Siphons in chemical reaction networks

2009/04/29 by Anne Shiu, Bernd Sturmfels, Shiu, Anne +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Commutative Algebra (math.AC) #FOS: Biological sciences #FOS: Mathematics #Formal Methods in Verification #Molecular Networks (q-bio.MN) #Petri Nets in System Modeling #Slime Mold and Myxomycetes Research #math.AC #q-bio.MN

paper · pdf · doi:10.48550/arxiv.0904.4529

openalex publication_date 2009/04/29 · arxiv created 2010/01/05 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Algebraic Methods for Inferring Biochemical Networks: a Maximum Likelihood Approach
• The dynamics of weakly reversible population processes near facets

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• The Boundary Reproduction Number for Determining Boundary Steady State Stability in Chemical Reaction Systems

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