MANUSCRIPT FOR INCLUSION IN: 

INTERNATIONAL TABLES FOR MACROMOLECULAR CRYSTALLOGRAPHY

Editors: Rossmann and Arnold

Topic: Molecular Geometry and Features (22 b)

Title: Protein Geometry: Volumes, Areas, and Distances

Authors: M. Gerstein and F.M. Richards

 

I. Introduction

II. Geometric Definitions

II.A. Definitions of Volume

II.A.1. The Voronoi Construction

II.A.2. The Delaunay Triangulation

II.B The Problem of the Protein Surface

II.C Definitions of Surface

II.D Definitions of Atomic Radii

II.D.1. van der Waals radii

II.D.2. Probe radius

III. Applications and Results

III.A Packing

III.A.1. Using Volume to Measure Packing Efficiency

III.A.2. How tightly packed is the protein core?

III.A.3. Surface Packing

III.A.4. Internal Interfaces and Motions

III.B Cavities

 

Figure #1 - 2D schematic of the Voronoi Construction

Figure #2 - A Voronoi Polyhedron in 3D

Figure #3 - The Positioning of the Dividing Plane

Figure #4 - The Delaunay Triangulation

Figure #5 - Open Polyhedra on the Protein Surface

Figure #6 - Various Definitions of Protein Area

Figure #7 - Packing Efficiency

Figure #8 - Tight Packing vs. Loose Packing

 

Table #1 - Lists of vdW radii

Table #2 - Some Surfaces

Table #4 - Standard Volumes for Atoms in the Core

 

(This document is http://bioinfo.mbb.yale.edu/Geometry/int-tab-ol.html)