J. Phys. I France
Volume 1, Numéro 12, December 1991
Page(s) 1759 - 1784
DOI: 10.1051/jp1:1991239
J. Phys. I France 1 (1991) 1759-1784

Repton model of gel electrophoresis and diffusion

B. Widom, J. L. Viovy and A. D. Defontaines

Laboratoire de Physicochimie Théorique, ESPCI, 10 rue Vauquelin, F-75231 Paris Cedex 05, France

(Received 3 June 1991, revised 13 August, accepted 14 August)

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 $3^{N-1}\times 3^{N-1}$ matrix. For short chains exact results are obtained analytically: V/aw for all eE for $1\leqslant N \leqslant 4$, and D/a2w for $1\leqslant N \leqslant 5$. 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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