Ramon Grima, University of Edinburgh

Spatial stochastic models of intracellular dynamics in dilute and crowded conditions

Stochastic effects in biochemical reaction systems are commonly studied by means of the Reaction-Diffusion Master equation (RDME). The RDME is computationally efficient and has the advantage of being amenable to analysis. However the RDME assumes point particle interactions, i.e. dilute conditions. This presents a problem because the intracellular environment can be highly crowded with up to 40% of its volume being occupied by various macromolecules. In this talk I will discuss our recent work showing how the RDME can be modified to take into account volume-excluded interactions. This can be solved in certain conditions yielding explicit expressions for the dependence of reactant number fluctuations on the available volume fraction of space. I will also discuss how one can use the modified RDME to derive coupled nonlinear partial differential equations which describe molecular movement in highly heterogeneous crowded environments and which hence offer a realistic alternative to the classical diffusion equation. All results will be contrasted with those obtained from Brownian dynamics.

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