Structural Bifurcation Analysis in Chemical Reaction Networks

TL;DR

This paper introduces a new mathematical approach to analyze bifurcation behaviors in chemical reaction networks by decomposing the network into subnetworks based on buffering structures, enabling independent bifurcation analysis.

Contribution

The paper presents a novel method that analyzes bifurcations in reaction networks solely from their structure, without requiring detailed kinetic parameters.

Findings

The method successfully identifies bifurcation parameters in hypothetical networks.

Application to real networks demonstrates practical utility.

The approach simplifies bifurcation analysis in complex biological systems.

Abstract

In living cells, chemical reactions form a complex network. Complicated dynamics arising from such networks are the origins of biological functions. We propose a novel mathematical method to analyze bifurcation behaviors of a reaction system from the network structure alone. The whole network is decomposed into subnetworks based on "buffering structures". For each subnetwork, the bifurcation condition is studied independently, and the parameters that can induce bifurcations and the chemicals that can exhibit bifurcations are determined. We demonstrate our theory using hypothetical and real networks.