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

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 rate-equation 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 Np*, which decreases with increasing field. In the regime relevant to the experiments by Ulanowsky et al., we predict Np* approximately E-2/3. The predictions are in good qualitative agreement with presently available experiments, but further experimental investigations are suggested.