Electrophoresis of Protein Charge Ladders: A Comparison of Experiment with Various Continuum Primitive Models

Abstract

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 œ, 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 ¢Z, the change in net charge of proteins due to the chemical modification of charged groups. Knowledge of ¢Z 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 distribution 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