Brownian Dynamics Studies on DNA Gel Electrophoresis. I. Numerical Method and Quasi-Periodic Behavior of Elongation-Contraction Motions

Dynamics of individual DNA undergoing constant field gel electrophoresis (CFGE) is studied by a Brownian dynamics (BD) simulation method which we have developed. The method simulates electrophoresis of DNA in a 3 dimensional (3D) space by a chain of electrolyte beads of hard spheres. Under the constraint that the separation of each pair of bonded beads is restricted to be less than a certain fixed value, as well as with the excluded volume effect, the Langevin equation of motion for the beads is solved by means of the Lagrangian multiplier method. The resultant mobilities, $\mu$, as a function of the 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 quasi-periodic behavior is found in the chain dynamics, and is examined through the time evolution of the radius of the longer principal axis, $R_l(t)$. It is found that the mean width of a peak in $R_l(t)$, 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 proportional to $M^0$ 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 $\mu \propto M^0$. This explains why CFGE cannot separate DNA according to their size $L (\propto M)$ for large $L$.