Numerical calculation of molecular surface area. I. Assessment of errors

Several points distributions have been used to calculate van der Waals surface areas of a set of molecules. It is shown that there is no strict correlation between the global statistical characteristics of the points distribution, such as deviation and standard deviation, and the accuracy of the calculation of molecular surface. Information about details of the points distribution is needed for predicting the precision of the results. The results show that points distributions produced by optimization of the U function of Le Grand and Merz [J. Comput. Chem., 14, 349 (1993)] give the most accurate estimation of the molecular surface in numerical calculations. The precision of the numerical evaluation of the van der Waals surface areas has been assessed for 256, 512, 1024, and 2048 points on a single sphere. © 1996 by John Wiley & Sons, Inc.

[1]  Timothy Clark,et al.  A numerical self-consistent reaction field (SCRF) model for ground and excited states in NDDO-based methods , 1993 .

[2]  Donald G. Truhlar,et al.  AM1-SM2 and PM3-SM3 parameterized SCF solvation models for free energies in aqueous solution , 1992, J. Comput. Aided Mol. Des..

[3]  Ian K. Crain,et al.  The Monte-Carlo generation of random polygons , 1978 .

[4]  Ruben Abagyan,et al.  ICM—A new method for protein modeling and design: Applications to docking and structure prediction from the distorted native conformation , 1994, J. Comput. Chem..

[5]  M L Connolly,et al.  The molecular surface package. , 1993, Journal of molecular graphics.

[6]  A. Klamt,et al.  COSMO : a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient , 1993 .

[7]  Iñaki Tuñón,et al.  GEPOL: An improved description of molecular surfaces II. Computing the molecular area and volume , 1991 .

[8]  H. Scheraga,et al.  Empirical solvation models can be used to differentiate native from near‐native conformations of bovine pancreatic trypsin inhibitor , 1991, Proteins.

[9]  A. Shrake,et al.  Environment and exposure to solvent of protein atoms. Lysozyme and insulin. , 1973, Journal of molecular biology.

[10]  Frank Eisenhaber,et al.  Improved strategy in analytic surface calculation for molecular systems: Handling of singularities and computational efficiency , 1993, J. Comput. Chem..

[11]  Chris Sander,et al.  The double cubic lattice method: Efficient approaches to numerical integration of surface area and volume and to dot surface contouring of molecular assemblies , 1995, J. Comput. Chem..

[12]  Michel Petitjean,et al.  On the analytical calculation of van der Waals surfaces and volumes: Some numerical aspects , 1994, J. Comput. Chem..

[13]  Eamonn F. Healy,et al.  Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model , 1985 .

[14]  Iñaki Tuñón,et al.  GEPOL: An improved description of molecular surfaces. III. A new algorithm for the computation of a solvent‐excluding surface , 1994, J. Comput. Chem..

[15]  Doros N. Theodorou,et al.  Analytical treatment of the volume and surface area of molecules formed by an arbitrary collection of unequal spheres intersected by planes , 1991 .

[16]  Mark A. Spackman,et al.  Potential derived charges using a geodesic point selection scheme , 1996, J. Comput. Chem..

[17]  K. Sharp,et al.  Accurate Calculation of Hydration Free Energies Using Macroscopic Solvent Models , 1994 .

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

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

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

[21]  F M Richards,et al.  Areas, volumes, packing and protein structure. , 1977, Annual review of biophysics and bioengineering.

[22]  Kenneth M. Merz,et al.  Rapid approximation to molecular surface area via the use of Boolean logic and look‐up tables , 1993, J. Comput. Chem..

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

[24]  Georges Voronoi Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire. Recherches sur les parallélloèdres primitifs. , 1908 .