Protein-DNA interaction, random walks and polymer statistics

Abstract

In Part I of the thesis, a general physical framework describing the kinetics of protein- DNA interaction is developed. Recognition and binding of specific sites on DNA by proteins is central for many cellular functions such as transcription, replication, and recombination. In the process of recognition, a protein rapidly searches for its specific site on a long DNA molecule and then strongly binds this site. Earlier studies have suggested that rapid search involves sliding of the protein along the DNA. I treat sliding as a one-dimensional diffusion in a sequence-dependent rough energy landscape. I demonstrate that, despite the landscape's roughness, rapid search can. be achieved if one-dimensional sliding is accompanied by three-dimensional diffusion. I estimate the range of the specific and nonspecific DNA-binding energy required for rapid search and suggest experiments that can test the proposed mechanism. It appears that realistic energy functions cannot provide both rapid search and strong binding of a rigid protein. To reconcile these two fundamental requirements, a search-and-fold mechanism is proposed that involves the coupling of protein binding and partial protein folding. In this regard, I propose an effective energy landscape that incorporates longitudinal (sliding) and transversal (folding) dynamics. I also study the influence of finite correlation length in the binding potential profile on the one-dimensional diffusion. The proposed mechanism has several important biological implications for search in the presence of other proteins and nucleosomes, simultaneous search by several proteins, etc.

(cont.) In Part II, I analyze the behavior of random walks in presence of smooth manifolds. First, I treat a random walk (or gaussian polymer) confined to a half-space using a field-theoretic approach. Using path integrals, I derive basic scaling relations and the probability distribution function for arbitrary coupling strength between the polymer and the manifold. Next, I consider self-avoiding polymers attached to the tip of an impenetrable probe. The scaling exponents [gamma] ₁ and [gamma]₂, characterizing the number of configurations for the attachment of the polymer by one end, or at its midpoint, are shown to vary continuously with the tip's angle. These apex exponents are calculated analytically by [epsilon]-expansion and compared to numerical simulations in three dimensions. I find that when the polymer can move through the attachment point, it typically slides to one end; the apex exponents quantify the entropic barrier to threading the eye of the probe.