Gel mobilities of linking-number topoisomers and their dependence on DNA helical repeat and elasticity

Agarose-gel electrophoresis has been used for more than thirty years to characterize the linking-number (Lk) distribution of closed-circular DNA molecules. Although the physical basis of this technique remains poorly understood, the gel-electrophoretic behavior of covalently closed DNAs has been used to determine the local unwinding of DNA by proteins and small-molecule ligands, characterize supercoiling-dependent conformational transitions in duplex DNA, and to measure helical-repeat changes due to shifts in temperature and ionic strength. Those results have been analyzed by assuming that the absolute mobility of a particular topoisomer is mainly a function of the integral number of superhelical turns, and thus a slowly varying function of plasmid molecular weight. In examining the mobilities of Lk topoisomers for a series of plasmids that differ incrementally in size over more than one helical turn, we found that the size-dependent agarose-gel mobility of individual topoisomers with identical values of Lk (but different values of the excess linking number, DeltaLk) vary dramatically over a duplex turn. Our results suggest that a simple semi-empirical relationship holds between the electrophoretic mobility of linking-number topoisomers and their average writhe in solution.