ИСТИНА

Problems of search and recognition appear over different scales in biological systems. These range from molecular recognition in biochemical reactions to searches for food by higher organisms. In this thesis we concentrate on a few aspects of this problem. The thesis considers several different issues. First, we study a model for a protein using facilitated diffusion. The model includes three distinct pathways for facilitated diffusion: (a) sliding - in which the protein diffuses along the contour of the DNA (b) jumping - where the protein travels between two sites along the DNA by three-dimensional diffusion, and finally (c) intersegmental transfer - which allows the protein to move from one site to another by transiently binding both at the same time. The typical search time is calculated using scaling arguments which are verified numerically. Our results suggest that the inclusion of intersegmental transfer (i) decreases the search time considerably (ii) makes the search time much more robust to variations in the parameters of the model and (iii) that the optimal search time occurs in a regime very different than that found for models which ignore intersegmental transfers. The behavior we find is rich and shows surprising dependencies, for example, on the DNA length. Next, we focus on the challenges posed by interactions between the transcription factor and different DNA sites. Equilibrium experiments show that regulatory proteins bind tightly to their target site. However, they also find strong binding to other non-specific sites which act as traps that can dramatically increase the time needed to locate the target. This gives rise to a conflict between the speed and stability requirements. Here we suggest a simple mechanism which can resolve this long-standing paradox by allowing the target sites to be located by proteins within short time scales even in the presence of traps. Our theoretical analysis shows that the mechanism is robust in the presence of generic disorder in the DNA sequence and does not require a specially designed target site. We show that using this mechanism interesting non-equilibrium effects appear. Finally, motivated by the problem of the extended searchers (e.g. homologous recombination process), we present an analytical approximation scheme for the first passage time distribution on a finite interval of a random walker on a random forcing energy landscape. The approximation scheme captures the behavior of the distribution over all timescales in the problem. The results are carefully checked against numerical simulations.