TY - JOUR

T1 - Absolute concentration robustness and multistationarity in reaction networks

T2 - Conditions for coexistence

AU - Kaihnsa, Nidhi

AU - Nguyen, Tung

AU - Shiu, Anne

N1 - Publisher Copyright: © The Author(s), 2024. Published by Cambridge University Press.

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

KW - absolute concentration robustness

KW - Keywords:

KW - Multistationarity

KW - reaction networks

KW - sparse polynomials

U2 - 10.1017/S0956792523000335

DO - 10.1017/S0956792523000335

M3 - Journal article

AN - SCOPUS:85181457261

JO - European Journal of Applied Mathematics

JF - European Journal of Applied Mathematics

SN - 0956-7925

ER -