Precise boundary element computation of protein transport properties: Diffusion tensors, specific volume, and hydration

Abstract

A precise boundary element method for the computation of hydrodynamic properties has been applied to the study of a large suite of 41 soluble proteins ranging from 6.5 to 377 kDa in molecular mass. A hydrodynamic model consisting of a rigid protein excluded volume, obtained from crystallographic coordinates, surrounded by a uniform hydration thickness has been found to yield properties in excellent agreement with experiment. The hydration thickness was determined to be delta = 1.1 +/- 0.1 A. Using this value, standard deviations from experimental measurements are: 2% for the specific volume; 2% for the translational diffusion coefficient, and 6% for the rotational diffusion coefficient. These deviations are comparable to experimental errors in these properties. The precision of the boundary element method allows the unified description of all of these properties with a single hydration parameter, thus far not achieved with other methods. An approximate method for computing transport properties with a statistical precision of 1% or better (compared to 0.1-0.2% for the full computation) is also presented. We have also estimated the total amount of hydration water with a typical -9% deviation from experiment in the case of monomeric proteins. Both the water of hydration and the more precise translational diffusion data hint that some multimeric proteins may not have the same solution structure as that in the crystal because the deviations are systematic and larger than in the monomeric case. On the other hand, the data for monomeric proteins conclusively show that there is no difference in the protein structure going from the crystal into solution.

FIGURE 1

(A) Connolly ball rolling over the atoms defines the molecular surface, which encloses the protein-excluded volume, V₀. (B) To represent hydration, the atomic radii are increased by an amount δ and the Connolly ball is rolled over the atoms again. The new larger volume, V(δ), is surrounded by the hydrated surface.

FIGURE 2

Lysozyme: space-filled model (2CDS) and triangulation of molecular surface by MSROLL.

FIGURE 3

Linear extrapolation of the trace of the translational diffusion tensor for ribonuclease versus 1/N. N varies between 2590 and 4950 triangles. A linear least-squares fit to the data (cm²/s) yields an intercept of 1.0832 10⁻⁶ (standard error = 2.6 10⁻¹⁰, Tstat = 4189), a slope of 3.50 10⁻⁵ (standard error = 8.7 10⁻⁷, Tstat = 40), and a variance of 1.38 10⁻²⁰. Tstat is the T statistic indicating the appropriateness of a linear fit. The statistical error in the intercept is 0.024%.

FIGURE 4

Graph of the translational diffusion coefficient as a function of hydration layer thickness for myoglobin (○), lysozyme (•), and chymotrypsinogen (▪).