
                # 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_q4ga">
    <listOfCompartments>
      <compartment id="id_o0va" size="1"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="id_dlm5" compartment="id_o0va" initialConcentration="0"/>
      <species id="id_v9bo" compartment="id_o0va" initialConcentration="100" boundaryCondition="true" constant="true"/>
      <species id="id_acno" compartment="id_o0va" initialConcentration="0"/>
      <species id="id_wgvc" compartment="id_o0va" initialConcentration="0"/>
    </listOfSpecies>
  </model>
</sbml>


                ## Max iterations
                20

                Format your response according to the instructions in the system message.
                
**My Initial Approach to Uncovering Missing Reactions**

Okay, so I'm tasked with finding missing reactions in this biological system. I'm given an SBML model as a starting point, which is essentially a blank canvas at this stage. I've got four species to work with: `id_dlm5`, `id_v9bo`, `id_acno`, and `id_wgvc`.  I see that `id_v9bo` is a fixed boundary condition at 100, acting like a constant source or sink. The other three species all start at zero.  This is a good, clean starting point.

My immediate instinct is to get a baseline.  I need to understand what this system does *without* any reactions.  So, I'm going to set up an "observe" experiment to gather data with default settings.  I'll let the simulation run and meticulously record how the concentrations of these species evolve over time.  That raw data will be invaluable.

Once I have that baseline data, I'll dive in and analyze it like a hawk. I'm going to look for any observable concentration changes, or patterns that might suggest hidden reactions.  The data will be my guide, pointing me towards potential reaction candidates. I'm thinking of this as detective work, where the data is the evidence I'll use to crack the case of the missing reactions.

# 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: 10001 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_dlm5  id_acno  id_wgvc  id_v9bo
0         0        0        0 1.00e+02
...
1.63e+01  4.20e+00 9.85e+01 1.16e+05 1.00e+02
...
3.26e+01  8.49e+00 1.20e+02 1.73e+05 1.00e+02
...
4.90e+01  1.15e+01 1.30e+02 2.01e+05 1.00e+02
...
6.53e+01  1.33e+01 1.34e+02 2.14e+05 1.00e+02
...
8.16e+01  1.45e+01 1.36e+02 2.21e+05 1.00e+02
...
9.79e+01  1.51e+01 1.37e+02 2.24e+05 1.00e+02
...
1.14e+02  1.55e+01 1.38e+02 2.26e+05 1.00e+02
...
1.31e+02  1.57e+01 1.38e+02 2.27e+05 1.00e+02
...
1.47e+02  1.58e+01 1.38e+02 2.27e+05 1.00e+02
...
1.63e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
1.80e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
1.96e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.12e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.28e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.45e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.61e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.77e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.94e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.10e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.26e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.43e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.59e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.75e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.92e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.08e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.24e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.41e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.57e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.73e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.90e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.06e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.22e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.39e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.55e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.71e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.88e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.04e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.20e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.36e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.53e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.69e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.85e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.02e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.18e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.34e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.51e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.67e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.83e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
8.00e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02

## 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
**Analysis of Species Dynamics and Model Development**

Okay, so I've been presented with some experimental results that describe the behavior of a few species over time: `id_dlm5`, `id_acno`, and `id_wgvc`. They all start at zero concentration and eventually reach a steady state, while a species `id_v9bo` remains constant. Since I'm working with a system where chemical reactions are taking place, I can interpret these observations to derive plausible models.

Initially, I considered the simplest case: each of the three species is produced directly from `id_v9bo`. The fact that the concentrations level off suggests that each species is being degraded/consumed. To get this right, I'll need to figure out appropriate rate constants. I can deduce the production rates and degradation rates from the starting concentrations and the steady-state concentrations.

Based on the nature of the chemical kinetics I was looking at here, I decided to build a simple linear chain where `id_v9bo` converts to `id_dlm5` and then `id_acno`, and so on. But this assumption didn't quite fit the data. The levels that each species reached weren't quite right. Next, I took another look and decided to try another approach where `id_v9bo` produces each of the other three species independently, and each has its own degradation rate. I had to go back to the drawing board!

To figure this out, I'm setting up a model of reactions using the parameters I have. I know the concentrations at the beginning and what they become. I have to put this information into a system of equations, and then solve these equations to work out suitable values for the parameters I'm using, and simulate it to see if the outcome is realistic. These are the rates for each reaction.

In order to do this I need to make some assumptions - for example, are the rates of the reactions at all stages about the same? Probably not. The simulation then returns something that I can measure. I have written the code to simulate the model.

Let me try running this code! I am trying to compare the simulation results to the data I have collected from the experiment to check if it's producing something similar!

Ok, the simulation gave me some numbers and these match the data. I've now produced a model that I believe can describe the experimental results. I will implement this!
# Observation

## Code Stdout
Comparison of Experimental Data and Simulation Results:
==================================================
Time       | Species    | Exp Value       | Sim Value      
--------------------------------------------------
0.0        | id_dlm5    | 0.00e+00        | 0.00e+00        (t_exp=0.0, t_sim=0.0)
0.0        | id_acno    | 0.00e+00        | 0.00e+00        (t_exp=0.0, t_sim=0.0)
0.0        | id_wgvc    | 0.00e+00        | 0.00e+00        (t_exp=0.0, t_sim=0.0)
--------------------------------------------------
16.3       | id_dlm5    | 4.20e+00        | 4.20e+00        (t_exp=16.3, t_sim=16.3)
16.3       | id_acno    | 9.85e+01        | 9.84e+01        (t_exp=16.3, t_sim=16.3)
16.3       | id_wgvc    | 1.16e+05        | 1.16e+05        (t_exp=16.3, t_sim=16.3)
--------------------------------------------------
50.0       | id_dlm5    | 1.16e+01        | 9.69e+00        (t_exp=50.0, t_sim=50.0)
50.0       | id_acno    | 1.30e+02        | 1.35e+02        (t_exp=50.0, t_sim=50.0)
50.0       | id_wgvc    | 2.02e+05        | 2.02e+05        (t_exp=50.0, t_sim=50.0)
--------------------------------------------------
100.0      | id_dlm5    | 1.52e+01        | 1.35e+01        (t_exp=100.0, t_sim=100.0)
100.0      | id_acno    | 1.37e+02        | 1.38e+02        (t_exp=100.0, t_sim=100.0)
100.0      | id_wgvc    | 2.24e+05        | 2.24e+05        (t_exp=100.0, t_sim=100.0)
--------------------------------------------------
150.0      | id_dlm5    | 1.58e+01        | 1.50e+01        (t_exp=150.0, t_sim=150.0)
150.0      | id_acno    | 1.38e+02        | 1.38e+02        (t_exp=150.0, t_sim=150.0)
150.0      | id_wgvc    | 2.27e+05        | 2.27e+05        (t_exp=150.0, t_sim=150.0)
--------------------------------------------------
300.0      | id_dlm5    | 1.59e+01        | 1.58e+01        (t_exp=300.0, t_sim=300.0)
300.0      | id_acno    | 1.38e+02        | 1.38e+02        (t_exp=300.0, t_sim=300.0)
300.0      | id_wgvc    | 2.27e+05        | 2.27e+05        (t_exp=300.0, t_sim=300.0)
--------------------------------------------------
800.0      | id_dlm5    | 1.59e+01        | 1.59e+01        (t_exp=800.0, t_sim=800.0)
800.0      | id_acno    | 1.38e+02        | 1.38e+02        (t_exp=800.0, t_sim=800.0)
800.0      | id_wgvc    | 2.27e+05        | 2.27e+05        (t_exp=800.0, t_sim=800.0)
--------------------------------------------------

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0)
- `shared_variables`: all variables you have saved from the previous iterations. (current_model_sbml, sim_results_iteration_1)

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


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



# Iteration 2
**Analysis of Simulation Results and Future Directions**

Okay, so I've been poring over the Model B simulation results, specifically the ones with independent production and first-order degradation. And you know what? They're pretty darn close to the experimental data. At t=0, 16.3s, and then later on (after 150s), the simulated values align really well with the experimental ones for all three species, which is encouraging.

For `id_acno` and `id_wgvc`, it's a solid match across most of the time points. However, there's this slight blip for `id_dlm5` around the 50s and 100s mark. The model is underestimating its concentration during that intermediate phase. My initial hunch is that either the production rate for `id_dlm5` might be slightly off, or the degradation rate could be a tad overestimated. Or, and this is always a possibility, there could be some positive feedback or a more nuanced production mechanism for `id_dlm5` at play during this intermediate time.

But, given that the model is already performing well, especially at the extremes of the time scale, the overall structure seems correct. The discrepancies for `id_dlm5` are relatively minor. Before I start tweaking parameters or adding complexity, I want to confirm that my assumption of independent pathways for these species is valid.

I'm thinking a good test would be to perturb the initial concentration of one of the produced species, say `id_dlm5`. If their production/degradation really *are* independent, changing the initial concentration of `id_dlm5` should not affect the other species. It should be a clean, isolated effect.

So, I'm going to propose an experiment. I'll request to set the initial concentration of `id_dlm5` to half its observed steady-state value (~8.0). I'll keep the other initial concentrations the same: 0 for `id_acno` and `id_wgvc`, and 100 for `id_v9bo`.

If the experimental results show that the dynamics of `id_acno` or `id_wgvc` are altered, then my assumption of independence is wrong, and I'll need to go back to the drawing board and revise the model to include cross-talk between the species. If, on the other hand, their dynamics remain unchanged, it would further validate the current model structure. In that case, the minor discrepancies for `id_dlm5` might just require parameter fine-tuning or, potentially, a simple self-regulation model for `id_dlm5`. Let's see what the experiment reveals!

# Observation

## Experiment Result
Experiment ID: iteration_2
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_2]

Total size: 10001 rows × 5 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_2] for the full data

Time   id_dlm5  id_acno  id_wgvc  id_v9bo
0  8.00e+00        0        0 1.00e+02
...
1.63e+01  8.30e+00 9.85e+01 1.16e+05 1.00e+02
...
3.26e+01  1.06e+01 1.20e+02 1.73e+05 1.00e+02
...
4.90e+01  1.25e+01 1.30e+02 2.01e+05 1.00e+02
...
6.53e+01  1.39e+01 1.34e+02 2.14e+05 1.00e+02
...
8.16e+01  1.47e+01 1.36e+02 2.21e+05 1.00e+02
...
9.79e+01  1.53e+01 1.37e+02 2.24e+05 1.00e+02
...
1.14e+02  1.56e+01 1.38e+02 2.26e+05 1.00e+02
...
1.31e+02  1.57e+01 1.38e+02 2.27e+05 1.00e+02
...
1.47e+02  1.58e+01 1.38e+02 2.27e+05 1.00e+02
...
1.63e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
1.80e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
1.96e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.12e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.28e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.45e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.61e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.77e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.94e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.10e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.26e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.43e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.59e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.75e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.92e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.08e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.24e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.41e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.57e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.73e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.90e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.06e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.22e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.39e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.55e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.71e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.88e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.04e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.20e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.36e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.53e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.69e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.85e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.02e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.18e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.34e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.51e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.67e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.83e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
8.00e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_model_sbml, sim_results_iteration_1)

### 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 experiment `iteration_2` involved changing the initial concentration of `id_dlm5` to 8.0. The other species `id_acno` and `id_wgvc` started at 0.
Comparing the results of `iteration_2` with `iteration_0` (baseline):
- `id_dlm5` starts at 8.0 and approaches its steady-state of ~15.9.
- `id_acno` and `id_wgvc` dynamics appear very similar to `iteration_0`. For example, at t=16.3s:
    - `iteration_0`: `id_acno` = 9.85e+01, `id_wgvc` = 1.16e+05
    - `iteration_2`: `id_acno` = 9.85e+01, `id_wgvc` = 1.16e+05
- The steady-state values for all species in `iteration_2` are the same as in `iteration_0`.

This strongly suggests that `id_dlm5` does not influence the production or degradation of `id_acno` or `id_wgvc`. The pathways for `id_acno` and `id_wgvc` seem independent of `id_dlm5`.

Now, I will simulate my current model (`shared_variables.access("current_model_sbml")`) with the perturbed initial condition (`id_dlm5` = 8.0) and compare it to the experimental data from `iteration_2`. This will help confirm if the model accurately predicts the behavior of `id_dlm5` under this perturbation and if the independence of other species is correctly captured.

The slight discrepancy observed earlier for `id_dlm5` in the baseline simulation might still be present, but this experiment primarily tests for cross-talk between pathways.

## Action

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

# Retrieve the current model SBML string
current_model_sbml = shared_variables.access("current_model_sbml")

# Modify the initial concentration of id_dlm5 in the model
sbml_doc = libsbml.readSBMLFromString(current_model_sbml)
model = sbml_doc.getModel()
species_dlm5 = model.getSpecies("id_dlm5")
if species_dlm5:
    species_dlm5.setInitialConcentration(8.0)
else:
    print("Error: Species id_dlm5 not found in the model.")

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

# Simulate the perturbed model
sim_results_perturbed_df = simulate(perturbed_model_sbml)
shared_variables.add("sim_results_iteration_3_perturbed", sim_results_perturbed_df)

# Compare with experimental data from iteration_2
exp_data_perturbed_df = experiment_history['iteration_2']

# Print comparison at specific time points
time_points_to_compare = [0.0, 16.3, 50.0, 100.0, 150.0, 300.0, 800.0]
s_dlm5 = "id_dlm5"
s_acno = "id_acno"
s_wgvc = "id_wgvc"

print("Comparison of Perturbed Experimental Data (iteration_2) and Simulation Results:")
print("="*70)
print(f"{'Time':<10} | {'Species':<10} | {'Exp Value':<15} | {'Sim Value':<15} | {'Abs Diff':<15}")
print("-"*70)

for t in time_points_to_compare:
    exp_row = exp_data_perturbed_df.iloc[(exp_data_perturbed_df['Time'] - t).abs().argsort()[:1]]
    sim_row = sim_results_perturbed_df.iloc[(sim_results_perturbed_df['Time'] - t).abs().argsort()[:1]]
    
    if exp_row.empty or sim_row.empty:
        continue

    t_exp = exp_row['Time'].iloc[0]
    t_sim = sim_row['Time'].iloc[0]

    for species_id in [s_dlm5, s_acno, s_wgvc]:
        exp_val = exp_row[species_id].iloc[0]
        sim_val = sim_row[species_id].iloc[0]
        abs_diff = abs(exp_val - sim_val)
        print(f"{t:<10.1f} | {species_id:<10} | {exp_val:<15.2e} | {sim_val:<15.2e} | {abs_diff:<15.2e} (t_exp={t_exp:.1f}, t_sim={t_sim:.1f})")
    print("-"*70)

# Check if the initial concentration was set correctly in the simulation
print("\nInitial concentrations in simulation (Time ~ 0):")
print(sim_results_perturbed_df.head(1))
```
# Observation

## Code Stdout
Comparison of Perturbed Experimental Data (iteration_2) and Simulation Results:
======================================================================
Time       | Species    | Exp Value       | Sim Value       | Abs Diff       
----------------------------------------------------------------------
0.0        | id_dlm5    | 8.00e+00        | 8.00e+00        | 0.00e+00        (t_exp=0.0, t_sim=0.0)
0.0        | id_acno    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0, t_sim=0.0)
0.0        | id_wgvc    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0, t_sim=0.0)
----------------------------------------------------------------------
16.3       | id_dlm5    | 8.30e+00        | 1.01e+01        | 1.79e+00        (t_exp=16.3, t_sim=16.3)
16.3       | id_acno    | 9.85e+01        | 9.84e+01        | 1.14e-01        (t_exp=16.3, t_sim=16.3)
16.3       | id_wgvc    | 1.16e+05        | 1.16e+05        | 4.41e+02        (t_exp=16.3, t_sim=16.3)
----------------------------------------------------------------------
50.0       | id_dlm5    | 1.26e+01        | 1.28e+01        | 1.75e-01        (t_exp=50.0, t_sim=50.0)
50.0       | id_acno    | 1.30e+02        | 1.35e+02        | 4.88e+00        (t_exp=50.0, t_sim=50.0)
50.0       | id_wgvc    | 2.02e+05        | 2.02e+05        | 4.66e+02        (t_exp=50.0, t_sim=50.0)
----------------------------------------------------------------------
100.0      | id_dlm5    | 1.53e+01        | 1.47e+01        | 6.07e-01        (t_exp=100.0, t_sim=100.0)
100.0      | id_acno    | 1.37e+02        | 1.38e+02        | 7.56e-01        (t_exp=100.0, t_sim=100.0)
100.0      | id_wgvc    | 2.24e+05        | 2.24e+05        | 3.20e+02        (t_exp=100.0, t_sim=100.0)
----------------------------------------------------------------------
150.0      | id_dlm5    | 1.58e+01        | 1.54e+01        | 4.11e-01        (t_exp=150.0, t_sim=150.0)
150.0      | id_acno    | 1.38e+02        | 1.38e+02        | 5.76e-02        (t_exp=150.0, t_sim=150.0)
150.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.81e+02        (t_exp=150.0, t_sim=150.0)
----------------------------------------------------------------------
300.0      | id_dlm5    | 1.59e+01        | 1.59e+01        | 7.54e-02        (t_exp=300.0, t_sim=300.0)
300.0      | id_acno    | 1.38e+02        | 1.38e+02        | 3.57e-02        (t_exp=300.0, t_sim=300.0)
300.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.73e+02        (t_exp=300.0, t_sim=300.0)
----------------------------------------------------------------------
800.0      | id_dlm5    | 1.59e+01        | 1.59e+01        | 4.77e-02        (t_exp=800.0, t_sim=800.0)
800.0      | id_acno    | 1.38e+02        | 1.38e+02        | 3.58e-02        (t_exp=800.0, t_sim=800.0)
800.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.73e+02        (t_exp=800.0, t_sim=800.0)
----------------------------------------------------------------------

Initial concentrations in simulation (Time ~ 0):
   id_dlm5  id_acno  id_wgvc  id_v9bo  Time
0      8.0      0.0      0.0    100.0   0.0

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 17/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2)
- `shared_variables`: all variables you have saved from the previous iterations. (current_model_sbml, sim_results_iteration_1, sim_results_iteration_3_perturbed)

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


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



# Iteration 4
## Thoughts

The simulation of the current model with `id_dlm5` initial concentration set to 8.0 shows:
- `id_acno` and `id_wgvc`: The simulated values match the experimental data from `iteration_2` very well. The absolute differences are small, especially considering the magnitudes of `id_wgvc`. This reinforces the hypothesis that their pathways are independent of `id_dlm5`.
- `id_dlm5`:
    - At t=0, the match is perfect (as expected, since it was the initial condition).
    - At t=16.3s, Exp: 8.30e+00, Sim: 1.01e+01. The simulation overshoots slightly.
    - At t=50.0s, Exp: 1.26e+01, Sim: 1.28e+01. The match is very good.
    - At later time points (100s, 150s, 300s, 800s), the simulation matches the experimental data well, converging to the same steady state.

The model seems to capture the overall dynamics quite well, including the independence of `id_acno` and `id_wgvc` from `id_dlm5`. The slight discrepancies for `id_dlm5` in the early phase of the perturbed experiment (overshoot at 16.3s) and the undershoot in the baseline experiment (iteration 1, t=50s, 100s) might indicate that the simple production/degradation model for `id_dlm5` is not perfect, or the parameters could be fine-tuned.

However, given that the task is to discover *missing reactions* and the current model structure (independent pathways) seems robust to the perturbation, I will now try a different perturbation. I will change the initial concentration of `id_acno` to see if it affects `id_dlm5` or `id_wgvc`. This will test the independence assumption from another angle. I'll set `id_acno` to approximately half its steady-state value, e.g., 70.0.

If this experiment also shows independence, it would strongly suggest that the current model structure is correct, and any remaining minor discrepancies are likely due to parameter estimation rather than missing reactions between these species.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_acno": 70.0
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_4
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_4]

Total size: 10001 rows × 5 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_4] for the full data

Time   id_dlm5  id_acno  id_wgvc  id_v9bo
0         0 7.00e+01        0 1.00e+02
...
1.63e+01  4.20e+00 9.85e+01 1.16e+05 1.00e+02
...
3.26e+01  8.49e+00 1.20e+02 1.73e+05 1.00e+02
...
4.90e+01  1.15e+01 1.30e+02 2.01e+05 1.00e+02
...
6.53e+01  1.33e+01 1.34e+02 2.14e+05 1.00e+02
...
8.16e+01  1.45e+01 1.36e+02 2.21e+05 1.00e+02
...
9.79e+01  1.51e+01 1.37e+02 2.24e+05 1.00e+02
...
1.14e+02  1.55e+01 1.38e+02 2.26e+05 1.00e+02
...
1.31e+02  1.57e+01 1.38e+02 2.27e+05 1.00e+02
...
1.47e+02  1.58e+01 1.38e+02 2.27e+05 1.00e+02
...
1.63e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
1.80e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
1.96e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.12e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.28e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.45e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.61e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.77e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.94e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.10e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.26e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.43e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.59e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.75e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.92e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.08e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.24e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.41e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.57e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.73e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.90e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.06e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.22e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.39e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.55e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.71e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.88e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.04e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.20e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.36e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.53e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.69e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.85e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.02e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.18e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.34e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.51e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.67e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.83e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
8.00e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 16/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_4)
- `shared_variables`: all variables you have saved from the previous iterations. (current_model_sbml, sim_results_iteration_1, sim_results_iteration_3_perturbed)

### 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

Experiment `iteration_4` involved changing the initial concentration of `id_acno` to 70.0, while `id_dlm5` and `id_wgvc` started at 0.
Comparing the results of `iteration_4` with `iteration_0` (baseline):
- `id_acno` starts at 70.0 and approaches its steady-state of ~138.
- `id_dlm5` and `id_wgvc` dynamics appear identical to `iteration_0`. For example, at t=16.3s:
    - `iteration_0`: `id_dlm5` = 4.20e+00, `id_wgvc` = 1.16e+05
    - `iteration_4`: `id_dlm5` = 4.20e+00, `id_wgvc` = 1.16e+05
- At t=49.0s:
    - `iteration_0`: `id_dlm5` = 1.15e+01, `id_wgvc` = 2.01e+05
    - `iteration_4`: `id_dlm5` = 1.15e+01, `id_wgvc` = 2.01e+05
- The steady-state values for all species in `iteration_4` are the same as in `iteration_0`.

This result strongly indicates that `id_acno` does not influence the production or degradation of `id_dlm5` or `id_wgvc`. The pathways for `id_dlm5` and `id_wgvc` seem independent of `id_acno`.

Combined with the previous perturbation experiment (`iteration_2`), this provides strong evidence for the hypothesis that `id_dlm5`, `id_acno`, and `id_wgvc` are produced from `id_v9bo` and degrade through independent pathways.

I will now simulate my current model (`shared_variables.access("current_model_sbml")`) with the perturbed initial condition (`id_acno` = 70.0) and compare it to the experimental data from `iteration_4`. This will verify if the model correctly predicts the behavior of `id_acno` under this perturbation and confirms the independence of the other species.

## Action

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

# Retrieve the current model SBML string
current_model_sbml = shared_variables.access("current_model_sbml")

# Modify the initial concentration of id_acno in the model
sbml_doc = libsbml.readSBMLFromString(current_model_sbml)
model = sbml_doc.getModel()

# Reset id_dlm5 to 0, as it was changed in the previous simulation's SBML string
species_dlm5_reset = model.getSpecies("id_dlm5")
if species_dlm5_reset:
    species_dlm5_reset.setInitialConcentration(0.0)

species_acno = model.getSpecies("id_acno")
if species_acno:
    species_acno.setInitialConcentration(70.0)
else:
    print("Error: Species id_acno not found in the model.")

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

# Simulate the perturbed model
sim_results_perturbed_acno_df = simulate(perturbed_model_sbml_acno)
shared_variables.add("sim_results_iteration_5_perturbed_acno", sim_results_perturbed_acno_df)

# Compare with experimental data from iteration_4
exp_data_perturbed_acno_df = experiment_history['iteration_4']

# Print comparison at specific time points
time_points_to_compare = [0.0, 16.3, 50.0, 100.0, 150.0, 300.0, 800.0]
s_dlm5 = "id_dlm5"
s_acno = "id_acno"
s_wgvc = "id_wgvc"

print("Comparison of Perturbed Experimental Data (iteration_4) and Simulation Results:")
print("="*70)
print(f"{'Time':<10} | {'Species':<10} | {'Exp Value':<15} | {'Sim Value':<15} | {'Abs Diff':<15}")
print("-"*70)

for t in time_points_to_compare:
    exp_row = exp_data_perturbed_acno_df.iloc[(exp_data_perturbed_acno_df['Time'] - t).abs().argsort()[:1]]
    sim_row = sim_results_perturbed_acno_df.iloc[(sim_results_perturbed_acno_df['Time'] - t).abs().argsort()[:1]]
    
    if exp_row.empty or sim_row.empty:
        continue

    t_exp = exp_row['Time'].iloc[0]
    t_sim = sim_row['Time'].iloc[0]

    for species_id in [s_dlm5, s_acno, s_wgvc]:
        exp_val = exp_row[species_id].iloc[0]
        sim_val = sim_row[species_id].iloc[0]
        abs_diff = abs(exp_val - sim_val)
        print(f"{t:<10.1f} | {species_id:<10} | {exp_val:<15.2e} | {sim_val:<15.2e} | {abs_diff:<15.2e} (t_exp={t_exp:.1f}, t_sim={t_sim:.1f})")
    print("-"*70)

# Print initial concentrations from simulation
print("\nInitial concentrations in simulation (Time ~ 0):")
print(sim_results_perturbed_acno_df.head(1))
```
# Observation

## Code Stdout
Comparison of Perturbed Experimental Data (iteration_4) and Simulation Results:
======================================================================
Time       | Species    | Exp Value       | Sim Value       | Abs Diff       
----------------------------------------------------------------------
0.0        | id_dlm5    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0, t_sim=0.0)
0.0        | id_acno    | 7.00e+01        | 7.00e+01        | 0.00e+00        (t_exp=0.0, t_sim=0.0)
0.0        | id_wgvc    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0, t_sim=0.0)
----------------------------------------------------------------------
16.3       | id_dlm5    | 4.20e+00        | 4.20e+00        | 5.58e-03        (t_exp=16.3, t_sim=16.3)
16.3       | id_acno    | 9.85e+01        | 1.18e+02        | 2.00e+01        (t_exp=16.3, t_sim=16.3)
16.3       | id_wgvc    | 1.16e+05        | 1.16e+05        | 4.72e+02        (t_exp=16.3, t_sim=16.3)
----------------------------------------------------------------------
50.0       | id_dlm5    | 1.16e+01        | 9.69e+00        | 1.92e+00        (t_exp=50.0, t_sim=50.0)
50.0       | id_acno    | 1.30e+02        | 1.37e+02        | 6.41e+00        (t_exp=50.0, t_sim=50.0)
50.0       | id_wgvc    | 2.02e+05        | 2.02e+05        | 4.72e+02        (t_exp=50.0, t_sim=50.0)
----------------------------------------------------------------------
100.0      | id_dlm5    | 1.52e+01        | 1.35e+01        | 1.70e+00        (t_exp=100.0, t_sim=100.0)
100.0      | id_acno    | 1.37e+02        | 1.38e+02        | 7.88e-01        (t_exp=100.0, t_sim=100.0)
100.0      | id_wgvc    | 2.24e+05        | 2.24e+05        | 3.20e+02        (t_exp=100.0, t_sim=100.0)
----------------------------------------------------------------------
150.0      | id_dlm5    | 1.58e+01        | 1.50e+01        | 8.71e-01        (t_exp=150.0, t_sim=150.0)
150.0      | id_acno    | 1.38e+02        | 1.38e+02        | 5.84e-02        (t_exp=150.0, t_sim=150.0)
150.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.81e+02        (t_exp=150.0, t_sim=150.0)
----------------------------------------------------------------------
300.0      | id_dlm5    | 1.59e+01        | 1.58e+01        | 1.04e-01        (t_exp=300.0, t_sim=300.0)
300.0      | id_acno    | 1.38e+02        | 1.38e+02        | 3.57e-02        (t_exp=300.0, t_sim=300.0)
300.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.73e+02        (t_exp=300.0, t_sim=300.0)
----------------------------------------------------------------------
800.0      | id_dlm5    | 1.59e+01        | 1.59e+01        | 4.77e-02        (t_exp=800.0, t_sim=800.0)
800.0      | id_acno    | 1.38e+02        | 1.38e+02        | 3.58e-02        (t_exp=800.0, t_sim=800.0)
800.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.73e+02        (t_exp=800.0, t_sim=800.0)
----------------------------------------------------------------------

Initial concentrations in simulation (Time ~ 0):
   id_dlm5  id_acno  id_wgvc  id_v9bo  Time
0      0.0     70.0      0.0    100.0   0.0

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_4)
- `shared_variables`: all variables you have saved from the previous iterations. (current_model_sbml, sim_results_iteration_1, sim_results_iteration_3_perturbed, sim_results_iteration_5_perturbed_acno)

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


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



# Iteration 6
## Thoughts

The simulation of the current model with `id_acno` initial concentration set to 70.0 shows:
- `id_dlm5` and `id_wgvc`: The simulated values match the experimental data from `iteration_4` very well.
    - For `id_dlm5`, the simulation shows the same undershoot at intermediate time points (e.g., t=50s, Exp: 1.16e+01, Sim: 9.69e+00) as observed in the baseline simulation (iteration 1). This is consistent.
    - For `id_wgvc`, the match is excellent throughout.
    - This confirms their independence from `id_acno`'s initial state, as predicted by the model.
- `id_acno`:
    - At t=0, the match is perfect.
    - At t=16.3s, Exp: 9.85e+01, Sim: 1.18e+02. The simulation overshoots the experimental value.
    - At t=50.0s, Exp: 1.30e+02, Sim: 1.37e+02. The simulation is still slightly higher but closer.
    - At later time points (100s onwards), the simulation matches the experimental data very well, converging to the same steady state.

The model correctly predicts the independence of `id_dlm5` and `id_wgvc` from `id_acno`. The discrepancy for `id_acno` in the early phase (overshoot when starting from 70.0) is similar to the `id_dlm5` behavior in the previous perturbation (overshoot when starting from 8.0). This might suggest that the degradation rates estimated from the "0 initial concentration" experiment might be slightly too slow, or production rates slightly too high, when the species starts from a non-zero concentration and is below its steady state. However, the model converges to the correct steady states.

Given that the primary goal is to find *missing reactions* and the model structure of independent pathways seems to hold under perturbations of `id_dlm5` and `id_acno`, I will perform one more perturbation. I will change the initial concentration of `id_wgvc`. This is the species with the largest concentration, so any subtle effects might be more pronounced. I'll set `id_wgvc` to approximately half its steady-state value, e.g., 1.0e5.

If this experiment also shows independence for `id_dlm5` and `id_acno`, I will be confident that the current model structure (three independent production/degradation pathways from `id_v9bo`) is correct. The minor discrepancies in transient phases are likely due to the simplicity of the mass-action kinetics or parameter fitting nuances rather than missing cross-pathway reactions.

## Action

### Experiment
```json
{
    "action": "change_initial_concentration",
    "meta_data": {
        "id_wgvc": 1.0e5
    }
}
```
# Observation

## Experiment Result
Experiment ID: iteration_6
Your requested experiment has finished. The details results are saved as a dataframe in experiment_history[iteration_6]

Total size: 10001 rows × 5 columns. 

Below shows a subset of the table for your convenience. You should access experiment_history[iteration_6] for the full data

Time   id_dlm5  id_acno  id_wgvc  id_v9bo
0         0        0 1.00e+05 1.00e+02
...
1.63e+01  6.11e+00 1.18e+02 1.65e+05 1.00e+02
...
3.26e+01  1.01e+01 1.28e+02 1.97e+05 1.00e+02
...
4.90e+01  1.26e+01 1.33e+02 2.12e+05 1.00e+02
...
6.53e+01  1.41e+01 1.36e+02 2.20e+05 1.00e+02
...
8.16e+01  1.49e+01 1.37e+02 2.24e+05 1.00e+02
...
9.79e+01  1.54e+01 1.38e+02 2.26e+05 1.00e+02
...
1.14e+02  1.56e+01 1.38e+02 2.26e+05 1.00e+02
...
1.31e+02  1.58e+01 1.38e+02 2.27e+05 1.00e+02
...
1.47e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
1.63e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
1.80e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
1.96e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.12e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.28e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.45e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.61e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.77e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
2.94e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.10e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.26e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.43e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.59e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.75e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
3.92e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.08e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.24e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.41e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.57e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.73e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
4.90e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.06e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.22e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.39e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.55e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.71e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
5.88e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.04e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.20e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.36e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.53e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.69e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
6.85e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.02e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.18e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.34e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.51e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.67e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
7.83e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02
...
8.00e+02  1.59e+01 1.38e+02 2.27e+05 1.00e+02

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 14/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_4, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (current_model_sbml, sim_results_iteration_1, sim_results_iteration_3_perturbed, sim_results_iteration_5_perturbed_acno)

### 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

Experiment `iteration_6` involved changing the initial concentration of `id_wgvc` to 1.0e5, while `id_dlm5` and `id_acno` started at 0.
Comparing the results of `iteration_6` with `iteration_0` (baseline):
- `id_wgvc` starts at 1.0e5 and approaches its steady-state of ~2.27e5.
- `id_dlm5` and `id_acno` dynamics appear different from `iteration_0` in the early phase.
    - At t=16.3s:
        - `iteration_0`: `id_dlm5` = 4.20e+00, `id_acno` = 9.85e+01
        - `iteration_6`: `id_dlm5` = 6.11e+00, `id_acno` = 1.18e+02
    - At t=32.6s:
        - `iteration_0`: `id_dlm5` = 8.49e+00, `id_acno` = 1.20e+02
        - `iteration_6`: `id_dlm5` = 1.01e+01, `id_acno` = 1.28e+02
- However, the steady-state values for all species in `iteration_6` are the same as in `iteration_0` (e.g., at t=800s, `id_dlm5` ~15.9, `id_acno` ~138, `id_wgvc` ~2.27e5).

This is a crucial observation! The initial concentration of `id_wgvc` *does* affect the transient dynamics of `id_dlm5` and `id_acno`. Specifically, when `id_wgvc` starts higher, `id_dlm5` and `id_acno` also rise faster initially. This indicates that there is some form of coupling or shared resource that was not captured by my previous model of independent pathways.

The fact that `id_v9bo` is a boundary species and the source for all three in my current model is a key point. If the production of all three species depends on `id_v9bo`, and `id_v9bo` is consumed in these reactions (even if its concentration is "fixed" by being a boundary species, the *flux* through it might be limited or its availability might be implicitly shared), then a change in the "demand" by one pathway (e.g., `id_wgvc` production being closer to its steady state, thus potentially drawing less from `id_v9bo`) could affect the others.

However, the kinetic laws I used (`k_prod * id_v9bo`) assume that `id_v9bo` is an infinite source for each reaction independently. This experimental result challenges that assumption if `id_v9bo` is indeed the sole common precursor.

Let's re-examine the data:
- `id_dlm5` (t=16.3): 4.20 (base) vs 6.11 (wgvc_high_init) -> faster rise
- `id_acno` (t=16.3): 98.5 (base) vs 118 (wgvc_high_init) -> faster rise

This suggests that when `id_wgvc` is already high, more of `id_v9bo` (or whatever the true precursor is) is available for the production of `id_dlm5` and `id_acno`. This is counterintuitive if `id_v9bo` is simply consumed.

Could `id_wgvc` somehow promote the production of `id_dlm5` and `id_acno`? Or perhaps `id_wgvc` inhibits its own production from `id_v9bo`, and when `id_wgvc` is high, this self-inhibition is stronger, freeing up `id_v9bo` for the other pathways.

Let's consider a scenario:
1.  `id_v9bo -> id_dlm5`
2.  `id_v9bo -> id_acno`
3.  `id_v9bo -> id_wgvc`
4.  `id_wgvc` inhibits reaction 3 (its own production). So, rate law for R3 becomes `k_prod_wgvc * id_v9bo / (1 + K_i_wgvc * id_wgvc)`.

If this were the case, when `id_wgvc` starts high (1.0e5), its own production rate would be lower. If `id_v9bo` is a limited shared resource that is consumed, this would mean more `id_v9bo` is available for `id_dlm5` and `id_acno` production, leading to their faster rise. This aligns with the observation.

This implies that `id_v9bo` is not an infinite pool for the reactions, but rather its consumption rate matters. However, `id_v9bo` is a boundary species, meaning its concentration is held constant. This usually implies it's an infinite source/sink. The interaction must be more subtle.

Alternative: `id_wgvc` positively influences the production of `id_dlm5` and `id_acno`.
- `id_v9bo + id_wgvc -> id_dlm5 + id_wgvc` (catalytic effect of `id_wgvc` on `id_dlm5` production)
- `id_v9bo + id_wgvc -> id_acno + id_wgvc` (catalytic effect of `id_wgvc` on `id_acno` production)
This would mean the production rates of `id_dlm5` and `id_acno` would be dependent on `id_wgvc`.
Rate for `id_dlm5` prod: `(k_base_dlm5 + k_cat_wgvc_dlm5 * id_wgvc) * id_v9bo`
Rate for `id_acno` prod: `(k_base_acno + k_cat_wgvc_acno * id_wgvc) * id_v9bo`

Let's test this hypothesis. I will simulate the current model (which does *not* have this interaction) with the perturbed initial condition (`id_wgvc` = 1.0e5) and compare it to the experimental data from `iteration_6`. The current model should predict *no change* in `id_dlm5` and `id_acno` dynamics. The discrepancy will highlight the missing interaction.

## Action

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

# Retrieve the current model SBML string
current_model_sbml = shared_variables.access("current_model_sbml")

# Modify the initial concentration of id_wgvc in the model
sbml_doc = libsbml.readSBMLFromString(current_model_sbml)
model = sbml_doc.getModel()

# Reset id_dlm5 and id_acno to 0.0, as they might have been changed in previous SBML string manipulations
# (though the current_model_sbml should be the one from iteration 1, where they are 0)
species_dlm5_reset = model.getSpecies("id_dlm5")
if species_dlm5_reset:
    species_dlm5_reset.setInitialConcentration(0.0)

species_acno_reset = model.getSpecies("id_acno")
if species_acno_reset:
    species_acno_reset.setInitialConcentration(0.0)

species_wgvc = model.getSpecies("id_wgvc")
if species_wgvc:
    species_wgvc.setInitialConcentration(1.0e5)
else:
    print("Error: Species id_wgvc not found in the model.")

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

# Simulate the perturbed model
sim_results_perturbed_wgvc_df = simulate(perturbed_model_sbml_wgvc)
shared_variables.add("sim_results_iteration_7_perturbed_wgvc", sim_results_perturbed_wgvc_df)

# Compare with experimental data from iteration_6
exp_data_perturbed_wgvc_df = experiment_history['iteration_6']

# Print comparison at specific time points
time_points_to_compare = [0.0, 16.3, 32.6, 50.0, 100.0, 800.0]
s_dlm5 = "id_dlm5"
s_acno = "id_acno"
s_wgvc = "id_wgvc"

print("Comparison of Perturbed Experimental Data (iteration_6) and Current Model Simulation:")
print("="*70)
print(f"{'Time':<10} | {'Species':<10} | {'Exp Value':<15} | {'Sim Value':<15} | {'Abs Diff':<15}")
print("-"*70)

for t in time_points_to_compare:
    exp_row = exp_data_perturbed_wgvc_df.iloc[(exp_data_perturbed_wgvc_df['Time'] - t).abs().argsort()[:1]]
    sim_row = sim_results_perturbed_wgvc_df.iloc[(sim_results_perturbed_wgvc_df['Time'] - t).abs().argsort()[:1]]
    
    if exp_row.empty or sim_row.empty:
        continue

    t_exp = exp_row['Time'].iloc[0]
    t_sim = sim_row['Time'].iloc[0]

    for species_id in [s_dlm5, s_acno, s_wgvc]:
        exp_val = exp_row[species_id].iloc[0]
        sim_val = sim_row[species_id].iloc[0]
        abs_diff = abs(exp_val - sim_val)
        print(f"{t:<10.1f} | {species_id:<10} | {exp_val:<15.2e} | {sim_val:<15.2e} | {abs_diff:<15.2e} (t_exp={t_exp:.1f}, t_sim={t_sim:.1f})")
    print("-"*70)

# Print initial concentrations from simulation
print("\nInitial concentrations in simulation (Time ~ 0):")
print(sim_results_perturbed_wgvc_df.head(1))

# For reference, print the baseline simulation (iteration 1) for id_dlm5 and id_acno at t=16.3
baseline_sim_df = shared_variables.access("sim_results_iteration_1") # Model B simulation
baseline_sim_row_16_3 = baseline_sim_df.iloc[(baseline_sim_df['Time'] - 16.3).abs().argsort()[:1]]
print("\nBaseline Model (Iteration 1) Simulation at t=16.3s:")
if not baseline_sim_row_16_3.empty:
    print(f"id_dlm5: {baseline_sim_row_16_3[s_dlm5].iloc[0]:.2e}")
    print(f"id_acno: {baseline_sim_row_16_3[s_acno].iloc[0]:.2e}")

```
# Observation

## Code Stdout
Comparison of Perturbed Experimental Data (iteration_6) and Current Model Simulation:
======================================================================
Time       | Species    | Exp Value       | Sim Value       | Abs Diff       
----------------------------------------------------------------------
0.0        | id_dlm5    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0, t_sim=0.0)
0.0        | id_acno    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0, t_sim=0.0)
0.0        | id_wgvc    | 1.00e+05        | 1.00e+05        | 0.00e+00        (t_exp=0.0, t_sim=0.0)
----------------------------------------------------------------------
16.3       | id_dlm5    | 6.11e+00        | 4.20e+00        | 1.91e+00        (t_exp=16.3, t_sim=16.3)
16.3       | id_acno    | 1.18e+02        | 9.84e+01        | 1.91e+01        (t_exp=16.3, t_sim=16.3)
16.3       | id_wgvc    | 1.65e+05        | 1.65e+05        | 2.76e+02        (t_exp=16.3, t_sim=16.3)
----------------------------------------------------------------------
32.6       | id_dlm5    | 1.01e+01        | 7.29e+00        | 2.85e+00        (t_exp=32.6, t_sim=32.6)
32.6       | id_acno    | 1.28e+02        | 1.27e+02        | 1.81e+00        (t_exp=32.6, t_sim=32.6)
32.6       | id_wgvc    | 1.97e+05        | 1.97e+05        | 3.63e+02        (t_exp=32.6, t_sim=32.6)
----------------------------------------------------------------------
50.0       | id_dlm5    | 1.27e+01        | 9.69e+00        | 3.04e+00        (t_exp=50.0, t_sim=50.0)
50.0       | id_acno    | 1.34e+02        | 1.35e+02        | 1.34e+00        (t_exp=50.0, t_sim=50.0)
50.0       | id_wgvc    | 2.13e+05        | 2.13e+05        | 3.59e+02        (t_exp=50.0, t_sim=50.0)
----------------------------------------------------------------------
100.0      | id_dlm5    | 1.54e+01        | 1.35e+01        | 1.94e+00        (t_exp=100.0, t_sim=100.0)
100.0      | id_acno    | 1.38e+02        | 1.38e+02        | 3.78e-01        (t_exp=100.0, t_sim=100.0)
100.0      | id_wgvc    | 2.26e+05        | 2.25e+05        | 2.96e+02        (t_exp=100.0, t_sim=100.0)
----------------------------------------------------------------------
800.0      | id_dlm5    | 1.59e+01        | 1.59e+01        | 4.77e-02        (t_exp=800.0, t_sim=800.0)
800.0      | id_acno    | 1.38e+02        | 1.38e+02        | 3.58e-02        (t_exp=800.0, t_sim=800.0)
800.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.73e+02        (t_exp=800.0, t_sim=800.0)
----------------------------------------------------------------------

Initial concentrations in simulation (Time ~ 0):
   id_dlm5  id_acno   id_wgvc  id_v9bo  Time
0      0.0      0.0  100000.0    100.0   0.0

Baseline Model (Iteration 1) Simulation at t=16.3s:
id_dlm5: 4.20e+00
id_acno: 9.84e+01

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_4, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (current_model_sbml, sim_results_iteration_1, sim_results_iteration_3_perturbed, sim_results_iteration_5_perturbed_acno, sim_results_iteration_7_perturbed_wgvc)

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


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



# Iteration 8
## Thoughts

The simulation results confirm the discrepancy:
- When `id_wgvc` starts at 1.0e5 (experiment `iteration_6`), `id_dlm5` and `id_acno` rise faster than in the baseline (`iteration_0`).
    - Exp `id_dlm5` at t=16.3s: 6.11e+00
    - Exp `id_acno` at t=16.3s: 1.18e+02
- My current model (simulated with `id_wgvc` initial at 1.0e5) predicts no change in `id_dlm5` and `id_acno` dynamics compared to its own baseline simulation (where `id_wgvc` starts at 0).
    - Sim `id_dlm5` at t=16.3s: 4.20e+00 (matches baseline sim `sim_results_iteration_1`)
    - Sim `id_acno` at t=16.3s: 9.84e+01 (matches baseline sim `sim_results_iteration_1`)
- The absolute differences are significant:
    - `id_dlm5` at t=16.3s: Exp 6.11, Sim 4.20 (Diff 1.91)
    - `id_acno` at t=16.3s: Exp 118, Sim 98.4 (Diff 19.1)

This clearly indicates that the model is missing a mechanism by which `id_wgvc` influences the production of `id_dlm5` and `id_acno`. The influence is positive: higher `id_wgvc` leads to faster initial production of the other two.

Hypothesis: `id_wgvc` acts as a catalyst or positive modulator for the production of `id_dlm5` and `id_acno` from `id_v9bo`.
The reactions would be:
1.  R1: `id_v9bo -> id_dlm5` (modified kinetic law)
2.  R2: `id_dlm5 -> null` (k_deg_dlm5 * id_dlm5)
3.  R3: `id_v9bo -> id_acno` (modified kinetic law)
4.  R4: `id_acno -> null` (k_deg_acno * id_acno)
5.  R5: `id_v9bo -> id_wgvc` (k_prod_wgvc * id_v9bo)
6.  R6: `id_wgvc -> null` (k_deg_wgvc * id_wgvc)

Modified kinetic laws for R1 and R3:
-   R1: `(k_prod_dlm5_basal + k_prod_dlm5_cat * id_wgvc) * id_v9bo`
-   R3: `(k_prod_acno_basal + k_prod_acno_cat * id_wgvc) * id_v9bo`

The original `k_prod_dlm5` and `k_prod_acno` would become the `_basal` rates. We need to estimate `k_prod_dlm5_cat` and `k_prod_acno_cat`.

Let's analyze the data from `iteration_0` (baseline) and `iteration_6` (high initial `id_wgvc`).
At t=16.3s:
- `id_v9bo` = 100
- Degradation rates: `k_deg_dlm5 = 0.0188`, `k_deg_acno = 0.0765` (from iteration 1)

**For id_dlm5:**
Net rate of change `d(id_dlm5)/dt = Production - Degradation`
Approximate production rate = `(C(t) - C(0)) / t + k_deg * C_avg_during_interval`
Using `C(0)=0` and `C_avg_during_interval ~ C(t)/2` for early time points.
Production_dlm5(t) = `C_dlm5(t)/t + k_deg_dlm5 * C_dlm5(t)/2`

Baseline (`iteration_0`, `id_wgvc` starts at 0, at t=16.3, `id_wgvc` ~ 1.16e5):
`C_dlm5(16.3) = 4.20`
`Prod_dlm5_base = 4.20/16.3 + 0.0188 * 4.20/2 = 0.2577 + 0.03948 = 0.29718`
This production rate is `(k_prod_dlm5_basal + k_prod_dlm5_cat * id_wgvc_avg_base) * id_v9bo`.
Let's assume `id_wgvc_avg_base` during this interval is roughly `1.16e5 / 2 = 5.8e4`.
So, `0.29718 = (k_prod_dlm5_basal + k_prod_dlm5_cat * 5.8e4) * 100` (Equation A)
The original `k_prod_dlm5` was `0.0029892`. This was `Prod_dlm5_ss / id_v9bo`.
At steady state, `Prod_dlm5_ss = k_deg_dlm5 * id_dlm5_ss = 0.0188 * 15.9 = 0.29892`.
So, `(k_prod_dlm5_basal + k_prod_dlm5_cat * id_wgvc_ss) * id_v9bo = 0.29892`.
With `id_wgvc_ss = 2.27e5`, `(k_prod_dlm5_basal + k_prod_dlm5_cat * 2.27e5) * 100 = 0.29892` (Equation B)

Perturbed (`iteration_6`, `id_wgvc` starts at 1.0e5, at t=16.3, `id_wgvc` ~ 1.65e5):
`C_dlm5(16.3) = 6.11`
`Prod_dlm5_pert = 6.11/16.3 + 0.0188 * 6.11/2 = 0.3748 + 0.05743 = 0.43223`
`id_wgvc_avg_pert` during this interval is roughly `(1.0e5 + 1.65e5)/2 = 1.325e5`.
So, `0.43223 = (k_prod_dlm5_basal + k_prod_dlm5_cat * 1.325e5) * 100` (Equation C)

We have two equations (B and C) and two unknowns (`k_prod_dlm5_basal`, `k_prod_dlm5_cat`).
From B: `k_prod_dlm5_basal + k_prod_dlm5_cat * 2.27e5 = 0.0029892`
From C: `k_prod_dlm5_basal + k_prod_dlm5_cat * 1.325e5 = 0.0043223`

Subtracting: `k_prod_dlm5_cat * (2.27e5 - 1.325e5) = 0.0029892 - 0.0043223`
`k_prod_dlm5_cat * 0.945e5 = -0.0013331`
`k_prod_dlm5_cat = -0.0013331 / 0.945e5 = -1.4106e-8`

This negative catalytic constant is problematic, as it implies `id_wgvc` *inhibits* `id_dlm5` production, which is the opposite of what we observed (higher `id_wgvc` led to faster `id_dlm5` rise).
The assumption of `id_wgvc_avg` might be too coarse, or the model structure is still not quite right.

Let's re-think. The original `k_prod_dlm5 = 0.0029892` was derived from steady state where `id_wgvc` is also at steady state (`2.27e5`).
So, `k_prod_dlm5_original = k_prod_dlm5_basal + k_prod_dlm5_cat * id_wgvc_ss`
`0.0029892 = k_prod_dlm5_basal + k_prod_dlm5_cat * 2.27e5` (This is Equation B divided by 100)

Now consider the initial production rate when `id_wgvc` is 0 (or very low).
From `iteration_0` (baseline), `id_wgvc` starts at 0.
`Prod_dlm5_base_initial / 100 = k_prod_dlm5_basal` (since `id_wgvc` is initially 0)
The initial production rate for `id_dlm5` in `iteration_0` (where `id_wgvc` starts at 0) is `0.29718 / 100 = 0.0029718`.
So, `k_prod_dlm5_basal = 0.0029718`. This is very close to the original `k_prod_dlm5`. This would imply `k_prod_dlm5_cat` is very small if the formula is additive.

Let's use the production rates directly:
`P_dlm5_0 = (k_b_d + k_c_d * wgvc_0) * v9bo`
`P_dlm5_6 = (k_b_d + k_c_d * wgvc_6) * v9bo`

At t=16.3:
`iteration_0`: `id_wgvc(16.3) = 1.16e5`. `Prod_dlm5_0(16.3) = 0.29718`.
`iteration_6`: `id_wgvc(16.3) = 1.65e5`. `Prod_dlm5_6(16.3) = 0.43223`. (Here `id_wgvc` started at 1e5)

This is tricky because `id_wgvc` itself is changing.
Let's assume the *initial* production rate (at t=0) is affected.
At t=0 for `iteration_0`: `id_wgvc = 0`. Production rate `R_dlm5_init_0 = k_prod_dlm5_basal * id_v9bo`.
At t=0 for `iteration_6`: `id_wgvc = 1.0e5`. Production rate `R_dlm5_init_6 = (k_prod_dlm5_basal + k_prod_dlm5_cat * 1.0e5) * id_v9bo`.

We need to estimate these initial rates from the data.
`d(id_dlm5)/dt_initial = R_dlm5_initial` (since degradation is 0 at t=0 if `id_dlm5` is 0).
From `iteration_0`: `id_dlm5(t_small) / t_small`. Let's use the first non-zero point if available, or approximate from 16.3.
`id_dlm5(16.3) = 4.20`. Initial rate approx `4.20 / 16.3 = 0.2577`.
So, `k_prod_dlm5_basal * 100 = 0.2577` => `k_prod_dlm5_basal = 0.002577`.

From `iteration_6`: `id_dlm5(16.3) = 6.11`. Initial rate approx `6.11 / 16.3 = 0.3748`.
So, `(k_prod_dlm5_basal + k_prod_dlm5_cat * 1.0e5) * 100 = 0.3748`.
`(0.002577 + k_prod_dlm5_cat * 1.0e5) * 100 = 0.3748`
`0.002577 + k_prod_dlm5_cat * 1.0e5 = 0.003748`
`k_prod_dlm5_cat * 1.0e5 = 0.003748 - 0.002577 = 0.001171`
`k_prod_dlm5_cat = 0.001171 / 1.0e5 = 1.171e-8`. This is positive, which is good.

Now, let's check consistency with steady state.
The overall production constant at steady state (where `id_wgvc_ss = 2.27e5`) should be the original `k_prod_dlm5 = 0.0029892`.
New `k_prod_dlm5_effective_ss = k_prod_dlm5_basal + k_prod_dlm5_cat * id_wgvc_ss`
`= 0.002577 + (1.171e-8 * 2.27e5)`
`= 0.002577 + 0.00265617`
`= 0.00523317`
This is higher than the original `0.0029892`. This means my estimation of `k_prod_dlm5_basal` from the initial slope of `iteration_0` might be too low, or the catalytic effect is overestimated, or the model for catalysis is too simple.

The original `k_prod_dlm5 = 0.0029892` was calculated to match the steady state `id_dlm5_ss = 15.9` with `k_deg_dlm5 = 0.0188`, assuming `Prod = k_prod * id_v9bo`.
So, `(k_prod_dlm5_basal + k_prod_dlm5_cat * id_wgvc_ss) = 0.0029892`.
`(k_b_d + k_c_d * 2.27e5) = 0.0029892` (Eq 1)

From `iteration_6` initial slope for `id_dlm5`: `(k_b_d + k_c_d * 1.0e5) * 100 = 0.3748` (using `id_wgvc_init = 1.0e5`)
`(k_b_d + k_c_d * 1.0e5) = 0.003748` (Eq 2)
This is problematic: Eq 2 gives a higher value than Eq 1, even though `1.0e5 < 2.27e5`. This implies `k_c_d` would be negative.

The approximation `C(t)/t` for initial rate is only valid if degradation is negligible.
`dC/dt = P - k_deg * C`. `C(t) = (P/k_deg) * (1 - exp(-k_deg * t))`.
Initial slope `dC/dt|_{t=0} = P`.
`C(t)/t = (P / (k_deg * t)) * (1 - exp(-k_deg * t))`.
As `t -> 0`, `(1 - exp(-k_deg*t)) / (k_deg*t) -> 1`. So `C(t)/t -> P`. This approximation is okay for small `t`.
`t=16.3` is not extremely small. `k_deg_dlm5 * t = 0.0188 * 16.3 = 0.306`. `exp(-0.306) = 0.736`.
Factor is `(1 - 0.736) / 0.306 = 0.264 / 0.306 = 0.86`.
So, `P_dlm5_actual_initial = (C(16.3) / 16.3) / 0.86`.

Recalculate initial production rates:
`P_dlm5_init_0_corrected = (4.20 / 16.3) / 0.86 = 0.2577 / 0.86 = 0.29965`.
So, `k_prod_dlm5_basal * 100 = 0.29965` => `k_prod_dlm5_basal = 0.0029965`.
This is almost identical to the original `k_prod_dlm5 = 0.0029892`. This implies that if `id_wgvc` starts at 0, the initial production matches the steady-state effective production constant. This would mean `k_prod_dlm5_cat * id_wgvc_ss` is negligible if `id_wgvc` starts at 0 and reaches `id_wgvc_ss`. This doesn't make sense.

The term `id_wgvc` in the kinetic law should be the *current* concentration of `id_wgvc`.
The original parameters were derived assuming `Prod = k_eff * id_v9bo`.
This `k_eff` must be `k_basal + k_cat * id_wgvc_ss_value`.
So, `0.0029892 = k_prod_dlm5_basal + k_prod_dlm5_cat * 2.27e5` (Eq SS_dlm5)

Now, for `iteration_6` (high initial `id_wgvc = 1.0e5`):
`P_dlm5_init_6_corrected = (6.11 / 16.3) / 0.86 = 0.3748 / 0.86 = 0.4358`.
This initial production rate occurs when `id_wgvc` is `1.0e5` (its initial value).
So, `(k_prod_dlm5_basal + k_prod_dlm5_cat * 1.0e5) * 100 = 0.4358`.
`k_prod_dlm5_basal + k_prod_dlm5_cat * 1.0e5 = 0.004358` (Eq PERT_dlm5)

Now solve Eq SS_dlm5 and Eq PERT_dlm5:
1) `k_b + k_c * 2.27e5 = 0.0029892`
2) `k_b + k_c * 1.00e5 = 0.004358`
Subtract (1) - (2):
`k_c * (2.27e5 - 1.00e5) = 0.0029892 - 0.004358`
`k_c * 1.27e5 = -0.0013688`
`k_prod_dlm5_cat = -0.0013688 / 1.27e5 = -1.0778e-8`.
Still negative. This is consistently showing up.

This means my interpretation of "faster rise" is perhaps confounded by the `id_wgvc` value used in the catalytic term.
If `id_wgvc` positively affects production, then when `id_wgvc` is high, production should be high.
The experimental data:
- `iter_0`: `id_wgvc` goes from 0 to `1.16e5` at 16.3s. `id_dlm5` reaches 4.20.
- `iter_6`: `id_wgvc` goes from `1.0e5` to `1.65e5` at 16.3s. `id_dlm5` reaches 6.11.
Since `id_wgvc` is higher throughout the 0-16.3s interval in `iter_6` than in `iter_0`, and `id_dlm5` is also higher, this *does* support a positive catalytic role for `id_wgvc`.

Why is the parameter estimation yielding negative `k_cat`?
The issue might be that the "steady state" `k_prod_dlm5 = 0.0029892` already incorporates the effect of steady-state `id_wgvc = 2.27e5`.
And the "perturbed" production rate `0.004358` is when `id_wgvc` is `1.0e5`.
If `k_cat` is positive:
Rate with `id_wgvc_low = k_basal + k_cat * id_wgvc_low`
Rate with `id_wgvc_high = k_basal + k_cat * id_wgvc_high`
If `id_wgvc_low < id_wgvc_high`, then Rate_low should be < Rate_high.
Here, `id_wgvc_ss = 2.27e5` (high) corresponds to rate `0.0029892`.
And `id_wgvc_init_pert = 1.0e5` (low) corresponds to rate `0.004358`.
This is `Rate_high < Rate_low` for `id_wgvc_high > id_wgvc_low`. This implies `k_cat` must be negative.

This means the effect is opposite: `id_wgvc` *inhibits* the production of `id_dlm5`.
If `id_wgvc` inhibits `id_dlm5` production:
Then when `id_wgvc` is high (e.g., `iter_6` initial condition `1.0e5`), `id_dlm5` production should be *slower*.
But `id_dlm5` rises *faster* (6.11 vs 4.20 at 16.3s).

This is a contradiction. Let me re-check the experimental values:
`iteration_0` (wgvc starts 0): `id_dlm5(16.3) = 4.20`, `id_acno(16.3) = 98.5`, `id_wgvc(16.3) = 1.16e5`
`iteration_6` (wgvc starts 1e5): `id_dlm5(16.3) = 6.11`, `id_acno(16.3) = 118`, `id_wgvc(16.3) = 1.65e5`

The simulation of the *current model* (no wgvc effect) for `iteration_6` conditions:
Sim `id_dlm5(16.3) = 4.20`
Sim `id_acno(16.3) = 98.4`
The experimental values (6.11 and 118) are indeed higher than what the current model predicts.
So, the presence of higher `id_wgvc` (in `iter_6`) *accelerates* `id_dlm5` and `id_acno` production.
The catalytic constant `k_cat` must be positive.

The problem is in the equations:
1) `k_b + k_c * id_wgvc_at_SS_for_k_eff = k_eff_SS`
   `k_b + k_c * 2.27e5 = 0.0029892`
2) `k_b + k_c * id_wgvc_at_init_for_k_eff_pert = k_eff_pert`
   `k_b + k_c * 1.0e5 = 0.004358` (This is the effective production constant when `id_wgvc` is `1.0e5`)

If `k_c > 0`:
If `X1 < X2`, then `k_b + k_c * X1 < k_b + k_c * X2`.
Here, `1.0e5 < 2.27e5`. So we should have `0.004358 < 0.0029892`. This is false.

What if the `id_v9bo` is somehow limited, and `id_wgvc` production consumes less of it when `id_wgvc` is already high (due to product inhibition on its own synthesis, for example)?
R5: `id_v9bo -> id_wgvc`, rate `k_prod_wgvc * id_v9bo / (1 + K_I_wgvc * id_wgvc)`
If `id_wgvc` is high, its own production rate is low.
If `id_v9bo` is a shared, limited precursor (even if its concentration is fixed, its *flux capacity* might be shared), then lower consumption by `id_wgvc` pathway would leave more `id_v9bo` "available" for `id_dlm5` and `id_acno` production, making them faster.
This is an indirect effect. The problem states `id_v9bo` is a boundary condition, constant. This usually means it's an infinite pool. If it's an infinite pool, then consumption by one reaction should not affect its availability for another, unless the reactions are competing for an enzyme that uses `id_v9bo`.

Let's assume the direct catalysis model: `Rate = (k_basal + k_cat * id_wgvc) * id_v9bo`.
The issue is with the parameter values derived.
The `k_eff_SS = 0.0029892` is the rate constant when `id_wgvc = 2.27e5`.
The `k_eff_pert = 0.004358` is the rate constant when `id_wgvc = 1.0e5`.
This data implies that when `id_wgvc` decreases from `2.27e5` to `1.0e5`, the rate constant *increases* from `0.0029892` to `0.004358`.
This means `id_wgvc` has an *inhibitory* effect on the production of `id_dlm5`.
Rate form: `(k_base / (1 + K_i * id_wgvc)) * id_v9bo` or `(k_base - k_inh * id_wgvc) * id_v9bo`.
Let's try `k_eff = k_basal_prime - k_inhib_prime * id_wgvc`.
1) `k_b' - k_i' * 2.27e5 = 0.0029892`
2) `k_b' - k_i' * 1.0e5 = 0.004358`
Subtract (2) - (1):
`(-k_i' * 1.0e5) - (-k_i' * 2.27e5) = 0.004358 - 0.0029892`
`k_i' * (2.27e5 - 1.0e5) = 0.0013688`
`k_i' * 1.27e5 = 0.0013688`
`k_inhib_prime = 0.0013688 / 1.27e5 = 1.0778e-8`. This is positive, so it's a valid inhibition constant.
Then `k_basal_prime = 0.004358 + k_inhib_prime * 1.0e5 = 0.004358 + 1.0778e-8 * 1.0e5 = 0.004358 + 0.0010778 = 0.0054358`.

So, for `id_dlm5` production: `(0.0054358 - 1.0778e-8 * id_wgvc) * id_v9bo`.
Let's check:
If `id_wgvc = 0`, rate const = `0.0054358`.
If `id_wgvc = 1.0e5`, rate const = `0.0054358 - 0.0010778 = 0.004358`. (Matches)
If `id_wgvc = 2.27e5` (SS), rate const = `0.0054358 - 1.0778e-8 * 2.27e5 = 0.0054358 - 0.0024468 = 0.002989`. (Matches)

This model (id_wgvc inhibits id_dlm5 production) would mean:
- In `iteration_0` (wgvc starts 0, rises): inhibition is initially low, then increases.
- In `iteration_6` (wgvc starts 1.0e5, rises): inhibition is initially high, then increases further.
This would predict that `id_dlm5` rises *slower* in `iteration_6` than in `iteration_0`.
This is the OPPOSITE of the experimental observation (`id_dlm5` 6.11 vs 4.20 at 16.3s).

I am stuck on this contradiction. The data says: high `id_wgvc` -> faster `id_dlm5`/`id_acno` rise.
The parameter fitting from effective rates says: high `id_wgvc` -> lower effective rate constant.

Could the `id_v9bo` concentration in the kinetic law be wrong? It's a boundary species, so its value is fixed.
The only way `k_cat` can be positive is if `k_eff_pert (at id_wgvc=1e5)` is `0.0029892` and `k_eff_SS (at id_wgvc=2.27e5)` is `0.004358`. But this is swapping the values.

Let's re-evaluate the "initial production rates" P:
`P_dlm5_iter0 = 0.29965` (when `id_wgvc` is effectively 0 at t=0)
`P_dlm5_iter6 = 0.4358` (when `id_wgvc` is effectively `1.0e5` at t=0)
These are `P = k_eff * id_v9bo`. So `k_eff = P / id_v9bo`.
`k_eff_iter0 = 0.29965 / 100 = 0.0029965` (this is `k_basal` if model is `(k_basal + k_cat * id_wgvc) * id_v9bo`)
`k_eff_iter6 = 0.4358 / 100 = 0.004358` (this is `k_basal + k_cat * 1.0e5`)

So:
1) `k_prod_dlm5_basal = 0.0029965`
2) `k_prod_dlm5_basal + k_prod_dlm5_cat * 1.0e5 = 0.004358`
From (2), `0.0029965 + k_prod_dlm5_cat * 1.0e5 = 0.004358`
`k_prod_dlm5_cat * 1.0e5 = 0.004358 - 0.0029965 = 0.0013615`
`k_prod_dlm5_cat = 0.0013615 / 1.0e5 = 1.3615e-8`. This is positive!

Now, what is the effective production constant at steady state (`id_wgvc_ss = 2.27e5`) using these new parameters?
`k_eff_ss_new = k_prod_dlm5_basal + k_prod_dlm5_cat * 2.27e5`
`= 0.0029965 + (1.3615e-8 * 2.27e5)`
`= 0.0029965 + 0.003090605`
`= 0.006087105`
This new `k_eff_ss_new` should be equal to the original `k_prod_dlm5 = 0.0188 * 15.9 / 100 = 0.0029892`.
They are not equal: `0.006087` vs `0.0029892`. The new one is much larger. This would lead to a much higher steady state for `id_dlm5`.

The problem is that the "basal" rate derived from `iteration_0` (where `id_wgvc` starts at 0 but then grows) is not truly basal if `id_wgvc` contributes throughout.
The original `k_prod_dlm5 = 0.0029892` is the effective constant that gives the correct steady state when `id_wgvc` is also at its steady state.
So, `k_prod_dlm5_basal + k_prod_dlm5_cat * id_wgvc_ss = 0.0029892`. (Eq A)

The initial rate in `iteration_0` (where `id_wgvc` is 0 at t=0) is `P_dlm5_init_0_corrected = 0.29965`.
This rate should be `k_prod_dlm5_basal * id_v9bo`.
So, `k_prod_dlm5_basal = 0.29965 / 100 = 0.0029965`. (Eq B)

Substitute (B) into (A):
`0.0029965 + k_prod_dlm5_cat * 2.27e5 = 0.0029892`
`k_prod_dlm5_cat * 2.27e5 = 0.0029892 - 0.0029965 = -0.0000073`
`k_prod_dlm5_cat = -7.3e-6 / 2.27e5 = -3.215e-11`.
This is very small and negative. This implies that the basal rate (when `id_wgvc` is 0) is almost identical to the effective rate when `id_wgvc` is at steady state, meaning the catalytic term `k_cat * id_wgvc_ss` is negligible or slightly negative. This contradicts the observation from `iteration_6` where high initial `id_wgvc` clearly boosted production.

This suggests the model `(k_basal + k_cat * id_wgvc) * id_v9bo` with parameters derived this way won't work.
The initial slope method might be too sensitive or the model is wrong.

Let's try to find `k_cat` values that would explain the *boost* observed.
In `iteration_0`, `id_dlm5` reaches 4.20 at 16.3s. `id_wgvc` is ~0 initially, average maybe `0.5 * 1.16e5 = 0.58e5`.
In `iteration_6`, `id_dlm5` reaches 6.11 at 16.3s. `id_wgvc` is ~1e5 initially, average maybe `0.5 * (1e5 + 1.65e5) = 1.325e5`.

Let `P(wgvc) = (k_b + k_c * wgvc_avg) * v9bo`.
`P_0 = (k_b + k_c * 0.58e5) * 100 = (4.20/16.3) / 0.86 = 0.29965`
`P_6 = (k_b + k_c * 1.325e5) * 100 = (6.11/16.3) / 0.86 = 0.4358`

1) `k_b + k_c * 0.58e5 = 0.0029965`
2) `k_b + k_c * 1.325e5 = 0.004358`
Subtract (1) from (2):
`k_c * (1.325e5 - 0.58e5) = 0.004358 - 0.0029965`
`k_c * 0.745e5 = 0.0013615`
`k_c_dlm5 = 0.0013615 / 0.745e5 = 1.8275e-8`. This is positive.
Then `k_b_dlm5 = 0.0029965 - 1.8275e-8 * 0.58e5 = 0.0029965 - 0.00105995 = 0.00193655`.

New parameters for `id_dlm5` production:
`k_prod_dlm5_basal = 0.00193655`
`k_prod_dlm5_cat_wgvc = 1.8275e-8`
Law: `(k_prod_dlm5_basal + k_prod_dlm5_cat_wgvc * id_wgvc) * id_v9bo`

Let's do the same for `id_acno`.
`k_deg_acno = 0.0765`. `k_deg_acno * t = 0.0765 * 16.3 = 1.24695`. `exp(-1.24695) = 0.287`.
Factor is `(1 - 0.287) / 1.24695 = 0.713 / 1.24695 = 0.5718`.
`P_acno_actual_initial = (C(16.3) / 16.3) / 0.5718`.

`iteration_0`: `id_acno(16.3) = 98.5`. `id_wgvc_avg = 0.58e5`.
`P_acno_0 = (98.5 / 16.3) / 0.5718 = 6.043 / 0.5718 = 10.568`.
`iteration_6`: `id_acno(16.3) = 118`. `id_wgvc_avg = 1.325e5`.
`P_acno_6 = (118 / 16.3) / 0.5718 = 7.239 / 0.5718 = 12.66`.

1) `(k_b_acno + k_c_acno * 0.58e5) * 100 = 10.568` => `k_b_acno + k_c_acno * 0.58e5 = 0.10568`
2) `(k_b_acno + k_c_acno * 1.325e5) * 100 = 12.66` => `k_b_acno + k_c_acno * 1.325e5 = 0.1266`
Subtract (1) from (2):
`k_c_acno * (1.325e5 - 0.58e5) = 0.1266 - 0.10568`
`k_c_acno * 0.745e5 = 0.02092`
`k_c_acno = 0.02092 / 0.745e5 = 2.808e-7`. Positive.
`k_b_acno = 0.10568 - 2.808e-7 * 0.58e5 = 0.10568 - 0.0162864 = 0.0893936`.

New parameters for `id_acno` production:
`k_prod_acno_basal = 0.0893936`
`k_prod_acno_cat_wgvc = 2.808e-7`
Law: `(k_prod_acno_basal + k_prod_acno_cat_wgvc * id_wgvc) * id_v9bo`

The original degradation parameters and `id_wgvc` production/degradation parameters remain the same.
I need to build a new model with these updated kinetic laws for `id_dlm5` and `id_acno` production.
Then simulate this new model under conditions of `iteration_0` and `iteration_6` to see if it matches better.

This is a significant model revision.

Model C:
- R1: `id_v9bo -> id_dlm5`, rate `(k_b_d + k_c_d_wgvc * id_wgvc) * id_v9bo`
- R2: `id_dlm5 -> null`, rate `k_deg_dlm5 * id_dlm5`
- R3: `id_v9bo -> id_acno`, rate `(k_b_a + k_c_a_wgvc * id_wgvc) * id_v9bo`
- R4: `id_acno -> null`, rate `k_deg_acno * id_acno`
- R5: `id_v9bo -> id_wgvc`, rate `k_prod_wgvc * id_v9bo` (original: 99.426)
- R6: `id_wgvc -> null`, rate `k_deg_wgvc * id_wgvc` (original: 0.0438)

Degradation parameters:
`k_deg_dlm5 = 0.0188`
`k_deg_acno = 0.0765`
`k_deg_wgvc = 0.0438`

Production of `id_wgvc`:
`k_prod_wgvc = 99.426` (This was `k_deg_wgvc * id_wgvc_ss / id_v9bo = 0.0438 * 2.27e5 / 100`)

This seems like a plausible new hypothesis.

## Action

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

# Load the initial SBML model (it's cleaner than modifying the existing one extensively)
sbml_doc_new = libsbml.readSBMLFromString(input_sbml_string) # Start from the base empty model
model_new = sbml_doc_new.getModel()

s_dlm5 = "id_dlm5"
s_v9bo = "id_v9bo"
s_acno = "id_acno"
s_wgvc = "id_wgvc"

# Define new parameters for Model C
params_c = {
    "k_prod_dlm5_basal": 0.00193655,
    "k_prod_dlm5_cat_wgvc": 1.8275e-8,
    "k_deg_dlm5": 0.0188,
    "k_prod_acno_basal": 0.0893936,
    "k_prod_acno_cat_wgvc": 2.808e-7,
    "k_deg_acno": 0.0765,
    "k_prod_wgvc": 99.426, # Original value
    "k_deg_wgvc": 0.0438   # Original value
}

for p_id, p_val in params_c.items():
    p = model_new.createParameter()
    p.setId(p_id)
    p.setValue(p_val)
    p.setConstant(True)

# Reaction 1: id_v9bo -> id_dlm5 (catalyzed by id_wgvc)
r1_new = model_new.createReaction()
r1_new.setId("R1_prod_dlm5_cat_wgvc")
r1_new.setReversible(False)
r1_new.setFast(False)
# Reactant id_v9bo is implicitly in kinetic law through its ID
# Product id_dlm5
product_r1_new = r1_new.createProduct()
product_r1_new.setSpecies(s_dlm5)
product_r1_new.setStoichiometry(1)
product_r1_new.setConstant(False)
# Modifier id_wgvc (optional to list as modifier if only in rate law)
# mod_r1_wgvc = r1_new.createModifier()
# mod_r1_wgvc.setSpecies(s_wgvc)
kinetic_law_r1_new = r1_new.createKineticLaw()
kinetic_law_r1_new.setMath(libsbml.parseL3Formula(f"(k_prod_dlm5_basal + k_prod_dlm5_cat_wgvc * {s_wgvc}) * {s_v9bo}"))

# Reaction 2: id_dlm5 -> null
r2_new = model_new.createReaction()
r2_new.setId("R2_deg_dlm5")
r2_new.setReversible(False)
r2_new.setFast(False)
reactant_r2_new = r2_new.createReactant()
reactant_r2_new.setSpecies(s_dlm5)
reactant_r2_new.setStoichiometry(1)
reactant_r2_new.setConstant(False)
kinetic_law_r2_new = r2_new.createKineticLaw()
kinetic_law_r2_new.setMath(libsbml.parseL3Formula(f"k_deg_dlm5 * {s_dlm5}"))

# Reaction 3: id_v9bo -> id_acno (catalyzed by id_wgvc)
r3_new = model_new.createReaction()
r3_new.setId("R3_prod_acno_cat_wgvc")
r3_new.setReversible(False)
r3_new.setFast(False)
product_r3_new = r3_new.createProduct()
product_r3_new.setSpecies(s_acno)
product_r3_new.setStoichiometry(1)
product_r3_new.setConstant(False)
kinetic_law_r3_new = r3_new.createKineticLaw()
kinetic_law_r3_new.setMath(libsbml.parseL3Formula(f"(k_prod_acno_basal + k_prod_acno_cat_wgvc * {s_wgvc}) * {s_v9bo}"))

# Reaction 4: id_acno -> null
r4_new = model_new.createReaction()
r4_new.setId("R4_deg_acno")
r4_new.setReversible(False)
r4_new.setFast(False)
reactant_r4_new = r4_new.createReactant()
reactant_r4_new.setSpecies(s_acno)
reactant_r4_new.setStoichiometry(1)
reactant_r4_new.setConstant(False)
kinetic_law_r4_new = r4_new.createKineticLaw()
kinetic_law_r4_new.setMath(libsbml.parseL3Formula(f"k_deg_acno * {s_acno}"))

# Reaction 5: id_v9bo -> id_wgvc (original)
r5_new = model_new.createReaction()
r5_new.setId("R5_prod_wgvc")
r5_new.setReversible(False)
r5_new.setFast(False)
# Reactant id_v9bo is implicitly in kinetic law
product_r5_new = r5_new.createProduct()
product_r5_new.setSpecies(s_wgvc)
product_r5_new.setStoichiometry(1)
product_r5_new.setConstant(False)
kinetic_law_r5_new = r5_new.createKineticLaw()
kinetic_law_r5_new.setMath(libsbml.parseL3Formula(f"k_prod_wgvc * {s_v9bo}"))

# Reaction 6: id_wgvc -> null (original)
r6_new = model_new.createReaction()
r6_new.setId("R6_deg_wgvc")
r6_new.setReversible(False)
r6_new.setFast(False)
reactant_r6_new = r6_new.createReactant()
reactant_r6_new.setSpecies(s_wgvc)
reactant_r6_new.setStoichiometry(1)
reactant_r6_new.setConstant(False)
kinetic_law_r6_new = r6_new.createKineticLaw()
kinetic_law_r6_new.setMath(libsbml.parseL3Formula(f"k_deg_wgvc * {s_wgvc}"))

writer = libsbml.SBMLWriter()
model_c_sbml_string = writer.writeSBMLToString(sbml_doc_new)
shared_variables.add("model_c_sbml", model_c_sbml_string)

# --- Simulation 1: Baseline conditions (matches experiment iteration_0) ---
# Initial concentrations are default 0 for dlm5, acno, wgvc in the SBML string
sim_model_c_baseline_df = simulate(model_c_sbml_string)
shared_variables.add("sim_model_c_baseline", sim_model_c_baseline_df)
exp_data_baseline_df = experiment_history['iteration_0']

print("Model C vs Experiment iteration_0 (Baseline)")
print("="*70)
print(f"{'Time':<10} | {'Species':<10} | {'Exp Value':<15} | {'Sim Value':<15} | {'Abs Diff':<15}")
print("-"*70)
time_points_to_compare = [0.0, 16.3, 50.0, 150.0, 800.0]
for t in time_points_to_compare:
    exp_row = exp_data_baseline_df.iloc[(exp_data_baseline_df['Time'] - t).abs().argsort()[:1]]
    sim_row = sim_model_c_baseline_df.iloc[(sim_model_c_baseline_df['Time'] - t).abs().argsort()[:1]]
    if exp_row.empty or sim_row.empty: continue
    t_exp, t_sim = exp_row['Time'].iloc[0], sim_row['Time'].iloc[0]
    for species_id in [s_dlm5, s_acno, s_wgvc]:
        exp_val, sim_val = exp_row[species_id].iloc[0], sim_row[species_id].iloc[0]
        print(f"{t:<10.1f} | {species_id:<10} | {exp_val:<15.2e} | {sim_val:<15.2e} | {abs(exp_val-sim_val):<15.2e} (t_exp={t_exp:.1f})")
    print("-"*70)

# --- Simulation 2: Perturbed id_wgvc (matches experiment iteration_6) ---
sbml_doc_pert_wgvc = libsbml.readSBMLFromString(model_c_sbml_string)
model_pert_wgvc = sbml_doc_pert_wgvc.getModel()
species_to_perturb = model_pert_wgvc.getSpecies(s_wgvc)
if species_to_perturb:
    species_to_perturb.setInitialConcentration(1.0e5)
model_c_pert_wgvc_sbml_string = writer.writeSBMLToString(sbml_doc_pert_wgvc)

sim_model_c_pert_wgvc_df = simulate(model_c_pert_wgvc_sbml_string)
shared_variables.add("sim_model_c_pert_wgvc", sim_model_c_pert_wgvc_df)
exp_data_pert_wgvc_df = experiment_history['iteration_6']

print("\nModel C vs Experiment iteration_6 (id_wgvc initial = 1.0e5)")
print("="*70)
print(f"{'Time':<10} | {'Species':<10} | {'Exp Value':<15} | {'Sim Value':<15} | {'Abs Diff':<15}")
print("-"*70)
for t in time_points_to_compare: # Using same time points
    exp_row = exp_data_pert_wgvc_df.iloc[(exp_data_pert_wgvc_df['Time'] - t).abs().argsort()[:1]]
    sim_row = sim_model_c_pert_wgvc_df.iloc[(sim_model_c_pert_wgvc_df['Time'] - t).abs().argsort()[:1]]
    if exp_row.empty or sim_row.empty: continue
    t_exp, t_sim = exp_row['Time'].iloc[0], sim_row['Time'].iloc[0]
    for species_id in [s_dlm5, s_acno, s_wgvc]:
        exp_val, sim_val = exp_row[species_id].iloc[0], sim_row[species_id].iloc[0]
        print(f"{t:<10.1f} | {species_id:<10} | {exp_val:<15.2e} | {sim_val:<15.2e} | {abs(exp_val-sim_val):<15.2e} (t_exp={t_exp:.1f})")
    print("-"*70)
```
# Observation

## Code Stdout
Model C vs Experiment iteration_0 (Baseline)
======================================================================
Time       | Species    | Exp Value       | Sim Value       | Abs Diff       
----------------------------------------------------------------------
0.0        | id_dlm5    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
0.0        | id_acno    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
0.0        | id_wgvc    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
----------------------------------------------------------------------
16.3       | id_dlm5    | 4.20e+00        | 4.46e+00        | 2.63e-01        (t_exp=16.3)
16.3       | id_acno    | 9.85e+01        | 1.03e+02        | 4.78e+00        (t_exp=16.3)
16.3       | id_wgvc    | 1.16e+05        | 1.16e+05        | 4.38e+02        (t_exp=16.3)
----------------------------------------------------------------------
50.0       | id_dlm5    | 1.16e+01        | 1.51e+01        | 3.49e+00        (t_exp=50.0)
50.0       | id_acno    | 1.30e+02        | 1.78e+02        | 4.81e+01        (t_exp=50.0)
50.0       | id_wgvc    | 2.02e+05        | 2.02e+05        | 4.64e+02        (t_exp=50.0)
----------------------------------------------------------------------
150.0      | id_dlm5    | 1.58e+01        | 2.95e+01        | 1.36e+01        (t_exp=150.0)
150.0      | id_acno    | 1.38e+02        | 2.00e+02        | 6.20e+01        (t_exp=150.0)
150.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.81e+02        (t_exp=150.0)
----------------------------------------------------------------------
800.0      | id_dlm5    | 1.59e+01        | 3.24e+01        | 1.64e+01        (t_exp=800.0)
800.0      | id_acno    | 1.38e+02        | 2.00e+02        | 6.21e+01        (t_exp=800.0)
800.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.73e+02        (t_exp=800.0)
----------------------------------------------------------------------

Model C vs Experiment iteration_6 (id_wgvc initial = 1.0e5)
======================================================================
Time       | Species    | Exp Value       | Sim Value       | Abs Diff       
----------------------------------------------------------------------
0.0        | id_dlm5    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
0.0        | id_acno    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
0.0        | id_wgvc    | 1.00e+05        | 1.00e+05        | 0.00e+00        (t_exp=0.0)
----------------------------------------------------------------------
16.3       | id_dlm5    | 6.11e+00        | 6.26e+00        | 1.56e-01        (t_exp=16.3)
16.3       | id_acno    | 1.18e+02        | 1.21e+02        | 3.14e+00        (t_exp=16.3)
16.3       | id_wgvc    | 1.65e+05        | 1.65e+05        | 2.76e+02        (t_exp=16.3)
----------------------------------------------------------------------
50.0       | id_dlm5    | 1.27e+01        | 1.71e+01        | 4.41e+00        (t_exp=50.0)
50.0       | id_acno    | 1.34e+02        | 1.86e+02        | 5.23e+01        (t_exp=50.0)
50.0       | id_wgvc    | 2.13e+05        | 2.13e+05        | 3.59e+02        (t_exp=50.0)
----------------------------------------------------------------------
150.0      | id_dlm5    | 1.59e+01        | 2.99e+01        | 1.40e+01        (t_exp=150.0)
150.0      | id_acno    | 1.38e+02        | 2.00e+02        | 6.20e+01        (t_exp=150.0)
150.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.77e+02        (t_exp=150.0)
----------------------------------------------------------------------
800.0      | id_dlm5    | 1.59e+01        | 3.24e+01        | 1.64e+01        (t_exp=800.0)
800.0      | id_acno    | 1.38e+02        | 2.00e+02        | 6.21e+01        (t_exp=800.0)
800.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.73e+02        (t_exp=800.0)
----------------------------------------------------------------------

## Reminder

 ### Remaining Iterations for Interactions:
- Iterations: 12/20



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_4, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (current_model_sbml, sim_results_iteration_1, sim_results_iteration_3_perturbed, sim_results_iteration_5_perturbed_acno, sim_results_iteration_7_perturbed_wgvc, model_c_sbml, sim_model_c_baseline, sim_model_c_pert_wgvc)

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


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



# Iteration 9
## Thoughts

The new Model C, which incorporates `id_wgvc` as a positive catalyst for the production of `id_dlm5` and `id_acno`, shows mixed results:

**Positive aspects:**
-   For the perturbed case (`iteration_6`, `id_wgvc` initial = 1.0e5):
    -   At t=16.3s, the simulated values for `id_dlm5` (Sim: 6.26e+00, Exp: 6.11e+00) and `id_acno` (Sim: 1.21e+02, Exp: 1.18e+02) are much closer to the experimental data than the previous model (which predicted 4.20e+00 and 9.84e+01 respectively). This indicates the catalytic effect of `id_wgvc` is correctly captured in direction and magnitude for the early phase of this perturbation.

**Negative aspects:**
-   Steady States: The model now predicts much higher steady-state concentrations for `id_dlm5` (Sim: 3.24e+01, Exp: 1.59e+01) and `id_acno` (Sim: 2.00e+02, Exp: 1.38e+02). This is a major issue. The new parameters `k_prod_..._basal` and `k_prod_..._cat_wgvc` were estimated based on initial rates, but they don't maintain the original steady states.
-   Baseline (`iteration_0`):
    -   While the initial rise at t=16.3s is reasonably matched for `id_dlm5` (Sim: 4.46e+00, Exp: 4.20e+00) and `id_acno` (Sim: 1.03e+02, Exp: 9.85e+01), the simulation quickly overshoots and leads to the incorrect higher steady states.

The problem lies in how the parameters were derived. The effective production rate at steady state `P_ss = k_deg * C_ss` must hold.
For `id_dlm5`: `(k_b_d + k_c_d * id_wgvc_ss) * id_v9bo = k_deg_dlm5 * id_dlm5_ss`
`k_b_d + k_c_d * 2.27e5 = (0.0188 * 15.9) / 100 = 0.0029892` (Eq SS_dlm5)

For `id_acno`: `(k_b_a + k_c_a * id_wgvc_ss) * id_v9bo = k_deg_acno * id_acno_ss`
`k_b_a + k_c_a * 2.27e5 = (0.0765 * 138) / 100 = 0.10557` (Eq SS_acno)

The parameters `k_b_d = 0.00193655`, `k_c_d_wgvc = 1.8275e-8` give:
`0.00193655 + 1.8275e-8 * 2.27e5 = 0.00193655 + 0.004148425 = 0.006084975`. This is not `0.0029892`.

The parameters `k_b_a = 0.0893936`, `k_c_a_wgvc = 2.808e-7` give:
`0.0893936 + 2.808e-7 * 2.27e5 = 0.0893936 + 0.0637416 = 0.1531352`. This is not `0.10557`.

The estimation method using average `id_wgvc` over the initial interval and fitting two points (baseline and perturbation) was an attempt to capture the dynamics but failed to constrain the steady state.

We need to use the steady-state equations as constraints.
Let's use:
1.  The initial production rate for `iteration_0` (where `id_wgvc` is 0 at t=0, so production is `k_basal * id_v9bo`).
    `P_dlm5_init_0_corrected = 0.29965` => `k_b_d * 100 = 0.29965` => `k_b_d = 0.0029965`.
    `P_acno_init_0_corrected = 10.568` => `k_b_a * 100 = 10.568` => `k_b_a = 0.10568`.
2.  The steady-state equations:
    For `id_dlm5`: `k_b_d + k_c_d * 2.27e5 = 0.0029892`.
    Substitute `k_b_d`: `0.0029965 + k_c_d * 2.27e5 = 0.0029892`.
    `k_c_d * 2.27e5 = 0.0029892 - 0.0029965 = -0.0000073`.
    `k_c_d = -7.3e-6 / 2.27e5 = -3.215e-11`. This is the small negative value again.

    For `id_acno`: `k_b_a + k_c_a * 2.27e5 = 0.10557`.
    Substitute `k_b_a`: `0.10568 + k_c_a * 2.27e5 = 0.10557`.
    `k_c_a * 2.27e5 = 0.10557 - 0.10568 = -0.00011`.
    `k_c_a = -1.1e-4 / 2.27e5 = -4.8458e-10`. Also small negative.

This approach means that the basal production rate (when `id_wgvc=0`) is almost entirely responsible for achieving the steady state, and the catalytic term `k_c * id_wgvc_ss` is negligible or slightly corrective (negative). This contradicts the observation that `id_wgvc` boosts production in `iteration_6`.

The contradiction implies that the model `P = (k_basal + k_cat * id_wgvc) * Source` cannot simultaneously explain:
a) The initial rate when `id_wgvc=0` (from `iter_0` start).
b) The initial rate when `id_wgvc=1e5` (from `iter_6` start).
c) The steady state where `id_wgvc=2.27e5`.
...if `k_cat` is to be positive.

Let's assume the steady state is sacrosanct:
`k_b + k_c * wgvc_ss = k_eff_ss`
And the perturbed initial rate is also key:
`k_b + k_c * wgvc_init_pert = k_eff_pert_init`

For `id_dlm5`:
1) `k_b_d + k_c_d * 2.27e5 = 0.0029892` (SS condition)
2) `k_b_d + k_c_d * 1.0e5 = 0.004358` (from `iter_6` initial rate: `P_dlm5_iter6_corrected / 100`)
Solving this system (as done in thought process of Iteration 8, which led to negative `k_c_d`):
`k_c_d = -1.0778e-8`
`k_b_d = 0.0054358`
This implies `id_wgvc` is inhibitory. But the data shows it's catalytic.

This is a fundamental conflict.
Possibilities:
1.  The experimental data has noise that makes this parameterization impossible.
2.  The model structure `(k_basal + k_cat * id_wgvc)` is too simple or incorrect.
3.  `id_v9bo` is not a simple source but its availability is modulated by `id_wgvc` in a more complex way. E.g., `id_v9bo` is activated by `id_wgvc` to form `id_v9bo_active`, which is then the precursor.
    `id_v9bo + id_wgvc <=> id_v9bo_active + id_wgvc` (fast equilibrium)
    `id_v9bo_active -> id_dlm5`
    `id_v9bo_active -> id_acno`
    This would make production rates proportional to `id_v9bo_active`. `[v9bo_active] = K_eq * [v9bo] * [wgvc]`.
    So, `Rate_dlm5 = k' * [v9bo_active] = k' * K_eq * [v9bo] * [wgvc]`.
    This is a purely catalytic model, `Rate = k_overall_cat * id_wgvc * id_v9bo`. No basal term.
    If this is true:
    - Initial rate in `iter_0` (wgvc=0) should be 0. But `id_dlm5` does rise. So there must be a basal term.

What if the "basal" production observed in `iteration_0` is not truly when `id_wgvc` is zero, because `id_wgvc` itself is being produced?
The rate `P_dlm5_init_0_corrected = 0.29965` was calculated at t=16.3s, where `id_wgvc` is already `1.16e5`.
So, this rate corresponds to `id_wgvc = 1.16e5` (approximately, as an average over the interval or value at that point).
Let's use point values of `id_wgvc` for rate calculations.
Rate `R(t) = (dC/dt) + k_deg * C(t)`.
`dC/dt` can be approximated from data.

Data points:
`iter_0`:
  t=0:    dlm5=0, acno=0, wgvc=0
  t=16.3: dlm5=4.20, acno=98.5, wgvc=1.16e5
  t=32.6: dlm5=8.49, acno=120, wgvc=1.73e5
`iter_6`:
  t=0:    dlm5=0, acno=0, wgvc=1.0e5
  t=16.3: dlm5=6.11, acno=118, wgvc=1.65e5
  t=32.6: dlm5=10.1, acno=128, wgvc=1.97e5

Approximate `d(dlm5)/dt` at t=16.3 for `iter_0`: `(8.49-0)/(32.6-0)` (avg over 0-32.6) or `(8.49-4.20)/(32.6-16.3)` (forward diff from 16.3) = `4.29/16.3 = 0.263`.
Let's use central difference if possible, or stick to the `(C(t)/k_deg_t)*(1-exp(-k_deg_t)) -> P` formula for initial phase.

The `P_dlm5_init_0_corrected = 0.29965` was the production rate needed to reach `C(16.3)=4.20` if `id_wgvc` was 0. This is `k_basal * id_v9bo`.
The `P_dlm5_iter6_corrected = 0.4358` was production rate if `id_wgvc` was `1.0e5`. This is `(k_basal + k_cat * 1.0e5) * id_v9bo`.
These led to `k_basal = 0.0029965` and `k_cat = 1.3615e-8`.
With these, the effective rate at `id_wgvc_ss = 2.27e5` is `0.0029965 + 1.3615e-8 * 2.27e5 = 0.0029965 + 0.0030906 = 0.0060871`.
This should be `k_deg_dlm5 * id_dlm5_ss / id_v9bo = 0.0029892`.
The calculated `0.0060871` is too high.

This means the catalytic effect `k_cat * id_wgvc_ss` is making the steady state too high with the `k_basal` derived from `id_wgvc=0` initial condition.
The model must satisfy all three conditions:
1. Rate at `wgvc=0`: `k_b * v9bo = P_0`
2. Rate at `wgvc=1e5`: `(k_b + k_c * 1e5) * v9bo = P_6`
3. Rate at `wgvc=2.27e5 (SS)`: `(k_b + k_c * 2.27e5) * v9bo = P_SS`

`k_b = P_0 / v9bo`
`k_b + k_c * 1e5 = P_6 / v9bo` => `P_0/v9bo + k_c * 1e5 = P_6/v9bo` => `k_c = (P_6 - P_0) / (v9bo * 1e5)`
`k_b + k_c * 2.27e5 = P_SS / v9bo`

Using `P_0 = 0.29965` (for dlm5), `P_6 = 0.4358`, `P_SS = 0.29892`. `v9bo=100`.
`k_b_d = 0.0029965`.
`k_c_d = (0.4358 - 0.29965) / (100 * 1e5) = 0.13615 / 1e7 = 1.3615e-8`. (Same as before)
Check SS: `(k_b_d + k_c_d * 2.27e5) * 100 = (0.0029965 + 1.3615e-8 * 2.27e5) * 100`
`= (0.0029965 + 0.003090605) * 100 = 0.006087105 * 100 = 0.6087105`.
This should be `P_SS = 0.29892`. It's not.

The system of equations is overdetermined and inconsistent with this model structure.
The rate of production is not simply `(k_b + k_c * wgvc) * v9bo`.

What if `id_wgvc` affects the degradation of `id_dlm5`/`id_acno`?
If `id_wgvc` inhibits degradation: `k_deg_eff = k_deg_base / (1 + K_inh_wgvc * id_wgvc)`.
Higher `id_wgvc` -> lower `k_deg_eff` -> higher accumulation. This could explain faster rise.
Let's test this idea.
Original model: `dC/dt = P - k_deg * C`.
New model: `dC/dt = P_orig - (k_deg_orig / (1 + K_m * id_wgvc)) * C`.
`P_orig_dlm5 = 0.0029892 * 100 = 0.29892`. `k_deg_orig_dlm5 = 0.0188`.

At `t=16.3` in `iter_0`: `id_wgvc = 1.16e5`. `id_dlm5 = 4.20`.
`d(dlm5)/dt + k_deg_eff * dlm5 = P_orig`.
`0.2577 + (0.0188 / (1 + K_m * 1.16e5)) * 4.20 = 0.29892`. (Using `dC/dt = C/t` as rough approx)
`(0.0188 * 4.20) / (1 + K_m * 1.16e5) = 0.04122`.
`0.07896 = 0.04122 * (1 + K_m * 1.16e5)`.
`1.915 = 1 + K_m * 1.16e5`.
`0.915 = K_m * 1.16e5` => `K_m_dlm5 = 0.915 / 1.16e5 = 7.88e-6`.

At `t=16.3` in `iter_6`: `id_wgvc = 1.65e5` (used avg `(1e5+1.65e5)/2 = 1.325e5` for `id_wgvc` in rate calc, let's use point `1.65e5`). `id_dlm5 = 6.11`.
`d(dlm5)/dt = 6.11/16.3 = 0.3748`.
`0.3748 + (0.0188 / (1 + K_m * 1.65e5)) * 6.11 = 0.29892`.
`(0.0188 * 6.11) / (1 + K_m * 1.65e5) = 0.29892 - 0.3748 = -0.07588`. This implies `K_m` is negative, which is not possible.
So, `id_wgvc` inhibiting degradation is not the right model either if production is constant.

The core issue is that the "boost" from `id_wgvc` seems to be transient or only affects the approach to steady state, but not the steady state itself (as all experiments converge to same SS).
If `Rate = (k_b + k_c * id_wgvc) * id_v9bo`, then `id_wgvc_ss` would alter `id_dlm5_ss` unless `k_c` is zero.
This means the catalytic term `k_c * id_wgvc` must somehow vanish or be perfectly compensated at steady state.

This could happen if `id_wgvc` is consumed in the catalysis:
`id_v9bo + id_wgvc -> id_dlm5 + P_wgvc_decay_product`
This would add a consumption term for `id_wgvc` and link its level to `id_dlm5` production.
But `id_wgvc` is a catalyst, usually not consumed.

What if the parameters I used for Model C were not that bad for the dynamics, and the SS is wrong due to the `k_deg` values?
No, `k_deg` values were derived from `C_ss * (1 - exp(-k_deg * t))` and `P = k_deg * C_ss`. They should be consistent with the observed SS if the production `P` is correct for that SS.

The fact that `id_dlm5` and `id_acno` reach the *same* steady state regardless of `id_wgvc`'s initial condition is very telling.
If `id_dlm5_ss = P_dlm5_ss / k_deg_dlm5`, and `P_dlm5_ss = (k_b_d + k_c_d * id_wgvc_ss) * id_v9bo`.
Since `id_wgvc_ss` is always the same (`2.27e5`), then `P_dlm5_ss` would always be the same with this model, and `id_dlm5_ss` would be the same. This is consistent.
The problem was that the Model C parameters (`k_b_d = 0.00193655`, `k_c_d_wgvc = 1.8275e-8`) resulted in `P_dlm5_ss / id_v9bo = 0.00608`, while the original model that fit SS had `P_dlm5_ss / id_v9bo = 0.0029892`.
The Model C parameters *overestimated* the steady-state production rate.

The parameters `k_b_d = 0.00193655`, `k_c_d_wgvc = 1.8275e-8` were fitted to match:
- `iter_0` dynamics (where `id_wgvc_avg_0_16.3 ~ 0.58e5`)
- `iter_6` dynamics (where `id_wgvc_avg_0_16.3 ~ 1.325e5`)
These parameters should then be tested against the steady state condition:
`P_dlm5_ss = (0.00193655 + 1.8275e-8 * 2.27e5) * 100 = (0.00193655 + 0.004148425) * 100 = 0.006084975 * 100 = 0.6084975`.
The required `P_dlm5_ss` for the observed steady state is `k_deg_dlm5 * id_dlm5_ss = 0.0188 * 15.9 = 0.29892`.
The calculated `P_dlm5_ss` (0.6085) is about twice the required one (0.29892). This is why SS is too high in Model C.

The fitting method needs to incorporate the SS constraint.
We need `k_b`, `k_c` such that:
1. `(k_b + k_c * wgvc_avg_iter0) * v9bo = P_dynamic_iter0`
2. `(k_b + k_c * wgvc_avg_iter6) * v9bo = P_dynamic_iter6`
3. `(k_b + k_c * wgvc_ss) * v9bo = P_ss_observed`

This is 3 equations for 2 unknowns (`k_b`, `k_c`). It's overdetermined.
We need to find a best fit. Or one of the assumptions about `wgvc_avg` or `P_dynamic` is off.

Let's use the `P_SS_observed` as a hard constraint.
For `id_dlm5`: `k_b_d + k_c_d * 2.27e5 = 0.0029892` (Eq SS)
Now we need one more equation. Let's use the boost factor from `iter_0` to `iter_6`.
Ratio of production rates: `P_6 / P_0 = ((k_b + k_c * wgvc_avg6)*v9bo) / ((k_b + k_c * wgvc_avg0)*v9bo)`
`P_6_dlm5 / P_0_dlm5 = 0.4358 / 0.29965 = 1.454`.
So, `(k_b_d + k_c_d * 1.325e5) / (k_b_d + k_c_d * 0.58e5) = 1.454`. (Eq Ratio)

Solve Eq SS and Eq Ratio. This is non-linear.
From SS: `k_b_d = 0.0029892 - k_c_d * 2.27e5`. Substitute into Ratio.
Let `k_c_d = x`. `k_b_d = A - Bx` where `A=0.0029892`, `B=2.27e5`.
`(A - Bx + C1*x) / (A - Bx + C0*x) = Ratio` where `C1=1.325e5`, `C0=0.58e5`.
`(A - (B-C1)x) / (A - (B-C0)x) = Ratio`
`A - (B-C1)x = Ratio * (A - (B-C0)x)`
`A - Ratio*A = (B-C1)x - Ratio*(B-C0)x`
`A(1-Ratio) = x * [ (B-C1) - Ratio*(B-C0) ]`
`x = A(1-Ratio) / [ (B-C1) - Ratio*(B-C0) ]`

`B-C1 = 2.27e5 - 1.325e5 = 0.945e5`
`B-C0 = 2.27e5 - 0.58e5 = 1.69e5`
`1-Ratio = 1 - 1.454 = -0.454`
`A(1-Ratio) = 0.0029892 * (-0.454) = -0.0013570968`
Denominator: `0.945e5 - 1.454 * 1.69e5 = 0.945e5 - 2.45726e5 = -1.51226e5`
`k_c_d = -0.0013570968 / -1.51226e5 = 8.974e-9`. Positive, good.
`k_b_d = 0.0029892 - 8.974e-9 * 2.27e5 = 0.0029892 - 0.002037098 = 0.0009521`.

New params for dlm5: `k_b_d = 0.0009521`, `k_c_d = 8.974e-9`.
Let's check:
Rate at `wgvc_avg0=0.58e5`: `(0.0009521 + 8.974e-9 * 0.58e5)*100 = (0.0009521 + 0.000520492)*100 = 0.001472592*100 = 0.1472592`.
This should be `P_0_dlm5 = 0.29965`. It's not matching. The ratio method is also problematic.

The problem is that the "average wgvc" is a poor proxy.
The model is likely correct in structure: `id_wgvc` catalyzes production of `id_dlm5` and `id_acno`. The parameter fitting is the hard part.
Given the time constraints, I might have to accept Model C's parameters as an approximation that captures the catalytic effect but misses the exact SS, or try one more quick parameter refinement.

The simplest way to ensure SS is correct is to use the original `k_prod_dlm5` and `k_prod_acno` as the *total effective production constants at steady state*.
So, `k_prod_dlm5_total_ss = params_old['k_prod_dlm5'] = 0.0029892`.
`k_prod_dlm5_total_ss = k_b_d + k_c_d * id_wgvc_ss`.
`0.0029892 = k_b_d + k_c_d * 2.27e5`.
And for `id_acno`: `0.10557 = k_b_a + k_c_a * 2.27e5`.

Now, use the *boost* observed in `iteration_6` vs `iteration_0` at `t=16.3s`.
`id_dlm5`: Exp `iter_6` (6.11) vs Exp `iter_0` (4.20). Ratio `6.11/4.20 = 1.45`.
This ratio applies to concentrations, which are integrals of rates.
Assume this ratio roughly applies to initial production rates too.
`P_6 / P_0 = 1.45`.
`P_6 = (k_b_d + k_c_d * id_wgvc_init_pert) * id_v9bo` (where `id_wgvc_init_pert = 1e5`)
`P_0 = (k_b_d + k_c_d * id_wgvc_init_baseline) * id_v9bo` (where `id_wgvc_init_baseline = 0`)
So, `(k_b_d + k_c_d * 1e5) / k_b_d = 1.45`.
`k_b_d + k_c_d * 1e5 = 1.45 * k_b_d`.
`k_c_d * 1e5 = 0.45 * k_b_d` => `k_c_d = 0.45 * k_b_d / 1e5 = 4.5e-6 * k_b_d`.

Substitute into SS equation for dlm5:
`k_b_d + (4.5e-6 * k_b_d) * 2.27e5 = 0.0029892`.
`k_b_d * (1 + 4.5e-6 * 2.27e5) = 0.0029892`.
`k_b_d * (1 + 1.0215) = 0.0029892`.
`k_b_d * 2.0215 = 0.0029892`.
`k_b_d = 0.0029892 / 2.0215 = 0.0014787`.
`k_c_d = 4.5e-6 * 0.0014787 = 6.654e-9`.

Parameters for dlm5 (Set 3):
`k_prod_dlm5_basal = 0.0014787`
`k_prod_dlm5_cat_wgvc = 6.654e-9`

For `id_acno`: Exp `iter_6` (118) vs Exp `iter_0` (98.5). Ratio `118/98.5 = 1.198`.
`(k_b_a + k_c_a * 1e5) / k_b_a = 1.198`.
`k_c_a * 1e5 = 0.198 * k_b_a` => `k_c_a = 1.98e-6 * k_b_a`.
Substitute into SS equation for acno:
`k_b_a + (1.98e-6 * k_b_a) * 2.27e5 = 0.10557`.
`k_b_a * (1 + 1.98e-6 * 2.27e5) = 0.10557`.
`k_b_a * (1 + 0.44946) = 0.10557`.
`k_b_a * 1.44946 = 0.10557`.
`k_b_a = 0.10557 / 1.44946 = 0.072834`.
`k_c_a = 1.98e-6 * 0.072834 = 1.442e-7`.

Parameters for acno (Set 3):
`k_prod_acno_basal = 0.072834`
`k_prod_acno_cat_wgvc = 1.442e-7`

These parameters (Set 3) are derived by ensuring:
1. Correct steady state.
2. Ratio of initial production rates (approximated by ratio of concentrations at t=16.3s) matches observations when `id_wgvc` is 0 vs 1e5.

This seems like the most robust approach given the data. I will use these new parameters for Model C and re-simulate.

## Action

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

# Retrieve Model C SBML string (built in Iteration 8)
model_c_sbml_old_params = shared_variables.access("model_c_sbml")
sbml_doc_model_c = libsbml.readSBMLFromString(model_c_sbml_old_params)
model_c = sbml_doc_model_c.getModel()

s_dlm5 = "id_dlm5"
s_v9bo = "id_v9bo"
s_acno = "id_acno"
s_wgvc = "id_wgvc"

# New parameters (Set 3)
params_set3 = {
    "k_prod_dlm5_basal": 0.0014787,
    "k_prod_dlm5_cat_wgvc": 6.654e-9,
    # k_deg_dlm5: 0.0188 (already in model)
    "k_prod_acno_basal": 0.072834,
    "k_prod_acno_cat_wgvc": 1.442e-7,
    # k_deg_acno: 0.0765 (already in model)
    # k_prod_wgvc: 99.426 (already in model)
    # k_deg_wgvc: 0.0438 (already in model)
}

# Update parameters in Model C
for p_id, p_val in params_set3.items():
    p = model_c.getParameter(p_id)
    if p:
        p.setValue(p_val)
    else:
        print(f"Error: Parameter {p_id} not found in model_c_sbml.")

writer = libsbml.SBMLWriter()
model_c_sbml_string_set3 = writer.writeSBMLToString(sbml_doc_model_c)
shared_variables.add("model_c_sbml_set3", model_c_sbml_string_set3) # Store this refined model

# --- Simulation 1: Baseline conditions (matches experiment iteration_0) ---
sim_model_c_baseline_set3_df = simulate(model_c_sbml_string_set3)
shared_variables.add("sim_model_c_baseline_set3", sim_model_c_baseline_set3_df)
exp_data_baseline_df = experiment_history['iteration_0']

print("Model C (Set 3 Params) vs Experiment iteration_0 (Baseline)")
print("="*70)
print(f"{'Time':<10} | {'Species':<10} | {'Exp Value':<15} | {'Sim Value':<15} | {'Abs Diff':<15}")
print("-"*70)
time_points_to_compare = [0.0, 16.3, 50.0, 150.0, 800.0]
for t in time_points_to_compare:
    exp_row = exp_data_baseline_df.iloc[(exp_data_baseline_df['Time'] - t).abs().argsort()[:1]]
    sim_row = sim_model_c_baseline_set3_df.iloc[(sim_model_c_baseline_set3_df['Time'] - t).abs().argsort()[:1]]
    if exp_row.empty or sim_row.empty: continue
    t_exp, t_sim = exp_row['Time'].iloc[0], sim_row['Time'].iloc[0]
    for species_id in [s_dlm5, s_acno, s_wgvc]:
        exp_val, sim_val = exp_row[species_id].iloc[0], sim_row[species_id].iloc[0]
        print(f"{t:<10.1f} | {species_id:<10} | {exp_val:<15.2e} | {sim_val:<15.2e} | {abs(exp_val-sim_val):<15.2e} (t_exp={t_exp:.1f})")
    print("-"*70)

# --- Simulation 2: Perturbed id_wgvc (matches experiment iteration_6) ---
sbml_doc_pert_wgvc_set3 = libsbml.readSBMLFromString(model_c_sbml_string_set3)
model_pert_wgvc_set3 = sbml_doc_pert_wgvc_set3.getModel()
species_to_perturb = model_pert_wgvc_set3.getSpecies(s_wgvc)
if species_to_perturb:
    species_to_perturb.setInitialConcentration(1.0e5) # Perturbation for iter_6
# Reset dlm5 and acno to 0, though they should be by default from the base model string
model_pert_wgvc_set3.getSpecies(s_dlm5).setInitialConcentration(0.0)
model_pert_wgvc_set3.getSpecies(s_acno).setInitialConcentration(0.0)

model_c_pert_wgvc_sbml_string_set3 = writer.writeSBMLToString(sbml_doc_pert_wgvc_set3)

sim_model_c_pert_wgvc_set3_df = simulate(model_c_pert_wgvc_sbml_string_set3)
shared_variables.add("sim_model_c_pert_wgvc_set3", sim_model_c_pert_wgvc_set3_df)
exp_data_pert_wgvc_df = experiment_history['iteration_6']

print("\nModel C (Set 3 Params) vs Experiment iteration_6 (id_wgvc initial = 1.0e5)")
print("="*70)
print(f"{'Time':<10} | {'Species':<10} | {'Exp Value':<15} | {'Sim Value':<15} | {'Abs Diff':<15}")
print("-"*70)
for t in time_points_to_compare: # Using same time points
    exp_row = exp_data_pert_wgvc_df.iloc[(exp_data_pert_wgvc_df['Time'] - t).abs().argsort()[:1]]
    sim_row = sim_model_c_pert_wgvc_set3_df.iloc[(sim_model_c_pert_wgvc_set3_df['Time'] - t).abs().argsort()[:1]]
    if exp_row.empty or sim_row.empty: continue
    t_exp, t_sim = exp_row['Time'].iloc[0], sim_row['Time'].iloc[0]
    for species_id in [s_dlm5, s_acno, s_wgvc]:
        exp_val, sim_val = exp_row[species_id].iloc[0], sim_row[species_id].iloc[0]
        print(f"{t:<10.1f} | {species_id:<10} | {exp_val:<15.2e} | {sim_val:<15.2e} | {abs(exp_val-sim_val):<15.2e} (t_exp={t_exp:.1f})")
    print("-"*70)
```
# Observation

## Code Stdout
Model C (Set 3 Params) vs Experiment iteration_0 (Baseline)
======================================================================
Time       | Species    | Exp Value       | Sim Value       | Abs Diff       
----------------------------------------------------------------------
0.0        | id_dlm5    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
0.0        | id_acno    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
0.0        | id_wgvc    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
----------------------------------------------------------------------
16.3       | id_dlm5    | 4.20e+00        | 2.71e+00        | 1.49e+00        (t_exp=16.3)
16.3       | id_acno    | 9.85e+01        | 7.81e+01        | 2.04e+01        (t_exp=16.3)
16.3       | id_wgvc    | 1.16e+05        | 1.16e+05        | 4.38e+02        (t_exp=16.3)
----------------------------------------------------------------------
50.0       | id_dlm5    | 1.16e+01        | 8.00e+00        | 3.60e+00        (t_exp=50.0)
50.0       | id_acno    | 1.30e+02        | 1.26e+02        | 4.14e+00        (t_exp=50.0)
50.0       | id_wgvc    | 2.02e+05        | 2.02e+05        | 4.64e+02        (t_exp=50.0)
----------------------------------------------------------------------
150.0      | id_dlm5    | 1.58e+01        | 1.46e+01        | 1.22e+00        (t_exp=150.0)
150.0      | id_acno    | 1.38e+02        | 1.38e+02        | 8.51e-02        (t_exp=150.0)
150.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.81e+02        (t_exp=150.0)
----------------------------------------------------------------------
800.0      | id_dlm5    | 1.59e+01        | 1.59e+01        | 4.79e-02        (t_exp=800.0)
800.0      | id_acno    | 1.38e+02        | 1.38e+02        | 3.92e-02        (t_exp=800.0)
800.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.73e+02        (t_exp=800.0)
----------------------------------------------------------------------

Model C (Set 3 Params) vs Experiment iteration_6 (id_wgvc initial = 1.0e5)
======================================================================
Time       | Species    | Exp Value       | Sim Value       | Abs Diff       
----------------------------------------------------------------------
0.0        | id_dlm5    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
0.0        | id_acno    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
0.0        | id_wgvc    | 1.00e+05        | 1.00e+05        | 0.00e+00        (t_exp=0.0)
----------------------------------------------------------------------
16.3       | id_dlm5    | 6.11e+00        | 3.37e+00        | 2.74e+00        (t_exp=16.3)
16.3       | id_acno    | 1.18e+02        | 8.71e+01        | 3.05e+01        (t_exp=16.3)
16.3       | id_wgvc    | 1.65e+05        | 1.65e+05        | 2.76e+02        (t_exp=16.3)
----------------------------------------------------------------------
50.0       | id_dlm5    | 1.27e+01        | 8.75e+00        | 3.98e+00        (t_exp=50.0)
50.0       | id_acno    | 1.34e+02        | 1.30e+02        | 3.71e+00        (t_exp=50.0)
50.0       | id_wgvc    | 2.13e+05        | 2.13e+05        | 3.59e+02        (t_exp=50.0)
----------------------------------------------------------------------
150.0      | id_dlm5    | 1.59e+01        | 1.48e+01        | 1.11e+00        (t_exp=150.0)
150.0      | id_acno    | 1.38e+02        | 1.38e+02        | 6.55e-02        (t_exp=150.0)
150.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.77e+02        (t_exp=150.0)
----------------------------------------------------------------------
800.0      | id_dlm5    | 1.59e+01        | 1.59e+01        | 4.79e-02        (t_exp=800.0)
800.0      | id_acno    | 1.38e+02        | 1.38e+02        | 3.92e-02        (t_exp=800.0)
800.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.73e+02        (t_exp=800.0)
----------------------------------------------------------------------

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_4, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (current_model_sbml, sim_results_iteration_1, sim_results_iteration_3_perturbed, sim_results_iteration_5_perturbed_acno, sim_results_iteration_7_perturbed_wgvc, model_c_sbml, sim_model_c_baseline, sim_model_c_pert_wgvc, model_c_sbml_set3, sim_model_c_baseline_set3, sim_model_c_pert_wgvc_set3)

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


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



# Iteration 10
## Thoughts

The Model C with "Set 3" parameters, which was designed to match steady states and the ratio of initial concentrations, shows the following:

**Baseline (iteration_0):**
-   Steady states (t=800s): Match perfectly for `id_dlm5`, `id_acno`, and `id_wgvc`. This is good, as it was a design constraint.
-   Dynamics (t=16.3s):
    -   `id_dlm5`: Sim 2.71e+00 vs Exp 4.20e+00 (Sim is too low)
    -   `id_acno`: Sim 7.81e+01 vs Exp 9.85e+01 (Sim is too low)
-   Dynamics (t=50.0s):
    -   `id_dlm5`: Sim 8.00e+00 vs Exp 1.16e+01 (Sim is too low)
    -   `id_acno`: Sim 1.26e+02 vs Exp 1.30e+02 (Sim is closer but still a bit low)

**Perturbed (iteration_6, id_wgvc initial = 1.0e5):**
-   Steady states (t=800s): Match perfectly. Good.
-   Dynamics (t=16.3s):
    -   `id_dlm5`: Sim 3.37e+00 vs Exp 6.11e+00 (Sim is significantly too low)
    -   `id_acno`: Sim 8.71e+01 vs Exp 1.18e+02 (Sim is significantly too low)
-   Dynamics (t=50.0s):
    -   `id_dlm5`: Sim 8.75e+00 vs Exp 1.27e+01 (Sim is too low)
    -   `id_acno`: Sim 1.30e+02 vs Exp 1.34e+02 (Sim is closer but still a bit low)

**Analysis:**
The model now correctly predicts the steady states. However, it underestimates the initial rise of `id_dlm5` and `id_acno` under both baseline and perturbed conditions.
Crucially, the *relative* boost is somewhat captured, but the absolute values are off.
For `id_dlm5` at t=16.3s:
- Exp: `iter_0`=4.20, `iter_6`=6.11. Ratio `6.11/4.20 = 1.45`
- Sim: `iter_0`=2.71, `iter_6`=3.37. Ratio `3.37/2.71 = 1.24`
The simulated ratio (1.24) is less than the experimental ratio (1.45). This means the catalytic effect of `id_wgvc` (parameter `k_c_d`) might be underestimated, or the basal rate (`k_b_d`) is too dominant in the calculation that forced the ratio.

The parameter estimation method `k_c = 0.45 * k_b / 1e5` (for dlm5) was based on `(k_b + k_c * 1e5) / k_b = Ratio_exp_conc`. This assumes that the concentration ratio directly reflects the production rate ratio at t=0. This is an approximation.

The model structure `P = (k_basal + k_cat * id_wgvc) * id_v9bo` seems to be the correct way to introduce the influence of `id_wgvc`. The challenge is fine-tuning the four parameters (`k_b_d`, `k_c_d`, `k_b_a`, `k_c_a`) to simultaneously match:
1.  Initial rise in baseline.
2.  Initial rise in `id_wgvc`-perturbed experiment.
3.  Correct steady states for all conditions.

The current Set 3 parameters prioritize steady state and the *ratio* of initial production. This led to an underestimation of the absolute initial production rates.

Perhaps the `k_basal` terms are too low.
If `k_basal` is increased, the initial rise will be faster.
But `k_basal + k_cat * id_wgvc_ss = k_eff_ss` must hold.
If `k_basal` increases, then `k_cat * id_wgvc_ss` must decrease to maintain `k_eff_ss`. This means `k_cat` must decrease if `id_wgvc_ss` is positive.
If `k_cat` decreases, the catalytic boost will be smaller.

This suggests a trade-off. The current model (Model C with Set 3 parameters) is the best I have achieved so far that includes the catalytic effect and respects steady states. The discrepancies in the transient phase are noted.

Given the complexity of manual parameter tuning to satisfy all these dynamic and steady-state constraints simultaneously for multiple species, and the fact that the model now incorporates the key missing interaction (catalysis by `id_wgvc`), I might be approaching the best possible fit without a formal optimization algorithm.

Let's review the previous models:
-   Model (iteration 1, no catalysis): Matched baseline SS well. Failed `iter_6` dynamics for dlm5/acno.
-   Model C (iteration 8, Set 2 params): Captured `iter_6` dynamics better but failed SS.
-   Model C (iteration 9, Set 3 params): Correct SS, captures direction of catalysis but underestimates magnitude of initial rise.

The current model (`model_c_sbml_set3`) is structurally more complete than the initial one. The quantitative fit for transient dynamics is not perfect, but the qualitative behavior (catalysis by `id_wgvc`, correct steady states) is better represented than in a model that ignores the `id_wgvc` interaction.

I will consider this model as my final candidate unless a clear path to significant improvement without overcomplicating the model (e.g., adding more species or very complex rate laws) emerges. The task is to discover missing reactions, and I have added two new effective reactions (catalysis modifying production rates).

I will perform one final check: simulate the model with the other perturbations (`id_dlm5` initial change, `id_acno` initial change) to ensure it still behaves reasonably and doesn't predict any new cross-talk that wasn't there before (it shouldn't, as `id_dlm5` and `id_acno` don't appear in each other's rate laws or `id_wgvc`'s rate laws).

## Action

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

# Retrieve Model C with Set 3 parameters
model_final_candidate_sbml = shared_variables.access("model_c_sbml_set3")
writer = libsbml.SBMLWriter()

s_dlm5 = "id_dlm5"
s_acno = "id_acno"
s_wgvc = "id_wgvc"

time_points_to_compare = [0.0, 16.3, 50.0, 150.0, 800.0]

# --- Simulation 3: Perturbed id_dlm5 (matches experiment iteration_2) ---
# Initial conditions: id_dlm5 = 8.0, others 0 (except v9bo)
sbml_doc_pert_dlm5 = libsbml.readSBMLFromString(model_final_candidate_sbml)
model_pert_dlm5 = sbml_doc_pert_dlm5.getModel()
model_pert_dlm5.getSpecies(s_dlm5).setInitialConcentration(8.0)
model_pert_dlm5.getSpecies(s_acno).setInitialConcentration(0.0) # Ensure others are reset
model_pert_dlm5.getSpecies(s_wgvc).setInitialConcentration(0.0)
model_final_pert_dlm5_sbml = writer.writeSBMLToString(sbml_doc_pert_dlm5)

sim_final_pert_dlm5_df = simulate(model_final_pert_dlm5_sbml)
exp_data_pert_dlm5_df = experiment_history['iteration_2']

print("\nModel C (Set 3 Params) vs Experiment iteration_2 (id_dlm5 initial = 8.0)")
print("="*70)
print(f"{'Time':<10} | {'Species':<10} | {'Exp Value':<15} | {'Sim Value':<15} | {'Abs Diff':<15}")
print("-"*70)
for t in time_points_to_compare:
    exp_row = exp_data_pert_dlm5_df.iloc[(exp_data_pert_dlm5_df['Time'] - t).abs().argsort()[:1]]
    sim_row = sim_final_pert_dlm5_df.iloc[(sim_final_pert_dlm5_df['Time'] - t).abs().argsort()[:1]]
    if exp_row.empty or sim_row.empty: continue
    t_exp, t_sim = exp_row['Time'].iloc[0], sim_row['Time'].iloc[0]
    for species_id in [s_dlm5, s_acno, s_wgvc]:
        exp_val, sim_val = exp_row[species_id].iloc[0], sim_row[species_id].iloc[0]
        print(f"{t:<10.1f} | {species_id:<10} | {exp_val:<15.2e} | {sim_val:<15.2e} | {abs(exp_val-sim_val):<15.2e} (t_exp={t_exp:.1f})")
    print("-"*70)

# --- Simulation 4: Perturbed id_acno (matches experiment iteration_4) ---
# Initial conditions: id_acno = 70.0, others 0 (except v9bo)
sbml_doc_pert_acno = libsbml.readSBMLFromString(model_final_candidate_sbml)
model_pert_acno = sbml_doc_pert_acno.getModel()
model_pert_acno.getSpecies(s_dlm5).setInitialConcentration(0.0)
model_pert_acno.getSpecies(s_acno).setInitialConcentration(70.0)
model_pert_acno.getSpecies(s_wgvc).setInitialConcentration(0.0)
model_final_pert_acno_sbml = writer.writeSBMLToString(sbml_doc_pert_acno)

sim_final_pert_acno_df = simulate(model_final_pert_acno_sbml)
exp_data_pert_acno_df = experiment_history['iteration_4']

print("\nModel C (Set 3 Params) vs Experiment iteration_4 (id_acno initial = 70.0)")
print("="*70)
print(f"{'Time':<10} | {'Species':<10} | {'Exp Value':<15} | {'Sim Value':<15} | {'Abs Diff':<15}")
print("-"*70)
for t in time_points_to_compare:
    exp_row = exp_data_pert_acno_df.iloc[(exp_data_pert_acno_df['Time'] - t).abs().argsort()[:1]]
    sim_row = sim_final_pert_acno_df.iloc[(sim_final_pert_acno_df['Time'] - t).abs().argsort()[:1]]
    if exp_row.empty or sim_row.empty: continue
    t_exp, t_sim = exp_row['Time'].iloc[0], sim_row['Time'].iloc[0]
    for species_id in [s_dlm5, s_acno, s_wgvc]:
        exp_val, sim_val = exp_row[species_id].iloc[0], sim_row[species_id].iloc[0]
        print(f"{t:<10.1f} | {species_id:<10} | {exp_val:<15.2e} | {sim_val:<15.2e} | {abs(exp_val-sim_val):<15.2e} (t_exp={t_exp:.1f})")
    print("-"*70)

# Decision: The model captures the key interaction and steady states.
# The transient dynamics are an approximation.
# I will submit this model.
final_sbml = model_final_candidate_sbml
print("\nFinal model selected: model_c_sbml_set3")
```
# Observation

## Code Stdout

Model C (Set 3 Params) vs Experiment iteration_2 (id_dlm5 initial = 8.0)
======================================================================
Time       | Species    | Exp Value       | Sim Value       | Abs Diff       
----------------------------------------------------------------------
0.0        | id_dlm5    | 8.00e+00        | 8.00e+00        | 0.00e+00        (t_exp=0.0)
0.0        | id_acno    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
0.0        | id_wgvc    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
----------------------------------------------------------------------
16.3       | id_dlm5    | 8.30e+00        | 8.60e+00        | 3.02e-01        (t_exp=16.3)
16.3       | id_acno    | 9.85e+01        | 7.81e+01        | 2.04e+01        (t_exp=16.3)
16.3       | id_wgvc    | 1.16e+05        | 1.16e+05        | 4.41e+02        (t_exp=16.3)
----------------------------------------------------------------------
50.0       | id_dlm5    | 1.26e+01        | 1.11e+01        | 1.51e+00        (t_exp=50.0)
50.0       | id_acno    | 1.30e+02        | 1.26e+02        | 4.14e+00        (t_exp=50.0)
50.0       | id_wgvc    | 2.02e+05        | 2.02e+05        | 4.66e+02        (t_exp=50.0)
----------------------------------------------------------------------
150.0      | id_dlm5    | 1.58e+01        | 1.51e+01        | 7.63e-01        (t_exp=150.0)
150.0      | id_acno    | 1.38e+02        | 1.38e+02        | 8.51e-02        (t_exp=150.0)
150.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.81e+02        (t_exp=150.0)
----------------------------------------------------------------------
800.0      | id_dlm5    | 1.59e+01        | 1.59e+01        | 4.79e-02        (t_exp=800.0)
800.0      | id_acno    | 1.38e+02        | 1.38e+02        | 3.92e-02        (t_exp=800.0)
800.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.73e+02        (t_exp=800.0)
----------------------------------------------------------------------

Model C (Set 3 Params) vs Experiment iteration_4 (id_acno initial = 70.0)
======================================================================
Time       | Species    | Exp Value       | Sim Value       | Abs Diff       
----------------------------------------------------------------------
0.0        | id_dlm5    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
0.0        | id_acno    | 7.00e+01        | 7.00e+01        | 0.00e+00        (t_exp=0.0)
0.0        | id_wgvc    | 0.00e+00        | 0.00e+00        | 0.00e+00        (t_exp=0.0)
----------------------------------------------------------------------
16.3       | id_dlm5    | 4.20e+00        | 2.71e+00        | 1.48e+00        (t_exp=16.3)
16.3       | id_acno    | 9.85e+01        | 9.82e+01        | 3.00e-01        (t_exp=16.3)
16.3       | id_wgvc    | 1.16e+05        | 1.16e+05        | 4.72e+02        (t_exp=16.3)
----------------------------------------------------------------------
50.0       | id_dlm5    | 1.16e+01        | 8.00e+00        | 3.60e+00        (t_exp=50.0)
50.0       | id_acno    | 1.30e+02        | 1.27e+02        | 2.61e+00        (t_exp=50.0)
50.0       | id_wgvc    | 2.02e+05        | 2.02e+05        | 4.72e+02        (t_exp=50.0)
----------------------------------------------------------------------
150.0      | id_dlm5    | 1.58e+01        | 1.46e+01        | 1.22e+00        (t_exp=150.0)
150.0      | id_acno    | 1.38e+02        | 1.38e+02        | 8.43e-02        (t_exp=150.0)
150.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.81e+02        (t_exp=150.0)
----------------------------------------------------------------------
800.0      | id_dlm5    | 1.59e+01        | 1.59e+01        | 4.79e-02        (t_exp=800.0)
800.0      | id_acno    | 1.38e+02        | 1.38e+02        | 3.92e-02        (t_exp=800.0)
800.0      | id_wgvc    | 2.27e+05        | 2.27e+05        | 2.73e+02        (t_exp=800.0)
----------------------------------------------------------------------

Final model selected: model_c_sbml_set3

## Reminder

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



### Available Global Variables
- `input_sbml_string`: Original incomplete model
- `experiment_history`: Results from all previous experiments (iteration_0, iteration_2, iteration_4, iteration_6)
- `shared_variables`: all variables you have saved from the previous iterations. (current_model_sbml, sim_results_iteration_1, sim_results_iteration_3_perturbed, sim_results_iteration_5_perturbed_acno, sim_results_iteration_7_perturbed_wgvc, model_c_sbml, sim_model_c_baseline, sim_model_c_pert_wgvc, model_c_sbml_set3, sim_model_c_baseline_set3, sim_model_c_pert_wgvc_set3)

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


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



# Iteration 11
## Thoughts

The simulations for perturbations of initial `id_dlm5` (iteration_2 data) and initial `id_acno` (iteration_4 data) using Model C (Set 3 parameters) show:
-   **Steady States:** All species reach the correct experimental steady-state values. This is consistent because the parameters were tuned to achieve this, and the perturbations of `id_dlm5` or `id_acno` do not affect `id_wgvc_ss`, which is the catalyst.
-   **Independence:**
    -   When `id_dlm5` is perturbed, `id_acno` and `id_wgvc` dynamics are largely unaffected in the simulation, matching the experimental observation that these pathways are independent of `id_dlm5`'s state (beyond `id_wgvc`'s catalytic role which depends on its own concentration, not `id_dlm5`'s).
    -   When `id_acno` is perturbed, `id_dlm5` and `id_wgvc` dynamics are largely unaffected in the simulation, matching experimental observations.
-   **Transient Dynamics:**
    -   For the perturbed species (`id_dlm5` in iter_2 sim, `id_acno` in iter_4 sim), the model shows a reasonable fit to the experimental trajectory as it returns to steady state.
    -   For the unperturbed species in these simulations (e.g., `id_acno` during `id_dlm5` perturbation), their simulated initial rise is still underestimated compared to experimental data (e.g., `id_acno` at 16.3s in iter_2 sim: 7.81e+01 vs exp 9.85e+01). This is the same underestimation seen in the baseline simulation with this model.

The model `model_c_sbml_set3` correctly captures:
1.  The steady-state concentrations of all species.
2.  The catalytic role of `id_wgvc` in positively modulating the production of `id_dlm5` and `id_acno`.
3.  The independence of `id_dlm5`, `id_acno`, and `id_wgvc` pathways from each other, except for the `id_wgvc` catalysis.

The main remaining discrepancy is the underestimation of the initial accumulation speed of `id_dlm5` and `id_acno`, even with the catalytic term. However, the model structure seems to incorporate the main discovered mechanism. Further refinement of parameters might improve the transient fit, but it's unlikely to reveal new *reactions* which is the primary goal. The current model is a significant improvement over the initial one, which had no reactions, and over the intermediate one, which missed the `id_wgvc` interaction.

Given the constraints and the primary goal of discovering mechanisms, this model represents a good balance of capturing the observed phenomena.

I am satisfied with this model structure and parameter set as a representation of the system's key mechanisms.

## Action

### Submit
```python
# The final_sbml variable should contain the SBML string of the model to be submitted.
# This model is 'model_c_sbml_set3' which was stored in shared_variables.
final_sbml = shared_variables.access("model_c_sbml_set3")

# Sanity check: print first 500 chars of the model to be submitted
# print("Submitting SBML model (first 500 characters):")
# print(final_sbml[:500])
```
