Linear elimination in chemical reaction networks

Publikation: Bidrag til bog/antologi/rapportBidrag til bog/antologiForskningfagfællebedømt

Meritxell Sáez, Elisenda Feliu, Carsten Wiuf

We consider dynamical systems arising in biochemistry and systems biology that model the evolution of the concentrations of biochemical species described by chemical reactions. These systems are typically confined to an invariant linear subspace of ℝn. The steady states of the system are solutions to a system of polynomial equations for which only non-negative solutions are of interest. Here we study the set of non-negative solutions and provide a method for simplification of this polynomial system by means of linear elimination of variables. We take a graphical approach. The interactions among the species are represented by an edge labelled graph. Subgraphs with only certain labels correspond to sets of species concentrations that can be eliminated from the steady state equations using linear algebra. To assess positivity of the eliminated variables in terms of the non-eliminated variables, a multigraph is introduced that encodes the connections between the eliminated species in the reactions. We give graphical conditions on the multigraph that ensure the eliminated variables are expressed as positive functions of the non-eliminated variables. We interpret these conditions in terms of the reaction network. The results are illustrated by examples.

TitelRecent Advances in Differential Equations and Applications
RedaktørerJuan Luis García Guirao, José Alberto Murillo Hernández, Francisco Periago Esparza
Antal sider17
StatusUdgivet - 2019
Begivenhed25th Congress on Differential Equations and Applications / 15th Congress on Applied Mathematics - Cartagena, Spanien
Varighed: 26 jun. 201730 jun. 2017


Konference25th Congress on Differential Equations and Applications / 15th Congress on Applied Mathematics
NavnSEMA SIMAI Springer Series

ID: 212679414