Asymmetric random walk in a reaction intermediate of homologous recombination

At an intermediate step of the homologous recombination between two double-stranded DNA molecules, a point (often called Holliday structure) connecting two strands coming from two recombining partners migrates along the homologous region. Assuming random walk of a connecting point, we previously explained the dependence of recombination frequency on the homology length observed in vivo. In this model, the random walk was assumed to be symmetric in that the forward transition rate equals the backward one. According to observations in vitro, however, catalysed migration appears unidirectional. Taking into account possible asymmetry, we thus reformulate our random walk model to reexamine the observations in vivo. We also derive some theoretical results to analyse dynamic processes observed in vitro.