Slater G W, Guo H L
Department of Physics, University of Ottawa, Ontario, Canada. gary@ physics.uottawa.ca
Electrophoresis. 1996 Jun;17(6):977-88. doi: 10.1002/elps.1150170604.
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.
凝胶电泳的奥格斯顿 - 莫里斯 - 罗德巴德 - 钱布巴赫模型（OMRCM）假定带电粒子的迁移率（μ）与凝胶中可供其使用的分数体积（f）成正比。许多作者针对各种粒子形状详细研究了分数体积f，但最初的假设，即μ ∝ f，尚未得到认真审视。实际上，这种电泳几何模型并未考虑凝胶孔的连通性或精确的凝胶结构。最近（G.W. 斯莱特和H.L. 郭，《电泳》，1995年，16卷，11 - 15页）我们开发了一种蒙特卡罗计算机模拟算法，用于研究在任意强度电场存在下简单粒子在凝胶中的电泳运动。我们的初步结果表明迁移率和分数体积通常并非彼此成正比。在本文中，我们展示了如何在电场强度趋近于零的极限情况下，计算二维或更多维中任何类型凝胶中粒子的精确电泳迁移率。我们在此针对一些简单二维系统给出的结果表明，粒子在可获得相同分数可用体积f的凝胶中可具有不同的电泳迁移率。弗格森图的曲率显示与表征凝胶的对称性和随机程度有关。我们还证明，实际上OMRCM是一种对应于均匀、退火凝胶的平均场近似。因此我们得出结论，电泳迁移率与凝胶浓度（C）之间的关系是凝胶结构的精细函数，并且要全面表征分离介质中迁移粒子的传输特性，所需的不仅仅是分数体积f。我们给出了模型凝胶中迁移率μ与凝胶浓度C之间的精确关系。
