Repton model of gel electrophoresis and diffusion

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Abstract
We analyse the repton model of Rubinstein as adapted by Duke as a model for the gel electrophoresis of DNA. Parameters in the model are the number N of reptons in the chain, a length a, a microscopic transition frequency w, and the product eE of the electric field E (assumed constant) and the charge e per repton. Formally exact formulas are derived for the dimensionless diffusion coefficient D/a2w and drift velocity V/aw, the latter as a function of the field. Calculation of V/aw requires the eigenvector associated with the leading eigenvalue of a 3N-1×3N-1 matrix. For short chains exact results are obtained analytically: V/aw for all eE for 1≤N ≤4, and D/a2w for 1≤N ≤5. For large N we deduce that D/a2w vanishes proportionally to 1/N2, the standard de Gennes reptation result, but we have not evaluated the coefficient analytically. We have determined D/a2w for N up to 150 by simulation and verified the 1/N2 law

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