Gel electrophoresis and diffusion of ring-shaped DNA

A model for the motion of ring-shaped DNA in a gel is introduced and studied by numerical simulations and a mean-field approximation. The ring motion is mediated by finger-shaped loops that move in an amoebalike fashion around the gel obstructions. This constitutes an extension of previous reptation tube treatments. It is shown that tension is essential for describing the dynamics in the presence of loops. It is included in the model as long-range interactions over stretched DNA regions. The mobility of ring-shaped DNA is found to saturate much as in the well-studied case of linear DNA. Experiments in agarose gels, however, show that the mobility drops exponentially with the DNA ring size. This is commonly attributed to dangling ends in the gel that can impale the ring. The predictions of the present model are expected to apply to artificial two-dimensional obstacle arrays [W. D. Volkmuth and R. H. Austin, Nature 358, 600 (1992)] which have no dangling ends. In the zero-field case an exact solution of the model steady state is obtained, and quantities such as the average ring size are calculated. An approximate treatment of the ring dynamics is given, and the diffusion coefficient is derived. The model is also discussed in the context of spontaneous symmetry breaking in one dimension.