--- _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' ...