Step 1 – Kinetic Fits (Upregulation & Downregulation)

Script(s):

  • step_1a_fit_upregulation.py
  • step_1b_fit_downregulation.py
  • step_1c_fit_hill_curves.py (dose–response part is covered in the next page)

Biological question

How fast do degron-controlled Cas repressors turn ON and OFF in response to dTAG changes?

This is captured by:

  • upregulation half-time t₁/₂↑: how quickly tBFP (repressor) rises after removing dTAG,
  • downregulation half-time t₁/₂↓: how quickly tBFP decays after adding dTAG.

These half-times set the timescale for gene repression/derepression.

Inputs

  • Gated FCS data for:
    • upregulation time courses (dTAG withdrawal),
    • downregulation time courses (dTAG addition),
  • NFC samples for background subtraction (from config.yaml),
  • Experimental metadata (mapping file names to constructs/time points).

Method

  1. Gating and preprocessing

    • boundary gate (FSC/SSC),
    • singlet gate (FSC-H/FSC-A),
    • remove NFC background,
    • compute median tBFP per (construct, experiment, time).

  2. Normalisation

    • for each construct, rescale BFP into [0, 1]:
      • 0 → lowest observed level (fully degraded),
      • 1 → plateau level (steady state).

  3. Exponential kinetic fits

    • For upregulation (t₁/₂↑):
      • fit an exponential rise function: [ BFP(t) = 1 - \exp(-k_{\text{up}} t) ]
    • For downregulation (t₁/₂↓): [ BFP(t) = \exp(-k_{\text{down}} t) ]
    • Convert rate constants to half-times: [ t_{1/2} = \frac{\ln 2}{k} ]

  4. Quality checks

    • keep only constructs with enough time points and good fit quality,
    • plot fits overlaid with data for visual inspection.

Outputs

  • parameters/half_times_upregulation.csv
  • parameters/half_times_downregulation.csv
  • Diagnostic plots for each construct in plots/kinetics/ (mirrored into the final report).

Each row includes:

  • construct ID,
  • experiment/replicate,
  • estimated t₁/₂↑ or t₁/₂↓,
  • fit error metrics.

How to interpret

  • Small t₁/₂↑ → repressor accumulates quickly after dTAG removal.
  • Small t₁/₂↓ → repressor is removed quickly after dTAG re-addition.
  • Comparing constructs tells you:
    • which design gives fast control,
    • whether different systems (hHDAC4–dCas9, CasRx, KRAB) differ primarily at the degron level or in downstream chromatin/RNA processing.

These half-times are later used as fixed or initial parameters in the ODE model.