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Definitions of protein volume
International Tables for Crystallography (2012). Vol. F, Section 22.1.2, pp. 703-706 [ doi:10.1107/97809553602060000885 ]
... does not amount to more than 1 part in 500 (Gerstein et al., 1995). 22.1.2.3.3. `Chopping-down' method of finding ... spheres. Discuss. Faraday Soc. 43, 62-69. Edelsbrunner, H., Facello, M. & Liang, J. (1996). On the Definition and Construction of ... Macromolecules, pp. 272-287. Singapore: World Scientific. Edelsbrunner, H., Facello, M., Ping, F. & Jie, L. (1995). Measuring proteins and ...
Radical-plane method
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.3.4, p. 705 [ doi:10.1107/97809553602060000885 ]
Radical-plane method 22.1.2.3.4. Radical-plane method The radical-plane method does not suffer from vertex error. In this method, the plane is positioned according to References International Tables for Crystallography (2012). Vol. F, ch. 22.1, p. 705 © International Union of Crystallography 2012 | home | resources | advanced search | purchase | contact us ...
`Chopping-down' method of finding vertices
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.3.3, p. 705 [ doi:10.1107/97809553602060000885 ]
`Chopping-down' method of finding vertices 22.1.2.3.3. `Chopping-down' method of finding vertices Because of vertex error and the complexities in locating vertices, a different algorithm has to be used for volume calculation with method B. (It can also be used with bisection.) First, surround the central atom (for which ...
Vertex error
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.3.2, p. 705 [ doi:10.1107/97809553602060000885 ]
... does not amount to more than 1 part in 500 (Gerstein et al., 1995). References Gerstein, M., Tsai, J. & Levitt, M. (1995). The volume of ...
Method B and a simplification of it: the ratio method
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.3.1, pp. 704-705 [ doi:10.1107/97809553602060000885 ]
... deviations about the mean). References Tsai, J., Voss, N. & Gerstein, M. (2001). Voronoi calculations of protein volumes: sensitivity analysis and ...
Adapting Voronoi polyhedra to proteins
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.3, pp. 704-705 [ doi:10.1107/97809553602060000885 ]
... does not amount to more than 1 part in 500 (Gerstein et al., 1995). 22.1.2.3.3. `Chopping-down' method of finding ... to the Voronoi procedure. J. Mol. Biol. 161, 305-322. Gerstein, M., Tsai, J. & Levitt, M. (1995). The volume of ...
Collecting vertices and calculating volumes
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.2.3, p. 704 [ doi:10.1107/97809553602060000885 ]
Collecting vertices and calculating volumes 22.1.2.2.3. Collecting vertices and calculating volumes To collect the vertices associated with an atom systematically, label each one by the indices of the four atoms with which it is associated (Fig. 22.1.2.2). To traverse the vertices on one face of a polyhedron, find all vertices ...
Finding polyhedron vertices
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.2.2, p. 704 [ doi:10.1107/97809553602060000885 ]
Finding polyhedron vertices 22.1.2.2.2. Finding polyhedron vertices In the basic Voronoi construction (Fig. 22.1.2.1), each atom is surrounded by a unique limiting polyhedron such that all points within an atom's polyhedron are closer to this atom than all other atoms. Consequently, points equidistant from two atoms lie on a dividing ...
Integrating on a grid
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.2.1, pp. 703-704 [ doi:10.1107/97809553602060000885 ]
Integrating on a grid 22.1.2.2.1. Integrating on a grid The simplest method for calculating volumes with Voronoi polyhedra is to put all atoms in the system on a fine grid. Then go to each grid point (i.e. voxel) and add its infinitesimal volume to the atom centre closest to it. This ...
The basic Voronoi construction
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.2, pp. 703-704 [ doi:10.1107/97809553602060000885 ]
The basic Voronoi construction 22.1.2.2. The basic Voronoi construction 22.1.2.2.1. Integrating on a grid | | The simplest method for calculating volumes with Voronoi polyhedra is to put all atoms in the system on a fine grid. Then go to each grid point (i.e. voxel) and add its infinitesimal volume to the atom ...
International Tables for Crystallography (2012). Vol. F, Section 22.1.2, pp. 703-706 [ doi:10.1107/97809553602060000885 ]
... does not amount to more than 1 part in 500 (Gerstein et al., 1995). 22.1.2.3.3. `Chopping-down' method of finding ... spheres. Discuss. Faraday Soc. 43, 62-69. Edelsbrunner, H., Facello, M. & Liang, J. (1996). On the Definition and Construction of ... Macromolecules, pp. 272-287. Singapore: World Scientific. Edelsbrunner, H., Facello, M., Ping, F. & Jie, L. (1995). Measuring proteins and ...
Radical-plane method
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.3.4, p. 705 [ doi:10.1107/97809553602060000885 ]
Radical-plane method 22.1.2.3.4. Radical-plane method The radical-plane method does not suffer from vertex error. In this method, the plane is positioned according to References International Tables for Crystallography (2012). Vol. F, ch. 22.1, p. 705 © International Union of Crystallography 2012 | home | resources | advanced search | purchase | contact us ...
`Chopping-down' method of finding vertices
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.3.3, p. 705 [ doi:10.1107/97809553602060000885 ]
`Chopping-down' method of finding vertices 22.1.2.3.3. `Chopping-down' method of finding vertices Because of vertex error and the complexities in locating vertices, a different algorithm has to be used for volume calculation with method B. (It can also be used with bisection.) First, surround the central atom (for which ...
Vertex error
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.3.2, p. 705 [ doi:10.1107/97809553602060000885 ]
... does not amount to more than 1 part in 500 (Gerstein et al., 1995). References Gerstein, M., Tsai, J. & Levitt, M. (1995). The volume of ...
Method B and a simplification of it: the ratio method
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.3.1, pp. 704-705 [ doi:10.1107/97809553602060000885 ]
... deviations about the mean). References Tsai, J., Voss, N. & Gerstein, M. (2001). Voronoi calculations of protein volumes: sensitivity analysis and ...
Adapting Voronoi polyhedra to proteins
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.3, pp. 704-705 [ doi:10.1107/97809553602060000885 ]
... does not amount to more than 1 part in 500 (Gerstein et al., 1995). 22.1.2.3.3. `Chopping-down' method of finding ... to the Voronoi procedure. J. Mol. Biol. 161, 305-322. Gerstein, M., Tsai, J. & Levitt, M. (1995). The volume of ...
Collecting vertices and calculating volumes
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.2.3, p. 704 [ doi:10.1107/97809553602060000885 ]
Collecting vertices and calculating volumes 22.1.2.2.3. Collecting vertices and calculating volumes To collect the vertices associated with an atom systematically, label each one by the indices of the four atoms with which it is associated (Fig. 22.1.2.2). To traverse the vertices on one face of a polyhedron, find all vertices ...
Finding polyhedron vertices
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.2.2, p. 704 [ doi:10.1107/97809553602060000885 ]
Finding polyhedron vertices 22.1.2.2.2. Finding polyhedron vertices In the basic Voronoi construction (Fig. 22.1.2.1), each atom is surrounded by a unique limiting polyhedron such that all points within an atom's polyhedron are closer to this atom than all other atoms. Consequently, points equidistant from two atoms lie on a dividing ...
Integrating on a grid
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.2.1, pp. 703-704 [ doi:10.1107/97809553602060000885 ]
Integrating on a grid 22.1.2.2.1. Integrating on a grid The simplest method for calculating volumes with Voronoi polyhedra is to put all atoms in the system on a fine grid. Then go to each grid point (i.e. voxel) and add its infinitesimal volume to the atom centre closest to it. This ...
The basic Voronoi construction
International Tables for Crystallography (2012). Vol. F, Section 22.1.2.2, pp. 703-704 [ doi:10.1107/97809553602060000885 ]
The basic Voronoi construction 22.1.2.2. The basic Voronoi construction 22.1.2.2.1. Integrating on a grid | | The simplest method for calculating volumes with Voronoi polyhedra is to put all atoms in the system on a fine grid. Then go to each grid point (i.e. voxel) and add its infinitesimal volume to the atom ...
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