Appendix: Molecular Surface Technical Details

Imagine rolling a ball over the assembly of spheres constituting the van der Waals surface. Where the outside of the ball contacts the van der Waals spheres, the surfaces coincide. But where two vdW spheres come together, the Connolly surface follows the surface of the solvent sphere, giving fillets rather than cusps where the van der Waals spheres intersect. True Connolly surfaces are very expensive to generate, in general; therefore often an approximation is used.

In the ball-rolling description of an extended surface, the locus of points described by the surface of the probe sphere closest to the molecular system constitutes the molecular surface. The molecular surface follows the van der Waals surface except where the surfaces of two atomic spheres are closer together than a probe diameter. In such regions (termed "re-entrant"), the molecular surface is bridged over by a surface section that follows the probe surface. The concept of molecular surface is usually associated with Connolly (Connolly, M.L. Analytical molecular surface calculation, J. Appl. Crystallogr.1983, 16, 548-558). However, Maestro does not use Connolly's algorithm for producing the molecular surface.

The method used by Maestro to create the molecular surface is an elaboration of what is sometimes called the "ink-blot" method. In the ink-blot method, the volume enclosed by the extended surface is first constructed. Then any points within this volume that lie interior to the generating solvent probe are declared to be external. After this process is complete, the boundary of the remaining internal volume is the molecular surface.

Maestro first sets up the grid for the extended surface and interpolates within it to produce the extended surface, as in the extended-surface algorithm described above. Recall that interior grid points have values less then unity and exterior points have values greater than unity. These values are reset so that exterior points are given a value of zero and interior points are given a value much greater than unity. Then a probe sphere is placed on each vertex of the extended surface in turn. For each placement, for all grid vertices in the probe sphere's minimal enclosing grid cube, the grid vertices are given the value Min(d/r, previous_value). Outside the extended surface, the value will always remain zero. Inside the extended surface, the value will rise from near zero close to the probe center to somewhat greater than unity at the grid cube boundaries. The vertices of the molecular surface are then created by interpolation to unity on the grid.

The molecular surface appears from the outside to closely resemble the van der Waals surface, since it follows the van der Waals surface, except for the bridging re-entrant portions. We mentioned earlier that interior atoms of an extended surface are buried (have no surface points on their atomic spheres), but that few, if any, atoms are buried in this sense for a van der Waals surface. Atoms that are buried in an extended surface will also be buried in a molecular surface, since no atomic sphere will have molecular surface points on it unless the atom is adjacent to a region in which a probe molecule will fit. Thus, in their tendency to bury atoms, molecular surfaces resemble extended surfaces rather than van der Waals surfaces.