Siphons in chemical reaction networks

TL;DR

This paper characterizes minimal siphons in chemical reaction networks using algebraic geometry and demonstrates how to compute them effectively, aiding in understanding steady states and boundary conditions.

Contribution

It introduces a novel algebraic approach to identify minimal siphons via primary decomposition of binomial ideals, linking geometry and computation.

Findings

Effective computation of siphons using computer algebra software

New method to determine boundary steady states from initial conditions

Characterization of minimal siphons through algebraic geometry

Abstract

Siphons in a chemical reaction system are subsets of the species that have the potential of being absent in a steady state. We present a characterization of minimal siphons in terms of primary decomposition of binomial ideals, we explore the underlying geometry, and we demonstrate the effective computation of siphons using computer algebra software. This leads to a new method for determining whether given initial concentrations allow for various boundary steady states.