Tropicalization and tropical equilibration of chemical reactions

TL;DR

This paper explores how tropical analysis can be applied to biochemical reaction networks to simplify their dynamics by identifying dominant terms through tropical equilibration, aiding in model reduction.

Contribution

It introduces a novel application of tropical geometry to analyze and reduce complex biochemical reaction systems with multiple time scales.

Findings

Tropical analysis effectively identifies dominant reaction terms.

Model reduction simplifies complex biochemical networks.

Tropical equilibration provides insights into system dynamics.

Abstract

Systems biology uses large networks of biochemical reactions to model the functioning of biological cells from the molecular to the cellular scale. The dynamics of dissipative reaction networks with many well separated time scales can be described as a sequence of successive equilibrations of different subsets of variables of the system. Polynomial systems with separation are equilibrated when at least two monomials, of opposite signs, have the same order of magnitude and dominate the others. These equilibrations and the corresponding truncated dynamics, obtained by eliminating the dominated terms, find a natural formulation in tropical analysis and can be used for model reduction.