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Voronoi cell: New method for allocation of space among atoms: Elimination of avoidable errors in calculation of atomic volume and density
Author(s) -
Goede A.,
Preissner R.,
Frömmel C.
Publication year - 1997
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/(sici)1096-987x(19970715)18:9<1113::aid-jcc1>3.0.co;2-u
Subject(s) - voronoi diagram , polyhedron , intersection (aeronautics) , spheres , van der waals radius , atomic radius , van der waals force , surface (topology) , vertex (graph theory) , combinatorics , atom (system on chip) , space (punctuation) , mathematics , geometry , physics , chemistry , computer science , quantum mechanics , molecule , operating system , graph , astronomy , engineering , embedded system , aerospace engineering
In computing the volume occupied by atoms and the density inproteins, one is faced with the problem of intersecting spheres. Toestimate either, the space between the atoms has to be divided according tothe location of the atoms relative to each other. Various methods, based onVoronoi's idea of approximating the atomic space by polyhedra, havebeen proposed for this purpose. Comparing procedures concerned with theallocation of space among distinct atoms, we observe differentpartitionings of space, with deviations of more than 100% forparticular atoms. Furthermore, we find that the separating planes ofdifferent Voronoi procedures do not meet the intersection circles ofcovalently linked atoms. This leads to a misallocation of space of up to7% for atom pairs that largely differ in atomic size (e.g.,C—H). Several algorithms are negatively affected by small unallocatedpolyhedra (“vertex error”). These effects are cumulative for asmall protein up to a loss of some 60 Å 3 of total volume,which would correspond to the deletion of one complete residue. To overcomethese errors, instead of using dividing planes between the atoms, we usecurved surfaces, defined as the set of those geometrical loci with equalorthogonal distance to the surfaces of the van der Waals spheres underconsideration. The proposed dividing surface meets not only theintersection circle of the two van der Waals spheres but also theintersection circle of the two spheres enlarged by an arbitrary value(e.g., radius of water). This hyperbolic surface enveloping the Voronoicell can be easily constructed and offers the following advantages: nomisallocation of volume for atoms of different size, no vertex error,geometrically reasonable allocation of the volume among atoms, avoidance ofdiscontinuities between neighboring atoms, and improved applicability towater‐accessible protein surfaces. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1113–1123