Gel electrophoresis of an end-labeled DNA I. Dynamics and trapping in constant fields

Abstract

A theory for the gel electrophoresis of a flexible polyelectrolyte, bearing an uncharged bulky label or an uncharged section at one end, is presented. We first consider a gel that is fully permeable to the label: we calculate the degree of stretching of the polyelectrolyte and its mobility as a function of chain size, electric field and label friction. Various regimes are identified, and their “existence domains” are calculated. For increasing friction, we predict a transition from a mobility decreasing with chain size to a mobility increasing with chain size. Secondly, we consider the possibility that the label may get trapped at some locations of the gel, a situation relevant to a method of “trapping electrophoresis” recently proposed by Ulanovsky et al. for DNA sequencing. A molecular model for detrapping by thermally activated “backward reptation” is constructed and solved using the Kramers rateequation theory. Different closed analytical expressions and approximate scaling laws corresponding to different regimes of stretching and field strengths are predicted. The most striking result is a mobility which exponentially decreases past a critical size N , which decreases with increasing field. In the regime relevant to the experiments by Ulanowsky et al., we predict N ∼ E^−2/3. The predictions are in good qualitative agreement with presently available experiments, but further experimental investigations are suggested.