Magnetic relaxation dispersion measurements by Halle and others, as well as explicit solvent molecular dynamics computations have shown that water residence times at protein-water interfaces are in the 10-50 ps time scale while rotational correlation times of proteins are in the 10 ns time scale. These findings are incompatible with the conventional picture of a static fixed hydration layer used with stick boundary element computations in macromolecular hydrodynamics. Halle and coworkers have shown that water structure is perturbed at the protein-water interface and that such a perturbation can be modeled by a uniform thin layer of higher viscosity solvent around the macromolecule. The measured water rotational correlation times can be used to extract the equivalent fixed hydration layer thickness for stick boundary element computations, obtaining a value of 1.1 A. This value is in complete agreement with that extracted empirically by stick boundary element computations using BEST (Aragon, J. Comp.Chem. 25,1191, 2004) in a study of 49 proteins. However, if one applies the same calculational method to rigid aminoacids, one obtains a similar description, but a thinner perturbed layer and slip boundary conditions are required. The difference between aminoacids and a protein is the presence of surface roughness and surface dynamics in the latter, thus one arrives as the conclusion that the use of stick boundary conditions for macromolecules in aqueous solution is just a convenient mechanism to account for the larger amount of viscous energy dissipation imposed by the characteristics of the interface. Molecular dynamics studies of proteins show that the range of atomic motions of protein atoms is about 3.0 A within about 100 ps, thus the thickness of the perturbed layer of water should be about a water molecule thick, as slip would yield, and not 1.1 A, and this would agree with the magnetic relaxation dispersion measurements as well. Our work strongly suggests that the natural boundary condition for all hydrodynamic transport is the slip boundary condition and that the layer thickness required to agree with experiment varies by how much the solvent is perturbed at the solute interface. A rigid aminoacid perturbs much less than a protein. This view is also consistent with the required use of slip boundary conditions to explain coagulation rates in diffusion controlled reactions.

Natural boundary condition for hydrodynamic transport is the slip boundary condition for all molecule sizes and all solvents

249th National Meeting (2015)

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