|M.Sc Student||Alexander Finkelstein|
|Subject||Statistical Physics of Homologous Recombination|
|Department||Department of Physics||Supervisor||Full Professor Kafri Yariv|
|Full Thesis text|
In this thesis we analyze an explicit model of random heteropolymer interaction, in order to address the problem of extended searchers, a paradigmatic example of which is the crucial cellular process of Homologous Recombination. The model incorporates specific monomer-monomer interactions as well as nonspecific attraction and cooperativity. We work in the framework of random walks on disordered energy landscapes widely applied in biophysical theory (e.g. to protein folding and binding) and introduce efficient probabilistic techniques facilitating the solution of the models in hand. In certain regions of the models' parameters spaces we find nontrivial scaling regimes and heavy tailed distributions of the search time. To model the extended searcher behavior, we construct a search landscape of a hierarchical structure, leading to dynamics of alternating global relocations by diffusion till non-specific attachment and local sequence comparison events by reversible, sequence-dependent and cooperative monomer binding. We relate the mean sequence comparison time to the partition function of a 1D Random Field Ising Model and compute it exactly using transfer matrix techniques. For RecA search application, we extend our model to address the effects of parallel search by segments of long searchers and the effects of the experimentally established searcher stretching.
We find that the condition for a fast search is that the energy slope on target is negative while the (random) slope on competitors is 'strongly-positive' - the mean has to be large in case of a strong disorder. Interestingly, a strongly cooperative binding, in the sense that after one monomer has managed to cross the energetic barrier for an initial binding the others follow more easily, is imperative for a fast heteropolymer search. We also find a nonmonotonic dependence of the search time on nonspecific attraction with the optimum residing on the boundary of reaction-limited and diffusion-limited regimes. We also improve on existing work regarding the effect of RecA-generated extension of the DNA searcher on the search efficiency; specifically, we claim that the stretching reduces only the diffusion time but not the sequence testing time. Thus, in a crowded environment, the search time is inversely proportional to the searcher length only if we assume that different searcher segments act independently. We discuss the effects of parallelism and argue that it helps to settle seeming discrepancies between different experimental results; we propose it as a partial solution for the long-standing puzzle of surprisingly fast homology recognition.