Section 22.1.2.2.1. Introduction

The first method to be discussed allows the calculation of an accessible surface. The first method for calculating molecular surface involved raining water down on a model of a macromolecule and constructing a surface by making a net under the spheres in their landing positions (Greer & Bush, 1978). This ignored overhangs and was replaced by the dot surface method. More recently, methods were developed to make polyhedral surfaces of triangles by contouring between lattice points or by delimiting with arcs the spherical and toroidal surfaces and then subdividing the piece-wise quartic molecular surface. The surface is then composed of patches whose areas can be precisely integrated. van der Waals surfaces consist of convex spherical triangles whose areas can be estimated by the Gauss–Bonnet theorem. Re-entrant surfaces are comprised of concave spherical triangles whose areas can be similarly estimated and toroidal saddle-shaped patches whose areas can be calculated by analytical geometry and calculus.