Deterministic model of DNA gel electrophoresis in strong electric fields

We present a new model for the motion of a megabase-long DNA molecule undergoing gel electrophoresis. We assume that the dynamics of large segments of DNA is almost deterministic and can be described by a set of simple mechanical equations. This allows the numerical study of gel electrophoresis of ultra-high molecular weight DNA. A strong electric field forces DNA in a gel into a tree-like structure with branches-loops of different sizes. We determined the loop-size distribution function. This distribution has a power law form, confirming the hypothesis of the statistical self-similarity of a moving polymer. We find periodic configuration changes in the motion of a circular polymer, with the average period proportional to the molecular weight. During the period, a polymer goes through three distinct phases: a simple V-shape configuration, a growing tree, and a decaying tree. For a linear polymer this periodicity is much less pronounced because of additional perturbations to the dynamics caused by free ends. A circular polymer stays in a simple V-shaped configuration about 30% of the time, independent of molecular weight (10% for a linear polymer).