Asymptotic analysis of multiscale approximations to reaction networks
Asymptotic analysis of multiscale approximations to reaction networks
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DOI：
10.1214/105051606000000420
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发表时间：
2006-11-01
影响因子：
1.8
通讯作者：
Rempala, Greg
中科院分区：
文献类型：
--
作者：
Ball, Karen;Kurtz, Thomas G.;Rempala, Greg
反应网络是涉及多个反应和化学物种的化学系统。此类网络的随机模型将系统视为每个物种分子数量上的连续时间马尔可夫链，反应作为链的可能转移。在许多生物学上感兴趣的情况下，网络中的一些化学物质的丰度比其他化学物质大得多，反应速率常数可以在几个数量级上变化。我们认为这种模型的近似方法，考虑到系统的多尺度性质。我们的主要例子是一个细胞的病毒感染的模型，我们应用的平均和大数定律的参数相结合，以表明该模型的“慢”的组成部分可以近似由一个确定性方程和表征的“快”的组件的渐近分布。主要目标是说明可以用于降低更复杂模型的维数的技术。
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.