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

Daniel R. Grisham, Vikas Nanda

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)515-523
Number of pages9
JournalProteins: Structure, Function and Bioinformatics
Issue number5
StatePublished - May 2018

All Science Journal Classification (ASJC) codes

  • Structural Biology
  • Biochemistry
  • Molecular Biology


  • Gouy–Chapman electric double layer
  • Stokes–Einstein relation
  • hydrodynamic radius
  • slip plane position
  • zeta potential


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