Incoherent Feed-Forward Loop: Genetic Pulse Generator

An incoherent type-1 feed-forward loop is a three-gene wiring pattern found throughout bacterial regulatory networks and rebuilt from scratch as one of synthetic biology's foundational circuits. An inducer X switches on both a slow repressor Y and a fast reporter Z, and because Y eventually catches up and shuts Z back off, the circuit turns a sustained step input into a single transient pulse — a behavior that plain activation or repression alone cannot produce. This simulator renders each gene's protein population as an animated 3D swarm whose size tracks the live Hill-kinetics ODEs, alongside a real-time X/Y/Z trace, so you can step the inducer on and off and watch the pulse-generation and fold-change-detection properties emerge from the equations themselves.