GEOMETRY AND PHYSICS OF CATENANES APPLIED TO THE STUDY OF DNA-REPLICATION

The concept of ideal geometric configurations was recently applied to the classification and characterization of various knots. Different kn ots in their ideal form (i.e., the one requiring the shortest length o f a constant-diameter tube to form a given knot) were shown to have an overall compactness proportional to the time-averaged compactness of thermally agitated knotted polymers forming corresponding knots. This was useful for predicting the relative speed of electrophoretic migrat ion of different DNA knots. Here we characterize the ideal geometric c onfigurations of catenanes (called links by mathematicians), i.e., clo sed curves in space that are topologically linked to each other. We de monstrate that the ideal configurations of different catenanes show in terrelations very similar to those observed in the ideal configuration s of knots. By analyzing literature data on electrophoretic separation s of the torus-type of DNA catenanes with increasing complexity, we ob served that their electrophoretic migration is roughly proportional to the overall compactness of ideal representations of the corresponding catenanes. This correlation does not apply, however, to electrophoret ic migration of certain replication intermediates, believed up to now to represent the simplest torus-type catenanes. We propose, therefore, that freshly replicated circular DNA molecules, in addition to formin g regular catenanes, may also form hemicatenanes.