Six genes form a directed regulatory network with weighted edges W_ij (green = activation, red = repression). Each gene's mRNA level E_i relaxes toward a sigmoidal function of the weighted input from every regulator that targets it, while its protein level P_i lags behind translation of that mRNA — the two-layer "central dogma" readout used to validate inferred networks against multi-omics (transcriptomic + proteomic) measurements.
dE_i/dt = s · [ σ(Σ_j W_ij·E_j) − E_i ] + η·N(0,1)
σ(x) = 1 / (1 + e^-x)
dP_i/dt = k_p · (E_i − P_i)
R = corr(E, P) across all 6 genes
- Regulation strength (s): scales how fast mRNA relaxes toward its sigmoid target — higher values snap the network toward its attractor state faster.
- Stochastic noise (η): injects Gaussian jitter per gene per frame, modeling transcriptional bursting and measurement noise.
- Translation rate (k_p): how quickly protein tracks mRNA; low values decouple the omics layers and drop the mRNA-protein correlation R.
- Knock out: forces the selected gene's mRNA and protein to zero and removes its outgoing edges, letting you watch downstream genes lose their driving signal — the core perturbation experiment used to validate a proposed GRN topology.
This mirrors real GRN inference workflows: a candidate network (from ChIP-seq, ATAC-seq or expression correlation) is validated by simulating its dynamics and comparing predicted mRNA/protein trajectories against independent multi-omics measurements after a genetic perturbation.