Generalized theory of site-specific DNA-protein interactions

Abstract

We develop a generalized theory of the site-specific DNA-protein interactions, which includes both the static as well as the dynamical factors influencing the one-dimensional diffusion of the nonspecifically bound protein molecule which is in the process of searching for the specific site on the DNA lattice. We argue that the chemically driven condensation of the DNA molecule introduces a static distribution in the one-dimensional phenomenological diffusion coefficient associated with the protein molecule and the conformational dynamics of the DNA introduces temporal fluctuations in the one-dimensional diffusion coefficient over the static distribution. We further derive the generalized inequality conditions and the scaling laws which are required to enhance the three-dimensional diffusion controlled site-specific association rate to an arbitrary order. Our model predicts that when the degree of condensation of the DNA molecule under consideration is very high, then the probability distribution associated with the stationary state one-dimensional diffusion coefficient variable as well as the stationary state one-dimensional diffusion length variable will be a flat one. Further analysis reveals that to achieve a site-specific association rate which is higher than that of the three-dimensional diffusion controlled rate, the one-dimensional diffusion length associated with the dynamics of the nonspecifically bound protein molecule on the DNA lattice should fall in certain critical ranges. Comparison of our theoretical results with the recent experimental observations reveals that when the DNA molecule is under a stretched condition, then the static distribution of the one-dimensional diffusion coefficient associated with the dynamics of the protein molecule on the DNA lattice is a Gaussian and therefore the fluctuations in the one-dimensional diffusion coefficient generated by the dynamical factors are confined in a harmonic type potential.

Theory on the Dynamics of Feedforward Loops in the Transcription Factor Networks

“…We measure the timescales in terms of the lifetime of the TF protein C by dividing t by γ pc . Since the dynamics of binding-unbinding of the transcription factors with the respective promoters is a typical diffusion-controlled site-specific DNA-protein interaction, under in vivo conditions of bacterial cell we find that molecules −1 s −1 [22]–[24]. Here we have assumed an in vivo three dimensional diffusion controlled collision rate ∼10 6 M −1 s −1 .…”

Theory of site-specific DNA-protein interactions in the presence of nucleosome roadblocks

“…where i Z ∈ , wTF,i are the microscopic transition rates associated with the forward and reverse movements of TFs on DNA and p±i are the corresponding microscopic transition probabilities [8,41]. Here the step length ild is measured in terms of bps where we have defined ld = 1bps.…”

“…Clearly neither pure 1D nor pure 3D diffusion is efficient mode of searching for the specific binding sites [9,11]. Under ideal situation, maximum efficiency of random searching can be achieved only when TFs spend equal amount of times in both 1D as well as 3D diffusions [8,11]. This trade off balance of 1D and 3D diffusion times will be modulated by the presence of factors a-f. For example presence of roadblocks or sequence traps warrants more dissociations and 3D excursions of TFs rather than 1D sliding along DNA.…”

“…1A and B). Intersegmental transfers occur when two distal segments of the same DNA polymer come close over 3D space via ring closure events [7][8][9].…”

“…1B) [19][20][21] and (f) the nonspecific electrostatic attractive forces and the counteracting shielding effects of other solvent ions and water molecules acting at the DNA-protein interface [22]. Several theoretical [8,9,17,20,23], computational [24][25][26][27] and experimental studies have been carried out to understand the effects of various factors a-f on the site specific binding kinetics of TFs with DNA.…”