The problem with the offord equation: Hydration—a statistical investigation of the effect of charge size and confirmation of the effect of charge distribution upon electrophoretic mobilities

Summary

A previous study has demonstrated that the average electrophoretic behaviour (mobilities, μ_ep of eighteen peptides were well described by the inverse square law: μ_ep ∝ l/r ² (wherer is the hydrodynamic radius). However, examination of the dependence of μ_ep, upon the magnitude of the charge and its distribution led to the conclusion that deviations from the averaged behaviour arose from a charge-induced volumetric effect.

In the current work, we have sought to determine the generality of the above findings via a statistical examination of μ_ep for an independent and larger set of peptides. Both objective testing by the Offord eq and statistical analysis of the variation of the log μ_ep/Z function reveals a strong residual dependence upon the magnitude of the overall charge. Furthermore, it was found that an even finer distinction exists between peptides of differing charge distribution types. Terminal charges affect the peptide mobilities differently to those charges located within the amino acid sequence and isolated charges affect mobility differently to the same number of adjacent charges. The empirical addition of hydration to each charge type produces a linear log plot of the Offord equation (R ²=0.991) that has a gradient (0.64) very close to that theoretically expected (0.67). Hence hydration removes the observed deviations from the averaged electrophoretic behaviour that is associated with highly charged analytes and corrects the Offord equation. It is postulated that higher charge densities lead to more open structures, greater solvation and thus larger electromigrating molecular ions with smaller mobilities.