An All-Encompassing Global Convergence Result for Processive Multisite Phosphorylation Systems

TL;DR

This paper extends the global convergence results for processive multisite phosphorylation systems to more general reaction schemes, including irreversible reactions and product inhibition, using monotone systems theory and network reductions.

Contribution

It generalizes previous convergence results to encompass a broader class of phosphorylation networks with irreversible reactions and product inhibition.

Findings

Global convergence holds for a wider class of processive phosphorylation networks.

Monotone systems theory and network reduction techniques are effective for analyzing complex biochemical networks.

The results provide insights into how adding or removing reactions affects system stability.

Abstract

Phosphorylation, the enzyme-mediated addition of a phosphate group to a molecule, is a ubiquitous chemical mechanism in biology. Multisite phosphorylation, the addition of phosphate groups to multiple sites of a single molecule, may be distributive or processive. Distributive systems can be bistable, while processive systems were recently shown to be globally stable. However, this global convergence result was proven only for a specific mechanism of processive phosphorylation/dephosphorylation (namely, all catalytic reactions are reversible). Accordingly, we generalize this result to allow for processive phosphorylation networks in which each reaction may be irreversible, and also to account for possible product inhibition. We accomplish this by defining an all-encompassing processive network that encapsulates all of these schemes, and then appealing to recent results of Marcondes de Freitas, Wiuf, and Feliu that assert global convergence by way of monontone systems theory and network/graph reductions (which correspond to removal of intermediate complexes). Our results form a case study into the question of when global convergence is preserved when reactions and/or intermediate complexes are added to or removed from a network.