2016/08/30 by Murad Banaji, Banaji, Murad, Casian Pantea +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Gene Regulatory Network Analysis #Microbial Metabolic Engineering and Bioproduction #Advanced Thermodynamics and Statistical Mechanics
paper · pdf · doi:10.48550/arxiv.1608.08400
We study how the properties of allowing multiple positive nondegenerate\nequilibria (MPNE) and multiple positive linearly stable equilibria (MPSE) are\ninherited in chemical reaction networks (CRNs). Specifically, when is it that\nwe can deduce that a CRN admits MPNE or MPSE based on analysis of its\nsubnetworks? Using basic techniques from analysis we are able to identify a\nnumber of situations where MPNE and MPSE are inherited as we build up a\nnetwork. Some of these modifications are known while others are new, but all\nresults are proved using the same basic framework, which we believe will yield\nfurther results. The results are presented primarily for mass action kinetics,\nalthough with natural, and in some cases immediate, generalisation to other\nclasses of kinetics.\n