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Shape analysis of molecular surfaces
Author(s) -
Duncan Bruce S.,
Olson Arthur J.
Publication year - 1993
Publication title -
biopolymers
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.556
H-Index - 125
eISSN - 1097-0282
pISSN - 0006-3525
DOI - 10.1002/bip.360330205
Subject(s) - principal curvature , gaussian curvature , eigenvalues and eigenvectors , surface (topology) , gaussian , curvature , normal , scalar (mathematics) , gaussian function , mathematical analysis , matrix (chemical analysis) , geometry , chemistry , physics , mathematics , mean curvature , computational chemistry , quantum mechanics , chromatography
The description of molecular shape is important in the analysis of protein–protein and protein–ligand interactions. We describe volumetric and surface‐based techniques for computing shape properties of molecular surfaces. The surface is defined as an isocontour of an approximate electron density function. Each technique can compute several scalar and vector surface properties such as the Gaussian and mean curvature, principal curvatures, and principal curvature directions. Shape properties are derived from the eigenvalues and eigenvectors of a 3 by 3 matrix for each surface point. In the volumetric approach, the matrix is the second derivative of an approximate electron density function. In the surface‐based approach, the matrix is the approximate gradient of the surface normal. Derivatives 4 are computed by convolving the density or the surface normals with the derivatives of a Gaussian function. The variance of the Gaussian determines the effective length scale at which the surface is analyzed. Scalar surface properties are displayed as colored dots or shaded triangles, and vector properties are displayed as line segments from each surface point. This report describes the implementation of these procedures and their use in computing the shape properties of Cu‐Zu superoxide dismutase. © 1993 John Wiley & Sons, Inc.