Ultrasensitive molecular controllers for quasi-integral feedback

Abstract

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.

Noise Propagation in Chemical Reaction Networks: Analysis of a Molecular Subtractor Module

“…The first limit in (25) is trivially coherent with the hypothesis that, without the input u 2 , there is no accumulation of B. On the other hand, the second limit tells us that b definitely diverges to +∞ with u 2 according to a linear fashion.…”

“…This approach enables the development of a general method for the design of closedloop feedback control schemes in synthetic biology (like, e.g. the ones recently presented in [5], [15], [27], [23], [6], [25], [28]) by means of the most suitable selection and proper interconnection of distinct building blocks (similarly to classical control scheme design), each provided by the chosen CRN.…”

CoRa –A general approach for quantifying biological feedback control

“…Any feedback control system can be analyzed using CoRa, providing a unifying framework under which different feedback mechanisms can be rigorously compared. In fact, we were able to rapidly analyze a large number of distinct feedback control motifs proposed in the literature [2,4,6,7,11,13,15] (Fig. 3; Supplementary Information).…”

“…This behavior relates to the inevitable saturation of the repression function (see Supplementary Information for an example of an analytical treatment of this limit). A notable exception to this limit occurred for the "brink motif" feedback strategy, a motif that combines antithetic molecular sequestration with an activation-deactivation enzymatic cycle to produce a tuneable ultra-sensitive response [13] (Fig. 3K).…”

“…S5A-C). Furthermore, increasing the ultrasensitivity of the brink motif itself by increasing the deactivation rate in its enzymatic cycle [13] improved its ability to adapt (Fig. S5D).…”