Theory of Site-Specific DNA-Protein Interactions in the Presence of Conformational Fluctuations of DNA Binding Domains

We develop a theory that explains how the thermally driven conformational fluctuations in the DNA binding domains (DBDs) of the DNA binding proteins (DBPs) are effectively coupled to the one-dimensional searching dynamics of DBPs for their cognate sites on DNA. We show that the rate γ_opt, associated with the flipping of conformational states of DBDs beyond which the maximum search efficiency of DBPs is achieved, varies with the one-dimensional sliding length L as γ_opt ∝ L⁻² and with the number of roadblock protein molecules present on the same DNA m as γ_opt ∝ m². The required free energy barrier E_RTO associated with this flipping transition seems to be varying with L as E_RTO ∝ ln L². When the barrier height associated with the conformational flipping of DBDs is comparable with that of the thermal free energy, then the possible value of L under in vivo conditions seems to be L ≤ 70 bps.