Modeling the Electrophoresis of Peptides and Proteins:  Improvements in the “Bead Method” to Include Ion Relaxation and “Finite Size Effects”

Abstract

A bead model methodology developed in our lab (Xin et al. J. Phys. Chem. B 2006, 110, 1038) and applicable to modeling the free solution electrophoretic mobility of peptides and proteins is generalized in two significant ways. First, an approximate account is taken of the relaxation effect, which makes the methodology applicable to more highly charged peptides and proteins than was previously possible. Second, a more accurate account is taken of the finite size of the beads making up the model structure. This improvement makes the method applicable at higher salt concentrations and/or to models consisting of larger sized subunits. The relaxation effect is accounted for by correcting "unrelaxed" mobilities on the basis of model size and average electrostatic surface, or zeta potential. Correction factors are estimated using those of spheres with the same hydrodynamic radius and zeta potential as the model structure. The correction factors of spheres are readily determined. The more general methodology is first applied to two sets of peptides (74 different peptides total) varying in size from 2 to 42 amino acids. The sets also cover a wide range of net charges. It is shown that accounting for finite bead size results in a small change in model mobilities under the conditions of the experiments (35 mM monovalent salt). The correction for ion relaxation, however, can be significant for highly charged peptides and improves agreement between model and experimental mobilities. Our correction procedure is also tested by examining the electrophoretic mobility of a particular protein "charge ladder" (Carbeck et al. J. Am. Chem. Soc. 1999, 121, 10,671), where the protein charge is varied over a wide range yet the conformation remains essentially constant. In summary, the effects of ion relaxation can be significant if the absolute electrophoretic mobility of a peptide exceeds approximately 0.20 cm2/(kV s).

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

“…Given the discussion in Section 2.1, we rule out particle shape and distribution of charge as being responsible for the discrepancy. Although spherical models have been used to treat the relaxation effect, this procedure should also be fairly accurate when applied to ellipsoidal [47] and irregular, but globular particles in general [65]. Consequently, we shall next explore the possibility of multiple species due to complex formation, which has been proposed previously by independent investigators [13,14].…”

Using electrophoretic mobility and bead modeling to characterize the charge and secondary structure of peptides

“…This structurebased methodology is grounded on fundamental electrohydrodynamic theory. It has previously been applied to over 70 peptides ranging in size from 2 to 42 amino acids and, on average, yields model mobilities in good agreement with experiments [38,39]. In these studies, however, few restrictions were placed on the dihedral angles that determine the overall conformation of model peptides.…”

“…Once the (b, w) angles are specified, a unique conformation can be generated using the rotation matrix approach of Flory [55] and employed in previous works [38,39]. Consider the generation of a particular conformation and suppose 2k beads (representing k amino acids) have been generated.…”

“…Once generated, however, conformation can indluence the pK a and charge state of a particular peptide [45] as discussed in the Appendix. In addition, the effect of ion relaxation (distortion of the charge distribution from equilibrium) on mobility is accounted for to lowest order [39].…”

Recent developments in CE and CEC of peptides

“…A new approach, bead model for modeling electrophoretic mobility and diffusion of peptides and proteins, is based on an approximate structural model of peptides and it also takes into account the electrohydrodynamic theory [34,35]. A peptide formed by X amino acids is modeled as N = 2X beads with two beads representing each amino acid in the chain.…”