Many biological molecules\, including cell sur face receptors\, form densely-packed clusters tha t are weakly bound\, mechanically soft\, and have volumes on the same order as the volumes of the p roteins they interact with. Preventing the format ion of clusters dramatically attenuates proper cel l function in many examples (including T cell act ivation and allergen activation in Mast cells)\, but for unknown reason. Therefore\, receptor clust ers involve biology hidden at the mesoscale betwe en individual protein structure (~0.1nm) and the cell-scale signaling pathways of populations of di ffusing protein (~1000nm). In some parameter regi mes\, clusters comprise 10-100 molecules tied to fixed locations on the cell surface by molecular t ethers. The Dushek Lab is developing an in vitro setup that mimics this regime\, and find that the time courses of binding and enzymatic reactions a re non-trivial and cannot be fit to simple ODE mo dels. On the other hand\, fitting to explicitly sp atial simulatio ns with volume exclusion is prohi bitively slow. Here we present a fast algorithm f or tethered reactions with volume exclusion. The a lgorithm exploits\, first\, the spatially-fixed t ethers\, allowing us to construct a single nearest -neighbor tree\, and\, second\, a separation of t imescales 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 concentrat ions for the slow timescale of binding and catalys is\, which are simulated using a maximally-fast n ext-event algorithm. Crucially\, we employ dynami c connected-set-discovery subroutines to simulate the minimal subset of molecules each time step. T he algorithm has computational time scaling appro ximately with the number of molecules and can repr oduce the non-trivial time courses observed exper imentally.

Related Links

- http://allardlab.com - Jun Allard'\;s website \;