Incoherent Feed-Forward Loop: Genetic Pulse Generator (2D)

The 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 repressor Y and a reporter Z directly, and because Y accumulates and then represses Z, a circuit driven by a constant, sustained input still produces only a single transient pulse in Z. This 2D companion to the 3D swarm version renders the same coupled Hill-kinetics ODEs as a labeled gene-circuit diagram — X, Y and Z nodes joined by activation and repression arrows, node size and a live line trace both driven directly by the numerically integrated state — so you can step the inducer, retune production, decay and repression-threshold parameters, and watch pulse generation and fold-change detection emerge from the equations themselves.