The principal aim of this work is the proper interpretation of electrophoresis as an important tool for determining the immediate ionic environment of polyelectrolyte molecules like DNA. We also explore the relation with other experiments. We define an electrostatic model of double-stranded DNA in monovalent salt solutions. The electrical double layer is divided in an inner Stern layer, inside the surface of hydrodynamic shear of DNA, and a Gouy-Chapman type diffuse ionic atmosphere with cylindrical symmetry outside the shear surface. We discuss the assumptions made in applying to DNA the charge-potential relation and the electrical free-energy expression of the charged cylinder with a Gouy double layer. The conclusion is that reliable free-energy data, better than 1kT per phosphate group, require a detailed model of the Stern layer. On the other hand, the Gouy model of a charged cylinder should be fairly good for the interpretation of the electrophoretic mobility of DNA. We introduce several modifications of the linear electrophoresis theory of the cylinder (Henry-Gorin), related to the averaging over the orientations of DNA in the external electrical field, the relaxation effect, the nonlinear charge-potential relation, and to geometrical aspects of the DNA model. Applied to published mobility data the modified theory yields roughly the same ζ potentials as before, but DNA charges which are about twice as high as derived earlier from the linear Henry-Gorin theory. The charge calculation is quite sensitive to the assumed geometrical model of DNA. Our electrophoresis results are somewhat higher than the charges derived from Donnan equilibria of DNA in monovalent salt solutions measured by Strauss et al. The required self-consistency of electrophoretic charge and ζ potential of DNA as a function of the salt concentration is treated on the basis of adsorption of counterions to the DNA phosphate groups (site binding). It is predicted that at low ionic strength the electrophoretic charge of DNA should be independent of the salt concentration.

Electrical double layer, zeta potential, and electrophoretic charge of double-stranded DNA

Some progress has been made in the development of a satisfactory theory for the electrophoresis of proteins including the correlation of mobilities with their other physical properties. Thus Abramsonl has shown that in the region near the isoelectric point a proportionality exists between the mobility of the protein, as measured with the aid of the micro-cataphoretic method, and the amount of hydrogen ion bound to it as determined from the titration curve. To establish this proportionality he plots the pH as the abscissa for both the titration and mobility curves and shifts the former vertically until the acid bound by the protein is zero a t the isoelectric point, i. e., the pH a t which the mobility is zero. The scale of ordinates for the mobilitics is then selected to bring another point on this curve into coincidence with the titration curve and if the two curves then superpose, the proportionality is established. In most of the cases studied by Abramson and his collaborators the comparison has been made over a rather narrow pH interval in which the titration and mobility curves are approximately linear. It seemed desirable to extend the comparison over the entire pH-stability range of a typical protein the titration curve of which exhibits some characteristic feature that one might expect to be reproduced in the mobility curve. Ovalbumin is well adapted for this comparison since i t has a wide stability range, pH 2.6-12.0 a t 0' C., and has a characteristic plateau in its titration curve from pH 7.0 to 10.0. It is one of the purposes of this paper to report mobility measurements on ovalbumin over the pH interval from 1.8 to 12.8 and to compare these results with titration data on the same protein, The results have been interpreted with the aid of the DebyeHiickel-Henry theory. One of the uncertainties in the computations with this theory, i. e., the friction coefficient of the protein, has been eliminated with the aid of diffusion measurements on ovalbumin over the same pH range and these results are also reported here. The

THE INFLUENCE OF pH ON THE MOBILITY AND DIFFUSION OF OVALBUMIN

Electrophoretic mobility modeling of proteins in free zone capillary electrophoresis and its application to monoclonal antibody microheterogeneity analysis

The free zone electrophoretic mobility of proteins can be predicted from the protein's amino acid content by applying a model based on the Debye-Huckle-Henry theory and Henderson-Hasselbalch equation. Calculated mobilities are always greater than actual mobility but a pH-independent proportionality (described by the constant FZ) is found between the two. Thus, determination of a protein's mobility at one pH allows, with the use of the model and FZ, calculation of its mobility at other pH conditions. This leads directly to optimum conditions for the electrophoretic resolution of proteins in capillary zone electrophoresis. The fundamental nature of FZ is examined and found to be a function of a proteins molecular weight, charge, and solution ionic strength. This work aids in explaining the form of previously proposed empirically based equations for peptide and protein mobility.

H.A . Abramson

Papers

The Polar Groups of Protein and Amino Acid Surfaces in Liquids.