Diffusion Constant for the Repton Model of Gel Electrophoresis

The repton model is a simple model of the “reptation” motion by which DNA diffuses through a gel during electrophoresis. In this paper we show that the model can be mapped onto a system consisting of two types of particles with hard-sphere interactions diffusing on a one-dimensional lattice. Using this mapping we formulate an efficient Monte Carlo algorithm for the model which allows us to stimulate systems more than twice the size of those studied before. Our results confirm scaling hypotheses which have previously been put forward for the model. We also show how the particle version of the model can be used to construct a transfer matrix which allows us to solve exactly for the diffusion constant of small repton systems. We give results for systems of up to 20 reptons.