Density Scalable Atomic Spheres

The related recent development of Density Scalable Atomic Spheres, DSAS [255] allows one to build VDWS-like fused sphere approximations of MIDCO s for any density threshold value a (with the exception of very high densities such as those in the immediate vicinity of the nuclei). The basis of this technique is a family of scaling functions [255] developed for generating radii r Ca) of formal atomic spheres along which the electronic density of atom A is any selected constant value a, within a chemically important range of electronic densities. These "density scalable" radius functions rA(a) have been determined [255] for all the atoms A commonly encountered in molecular modeling problems. 

The technique of density scalable atomic spheres provides an inexpensive approximation for MIDCO s of large molecules, such as those studied in typical drug design and molecular engineering problems, if direct quantum chemical density calculations are not feasible. Furthermore, the density scalable radii also serve as natural starting points for the construction of the families of spheres required for the FSGH technique described above. 

Density Scalable Atomic Sphere (DSAS) surfaces [255]. This technique generates radii for atomic spheres for any desired electron density at the surface. The method is used for inexpensive representations of MIDCO s of large molecules, in combination with the Fused Sphere Guided Homotopy method (FSGH) [43]. 

Figure 7.1 Illustration of the principle of the Fused Spheres Guided Homotopy Method (FSGH), applied for the generation of dot representations of density scalable MIDCO surfaces for the water molecule. Three families of atomic spheres (thin lines) and their envelope surfaces (heavy lines) are shown in the upper part of the figure. In the lower part of the figure, the selected point sets on the innermost family of spheres are connected by interpolating lines to the exposed points (black dots) on the envelope surfaces of two enlarged families of spheres. Linear interpolation along the lines for two selected density values leads to two families of white dots, generating approximations of two MIDCO s (heavy lines in the lower figure).

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