A hidden ground-truth gene regulatory network (10 genes, directed activating/repressing edges) drives a Hill-function ODE system. Each gene's rate of change depends on its regulators:
dXi/dt = Σj wij · Xj^n/(K^n+Xj^n) − γ·Xi (repressors flip the Hill term)
You never see this network directly — only noisy expression snapshots sampled from the simulated time series, exactly as an RNA-seq experiment would produce. Three inference strategies reconstruct edges from that data:
- Correlation — Pearson correlation between every gene pair, thresholded. Fast, but a shared regulator or hidden confounder makes two unrelated genes co-vary, producing spurious ("false positive") edges — the classic confounding problem.
- Partial correlation — correlation between gene i and j after regressing out every other gene's effect (a linear stand-in for multivariate regression / Granger-style causal inference). Removes most indirect edges that pure correlation keeps.
- Perturbation (CRISPR-style) — the ground truth for validation: each gene is knocked out in turn and the resulting expression shift in every other gene is measured directly, exactly like a pooled CRISPR screen or TF-binding assay. This is slower (needs one experiment per gene) but is the only method immune to confounding, because it tests causality directly rather than inferring it from covariation.
Edges are colored by outcome against the hidden ground truth: green = correctly recovered, red = false positive (inferred but not real — often a confounder artifact), gray, dashed = false negative (real edge the method missed). Precision = TP/(TP+FP), Recall = TP/(TP+FN). Raise noise or shorten the time series to see accuracy degrade; toggle the confounder off to see correlation's false-positive rate collapse.