Diffusion constant for the repton model of gel electrophoresis

TL;DR

This paper maps the repton model of gel electrophoresis to a particle system, enabling efficient simulations and exact calculations of the diffusion constant for small systems, confirming previous scaling hypotheses.

Contribution

It introduces a particle-based mapping of the repton model, facilitating larger simulations and exact solutions for diffusion constants in small systems.

Findings

Confirmed scaling hypotheses for the repton model

Developed an efficient Monte Carlo algorithm for larger systems

Derived exact diffusion constants for systems up to 20 reptons

Abstract

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 simulate 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.