The Weighted Mean Curvature Derivative of a Space-Filling Diagram

Abstract

Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this yields the derivative of the morphometric expression of the solvation free energy.

Keywords

• molecular dynamics
• proteins
• space-filling diagrams
• intrinsic volume
• alpha shapes
• inclusion-exclusion
• derivatives
• discontinuities
• computer implementation
• 52a38
• 92e10