Systems biology treats a cell's behaviour as an emergent property of a gene regulatory network, not any single gene. Small recurring wiring patterns — network motifs — perform specific computations: a negative-feedback loop oscillates, a mutual-repression toggle switch is bistable, and a coherent feed-forward loop filters noisy pulses. The 3-node core circuit here drives a downstream protein-interaction network through its most connected node — the hub.
Repressor ODE (Hill kinetics):
dXi/dt = β · Kⁿ / (Kⁿ + Xj(t)ⁿ) − Xi
Network diffusion from hub h:
Xᵢ(t+dt) → lerp(Xᵢ, mean(X_neighbours)·coupling, rate)
- Circuit motif — feedback (repressilator, 3-gene oscillator), toggle (2-gene bistable switch) or feed-forward loop (delay/noise filter).
- Hill coefficient — cooperativity of repression/activation; higher n gives sharper, more switch-like responses.
- Network coupling — how strongly the hub's signal propagates outward through the interaction network each step.
- Hub protein knockout — silences the network's single most-connected node, the way a disease-causing mutation or drug can disable a hub; watch downstream activity collapse even though most nodes are untouched — a real signature of network fragility to hub attack versus robustness to random node loss.
Real-world relevance: cancer signalling models use exactly this logic — Boolean/ODE gene networks with hub nodes (e.g. p53, EGFR) whose loss reshapes the whole system's attractor landscape, guiding which combination therapies can compensate.