Stokes-flow computation of the diffusion coefficient and rotational diffusion tensor of lysozyme, a globular protein

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Based on a closed surface of triangles fitted to atomic coordinates determined crystallographically, Brune and Kim [Proc. Natl. Acad. Sci. USA 90, 3835-3839 (1993)] proposed a boundary-element Stokes-flow technique for ab initio computation of a translational diffusion coefficient and the rotational diffusion tensor Dr of globular proteins. They applied their approach to atomic coordinates for a tetragonal structure of hen egg-white lysozyme, and reported that computed values of a translational diffusion coefficient and Dr=tr(Dr)/3 agreed well with experiment. After establishing the identity between the infinite-dilution tracer diffusion coefficient of the protein macroion (D+ for lysozyme cation) and the "translational diffusion coefficient" computed by Brune and Kim, we adopt a somewhat different computational approach and show how convergence of D+ and Dr for tetragonal lysozyme depends on two computational parameters characterizing the fidelity of the geometric approximation to the protein surface and two others characterizing the accuracy of the Stokes-flow computations. We then compute D+ and Dr for lysozyme using atomic coordinates for the triclinic crystal structure, three structures determined by nuclear magnetic resonance spectroscopy in the liquid phase (presumably corresponding more closely to in vivo structures), the solvated tetragonal structure (with 108 water molecules) considered by Brune and Kim, and a "dry" version of the same structure. These computations show that D+ and Dr computed for all of the dry crystal structures are in excellent agreement with those for the liquid-phase conformations. Values of D+ and Dr computed for the solvated structure are lower, consistent with the larger volume and area of the corresponding polyhedral surface. We also show that several choices of the origin of the force system [discussed by Brenner, J. Colloid Interface Sci. 23, 407-436 (1967)] give rise to nearly identical translational diffusion coefficients. Finally, we show how to estimate the thickness of the "solvation shell" contributing to the hydrodynamic resistance of the protein cation, and use the binary Nernst-Hartley equation to then estimate the effective cation charge at the two pH values at which the binary diffusion coefficient has been accurately measured in recent interferometric experiments.

Original languageEnglish (US)
Pages (from-to)2376-2387
Number of pages12
JournalPhysics of fluids
Issue number7
StatePublished - Jul 2002

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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