Generalized theory on the mechanism of site-specific DNA–protein interactions

Abstract

We develop a generalized theoretical framework on the binding of transcription factor proteins (TFs) with specific sites on DNA that takes into account the interplay of various factors regarding overall electrostatic potential at the DNA–protein interface, occurrence of kinetic traps along the DNA sequence, presence of other roadblock protein molecules along DNA and crowded environment, conformational fluctuations in the DNA binding domains (DBDs) of TFs, and the conformational state of the DNA. Starting from a Smolochowski type theoretical framework on site-specific binding of TFs we logically build our model by adding the effects of these factors one by one. Our generalized two-step model suggests that the electrostatic attractive forces present inbetween the positively charged DBDs of TFs and the negatively charged phosphate backbone of DNA, along with the counteracting shielding effects of solvent ions, is the core factor that creates a fluidic type environment at the DNA–protein interface. This in turn facilitates various one-dimensional diffusion (1Dd) processes such as sliding, hopping and intersegmental transfers. These facilitating processes as well as flipping dynamics of conformational states of DBDs of TFs between stationary and mobile states can enhance the 1Dd coefficient on a par with three-dimensional diffusion (3Dd). The random coil conformation of DNA also plays critical roles in enhancing the site-specific association rate. The extent of enhancement over the 3Dd controlled rate seems to be directly proportional to the maximum possible 1Dd length. We show that the overall site-specific binding rate scales with the length of DNA in an asymptotic way. For relaxed DNA, the specific binding rate will be independent of the length of DNA as length increases towards infinity. For condensed DNA as in in vivo conditions, the specific binding rate depends on the length of DNA in a turnover way with a maximum. This maximum rate seems to scale with the maximum possible 1Dd length of TFs in a square root manner. Results suggest that 1Dd processes contribute much less to the enhancement of specific binding rate under in vivo conditions for condensed DNA. There exists a critical length of binding stretch of TFs beyond which the probability associated with the random occurrence of similar specific binding sites will be close to zero. TFs in natural systems from prokaryotes to eukaryotes seem to handle sequence-mediated kinetic traps via increasing the length of their recognition stretch or combinatorial binding. TFs overcome the hurdles of roadblocks via switching efficiently between sliding, hopping and intersegmental transfer modes. The site-specific binding rate as well as the maximum possible 1Dd length seem to be directly proportional to the square root of the probability (pR) of finding a nonspecific binding site to be free from dynamic roadblocks. Here pR seems to be a function of the number of nsbs available per DNA binding protein (ϕ) inside the living cell. It seems that pR > 0.8 when ϕ > ...

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

“…The overall random search time or mean first passage time (MFPT) U τ associated with the TF of interest to find its CRM via a combination of 3D and 1D diffusion can be written as follows [9].…”

“…Site specific binding of TFs with the genomic DNA seems to be influenced by several factors under in vivo conditions [9] viz. (a) conformational state of DNA [9,10] (b) spatial organization of various functionally related CRMs along the genomic DNA [11,12], (c) presence of other dynamic roadblock TF proteins and semi-stationary roadblocks such as nucleosomes especially in eukaryotes [13][14][15][16], (d) naturally occurring sequence traps on DNA [17,18], (e) conformational fluctuations in the DNA binding domains (DBDs) of TFs ( Fig. 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].…”

“…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.…”

“…In general, the efficiency of TFs in locating their cognate sites on DNA via random searching mechanism seems to be strongly dependent on the relative amount of times spent on 3D and 1D diffusion routes [11,20]. 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].…”

“…they (a) dynamically control the accessibility of specific as well as non-specific binding sites and, sequence mediated traps towards incoming TFs from the bulk cytoplasm and (b) introduce semi-stationary roadblocks across the 1D diffusion dynamics of TFs along the DNA polymer [16,31]. When CRMs are concealed by the bulky nucleosome complex, then TFs wander over nearby or some other location of the same DNA chain or wait until the slow dislocation of the nucleosome assembly [9]. Otherwise some other active or competitive passive machinery is required to dismantle the nucleosome complexes from the specific binding sites of TFs.…”