A Curved Panel Integration Technique for Molecular Surfaces

In this paper we present a surface formulation and curved panel integration method for computing the van der Waals interaction energy between a molecular solute and aqueous solvent. This modeling problem arises in computational drug design, where one wishes to understand the energetic tradeoff between a trial drug’s interactions with solvent and its interactions with the target. We use the divergence theorem to convert a volume integral to an integral over the solute– solvent boundary. Validation of the surface formulation reveals strong dependence on the accuracy of the boundary representation; to improve the surface discretization quality, we define a type of curved panel called a generalized spherical triangle. A straightforward extension of an earlier curved panel integration method allows us to integrate functions over the curved surfaces. Numerical results demonstrate the accuracy of the improved surface representation and the integration technique.