Reduction of dimensionality in a diffusion search process and kinetics of gene expression

In order to activate a gene in a DNA molecule a specific protein (transcrip tion factor) has to bind to the promoter of the gene. We formulate and part ially answer the following question: how much time does a transcription fac tor, which activates a given gene, need in order to find this gene inside t he nucleus of a cell? The estimate based on the simplest model of diffusion gives a very long time of days. We discuss various mechanisms by which the time can be reduced to seconds, in particular, the reduction of dimensiona lity, in which diffusion takes place, from three-dimensional space to two-d imensional space. The potential needed to keep the diffusing particle in 2D (i.e, at the surface of size L-2 in a volume of size L-3) should scale as U similar to k(B)T lnL. For at = 1 mu m and a target size a = 10 Angstrom w e find U = 8k(B)T, i.e., it is a potential strength of the order of the str ength of ionic interactions in water. (C) 2000 Elsevier Science B.V. All ri ghts reserved.