Coherent feed-forward loop

The direct path and the indirect path of a coherent feed-forward loop have matching overall signs. The all-activating case with an AND rule can delay activation while allowing rapid removal of the production signal when the direct input disappears.

The all-activating feed-forward loop combines direct activation of an output with indirect activation through an intermediate. Under AND logic the intermediate's accumulation delays production and can reject brief inputs. Removal of direct activation stops production immediately, while the output concentration still has its own decay time.

A persistence detector responds strongly to a sustained input and weakly to short isolated inputs. In an activating coherent feed-forward loop, an intermediate protein accumulates toward a threshold while the target also requires the direct input. Eliminating that intermediate by an instantaneous quasi-steady-state approximation removes its accumulation delay.