Conference abstracts

Session A2 - Computational Algebraic Geometry

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Elimination in steady state equations of chemical reaction networks

Meritxell Sáez Cornellana

University of Copenhagen, Denmark   -   meritxell@math.ku.dk

The steady states of a chemical reaction network with mass-action kinetics are solutions to a system of polynomial equations. Even for small systems, finding the steady states of the system is a very demanding task and therefore methods that reduce the number of variables are desirable. In [FW] the authors give one such method, in which so-called non-interacting species are eliminated from the system of steady state equations.

We extend this method for the elimination of what we call reactant non-interacting species and give some conditions that ensure the positivity of the elimination obtained, that is, for positive values of the reaction rate constants and the non-eliminated species, we ensure that the eliminated species are positive as well. In particular, if enough species can be eliminated, then this method provides a parametrisation of the positive part of the steady state variety. Such a parametrisation can be used, for instance, to study the number of steady states in each linear invariant subspace defined by the conservation laws [CFMW].

[FW] Feliu, Wiuf: Variable elimination in chemical reaction networks with mass-action kinetics. SIAM J. APPL. MATH.

[CFMW] Conradi, Feliu, Mincheva, Wiuf. Identifying parameter regions for multistationarity. (2016) arXiv:1608.03993.

Joint work with Elisenda Feliu (University of Copenhagen, Denmark) and Carsten Wiuf (University of Copenhagen, Denmark).

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