Linear elimination in chemical reaction networks
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Linear elimination in chemical reaction networks. / Sáez, Meritxell; Feliu, Elisenda; Wiuf, Carsten.
Recent Advances in Differential Equations and Applications. ed. / Juan Luis García Guirao; José Alberto Murillo Hernández; Francisco Periago Esparza. Springer, 2019. p. 177-193 (SEMA SIMAI Springer Series, Vol. 18).Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review
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TY - CHAP
T1 - Linear elimination in chemical reaction networks
AU - Sáez, Meritxell
AU - Feliu, Elisenda
AU - Wiuf, Carsten
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Conservation law
KW - Elimination
KW - Linear system
KW - Noninteracting
KW - Reaction network
KW - Steady states
UR - http://www.scopus.com/inward/record.url?scp=85060280858&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-00341-8_11
DO - 10.1007/978-3-030-00341-8_11
M3 - Book chapter
AN - SCOPUS:85060280858
T3 - SEMA SIMAI Springer Series
SP - 177
EP - 193
BT - Recent Advances in Differential Equations and Applications
A2 - Guirao, Juan Luis García
A2 - Hernández, José Alberto Murillo
A2 - Esparza, Francisco Periago
PB - Springer
T2 - 25th Congress on Differential Equations and Applications / 15th Congress on Applied Mathematics
Y2 - 26 June 2017 through 30 June 2017
ER -
ID: 212679414