Deformed Toric Ideal Constraints for Stoichiometric Networks

TL;DR

This paper introduces deformed toric ideal constraints derived from algebraic geometry to automatically constrain fluxes and concentrations in chemical reaction networks and metabolic pathways, improving modeling accuracy.

Contribution

It presents a novel algebraic geometric approach using deformed toric ideals to impose constraints on steady state fluxes without ad hoc assumptions.

Findings

Deformed toric ideal constraints fully constrain fluxes and concentrations in a chemical reaction network.

Partially constrain linear combination parameters of flux in a metabolic pathway.

Additional constraints like constant enzyme amount can fully determine fluxes and concentrations.

Abstract

We discuss chemical reaction networks and metabolic pathways based on stoichiometric network analysis, and introduce deformed toric ideal constraints by the algebraic geometrical approach. This paper concerns steady state flux of chemical reaction networks and metabolic pathways. With the deformed toric ideal constraints, the linear combination parameters of extreme pathways are automatically constrained without introducing ad hoc constraints. To illustrate the effectiveness of such constraints, we discuss two examples of chemical reaction network and metabolic pathway; in the former the flux and the concentrations are constrained completely by deformed toric ideal constraints, and in the latter, it is shown the deformed toric ideal constrains the linear combination parameters of flux at least partially. Even in the latter case, the flux and the concentrations are constrained completely with the additional constraint that the total amount of enzyme is constant.