Empirically Exploring the Space of Monostationarity in Dual Phosphorylation

TL;DR

This paper investigates the conditions under which dual phosphorylation networks exhibit monostationarity versus multistationarity, extending previous polynomial decomposition methods to better classify parameter regions.

Contribution

It introduces a systematic approach to classify polynomial decompositions, enhancing understanding of monostationarity conditions in phosphorylation networks.

Findings

Improved conditions for monostationarity regions.

Systematic classification of polynomial decompositions.

Empirical validation of theoretical results.

Abstract

The dual phosphorylation network provides an essential component of intracellular signaling, affecting the expression of phenotypes and cell metabolism. For particular choices of kinetic parameters, this system exhibits multistationarity, a property that is relevant in the decision-making of cells. Determining which reaction rate constants correspond to monostationarity and which produce multistationarity is an open problem. The system's monostationarity is linked to the nonnegativity of a specific polynomial. A previous study by Feliu et al. provides a sufficient condition for monostationarity via a decomposition of this polynomial into nonnegative circuit polynomials. However, this decomposition is not unique. We extend their work by a systematic approach to classifying such decompositions in the dual phosphorylation network. Using this result classification, we provide a qualitative comparison of the decompositions into nonnegative circuit polynomials via empirical experiments and improve on previous conditions for the region of monostationarity.