Absolute concentration robustness and multistationarity in reaction networks: Conditions for coexistence

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Many reaction networks arising in applications are multistationary, that is, they have the capacity for more than one steady state, while some networks exhibit absolute concentration robustness (ACR), which means that some species concentration is the same at all steady states. Both multistationarity and ACR are significant in biological settings, but only recently has attention focused on the possibility for these properties to coexist. Our main result states that such coexistence in at-most-bimolecular networks (which encompass most networks arising in biology) requires at least three species, five complexes and three reactions. We prove additional bounds on the number of reactions for general networks based on the number of linear conservation laws. Finally, we prove that, outside of a few exceptional cases, ACR is equivalent to non-multistationarity for bimolecular networks that are small (more precisely, one-dimensional or up to two species). Our proofs involve analyses of systems of sparse polynomials, and we also use classical results from chemical reaction network theory.
TidsskriftEuropean Journal of Applied Mathematics
StatusE-pub ahead of print - 2024

Bibliografisk note

Funding Information:
This project began at an AIM workshop on “Limits and control of stochastic reaction networks” held online in July 2021. AS was supported by the NSF (DMS-1752672). NK has been funded by the Independent Research Fund of Denmark.

Publisher Copyright:
© The Author(s), 2024. Published by Cambridge University Press.

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