Random walk models for DNA synapsis by resolvase.

During site-specific recombination by resolvase, the protein binds to two sites on a supercoiled DNA molecule and the loaded sites then interact with each other to form a synaptic complex. The kinetics of synapsis show non-exponential behaviour extending over five log units of time and are independent of the length of the DNA molecule and the length of DNA between the sites. In this study, numerical models were developed in order to account for how fluctuations in the structure of supercoiled DNA might lead to the juxtaposition of distant sites in a manner consistent with the experimental data on synapsis by resolvase. Models where the juxtaposition arises from fluctuations around branch points in the superhelix failed to match the data: they yielded non-exponential kinetics but only over two log units of time and they predicted longer synapsis times for both larger DNA molecules and larger inter-site spacings. In another model, one fraction of the juxtaposition events gives rise directly to the productive complex while the remaining fraction initially yields a non-productive complex: the latter molecules undergo no further fluctuations until the abortive synapse dissociates at the end of a delay period. This model again failed to match the experimental data. However, the inclusion of three sorts of non-productive complexes, each with a different delay constant, led to progress curves that concurred with the data. Schemes were also developed to account for the juxtaposition of three sites at a branch point in supercoiled DNA.