Electrophoresis of Protein Charge Ladders: A Comparison of Experiment with Various Continuum Primitive Models Stuart A. Allison,* ,² Jeffrey D. Carbeck, ‡ Chuanying Chen, ²,§ and Felicia Burkes ² Department of Chemistry, Georgia State UniVersity, Atlanta, Georgia 30303, and Department of Chemical Engineering, Princeton UniVersity, Room A319, E-Quad, Princeton, New Jersey 08540 ReceiVed: October 31, 2003; In Final Form: January 19, 2004 Detailed modeling of the free solution electrophoresis of five proteins (bovine R-lactalbumin, hen egg white lysozyme, bovine superoxide dismutase, human carbonic anhydrase II, and hen ovalbumin) is carried out within the framework of the continuum primitive model. Protein crystal structures and translational diffusion constants are used to design and parametrize the models. The modeling results are compared with experimental mobilities of protein charge ladders, collections of protein derivatives where the number of charge groups is varied by partial acylation of lysine residues or by amidation of glutamic and aspartic acid residues. The simplest model considered is the Yoon and Kim model of a prolate/oblate ellipsoid with uniform surface potential, electrostatics treated at the level of the linear Poisson-Boltzmann equation, and distortion of the ion atmosphere from equilibrium (ion relaxation) ignored (Yoon, B. J.; Kim, S. J. Colloid Interface Sci. 1989, 128, 275). This model provides good agreement with experiment but only if the net absolute protein charge is low or the average absolute surface, or , potential is less than ∼25 mV. Boundary element (BE) modeling is also carried out in which detailed surface models are employed and the electrostatics are solved at the level of the nonlinear Poisson-Boltzmann equation. Ion relaxation is also included in some of the BE studies. All of the experimental mobilities are in good (human carbonic anhydrase II and hen ovalbumin) to excellent (bovine R-lactalbumin, hen egg white lysozyme, and bovine superoxide dismutase) agreement with BE modeling that includes ion relaxation. We believe that these results taken as a whole serve to confirm the ability of the continuum primitive model to predict, with quantitative accuracy, the free solution electrophoretic mobilities of proteins, provided the underlying models are sufficiently realistic. When a discrepancy occurs, it may be due to error in modeling either the protein charge or the solution conformation. The models described in this work also provide a useful approach for determining values of ΔZ, the change in net charge of proteins due to the chemical modification of charged groups. Knowledge of ΔZ is essential for the use of protein charge ladders in the quantitative description of the electrostatic properties and interactions of proteins. This paper supports the view that the continuum primitive model may be more appropriate for the modeling of electrokinetics than for electrostatics. The main challenge to the accurate predictions of electrophoretic mobilities may lie primarily in the modeling of electrostatics, not electrokinetics. I. Introduction The prediction of electrophoretic mobilities of proteins from their sequences and structures is challenging because such predictions require accurate models of both the electrostatic and the electrokinetic properties of proteins. Electrostatic models are used to predict the distribution of charges on the protein due to the reversible binding of protons to ionizable groups and also the electrostatic potential in the vicinity of the model protein. Electrokinetic models take as input a particular distribu- tion of charge and electrostatic potential and predict the electrophoretic mobility. Both types of models are generally based on the continuum primitive model. The combination of capillary electrophoresis (CE) and protein charge ladders is a useful experimental system for addressing this challenge, as it provides values of electrophoretic mobilities for a collection of protein derivatives that differ incrementally in the number of ionizable groups. In the prediction of electrophoretic mobilities of protein charge ladders, most of the effort has been devoted to modeling of the electrostatics; only simple models of the electrokinetics have been applied. The objective of this paper is to compare experimental mobilities with several electrokinetic models and to determine the degree to which these models can accurately predict the electrophoretic mobilities of proteins. The combination of CE and charge ladders has been used for the characterization of a variety of physical properties and interactions of proteins: examples include their net charges, 1 hydrodynamic sizes, 2 molecular weights, 3 dissociation of titrat- able groups, 4,5 and stabilities. 6 Charge ladders are produced by the partial and chemical modification of charged groups on the protein. The most common procedures involve the acylation of lysine residues with acetic anhydride 3 or the conversion of aspartic and glutamic acid residues to hydroxamic groups (amidation) with hydroxylamine. 7 In free solution capillary electrophoresis, these modified proteins separate into distinct bands, or “rungs”, in which each rung consists of species with * To whom correspondence should be addressed. Phone: (404)651-1986. E-mail: chesaa@panther.gsu.edu. ² Georgia State University. ‡ Princeton University. § Current address: Department of Chemistry, University of Houston, Houston, TX 77004. 4516 J. Phys. Chem. B 2004, 108, 4516-4524 10.1021/jp0312215 CCC: $27.50 © 2004 American Chemical Society Published on Web 03/13/2004