Ultrasensitive molecular controllers for quasi-integral feedback

Feedback control has enabled the success of automated technologies by mitigating the effects of variability, unknown disturbances, and noise. Similarly, feedback loops in biology reduce the impact of noise and help shape kinetic responses, but it is still unclear how to rationally design molecular controllers that approach the performance of controllers in traditional engineering applications, in particular the performance of integral controllers. Here, we describe a strategy to build molecular quasi-integral controllers by following two design principles: (1) a highly ultrasensitive response, which guarantees a small steady-state error, and (2) a tunable ultrasensitivity threshold, which determines the system equilibrium point (reference). We describe a molecular reaction network, which we name Brink motif, that satisfies these requirements by combining sequestration and an activation/deactivation cycle. We show that if ultrasensitivity conditions are satisfied, this motif operates as a quasi-integral controller and promotes homeostatic behavior of the closed-loop system (robust tracking of the input reference while rejecting disturbances). We propose potential biological implementations of Brink controllers and we illustrate different example applications with computational models.