2020/01/01 by Hamid Rahkooy, Ovidiu Radulescu, Thomas Sturm
Biochemistry, Genetics and Molecular Biology · Chemistry · Computer Science · Mathematics · #Algebra over a field #Algorithm #Chemistry #Computational Drug Discovery Methods #Computer science #Formal Methods in Verification #Gene Regulatory Network Analysis #Linear algebra #Mathematics #Physical chemistry #Pure mathematics #State (computer science) #Steady state (chemistry) #cs.SC #q-bio.MN
paper · pdf · doi:10.1007/978-3-030-60026-6_29
published as Proc. CASC 2020, LNCS 12291, pp.492-509, Springer 2020
openalex publication_date 2020/01/01 · arxiv created 2020/06/15 · arxiv updated 2020/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Motivated by problems from Chemical Reaction Network Theory, we investigate whether steady state ideals of reversible reaction networks are generated by binomials. We take an algebraic approach considering, besides concentrations of species, also rate constants as indeterminates. This leads us to the concept of unconditional binomiality, meaning binomiality for all values of the rate constants. This concept is different from conditional binomiality that applies when rate constant values or relations among rate constants are given. We start by representing the generators of a steady state ideal as sums of binomials, which yields a corresponding coefficient matrix. On these grounds we propose an efficient algorithm for detecting unconditional binomiality. That algorithm uses exclusively elementary column and row operations on the coefficient matrix. We prove asymptotic worst case upper bounds on the time complexity of our algorithm. Furthermore, we experimentally compare its performance with other existing methods.