Fig 10. Motif 1 autocatalytic integral controller.

The controller species E is produced by an enzymatic zero-order process from compound M, but E activates its own production and the transporter-based compensatory flux. The negative feedback is due to the inflow activation of A by E through transporter T, while A activates the (first-order) recycling of E to M. Outflow perturbation in A is described by the rate k₃⋅A, where k₃ is either a constant or increases linearly with time. $k_E^{in}$ and $k_E^{out}$ represent background reactions creating and removing E.