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

• Published in: Proteins, structure, function, and bioinformatics Vol. 86; no. 5; pp. 515 - 523
• Main Authors: Grisham, Daniel R., Nanda, Vikas
• Format: Journal Article
• Language: English
• Published: United States Wiley Subscription Services, Inc 01.05.2018
• Subjects: Albumen; Computer applications; Crystal structure; Diffusion layers; Drug development; Einstein equations; Electric double layer; Electrokinetics; Electrophoresis; Electrophoretic mobility; Electrostatic properties; Energy charge; Gouy–Chapman electric double layer; hydrodynamic radius; Lysozyme; Molecular structure; Protein structure; Proteins; Slip; slip plane position; Solvation; Stability analysis; Stokes–Einstein relation; Zeta potential; slip plane position; Gouy-Chapman electric double layer; zeta potential; Stokes-Einstein relation; hydrodynamic radius
• ISSN: 0887-3585; 1097-0134
• DOI: 10.1002/prot.25469

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 (XSP), a distance from the protein surface where ζ is theoretically defined. This study tests the hypothesis that the XSP can be estimated by the Stokes–Einstein hydrodynamic radius (Rh), using globular hen egg white lysozyme as a model system. Although the XSP and Rh differ in their theoretical definitions, with the XSP being the position of the ζ during electrokinetic phenomena (e.g., electrophoresis) and the Rh 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 XSP 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.