The Weighted Mean Curvature Derivative of a Space-Filling Diagram

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 l...

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Bibliographic Details
Published inComputational and Mathematical Biophysics Vol. 8; no. 1; pp. 51 - 67
Main Authors Akopyan, Arsenyi, Edelsbrunner, Herbert
Format Journal Article
LanguageEnglish
Published De Gruyter 27.07.2020
Subjects
52A38
92E10
alpha shapes
computer implementation
derivatives
discontinuities
inclusion-exclusion
intrinsic volume
Molecular dynamics
proteins
space-filling diagrams
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Summary: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.
ISSN:2544-7297
2544-7297
DOI:10.1515/cmb-2020-0100