Buried atoms

The Voronoi calculation can be performed on protein atoms buried at interfaces as well as inside proteins. However, the procedure has a serious limitation a Voronoi polyhedron can be drawn around an atom only if it is completely surrounded by other atoms. At interfaces, only about one-third of the atoms that contribute to the interface area B have zero accessible surface area. These atoms are located mostly at the center of the interface, which biases the F/Fq ratio in an opposite way to the gap index, which is biased toward the periphery. However, high-resolution X-ray structures usually report positions for immobilized water molecules, which are abundant at interfaces (see Section II,D). These molecules may also be used to close the polyhedra, making the evaluation of Voronoi volumes possible for atoms which are surrounded by both protein atoms and immobilized water molecules (Fig. 4). On average, there are as many such interface atoms as there are completely buried atoms. Thus, a Voronoi calculation taking into account the crystallographic water molecules applies to two-thirds of the interface atoms on average instead of only one-third and up to 90% in specific cases (Lo Conte et al., 1999). 

In the 75 protein-protein complexes of Lo Conte et al. (1999), 96% of the interfaces have V/Vq in the range 0.97-1.06. Thus, the packing of atoms buried at protein-protein interfaces is very similar to that of the protein interior. In 36 complexes with X-ray structures at a resolution of 2.5 A and better, the V/Vq ratios calculated in the presence of water molecules were distributed over a narrow range of 0.97-1.03 (Fig. 5, top). Therefore, their interfaces are packed like the protein core, except that water, which is almost entirely excluded from the protein core, makes an important contribution to the packing at protein-protein interfaces. There is one exception to this rule in the sample analyzed by Lo Conte et al. (1999) the complex between cytochrome peroxidase and cytochrome c [PDB code, Iccp (Pelletier and Kraut, 1992)]. Its interface is small and has only a few buried atoms and a large volume ratio (1.07). In contrast, the 19 protease-inhibitor and the 19 antigen-antibody complexes of this sample have mean V/Vq ratios of 1.00 and 1.01, respectively. Thus, unlike 5c and the gap index, the volume ratio indicates that these two types of interfaces are close-packed and shows no difference in their packing density, at least for their buried atoms. 

In principle, the three-dimensional RISM (3D-RISM) theory described in Chapter 4 is significantly more accurate than the RISM theory employed so far which can be distinguished from the 3D-RISM theory by calling it the one-dimensional RISM (ID-RISM) theory. This is because the 3D-RISM theory, in contrast to the ID-RISM theory, takes orientational average of the molecular Ornstein-Zernike (OZ) equation for solvent molecules only, keeping full description of the shape and orientation of the solute molecule. In reality, a solvent site cannot access to a completely buried atom in the solute molecule. Even if is... 

D. C. Rees, unpublished results, 1995) that complements structures at low and room temperatures. The slopes of these lines divided by the atomic volume yield the coefficient of thermal expansion, which is 10 K for these proteins, similar to the results of solution studies. To first order, there appears little difference in the thermal expansion behavior of mesophilic and hyperthermophilic proteins, at least between liquid nitrogen and room temperatures. There is a hint that the volume of buried atoms in the P. furiosus rubredoxin may not increase as rapidly at higher temperatures, but this remains to be established confidently. Undoubtedly, further woik is needed to address the thermal properties of hyperthermophilic proteins and whether this has any relationship to stability. 

Deviations of atomic volumes do not indicate directly that a defective protein exists because deviations in atomic volumes can be attributed to other physical phenomena. It is for this reason that the authors of PROVE correlated the atom volume deviations with crystallographic qualities of the protein X-ray structure including the resolution (lowest resolvable separation between two carbon atoms), the R-factor (measure of how well the refined structure agrees with the experimental model/electron density maps/raw data), and B-factors (isotropic temperature factor).A test set of 900 protein structures was constructed, each containing a minimum of 100 buried atoms. The resolution of the protein structures ranged from 1.0 to 3.9 A. The authors found that for high-resolution structures (1.0 to 1.6 A), the average Zrmsd was approximately 1.0. When poorer quality crystal structures were considered, the Zrmsd increased. The correlation coefficient for a plot of Zrmsd versus experimental resolution was 0.89 for all protein structures in the test set... 

---