Tianhai Tian

TL;DR: It is shown, using in silico and in vivo analyses of mitogen-activated protein (MAP) kinase signalling, that Ras nanoclusters operate as sensitive switches, converting graded ligand inputs into fixed outputs of activated extracellular signal-regulated kinase (ERK).

TL;DR: Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches.

TL;DR: This paper introduces delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation, and shows that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

TL;DR: A previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations is developed.

TL;DR: A review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations can be found in this article, where the authors give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications.