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The Smallest Multistationary Mass-Preserving Chemical Reaction Network

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Algebraic Biology (AB 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5147))

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Abstract

Biochemical models that exhibit bistability are of interest to biologists and mathematicians alike. Chemical reaction network theory can provide sufficient conditions for the existence of bistability, and on the other hand can rule out the possibility of multiple steady states. Understanding small networks is important because the existence of multiple steady states in a subnetwork of a biochemical model can sometimes be lifted to establish multistationarity in the larger network. This paper establishes the smallest reversible, mass-preserving network that admits bistability and determines the semi-algebraic set of parameters for which more than one steady state exists.

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Authors and Affiliations

  1. Dept. of Mathematics, University of California, Berkeley, CA 94720-3840, USA

    Anne Shiu

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  1. Anne Shiu
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Editor information

Katsuhisa Horimoto Georg Regensburger Markus Rosenkranz Hiroshi Yoshida

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© 2008 Springer-Verlag Berlin Heidelberg

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Shiu, A. (2008). The Smallest Multistationary Mass-Preserving Chemical Reaction Network. In: Horimoto, K., Regensburger, G., Rosenkranz, M., Yoshida, H. (eds) Algebraic Biology. AB 2008. Lecture Notes in Computer Science, vol 5147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85101-1_13

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  • DOI: https://doi.org/10.1007/978-3-540-85101-1_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85100-4

  • Online ISBN: 978-3-540-85101-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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