Hydrodynamic radius coincides with the slip plane position in the electrokinetic behavior of lysozyme

The zeta potential (ζ) is the effective charge energy of a solvated protein, describing the magnitude of electrostatic interactions in solution. It is commonly used in the assessment of adsorption processes and dispersion stability. Predicting ζ from molecular structure would be useful to the structure-based molecular design of drugs, proteins, and other molecules that hold charge-dependent function while remaining suspended in solution. One challenge in predicting ζ is identifying the location of the slip plane (X_SP ), a distance from the protein surface where ζ is theoretically defined. This study tests the hypothesis that the X_SP can be estimated by the Stokes-Einstein hydrodynamic radius (R_h ), using globular hen egg white lysozyme as a model system. Although the X_SP and R_h differ in their theoretical definitions, with the X_SP being the position of the ζ during electrokinetic phenomena (e.g., electrophoresis) and the R_h being a radius pertaining to the edge of solvation during diffusion, they both represent the point where water and ions no longer adhere to a molecule. This work identifies the limited range of ionic strengths in which the X_SP can be determined using diffusivity measurements and the Stokes-Einstein equation. In addition, a computational protocol is developed for determining the ζ from a protein crystal structure. At low ionic strengths, a hyperdiffusivity regime exists, requiring direct measurement of electrophoretic mobility to determine ζ. This work, therefore, supports a basic tenant of EDL theory that the electric double layer during diffusion and electrophoresis are equivalent in the Stokes-Einstein regime.