Feedforward Loop Network Motif

The C1-FFL motif (Mangan & Alon 2003): X activates both Y and Z; Y also activates Z; Z requires AND logic on both X and Y. The result is a sign-sensitive delay: Z turns ON only after X has been active long enough for Y to accumulate past threshold θ_Y — this filters short spurious input pulses (noise). But Z turns OFF immediately when X turns off (because X drives Z directly and Y's accumulated level is irrelevant). Compare with simple X→Z: Z tracks X with no delay and no filtering. The C1-FFL is enriched ~10× over random in E. coli and yeast gene networks, suggesting it is selected for its filtering and delay properties.