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 , 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.

Solvent reaction field potential inside an uncharged globular protein: A bridge between implicit and explicit solvent models?

“…ζ (r), the direction of molecular dipole moment vectors relative to the protein surface normal, was computed for each water molecule at each frame of the simulation trajectory using Equation 4, (4) where n (r) is the biomolecular surface normal vector computed by finding the nearest protein atom to each grid point. This quantity still left some ambiguity in the orientations of water molecules; for instance, ζ (r) = 0 could mean that, on average, water molecules at point r pointed one hydrogen toward the protein and pointed the other away, or it could mean that water molecules at r pointed both hydrogens parallel to the protein surface.…”

“…The electrostatic properties of solvated biomolecules are a subject of intense computational [1][2][3] as well as experimental interest [4][5][6][7]. The polar nature of water molecules influences the structure of proteins, nucleic acids, and lipid membranes.…”

The dependence of the electrophoretic mobility of small organic ions on ionic strength and complex formation

“…Significant applications include separation of short peptides [6][7][8][9][10][11][12], organic anions [13,14], proteins, and protein ''charge ladders'' [15][16][17], stereoisomers [18], and also the study of complex formation [12,[19][20][21]. There are a number of factors that influence the effectiveness of separating species in a particular system and these include the solvent, composition of BGE, temperature, pH, sample concentration, nature of the capillary (its diameter, whether it is ''coated'', etc.…”

Capillary electrophoresis of proteins 2003–2005

“…Combination of the Offord model with a corrected steric substituent constant and molar refractivity descriptors improved, however, the predictivity of the model, especially for peptides containing basic amino acids [9]. Similarly, CZE of five model proteins resulted in the conclusion that a primitive continuum model is appropriate for predicting mobilities of proteins [10].…”