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Siphons in Chemical Reaction Networks

Bulletin of Mathematical Biology volume 72, pages 1448–1463 (2010)Cite this article

Abstract

Siphons in a chemical reaction system are subsets of the species that have the potential of being absent in a steady state. We present a characterization of minimal siphons in terms of primary decomposition of binomial ideals, we explore the underlying geometry, and we demonstrate the effective computation of siphons using computer algebra software. This leads to a new method for determining whether given initial concentrations allow for various boundary steady states.

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Affiliations

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

    Anne Shiu & Bernd Sturmfels

Authors
  1. Anne Shiu
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  2. Bernd Sturmfels
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Correspondence to Anne Shiu.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Shiu, A., Sturmfels, B. Siphons in Chemical Reaction Networks. Bull. Math. Biol. 72, 1448–1463 (2010). https://doi.org/10.1007/s11538-010-9502-y

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  • DOI: https://doi.org/10.1007/s11538-010-9502-y

Keywords

  • Chemical reaction systems
  • Siphon
  • Steady state
  • Monomial ideal
  • Binomial ideal
  • Primary decomposition