Symbolic proof of bistability in reaction networks
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Symbolic proof of bistability in reaction networks. / Torres Bustos, Angelica Marcela; Feliu, Elisenda.
In: S I A M Journal on Applied Dynamical Systems, Vol. 20, No. 1, 05.01.2021, p. 1-37.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Symbolic proof of bistability in reaction networks
AU - Torres Bustos, Angelica Marcela
AU - Feliu, Elisenda
PY - 2021/1/5
Y1 - 2021/1/5
N2 - Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is, has at least two asymptotically stable steady states for some choice of parameters, is a hard problem. For systems modeling biochemical reaction networks, we introduce a procedure to determine, exclusively via symbolic computations, the stability of the steady states for unspecified parameter values. In particular, our approach fully determines the stability type of all steady states of a broad class of networks. To this end, we combine the Hurwitz criterion, reduction of the steady state equations to one univariate equation, and structural reductions of the reaction network. Using our method, we prove that bistability occurs in open regions in parameter space for many relevant motifs in cell signaling.Read More: https://epubs.siam.org/doi/10.1137/20M1326672
AB - Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is, has at least two asymptotically stable steady states for some choice of parameters, is a hard problem. For systems modeling biochemical reaction networks, we introduce a procedure to determine, exclusively via symbolic computations, the stability of the steady states for unspecified parameter values. In particular, our approach fully determines the stability type of all steady states of a broad class of networks. To this end, we combine the Hurwitz criterion, reduction of the steady state equations to one univariate equation, and structural reductions of the reaction network. Using our method, we prove that bistability occurs in open regions in parameter space for many relevant motifs in cell signaling.Read More: https://epubs.siam.org/doi/10.1137/20M1326672
U2 - 10.1137/20M1326672
DO - 10.1137/20M1326672
M3 - Tidsskriftartikel
VL - 20
SP - 1
EP - 37
JO - SIAM Journal on Applied Dynamical Systems
JF - SIAM Journal on Applied Dynamical Systems
SN - 1536-0040
IS - 1
ER -
ID: 256319347