The accurate modeling of molecules in solution using molecular mechanics requires realistic models for the interaction of the solvent with the molecule. To treat such a medium (usually water) in a molecular calculation, both explicit and implicit models have been developed. Explicit solvent models rely on using hundreds or thousands of discrete solvent molecules. Such calculations converge only slowly because of the large number of particles involved. They generally require orders of magnitude more CPU time than corresponding gas phase calculations on the same molecule. Because explicit models are so computationally demanding, there is a significant interest in developing more rapid implicit solvent models that treat the solvent as a continuous medium having the average properties of the real solvent, and surrounding the solute beginning at the van der Waals surface. A variety of continuum models have been described over the years. Among these, the generalized Born-Surface Area (GB/SA) model has become very popular. GB/SA is the sum of two terms, one describing the effect of solvent on electrostatic interactions and the other describing non-polar interactions.

Non-polar interactions can be described using the accessible surface area (ASA) of each atom, a quantity that changes in complex ways during folding and other molecular motions. The ASA of all atoms of a protein can be computed from the dual complex of the molecule. We have also shown that the derivatives of these surface area terms with respect to atomic position can be computed using the same combinatorial structure. Furthermore, we have shown that the discontinuities of these derivatives occur only at degenerate placements of the atoms, and these degeneracies are rigorously treated in the process of computing the dual complex.

The computational cost of the Alpha Shape software was an issue we had to solve. One step of a molecular dynamics simulation in vacuo of a 90-residue proteins requires approximately 40 ms on a 600 Mhz Pentium III computer; the same simulation performed with explicit water simulations requires 240 ms. An implicit solvent simulation should therefore position itself between these two figures. We have fully rewritten the Alpha Shape software, focusing on speed efficiency, without loss in accuracy and robustness. With our new package, computation of the surface area and its derivatives of a 90-residue proteins requires approximately 60 ms. This figure fits well within our goal. The whole package is currently incorporated into a molecular simulation software, and will be made accessible to the scientific community.

Solvent also plays a role in screening the electrostatic interactions between charges of the solute. The Generalized Born model provides a pair additive energy function that accounts for this screening. An important element of this model is to evaluate the self energy of a charge of the solute in the presence of the continuous solvent model. This self energy is computed by integrating the electrostatic potential generated by the charge over the whole volume of the solute. This integration is usually performed by representing the solute as a union of balls, and ignoring high order (>2) overlap between these balls. We are working on improving upon this assumption by performing an exact integration, using the alpha shape formalism to deal with ball overlaps.