Piecewise linear models of chemical reaction networks

TL;DR

This paper demonstrates that complex nonlinear chemical reaction networks with Hill functions can be approximated by simpler piecewise linear models, enabling easier analysis of their behavior.

Contribution

The authors introduce a method to approximate nonlinear reaction networks with piecewise linear systems, justified by geometric singular perturbation theory, and illustrate it with genetic network examples.

Findings

Piecewise linear models closely approximate nonlinear systems.

Closed-form solutions facilitate understanding of system dynamics.

Applicable to genetic switches and oscillators.

Abstract

We show that certain non-linear dynamical systems with non-linearities in the form of Hill functions, can be approximated by piecewise linear dynamical systems. The resulting piecewise systems have closed form solutions that can be used to understand the behavior of the fully nonlinear system. We justify the reduction using geometric singular perturbation theory, and illustrate the results in networks modeling a genetic switch and a genetic oscillator.