(105a) Translocation Dynamics of DNA-Binding Proteins

The transport behavior of DNA-binding proteins is a critical component in understanding genetic regulation, where a relatively small number of proteins must quickly act on their DNA target sites in response to constantly changing cellular conditions. This process is remarkably fast; the canonical DNA-binding protein lac repressor exhibits an experimental binding constant that is three orders of magnitude higher than predicted by free diffusion alone. The precise mechanism behind target-site search remains an important open question in biology. A robust description of DNA-binding proteins' translocation dynamics is also necessary for the realization of engineering designs that require proteins to find their target sites on DNA under a variety of time- and length-scale restrictions, including intracellular conditions. We address this fundamental biological problem through a reaction-diffusion model that examines the effect of DNA conformation and discuss the consequences of our findings for a number of experimental situations.

It has been proposed that nonspecific binding aids target-site search by allowing proteins to slide and hop along DNA in a process called facilitated diffusion. We have developed a reaction-diffusion theory of facilitated diffusion that accounts for transport both on and off the strand and incorporates the physical conformation of DNA. Previously, we identified conditions that optimize translocation rate and search efficiency for linear DNA, and we now extend this analysis to other conformations of interest. In particular, we examine the effect of supercoiling on protein translocation. We use our theory in combination with dynamic Monte Carlo simulations to show that the increased proximity of distal segments leads to superdiffusive transport and, consequently, faster translocation rates, in agreement with experimental results.

This comprehensive picture of regulatory protein translocation can also be used to analyze a variety of phenomena that rely on protein transport along DNA, especially those where larger-scale observations mask relevant behavior at the molecular level. Accordingly, we extend our theory to address the effect of imperceptible molecular events during single-molecule experiments of naked and nucleosomal DNA. We find that, in general, observable 1-D diffusion and unbinding rate constants exhibit significant deviations at high unbinding and binding rates, respectively, and quantify these effects. We examine these predictions in the context of current experiments and identify the limits of spatial resolution where experimental measurements remain reliable. Finally, we discuss the consequences of our findings on the observable salt dependence of unbinding rates of DNA-binding proteins.