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Mathematics > Dynamical Systems

arXiv:1805.09295 (math)
[Submitted on 23 May 2018]

Title:A deficiency-based approach to parametrizing positive equilibria of biochemical reaction systems

Authors:Matthew D. Johnston, Stefan Müller, Casian Pantea
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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 (i) 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 (ii) 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 (ACR), as we demonstrate for the EnvZ-OmpR pathway.
Comments: 23 pages, 0 figures
Subjects: Dynamical Systems (math.DS); Algebraic Geometry (math.AG)
MSC classes: 92C42, 34A34
Cite as: arXiv:1805.09295 [math.DS]
  (or arXiv:1805.09295v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1805.09295

Submission history

From: Matthew Johnston [view email]
[v1] Wed, 23 May 2018 17:29:53 UTC (35 KB)
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