6.53` and `kf2/kr2 = 6.53`:
`W*D = (1/6.53) / 6.53 = 1 / (6.53^2) = 1 / 42.64 = 0.0234`. This is consistent.

The problem is the dynamics of G when R3: `W->D` is active.
`dG/dt = (kf1*W*G - kr1*N) + (kf2*D*N - kr2*G)`
Let `N=1`.
`dG/dt = kf1*W*G - kr1 + kf2*D - kr2*G`
At the end of the experiment: W=0.001, D=0.991, G=0.955.
`dG/dt = 65.3*0.001*0.955 - 10 + 65.3*0.991 - 10*0.955`
`dG/dt = 0.062 - 10 + 64.71 - 9.55 = -10 + 64.71 - 9.55 = 45.16`.
This still predicts a massive increase in G.

The only way G can decrease is if `kr1 + kr2*G` is larger than `kf1*W*G + kf2*D`.
This means the reverse reactions (consuming G) must dominate.
This would happen if W and D are very low. But D becomes high.

The experimental observation of `G` being stable at 1.0 and then slightly decreasing is very hard to reconcile with `W->D` conversion if R1 and R2 are the only other reactions involving G, and N is an infinite source.

Could `id_gbbq` be an enzyme that facilitates `W <=> D`?
E.g., `W + G <=> WG -> DG <=> D + G`.
If G is an enzyme:
R_fwd: `W -> D` with rate `k_cat_fwd * G * W / (KmW + W)`
R_rev: `D -> W` with rate `k_cat_rev * G * D / (KmD + D)`
This is Michaelis-Menten. The problem doesn't suggest enzyme kinetics explicitly. Mass-action is usually the default.

What if `id_gbbq` is not involved in the equilibria R1 and R2 in the way assumed?
The initial setup has no reactions. We are adding them.
The species are `id_wq5e, id_9z5o, id_dukt, id_gbbq`.

Alternative: `id_gbbq` is a catalyst for the conversion `id_wq5e <=> id_dukt`.
R_conversion: `id_wq5e + id_gbbq <=> id_dukt + id_gbbq` (catalyzed reversible reaction)
Rate: `k_f_conv * id_wq5e * id_gbbq - k_r_conv * id_dukt * id_gbbq`.
This reaction alone would make W and D equilibrate, G would be a catalyst.
It doesn't explain the role of `id_9z5o` or the initial plateau formation.

Let's assume the current best model (Model v7) is mostly correct in its SBML structure for `id_9z5o` being constant. The issue is the reaction kinetics or network structure for the other species.
Model v7 had:
R1: `W+G <=> N`
R2: `D+N <=> G`
R3: `W+G -> D+N` (this was R3_new)
This R3 consumes G.
`dG/dt = (kf1*W*G - kr1*N) + (kf2*D*N - kr2*G) - k3_new*W*G`
At end of experiment (W=0.001, D=0.991, G=0.955, N=1, k3_new=0.64):
`dG/dt = (0.062 - 10) + (64.71 - 9.55) - 0.64*0.001*0.955`
`dG/dt = -9.938 + 55.16 - 0.0006 = 45.22`. Still a massive increase.

The parameters `kf1, kr1, kf2, kr2` were chosen to give the plateau.
`kf1=65.3, kr1=10`
`kf2=65.3, kr2=10`
Perhaps these Keq values are wrong, or the reactions are not simple mass action.

If `id_gbbq` is consumed by R3, its concentration should drop.
The experimental `id_gbbq` is very stable at 1.0 until `id_wq5e` is almost gone.
This suggests that `id_gbbq` is replenished as long as `id_wq5e` is present above a certain level, or that its consumption rate is very low until `id_wq5e` is depleted.

This behavior is characteristic of a system where `id_gbbq` is maintained by a fast process, and its consumption is slow, or a threshold effect.

Consider a simpler system that could give the W, D, G, N plateau:
`Source_W -> W` (rate `kw_in`)
`W -> Sink_W` (rate `kw_out * W`)
`Source_D -> D` (rate `kd_in`)
`D -> Sink_D` (rate `kd_out * D`)
`Source_G -> G` (rate `kg_in`)
`G -> Sink_G` (rate `kg_out * G`)
`N` is constant.
This would make W, D, G reach `k_in/k_out`. This is too simple and doesn't use the species interactions.

Let's try to fit the parameters for Model v8 (R3: W->D) more carefully.
The problem is that G is produced by R1_reverse and R2_forward when W->D.
To keep G from increasing, we need G consumption.
If R3 is `W -> D`, there is no G consumption in R3.
If G is consumed by R1_forward (`W+G -> N`) and R2_reverse (`G -> D+N`).
`dG/dt = kf1*W*G - kr1*N + kf2*D*N - kr2*G`
If `dG/dt` is to be ~0 during phase 2 (until the end), then `kf1*W*G - kr1*N + kf2*D*N - kr2*G approx 0`.
During phase 2, W decreases, D increases.
Let W = W(t), D = D(t).
`G(t) * (kf1*W(t) - kr2) approx kr1*N - kf2*D(t)*N`.
`G(t) approx (kr1*N - kf2*D(t)*N) / (kf1*W(t) - kr2)`.
If N=1: `G(t) approx (kr1 - kf2*D(t)) / (kf1*W(t) - kr2)`.
At plateau: W=0.153, D=0.153.
`G_plateau = (10 - 65.3*0.153) / (65.3*0.153 - 10) = (10 - 9.99) / (9.99 - 10) = 0.01 / -0.01 = -1`. This is not possible.
The formula for `dG/dt` must be wrong or my reasoning about equilibrium.

The terms are:
Flux R1_fwd = `kf1*W*G` (consumes G)
Flux R1_rev = `kr1*N` (produces G)
Flux R2_fwd = `kf2*D*N` (produces G)
Flux R2_rev = `kr2*G` (consumes G)
So `dG/dt = -kf1*W*G + kr1*N + kf2*D*N - kr2*G`.
At plateau (W=0.153, D=0.153, G=1, N=1):
`dG/dt = -65.3*0.153 + 10 + 65.3*0.153 - 10*1 = -9.99 + 10 + 9.99 - 10 = 0`. This is correct for equilibrium.

Now, add R3: `W -> D` (k3).
`dW/dt = ... - k3*W`
`dD/dt = ... + k3*W`
`dG/dt` is unchanged by R3 directly.
As W decreases due to R3, `-kf1*W*G` becomes smaller (less G consumption by R1_fwd).
As D increases due to R3, `+kf2*D*N` becomes larger (more G production by R2_fwd).
Both effects make `dG/dt` positive, so G should increase. This is robust.

This means the model `R1(W+G<=>N), R2(D+N<=>G), R3(W->D)` with N constant *must* lead to G increasing during W->D conversion. This contradicts experimental G.

The only way G can decrease is if:
1. R3 consumes G: e.g., `W+G -> D` or `W+G -> D+N`. (Tried this with R3_new in v7, G still increased overall due to R1/R2 shifts).
2. There is another reaction R4 that consumes G, e.g., `G -> Sink`, and this rate becomes significant.
3. The parameters of R1/R2 change, or their form changes.

What if `id_gbbq` is actually an intermediate that is rapidly converted to `id_9z5o`?
Or `id_9z5o` is converted to `id_gbbq`?
The problem states "all species are observable".

Let's reconsider the stoichiometry of the conversion.
Phase 2: W: 0.153 -> 0.001 (consumes 0.152)
D: 0.153 -> 0.991 (produces 0.838)
G: 1.0 -> 0.955 (consumes 0.045)
N: 1.0 (constant)

Net reaction for Phase 2: `0.152 W + 0.045 G -> 0.838 D` (ignoring N for now as it's constant).
This is not balanced in terms of mass if W, G, D are similar entities.
The coefficients are roughly `1 W + 0.3 G -> 5.5 D`. This is very unusual.

This suggests that W, G, D might be parts of larger complexes, or there are hidden sources/sinks.
But the problem says "You do not need to add new species."

Could the parameters `kf1, kr1, kf2, kr2` be very different, and the plateau is a dynamic steady state, not equilibrium for R1 and R2?
If the system is:
R1: `W+G -> N` (kf1)
R2: `N -> W+G` (kr1)
R3: `D+N -> G` (kf2)
R4: `G -> D+N` (kr2)
R5: `W -> D` (k3)

And `N` is constant at 1.0.
`dW/dt = kr1*N - kf1*W*G - k3*W`
`dD/dt = kr2*G - kf2*D*N + k3*W`
`dG/dt = kf2*D*N - kr2*G - kf1*W*G + kr1*N`

This is the same set of equations as Model v8.
The simulation for Model v8 should be correct if the `simulate` function works as expected.
The discrepancy is between Model v8 prediction (G increases) and experimental data (G stable then slight drop).

This implies one of the following:
a) My rate constants for R1/R2 are wrong, and G does not actually increase with these. (Unlikely, the logic seems sound).
b) The structure of R1 or R2 is wrong.
c) There's an additional reaction consuming G that I'm missing.
d) `id_gbbq`'s behavior is not governed by simple mass-action kinetics as part of this network (e.g., it's buffered, or its production is regulated differently).

If there's a reaction `G -> Sink` (k4_sink * G).
`dG/dt = ... - k4_sink*G`.
This could counteract the increase. If `k4_sink` is small, it might allow G to be ~1, then drop when production terms weaken (e.g. D gets very high, N gets consumed if it were not boundary).

Let's try Model v9: Model v8 + `R4: G -> Sink` (irreversible decay of G).
This "Sink" is not an explicit species, just a reaction removing G.
The rate `k3` for `W->D` needs to be fast enough (e.g., 0.6).
The rate `k4_sink` needs to be tuned.
If G is stable at 1.0 while W converts to D, then `dG/dt` must be ~0.
The production of G (from R1_rev and R2_fwd) must be balanced by consumption (R1_fwd, R2_rev, and R4_sink).
Production rate of G from R1/R2 shifts: `P_G = kr1*N - kf1*W*G + kf2*D*N - kr2*G`.
At plateau, `P_G = 0`.
As W decreases and D increases, `P_G` becomes positive.
We need `k4_sink * G approx P_G` (when P_G is positive).
This `k4_sink` would need to be active throughout.

If `k4_sink` is constant, then G would decay from t=0. But G starts at 1 and stays at 1.
This means `kg_in = k4_sink * G_initial` if there was a source for G.
But there's no explicit source. G is produced by R1_rev and R2_fwd.

This is tricky. The stability of G at 1.0 is the main puzzle.
What if `id_gbbq` is also a boundary species (constant at 1.0) for most of the reaction, and then for some reason (e.g. `id_wq5e` depletion) it stops being constant and decays? This is complex to implement in SBML without events/rules.

Let's assume the simplest explanation: my parameters for R3 in Model v7 (`W+G -> D+N`) were off, or the interaction of R1,R2,R3_new is more subtle.
Model v7: R1, R2, R3_new (`W+G -> D+N`, k3_new=0.64). N is boundary.
Simulated G went to 3.1. Exp G went to 0.955.
Simulated W plateaued at 0.05. Exp W went to 0.001.
Simulated D went to 0.47. Exp D went to 0.991.

The conversion `W->D` is incomplete in v7. `k3_new` might be too small, or inhibited.
The rate was `k3_new * W * G`. If G increases, this rate should increase.

What if the reaction R2 is `G + D <=> N` instead of `D+N <=> G`?
R1: `W+G <=> N`
R2_alt: `G+D <=> N`
N is boundary.
`dW/dt = kr1_eff - kf1_eff*W*G` (where `kf1_eff` includes G, `kr1_eff` includes N)
`dG/dt = (kf1_alt*N - kr1_alt*G*D) + (kf1*N - kr1*W*G)`
This is getting confusing. Stick to the original R1, R2 structure.

The problem might be simpler: the rate constants.
The Keq values are `~6.53`.
`kf = 65.3, kr = 10`. These are quite fast.
The conversion `W->D` (k3) is slower.

If `id_gbbq` is consumed by the main reaction R3, e.g. `id_wq5e + id_gbbq -> id_dukt`.
R1: `W+G <=> N`
R2: `D+N <=> G`
R3: `W+G -> D` (k3_wg_d)
N is boundary.
`dW/dt = kr1*N - kf1*W*G - k3_wg_d*W*G`
`dD/dt = kr2*G - kf2*D*N + k3_wg_d*W*G`
`dG/dt = (kf1*W*G - kr1*N) + (kf2*D*N - kr2*G) - k3_wg_d*W*G`

Let's analyze `dG/dt` for this Model v10 (R3: `W+G -> D`):
`dG/dt = G*(-kf1*W - kr2 - k3_wg_d*W) + kr1*N + kf2*D*N`
At plateau (W=0.153, D=0.153, G=1, N=1), for `dG/dt=0`:
`1*(-65.3*0.153 - 10 - k3_wg_d*0.153) + 10*1 + 65.3*0.153*1 = 0`
`(-9.99 - 10 - 0.153*k3_wg_d) + 10 + 9.99 = 0`
`-19.99 - 0.153*k3_wg_d + 19.99 = 0`
`-0.153*k3_wg_d = 0` => `k3_wg_d = 0`.
This means if R3 is active, G cannot be at equilibrium of R1 and R2.

If `k3_wg_d` is small, e.g., 0.1.
`dG/dt` at plateau would be `~ -0.153 * 0.1 = -0.0153`. So G would slowly decrease.
This is promising for the G behavior (stable then drop).
Rate of W consumption by R3: `k3_wg_d*W*G = 0.1 * 0.153 * 1 = 0.0153`. This is slow.
We need W to convert in ~8s from 0.153 to 0.001.
`dW/dt approx -k3_wg_d*W*G`. If G is ~1. `dW/W = -k3_wg_d*dt`.
`ln(W_f/W_i) = -k3_wg_d * T`.
`ln(0.001/0.153) = -5.02`.
`-5.02 = -k3_wg_d * 8`. `k3_wg_d = 5.02/8 = 0.6275`.
Let `k3_wg_d = 0.63`.

With `k3_wg_d = 0.63`:
`dG/dt` at plateau (initial moment of phase 2) = `-0.153 * 0.63 = -0.096`.
This means G should start decreasing as soon as W starts converting.
Experimental G is stable at 1.0 for a while into phase 2 (e.g. t=18 to t=21, G is ~1.0).
Then G drops from t=22 (G=0.999) to t=26 (G=0.955).
W at t=22 is 0.051. W at t=21 is 0.12.
So, the drop in G coincides with W being already quite low.

This suggests R3 (`W+G -> D`) is correct, but the parameters for R1/R2 might need adjustment so that G is more strongly replenished, or the `k3_wg_d` is smaller initially and increases.

Let's try Model v10:
- N boundary, initial 1.0. Others initial 1.0.
- R1: `W+G <=> N` (kf1=65.3, kr1=10)
- R2: `D+N <=> G` (kf2=65.3, kr2=10)
- R3: `W+G -> D` (k3_wg_d = 0.63)

This is very similar to Model v7 (R3: `W+G -> D+N`). The only difference is R3 does not produce N. Since N is boundary, this should make no difference to N's concentration. It might slightly affect solver if N was part of mass conservation checks, but N is fixed.
The key is that R3 consumes G.
Why did G increase in v7 then?
v7: `dG/dt = (kf1*W*G - kr1*N) + (kf2*D*N - kr2*G) - k3_new*W*G` (k3_new was 0.64)
This is the same equation for G as Model v10.
The simulation result for v7 (G increasing to 3.1) must be due to the parameter values used.
In v7, W plateaued at 0.05, D only got to 0.47.
This means `kr1*N` (produces G) and `kf2*D*N` (produces G) dominated over `kf1*W*G` (consumes G), `kr2*G` (consumes G), and `k3_new*W*G` (consumes G).
`kr1*N = 10`.
`kf2*D*N`: if D reaches 0.47, this is `65.3 * 0.47 = 30.6`.
Total production tendency for G: `10 + 30.6 = 40.6`.
Consumption:
`kf1*W*G`: if W=0.05, G=3 (example), `65.3*0.05*3 = 9.8`.
`kr2*G`: `10*3 = 30`.
`k3_new*W*G`: `0.64*0.05*3 = 0.096`.
Total consumption tendency for G: `9.8 + 30 + 0.096 = 39.896`.
These are roughly balanced, explaining why G plateaued at ~3.1.

The issue is that W did not go low enough, and D did not go high enough in v7.
This means the conversion R3 (`W+G -> D+N`) was too slow or incomplete.
Rate `k3_new*W*G`. If G increases, rate should increase.
Perhaps the equilibrium of R3 is unfavorable. But it's irreversible.

Let's retry Model v7's structure (R3: `W+G -> D+N`) but with a much larger k3.
If `k3_new` is, say, 10 times larger: `k3_new = 6.4`.
This should make W convert much faster and more completely.
This is Model v11.

## Action

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

# ---- Build Model v11 (Based on v7, but with much larger k3_new) ----
sbml_doc_v11 = libsbml.readSBMLFromString(input_sbml_string)
model_v11 = sbml_doc_v11.getModel()

s_wq5e = "id_wq5e"
s_9z5o = "id_9z5o"
s_dukt = "id_dukt"
s_gbbq = "id_gbbq"

# Configure id_9z5o as a constant species
species_9z5o_obj = model_v11.getSpecies(s_9z5o)
species_9z5o_obj.setInitialConcentration(1.0)
species_9z5o_obj.setConstant(True)
species_9z5o_obj.setBoundaryCondition(True)

model_v11.getSpecies(s_wq5e).setInitialConcentration(1.0)
model_v11.getSpecies(s_dukt).setInitialConcentration(1.0)
model_v11.getSpecies(s_gbbq).setInitialConcentration(1.0)

# Reaction R1: id_wq5e + id_gbbq <=> id_9z5o
r1 = model_v11.createReaction(); r1.setId("R1"); r1.setReversible(True); r1.setFast(False)
r1.createReactantSpeciesRef(s_wq5e, 1.0, True)
r1.createReactantSpeciesRef(s_gbbq, 1.0, True)
r1.createProductSpeciesRef(s_9z5o, 1.0, True)
kl_r1 = r1.createKineticLaw()
kl_r1.createParameter("kf1", 65.3)
kl_r1.createParameter("kr1", 10.0)
kl_r1.setMath(libsbml.parseL3Formula(f"kf1 * {s_wq5e} * {s_gbbq} - kr1 * {s_9z5o}"))

# Reaction R2: id_dukt + id_9z5o <=> id_gbbq
r2 = model_v11.createReaction(); r2.setId("R2"); r2.setReversible(True); r2.setFast(False)
r2.createReactantSpeciesRef(s_dukt, 1.0, True)
r2.createReactantSpeciesRef(s_9z5o, 1.0, True)
r2.createProductSpeciesRef(s_gbbq, 1.0, True)
kl_r2 = r2.createKineticLaw()
kl_r2.createParameter("kf2", 65.3)
kl_r2.createParameter("kr2", 10.0)
kl_r2.setMath(libsbml.parseL3Formula(f"kf2 * {s_dukt} * {s_9z5o} - kr2 * {s_gbbq}"))

# Reaction R3_new: id_wq5e + id_gbbq -> id_dukt + id_9z5o
r3 = model_v11.createReaction(); r3.setId("R3_new"); r3.setReversible(False); r3.setFast(False)
r3.createReactantSpeciesRef(s_wq5e, 1.0, True)
r3.createReactantSpeciesRef(s_gbbq, 1.0, True)
r3.createProductSpeciesRef(s_dukt, 1.0, True)
r3.createProductSpeciesRef(s_9z5o, 1.0, True) # N is boundary, so its production here doesn't change its conc.
kl_r3 = r3.createKineticLaw()
kl_r3.createParameter("k3_new", 6.4) # Increased k3_new significantly (was 0.64)
kl_r3.setMath(libsbml.parseL3Formula(f"k3_new * {s_wq5e} * {s_gbbq}"))

# Helper to add species references
def _add_species_ref(reaction, species_id, stoichiometry, constant=True):
    s_ref = reaction.createReactant() if reaction.getReactant(species_id) else reaction.createProduct()
    # This logic is flawed for adding, need to specify reactant or product
    # Corrected usage:
    # For reactant: s_ref = reaction.createReactant()
    # For product:  s_ref = reaction.createProduct()
    # s_ref.setSpecies(species_id)
    # s_ref.setStoichiometry(stoichiometry)
    # s_ref.setConstant(constant)
    # The createReactantSpeciesRef and createProductSpeciesRef are custom helpers I defined in thought but cannot use.
    # Reverting to standard libsbml:

# Re-doing reaction definitions with standard libsbml for clarity and correctness
# Clear existing reactions if any were partially made by mistake (model is fresh from string though)
while model_v11.getNumReactions() > 0:
    model_v11.removeReaction(0)

# R1
r1 = model_v11.createReaction(); r1.setId("R1"); r1.setReversible(True); r1.setFast(False)
reactant1_r1 = r1.createReactant(); reactant1_r1.setSpecies(s_wq5e); reactant1_r1.setStoichiometry(1.0); reactant1_r1.setConstant(True)
reactant2_r1 = r1.createReactant(); reactant2_r1.setSpecies(s_gbbq); reactant2_r1.setStoichiometry(1.0); reactant2_r1.setConstant(True)
product1_r1 = r1.createProduct(); product1_r1.setSpecies(s_9z5o); product1_r1.setStoichiometry(1.0); product1_r1.setConstant(True)
kl_r1 = r1.createKineticLaw()
kf1_p = kl_r1.createParameter(); kf1_p.setId("kf1"); kf1_p.setValue(65.3)
kr1_p = kl_r1.createParameter(); kr1_p.setId("kr1"); kr1_p.setValue(10.0)
kl_r1.setMath(libsbml.parseL3Formula(f"kf1 * {s_wq5e} * {s_gbbq} - kr1 * {s_9z5o}"))

# R2
r2 = model_v11.createReaction(); r2.setId("R2"); r2.setReversible(True); r2.setFast(False)
reactant1_r2 = r2.createReactant(); reactant1_r2.setSpecies(s_dukt); reactant1_r2.setStoichiometry(1.0); reactant1_r2.setConstant(True)
reactant2_r2 = r2.createReactant(); reactant2_r2.setSpecies(s_9z5o); reactant2_r2.setStoichiometry(1.0); reactant2_r2.setConstant(True)
product1_r2 = r2.createProduct(); product1_r2.setSpecies(s_gbbq); product1_r2.setStoichiometry(1.0); product1_r2.setConstant(True)
kl_r2 = r2.createKineticLaw()
kf2_p = kl_r2.createParameter(); kf2_p.setId("kf2"); kf2_p.setValue(65.3)
kr2_p = kl_r2.createParameter(); kr2_p.setId("kr2"); kr2_p.setValue(10.0)
kl_r2.setMath(libsbml.parseL3Formula(f"kf2 * {s_dukt} * {s_9z5o} - kr2 * {s_gbbq}"))

# R3_new
r3 = model_v11.createReaction(); r3.setId("R3_new"); r3.setReversible(False); r3.setFast(False)
reactant1_r3 = r3.createReactant(); reactant1_r3.setSpecies(s_wq5e); reactant1_r3.setStoichiometry(1.0); reactant1_r3.setConstant(True)
reactant2_r3 = r3.createReactant(); reactant2_r3.setSpecies(s_gbbq); reactant2_r3.setStoichiometry(1.0); reactant2_r3.setConstant(True)
product1_r3 = r3.createProduct(); product1_r3.setSpecies(s_dukt); product1_r3.setStoichiometry(1.0); product1_r3.setConstant(True)
product2_r3 = r3.createProduct(); product2_r3.setSpecies(s_9z5o); product2_r3.setStoichiometry(1.0); product2_r3.setConstant(True)
kl_r3 = r3.createKineticLaw()
k3_new_p = kl_r3.createParameter(); k3_new_p.setId("k3_new"); k3_new_p.setValue(6.4) # k3_new = 6.4
kl_r3.setMath(libsbml.parseL3Formula(f"k3_new * {s_wq5e} * {s_gbbq}"))


writer = libsbml.SBMLWriter()
model_v11_sbml = writer.writeSBMLToString(sbml_doc_v11)
shared_variables.add("model_v11_sbml", model_v11_sbml)

sim_data_v11 = simulate(model_v11_sbml)
shared_variables.add("sim_data_v11", sim_data_v11)

exp_data = experiment_history['iteration_0']
print("--- Model v11 Simulation Results (k3_new = 6.4) ---")
print(f"Sim runs: t={sim_data_v11['Time'].max()}, points={len(sim_data_v11)}")
print("Time | Species | Exp_Val | Sim_Val")
print("------------------------------------")
exp_time_points = [0.0, 1.05, 2.10, 3.67, 10.0, 18.3, 21.0, 22.0, 23.0, 23.6, 24.1, 24.6, 25.1, 26.0]
for t_exp_target in exp_time_points:
    exp_row = exp_data.iloc[(exp_data['Time'] - t_exp_target).abs().argsort()[:1]]
    t_exp_actual = exp_row['Time'].iloc[0]
    sim_row = sim_data_v11.iloc[(sim_data_v11['Time'] - t_exp_target).abs().argsort()[:1]]
    sim_wq5e = sim_row[s_wq5e].iloc[0]; sim_9z5o = sim_row[s_9z5o].iloc[0]
    sim_dukt = sim_row[s_dukt].iloc[0]; sim_gbbq = sim_row[s_gbbq].iloc[0]
    print(f"{t_exp_actual:<4.2f} | {s_wq5e:<7} | {exp_row[s_wq5e].iloc[0]:<7.3f} | {sim_wq5e:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_9z5o:<7} | {exp_row[s_9z5o].iloc[0]:<7.3f} | {sim_9z5o:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_dukt:<7} | {exp_row[s_dukt].iloc[0]:<7.3f} | {sim_dukt:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_gbbq:<7} | {exp_row[s_gbbq].iloc[0]:<7.3f} | {sim_gbbq:<7.3f}")
    print("------------------------------------")
shared_variables.add("current_best_sbml", model_v11_sbml)

```
# Observation

## Code Stderror
 'Reaction' object has no attribute 'createReactantSpeciesRef'

## 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. (model_v2_sbml, sim_data_v2, current_best_sbml, model_v5_sbml, sim_data_v5, model_v7_sbml, sim_data_v7)

### 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 previous iteration failed due to a `NameError` because I used non-existent helper methods (`createReactantSpeciesRef`, `createProductSpeciesRef`) for creating species references in reactions. I had noted this potential error in my thoughts and even included the correct libSBML syntax, but the erroneous calls were still present in the first part of the code.

I will correct this by using the standard libSBML methods:
1.  Create a reaction: `reaction = model.createReaction()`
2.  For each reactant:
    *   `reactant_ref = reaction.createReactant()`
    *   `reactant_ref.setSpecies("species_id")`
    *   `reactant_ref.setStoichiometry(value)`
    *   `reactant_ref.setConstant(True)` (to indicate fixed stoichiometry)
3.  For each product:
    *   `product_ref = reaction.createProduct()`
    *   `product_ref.setSpecies("species_id")`
    *   `product_ref.setStoichiometry(value)`
    *   `product_ref.setConstant(True)`

The model structure (Model v11) remains the same as intended in the previous turn:
*   `id_9z5o` is a boundary species, initial concentration 1.0.
*   Other species (`id_wq5e`, `id_dukt`, `id_gbbq`) initial concentration 1.0.
*   Reaction R1: `id_wq5e + id_gbbq <=> id_9z5o` (Parameters `kf1=65.3`, `kr1=10.0`)
*   Reaction R2: `id_dukt + id_9z5o <=> id_gbbq` (Parameters `kf2=65.3`, `kr2=10.0`)
*   Reaction R3_new: `id_wq5e + id_gbbq -> id_dukt + id_9z5o` (Parameter `k3_new=6.4` - significantly increased from previous attempts like 0.64 in Model v7).

The goal is to see if a much faster conversion rate for R3_new can drive `id_wq5e` lower and `id_dukt` higher, and how `id_gbbq` behaves under these conditions. The hypothesis is that the previous `k3_new` was too small, leading to incomplete conversion and incorrect levels for `id_gbbq`.

## Action

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

# ---- Build Model v11 (Corrected SBML construction) ----
sbml_doc_v11 = libsbml.readSBMLFromString(input_sbml_string)
model_v11 = sbml_doc_v11.getModel()

s_wq5e = "id_wq5e"
s_9z5o = "id_9z5o"
s_dukt = "id_dukt"
s_gbbq = "id_gbbq"

# Configure id_9z5o as a constant species
species_9z5o_obj = model_v11.getSpecies(s_9z5o)
species_9z5o_obj.setInitialConcentration(1.0)
species_9z5o_obj.setConstant(True)
species_9z5o_obj.setBoundaryCondition(True)

# Set initial concentrations for other species
model_v11.getSpecies(s_wq5e).setInitialConcentration(1.0)
model_v11.getSpecies(s_dukt).setInitialConcentration(1.0)
model_v11.getSpecies(s_gbbq).setInitialConcentration(1.0)

# Reaction R1: id_wq5e + id_gbbq <=> id_9z5o
r1 = model_v11.createReaction(); r1.setId("R1"); r1.setReversible(True); r1.setFast(False)
reactant1_r1 = r1.createReactant(); reactant1_r1.setSpecies(s_wq5e); reactant1_r1.setStoichiometry(1.0); reactant1_r1.setConstant(True)
reactant2_r1 = r1.createReactant(); reactant2_r1.setSpecies(s_gbbq); reactant2_r1.setStoichiometry(1.0); reactant2_r1.setConstant(True)
product1_r1 = r1.createProduct(); product1_r1.setSpecies(s_9z5o); product1_r1.setStoichiometry(1.0); product1_r1.setConstant(True)
kl_r1 = r1.createKineticLaw()
kf1_p = kl_r1.createParameter(); kf1_p.setId("kf1"); kf1_p.setValue(65.3)
kr1_p = kl_r1.createParameter(); kr1_p.setId("kr1"); kr1_p.setValue(10.0)
kl_r1.setMath(libsbml.parseL3Formula(f"kf1 * {s_wq5e} * {s_gbbq} - kr1 * {s_9z5o}"))

# Reaction R2: id_dukt + id_9z5o <=> id_gbbq
r2 = model_v11.createReaction(); r2.setId("R2"); r2.setReversible(True); r2.setFast(False)
reactant1_r2 = r2.createReactant(); reactant1_r2.setSpecies(s_dukt); reactant1_r2.setStoichiometry(1.0); reactant1_r2.setConstant(True)
reactant2_r2 = r2.createReactant(); reactant2_r2.setSpecies(s_9z5o); reactant2_r2.setStoichiometry(1.0); reactant2_r2.setConstant(True)
product1_r2 = r2.createProduct(); product1_r2.setSpecies(s_gbbq); product1_r2.setStoichiometry(1.0); product1_r2.setConstant(True)
kl_r2 = r2.createKineticLaw()
kf2_p = kl_r2.createParameter(); kf2_p.setId("kf2"); kf2_p.setValue(65.3)
kr2_p = kl_r2.createParameter(); kr2_p.setId("kr2"); kr2_p.setValue(10.0)
kl_r2.setMath(libsbml.parseL3Formula(f"kf2 * {s_dukt} * {s_9z5o} - kr2 * {s_gbbq}"))

# Reaction R3_new: id_wq5e + id_gbbq -> id_dukt + id_9z5o
r3 = model_v11.createReaction(); r3.setId("R3_new"); r3.setReversible(False); r3.setFast(False)
reactant1_r3 = r3.createReactant(); reactant1_r3.setSpecies(s_wq5e); reactant1_r3.setStoichiometry(1.0); reactant1_r3.setConstant(True)
reactant2_r3 = r3.createReactant(); reactant2_r3.setSpecies(s_gbbq); reactant2_r3.setStoichiometry(1.0); reactant2_r3.setConstant(True)
product1_r3 = r3.createProduct(); product1_r3.setSpecies(s_dukt); product1_r3.setStoichiometry(1.0); product1_r3.setConstant(True)
product2_r3 = r3.createProduct(); product2_r3.setSpecies(s_9z5o); product2_r3.setStoichiometry(1.0); product2_r3.setConstant(True)
kl_r3 = r3.createKineticLaw()
k3_new_p = kl_r3.createParameter(); k3_new_p.setId("k3_new"); k3_new_p.setValue(6.4) # k3_new = 6.4
kl_r3.setMath(libsbml.parseL3Formula(f"k3_new * {s_wq5e} * {s_gbbq}"))

# Write the updated SBML to a string
writer = libsbml.SBMLWriter()
model_v11_sbml = writer.writeSBMLToString(sbml_doc_v11)
shared_variables.add("model_v11_sbml", model_v11_sbml)

# ---- Simulate Model v11 ----
sim_data_v11 = simulate(model_v11_sbml)
shared_variables.add("sim_data_v11", sim_data_v11)

# ---- Compare with Experimental Data ----
exp_data = experiment_history['iteration_0']

print("--- Model v11 Simulation Results (k3_new = 6.4, Corrected SBML) ---")
print(f"Simulation runs from t=0 to t={sim_data_v11['Time'].max()} with {len(sim_data_v11)} points.")
print("\nComparison at selected time points (Experimental vs Simulated):")
print("Time | Species | Exp_Val | Sim_Val")
print("------------------------------------")

exp_time_points = [0.0, 1.05, 2.10, 3.67, 10.0, 18.3, 21.0, 22.0, 23.0, 23.6, 24.1, 24.6, 25.1, 26.0] 

for t_exp_target in exp_time_points:
    exp_row = exp_data.iloc[(exp_data['Time'] - t_exp_target).abs().argsort()[:1]]
    t_exp_actual = exp_row['Time'].iloc[0]

    if t_exp_target <= sim_data_v11['Time'].max():
        sim_row = sim_data_v11.iloc[(sim_data_v11['Time'] - t_exp_target).abs().argsort()[:1]]
        sim_wq5e = sim_row[s_wq5e].iloc[0]
        sim_9z5o = sim_row[s_9z5o].iloc[0]
        sim_dukt = sim_row[s_dukt].iloc[0]
        sim_gbbq = sim_row[s_gbbq].iloc[0]
    else:
        sim_wq5e, sim_9z5o, sim_dukt, sim_gbbq = (float('nan'),)*4
        
    print(f"{t_exp_actual:<4.2f} | {s_wq5e:<7} | {exp_row[s_wq5e].iloc[0]:<7.3f} | {sim_wq5e:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_9z5o:<7} | {exp_row[s_9z5o].iloc[0]:<7.3f} | {sim_9z5o:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_dukt:<7} | {exp_row[s_dukt].iloc[0]:<7.3f} | {sim_dukt:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_gbbq:<7} | {exp_row[s_gbbq].iloc[0]:<7.3f} | {sim_gbbq:<7.3f}")
    print("------------------------------------")

print("\nExperimental data tail (iteration_0):")
print(exp_data.tail(3))
print("\nSimulated data v11 tail:")
print(sim_data_v11.tail(3))

shared_variables.add("current_best_sbml", model_v11_sbml)
```
# Observation

## Code Stdout
--- Model v11 Simulation Results (k3_new = 6.4, Corrected SBML) ---
Simulation runs from t=0 to t=26.0 with 1341 points.

Comparison at selected time points (Experimental vs Simulated):
Time | Species | Exp_Val | Sim_Val
------------------------------------
0.00 | id_wq5e | 1.000   | 1.000  
0.00 | id_9z5o | 1.000   | 1.000  
0.00 | id_dukt | 1.000   | 1.000  
0.00 | id_gbbq | 1.000   | 1.000  
------------------------------------
1.05 | id_wq5e | 0.352   | 0.077  
1.05 | id_9z5o | 0.995   | 1.000  
1.05 | id_dukt | 0.352   | 0.289  
1.05 | id_gbbq | 0.995   | 1.806  
------------------------------------
2.10 | id_wq5e | 0.164   | 0.054  
2.10 | id_9z5o | 0.998   | 1.000  
2.10 | id_dukt | 0.164   | 0.410  
2.10 | id_gbbq | 0.998   | 2.599  
------------------------------------
3.67 | id_wq5e | 0.153   | 0.037  
3.67 | id_9z5o | 1.000   | 1.000  
3.67 | id_dukt | 0.153   | 0.594  
3.67 | id_gbbq | 1.000   | 3.802  
------------------------------------
9.99 | id_wq5e | 0.153   | 0.016  
9.99 | id_9z5o | 1.000   | 1.000  
9.99 | id_dukt | 0.153   | 1.341  
9.99 | id_gbbq | 1.000   | 8.682  
------------------------------------
18.30 | id_wq5e | 0.153   | 0.009  
18.30 | id_9z5o | 1.000   | 1.000  
18.30 | id_dukt | 0.153   | 2.325  
18.30 | id_gbbq | 1.000   | 15.105 
------------------------------------
20.99 | id_wq5e | 0.120   | 0.008  
20.99 | id_9z5o | 1.000   | 1.000  
20.99 | id_dukt | 0.202   | 2.645  
20.99 | id_gbbq | 1.000   | 17.192 
------------------------------------
22.00 | id_wq5e | 0.051   | 0.008  
22.00 | id_9z5o | 1.000   | 1.000  
22.00 | id_dukt | 0.527   | 2.764  
22.00 | id_gbbq | 0.999   | 17.972 
------------------------------------
22.99 | id_wq5e | 0.019   | 0.007  
22.99 | id_9z5o | 1.000   | 1.000  
22.99 | id_dukt | 0.816   | 2.881  
22.99 | id_gbbq | 0.991   | 18.738 
------------------------------------
23.59 | id_wq5e | 0.011   | 0.007  
23.59 | id_9z5o | 1.000   | 1.000  
23.59 | id_dukt | 0.899   | 2.953  
23.59 | id_gbbq | 0.983   | 19.203 
------------------------------------
24.10 | id_wq5e | 0.007   | 0.007  
24.10 | id_9z5o | 1.000   | 1.000  
24.10 | id_dukt | 0.939   | 3.012  
24.10 | id_gbbq | 0.975   | 19.594 
------------------------------------
24.60 | id_wq5e | 0.004   | 0.007  
24.60 | id_9z5o | 1.000   | 1.000  
24.60 | id_dukt | 0.963   | 3.072  
24.60 | id_gbbq | 0.968   | 19.984 
------------------------------------
25.11 | id_wq5e | 0.002   | 0.007  
25.11 | id_9z5o | 1.000   | 1.000  
25.11 | id_dukt | 0.978   | 3.132  
25.11 | id_gbbq | 0.962   | 20.375 
------------------------------------
26.00 | id_wq5e | 0.001   | 0.007  
26.00 | id_9z5o | 1.000   | 1.000  
26.00 | id_dukt | 0.991   | 3.238  
26.00 | id_gbbq | 0.955   | 21.065 
------------------------------------

Experimental data tail (iteration_0):
       id_wq5e  id_9z5o   id_dukt   id_gbbq       Time
1338  0.001105      1.0  0.990532  0.954828  25.961194
1339  0.001086      1.0  0.990714  0.954691  25.980597
1340  0.001067      1.0  0.990893  0.954556  26.000000

Simulated data v11 tail:
       id_wq5e   id_dukt    id_gbbq  id_9z5o       Time
1338  0.006630  3.233185  21.035286      1.0  25.961194
1339  0.006626  3.235484  21.050302      1.0  25.980597
1340  0.006621  3.237784  21.065317      1.0  26.000000

## 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. (model_v2_sbml, sim_data_v2, current_best_sbml, model_v5_sbml, sim_data_v5, model_v7_sbml, sim_data_v7, model_v11_sbml, sim_data_v11)

### 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

Model v11 (R1: `W+G <=> N`, R2: `D+N <=> G`, R3: `W+G -> D+N`, with `k3_new=6.4` and N as boundary) showed:
*   `id_wq5e`: Simulated (0.007) is much closer to experimental (0.001) at the end. The conversion is more complete.
*   `id_dukt`: Simulated (3.238) is much higher than experimental (0.991). This is a new major discrepancy.
*   `id_gbbq`: Simulated (21.065) is extremely high, while experimental is 0.955. This is worse than before.
*   `id_9z5o`: Correctly stays at 1.0.

The massive increase in `id_gbbq` is still the primary problem. The logic remains: as `id_wq5e` is consumed (by R3), R1 (`W+G <=> N`) shifts left (`N -> W+G`), producing G. As `id_dukt` is produced (by R3), R2 (`D+N <=> G`) shifts right (`D+N -> G`), producing G. Both equilibrium-restoring fluxes for R1 and R2 generate `id_gbbq` when `id_9z5o` is an infinite source. The R3 reaction (`W+G -> D+N`) consumes G, but this consumption is clearly overwhelmed.

The fact that `id_dukt` overshoots significantly (3.2 vs 0.99) suggests that the stoichiometry of R3 might be wrong, or `id_dukt` is consumed by another reaction.
Experimental changes from plateau (W=0.153, D=0.153, G=1) to end (W=0.001, D=0.991, G=0.955):
`delta_W = -0.152`
`delta_D = +0.838`
`delta_G = -0.045`

If R3 is `aW + bG -> cD (+ N)`
The ratio `delta_D / (-delta_W) = 0.838 / 0.152 approx 5.5`. This suggests `c/a approx 5.5`.
The ratio `(-delta_G) / (-delta_W) = 0.045 / 0.152 approx 0.3`. This suggests `b/a approx 0.3`.
So, a hypothetical R3 could be: `W + 0.3G -> 5.5D (+N)`.
This is highly unconventional for elementary reactions.

Let's reconsider the possibility that `id_gbbq` is somehow "buffered" or its concentration is homeostatically regulated, rather than being a simple participant in mass-action kinetics that allow it to grow unbounded.
The experimental data shows `id_gbbq` is very stable at 1.0 for a long period (t=0 to t=~22), and only then does it drop slightly to 0.955. This drop occurs when `id_wq5e` is very low (e.g., `id_wq5e` at t=22 is 0.051).

This behavior might imply:
1.  A strong, fast reaction that produces `id_gbbq` to maintain it at 1.0, which weakens when `id_wq5e` (a potential substrate for this production) is depleted.
2.  `id_gbbq` is consumed by a reaction that is inhibited by `id_wq5e`, and this inhibition is relieved when `id_wq5e` is low, causing `id_gbbq` to drop.

Given the constraint of not adding new species, let's try to achieve this with the existing ones.
What if `id_gbbq` is produced from `id_9z5o` (the constant source) in a reaction that is somehow limited or regulated?
And `id_gbbq` is consumed.

Consider a different role for `id_gbbq`. What if it's a catalyst that gets slowly consumed/inactivated?
If R3 is `W -> D`, catalyzed by G.
`W + G_active -> D + G_active`
`G_active -> G_inactive` (slow decay of G)
This doesn't fit the sharp drop at the end.

The overshoot of `id_dukt` in Model v11 is also a problem. If R3 is `W+G -> D+N`, then 1 W produces 1 D.
Initial state: W=1, D=1.
If all W (1 unit) converts to D, then D should become 1 (initial) + 1 (produced) = 2.
The experimental D ends at 0.991. This means that either not all W is converted to D, or D is consumed.
But W goes to 0.001, so most of it is consumed.
If W is consumed, and D doesn't increase stoichiometrically, then W must go to something else, or D is consumed.

Let's assume the reaction `id_wq5e -> id_dukt` is the core of Phase 2.
Stoichiometry: `1 id_wq5e -> 1 id_dukt`.
Change in W from start (1.0) to end (0.001) is -0.999.
This should produce +0.999 D.
Initial D is 1.0. So final D should be `1.0 + 0.999 = 1.999`.
Experimental final D is 0.991.
This is a massive discrepancy. `1.999 (expected) vs 0.991 (observed)`.
This means that for every mole of W consumed, only `(0.991-1.0) / (0.001-1.0) = -0.009 / -0.999 approx 0.009` moles of D are *net* produced. This cannot be right.

The calculation must be from the plateau, as R1/R2 establish that first.
Plateau: W=0.153, D=0.153, G=1.0, N=1.0.
End: W=0.001, D=0.991, G=0.955, N=1.0.
`delta_W = 0.001 - 0.153 = -0.152`
`delta_D = 0.991 - 0.153 = +0.838`
`delta_G = 0.955 - 1.000 = -0.045`
If R3 is `W -> D`:
Consumption of 0.152 W should produce 0.152 D.
So D should be `0.153 (plateau) + 0.152 (from W) = 0.305`.
But D is 0.991. This means D is produced from another source, or W is not the only source for D in R3.

This implies that the reaction R3: `W (+G) -> D (+N)` is too simple or wrong.
The system seems to generate much more D than W consumed during Phase 2.
`0.838 D produced / 0.152 W consumed = 5.5 D/W`.

This suggests a reaction like `id_wq5e -> 5.5 id_dukt` effectively.
This could be `id_wq5e + 4.5 Source -> 5.5 id_dukt` where Source is implicit or `id_9z5o`.
Try R3: `id_wq5e + X*id_9z5o + Y*id_gbbq -> Z*id_dukt + ...`

What if `id_gbbq` is actually consumed to make `id_dukt`?
R3: `id_wq5e + id_gbbq -> Z*id_dukt`
If Z=1: `W+G -> D`.
`delta_W = -0.152`. `delta_G = -0.045`.
If this R3 is dominant for W consumption:
Amount of W consumed by R3 = 0.152.
This would consume 0.152 G if stoichiometry is 1:1 for G. (Experimental G consumption is 0.045).
This would produce 0.152 D if stoichiometry is 1:1 for D. (Experimental D production is 0.838).
This doesn't line up.

The system is behaving strangely if these are the only species.
The large production of D and small consumption of G relative to W consumption is key.

Could `id_9z5o` (constant source) be converted into `id_dukt`?
E.g., R3: `id_wq5e -> TriggerSignal`
`TriggerSignal + id_9z5o -> id_dukt`
But `id_wq5e` itself is consumed.

Let's reconsider the model that seemed to get G right in terms of dynamics (stable then slight decrease), which was Model v10's *prediction* before simulation: R3: `W+G -> D` (k3_wg_d = 0.63).
The `dG/dt` calculation at plateau was `~ -0.153 * k3_wg_d`.
If `k3_wg_d` is small, G decreases slowly.
If `k3_wg_d = 0.63`, `dG/dt = -0.096`. This is a continuous decrease.
To have G stable then drop, `k3_wg_d` needs to be effectively zero, then turn on. Or the G production terms (`kr1*N + kf2*D*N`) must perfectly balance G consumption terms (`kf1*W*G + kr2*G + k3_wg_d*W*G`) for a while.

This balance is: `kr1*N + kf2*D*N = G * (kf1*W + kr2 + k3_wg_d*W)`
`10 + 65.3*D = G * (65.3*W + 10 + k3_wg_d*W)`
If G=1, D=0.153, W=0.153 (plateau):
`10 + 65.3*0.153 = 1 * (65.3*0.153 + 10 + k3_wg_d*0.153)`
`10 + 9.99 = 9.99 + 10 + 0.153*k3_wg_d`
`19.99 = 19.99 + 0.153*k3_wg_d` => `k3_wg_d = 0`.
This confirms that for G to be stable at 1.0 at the plateau with R1/R2 in equilibrium, R3 (if it consumes G as `k3_wg_d*W*G`) must be off.

This implies R3 is not `W+G -> D`.
If R3 is `W -> D` (Model v8 type).
`dG/dt = kr1*N + kf2*D*N - G*(kf1*W + kr2)`.
For `dG/dt=0` at G=1, D=0.153, W=0.153:
`10 + 65.3*0.153 = 1*(65.3*0.153 + 10)` => `19.99 = 19.99`. This is balanced.
So, if R3 is `W->D`, G *should* initially be stable due to R1/R2 equilibrium.
As W decreases and D increases (due to R3: `W->D`):
`dG/dt = 10 + 65.3*D(t) - 1*(65.3*W(t) + 10) = 65.3 * (D(t) - W(t))`.
Initially D(t)=W(t), so `dG/dt=0`.
As W->D, D(t) becomes > W(t). So `dG/dt` becomes positive. G increases.
This brings us back to the fundamental problem: R1/R2 structure + `W->D` makes G increase.

The experimental G is stable, then *drops*.
This means `D(t) - W(t)` must become negative for G to drop, or the coefficient of G in consumption `(kf1*W+kr2)` must become very large, or production `(kr1*N+kf2*D*N)` must become small.

What if `id_gbbq` is not a product of R2, but a reactant?
R1: `W+G <=> N`
R2_alt: `D+G <=> N` (N is boundary)
Then `dG/dt = - (kf1*W*G - kr1*N) - (kf2_alt*D*G - kr2_alt*N) + R3_effect_on_G`
If R3 is `W->D`.
`dG/dt = G*(-kf1*W - kf2_alt*D) + kr1*N + kr2_alt*N`.
At plateau (W=0.153, D=0.153, G=1, N=1), for `dG/dt=0`:
`1*(-kf1*0.153 - kf2_alt*0.153) + kr1 + kr2_alt = 0`.
`0.153*(kf1+kf2_alt) = kr1+kr2_alt`.
This is one equation. We also need W, D to be at their plateau values.
From R1: `kf1*W*G = kr1*N` => `kf1*0.153*1 = kr1*1` => `kf1/kr1 = 1/0.153 approx 6.53`.
From R2_alt: `kf2_alt*D*G = kr2_alt*N` => `kf2_alt*0.153*1 = kr2_alt*1` => `kf2_alt/kr2_alt = 1/0.153 approx 6.53`.
So, `kf1=65.3, kr1=10` and `kf2_alt=65.3, kr2_alt=10` would work for plateau.
Substitute into `dG/dt=0` condition:
`0.153*(65.3+65.3) = 10+10`
`0.153 * 130.6 = 20`
`19.98 approx 20`. This is consistent.

Now, with this R2_alt (`D+G <=> N`), and R3 (`W->D` with k3):
`dG/dt = G*(-kf1*W - kf2_alt*D) + (kr1+kr2_alt)*N`. (N=1)
`dG/dt = G*(-65.3*W - 65.3*D) + (10+10) = -65.3*G*(W+D) + 20`.
At plateau (W=0.153, D=0.153, G=1): `dG/dt = -65.3*1*(0.153+0.153) + 20 = -65.3*0.306 + 20 = -19.98 + 20 approx 0`.
As W->D (W decreases, D increases, W+D sum might change).
If W is converted to D, `W_new = W_old - x`, `D_new = D_old + x`. So `W_new+D_new = W_old+D_old`.
The sum `W+D` remains `0.306`.
So `dG/dt approx -65.3*G*(0.306) + 20 = -19.98*G + 20`.
If G starts at 1, `dG/dt approx 0`. G is stable.
This model (Model v12) predicts G remains stable at 1.0 as long as W is converted to D and R1, R2_alt are fast.
This does not explain the drop in G at the end.

However, this Model v12 is the first one that robustly keeps G stable during W->D conversion.
The drop in G must be due to something else when W is very low.
What if, when W is very low, D also starts to be consumed by another path, or production of D from W stops, and D itself is converted back to N via R2_alt, consuming G?
If R3 (`W->D`) stops when W is depleted. Then D is high.
`dG/dt = G*(-kf1*W_low - kf2_alt*D_high) + (kr1+kr2_alt)*N`.
If W_low is ~0: `dG/dt = G*(-kf2_alt*D_high) + (kr1+kr2_alt)*N`.
`dG/dt = G*(-65.3*D_high) + 20`.
If D_high is 0.991 (experimental end value):
`dG/dt = G*(-65.3*0.991) + 20 = G*(-64.71) + 20`.
For `dG/dt` to be negative (G drops), `G*64.71 > 20`. If G=1, `64.71 > 20`, so `dG/dt` is negative.
This model predicts G will drop when W is depleted and D is high! This is very promising.

Now, for the D dynamics:
`dD/dt = k3*W - (kf2_alt*D*G - kr2_alt*N)`.
We need D to go from 0.153 to 0.991.
The term `k3*W` produces D. The term `(kf2_alt*D*G - kr2_alt*N)` is the flux of R2_alt.
At equilibrium of R2_alt, this flux is 0.
If R2_alt is fast, `D*G approx kr2_alt*N / kf2_alt = 10/65.3 = 0.153`.
So `D approx 0.153/G`. If G is stable at 1, then D is driven towards 0.153 by R2_alt.
This means R3 (`W->D`) must be strong enough to push D above 0.153, against R2_alt.
And `k3` must be chosen to match the D profile.
The conversion of W (0.152 units) happens over ~8s. Average rate `0.152/8 approx 0.019`.
If `k3*W_avg = 0.019`. `W_avg` is (0.153+0.001)/2 = 0.077.
`k3 * 0.077 = 0.019` => `k3 = 0.019/0.077 approx 0.247`. Let's try `k3=0.25`.

Model v12:
- N boundary, initial 1.0. Others initial 1.0.
- R1: `W+G <=> N` (kf1=65.3, kr1=10)
- R2_alt: `D+G <=> N` (kf2_alt=65.3, kr2_alt=10)
- R3: `W -> D` (k3=0.25)

This model seems to have the potential to explain:
1. Plateau W, D, G, N values.
2. Stability of G at 1.0 while W converts to D.
3. Drop in G when W is depleted and D is high.
4. Conversion of W to D. (Need to check if D reaches 0.991).

Final check on D level:
If R2_alt (`D+G <=> N`) is in equilibrium, `D = (kr2_alt/kf2_alt) * N/G = 0.153 / G`.
If G drops to 0.955 at the end, D should be `0.153 / 0.955 = 0.160`.
This is far from experimental D=0.991.
So R2_alt cannot be in full equilibrium at the end if D is that high.
This means the rate of R3 (`k3*W`) must be fast enough to produce D, and when W is gone, D is left high, and then R2_alt slowly consumes D (and G).
The simulation will show the dynamics. `k3=0.25` might be too slow if D needs to reach 0.991.
The previous `k3_new=6.4` (Model v11) was for `R3: W+G -> D+N`. Rate `k3_new*W*G`.
Here R3 is `W->D`. Rate `k3*W`.
If W=0.1, G=1, rate in v11 was `6.4*0.1*1 = 0.64`.
Rate in v12 is `k3*0.1`. If `k3=0.25`, rate is `0.025`. This is much slower.
To get a similar rate of W consumption, `k3` should be closer to `6.4` (if G was ~1 in the R3 of v11).
Let's try `k3 = 5.0` for Model v12.

## Action

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

# ---- Build Model v12 ----
sbml_doc_v12 = libsbml.readSBMLFromString(input_sbml_string)
model_v12 = sbml_doc_v12.getModel()

s_wq5e = "id_wq5e"
s_9z5o = "id_9z5o"
s_dukt = "id_dukt"
s_gbbq = "id_gbbq"

# Configure id_9z5o as a constant species
species_9z5o_obj = model_v12.getSpecies(s_9z5o)
species_9z5o_obj.setInitialConcentration(1.0)
species_9z5o_obj.setConstant(True)
species_9z5o_obj.setBoundaryCondition(True)

# Set initial concentrations for other species
model_v12.getSpecies(s_wq5e).setInitialConcentration(1.0)
model_v12.getSpecies(s_dukt).setInitialConcentration(1.0)
model_v12.getSpecies(s_gbbq).setInitialConcentration(1.0)

# Reaction R1: id_wq5e + id_gbbq <=> id_9z5o
r1 = model_v12.createReaction(); r1.setId("R1"); r1.setReversible(True); r1.setFast(False)
reactant1_r1 = r1.createReactant(); reactant1_r1.setSpecies(s_wq5e); reactant1_r1.setStoichiometry(1.0); reactant1_r1.setConstant(True)
reactant2_r1 = r1.createReactant(); reactant2_r1.setSpecies(s_gbbq); reactant2_r1.setStoichiometry(1.0); reactant2_r1.setConstant(True)
product1_r1 = r1.createProduct(); product1_r1.setSpecies(s_9z5o); product1_r1.setStoichiometry(1.0); product1_r1.setConstant(True)
kl_r1 = r1.createKineticLaw()
kf1_p = kl_r1.createParameter(); kf1_p.setId("kf1"); kf1_p.setValue(65.3)
kr1_p = kl_r1.createParameter(); kr1_p.setId("kr1"); kr1_p.setValue(10.0)
kl_r1.setMath(libsbml.parseL3Formula(f"kf1 * {s_wq5e} * {s_gbbq} - kr1 * {s_9z5o}"))

# Reaction R2_alt: id_dukt + id_gbbq <=> id_9z5o  (Note: G is now a reactant with D)
r2 = model_v12.createReaction(); r2.setId("R2_alt"); r2.setReversible(True); r2.setFast(False)
reactant1_r2 = r2.createReactant(); reactant1_r2.setSpecies(s_dukt); reactant1_r2.setStoichiometry(1.0); reactant1_r2.setConstant(True)
reactant2_r2 = r2.createReactant(); reactant2_r2.setSpecies(s_gbbq); reactant2_r2.setStoichiometry(1.0); reactant2_r2.setConstant(True) # G is reactant
product1_r2 = r2.createProduct(); product1_r2.setSpecies(s_9z5o); product1_r2.setStoichiometry(1.0); product1_r2.setConstant(True)    # N is product
kl_r2 = r2.createKineticLaw()
kf2_alt_p = kl_r2.createParameter(); kf2_alt_p.setId("kf2_alt"); kf2_alt_p.setValue(65.3) # Renamed for clarity
kr2_alt_p = kl_r2.createParameter(); kr2_alt_p.setId("kr2_alt"); kr2_alt_p.setValue(10.0) # Renamed for clarity
kl_r2.setMath(libsbml.parseL3Formula(f"kf2_alt * {s_dukt} * {s_gbbq} - kr2_alt * {s_9z5o}"))

# Reaction R3: id_wq5e -> id_dukt
r3 = model_v12.createReaction(); r3.setId("R3"); r3.setReversible(False); r3.setFast(False)
reactant1_r3 = r3.createReactant(); reactant1_r3.setSpecies(s_wq5e); reactant1_r3.setStoichiometry(1.0); reactant1_r3.setConstant(True)
product1_r3 = r3.createProduct(); product1_r3.setSpecies(s_dukt); product1_r3.setStoichiometry(1.0); product1_r3.setConstant(True)
kl_r3 = r3.createKineticLaw()
k3_p = kl_r3.createParameter(); k3_p.setId("k3"); k3_p.setValue(5.0) # Adjusted k3
kl_r3.setMath(libsbml.parseL3Formula(f"k3 * {s_wq5e}"))

# Write the updated SBML to a string
writer = libsbml.SBMLWriter()
model_v12_sbml = writer.writeSBMLToString(sbml_doc_v12)
shared_variables.add("model_v12_sbml", model_v12_sbml)

# ---- Simulate Model v12 ----
sim_data_v12 = simulate(model_v12_sbml)
shared_variables.add("sim_data_v12", sim_data_v12)

# ---- Compare with Experimental Data ----
exp_data = experiment_history['iteration_0']

print("--- Model v12 Simulation Results ---")
print(f"Simulation runs from t=0 to t={sim_data_v12['Time'].max()} with {len(sim_data_v12)} points.")
print("\nComparison at selected time points (Experimental vs Simulated):")
print("Time | Species | Exp_Val | Sim_Val")
print("------------------------------------")

exp_time_points = [0.0, 1.05, 2.10, 3.67, 10.0, 18.3, 21.0, 22.0, 23.0, 23.6, 24.1, 24.6, 25.1, 26.0] 

for t_exp_target in exp_time_points:
    exp_row = exp_data.iloc[(exp_data['Time'] - t_exp_target).abs().argsort()[:1]]
    t_exp_actual = exp_row['Time'].iloc[0]

    if t_exp_target <= sim_data_v12['Time'].max():
        sim_row = sim_data_v12.iloc[(sim_data_v12['Time'] - t_exp_target).abs().argsort()[:1]]
        sim_wq5e = sim_row[s_wq5e].iloc[0]
        sim_9z5o = sim_row[s_9z5o].iloc[0]
        sim_dukt = sim_row[s_dukt].iloc[0]
        sim_gbbq = sim_row[s_gbbq].iloc[0]
    else:
        sim_wq5e, sim_9z5o, sim_dukt, sim_gbbq = (float('nan'),)*4
        
    print(f"{t_exp_actual:<4.2f} | {s_wq5e:<7} | {exp_row[s_wq5e].iloc[0]:<7.3f} | {sim_wq5e:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_9z5o:<7} | {exp_row[s_9z5o].iloc[0]:<7.3f} | {sim_9z5o:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_dukt:<7} | {exp_row[s_dukt].iloc[0]:<7.3f} | {sim_dukt:<7.3f}")
    print(f"{t_exp_actual:<4.2f} | {s_gbbq:<7} | {exp_row[s_gbbq].iloc[0]:<7.3f} | {sim_gbbq:<7.3f}")
    print("------------------------------------")

print("\nExperimental data tail (iteration_0):")
print(exp_data.tail(3))
print("\nSimulated data v12 tail:")
print(sim_data_v12.tail(3))

shared_variables.add("current_best_sbml", model_v12_sbml)
```
# Observation

## Code Stdout
--- Model v12 Simulation Results ---
Simulation runs from t=0 to t=26.0 with 1341 points.

Comparison at selected time points (Experimental vs Simulated):
Time | Species | Exp_Val | Sim_Val
------------------------------------
0.00 | id_wq5e | 1.000   | 1.000  
0.00 | id_9z5o | 1.000   | 1.000  
0.00 | id_dukt | 1.000   | 1.000  
0.00 | id_gbbq | 1.000   | 1.000  
------------------------------------
1.05 | id_wq5e | 0.352   | 0.475  
1.05 | id_9z5o | 0.995   | 1.000  
1.05 | id_dukt | 0.352   | 0.771  
1.05 | id_gbbq | 0.995   | 0.246  
------------------------------------
2.10 | id_wq5e | 0.164   | 0.475  
2.10 | id_9z5o | 0.998   | 1.000  
2.10 | id_dukt | 0.164   | 0.771  
2.10 | id_gbbq | 0.998   | 0.246  
------------------------------------
3.67 | id_wq5e | 0.153   | 0.475  
3.67 | id_9z5o | 1.000   | 1.000  
3.67 | id_dukt | 0.153   | 0.771  
3.67 | id_gbbq | 1.000   | 0.246  
------------------------------------
9.99 | id_wq5e | 0.153   | 0.475  
9.99 | id_9z5o | 1.000   | 1.000  
9.99 | id_dukt | 0.153   | 0.771  
9.99 | id_gbbq | 1.000   | 0.246  
------------------------------------
18.30 | id_wq5e | 0.153   | 0.475  
18.30 | id_9z5o | 1.000   | 1.000  
18.30 | id_dukt | 0.153   | 0.771  
18.30 | id_gbbq | 1.000   | 0.246  
------------------------------------
20.99 | id_wq5e | 0.120   | 0.475  
20.99 | id_9z5o | 1.000   | 1.000  
20.99 | id_dukt | 0.202   | 0.771  
20.99 | id_gbbq | 1.000   | 0.246  
------------------------------------
22.00 | id_wq5e | 0.051   | 0.475  
22.00 | id_9z5o | 1.000   | 1.000  
22.00 | id_dukt | 0.527   | 0.771  
22.00 | id_gbbq | 0.999   | 0.246  
------------------------------------
22.99 | id_wq5e | 0.019   | 0.475  
22.99 | id_9z5o | 1.000   | 1.000  
22.99 | id_dukt | 0.816   | 0.771  
22.99 | id_gbbq | 0.991   | 0.246  
------------------------------------
23.59 | id_wq5e | 0.011   | 0.475  
23.59 | id_9z5o | 1.000   | 1.000  
23.59 | id_dukt | 0.899   | 0.771  
23.59 | id_gbbq | 0.983   | 0.246  
------------------------------------
24.10 | id_wq5e | 0.007   | 0.475  
24.10 | id_9z5o | 1.000   | 1.000  
24.10 | id_dukt | 0.939   | 0.771  
24.10 | id_gbbq | 0.975   | 0.246  
------------------------------------
24.60 | id_wq5e | 0.004   | 0.475  
24.60 | id_9z5o | 1.000   | 1.000  
24.60 | id_dukt | 0.963   | 0.771  
24.60 | id_gbbq | 0.968   | 0.246  
------------------------------------
25.11 | id_wq5e | 0.002   | 0.475  
25.11 | id_9z5o | 1.000   | 1.000  
25.11 | id_dukt | 0.978   | 0.771  
25.11 | id_gbbq | 0.962   | 0.246  
------------------------------------
26.00 | id_wq5e | 0.001   | 0.475  
26.00 | id_9z5o | 1.000   | 1.000  
26.00 | id_dukt | 0.991   | 0.771  
26.00 | id_gbbq | 0.955   | 0.246  
------------------------------------

Experimental data tail (iteration_0):
       id_wq5e  id_9z5o   id_dukt   id_gbbq       Time
1338  0.001105      1.0  0.990532  0.954828  25.961194
1339  0.001086      1.0  0.990714  0.954691  25.980597
1340  0.001067      1.0  0.990893  0.954556  26.000000

Simulated data v12 tail:
       id_wq5e   id_dukt   id_gbbq  id_9z5o       Time
1338  0.474982  0.770859  0.245841      1.0  25.961194
1339  0.474982  0.770859  0.245841      1.0  25.980597
1340  0.474982  0.770859  0.245841      1.0  26.000000

## 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. (model_v2_sbml, sim_data_v2, current_best_sbml, model_v5_sbml, sim_data_v5, model_v7_sbml, sim_data_v7, model_v11_sbml, sim_data_v11, model_v12_sbml, sim_data_v12)

### 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 previous iterations have highlighted significant challenges in matching all species dynamics simultaneously, especially for `id_gbbq` (G) and `id_dukt` (D).
Model v12 (R1: `W+G <=> N`, R2_alt: `D+G <=> N`, R3: `W -> D`) showed a promising G dynamic shape (stable then drop) in theory, but the simulation results (with `k3=5.0`) were far from the experimental data because it settled into an incorrect steady state too quickly. The core issue was that the model couldn't simultaneously achieve:
1.  The initial experimental plateau (W=0.153, D=0.153, G=1.0).
2.  The final experimental values (W=0.001, D=0.991, G=0.955).
3.  The dynamic shapes, particularly the G stability then slight drop.

The analysis showed that for Model v12 structure, `G_steady_state = (kr1+kr2_alt) / ( (kf1+kf2_alt) * (W+D) )`. This relationship means that if `(W+D)` changes significantly (as it does experimentally, from 0.306 to 0.992), G must also change significantly to maintain this steady state. The experimental G changes only slightly (1.0 to 0.955), which contradicts this model structure if R1 and R2_alt are solely responsible for G's level.

Given the constraints and the difficulty in finding a simple mass-action model that fits all aspects, especially the G behavior and the large increase in D, I will make a pragmatic choice for submission.
The problem asks for "discovering the true underlying mechanisms rather than overfitting". A perfect fit might be impossible without more complex kinetics or unobserved species/regulators.

Model v11 (R1: `W+G <=> N`, R2: `D+N <=> G`, R3: `W+G -> D+N` with `k3_new=6.4`) managed to get `id_wq5e` (W) to decay to a low level (0.007), close to the experimental 0.001. This is a key dynamic. However, it resulted in `id_dukt` (D) being too high (3.2 vs 0.991) and `id_gbbq` (G) being extremely high (21 vs 0.955).

The fact that D becomes `~1.0` (from initial 1.0, plateau 0.153, end 0.991) while W also starts at 1.0 (plateau 0.153, end 0.001) is puzzling if R3 is a simple 1:1 conversion.
Net W consumed (from start to end) = `1.0 - 0.001 = 0.999`.
Net D change (from start to end) = `0.991 - 1.0 = -0.009`.
This implies that D is largely reformed to its initial value, or W is not the source of D in a simple way.

Let's consider the change from plateau:
`delta_W = -0.152` (0.153 -> 0.001)
`delta_D = +0.838` (0.153 -> 0.991)
`delta_G = -0.045` (1.0 -> 0.955)

If R3 is `W+G -> D+N` (as in Model v11):
-   Consumption of 0.152 W (from plateau) would produce 0.152 D.
    So D would become `0.153 (plateau) + 0.152 = 0.305`. This is far from 0.991.
    This means the high `k3_new=6.4` in Model v11, while depleting W, must have relied on initial W (from 1.0) not just plateau W.
    If R3 (`W+G -> D+N`) consumes almost all initial W (1.0 unit), it produces 1.0 unit of D. So D becomes `1.0 (initial) + 1.0 (produced) = 2.0`.
    The simulated D in Model v11 was 3.2, suggesting even more D production or less consumption than this simple accounting. The high G (21) in simulation would boost the `k3_new*W*G` rate.

The problem is complex. I will submit a model that captures some key features, acknowledging its limitations.
Model v11 had good W decay. The main issues were D and G.
To control D from overshooting, perhaps D is also consumed.
To control G from overshooting, its production via R1/R2 shifts needs to be curtailed, or it needs a consumption path.

Given the limited iterations left, I will try a slight modification of Model v11 to see if D can be controlled.
Model v16:
-   N boundary, initial 1.0. Others initial 1.0.
-   R1: `W+G <=> N` (kf1=65.3, kr1=10)
-   R2: `D+N <=> G` (kf2=65.3, kr2=10)
-   R3: `W+G -> D+N` (k3_new=6.4, from v11, for W decay)
-   R4: `D -> N` (rate `k4_decay*D`). This is a new reaction to consume excess D.
    The purpose of R4 is to bring D down from the high values seen in Model v11 (simulated ~3.2) towards the experimental ~1.0.
    If D needs to be around 1.0 at steady state (after W is gone), and R3 is no longer producing D.
    Then `dD/dt = (kr2*G - kf2*D*N) - k4_decay*D approx 0`.
    If G is also very high (e.g., G=20 from v11), then `kr2*G = 10*20 = 200`. `kf2*D*N = 65.3*D`.
    `200 - 65.3*D - k4_decay*D = 0`.
    `D = 200 / (65.3 + k4_decay)`. If D_target is 1.0, `65.3 + k4_decay = 200` => `k4_decay = 134.7`. This is a very fast decay.
    This will likely affect G as well.

This is a shot in the dark for R4 parameters. Let's try a moderate `k4_decay`, e.g., `k4_decay = 1.0`.

This is my final attempt to refine the model.

## Action

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

# ---- Build Final Model (Model v16) ----
# Based on Model v11, adding decay for D to control its overproduction.
# This is a pragmatic attempt to improve D behavior while retaining W decay.
# G behavior is still expected to be problematic.

final_sbml_doc = libsbml.readSBMLFromString(input_sbml_string)
final_model = final_sbml_doc.getModel()

s_wq5e = "id_wq5e"
s_9z5o = "id_9z5o"
s_dukt = "id_dukt"
s_gbbq = "id_gbbq"

# Configure id_9z5o as a constant species
species_9z5o_obj = final_model.getSpecies(s_9z5o)
species_9z5o_obj.setInitialConcentration(1.0)
species_9z5o_obj.setConstant(True)
species_9z5o_obj.setBoundaryCondition(True)

# Set initial concentrations for other species
final_model.getSpecies(s_wq5e).setInitialConcentration(1.0)
final_model.getSpecies(s_dukt).setInitialConcentration(1.0)
final_model.getSpecies(s_gbbq).setInitialConcentration(1.0)

# Reaction R1: id_wq5e + id_gbbq <=> id_9z5o
r1 = final_model.createReaction(); r1.setId("R1"); r1.setReversible(True); r1.setFast(False)
reactant1_r1 = r1.createReactant(); reactant1_r1.setSpecies(s_wq5e); reactant1_r1.setStoichiometry(1.0); reactant1_r1.setConstant(True)
reactant2_r1 = r1.createReactant(); reactant2_r1.setSpecies(s_gbbq); reactant2_r1.setStoichiometry(1.0); reactant2_r1.setConstant(True)
product1_r1 = r1.createProduct(); product1_r1.setSpecies(s_9z5o); product1_r1.setStoichiometry(1.0); product1_r1.setConstant(True)
kl_r1 = r1.createKineticLaw()
kf1_p = kl_r1.createParameter(); kf1_p.setId("kf1"); kf1_p.setValue(65.3)
kr1_p = kl_r1.createParameter(); kr1_p.setId("kr1"); kr1_p.setValue(10.0)
kl_r1.setMath(libsbml.parseL3Formula(f"kf1 * {s_wq5e} * {s_gbbq} - kr1 * {s_9z5o}"))

# Reaction R2: id_dukt + id_9z5o <=> id_gbbq
r2 = final_model.createReaction(); r2.setId("R2"); r2.setReversible(True); r2.setFast(False)
reactant1_r2 = r2.createReactant(); reactant1_r2.setSpecies(s_dukt); reactant1_r2.setStoichiometry(1.0); reactant1_r2.setConstant(True)
reactant2_r2 = r2.createReactant(); reactant2_r2.setSpecies(s_9z5o); reactant2_r2.setStoichiometry(1.0); reactant2_r2.setConstant(True)
product1_r2 = r2.createProduct(); product1_r2.setSpecies(s_gbbq); product1_r2.setStoichiometry(1.0); product1_r2.setConstant(True)
kl_r2 = r2.createKineticLaw()
kf2_p = kl_r2.createParameter(); kf2_p.setId("kf2"); kf2_p.setValue(65.3)
kr2_p = kl_r2.createParameter(); kr2_p.setId("kr2"); kr2_p.setValue(10.0)
kl_r2.setMath(libsbml.parseL3Formula(f"kf2 * {s_dukt} * {s_9z5o} - kr2 * {s_gbbq}"))

# Reaction R3: id_wq5e + id_gbbq -> id_dukt + id_9z5o
# This reaction drives W consumption and D production.
r3 = final_model.createReaction(); r3.setId("R3_conversion"); r3.setReversible(False); r3.setFast(False)
reactant1_r3 = r3.createReactant(); reactant1_r3.setSpecies(s_wq5e); reactant1_r3.setStoichiometry(1.0); reactant1_r3.setConstant(True)
reactant2_r3 = r3.createReactant(); reactant2_r3.setSpecies(s_gbbq); reactant2_r3.setStoichiometry(1.0); reactant2_r3.setConstant(True)
product1_r3 = r3.createProduct(); product1_r3.setSpecies(s_dukt); product1_r3.setStoichiometry(1.0); product1_r3.setConstant(True)
product2_r3 = r3.createProduct(); product2_r3.setSpecies(s_9z5o); product2_r3.setStoichiometry(1.0); product2_r3.setConstant(True)
kl_r3 = r3.createKineticLaw()
k3_conv_p = kl_r3.createParameter(); k3_conv_p.setId("k3_conv"); k3_conv_p.setValue(6.4) # From Model v11, gave good W decay
kl_r3.setMath(libsbml.parseL3Formula(f"k3_conv * {s_wq5e} * {s_gbbq}"))

# Reaction R4: id_dukt -> id_9z5o (Decay of D to control overproduction)
# N (id_9z5o) is a boundary species, so it acts as a sink here.
r4 = final_model.createReaction(); r4.setId("R4_D_decay"); r4.setReversible(False); r4.setFast(False)
reactant1_r4 = r4.createReactant(); reactant1_r4.setSpecies(s_dukt); reactant1_r4.setStoichiometry(1.0); reactant1_r4.setConstant(True)
product1_r4 = r4.createProduct(); product1_r4.setSpecies(s_9z5o); product1_r4.setStoichiometry(1.0); product1_r4.setConstant(True)
kl_r4 = r4.createKineticLaw()
# k4_decay value needs to be chosen. If Dsim ~3 and Dexp ~1, this reaction needs to consume ~2 units of D.
# The rate of R2 also affects D. This is a rough guess.
k4_decay_p = kl_r4.createParameter(); k4_decay_p.setId("k4_decay"); k4_decay_p.setValue(1.0) 
kl_r4.setMath(libsbml.parseL3Formula(f"k4_decay * {s_dukt}"))

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

# The variable `final_sbml` is now ready for submission.
# print(final_sbml) # For verification if needed
```
