Brownian dynamics studies on DNA gel electrophoresis. I. Numerical method and “periodic” behavior of elongation-contraction motions

Abstract

The dynamics of a DNA molecule which is undergoing constant field gel electrophoresis (CFGE) is studied by a Brownian dynamics simulation method we have developed. In the method a DNA molecule is modeled as a chain of spherical electrolyte beads and the gel as a three-dimensional array of immobile beads. With the constraint for the separation of each pair of bonded beads to be less than a certain fixed value, as well as with the excluded volume effect, the simultaneous Langevin equations of motion for the beads are solved by means of the Lagrangian multiplier method. The resultant mobilities μ as a function of electric field coincide satisfactorily with the corresponding experimental results, once the time, the length, and the field of the simulation are properly scaled. In relatively strong fields “periodic” behavior is found in the chain dynamics and is examined through the time evolution of the radius of the longer principal axis, Rl(t). It is found that the mean width of a peak in Rl(t), or a period of one elongation-contraction process of the chain, is proportional to the number of beads in the chain, M, while the mean period between two such adjacent peaks is independent of M for large M. These results, combined with the observation that the chain moves to the field direction by the distance proportional to M in each elongation-contraction motion, yield the saturation of mobility for large M. This explains the reason that CFGE cannot separate DNA according to their size L(∝M) for large L.