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The recently introduced method of excess collisions (MEC) is modified toestimate diffusion-controlled reaction times inside systems of arbitrary size.The resulting MEC-E equations contain a set of empirical parameters, which haveto be calibrated in numerical simulations inside a test system of moderatesize. Once this is done, reaction times of systems of arbitrary dimensions arederived by extrapolation, with an accuracy of 10 to 15 percent. The achievedspeed up, when compared to explicit simulations of the reaction process, isincreasing proportional to the extrapolated volume of the cell.Comment: 8 pages, 4 figures, submitted to J. Chem. Phy

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