Diffusion constant of a nonspecifically bound protein undergoing curvilinear motion along DNA

The mechanism of a protein's diffusion along a DNA segment is a subject of much current interest because of the involvement of this diffusion in numerous biological processes, including the recognition of DNA sequences and chemical modifications of DNA. In this work we present a theoretical derivation of the diffusion coefficient of a nonspecifically bound protein, assuming that the protein follows a helical track along the DNA. It is shown that, for protein-sized molecules, the principal contribution to the total translational friction comes from the curvilinear motion along the helix, and this contribution is given by 6&#960;&#951;RR<SUB>OC</SUB><SUP>2</SUP> + 8&#960;&#951;R<SUP>3</SUP>, where R is the protein radius, R<SUB>OC</SUB> is the distance of separation between the center of mass of the protein and the helical axis of DNA, and &#951; is the viscosity of the medium. The translational diffusion of the protein along the helical track of DNA is thus predicted to have a nearly R<SUP>-3</SUP> size dependence, not the R<SUP>-1</SUP> dependence characterizing simple translational diffusion. It is shown that this expression gives rather good estimates of the translational diffusion coefficient measured in single molecule experiments