Qualitative dynamics of chemical reaction networks: an investigation using partial tropical equilibrations

TL;DR

This paper introduces a method using partial tropical equilibration solutions to analyze the qualitative dynamics of chemical reaction networks, enabling symbolic representation and model reduction, demonstrated on a cell cycle model.

Contribution

It presents an algorithmic approach to find partial tropical equilibrations that serve as proxies for symbolic states in mass-action networks with timescale separation.

Findings

Successfully applied to a biochemical cell cycle model

Provides a scalable way to perform model reduction

Enables symbolic dynamics representation of complex networks

Abstract

We discuss a method to describe the qualitative dynamics of chemical reaction networks in terms of symbolic dynamics. The method, that can be applied to mass-action reaction networks with separated timescales, uses solutions of the partial tropical equilibration problem as proxies for symbolic states. The partial tropical equilibration solutions are found algorithmically. These solutions also provide the scaling needed for slow-fast decomposition and model reduction. Any trace of the model can thus be represented as a sequence of local approximations of the full model. We illustrate the method using as case study a biochemical model of the cell cycle.