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 γopt, 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 γopt ∝ L-2 and with the number of roadblock protein molecules present on the same DNA m as γopt ∝ m2. The required free energy barrier ERTO associated with this flipping transition seems to be varying with L as ERTO ∝ In 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. © 2010 by the Biophysical Society.