Step 5 – Model-Driven Design Space Scan

Script:

  • step_4b_model_driven_design_scan.py

Biological question

Given the parameter ranges we observe experimentally, which hypothetical designs would give us the best behaviour (dynamic range, speed, minimal overshoot)?

This step turns measurements into a forward model for exploring what CasTuner designs are even possible.

Inputs

  • parameters/half_times_upregulation.csv
  • parameters/half_times_downregulation.csv
  • parameters/Hill_parameters.csv
  • parameters/alphamcherry.csv
  • parameters/delays_derepression.csv
  • parameters/delays_repression.csv

From these, the script derives realistic ranges for:

  • Hill midpoint K,
  • Hill coefficient n,
  • half-times,
  • α,
  • delays.

Method

  1. Define parameter ranges

For each parameter (e.g. K, n, t₁/₂, α, Δt), extract:

- minimum,
- maximum,
- possibly trimmed quantiles to avoid outliers.
  1. Sample synthetic designs

Options include:

- grid sampling,
- Latin hypercube,
- or a random sample within hyper-rectangular bounds.

Each synthetic design = one parameter combination:

$$ \theta = (K, n, \alpha, t_{1/2,\uparrow}, t_{1/2,\downarrow}, \Delta t_\text{rev}, \Delta t_\text{kd}) $$

  1. Simulate trajectories

For each \(\theta\):

- simulate ODE during a repression protocol (or derepression, depending on design),
- record `Y(t)` over a fixed window.
  1. Compute performance metrics

From each trajectory, extract:

- dynamic range (max/min steady-state),
- time to 50% change (**t₅₀**),
- rise/decay times (e.g. t₁₀–₉₀),
- overshoot or undershoot,
- residual steady-state error.

These are combined into one or multiple scores.

  1. Score & rank

    • assign composite scores (e.g. “high dynamic range + low t₅₀”),
    • keep all designs but mark top performers.

Outputs

  • parameters/design_space_scan_repression.csv containing:
    • sampled parameter sets,
    • derived performance metrics,
    • ranking scores.

These results feed directly into Step 7 (design selection & map).

How to interpret

This is where you can ask “what if” questions:

  • What parameter regimes give fast yet gentle repression?
  • Is there a trade-off between dynamic range and noise or speed?
  • Are our current constructs anywhere near the optimal region?

Because the scan is based on experimentally grounded ranges, it remains biologically realistic while still exploring combinations that may not yet exist in the current plasmid library.