Facilitated diffusion of DNA-binding proteins: Efficient simulation with the method of excess collisions (MEC)

In this paper, a new method to efficiently simulate diffusion controlled second order chemical reactions is derived and applied to site-specific DNA-binding proteins. The protein enters a spherical cell and propagates via two competing modes, a free diffusion and a DNA-sliding mode, to search for its specific binding site in the center of the cell. There is no need for a straightforward simulation of this process. Instead, an alternative and exact approach is shown to be essentially faster than explicit random-walk simulations. The speed-up of this novel simulation technique is rapidly growing with system size.