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 extracellular signal-regulated kinase (ERK). By generating Ras nanoclusters in direct proportion to ligand input, cells build an analogue-digital-analogue circuit relay that transmits a signal across the plasma membrane with high fidelity. Signal transmission is completely dependent on Ras spatial organization and fails if nanoclustering is abrogated. A requirement for high-fidelity signalling may explain the non-random distribution of other plasma membrane signalling complexes.
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 explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.
This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the -leap and midpoint -leap methods of Gillespie ͓D. T. Gillespie, J. Chem. Phys. 115, 1716 ͑2001͔͒, binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. 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.
Bistability arises within a wide range of biological systems from the 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 noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop 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. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.genetic regulatory network ͉ stochastic modeling ͉ stochastic simulation ͉ noise O ne of the major challenges in systems biology is the development of quantitative mathematical models for studying regulatory mechanisms in complex biological systems. Bistability is a fundamental behavior of biological systems and has been studied extensively through experiments, theoretical analysis, and numerical simulations (1-5). A bistable system has two distinct steady states, and any initial setting of a system state will eventually lead the system into one of the steady states. Biological examples of bistable systems include the phage lysis-lysogeny switch (6-9), the genetic toggle switch (10-12), the lactose operon repressor system (13-15), cellular signal transduction pathways (16)(17)(18)(19), and the system of cell-cycle control (20). In contrast to monostable systems, regulatory mechanisms are the key in realizing switching of bistable systems. Regulatory mechanisms in bistable biological systems include inhibition͞activation, positive feedback, double-negative feedback, and multisite phosphorylation (19). A bistable system can switch from one steady state to the other by increasing stimulation or inhibition or by changing other regulatory mechanisms. Recent studies through biological experiments have indicated that noise plays a very important role in the dynamic behavior of bistable systems. For example, bimodal population ...
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.
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