ArticleBulletin of mathematical biology2014
Translated chemical reaction networks.
Article in Bulletin of mathematical biology, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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12 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
- Kinetic modules are sources of concentration robustness in biochemical networks.Science advances · 2025Article
- Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them.Entropy (Basel, Switzerland) · 2024Article
- The effective deficiency of biochemical networks.Scientific reports · 2023Article
- The unraveling of balanced complexes in metabolic networks.Scientific reports · 2023Article
- A framework for deriving analytic steady states of biochemical reaction networks.PLoS computational biology · 2023Article
- Derivation of stationary distributions of biochemical reaction networks via structure transformation.Communications biology · 2021Article
- Joining and decomposing reaction networks.Journal of mathematical biology · 2020Article
- A Deficiency-Based Approach to Parametrizing Positive Equilibria of Biochemical Reaction Systems.Bulletin of mathematical biology · 2019Article
- Conditions for extinction events in chemical reaction networks with discrete state spaces.Journal of mathematical biology · 2018Article
- A computational approach to persistence, permanence, and endotacticity of biochemical reaction systems.Journal of mathematical biology · 2016Article
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Abstract
Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems of polynomial ordinary differential equations. The steady states of these mass action systems have been analyzed via a variety of techniques, including stoichiometric network analysis, deficiency theory, and algebraic techniques (e.g., Gröbner bases). In this paper, we present a novel method for characterizing the steady states of mass action systems. Our method explicitly links a network's capacity to permit a particular class of steady states, called toric steady states, to topological properties of a generalized network called a translated chemical reaction network. These networks share their reaction vectors with their source network but are permitted to have different complex stoichiometries and different network topologies. We apply the results to examples drawn from the biochemical literature.
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