2018/05/23 by Matthew D. Johnston, Stefan C. Müller, Johnston, Matthew D. +3 · 3 citations
Biochemistry, Genetics and Molecular Biology · #34A34 #92C42 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Microbial Metabolic Engineering and Bioproduction #Receptor Mechanisms and Signaling
paper · pdf · doi:10.48550/arxiv.1805.09295
openalex publication_date 2018/05/23 · openalex created_date 2022/08/23 · openalex updated_date 2026/07/28
We present conditions which guarantee a parametrization of the set of\npositive equilibria of a generalized mass-action system. Our main results state\nthat (i) if the underlying generalized chemical reaction network has an\neffective deficiency of zero, then the set of positive equilibria coincides\nwith the parametrized set of complex-balanced equilibria and (ii) if the\nnetwork is weakly reversible and has a kinetic deficiency of zero, then the\nequilibrium set is nonempty and has a positive, typically rational,\nparametrization. Via the method of network translation, we apply our results to\nclassical mass-action systems studied in the biochemical literature, including\nthe EnvZ-OmpR and shuttled WNT signaling pathways. A parametrization of the set\nof positive equilibria of a (generalized) mass-action system is often a\nprerequisite for the study of multistationarity and allows an easy check for\nthe occurrence of absolute concentration robustness (ACR), as we demonstrate\nfor the EnvZ-OmpR pathway.\n