---
_id: '3992'
abstract:
- lang: eng
text: 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.
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Patrice
full_name: Koehl, Patrice
last_name: Koehl
citation:
ama: Edelsbrunner H, Koehl P. The weighted-volume derivative of a space-filling
diagram. PNAS. 2003;100(5):2203-2208. doi:10.1073/pnas.0537830100
apa: Edelsbrunner, H., & Koehl, P. (2003). The weighted-volume derivative of
a space-filling diagram. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.0537830100
chicago: Edelsbrunner, Herbert, and Patrice Koehl. “The Weighted-Volume Derivative
of a Space-Filling Diagram.” PNAS. National Academy of Sciences, 2003.
https://doi.org/10.1073/pnas.0537830100.
ieee: H. Edelsbrunner and P. Koehl, “The weighted-volume derivative of a space-filling
diagram,” PNAS, vol. 100, no. 5. National Academy of Sciences, pp. 2203–2208,
2003.
ista: Edelsbrunner H, Koehl P. 2003. The weighted-volume derivative of a space-filling
diagram. PNAS. 100(5), 2203–2208.
mla: 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.
short: H. Edelsbrunner, P. Koehl, PNAS 100 (2003) 2203–2208.
date_created: 2018-12-11T12:06:19Z
date_published: 2003-03-04T00:00:00Z
date_updated: 2024-02-27T12:31:59Z
day: '04'
doi: 10.1073/pnas.0537830100
extern: '1'
external_id:
pmid:
- '12601153'
intvolume: ' 100'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC151318/
month: '03'
oa: 1
oa_version: Published Version
page: 2203 - 2208
pmid: 1
publication: PNAS
publication_identifier:
issn:
- 0027-8424
publication_status: published
publisher: National Academy of Sciences
publist_id: '2133'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The weighted-volume derivative of a space-filling diagram
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 100
year: '2003'
...