Ogston gel electrophoretic sieving: how is the fractional volume available to a particle related to its mobility and diffusion coefficient(s)?

The Ogston-Morris-Rodbard-Chrambach model (OMRCM) of gel electrophoresis assumes that the mobility mu of charged particles is proportional to the fractional volume (f) of the gel that is available to them. If the gel is random, as described by Ogston, the (semi-log) Ferguson plot is the method of choice for analyzing experimental data since it permits an estimate of the gel's mean pore size to be made. However, the Ferguson plot is rarely linear; this is usually "explained" by the deformation of the anisotropy of the particle, the nonrandom or variable architecture or the gel, or the onset of some other migration mechanism. Many authors have refined this model, but the original assumption that mu varied; is directly proportional to f has not been seriously examined. Also, the model says nothing of the effect of the field intensity, the connectivity of the gel pores, nor anything about the diffusion coefficient. We have developed a Monte-Carlo computer simulation algorithm to study the electrophoretic sieving of simple particles in gels. In this brief communication, we report important preliminary results which indicate that the basic assumptions of the OMRCM are wrong. We use a two-dimensional periodic gel since the OMRCM becomes trivial in this case. Our results show that the relationship between f and mu is not the one assumed by the OMRCM. Moreover, we find that the Einstein relation between the diffusion coefficient and the mobility is not valid. This is due to the fact that the particles do not have a uniform probability of visiting the various sites that are available to them. We thus conclude that the Ferguson plot is intrinsically nonlinear; the curvature of the plot is, in fact, related to the intensity of the electric field as well as to the degree of randomness of the gel fibers.