---
_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. <i>PNAS</i>. 2003;100(5):2203-2208. doi:<a href="https://doi.org/10.1073/pnas.0537830100">10.1073/pnas.0537830100</a>
  apa: Edelsbrunner, H., &#38; Koehl, P. (2003). The weighted-volume derivative of
    a space-filling diagram. <i>PNAS</i>. National Academy of Sciences. <a href="https://doi.org/10.1073/pnas.0537830100">https://doi.org/10.1073/pnas.0537830100</a>
  chicago: Edelsbrunner, Herbert, and Patrice Koehl. “The Weighted-Volume Derivative
    of a Space-Filling Diagram.” <i>PNAS</i>. National Academy of Sciences, 2003.
    <a href="https://doi.org/10.1073/pnas.0537830100">https://doi.org/10.1073/pnas.0537830100</a>.
  ieee: H. Edelsbrunner and P. Koehl, “The weighted-volume derivative of a space-filling
    diagram,” <i>PNAS</i>, 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.” <i>PNAS</i>, vol. 100, no. 5, National Academy of Sciences,
    2003, pp. 2203–08, doi:<a href="https://doi.org/10.1073/pnas.0537830100">10.1073/pnas.0537830100</a>.
  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'
...