| Abstract: | Much theoretical work was recently devoted to the modelling of biophysical search processes, such as proteins looking for binding sites on DNA. Another scenario is an "extended searcher" - a piece of heteropolymer looking for a piece of similar sequence among a large heterologous substrate. This happens e.g. in the recognition phase of homologous recombination, a crucial cellular process. Describing the process in terms of cooperative reversible binding of individual monomers of different types, we formulate a general stochastic model which is exactly solvable by an analogy to a random-field 1D Ising model. The results include some nontrivial consequences of the disorder inherent in the problem. The search speed dependence on electrostatic and cooperative interactions is non-monotonic, putting our model in context of the recently proposed paradigm of 'intermittent search'. Extending our model to include effects of searcher stretching, we refine the conclusions of recent authors on the 'geometrical speed-up' mechanism. Finally, we discuss the application of our model to interpretation of experimental data.
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