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Multivariate moment closure techniques for stochastic kinetic models.

Published version
Peer-reviewed

Type

Article

Change log

Authors

Lakatos, Eszter 
Ale, Angelique 
Kirk, Paul DW 
Stumpf, Michael PH 

Abstract

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.

Description

Keywords

Kinetics, Models, Chemical, Multivariate Analysis, Stochastic Processes

Journal Title

J Chem Phys

Conference Name

Journal ISSN

0021-9606
1089-7690

Volume Title

143

Publisher

AIP Publishing