Tables for
Volume F
Crystallography of biological macromolecules
Edited by E. Arnold, D. M. Himmel and M. G. Rossmann

International Tables for Crystallography (2012). Vol. F, ch. 22.1, p. 706   | 1 | 2 |

Section The problem of the protein surface

M. Gersteina* and F. M. Richardsa

aDepartment of Molecular Biophysics & Biochemistry, 266 Whitney Avenue, Yale University, PO Box 208114, New Haven, CT 06520, USA
Correspondence e-mail: The problem of the protein surface

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When one is carrying out the Voronoi procedure, if a particular atom does not have enough neighbours the `polyhedron' formed around it will not be closed, but rather will have an open, concave shape. As it is not often possible to place enough water molecules in an X-ray crystal structure to cover all the surface atoms, these `open polyhedra' occur frequently on the protein surface (Fig.[link]. Furthermore, even when it is possible to define a closed polyhedron on the surface, it will often be distended and too large. This is the problem of the protein surface in relation to the Voronoi construction.


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The problem of the protein surface. This figure shows the difficulty in constructing Voronoi polyhedra for atoms on the protein surface. If all the water molecules near the surface are not resolved in a crystal structure, one often does not have enough neighbours to define a closed polyhedron. This figure should be compared with Fig.[link], illustrating the basic Voronoi construction. The two figures are the same except that in this figure, some of the atoms on the left are missing, giving the central atom an open polyhedron. The broken lines indicate planes that were initially included in the polyhedron but then removed by the `chopping-down' procedure (see Fig.[link]).

There are a number of practical techniques for dealing with this problem. First, one can use very high resolution protein crystal structures, which have many solvent atoms positioned (Gerstein & Chothia, 1996[link]). Alternatively, one can make up the positions of missing solvent molecules. These can be placed either according to a regular grid-like arrangement or, more realistically, according to the results of molecular simulation (Finney et al., 1980[link]; Gerstein et al., 1995[link]; Richards, 1974[link]).


Finney, J. L., Gellatly, B. J., Golton, I. C. & Goodfellow, J. (1980). Solvent effects and polar interactions in the structural stability and dynamics of globular proteins. Biophys. J. 32, 17–33.
Gerstein, M. & Chothia, C. (1996). Packing at the protein–water interface. Proc. Natl Acad. Sci. USA, 93, 10167–10172.
Gerstein, M., Tsai, J. & Levitt, M. (1995). The volume of atoms on the protein surface: calculated from simulation, using Voronoi polyhedra. J. Mol. Biol. 249, 955–966.
Richards, F. M. (1974). The interpretation of protein structures: total volume, group volume distributions and packing density. J. Mol. Biol. 82, 1–14.

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