Repton model of gel electrophoresis in the long chain limit

TL;DR

This paper models the movement of long polymers in gel electrophoresis using reptation theory, linking stored length diffusion to polymer conformation and deriving velocity dependence on end-to-end separation.

Contribution

It establishes a relation between stored length diffusion rate and the confining tube conformation, providing a scaling limit analysis for long polymers under weak electric fields.

Findings

Drift velocity depends on end-to-end separation in the field direction.

In the scaling limit, tube length and stored length density are unaffected by weak fields.

The model connects polymer conformation to electrophoretic mobility.

Abstract

Reptation governs motion of long polymers through a confining environment. Slack enters at the ends and diffuses along the polymer as stored length. The rate at which stored length diffuses limits the speed at which the chain can drift. This paper relates the rate of stored length diffusion to the conformation of the tube within which the polymer is confined. In the scaling limit of long polymer chains and weak applied electric fields, holding the product of polymer length times field finite, the tube length and stored length density take on their zero-field values. The drift velocity then depends only on the the polymer's end-to-end separation in the direction of the field.