Network Motifs & Feedforward Loops

Gene regulatory network dynamics and sign-sensitive delay

Circuit Type

Feedforward Loop Motifs

The feedforward loop (FFL) is the most statistically over-represented 3-node motif in biological networks (Milo et al., 2002). It consists of regulator X controlling Y, and both X and Y controlling output Z.

Ẏ = α·f(X) − βY    Ż = α·g(X,Y) − βZ

C1-FFL (coherent): X activates Y and Z; Y activates Z. Acts as a sign-sensitive delay — responds to sustained "ON" signals but filters brief pulses. Provides persistence detection.

I1-FFL (incoherent): X activates Z but Y (which X activates) represses Z. Produces a pulse of Z output — pulse generator and fold-change detector.

The colored nodes show live activation levels. The time-series below tracks X (input, purple), Y (intermediate, orange), and Z (output, green).

Signal detected: OFF  |  Z output: 0.00