Experiments indicate that unbinding rates of proteins from DNA can depend on the concentration of proteins in nearby solution. Here we present a theory of multi-step replacement of DNA-bound proteins by solution-phase proteins. For four different kinetic scenarios we calculate the depen- dence of protein unbinding and replacement rates on solution protein concentration. We find (1) strong effects of progressive rezipping of the solution-phase protein onto DNA sites liberated by unzipping of the originally bound protein; (2) that a model in which solution-phase proteins bind non-specifically to DNA can describe experiments on exchanges between the non specific DNA- binding proteins Fis-Fis and Fis-HU; (3) that a binding specific model describes experiments on the exchange of CueR proteins on specific binding sites.
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