Catalytic constants enable the emergence of bistability in dual phosphorylation
Carsten Conradi, Max Planck Institute for Dynamics of Complex Technical Systems

Dual phosphorylation of proteins is a principal component of intracellular signaling. 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 if 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.

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