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Ras proteins occupy dynamic plasma membrane nanodomains called nanoclusters. The significance of this spatial organization is unknown. Here we show, 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(More)
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)
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)
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)
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 spatial organization of K-Ras proteins into nanoclusters on the plasma membrane is essential for high-fidelity signal transduction. The mechanism underlying K-Ras nanoclustering is unknown. We show here that K-Ras.GTP recruits Galectin-3 (Gal-3) from the cytosol to the plasma membrane where it becomes an integral nanocluster component. Importantly, we(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)
In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of(More)
Bistability and switching are two important aspects of the genetic regulatory network of lambda phage. Positive and negative feedbacks are key regulatory mechanisms in this network. By the introduction of threshold values, the developmental pathway of lambda phage is divided into different stages. If the protein level reaches a threshold value, positive or(More)
The transcription factors PU.1 and GATA-1 are known to be important in the development of blood progenitor cells. Specifically they are thought to regulate the differentiation of progenitor cells into the granulocyte/macrophage lineage and the erythrocyte/megakaryocite lineage. While several mathematical models have been proposed to investigate the(More)