Applied Mathematics Seminar | Peter Ruoff, Reaction kinetics leading to integral control and robust homeostasis

Homeostatic and adaptive control mechanisms are essential for keeping organisms structurally and functionally stable. Integral control is a control engineering concept, which has long been known to keep a variable A robustly at a given set-point by feeding the integrated error back into the process where A is generated. However, how robust homeostasis and integral control is realized in biochemical systems is still not fully understood. We have recently identified two reaction kinetic conditions that permit to build integral control into chemical negative feedback structures and which allow to generate biochemical models of robust homeostatic controllers. In their simplest form such ”homeostats” consist of two compounds: the homeostatic controlled variable A and a controller molecule E, where the concentration of E is related to the integrated error between the concentration of A and its set-point. We show how combinations of basic controller motifs lead to homeostasis where uptake, storage, assimilation/transport and remobilization of a controlled compound are combined in an integrated manner. We further show how oscillatory homeostats can maintain stability in A by keeping the average concentration of A at the controller’s set-point due to a change in the oscillator’s frequency. Because in oscillatory homeostats the average level of the manipulated variable E is associated with the frequency of the compensatory flux, we show how robust frequency control may be achieved by controlling the average level of E. The occurrence of such behaviors in oscillatory signaling and in biological clock rhythms is discussed.