The multistationarity structure of networks with intermediates and a binomial core network

Abstract

This work addresses whether a reaction network, taken with mass-action kinetics, is multistationary, that is, admits more than one positive steady state in some stoichiometric compatibility class. We build on previous work on the effect that removing or adding intermediates has on multistationarity, and also on methods to detect multistationarity for networks with a binomial steady state ideal. In particular, we provide a new determinant criterion to decide whether a network is multistationary, which applies when the network obtained by removing intermediates has a binomial steady state ideal. We apply this method to easily characterize which subsets of complexes are responsible for multistationarity; this is what we call the \emph{multistationarity structure} of the network. We use our approach to compute the multistationarity structure of the $n$-site sequential distributive phosphorylation cycle for arbitrary n.

arXiv commentFinal version

References in corpus (3)

• Simplifying Biochemical Models With Intermediate Species
• A Case Study on the Parametric Occurrence of Multiple Steady States
• Improving the use of equational constraints in cylindrical algebraic decomposition

Cited by in corpus (5)

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• Polynomial Superlevel Set Representation of the Multistationarity Region of Chemical Reaction Networks
• A Linear Algebra Approach for Detecting Binomiality of Steady State Ideals of Reversible Chemical Reaction Networks
• Understanding Multistationarity of Fully Open Reaction Networks
• Testing Binomiality of Chemical Reaction Networks Using Comprehensive Gröbner Systems