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The facilitated diffusion of a regulatory protein in the process of searching for a specific target site on the DNA molecule is considered. On the basis of the hypothesis of ballistic motion of the protein between scatterings of pseudo-specific sites, we proposed a phenomenological model of one-dimensional translocation of the protein along DNA. Combining this approach with the model of discrete random walks we were able to get the relationships between the mean first passage time and such characteristics as the binding energy, the mean free path length between pseudo-specific sites, the speed of protein movement and the temperature. These dependencies allow revealing the thermal and energetic optima, at which minimum values of searching time are achieved.

The Random Walks between Pseudo-Specific DNA Sites as Model of the Facilitated Diffusion of DNA-Binding Proteins