VORONOI CELL - NEW METHOD FOR ALLOCATION OF SPACE AMONG ATOMS - ELIMINATION OF AVOIDABLE ERRORS IN CALCULATION OF ATOMIC VOLUME AND DENSITY

摘要

In computing Me volume occupied by atoms and the density in proteins, one Is faced with the problem of intersecting spheres. To estimate either, the space between the atoms has to be divided according to the location of the atoms relative to each other. Various methods, based on Voronoi's idea of approximating the atomic space by polyhedra, have been proposed for this purpose. Comparing procedures concerned with the allocation of space among distinct atoms, we observe different partitionings of space, with deviations of more than 100% for particular atoms. Furthermore, we find that the separating planes of different Voronoi procedures do not meet the intersection circles of covalently linked atoms. This leads to misallocation of space of up to 7% for atom pairs that largely differ in atomic size (e.g., C-H). Several algorithms are negatively affected by small unallocated polyhedra (''vertex error''). These effects are cumulative for a small protein up to a loss of some 60 Angstrom(3) of total volume, which would correspond to the deletion of one complete residue. To overcome these errors, instead of using dividing planes between the atoms, we use curved surfaces, defined as the set of those geometrical loci with equal orthogonal distance to the surfaces of the van der Waals spheres under consideration. The proposed dividing surface meets not only the intersection circle of the two van der Waals spheres but also the intersection circle of the two spheres enlarged by an arbitrary value (e.g., radius of water). This hyperbolic surface enveloping the Voronoi cell can be easily constructed and offers the following advantages: no misallocation of volume for atoms of different size, no vertex error, geometrically reasonable allocation of the volume among atoms, avoidance of discontinuities between neighboring atoms, and improved applicability to water-accessible protein surfaces. (C) 1997 by John Wiley & Sons, Inc. [References: 28]