A study of electrophoretic mobility of DNA in agarose and polyacrylamide gels

The aim of this paper is to clarify the mechanism of gel electrophoresis of DNA under constant-field conditions. We have conducted a large number of experiments on double-stranded DNA varying in length between approximately 10 and approximately 50,000 base-pairs, in both agarose and polyacrylamide gels ranging from 0.5% to 12% concentration, and with electric field strengths ranging from 0.5 to 8 V/cm. We have made (logarithmic) plots of velocity against length of DNA for all of the various test conditions. At the left-hand side of these plots, all of the empirical curves have a unique, standard shape. When the curves are normalized so that their left-hand parts coincide, a second feature emerges in that, while for any given test the curve follows the "master curve" up to a certain point, it then "breaks away" and becomes horizontal. We describe these two patterns of behaviour as "regions 1 and 2", respectively. We find simple yet comprehensive empirical formulae that fit the observations in the two regions of behaviour: these express the velocity in terms of length of DNA, electric field strength and gel concentration. We then construct two separate theories for the two regions of behaviour. The first theory involves the statistics of motion of an object through a random array of gel obstacles, with the instantaneous speed depending on the number of obstacles with which the object is currently in contact. The second theory is based on the mechanical hypothesis (for which there is other, independent support) that the DNA moves through the gel by piling up against a barrier, which eventually breaks or deforms under the resulting force, thereby allowing the DNA to move on to the next barrier. The statistical theory is an adaptation of existing work, while the mechanical one is new. We also describe experiments on the migration of repeated-sequence, curved DNA with length up to 1500 base-pairs, and we discuss its behaviour in terms of our two theories. Our studies by electron microscopy are consistent with the view that this repeated-sequence DNA adopts a superhelical configuration. Finally, we show that a very wide range of observations may be understood clearly by means of our two theoretical schemes.