Voronoi polyhedra as a tool for studying solvation structure

David, Elaine Eisler; David, Carl W

doi:10.1063/1.443540

Cited by 43 publications

(20 citation statements)

References 12 publications

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“…Note that formula (3) is mathematically exact, whereas our generalization (formulas (9) and (14)) is only a result of heuristic approximations. The authors hope that this paper will encourage mathematicians to create a rigorous theory of mean shell volumes in tessellations.…”

Section: Discussionmentioning

confidence: 98%

“…Thus for larger solute molecules the γ -factors for the far shells becomes smaller than for a single cell, see (9). However for the first shell it is the same as for a single central cell.…”

Section: Applicationsmentioning

confidence: 95%

“…This cell represents a volume belonging to the atom. This approach is very attractive for analysis of computer models of molecular systems and is used for many years [8,9].…”

Section: Introductionmentioning

confidence: 99%

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Hydration Shells in Voronoi Tessellations

Voloshin

Аникеенко

Medvedev

et al. 2010

2010 International Symposium on Voronoi Diagrams in Science and Engineering

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An interesting property of the Voronoi tessellation is studied in the context of its application to the analysis of hydration shells in computer simulation of solutions. Namely the shells around a randomly chosen cell in a Voronoi tessellation attract extra volume from outside. There is a theoretical result which says that the mean volume of the first shell around a randomly chosen cell is greater than the anticipated value. The paper investigates this phenomenon for Voronoi tessellations constructed for computer models of point patterns with different variability of the Voronoi cell volumes (Poisson point process, RSA systems of hard spheres and molecular dynamics models of water). It analyzes also the subsequent shells, and proposes formulas for the mean shell volumes for all shell numbers. The obtained results are of value in calculations of the contribution of hydration of water to the "apparent" volume of the solutes.

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Section: Discussionmentioning

confidence: 98%

Section: Applicationsmentioning

confidence: 95%

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Hydration Shells in Voronoi Tessellations

Voloshin

Аникеенко

Medvedev

et al. 2010

2010 International Symposium on Voronoi Diagrams in Science and Engineering

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“…A Voronoi cell consists of the space around one atom so that the distance of every spatial point in the cell to its atom is less than or equal to the distance to any other atom of the molecule. The Voronoi diagram has many applications in chemistry and biology (Finney, 1975;Richards, 1977;David & David, 1982;Gellatly & Finney, 1982;Richards, 1985;Procacci & Scateni, 1992;Gerstein et al, 1995). The Delaunay triangulation can be mapped directly from the Voronoi diagram.…”

Section: Methodsmentioning

confidence: 99%

Anatomy of protein pockets and cavities: Measurement of binding site geometry and implications for ligand design

1998

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Identification and size characterization of surface pockets and occluded cavities are initial steps in protein structurebased ligand design. A new program, CAST, for automatically locating and measuring protein pockets and cavities, is based on precise computational geometry methods, including alpha shape and discrete flow theory. CAST identifies and measures pockets and pocket mouth openings, as well as cavities. The program specifies the atoms lining pockets, pocket openings, and buried cavities; the volume and area of pockets and cavities; and the area and circumference of mouth openings. CAST analysis of over 100 proteins has been carried out; proteins examined include a set of SI monomeric enzyme-ligand structures, several elastase-inhibitor complexes, the pockets and cavities in protein crystal structures and quantifying their size. The method is a computational geometry treatment of complex shapes, based on alpha shape and discrete flow theory, and a related suite of programs,

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“…A long-standing, widely used method to achieve this is Voronoi tessellation 26 which defines polyhedra as the regions of space closest to each atom. [27][28][29][30][31][32][33][34][35] Atoms are defined as neighbors if their polyhedra share a common surface. While attractive in principle, the algorithm is computationally expensive, very sensitive to particle motion, and yields values of n much larger than those using g(r) cutoffs, being 10-20 for common liquids.…”

Section: Introductionmentioning

confidence: 99%

Instantaneous, parameter-free methods to define a solute’s hydration shell

Chatterjee

Higham

Henchman

2015

The Journal of Chemical Physics

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Modeling the hydration of mono-atomic anions from the gas phase to the bulk phase: The case of the halide Instantaneous, parameter-free methods to define a solute's hydration shell A range of methods are presented to calculate a solute's hydration shell from computer simulations of dilute solutions of monatomic ions and noble gas atoms. The methods are designed to be parameter-free and instantaneous so as to make them more general, accurate, and consequently applicable to disordered systems. One method is a modified nearest-neighbor method, another considers solute-water Lennard-Jones overlap followed by hydrogen-bond rearrangement, while three methods compare various combinations of water-solute and water-water forces. The methods are tested on a series of monatomic ions and solutes and compared with the values from cutoffs in the radial distribution function, the nearest-neighbor distribution functions, and the strongest-acceptor hydrogen bond definition for anions. The Lennard-Jones overlap method and one of the force-comparison methods are found to give a hydration shell for cations which is in reasonable agreement with that using a cutoff in the radial distribution function. Further modifications would be required, though, to make them capture the neighboring water molecules of noble-gas solutes if these weakly interacting molecules are considered to constitute the hydration shell. C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.[http://dx

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Voronoi polyhedra as a tool for studying solvation structure

Abstract: Voronoi polyhedra are employed to generate a coherent description of the immediate solvent sheath of complex solutes in water solution.

Cited by 43 publications

References 12 publications

Hydration Shells in Voronoi Tessellations

Hydration Shells in Voronoi Tessellations

Anatomy of protein pockets and cavities: Measurement of binding site geometry and implications for ligand design

Instantaneous, parameter-free methods to define a solute’s hydration shell

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