ArticleMathematical biosciences2012
Concordant chemical reaction networks.
Article in Mathematical biosciences, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed.
- Positive equilibria in mass action networks: geometry and bounds.Journal of mathematical biology · 2026Article
- A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks.PLoS computational biology · 2020Article
- Metrics for regulated biochemical pathway systems.Bioinformatics (Oxford, England) · 2019Article
- The role of the Hes1 crosstalk hub in Notch-Wnt interactions of the intestinal crypt.PLoS computational biology · 2017Article
- Logical-continuous modelling of post-translationally regulated bistability of curli fiber expression in Escherichia coli.BMC systems biology · 2015Article
- Sharper graph-theoretical conditions for the stabilization of complex reaction networks.Mathematical biosciences · 2015Article
- Dynamical properties of Discrete Reaction Networks.Journal of mathematical biology · 2014Article
- Translated chemical reaction networks.Bulletin of mathematical biology · 2014Article
- Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks.Mathematical biosciences and engineering : MBE · 2013Article
- Concordant chemical reaction networks and the Species-Reaction Graph.Mathematical biosciences · 2013Article
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2 authors.
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Abstract
We describe a large class of chemical reaction networks, those endowed with a subtle structural property called concordance. We show that the class of concordant networks coincides precisely with the class of networks which, when taken with any weakly monotonic kinetics, invariably give rise to kinetic systems that are injective - a quality that, among other things, precludes the possibility of switch-like transitions between distinct positive steady states. We also provide persistence characteristics of concordant networks, instability implications of discordance, and consequences of stronger variants of concordance. Some of our results are in the spirit of recent ones by Banaji and Craciun, but here we do not require that every species suffer a degradation reaction. This is especially important in studying biochemical networks, for which it is rare to have all species degrade.
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