GEL-ELECTROPHORESIS AND DIFFUSION OF RING-SHAPED DNA

A model for the motion of ring-shaped DNA in a gel is introduced and s tudied by numerical simulations and a mean-field approximation. The ri ng motion is mediated by finger-shaped loops that move in an amoebalik e fashion around the gel obstructions. This constitutes an extension o f previous reptation tube treatments. It is shown that tension is esse ntial for describing the dynamics in the presence of loops. It is incl uded in the model as long-range interactions over stretched DNA region s. 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. T his 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 obtaine d, and quantities such as the average ring size are calculated. An app roximate treatment of the ring dynamics is given, and the diffusion co efficient is derived. The model is also discussed in the context of sp ontaneous symmetry breaking in one dimension.