WATER SELF-DIFFUSION MODEL FOR PROTEIN-WATER NMR CROSS-RELAXATION

Analytical motional models are described for the interpretation of NMR cross relaxation between protein protons and water protons, treating bulk water as a self-diffusing continuum. Using intermolecular dipolar relaxation theory, scaling arguments, and numerical calculations, the distance dependence of the cross-relaxation rate constant between the protein proton and the first hydration shell is discussed for planar and spherical surface geometries. It is found that differential effects between NOESY and ROESY rate constants depend strongly on geometrical factors and do not directly reflect residence times of individual water molecules on the protein surface. Restriction of water diffusion to a coarse lattice leads qualitatively to the same NMR relaxation behavior, but X-ray crystallography would display well-ordered water structure, illustrating the complementary views of the two techniques on protein hydration.