Rules relating electrophoretic mobility, charge and molecular size of peptides and proteins

Abstract

The absence of supporting media in free solution high-performance capillary electrophoresis (HPCE) makes it an ideal system for the study of the relationship between electrophoretic mobility ( μ em) and the molecular size and charge of proteins and peptides. In this review, the theory of electrophoresis, developed for rigid, insulating, spherical particles, is modified to develop models for the electrophoretic behaviour of proteins and peptides. For a given set of experimental conditions, μ em of a protein/peptide is proportional to its charge ( q) and is inversely proportional to its Stoke's radius ( r). Furthermore, μ em is most sensitive to changes in q and, as a consequence, the reliability of equations relating μ em to protein/peptide q and r is dependent upon the accurate calculation or determination of q. For convenience, q and r of proteins and peptides are generally expressed in terms of calculated valence ( Z c) and molecular mass ( M), respectively, both of which can be determined from the amino acid sequence of the protein/peptide. However, the calculation of q using Z c is made more complex by the effects of electrostatic charge suppression, such that Z c is an overestimation of actual charge. Charge suppression becomes increasingly significant as the protein/peptide charge increases, such that, for peptides, the relationship between q and Z c can be approximated by a logarithmic function. The μ em for peptides, therefore, can be approximated by the equation: μ em = ln( Z c + 1)/ K M s where s varies between 1 3 and 2 3 , and K is a constant that is valid for a particular set of experimental conditions. The rather simplistic compensation for charge suppression in this equation is inadequate for proteins where the magnitude of charge suppression is greater and the mechanisms are more complex. For proteins, the relationship suggested for the prediction of μ em from Z c and M is: μ em = Z c/ KF z M s where s again varies between 1 3 and 2 3 and F z is a pH-independent proportionality factor defined as the quotient, Z c/ Z a, with Z a being actual protein valence. The factor F z can be determined empirically, however, it is valid only for the particular set of experimental conditions under which it is determined. For peptides, the mass exponent, s, approaches 1 3 when the peptides have high charge densities and open structures. However, s approaches 1 2 for peptides with lower charge densities that are capable of more randomized motion during electrophoresis. Finally, s approaches 2 3 for proteins, suggesting that the frictional forces acting on a protein undergoing electrophoretic motion are proportional to the surface area of these larger, more rigid, structures. In conclusion, the development of relationships between μ em, M and Z c for peptides and proteins offers a powerful tool, not only for predicting electrophoretic mobility, but also for optimising HPCE separations, studying structural modifications (e.g. phosphorylation, glycosylation, deamidation, etc.), and for the investigation of surface charge characteristics and conformation.