Elimination of intermediate species in multiscale stochastic reaction networks
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Elimination of intermediate species in multiscale stochastic reaction networks. / Cappelletti, Daniele; Wiuf, Carsten.
I: Annals of Applied Probability, Bind 26, Nr. 5, 01.10.2016, s. 2915-2958.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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
VL - 26
SP - 2915
EP - 2958
JO - Annals of Applied Probability
JF - Annals of Applied Probability
SN - 1050-5164
IS - 5
ER -
ID: 170349667