Elimination of intermediate species in multiscale stochastic reaction networks

TY - JOUR

T1 - Elimination of intermediate species in multiscale stochastic reaction networks

AU - Cappelletti, Daniele

AU - Wiuf, Carsten

PY - 2016/10/1

Y1 - 2016/10/1

N2 - We study networks of biochemical reactions modelled by continuoustime Markov processes. Such networks typically contain many molecular species and reactions and are hard to study analytically as well as by simulation. Particularly, we are interested in reaction networks with intermediate species such as the substrate-enzyme complex in the Michaelis-Menten mechanism. Such species are virtually in all real-world networks, they are typically short-lived, degraded at a fast rate and hard to observe experimentally. We provide conditions under which the Markov process of a multiscale reaction network with intermediate species is approximated by the Markov process of a simpler reduced reaction network without intermediate species. We do so by embedding the Markov processes into a one-parameter family of processes, where reaction rates and species abundances are scaled in the parameter. Further, we show that there are close links between these stochastic models and deterministic ODE models of the same networks.

AB - We study networks of biochemical reactions modelled by continuoustime Markov processes. Such networks typically contain many molecular species and reactions and are hard to study analytically as well as by simulation. Particularly, we are interested in reaction networks with intermediate species such as the substrate-enzyme complex in the Michaelis-Menten mechanism. Such species are virtually in all real-world networks, they are typically short-lived, degraded at a fast rate and hard to observe experimentally. We provide conditions under which the Markov process of a multiscale reaction network with intermediate species is approximated by the Markov process of a simpler reduced reaction network without intermediate species. We do so by embedding the Markov processes into a one-parameter family of processes, where reaction rates and species abundances are scaled in the parameter. Further, we show that there are close links between these stochastic models and deterministic ODE models of the same networks.

KW - Approximative dynamics

KW - Chemical reaction

KW - Limit distribution

KW - Markov process

KW - Model reduction

KW - Multiscale

KW - Reaction networks

UR - http://www.scopus.com/inward/record.url?scp=84994519935&partnerID=8YFLogxK

U2 - 10.1214/15-aap1166

DO - 10.1214/15-aap1166

M3 - Journal article

AN - SCOPUS:84994519935

SN - 1050-5164

VL - 26

SP - 2915

EP - 2958

JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 5

ER -