  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.
