The Multistationarity Structure of Networks with Intermediates and a Binomial Core Network
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This work addresses whether a reaction network, taken with mass-action kinetics, is multistationary, that is, admits more than one positive steady state in some stoichiometric compatibility class. We build on previous work on the effect that removing or adding intermediates has on multistationarity, and also on methods to detect multistationarity for networks with a binomial steady-state ideal. In particular, we provide a new determinant criterion to decide whether a network is multistationary, which applies when the network obtained by removing intermediates has a binomial steady-state ideal. We apply this method to easily characterize which subsets of complexes are responsible for multistationarity; this is what we call the multistationarity structure of the network. We use our approach to compute the multistationarity structure of the n-site sequential distributive phosphorylation cycle for arbitrary n.
KeywordsBinomial ideal Phosphorylation cycle Multistationarity Model reduction Determinant criterion Toric ideal
This work has been supported by the Independent Research Fund of Denmark. We thank Alicia Dickenstein, Martin Helmer and Angélica Torres for comments on a preliminary version of this manuscript.
- Bihan F, Dickenstein A, Giaroli M (2019) Lower bounds for positive roots and regions of multistationarity in chemical reaction networks. arXiv:1807.05157
- Bradford R, Davenport JH, England M, Errami H, Gerdt V, Grigoriev D, Hoyt C, Košta M, Radulescu O, Sturm T, Weber A (2017) A case study on the parametric occurrence of multiple steady states. In: Proceedings of the international symposium on symbolic and algebraic computation, ISSAC, pp 45–52. Association for Computing MachineryGoogle Scholar
- England M, Bradford R, Davenport JH (2015) Improving the use of equational constraints in cylindrical algebraic decomposition. In: Proceedings of the international symposium on symbolic and algebraic computation, ISSAC, pp 165–172. Association for Computing MachineryGoogle Scholar
- Feinberg M (1980) Lectures on chemical reaction networks. http://www.crnt.osu.edu/LecturesOnReactionNetworks
- Gunawardena J (2003) Chemical reaction network theory for in-silico biologists. http://vcp.med.harvard.edu/papers/crnt.pdf