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 gammaopt, 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 gammaopt proportional, L(-2) and with the number of roadblock protein molecules present on the same DNA m as gammaopt proportional, m2. The required free energy barrier ERTO associated with this flipping transition seems to be varying with L as ERTO proportional, variant 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

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.

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  > ...

The temporal dynamics of the concentrations of several proteins are tightly regulated, particularly for critical nodes in biological networks such as transcription factors. An important mechanism to control transcription factor levels is through autoregulatory feedback loops where the protein can bind its own promoter. Here we use theoretical tools and computational simulations to further our understanding of transcription-factor autoregulatory loops. We show that the stochastic dynamics of feedback and mRNA synthesis can significantly influence the speed of response of autoregulatory genetic networks toward external stimuli. The fluctuations in the response-times associated with the accumulation of the transcription factor in the presence of negative or positive autoregulation can be minimized by confining the ratio of mRNA/protein lifetimes within 1:10. This predicted range of mRNA/protein lifetime agrees with ranges observed empirically in prokaryotes and eukaryotes. The theory can quantitatively and systematically account for the influence of regulatory element binding and unbinding dynamics on the transcription-factor concentration rise-times. The simulation results are robust against changes in several system parameters of the gene expression machinery.