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      Molecular finite-size effects in stochastic models of equilibrium chemical systems


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          The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here we introduce the crowded reaction-diffusion master equation (cRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the cRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in molecular crowding can (i) lead to deviations from the classical inverse square root law for the noise-strength; (ii) flip the skewness of the probability distribution from right to left-skewed; (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed; (iv) strongly modulate the Fano factors and coefficients of variation. These crowding-induced effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws.Finally we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.

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          Most cited references 45

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          Stochastic simulation of chemical kinetics.

          Stochastic chemical kinetics describes the time evolution of a well-stirred chemically reacting system in a way that takes into account the fact that molecules come in whole numbers and exhibit some degree of randomness in their dynamical behavior. Researchers are increasingly using this approach to chemical kinetics in the analysis of cellular systems in biology, where the small molecular populations of only a few reactant species can lead to deviations from the predictions of the deterministic differential equations of classical chemical kinetics. After reviewing the supporting theory of stochastic chemical kinetics, I discuss some recent advances in methods for using that theory to make numerical simulations. These include improvements to the exact stochastic simulation algorithm (SSA) and the approximate explicit tau-leaping procedure, as well as the development of two approximate strategies for simulating systems that are dynamically stiff: implicit tau-leaping and the slow-scale SSA.
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            Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences.

            Expected and observed effects of volume exclusion on the free energy of rigid and flexible macromolecules in crowded and confined systems, and consequent effects of crowding and confinement on macromolecular reaction rates and equilibria are summarized. Findings from relevant theoretical/simulation and experimental literature published from 2004 onward are reviewed. Additional complexity arising from the heterogeneity of local environments in biological media, and the presence of nonspecific interactions between macromolecules over and above steric repulsion, are discussed. Theoretical and experimental approaches to the characterization of crowding- and confinement-induced effects in systems approaching the complexity of living organisms are suggested.
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              Noise in protein expression scales with natural protein abundance.

              Noise in gene expression is generated at multiple levels, such as transcription and translation, chromatin remodeling and pathway-specific regulation. Studies of individual promoters have suggested different dominating noise sources, raising the question of whether a general trend exists across a large number of genes and conditions. We examined the variation in the expression levels of 43 Saccharomyces cerevisiae proteins, in cells grown under 11 experimental conditions. For all classes of genes and under all conditions, the expression variance was approximately proportional to the mean; the same scaling was observed at steady state and during the transient responses to the perturbations. Theoretical analysis suggests that this scaling behavior reflects variability in mRNA copy number, resulting from random 'birth and death' of mRNA molecules or from promoter fluctuations. Deviation of coexpressed genes from this general trend, including high noise in stress-related genes and low noise in proteasomal genes, may indicate fluctuations in pathway-specific regulators or a differential activation pattern of the underlying gene promoters.

                Author and article information

                1510.03690 10.1063/1.4941583


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                cond-mat.stat-mech physics.chem-ph

                Condensed matter, Physical chemistry


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