Facilitated diffusion of DNA-binding proteins: Simulation of large   systems
  The recently introduced method of excess collisions (MEC) is modified to estimate diffusion-controlled reaction times inside systems of arbitrary size. The resulting MEC-E equations contain a set of empirical parameters, which have to be calibrated in numerical simulations inside a test system of moderate size. Once this is done, reaction times of systems of arbitrary dimensions are derived by extrapolation, with an accuracy of 10 to 15 percent. The achieved speed up, when compared to explicit simulations of the reaction process, is increasing proportional to the extrapolated volume of the cell. 
Holger Merlitz, Konstantin V. Klenin, Chen-Xu Wu, and J\"org Langowski