Asymptotic analysis of multiscale approximations to reaction networks
成果类型：
Article
署名作者：
Ball, Karen; Kurtz, Thomas G.; Popovic, Lea; Rempala, Greg
署名单位：
University of Minnesota System; University of Minnesota Twin Cities; University of Wisconsin System; University of Wisconsin Madison; University of Louisville
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/105051606000000420
发表日期：
2006
页码：
1925-1961
关键词：
摘要：
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as possible transitions of the chain. In many cases of biological interest some of the chemical species in the network are present in much greater abundance than others and reaction rate constants can vary over several orders of magnitude. We consider approaches to approximation of such models that take the multiscale nature of the system into account. Our primary example is a model of a cell's viral infection for which we apply a combination of averaging and law of large number arguments to show that the slow component of the model can be approximated by a deterministic equation and to characterize the asymptotic distribution of the fast components. The main goal is to illustrate techniques that can be used to reduce the dimensionality of much more complex models.