LAKES-STRAITS MODEL OF FIELD-INVERSION GEL-ELECTROPHORESIS OF DNA

We replace the tube in the simple reptation model of the gel electrophoresis of DNA by a chain of open spaces, "lakes" connected by narrow "straits". We also allow loops of DNA to "overflow" out of the sides of the lakes under the pull of the electric field; a method of estimating the frequency of such overflows is developed based on Kramers' theory of diffusion over a barrier. We study this model under both steady-field and inverting-field conditions. With small fields it explicitly gives an improved form of the simple-reptation formula, distinguishing between the contour length of the chain of lakes and the contour length of the DNA chain within them. With higher fields it is necessary to use computer simulation to integrate the equations of motion. For long chains the results show a very pronounced antiresonance, that is, a minimum, in the dependence of mobility on cycle period with cyclically reversing fields, in semiquantitative agreement with recent experiments. The antiresonance arises from the development of conformations shaped like the Greek letter lambda, LAMBDA, with two arms both pulled in the direction of the field and high tension in the chain near the vertex. Under these conditions the chain moves very slowly, but when the field inverts the lambda appears as a V, and the high tension causes the chain to move rapidly toward the vertex. The antiresonance appears when the timing of the field cycle matches the time of lambda formation, so that the fast motion in the short, backward part of the cycle nearly cancels the slow motion in the long, forward part. The period of the antiresonance is proportional to the time needed for the chain to traverse its own length in steady field; the dimensionless proportionality constant appears to have a value of 0.4 +/- 0.1 both in our simulations and in experiments from the literature over a variety of conditions.