Enzyme sharing as a cause of multistationarity in signaling systems

TL;DR

This paper analytically investigates the conditions under which small, feedback-free signaling motifs exhibit multistationarity, highlighting enzyme sharing as a key factor and providing explicit relationships between species concentrations and system parameters.

Contribution

It derives explicit mathematical conditions for multistationarity in signaling motifs, extending understanding of how enzyme sharing influences cellular decision-making.

Findings

Multistationarity depends on specific concentration relations.

Necessary conditions for stable steady states are identified.

Enzyme sharing is a critical factor in multistationarity.

Abstract

Multistationarity in biological systems is a mechanism of cellular decision making. In particular, signaling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological inputs. The features that lead to multistationarity are of particular interest to determine as well as the stability properties of the steady states. In this paper we determine conditions for the emergence of multistationarity in small motifs without feedback that repeatedly occur in signaling pathways. We derive an explicit mathematical relationship between the concentration of a chemical species at steady state and a conserved quantity of the system such as the total amount of substrate available. We show that the relation determines the number of steady states and provides a necessary condition for a steady state to be stable, that is, to be biologically attainable. Further, we identify characteristics of the motifs that lead to multistationarity, and extend the view that multistationarity in signaling pathways arises from multisite phosphorylation. Our approach relies on mass-action kinetics and the conclusions are drawn in full generality without resorting to simulations or random generation of parameters. The approach is extensible to other systems.