ArticleBulletin of mathematical biology2019
A Deficiency-Based Approach to Parametrizing Positive Equilibria of Biochemical Reaction Systems.
Article in Bulletin of mathematical biology, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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5 citing papers in PubMed.
- CRITERIA: A network decomposition and elementary flux mode translation-based tool for computing equilibria of biochemical systems.PLoS computational biology · 2026Article
- Parametrized systems of generalized polynomial inequalities via linear algebra and convex geometry.Positivity · 2026Article
- Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them.Entropy (Basel, Switzerland) · 2024Article
- A framework for deriving analytic steady states of biochemical reaction networks.PLoS computational biology · 2023Article
- Oscillations and bistability in a model of ERK regulation.Journal of mathematical biology · 2019Article
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Abstract
We present conditions which guarantee a parametrization of the set of positive equilibria of a generalized mass-action system. Our main results state that (1) if the underlying generalized chemical reaction network has an effective deficiency of zero, then the set of positive equilibria coincides with the parametrized set of complex-balanced equilibria and (2) if the network is weakly reversible and has a kinetic deficiency of zero, then the equilibrium set is nonempty and has a positive, typically rational, parametrization. Via the method of network translation, we apply our results to classical mass-action systems studied in the biochemical literature, including the EnvZ-OmpR and shuttled WNT signaling pathways. A parametrization of the set of positive equilibria of a (generalized) mass-action system is often a prerequisite for the study of multistationarity and allows an easy check for the occurrence of absolute concentration robustness, as we demonstrate for the EnvZ-OmpR pathway.
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