Catalytic constants enable the emergence of bistability in dual phosphorylation

Abstract

Dual phosphorylation of proteins is a principal component of intracellular signalling. Bistability is considered an important property of such systems and its origin is not yet completely understood. Theoretical studies have established parameter values for multistationarity and bistability for many types of proteins. However, up to now no formal criterion linking multistationarity and bistability to the parameter values characterizing dual phosphorylation has been established. Deciding whether an unclassified protein has the capacity for bistability, therefore requires careful numerical studies. Here, we present two general algebraic conditions in the form of inequalities. The first employs the catalytic constants, and if satisfied guarantees multistationarity (and hence the potential for bistability). The second involves the catalytic and Michaelis constants, and if satisfied guarantees uniqueness of steady states (and hence absence of bistability). Our method also allows for the direct computation of the total concentration values such that multistationarity occurs. Applying our results yields insights into the emergence of bistability in the ERK-MEK-MKP system that previously required a delicate numerical effort. Our algebraic conditions present a practical way to determine the capacity for bistability and hence will be a useful tool for examining the origin of bistability in many models containing dual phosphorylation.

Kinase Inhibition Leads to Hormesis in a Dual Phosphorylation-Dephosphorylation Cycle

“…In the absence of an inhibitor, the double phosphorylation motif Eq (1) can possess either a single or two stable steady states of the doubly-phosphorylated form of the substrate C PP , [50, 54, 58, 59]. Therefore in our study we consider two cases: first, when the motif Eq (1) is monostable and second, when this motif is bi-stable.…”

Mixed mechanisms of multi-site phosphorylation

“…Note that all potential binding/unbinding constants are fixed at the same nominal value, and, by analogous distributive mechanism, we mean the distributive mechanism with these binding/unbinding constants and the same sets of catalytic constants. A choice of sufficiently different catalytic constants in phosphorylation can result in bistability in a purely distributive model, as shown in figure 3a (also see [39]). By contrast, the two mixed models exhibit monostable behaviour.…”

Homo-Oligomerisation in Signal Transduction: Dynamics, Homeostasis, Ultrasensitivity, Bistability

“…An interesting and unique twist of this motif is that the bistability resulting from modication of the oligomer extends to the monomer due to intrinsic substrate competition and because both species are in equilibrium with each other. We also demonstrated that kinetic cooperativity of multisite modication systems is not a requirement for bistability if there are multiple enzymes regulating the modication steps and if some can only catalyse a subset of the individual modication steps, resulting eectively in the same kinetic asymmetry[22,23] as kinetic cooperativity. While oligomers might be particularly suited for this mechanism due their symmetrical structure, bistability through multi-enzyme regulation could in principle arise in any mul-tisite PTM system.…”