Symbolic proof of bistability in reaction networks

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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
Original languageDanish
JournalS I A M Journal on Applied Dynamical Systems
Volume20
Issue number1
Pages (from-to)1-37
ISSN1536-0040
DOIs
Publication statusPublished - 5 Jan 2021

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