Multistationarity in Structured Reaction Networks.

Bulletin of Mathematical Biology
Alicia DickensteinXiaoxian Tang

Abstract

Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an effective question in real algebraic geometry, it is in general difficult to determine whether a given network can give rise to a multistationary system, and if so, to identify witnesses to multistationarity, that is, specific parameter values for which the system exhibits multiple steady states. Here we investigate both problems. First, we build on work of Conradi, Feliu, Mincheva, and Wiuf, who showed that for certain reaction networks whose steady states admit a positive parametrization, multistationarity is characterized by whether a certain "critical function" changes sign. Here, we allow for more general parametrizations, which make it much easier to determine the existence of a sign change. This is particularly simple when the steady-state equations are linearly equivalent to binomials; we give necessary conditions for this to happen, which hold for many networks studied in the literature. We also give a sufficient condition for multistationarity of networks whose steady-state equations can b...Continue Reading

References

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Jun 5, 2012·Mathematical Biosciences·Guy Shinar, Martin Feinberg
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Sep 11, 2013·Bulletin of Mathematical Biology·Inomzhon Mirzaev, Jeremy Gunawardena
Sep 21, 2013·Bulletin of Mathematical Biology·Katharina HolsteinCarsten Conradi
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Nov 12, 2018·Journal of Mathematical Biology·Magalí GiaroliAlicia Dickenstein
Jan 2, 2019·Bulletin of Mathematical Biology·Matthew D JohnstonCasian Pantea
May 19, 2019·Bulletin of Mathematical Biology·AmirHosein Sadeghimanesh, Elisenda Feliu

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Citations

Jul 28, 2019·Journal of Mathematical Biology·Nida ObatakeAngélica Torres
Jul 25, 2019·Bulletin of Mathematical Biology·Carsten ConradiThomas Kahle
May 19, 2019·Bulletin of Mathematical Biology·AmirHosein Sadeghimanesh, Elisenda Feliu
Mar 12, 2021·Journal of Mathematical Biology·Carsten ConradiXiaoxian Tang
Jul 27, 2020··Alicia Dickenstein, Alicia Dickenstein

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