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, pp. 703-712   | 1 | 2 |

Chapter 22.1. Protein geometry: volumes, areas and distances

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:


Baker, E. N. & Hubbard, R. E. (1984). Hydrogen bonding in globular proteins. Prog. Biophys. Mol. Biol. 44, 97–179.
Bernal, J. D. & Finney, J. L. (1967). Random close-packed hard-sphere model II. Geometry of random packing of hard spheres. Discuss. Faraday Soc. 43, 62–69.
Bondi, A. (1964). van der Waals volumes and radii. J. Phys. Chem. 68, 441–451.
Bondi, A. (1968). Molecular crystals, liquids and glasses. New York: Wiley.
Brooks, B. R., Bruccoleri, R. E., Olafson, B. D., States, D. J., Swaminathan, S. & Karplus, M. (1983). CHARMM: a program for macromolecular energy, minimization, and dynamics calculations. J. Comput. Chem. 4, 187–217.
Chandler, D., Weeks, J. D. & Andersen, H. C. (1983). van der Waals picture of liquids, solids, and phase transformations. Science, 220, 787–794.
Chothia, C. (1975). Structural invariants in protein folding. Nature (London), 254, 304–308.
Chothia, C. & Janin, J. (1975). Principles of protein–protein recognition. Nature (London), 256, 705–708.
Connolly, M. (1986). Measurement of protein surface shape by solid angles. J. Mol. Graphics, 4, 3–6.
Connolly, M. L. (1991). Molecular interstitial skeleton. Comput. Chem. 15, 37–45.
Dunfield, L. G., Burgess, A. W. & Scheraga, H. A. (1979). Energy parameters in polypeptides. 8. Empirical potential energy algorithm for the conformational analysis of large molecules. J. Phys. Chem. 82, 2609.
Edelsbrunner, H., Facello, M. & Liang, J. (1996). On the Definition and Construction of Pockets in Macromolecules, pp. 272–287. Singapore: World Scientific.
Edelsbrunner, H., Facello, M., Ping, F. & Jie, L. (1995). Measuring proteins and voids in proteins. Proc. 28th Hawaii Intl Conf. Sys. Sci. pp. 256–264.
Edelsbrunner, H. & Mucke, E. (1994). Three-dimensional alpha shapes. ACM Trans. Graphics, 13, 43–72.
Finkelstein, A. (1994). Implications of the random characteristics of protein sequences for their three-dimensional structure. Curr. Opin. Struct. Biol. 4, 422–428.
Finney, J. L. (1975). Volume occupation, environment and accessibility in proteins. The problem of the protein surface. J. Mol. Biol. 96, 721–732.
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.
Gelin, B. R. & Karplus, M. (1979). Side-chain torsional potentials: effect of dipeptide, protein, and solvent environment. Biochemistry, 18, 1256–1268.
Gellatly, B. J. & Finney, J. L. (1982). Calculation of protein volumes: an alternative to the Voronoi procedure. J. Mol. Biol. 161, 305–322.
Gerstein, M. & Chothia, C. (1996). Packing at the protein–water interface. Proc. Natl Acad. Sci. USA, 93, 10167–10172.
Gerstein, M., Lesk, A. M., Baker, E. N., Anderson, B., Norris, G. & Chothia, C. (1993). Domain closure in lactoferrin: two hinges produce a see-saw motion between alternative close-packed interfaces. J. Mol. Biol. 234, 357–372.
Gerstein, M., Lesk, A. M. & Chothia, C. (1994). Structural mechanisms for domain movements. Biochemistry, 33, 6739–6749.
Gerstein, M. & Lynden-Bell, R. M. (1993a). Simulation of water around a model protein helix. 1. Two-dimensional projections of solvent structure. J. Phys. Chem. 97, 2982–2991.
Gerstein, M. & Lynden-Bell, R. M. (1993b). Simulation of water around a model protein helix. 2. The relative contributions of packing, hydrophobicity, and hydrogen bonding. J. Phys. Chem. 97, 2991–2999.
Gerstein, M. & Lynden-Bell, R. M. (1993c). What is the natural boundary for a protein in solution? J. Mol. Biol. 230, 641–650.
Gerstein, M., Sonnhammer, E. & Chothia, C. (1994). Volume changes on protein evolution. J. Mol. Biol. 236, 1067–1078.
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.
Harpaz, Y., Gerstein, M. & Chothia, C. (1994). Volume changes on protein folding. Structure, 2, 641–649.
Hubbard, S. J. & Argos, P. (1994). Cavities and packing at protein interfaces. Protein Sci. 3, 2194–2206.
Hubbard, S. J. & Argos, P. (1995). Evidence on close packing and cavities in proteins. Curr. Opin. Biotechnol. 6, 375–381.
Kapp, O. H., Moens, L., Vanfleteren, J., Trotman, C. N. A., Suzuki, T. & Vinogradov, S. N. (1995). Alignment of 700 globin sequences: extent of amino acid substitution and its correlation with variation in volume. Protein Sci. 4, 2179–2190.
Kleywegt, G. J. & Jones, T. A. (1994). Detection, delineation, measurement and display of cavities in macromolecular structures. Acta Cryst. D50, 178–185.
Kocher, J. P., Prevost, M., Wodak, S. J. & Lee, B. (1996). Properties of the protein matrix revealed by the free energy of cavity formation. Structure, 4, 1517–1529.
Kuhn, L. A., Siani, M. A., Pique, M. E., Fisher, C. L., Getzoff, E. D. & Tainer, J. A. (1992). The interdependence of protein surface topography and bound water molecules revealed by surface accessibility and fractal density measures. J. Mol. Biol. 228, 13–22.
Lee, B. & Richards, F. M. (1971). The interpretation of protein structures: estimation of static accessibility. J. Mol. Biol. 55, 379–400.
Leicester, S. E., Finney, J. L. & Bywater, R. P. (1988). Description of molecular surface shape using Fourier descriptors. J. Mol. Graphics, 6, 104–108.
Levitt, M., Hirshberg, M., Sharon, R. & Daggett, V. (1995). Potential energy function and parameters for simulations of the molecular dynamics of proteins and nucleic acids in solution. Comput. Phys. Comm. 91, 215–231.
Lim, V. I. & Ptitsyn, O. B. (1970). On the constancy of the hydrophobic nucleus volume in molecules of myoglobins and hemoglobins. Mol. Biol. (USSR), 4, 372–382.
Madan, B. & Lee, B. (1994). Role of hydrogen bonds in hydrophobicity: the free energy of cavity formation in water models with and without the hydrogen bonds. Biophys. Chem. 51, 279–289.
Matthews, B. W., Morton, A. G. & Dahlquist, F. W. (1995). Use of NMR to detect water within nonpolar protein cavities. (Letter.) Science, 270, 1847–1849.
Nemethy, G., Pottle, M. S. & Scheraga, H. A. (1983). Energy parameters in polypeptides. 9. Updating of geometrical parameters, nonbonded interactions and hydrogen bond interactions for the naturally occurring amino acids. J. Phys. Chem. 87, 1883–1887.
O'Rourke, J. (1994). Computational Geometry in C. Cambridge University Press.
Pattabiraman, N., Ward, K. B. & Fleming, P. J. (1995). Occluded molecular surface: analysis of protein packing. J. Mol. Recognit. 8, 334–344.
Pauling, L. (1960). The Nature of the Chemical Bond, 3rd ed. Ithaca: Cornell University Press.
Peters, K. P., Fauck, J. & Frommel, C. (1996). The automatic search for ligand binding sites in proteins of known three-dimensional structure using only geometric criteria. J. Mol. Biol. 256, 201–213.
Petitjean, M. (1994). On the analytical calculation of van der Waals surfaces and volumes: some numerical aspects. J. Comput. Chem. 15, 1–10.
Pontius, J., Richelle, J. & Wodak, S. J. (1996). Deviations from standard atomic volumes as a quality measure for protein crystal structures. J. Mol. Biol. 264, 121–136.
Procacci, P. & Scateni, R. (1992). A general algorithm for computing Voronoi volumes: application to the hydrated crystal of myoglobin. Int. J. Quant. Chem. 42, 151–152.
Rashin, A. A., Iofin, M. & Honig, B. (1986). Internal cavities and buried waters in globular proteins. Biochemistry, 25, 3619–3625.
Richards, F. M. (1974). The interpretation of protein structures: total volume, group volume distributions and packing density. J. Mol. Biol. 82, 1–14.
Richards, F. M. (1977). Areas, volumes, packing, and protein structure. Annu. Rev. Biophys. Bioeng. 6, 151–176.
Richards, F. M. (1979). Packing defects, cavities, volume fluctuations, and access to the interior of proteins. Including some general comments on surface area and protein structure. Carlsberg Res. Commun. 44, 47–63.
Richards, F. M. (1985). Calculation of molecular volumes and areas for structures of known geometry. Methods Enzymol. 115, 440–464.
Richards, F. M. & Lim, W. A. (1994). An analysis of packing in the protein folding problem. Q. Rev. Biophys. 26, 423–498.
Richmond, T. J. & Richards, F. M. (1978). Packing of alpha-helices: geometrical constraints and contact areas. J. Mol. Biol. 119, 537–555.
Rowland, R. S. & Taylor, R. (1996). Intermolecular nonbonded contact distances in organic crystal structures: comparison with distances expected from van der Waals radii. J. Phys. Chem. 100, 7384–7391.
Shrake, A. & Rupley, J. A. (1973). Environment and exposure to solvent of protein atoms. Lysozyme and insulin. J. Mol. Biol. 79, 351–371.
Sibbald, P. R. & Argos, P. (1990). Weighting aligned protein or nucleic acid sequences to correct for unequal representation. J. Mol. Biol. 216, 813–818.
Singh, R. K., Tropsha, A. & Vaisman, I. I. (1996). Delaunay tessellation of proteins: four body nearest-neighbor propensities of amino acid residues. J. Comput. Biol. 3, 213–222.
Sreenivasan, U. & Axelsen, P. H. (1992). Buried water in homologous serine proteases. Biochemistry, 31, 12785–12791.
Tsai, J., Gerstein, M. & Levitt, M. (1996). Keeping the shape but changing the charges: a simulation study of urea and its isosteric analogues. J. Chem. Phys. 104, 9417–9430.
Tsai, J., Gerstein, M. & Levitt, M. (1997). Estimating the size of the minimal hydrophobic core. Protein Sci. 6, 2606–2616.
Tsai, J., Taylor, R., Chothia, C. & Gerstein, M. (1999). The packing density in proteins: standard radii and volumes. J. Mol. Biol. 290, 253–266.
Tsai, J., Voss, N. & Gerstein, M. (2001). Voronoi calculations of protein volumes: sensitivity analysis and parameter database. Bioinformatics. In the press.
Voronoi, G. F. (1908). Nouvelles applications des paramétres continus à la théorie des formes quadratiques. J. Reine Angew. Math. 134, 198–287.
Williams, M. A., Goodfellow, J. M. & Thornton, J. M. (1994). Buried waters and internal cavities in monomeric proteins. Protein Sci. 3, 1224–1235.