Preaveraged Hydrodynamic Interaction Revisited via Boundary Element Computations

Abstract

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.

Modeling the Electrophoresis of Peptides and Proteins: Improvements in the “Bead Method” to Include Ion Relaxation and “Finite Size Effects”

“…Another assumption shall also be addressed in future work, and that is the assumption of pre-averaging the hydrodynamic interaction . This assumption has been extensively analyzed by a number of investigators − with regard to nonelectrophoretic transport properties such as translational and rotational diffusion as well as intrinsic viscosity. This approximation is quite inaccurate for rotational diffusion and intrinsic viscosity 45 but works much better for translational diffusion where its use results in overestimating the diffusion constants by 0 to 8.3% depending on the structure involved.…”

27Al NMR diffusometry of Al13 Keggin nanoclusters

“…It is important to note that when the BEST calculation was used in the primary literature source to simulate the transport of lysozyme macromolecules that the hydration shell thickness and number of solvating shells were used to tune the simulation output to experimental results. [53,54] F I G U R E 6 Theoretical calculation of ϵ-Al 13 diffusivity. Starting from a (a) 2 Â 2 Â 2 supercell of the salt, NaAl 13 O 4 (OH) 24 (H 2 O) 12 (SO 4 ) 4 Á10H 2 O, [32] (b) a single ϵ-Al 13 cluster was isolated.…”

“…In the crystal structures, [32] sulfur is drawn in yellow, oxygen in red, and aluminum in blue. Hydrogen is not drawn for simplicity Therefore, a similar procedure is used here, and hydration shells of 1.1 Å thickness [53,54] were sequentially added to the radius of the ϵ-Al 13 Keggin cluster hull. Analysis of the results, shown in Figure 5, indicates that three hydration shells of 1.1 Å thickness are necessary to improve agreement between experimental and theoretical results.…”

“…Hydrodynamic resistivity and diffusivity tensors were then calculated in Cartesian coordinates in the BEST software package. [53,54] The output of the BEST software package is included in the Supporting Information. The average translational diffusion coefficient of the mesh was then determined by averaging the translational diffusivity along three principal axis (D xx , D yy , and D zz ).…”

Polarizability and Kerr constant of proteins by boundary element methods

“…This approximation is removed by performing the calculation for increasing numbers of triangles, N, and extrapolating to infinity. When this procedure is implemented, there results a linear system of N equations given by: (3) where the NxN matrix of coefficients is given by, (4) and the vector integrals over the k th triangle Δ k are, (5) The linear system (3) is solved in double precision in our program POL using LAPACK with optimized BLAS for AMD Opteron processors. The vector integrals (5) are evaluated either analytically, or numerically to 16 digit precision.…”