A model of the motion of a long DNA chain in a pulsed electric field

We suggest here a model of the motion of a charged polymer chain in a pulsed electric field. The model takes into account the elastic “entropic” force of chain stretching during the process of the pulsed electrophoresis of large DNA fragments. Using a statistical approach, an equation is obtained for a chain of freely jointed links. This equation connects the internal stress and the density of the length of a chain in a gel pore and should be considered as the thermodynamic equation of state for a chain segment in a pore. The equilibrium of the electric forces, the gradient of the elastic forces, and the friction forces acting on the chain segment that occupies a gel pore are described by a nonlinear equation of the diffusion type. Hernias play a special role in the chain motion. Their competitive behavior permits an explanation of the noticeable orientation of the chains in the field direction observed even in rather weak fields. As extensive numerical calculations have shown, the deep minimum of the drift velocity (“antiresonance”) in periodic fields can be obtained only when one takes into account the interaction of herniated chain segments with one another in the gel pores that they occupy. The model permits a quantitative description of such anomalies as antiresonance and band inversion of the DNA chain mobility in periodic electric fields.