The Weighted Mean Curvature Derivative of a Space-Filling Diagram

• Main Authors: Akopyan Arsenyi, Edelsbrunner Herbert
• Format: Article
• Language: English
• Published: De Gruyter 2020-07-01
• Series: Computational and Mathematical Biophysics
• Subjects: molecular dynamics; proteins; space-filling diagrams; intrinsic volume; alpha shapes; inclusion-exclusion; derivatives; discontinuities; computer implementation; 52a38; 92e10
• Online Access: https://doi.org/10.1515/cmb-2020-0100

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.