An exactly solvable Ogston model of gel electrophoresis: VIII. Nonconducting gel fibers, curved field lines, and the Nernst-Einstein relation

Abstract

In this article, we examine the low-field electrophoretic migration of infinitely small analytes in dilute sieving media made of nonconducting gel fibers. Using an Ogston obstruction model, we show that the electrophoretic mobility is not affected by the presence of curved field lines. In other words, the Nernst-Einstein relation between the mobility and the diffusion coefficient is valid regardless of the electrical properties of the gel fibers. Although this finding may greatly simplify the development of obstruction models of electrophoretic sieving, it also represents a critical test for any analytical or computational approach.

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

“…Over the last decade, our group [47,72,[149][150][151][152][153][154] has developed a numerically exact calculation technique for the mobility m and the diffusion coefficient D (which are essentially the same in the zero field limit, see Section 14) of small analytes evolving on a lattice in the presence of immobile obstacles. In a recent paper [72], we presented an extension of our model that used the BFM to treat the case of macromolecules.…”

“…The fact that separation does occur experimentally can be attributed to various factors (such as partly conducting obstacles or the deformation of the macromolecules), but this example illustrates that a realistic representation of the field lines can become crucial in the interpretation of experimental results. On the other hand, the curvature of the field lines around obstacles does not always affect the dynamics; indeed, our group has shown that in general, in the zero-field limit, the electrophoretic mobility and the diffusion coefficient of a point-particle is independent of both the field lines curvature and the obstacle shape [47].…”

“…(16) that our group has, over the last several years, developed a new lattice model of gel electrophoresis [47,72,[149][150][151][152][153][154]. Although very simple, the model has the advantage that both the scaled mobility m* and the available volume f can be calculated exactly and independently; therefore, it provides a straightforward way to test Eq.…”

“…It was suggested by Locke and Trinh [143] that this assumption of uniform field lines, even near the fibers, is the reason why our results disagree with the Ogston hypothesis. This suggestion was tested by Slater et al in a recent paper [47] in which they extended their model to take into account the curvature of the field lines around nonconducting gel fibers. Their results showed that the dependence of the mobility of a point-like particle upon the concentration of the gel is not affected by the field line distortions in the low field intensity limit.…”

Electrokinetic transport of DNA in nanoslits

“…There are a number of phenomena missing in the ORMC model, such as the role of gel disorder, percolating pathways and dead-ends. Slater and co-workers [91][92][93][94][95][96][97][98][99][100] have called into question the fundamental validity of the ORMC model for describing gel electrophoresis in the limit R g < b.…”