2013/12/15 by Badal Joshi, Joshi, Badal
Biochemistry, Genetics and Molecular Biology · Computer Science · #Computational Drug Discovery Methods #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Microbial Metabolic Engineering and Bioproduction #Molecular Networks (q-bio.MN) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1312.4196
openalex publication_date 2013/12/15 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
Certain chemical reaction networks (CRNs) when modeled as a deterministic\ndynamical system taken with mass-action kinetics have the property of reaction\nnetwork detailed balance (RNDB) which is achieved by imposing network-related\nconstraints on the reaction rate constants. Markov chains (whether arising as\nmodels of CRNs or otherwise) have their own notion of detailed balance, imposed\nby the network structure of the graph of the transition matrix of the Markov\nchain. When considering Markov chains arising from chemical reaction networks\nwith mass-action kinetics, we will refer to this property as Markov chain\ndetailed balance (MCDB). Finally, we refer to the stochastic analog of RNDB as\nWhittle stochastic detailed balance (WSDB). It is known that RNDB and WSDB are\nequivalent. We prove that WSDB and MCDB are also intimately related but are not\nequivalent. While RNDB implies MCDB, the converse is not true. The conditions\non rate constants that result in networks with MCDB but without RNDB are\nstringent, and thus examples of this phenomenon are rare, a notable exception\nis a network whose Markov chain is a birth and death process. We give a new\nalgorithm to find conditions on the rate constants that are required for MCDB.\n