Model reduction of biochemical reactions networks by tropical analysis methods

TL;DR

This paper introduces a tropical analysis-based method for approximate model reduction of biochemical reaction networks, effectively simplifying complex systems with polynomial or rational rates by solving max-plus algebra equations.

Contribution

It presents a novel tropical equilibration approach for reducing biochemical networks, including those with nonlinear fast cycles, applicable to computational systems biology.

Findings

Method effectively reduces complex biochemical networks.

Applicable to networks with polynomial or rational reaction rates.

Handles nonlinear fast cycles through iterative tropical equilibration.

Abstract

We discuss a method of approximate model reduction for networks of biochemical reactions. This method can be applied to networks with polynomial or rational reaction rates and whose parameters are given by their orders of magnitude. In order to obtain reduced models we solve the problem of tropical equilibration that is a system of equations in max-plus algebra. In the case of networks with nonlinear fast cycles we have to solve the problem of tropical equilibration at least twice, once for the initial system and a second time for an extended system obtained by adding to the initial system the differential equations satisfied by the conservation laws of the fast subsystem. The two steps can be reiterated until the fast subsystem has no conservation laws different from the ones of the full model. Our method can be used for formal model reduction in computational systems biology.