TY - JOUR

T1 - Fast reactions with non-interacting species in stochastic reaction networks

AU - Hoessly, Linard

AU - Wiuf, Carsten

N1 - Funding Information: LH acknowledges funding from the Swiss National Science Foundations Early Postdoc.Mobility grant (P2FRP2 188023). The work presented in this article is supported by Novo Nordisk Foundation, grant NNF19OC0058354. Publisher Copyright: © 2022 the Author(s), licensee AIMS Press.

PY - 2022

Y1 - 2022

N2 - We consider stochastic reaction networks modeled by continuous-time Markov chains. Such reaction networks often contain many reactions, potentially occurring at different time scales, and have unknown parameters (kinetic rates, total amounts). This makes their analysis complex. We examine stochastic reaction networks with non-interacting species that often appear in examples of interest (e.g. in the two-substrate Michaelis Menten mechanism). Non-interacting species typically appear as intermediate (or transient) chemical complexes that are depleted at a fast rate. We embed the Markov process of the reaction network into a one-parameter family under a two time-scale approach, such that molecules of non-interacting species are degraded fast. We derive simplified reaction networks where the non-interacting species are eliminated and that approximate the scaled Markov process in the limit as the parameter becomes small. Then, we derive sufficient conditions for such reductions based on the reaction network structure for both homogeneous and time-varying stochastic settings, and study examples and properties of the reduction.

AB - We consider stochastic reaction networks modeled by continuous-time Markov chains. Such reaction networks often contain many reactions, potentially occurring at different time scales, and have unknown parameters (kinetic rates, total amounts). This makes their analysis complex. We examine stochastic reaction networks with non-interacting species that often appear in examples of interest (e.g. in the two-substrate Michaelis Menten mechanism). Non-interacting species typically appear as intermediate (or transient) chemical complexes that are depleted at a fast rate. We embed the Markov process of the reaction network into a one-parameter family under a two time-scale approach, such that molecules of non-interacting species are degraded fast. We derive simplified reaction networks where the non-interacting species are eliminated and that approximate the scaled Markov process in the limit as the parameter becomes small. Then, we derive sufficient conditions for such reductions based on the reaction network structure for both homogeneous and time-varying stochastic settings, and study examples and properties of the reduction.

KW - Continuous-time Markov process

KW - Markov process

KW - Mass-action system

KW - Reduction

KW - Singular perturbation

KW - Stochastic reaction networks

UR - http://www.scopus.com/inward/record.url?scp=85123455370&partnerID=8YFLogxK

U2 - 10.3934/MBE.2022124

DO - 10.3934/MBE.2022124

M3 - Journal article

AN - SCOPUS:85123455370

VL - 19

SP - 2720

EP - 2749

JO - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

SN - 1547-1063

IS - 3

ER -