The Goldbeter-Koshland switch in the first-order region and its response to dynamic disorder

TL;DR

This paper extends the understanding of the Goldbeter-Koshland switch by demonstrating its occurrence under comparable signal and substrate concentrations with cooperative catalysis, and analyzes its robustness to dynamic disorder.

Contribution

It shows that the biochemical switch can operate outside the zero-order region with cooperative catalysis and studies its robustness to stochastic enzymatic rate fluctuations.

Findings

Switch behavior occurs at comparable signal and substrate concentrations with cooperative catalysis.

System is robust to dynamic disorder at bulk concentration.

Large fluctuations occur under quasi-static disorder at low concentrations.

Abstract

In their classical work (Proc. Natl. Acad. Sci. USA, 1981, 78:6840-6844), Goldbeter and Koshland mathematically analyzed a reversible covalent modification system which is highly sensitive to the concentration of effectors. Its signal-response curve appears sigmoidal, constituting a biochemical switch. However, the switch behavior only emerges in the "zero-order region", i.e. when the signal molecule concentration is much lower than that of the substrate it modifies. In this work we showed that the switching behavior can also occur under comparable concentrations of signals and substrates, provided that the signal molecules catalyze the modification reaction in cooperation. We also studied the effect of dynamic disorders on the proposed biochemical switch, in which the enzymatic reaction rates, instead of constant, appear as stochastic functions of time. We showed that the system is robust to dynamic disorder at bulk concentration. But if the dynamic disorder is quasi-static, large fluctuations of the switch response behavior may be observed at low concentrations. Such fluctuation is relevant to many biological functions. It can be reduced by either increasing the conformation interconversion rate of the protein, or correlating the enzymatic reaction rates in the network.