Sedimentation and electrophoretic migration of DNA knots and catenanes

Various site-specific recombination enzymes produce different types of knots or catenanes while acting on circular DNA in vitro and in vivo. By analysing the types of knots or links produced, it is possible to reconstruct the order of events during the reaction and to deduce the molecular "architecture" of the complexes that different enzymes form with DNA. Until recently it was necessary to use laborious electron microscopy methods to identify the types of knots or catenanes that migrate in different bands on the agarose gels used to analyse the products of the reaction. We reported recently that electrophoretic migration of different knots and catenanes formed on the same size DNA molecules is simply related to the average crossing number of the ideal representations of the corresponding knots and catenanes. Here we explain this relation by demonstrating that the expected sedimentation coefficient of randomly fluctuating knotted or catenated DNA molecules in solution shows approximately linear correlation with the average crossing number of ideal configurations of the corresponding knots or catenanes.