---
_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
arxiv: 1
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. <i>Computational and Mathematical Biophysics</i>. 2020;8(1):74-88.
    doi:<a href="https://doi.org/10.1515/cmb-2020-0101">10.1515/cmb-2020-0101</a>
  apa: Akopyan, A., &#38; Edelsbrunner, H. (2020). The weighted Gaussian curvature
    derivative of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>.
    De Gruyter. <a href="https://doi.org/10.1515/cmb-2020-0101">https://doi.org/10.1515/cmb-2020-0101</a>
  chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature
    Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>.
    De Gruyter, 2020. <a href="https://doi.org/10.1515/cmb-2020-0101">https://doi.org/10.1515/cmb-2020-0101</a>.
  ieee: A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative
    of a space-filling diagram,” <i>Computational and Mathematical Biophysics</i>,
    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.” <i>Computational and Mathematical Biophysics</i>,
    vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:<a href="https://doi.org/10.1515/cmb-2020-0101">10.1515/cmb-2020-0101</a>.
  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
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  date_created: 2021-02-19T13:33:19Z
  date_updated: 2021-02-19T13:33:19Z
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language:
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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
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  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8
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...
---
_id: '9157'
abstract:
- lang: eng
  text: Representing an atom by a solid sphere in 3-dimensional Euclidean space, we
    get the space-filling diagram of a molecule by taking the union. Molecular dynamics
    simulates its motion subject to bonds and other forces, including the solvation
    free energy. The morphometric approach [12, 17] writes the latter 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 mean curvature. Together with the derivatives of the weighted volume
    in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this
    yields the derivative of the morphometric expression of the solvation free energy.
acknowledgement: "The authors of this paper thank Roland Roth for suggesting the analysis
  of the weighted\r\ncurvature derivatives for the purpose of improving molecular
  dynamics simulations and for his continued encouragement. 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 mean curvature derivative of a space-filling
    diagram. <i>Computational and Mathematical Biophysics</i>. 2020;8(1):51-67. doi:<a
    href="https://doi.org/10.1515/cmb-2020-0100">10.1515/cmb-2020-0100</a>
  apa: Akopyan, A., &#38; Edelsbrunner, H. (2020). The weighted mean curvature derivative
    of a space-filling diagram. <i>Computational and Mathematical Biophysics</i>.
    De Gruyter. <a href="https://doi.org/10.1515/cmb-2020-0100">https://doi.org/10.1515/cmb-2020-0100</a>
  chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature
    Derivative of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>.
    De Gruyter, 2020. <a href="https://doi.org/10.1515/cmb-2020-0100">https://doi.org/10.1515/cmb-2020-0100</a>.
  ieee: A. Akopyan and H. Edelsbrunner, “The weighted mean curvature derivative of
    a space-filling diagram,” <i>Computational and Mathematical Biophysics</i>, vol.
    8, no. 1. De Gruyter, pp. 51–67, 2020.
  ista: Akopyan A, Edelsbrunner H. 2020. The weighted mean curvature derivative of
    a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 51–67.
  mla: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Mean Curvature Derivative
    of a Space-Filling Diagram.” <i>Computational and Mathematical Biophysics</i>,
    vol. 8, no. 1, De Gruyter, 2020, pp. 51–67, doi:<a href="https://doi.org/10.1515/cmb-2020-0100">10.1515/cmb-2020-0100</a>.
  short: A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8
    (2020) 51–67.
date_created: 2021-02-17T15:13:01Z
date_published: 2020-06-20T00:00:00Z
date_updated: 2023-10-17T12:34:51Z
day: '20'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1515/cmb-2020-0100
ec_funded: 1
file:
- access_level: open_access
  checksum: cea41de9937d07a3b927d71ee8b4e432
  content_type: application/pdf
  creator: dernst
  date_created: 2021-02-19T13:56:24Z
  date_updated: 2021-02-19T13:56:24Z
  file_id: '9171'
  file_name: 2020_CompMathBiophysics_Akopyan2.pdf
  file_size: 562359
  relation: main_file
  success: 1
file_date_updated: 2021-02-19T13:56:24Z
has_accepted_license: '1'
intvolume: '         8'
issue: '1'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 51-67
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 mean 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
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...