An exactly solvable Ogston model of gel electrophoresis II. Sieving through periodic gels

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Abstract
Recently, we developed a lattice model to study the dynamics of particles being electrophoresed in gels (G. W. Slater, H. L. Guo, Electrophoresis 1995, 16, 11–15). In Part I of this series (G. W. Slater, H. L. Guo, Electrophoresis 1996, 17, 977–988), we showed how to calculate the exact electrophoretic mobility of one‐site particles in the limit where the electric field intensity E is vanishingly small. Since we can solve the model for arbitrary gel structures in two or more dimensions, we compared our results with those of the Ogston‐Morris‐Rodbard‐Chrambach model (OMRCM) of gel electrophoresis, which assumes that the mobility (μ) of charged particles is directly proportional to the fractional gel volume (f) that is available to them. Our results and theoretical analysis indicated that the OMRCM is a mean‐field approximation that can be useful as a rough guide; however, it generally misses the subtle sieving effects related to the correlations between the position of the obstacles in a given gel structure. In this paper (Part II) we study, for two‐dimensional periodic gels, the exact relationships between the zero‐field mobility μ and the gel concentration C for larger particle sizes. The fact that μ is a strong function of the particle size suggests that we can separate large particles using two‐dimensional periodic gels (similar to those fabricated by W. D. Volkmuth and R. H. Austin, Nature 1992, 358, 600–602). We analyze our data using Ferguson‐like plots and we show that one can indeed use a generalized retardation coefficient, K, to estimate the effective pore size, aK and effective fiber size rK for these model gels. We conclude that the retardation coefficient is a useful concept to characterize a sieving structure even though it does not permit the inference of the exact gel structure.