Using a modeling methodology developed in our laboratory previously, the free solution electrophoretic mobilities of several peptides are examined to see what they can tell us about: (i) the pK(a)s of specific side groups, and (ii) possible secondary structure. Modeling is first applied to mobility versus pH data of several small peptides (Messana, I. et al., J. Chromatogr. B 1997, 699, 149) where the only adjustable parameter associated with the charge state of the peptide is the pK(a )of the C-terminal. In addition to examining this parameter, the question of possible secondary structure is addressed. For two of the peptides considered, GGNA and GGQA, it is possible to account for the observed mobilities using "random" models with little restriction on the allowed range of Phi-Psi angles. For GGRA and RPPGF, "compact" models (possibly involving an I-turn) must be used to match modeling mobilities with experiment. Finally, three more complicated peptides ranging in size from 15 to 20 amino acids are also examined and characterized (Sitaram, B. R. et al., J. Chromatogr. A 1999, 857, 263). Here also, we find evidence of I-turns or some other "compact" structure in two of the three peptides examined.

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The electrophoretic mobility of low molecular mass oligoglycines is examined in this study using a "coarse-grained" bead modeling methodology [Pei, H., Allison, S. A., J. Chromatogr. A 2009, 1216, 1908-1916]. The advantage of focusing on these peptides is that their charge state is well known [Plasson, R., Cottet, H., Anal. Chem. 2006, 78, 5394-5402] and extensive electrophoretic mobility data are also available in different buffers [Survay, M. A., Goodall, D. M., Wren, S. A. C., Rowe, R. C., J. Chromatogr. A 1996, 741, 99-113] and over a broad range of temperatures [Plasson, R., Cottet, H., Anal Chem. 2005, 77, 6047-6054]. Except for assumptions about peptide secondary structure, the B model has no adjustable parameters. It is concluded that the oligoglycines adopt a random configuration at high temperature (50 degrees C and higher), but more compact conformations at lower temperature. It is proposed that triglycine through pentaglycine adopt compact cyclic structures at low temperature (up to about 25 degrees C) in aqueous solution. At 25 degrees C, buffer interactions are also examined and may or may not influence peptide conformation depending on the buffer species. In a borate buffer at high pH, the mobility data are consistent with complex formation between the oligoglycine and borate anion.

There are three objectives to the present work. First, starting from a boundary element (BE) formulation of low Reynolds number hydrodynamics, model the translational diffusion of macromolecules modeled as an array of non-overlapping beads, and show how this approach is equivalent to previous formulations of "bead hydrodynamics" and under what conditions. Second, show how this approach can be improved upon by accounting for the variation in forces over the surfaces of individual beads and also extending the approach to a gel modeled as an effective medium, EM. Third, develop a "combined obstruction and hydrodynamic effect" model of the translational diffusion of irregularly shaped macromolecules in a gel. In one of the cases studied, the BE approach is shown to be equivalent to previous "bead model" formulations in which intersubunit hydrodynamic interaction is modeled using the Rotne-Prager tensor. A bead model that accounts for the variation in hydrodynamic stress forces over the individual bead surfaces is shown to be in best agreement with exact results for simple bead arrays made up of 2-4 subunits. The translational diffusion of rods, modeled as strings of from 2 to 100 touching beads in dilute gels is examined. Interpolation formulas valid over a range of gel concentrations and rod lengths are derived for the parallel and perpendicular components of the diffusion tensor as well as the orientationally averaged diffusion tensor. The EM model accounts for the long-range hydrodynamic interaction exerted by the gel support matrix on the diffusing particle of interest but does not account for the reduction in diffusion caused by the direct obstruction of the gel, or steric effect. Both effects are accounted for by writing the translational diffusion in a gel as the product of two terms representing long-range hydrodynamic interaction and steric effects. Finally, the diffusion of a 564 base pair DNA in a 2% agarose gel is examined and model results are compared to experiment (Pluen, A.; Netti, P. A.; Jain, R. K.; Berk, D. A. Biophys. J. 1999, 77, 542-552). For reasonable choices of model parameters, fair agreement between theory and experiment is achieved.

The ionic strength dependence of the electrophoretic mobility of small organic anions with valencies up to -3 is investigated in this study. Provided the anions are not too aspherical, it is argued that shape and charge distribution have little influence on mobility. To a good approximation, the electrophoretic mobility of a small particle should be equal to that of a model sphere with the same hydrodynamic radius and same net charge. For small ions, the relaxation effect (distortion of the ion atmosphere from equilibrium due to external electric and flow fields) is significant even for monovalent ions. Alternative procedures of accounting for the relaxation effect are examined. In order to account for the ionic strength dependence of a specific set of nonaromatic and aromatic anions in aqueous solution, it is necessary to include complex formation between the anion with species in the BGE. A number of possible complexes are considered. When the BGE is Tris-acetate, the most important of these involves the complex formed between anion and Tris, the principle cation in the BGE. When the BGE is sodium borate, an anion-anion (borate) complex appears to be important, at least when the organic anion is monovalent. An algorithm is developed to analyze the ionic strength dependence of the electrophoretic mobility. This algorithm is applied to two sets of organic anions from two independent research groups.

Free solution and gel electrophoresis is an extremely useful tool in the separation of biopolymers. The complex nature of biopolymers, coupled with the usefulness of electrophoretic methods, has stimulated the development of theoretical modeling over the last 30 years. In this work, these developments are first reviewed with emphasis on Boundary Element and bead methodologies that enable the investigator to design realistic models of biopolymers. In the present work, the bead methodology is generalized to include the presence of a gel through the Effective Medium model. The biopolymer is represented as a bead array. A peptide, for example, made up of N amino acids is modeled as 2N beads. Duplex DNA is modeled as a discrete wormlike chain consisting of touching beads. The technical details of the method are placed in three Appendices. To illustrate the accuracy and effectiveness of the approach, two applications are considered. Model studies on both the free solution mobility of 73 peptides ranging in size from 2 to 42 amino acids, and the mobility of short duplex DNA in dilute agarose gels are discussed.