Step 4 – Single-Cell Noise & Hierarchical Analysis

Script:

  • step_4a_single_cell_hierarchical_noise.py

Biological question

How noisy is analog tuning at the single-cell level, and how is this noise structured across time and constructs?

Analog tuning is only useful if intermediate levels are stable and homogeneous across cells. This step quantifies noise in:

  • repressor levels (BFP),
  • target levels (mCherry/EGFP).

Inputs

  • Time-course .fcs files,
  • NFC controls,
  • Paths from config.yaml,
  • Previously defined gating strategy (reused).

Method

  1. Per-cell data extraction

    • apply FSC/SSC and singlet gates,
    • subtract NFC background,
    • keep BFP and mCherry/EGFP for each cell.

  2. Aggregate per condition For each (construct, experiment, replicate, time):

    • compute:
      • mean,
      • variance,
      • coefficient of variation squared CV²: $$ \text{CV}^2 = \frac{\sigma^2}{\mu^2} $$

  3. Hierarchical summary

    • treat per-replicate CV² estimates as observations,
    • fit a simple hierarchical (normal–normal) model:
      • each construct has a latent “true” CV²,
      • replicates scatter around that with measurement noise.
    • summarise:
      • construct-level mean CV²,
      • uncertainty (e.g. SE, CI).

  4. Export

    • single_cell_noise_timeseries.csv – raw time-series noise metrics,
    • single_cell_noise_hierarchical.csv – hierarchical summaries.

Outputs

  • Time-resolved noise trajectories,
  • Per-construct noise summaries,
  • Plots of noise vs mean BFP/mCherry.

How to interpret

  • Lower CV² at intermediate expression levels → clean analog tuning.
  • Elevated CV²:
    • may indicate intrinsic stochasticity,
    • or subpopulations and hidden bistability.

In combination with Hill parameters and ODE fits, noise analysis helps answer:

  • whether analog tuning is achieved without sacrificing stability,
  • whether certain parameter regimes (fast vs slow, steep vs shallow) correlate with higher noise.