Fiber decomposition of deterministic reaction networks with applications

TL;DR

This paper introduces a novel fiber decomposition method for deterministic reaction networks, enabling the lifting of networks while preserving key stationary properties, with broad applications in biological modeling.

Contribution

It proposes a new fiber decomposition technique for reaction networks that allows explicit lifting while maintaining important dynamical properties.

Findings

Lifting of mass-action RNs preserves stationarity and multistationarity.

The decomposition is simple, explicit, and broadly applicable.

Examples demonstrate construction of networks with preserved properties.

Abstract

Deterministic reaction networks (RNs) are tools to model diverse biological phenomena characterized by particle systems, when there are abundant number of particles. Examples include but are not limited to biochemistry, molecular biology, genetics, epidemiology, and social sciences. In this chapter we propose a new type of decomposition of RNs, called fiber decomposition. Using this decomposition, we establish lifting of mass-action RNs preserving stationary properties, including multistationarity and absolute concentration robustness. Such lifting scheme is simple and explicit which imposes little restriction on the reaction networks. We provide examples to illustrate how this lifting can be used to construct RNs preserving certain dynamical properties.