k ^ Vprobe where AV is the volume of a grid cube and the index k runs over the grid points occupied by the probe sphere. The grid spacing is usually 0.5 A. The electric displacement of every charge of the receptor can be approximated by the Coulomb field [13,34,37]:

where xi is the position of the receptor atom i and qi its partial charge. Equation 7 is an analytical approximation of the total electric displacement and fulfills the condition ofvalidity ofEquations 5 and 6, i.e., D (x) is independent of the dielectric environment. The receptor desolvation in the Coulomb field approximation results from Equation 6 together with Equation 7:

The accuracy of this approximation is discussed in the Methods section of SEED (see below).

It is important to note that the desolvation of a charged ion by a small nonpolar sphere at a distance r from the ion varies approximately as 1/r4 (Equation 8). This is a very short range effect compared with the ion electrostatic potential which varies as 1/r. Hence, the potential alone cannot properly describe electrostatic desolvation.

Graphical rendering

The hydrophobicity is color-displayed over the molecular surface (MS) [38], which is traced by the surface of the probe sphere rolling over the van der Waals surface of the receptor. The MS consists of the convex receptor surface/probe contact areas and the concave (or reentrant) receptor surface/probe areas, and is preferred to the SAS because it gives a more precise description of the small details at the surface of the receptor. A smooth MS covering the receptor is generated via the molecular graphics package GRASP [23] as an ensemble of triangles. The hydrophobicity at each vertex is the value of the binding energy of the probe sphere (Equation 1) in the closest position to the vertex. This value is then visually displayed with the help of colors ranging from green (hydrophobic) through white (intermediate) to blue (hydrophilic).

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