We present a model of DNA electrophoresis in unentangled polymer solutions based on a new separation mechanism in which the DNA drags along polymer molecules it encounters during migration. Taking into account the deformation and the hydrodynamic resistance of the polymers in the flow, the mutual disengagement time of the DNA and the polymer, and the average number of polymers dragged by one DNA, we build a self-consistent theory leading to predictions for the DNA velocity as a function of the experimental conditions. Our results agree with the data of Barron et al. (1994), and important separation regimes are also identified.

Although electrophoresis is one of the basic methods of the modern molecular biology laboratory, new ideas are being suggested at an accelerated rate, in large part because of the pressing demands of the biomedical community. Although we now have, at least for some methods, a fairly good theoretical understanding of the physical mechanisms that lead to the observed peak spacings, widths and shapes, this knowledge is often too qualitative to be used to guide further technical developments and improvements. In this article, we review some selected elements of the current state of our theoretical ignorance, focusing mostly on DNA electrophoresis, and we offer several suggestions for further theoretical investigations.

Electrophoretic separation of DNA molecules normally requires the use of an anticonvection, sieving polymer matrix such as a gel or an entangled polymer solution. Recently, it has been suggested that free-solution separation could be achieved in a capillary if an electrically neutral, friction-generating molecule is attached to the DNA molecules before electrophoresis is carried out. The electrophoretic mobilities are then predicted to be very large and the resulting separation is expected to yield excellent resolution. The size-dependence of the electrophoretic mobility is attributed to longer DNA molecules pulling the neutral molecule with a larger electric force, thus eluting earlier than shorter DNA molecules. In this article, we focus on the particular case where one attaches an uncharged, flexible polymer to the end of the DNA. Our self-consistent model takes into account the deformation and the hydrodynamic resistance of the polymer in the flow. We find various regimes, depending on the intensity of the electric field and the length of the polymer. The most favorable conditions for high-resolution separation of DNA are described.

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We generalize the reptation model to treat cases where the N segments of the primitive chain can interact with a static environment (such as a gel). The rates of tube segment renewal are calculated taking into account both an external field and local interaction energies. This model can be used, e.g., to study the migration of polymers in a random environments (where local entropic and elastic effects can play a role). We then present a study of polymer reptation in a tube with a random (annealed) energy landscape, similar to the one described by Lumpkin and Zimm. In particular, if an external field is applied, the predictions of the biased reptation model are modified. We find that for low field intensities, the electrophoretic mobility µ scales like 1/N 1+R where the exponent R g 0 increases with the strength of the random energies.