The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram

Abstract

The morphometric approach [11, 14] writes the solvation free energy 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 Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.

Keywords

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