A geometric method for model reduction of biochemical networks with polynomial rate functions

TL;DR

This paper introduces a geometric, symbolic method based on Newton polytopes and tropical equilibration to identify slow variables in biochemical networks with polynomial rate functions, facilitating model reduction.

Contribution

It presents a novel geometric and symbolic approach for model reduction, contrasting with existing numerical algorithms, and demonstrates its effectiveness on various biochemical network models.

Findings

Supports small minimal models despite many molecular actors

Method effectively identifies slow variables in biochemical networks

Applicable to large collections of biochemical models

Abstract

Model reduction of biochemical networks relies on the knowledge of slow and fast variables. We provide a geometric method, based on the Newton polytope, to identify slow variables of a biochemical network with polynomial rate functions. The gist of the method is the notion of tropical equilibration that provides approximate descriptions of slow invariant manifolds. Compared to extant numerical algorithms such as the intrinsic low dimensional manifold method, our approach is symbolic and utilizes orders of magnitude instead of precise values of the model parameters. Application of this method to a large collection of biochemical network models supports the idea that the number of dynamical variables in minimal models of cell physiology can be small, in spite of the large number of molecular regulatory actors.