On the analytical calculation of van der Waals surfaces and volumes: Some numerical aspects

A fast computer algorithm is presented for complete analytical calculation of van der Waals surfaces and volumes. Connolly's analytical algorithms, computing second‐ and third‐order atomic spheres overlaps, are shown to give insufficient numerical approximations of the exact van der Waals surfaces and volumes. The presented algorithm computes overlaps of any order. Practical situations frequently involve six‐order overlaps. Analytical computed surfaces and volumes of 63 chemicals are compared with Monte Carlo measured values. © 1994 by John Wiley & Sons, Inc.

[1]  K. D. Gibson,et al.  Exact calculation of the volume and surface area of fused hard-sphere molecules with unequal atomic radii , 1987 .

[2]  Shoshana J. Wodak,et al.  Detection of cavities in a set of interpenetrating spheres , 1991 .

[3]  A. Bondi.  van der Waals Volumes and Radii , 1964 .

[4]  Jay W. Ponder,et al.  Algorithms for calculating excluded volume and its derivatives as a function of molecular conformation and their use in energy minimization , 1991 .

[5]  John S. Rowlinson,et al.  The triplet distribution function in a fluid of hard spheres , 1963 .

[6]  Michel Petitjean,et al.  Topological statistics on a large structural file , 1990, J. Chem. Inf. Comput. Sci..

[7]  A. Y. Meyer.  Molecular mechanics and molecular shape. V. on the computation of the bare surface area of molecules , 1988 .

[8]  Harold A. Scheraga,et al.  Volume of the intersection of three spheres of unequal size: a simplified formula , 1987 .

[9]  M. L. Connolly.  Analytical molecular surface calculation , 1983 .

[10]  Michael L. Connolly,et al.  Computation of molecular volume , 1985 .

[11]  Osman F. Güner,et al.  Use of flexible queries for searching conformationally flexible molecules in databases of three-dimensional structures , 1992, J. Chem. Inf. Comput. Sci..

[12]  Amatzya Y. Meyer,et al.  More on the size of molecules , 1990 .

[13]  A. Gavezzotti,et al.  The calculation of molecular volumes and the use of volume analysis in the investigation of structured media and of solid-state organic reactivity , 1983 .

[14]  Akbar Nayeem,et al.  MSEED: A program for the rapid analytical determination of accessible surface areas and their derivatives , 1992 .

[15]  B. Lee,et al.  The interpretation of protein structures: estimation of static accessibility. , 1971, Journal of molecular biology.

[16]  K. D. Gibson,et al.  Surface area of the intersection of three spheres with unequal radii A simplified analytical formula , 1988 .

[17]  T. Richmond,et al.  Solvent accessible surface area and excluded volume in proteins. Analytical equations for overlapping spheres and implications for the hydrophobic effect. , 1984, Journal of molecular biology.

[18]  F. M. Richards,et al.  Calculation of molecular volumes and areas for structures of known geometry. , 1985, Methods in enzymology.