The weighted-volume derivative of a space-filling diagram

H. Edelsbrunner, P. Koehl, PNAS 100 (2003) 2203–2208.

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Abstract
Computing the volume occupied by individual atoms in macromolecular structures has been the subject of research for several decades. This interest has grown in the recent years, because weighted volumes are widely used in implicit solvent models. Applications of the latter in molecular mechanics simulations require that the derivatives of these weighted volumes be known. In this article, we give a formula for the volume derivative of a molecule modeled as a space-filling diagram made up of balls in motion. The formula is given in terms of the weights, radii, and distances between the centers as well as the sizes of the facets of the power diagram restricted to the space-filling diagram. Special attention is given to the detection and treatment of singularities as well as discontinuities of the derivative.
Publishing Year
Date Published
2003-03-04
Journal Title
PNAS
Volume
100
Issue
5
Page
2203 - 2208
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Edelsbrunner H, Koehl P. The weighted-volume derivative of a space-filling diagram. PNAS. 2003;100(5):2203-2208. doi:10.1073/pnas.0537830100
Edelsbrunner, H., & Koehl, P. (2003). The weighted-volume derivative of a space-filling diagram. PNAS, 100(5), 2203–2208. https://doi.org/10.1073/pnas.0537830100
Edelsbrunner, Herbert, and Patrice Koehl. “The Weighted-Volume Derivative of a Space-Filling Diagram.” PNAS 100, no. 5 (2003): 2203–8. https://doi.org/10.1073/pnas.0537830100.
H. Edelsbrunner and P. Koehl, “The weighted-volume derivative of a space-filling diagram,” PNAS, vol. 100, no. 5, pp. 2203–2208, 2003.
Edelsbrunner H, Koehl P. 2003. The weighted-volume derivative of a space-filling diagram. PNAS. 100(5), 2203–2208.
Edelsbrunner, Herbert, and Patrice Koehl. “The Weighted-Volume Derivative of a Space-Filling Diagram.” PNAS, vol. 100, no. 5, National Academy of Sciences, 2003, pp. 2203–08, doi:10.1073/pnas.0537830100.

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