Voronoi method

PROVE compares the atomic volumes of a protein model with standard atomic volume values derived from the set of 64 protein structures. Using the same Voronoi methods, the atomic volumes of the protein model under consideration are computed and compared with the normal atomic volumes. The difference between the standardized volumes and the protein model being studied is reported as two different types of Z-scores. The first Z-score involves a comparison between individual atom types as defined in Eq. [7] ... 

With the development of accurate computational methods for generating 3D conformations of chemical structures, QSAR approaches that employ 3D descriptors have been developed to address the problems of 2D QSAR techniques, e.g., their inability to distinguish stereoisomers. The examples of 3D QSAR include molecular shape analysis (MSA) [34], distance geometry [35,36], and Voronoi techniques [37]. 

Voronoi-Delaunay Method for Description of Corpuscular and Sponge-Like Porous Solids... 

The way of the best choice to model PS s structure on both molecular and supramolecular levels begins with allocation of primary building units (PBUs), which without gaps and overlaps would fill a 3D space occupied by a PS. An universal method for allocation of such PBUs in both ordered and randomly arranged PSs, formed of packings of convex particles (or pores), is based on the construction of the assembles of Voronoi polyhedra (V-polyhedra) and Delaunay simplexes (or D-poly-hedra), which form Voronoi-Delaunay tessellation [100],... 

The most popular grid-based QSAR techniques are - GRID method and -> CoMFA a number of related techniques has also been proposed such as - CoMSIA, - Voronoi Molecular Field Analysis, -> hydration free energy density, and the approach based on - G-WHIM descriptors. 

Srivastava, S., Richardson, W.W., Bradley, M.P. and Crippen, G.M. (1993). Three-Dimensional Receptor Modeling Using Distance Geometry and Voronoi Polyhedra. In 3D QSAR in Drug Design. Theory, Methods and Applications. (Kubinyi, H., ed.), ESCOM, Leiden (The Netherlands), pp. 409-430. 

Tanemura et al. examined crystallization in a liquid of soft spheres and found both fee and bcc structures. They used the method of Voronoi polyhedra to characterize the evolving solid clusters. Hsu and Rahman extended the use of Voronoi polyhedra in a systematic study of the effect of potential on the structure observed. They found that a model rubidium potential always crystallized to a bcc structure, while a truncated rubidium, Lennard-Jones,... 

Still based on molecular interaction fields, several other methods were successively proposed and, among them, there were Comparative Molecular Similarity Indices Analysis (CoMSIA) ]Klebe, Abraham et al, 1994], Compass method ]Jain, Koile et al, 1994], G-WHIM descriptors ]Todeschini, Moro et al, 1997], Voronoi field analysis [Chuman, Karasawa et al, 1998], VolSurf descriptors ]Crudani, Pastor et al, 2000], and GRIND descriptors ]Pastor, Cruciani et al, 2000]. 

Our techniques for probing local geometrical and topological structure in the liquid and solid are largely based on the Voronoi construction [187], which is perhaps the most frequently used method for characteriz-... 

Voronoi polyhedra have been useful in characterizing the nucleation event. Triplet correlation functions also have been discussed. In metastable liquid rubidium it has been shown by these methods that, as might be expected in this case, the initial growing nuclei have a body-centered-cubic structure. For the supercooled LJ liquid there have been separatereports of the formation of nuclei with body-centered-cubic and face-centered-cubic structures. These may not be entirely conflicting results, however, but a manifestation of a general point made some years ago by Wood concerning simulation experiments on dense fluids. ... 

Hirshfeld charges may be considered as a soft-boundary version of the Voronoi charges. An ambiguity in the Hirshfeld method is the source of the atomic densities. 

Ghosh, S. (2010) Micromechanical Analysis and Multi-scale Modeling Using the Voronoi Cell Finite Element Methods, CRC Press, Boca Raton, Florida. 

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