Three-dimensional Monte Carlo simulations of intracellular diffusion and reaction of signaling proteins.

We show that the Monte Carlo technique makes it possible to perform three-dimensional simulations of intracellular protein-mediated signal transduction with realistic ratio of the rates of protein diffusion and association with genes. Specifically, we illustrate that in the simplest case when the protein degradation and phosphorylation/dephosphorylation are negligible the distribution of the first passage time for this process is close to exponential provided that the number of target genes is between 1 and 100.