An exactly solvable Ogston model of gel electrophoresis VI. Towards a theory for macromolecules

In this article, we present a generalized version of our lattice model of low-field gel electrophoresis that allows us to treat the case of macromolecules such as short linear or circular oligomers and semi-flexible rods. We show that free-solution electrophoresis problems can be seen as random walks in the conformational space of the analyte. For sufficiently small molecules, our mathematical approach provides exact mobilities. In a quenched gel-like environment, however, both conformational and positional degrees of freedom must be used, but exact solutions can also be obtained. As an example, we then investigate several two-dimensional model gels, as well as a simple channel system where we see evidence of entropic effects that cannot be captured by the traditional Ogston concept of free volume.