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Clustering of cell surface receptors: Simulating the mesoscale between reaction-diffusion and atomistic scales

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SDBW04 - Spatially distributed stochastic dynamical systems in biology

Co-author: Omer Dushek (Oxford)

Many biological molecules, including cell surface receptors, form densely-packed clusters that are weakly bound, mechanically soft, and have volumes on the same order as the volumes of the proteins they interact with. Preventing the formation of clusters dramatically attenuates proper cell function in many examples (including T cell activation and allergen activation in Mast cells), but for unknown reason. Therefore, receptor clusters involve biology hidden at the mesoscale between individual protein structure (0.1nm) and the cell-scale signaling pathways of populations of diffusing protein (1000nm). In some parameter regimes, clusters comprise 10-100 molecules tied to fixed locations on the cell surface by molecular tethers. The Dushek Lab is developing an in vitro setup that mimics this regime, and find that the time courses of binding and enzymatic reactions are non-trivial and cannot be fit to simple ODE models. On the other hand, fitting to explicitly spatial simulatio ns with volume exclusion is prohibitively slow. Here we present a fast algorithm for tethered reactions with volume exclusion. The algorithm exploits, first, the spatially-fixed tethers, allowing us to construct a single nearest-neighbor tree, and, second, a separation of timescales between the fast diffusion of molecular domains and slow binding and catalytic reactions. This allows use of a hybrid Metropolis-Gillespie algorithm: on the fast timescale of domain motion, efficient equilibrium algorithms that include volume exclusion provide the effective concentrations for the slow timescale of binding and catalysis, which are simulated using a maximally-fast next-event algorithm. Crucially, we employ dynamic connected-set-discovery subroutines to simulate the minimal subset of molecules each time step. The algorithm has computational time scaling approximately with the number of molecules and can reproduce the non-trivial time courses observed experimentally.

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