2023/10/03 by Lucie Laurence, Philippe Robert, Laurence, Lucie +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Chemistry · #FOS: Mathematics #Gene Regulatory Network Analysis #Microbial Metabolic Engineering and Bioproduction #Probability (math.PR) #thermodynamics and calorimetric analyses
paper · pdf · doi:10.48550/arxiv.2310.01949
openalex publication_date 2023/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The asymptotic properties of some Markov processes associated to stochastic chemical reaction networks (CRNs) driven by the kinetics of the law of mass action are analyzed. The scaling regime introduced in the paper assumes that the norm of the initial state is converging to infinity. The reaction rate constants are kept fixed. The purpose of the paper is of showing, with simple examples, a scaling analysis in this context. The main difference with the scalings of the literature is that it does not change the graph structure of the CRN or its reaction rates. Several CRNs are investigated to illustrate the insight that can be gained on the qualitative properties of these networks. A detailed scaling analysis of a CRN with several interesting asymptotic properties, with a bi-modal behavior in particular, is worked out in the last section. Additionally, with several examples, we also show that a stability criterion due to Filonov for positive recurrence of Markov processes may simplify significantly the stability analysis of these networks.