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

Nidhi Kaihnsa*, Tung Nguyen, Anne Shiu

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

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.

Original languageEnglish
JournalEuropean Journal of Applied Mathematics
ISSN0956-7925
DOIs
Publication statusE-pub ahead of print - 2024

Bibliographical note

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

Keywords

  • absolute concentration robustness
  • Keywords:
  • Multistationarity
  • reaction networks
  • sparse polynomials

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