Calculation of protein volumes: An alternative to the Voronoi procedure

Abstract

All the methods that have been applied to assessing local volume occupation or packing in proteins have particular defects. For example, the Voronoi method used by Richards (method A) and by Finney misallocates both non-bonded and covalent contacts in a geometrically rigorous, though chemically inconsistent, manner. Richards' method B, in which covalent and non-bonded contacts are partitioned in chemically sensible ways, is unfortunately not completely rigorous, in that every polyhedron vertex has associated with it a small vertex-error polyhedron, which is not allocated to any atom. We present here a generalization of the Voronoi method that is particularly suited to multicomponent assemblies such as proteins. This radical plane partitioning of volume is completely rigorous; it gives rise to no vertex error, and handles the more numerous non-bonded contacts realistically. Its application to RNAase-S is described and the results compared with both Voronoi's method and Richards' method B. A particular advantage of both the radical plane and Richards' methods is a relative insensitivity to the treatment of the surface, a problem that has plagued other approaches to describing packing in proteins. Although the radical plane is seen to misallocate volume chemically between covalently-bonded neighbours, this problem vanishes when groups of atoms in side-chain residues are considered.