Step 6 – Goodness of Fit Diagnostics

Script:

  • step_6_goodness_of_fit.py

Biological question

Do our fitted models (Hill, ODE) actually describe the data well enough to be trusted for design?

We want to check:

  • how observed steady-state fold-changes compare to Hill predictions,
  • how observed time courses compare to ODE simulations.

Inputs

  • parameters/Hill_parameters.csv
  • parameters/half_times_upregulation.csv
  • parameters/half_times_downregulation.csv
  • parameters/alphamcherry.csv
  • parameters/delays_derepression.csv
  • parameters/delays_repression.csv
  • Derived tables used earlier for dose–response and time-course fits.

Method

  1. Rebuild predicted curves

    • For each construct:
      • use Hill parameters to compute predicted fold-change across the observed BFP range,
      • use ODE parameters to re-simulate mCherry time courses.

  2. Overlay with observed data

    • scatter plots of:
      • observed vs predicted fold-change (Hill),
      • observed vs predicted mCherry at each time point (ODE).

  3. Compute fit statistics

For each construct:

- R² (coefficient of determination),
- MAE or RMSE,
- possibly residual diagnostics.

  1. Summarise

    • per-construct summary table of goodness-of-fit,
    • global histogram/boxplots of fit quality.

Outputs

  • plots/goodness_of_fit/gof_hill_fc_obs_vs_pred.pdf
  • Additional GOF plots for ODE vs data (depending on script options).

How to interpret

  • High R² and low MAE → model is capturing the essential behaviour.
  • Systematic deviations:
    • might reveal missing processes (e.g. extra delays, feedback),
    • or parameter regimes where the simple Hill + first-order decay is insufficient.

This step is a sanity check before we take the design-space scan and design ranking too seriously.