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This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency(More)
Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well(More)
Bistability arises within a wide range of biological systems from the lambda phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that(More)
Recent advances in gene-expression profiling technologies provide large amounts of gene expression data. This raises the possibility for a functional understanding of genome dynamics by means of mathematical modelling. As gene expression involves intrinsic noise, stochastic models are essential for better descriptions of gene regulatory networks. However,(More)
The Raf-MEK-ERK MAP kinase cascade transmits signals from activated receptors into the cell to regulate proliferation and differentiation. The cascade is controlled by the Ras GTPase, which recruits Raf from the cytosol to the plasma membrane for activation. In turn, MEK, ERK, and scaffold proteins translocate to the plasma membrane for activation. Here, we(More)
MOTIVATION Kinetic rate in gene expression is a key measurement of the stability of gene products and gives important information for the reconstruction of genetic regulatory networks. Recent developments in experimental technologies have made it possible to measure the numbers of transcripts and protein molecules in single cells. Although estimation(More)
Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying(More)
In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge–Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations.(More)
Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour(More)
In this paper we study the linear stability properties of the Euler methods for stochastic diierential equations (SDEs) applied with constant stepsize. We extend the T-stability deened by Saito and Mitsui 11] from weak solutions to strong solutions. The extended deenition of T-stability is equivalent to the asymptotic stability property of a numerical(More)