An exactly solvable Ogston model of gel electrophoresis: I. The role of the symmetry and randomness of the gel structure.

The Ogston-Morris-Rodbard-Chrambach model (OMRCM) of gel electrophoresis assumes that the mobility (mu) of charged particles is directly proportional to the fractional volume (f) of the gel that is available to them. Many authors have studied the fractional volume f in detail for various particle shapes, but the original assumption, that mu sf, has not been scrutinized seriously. In fact, this geometrical model of electrophoresis does not take into account the connectivity of the gel pores or the precise gel architecture. Recently (G. W. Slater and H. L. Guo, Electrophoresis 1995, 16, 11-15) we developed a Monte Carlo computer simulation algorithm to study the electrophoretic motion of simple particles in gels in the presence of fields of arbitrary strength. Our preliminary results indicated that the mobility and the fractional volume were not generally proportional to one another. In this article, we show how to calculate, in the limit where the field intensity is vanishingly small, the exact electrophoretic mobility of particles in any type of gel in two or more dimensions. Our results, presented here for some simple two-dimensional systems, indicate that a particle can have different electrophoretic mobilities in gels in which it has access to the same fractional available volume f. The curvature of the Ferguson plot is shown to be related to the symmetry and the degree of randomness that characterize the gel. We also demonstrate that the OMRCM is, in fact, a mean field approximation that corresponds to a uniform, annealed gel. We thus conclude that the relation between the electrophoretic mobility and the gel concentration (C) is a delicate function of the gel architecture, and that one needs more than the fractional volume f to fully characterize the transport properties of migrating particles in separation media. Exact relationships between the mobility mu and the gel concentration C are given for our model gels.