---
_id: '9156'
abstract:
- lang: eng
text: The morphometric approach [11, 14] writes the solvation free energy 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 Gaussian curvature. Together with the derivatives of the weighted
volume in [7], the weighted area in [4], and the weighted mean curvature in [1],
this yields the derivative of the morphometric expression of solvation free energy.
acknowledgement: "The authors of this paper thank Roland Roth for suggesting the analysis
of theweighted\r\ncurvature derivatives for the purpose of improving molecular dynamics
simulations. They also thank Patrice Koehl for the implementation of the formulas
and for his encouragement and advise along the road. Finally, they thank two anonymous
reviewers for their constructive criticism.\r\nThis project has received funding
from the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (grant agreement No 78818 Alpha). It is also partially
supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry
and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF)."
article_processing_charge: No
article_type: original
author:
- first_name: Arseniy
full_name: Akopyan, Arseniy
id: 430D2C90-F248-11E8-B48F-1D18A9856A87
last_name: Akopyan
orcid: 0000-0002-2548-617X
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
citation:
ama: Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a
space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):74-88.
doi:10.1515/cmb-2020-0101
apa: Akopyan, A., & Edelsbrunner, H. (2020). The weighted Gaussian curvature
derivative of a space-filling diagram. Computational and Mathematical Biophysics.
De Gruyter. https://doi.org/10.1515/cmb-2020-0101
chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics.
De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0101.
ieee: A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative
of a space-filling diagram,” Computational and Mathematical Biophysics,
vol. 8, no. 1. De Gruyter, pp. 74–88, 2020.
ista: Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative
of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88.
mla: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature
Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics,
vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:10.1515/cmb-2020-0101.
short: A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8
(2020) 74–88.
date_created: 2021-02-17T15:12:44Z
date_published: 2020-07-21T00:00:00Z
date_updated: 2023-10-17T12:35:10Z
day: '21'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/cmb-2020-0101
ec_funded: 1
external_id:
arxiv:
- '1908.06777'
file:
- access_level: open_access
checksum: ca43a7440834eab6bbea29c59b56ef3a
content_type: application/pdf
creator: dernst
date_created: 2021-02-19T13:33:19Z
date_updated: 2021-02-19T13:33:19Z
file_id: '9170'
file_name: 2020_CompMathBiophysics_Akopyan.pdf
file_size: 707452
relation: main_file
success: 1
file_date_updated: 2021-02-19T13:33:19Z
has_accepted_license: '1'
intvolume: ' 8'
issue: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: 74-88
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: I02979-N35
name: Persistence and stability of geometric complexes
publication: Computational and Mathematical Biophysics
publication_identifier:
issn:
- 2544-7297
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
status: public
title: The weighted Gaussian curvature derivative of a space-filling diagram
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2020'
...