The boundary element (BE) method is used to implement a very precise computation of the intrinsic viscosity for rigid molecules of arbitrary shape. The formulation, included in our program BEST, is tested against the analytical Simha formula for ellipsoids of revolution, and the results are essentially numerically exact. Previously unavailable, very precise results for a series of Platonic solids are also presented. The formulation includes the optional determination of the center of viscosity; however, for globular proteins, the difference compared to the computation based on the centroid is insignificant. The main application is to a series of 30 proteins ranging in molecular weight from 12 to 465 kD. The computation starts from the crystal structure as obtained from the Protein Data Bank, and a hydration thickness of 1.1 Å obtained in previous work with BEST was used. The results (extrapolated to an infinite number of triangular boundary elements) for the proteins are separated into two groups: monomeric and multimeric proteins. The agreement with experimental measurements of the intrinsic viscosity in the case of monomeric proteins is excellent and within experimental error of 5%, demonstrating that the solution and crystal structure are hydrodynamically equivalent. However, for some multimeric proteins, we observe strong systematic deviations around -20%, which we interpret as a systematic deviation of the solution structure from the crystal structure. A possible description of the structural change is deduced by using simple ellipsoid model parameters. A method to obtain intrinsic viscosity values for proteins to 1-2% accuracy (better than experimental error) on the basis of a single BE computation (avoiding the need for an extrapolation on the number of surface triangles) is also presented.
In contrast to other retrospective multisurgeon series, our retrospective single-surgeon series suggests that microsurgical fenestration of the lamina terminalis may not reduce the incidence of shunt-dependent hydrocephalus or cerebral vasospasm after aneurysmal subarachnoid hemorrhage. A prospective multicenter trial is needed to definitively address the use of this maneuver.
The effect of preaveraging the Oseen tensor to yield a scalar approximation is examined for transport problems of rigid objects with stick boundary conditions using new very high accuracy computational codes. Nearly exact computations are compared to analytical results and preaveraged results for spheroids and, similarly, for a set of three globular proteins. In agreement with previous work, we find that the error in translational diffusion is less than 1%. However, in the case of rotational diffusion and intrinsic viscosity, the error is sensitively dependent on shape. In the case of the axial component of the rotational diffusion, the error is about -34% independent of shape, but for the perpendicular component, the error starts at -30% (sphere) and decreases as the axial ratio increases and then yields a similar but positive error. For the instrinsic viscosity, the errors are around 10% near spherical and decrease toward the needle or disk shape. For the globular proteins, the errors are similar to those found for the ellipsoids near the spherical shape. The calculations show that preaveraging is acceptable only for translational diffusion of rigid objects.
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