Protein--DNA interactions: reaching and recognizing the targets

Protein searching and recognizing the targets on DNA was the subject of many experimental and theoretical studies. It is often argued that some proteins are capable of finding their targets 10-100 times faster than predicted by the three-dimensional diffusion rate. However, recent single-molecule experiments showed that the diffusion constants of the protein motion along DNA are usually small. This controversy pushed us to revisit this problem. We present a theoretical approach that describes some physical-chemical aspects of the target search and recognition. We consider the search process as a sequence of cycles, with each cycle consisting of three-dimensional and one-dimensional tracks. It is argued that the search time contains three terms: for the motion on three-dimensional and one-dimensional segments, and the correlation term. Our analysis shows that the acceleration in the search time is achieved at some intermediate strength of the protein-DNA binding energy and it is partially "apparent" because it is in fact reached by parallel scanning for the target by many proteins. We also show how the complementarity of the charge patterns on a target DNA sequence and on the protein may result in electrostatic recognition of a specific track on DNA and subsequent protein pinning. Within the scope of a model, we obtain an analytical expression for the capturing well. We estimate the depth and width of such a potential well and the typical time that a protein spends in it.