Nonnegative linear elimination for chemical reaction networks
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Nonnegative linear elimination for chemical reaction networks. / Sáez, Meritxell; Wiuf, Carsten; Feliu, Elisenda.
In: SIAM Journal on Applied Mathematics, Vol. 79, No. 6, 2019, p. 2434-2455.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Nonnegative linear elimination for chemical reaction networks
AU - Sáez, Meritxell
AU - Wiuf, Carsten
AU - Feliu, Elisenda
PY - 2019
Y1 - 2019
N2 - We consider linear elimination of variables in the steady state equations of a chem- ical reaction network. Particular subsets of variables corresponding to sets of so-called reactant- noninteracting species, are introduced. The steady state equations for the variables in such a set, taken together with potential linear conservation laws in the variables, define a linear system of equa- tions. We give conditions that guarantee that the solution to this system is nonnegative, provided it is unique. The results are framed in terms of spanning forests of a particular multidigraph derived from the reaction network and thereby conditions for uniqueness and nonnegativity of a solution are derived by means of the multidigraph. Though our motivation comes from applications in systems biology, the results have general applicability in applied sciences.
AB - We consider linear elimination of variables in the steady state equations of a chem- ical reaction network. Particular subsets of variables corresponding to sets of so-called reactant- noninteracting species, are introduced. The steady state equations for the variables in such a set, taken together with potential linear conservation laws in the variables, define a linear system of equa- tions. We give conditions that guarantee that the solution to this system is nonnegative, provided it is unique. The results are framed in terms of spanning forests of a particular multidigraph derived from the reaction network and thereby conditions for uniqueness and nonnegativity of a solution are derived by means of the multidigraph. Though our motivation comes from applications in systems biology, the results have general applicability in applied sciences.
KW - Elimination
KW - Linear system
KW - Noninteracting
KW - Positive solution
KW - Spanning forest
UR - http://www.scopus.com/inward/record.url?scp=85076903982&partnerID=8YFLogxK
U2 - 10.1137/18M1197692
DO - 10.1137/18M1197692
M3 - Journal article
AN - SCOPUS:85076903982
VL - 79
SP - 2434
EP - 2455
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
SN - 0036-1399
IS - 6
ER -
ID: 233656511