Facilitated diffusion of DNA-binding proteins: Simulation of large systems

The recently introduced method of excess collisions to estimate reaction times of protein-DNA systems in the presence of facilitated diffusion ("sliding") requires a cell of full system size. This bottleneck is avoided with a modification, by which a set of empirical parameters is calibrated using numerical simulations of a small test system. Once this is done, reaction times for systems of arbitrary dimensions are derived by extrapolation. It is shown that at physiological sliding lengths a test system of the order of 100 nm radius suffices to extract accurate reaction times for realistic cell dimensions. The achieved speedup, when compared to explicit simulations of the reaction process, is increasing in third order of the extrapolated radius of the cell.