---
_id: '12544'
abstract:
- lang: eng
  text: Geometry is crucial in our efforts to comprehend the structures and dynamics
    of biomolecules. For example, volume, surface area, and integrated mean and Gaussian
    curvature of the union of balls representing a molecule are used to quantify its
    interactions with the water surrounding it in the morphometric implicit solvent
    models. The Alpha Shape theory provides an accurate and reliable method for computing
    these geometric measures. In this paper, we derive homogeneous formulas for the
    expressions of these measures and their derivatives with respect to the atomic
    coordinates, and we provide algorithms that implement them into a new software
    package, AlphaMol. The only variables in these formulas are the interatomic distances,
    making them insensitive to translations and rotations. AlphaMol includes a sequential
    algorithm and a parallel algorithm. In the parallel version, we partition the
    atoms of the molecule of interest into 3D rectangular blocks, using a kd-tree
    algorithm. We then apply the sequential algorithm of AlphaMol to each block, augmented
    by a buffer zone to account for atoms whose ball representations may partially
    cover the block. The current parallel version of AlphaMol leads to a 20-fold speed-up
    compared to an independent serial implementation when using 32 processors. For
    instance, it takes 31 s to compute the geometric measures and derivatives of each
    atom in a viral capsid with more than 26 million atoms on 32 Intel processors
    running at 2.7 GHz. The presence of the buffer zones, however, leads to redundant
    computations, which ultimately limit the impact of using multiple processors.
    AlphaMol is available as an OpenSource software.
acknowledgement: "P.K. acknowledges support from the University of California Multicampus
  Research Programs and Initiatives (Grant No. M21PR3267) and from the NSF (Grant
  No.1760485). H.E. acknowledges support from the European Research Council (ERC)
  under the European Union’s Horizon 2020 research and innovation program, Grant No.
  788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31,
  and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry
  and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35.\r\nOpen Access
  is funded by the Austrian Science Fund (FWF)."
article_processing_charge: No
article_type: original
author:
- first_name: Patrice
  full_name: Koehl, Patrice
  last_name: Koehl
- 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: Koehl P, Akopyan A, Edelsbrunner H. Computing the volume, surface area, mean,
    and Gaussian curvatures of molecules and their derivatives. <i>Journal of Chemical
    Information and Modeling</i>. 2023;63(3):973-985. doi:<a href="https://doi.org/10.1021/acs.jcim.2c01346">10.1021/acs.jcim.2c01346</a>
  apa: Koehl, P., Akopyan, A., &#38; Edelsbrunner, H. (2023). Computing the volume,
    surface area, mean, and Gaussian curvatures of molecules and their derivatives.
    <i>Journal of Chemical Information and Modeling</i>. American Chemical Society.
    <a href="https://doi.org/10.1021/acs.jcim.2c01346">https://doi.org/10.1021/acs.jcim.2c01346</a>
  chicago: Koehl, Patrice, Arseniy Akopyan, and Herbert Edelsbrunner. “Computing the
    Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives.”
    <i>Journal of Chemical Information and Modeling</i>. American Chemical Society,
    2023. <a href="https://doi.org/10.1021/acs.jcim.2c01346">https://doi.org/10.1021/acs.jcim.2c01346</a>.
  ieee: P. Koehl, A. Akopyan, and H. Edelsbrunner, “Computing the volume, surface
    area, mean, and Gaussian curvatures of molecules and their derivatives,” <i>Journal
    of Chemical Information and Modeling</i>, vol. 63, no. 3. American Chemical Society,
    pp. 973–985, 2023.
  ista: Koehl P, Akopyan A, Edelsbrunner H. 2023. Computing the volume, surface area,
    mean, and Gaussian curvatures of molecules and their derivatives. Journal of Chemical
    Information and Modeling. 63(3), 973–985.
  mla: Koehl, Patrice, et al. “Computing the Volume, Surface Area, Mean, and Gaussian
    Curvatures of Molecules and Their Derivatives.” <i>Journal of Chemical Information
    and Modeling</i>, vol. 63, no. 3, American Chemical Society, 2023, pp. 973–85,
    doi:<a href="https://doi.org/10.1021/acs.jcim.2c01346">10.1021/acs.jcim.2c01346</a>.
  short: P. Koehl, A. Akopyan, H. Edelsbrunner, Journal of Chemical Information and
    Modeling 63 (2023) 973–985.
corr_author: '1'
date_created: 2023-02-12T23:00:59Z
date_published: 2023-02-13T00:00:00Z
date_updated: 2025-04-15T07:16:52Z
day: '13'
ddc:
- '510'
- '540'
department:
- _id: HeEd
doi: 10.1021/acs.jcim.2c01346
ec_funded: 1
external_id:
  isi:
  - '000920370700001'
  pmid:
  - '36638318'
file:
- access_level: open_access
  checksum: 7d20562269edff1e31b9d6019d4983b0
  content_type: application/pdf
  creator: dernst
  date_created: 2023-08-16T12:21:13Z
  date_updated: 2023-08-16T12:21:13Z
  file_id: '14070'
  file_name: 2023_JCIM_Koehl.pdf
  file_size: 8069223
  relation: main_file
  success: 1
file_date_updated: 2023-08-16T12:21:13Z
has_accepted_license: '1'
intvolume: '        63'
isi: 1
issue: '3'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '02'
oa: 1
oa_version: Published Version
page: 973-985
pmid: 1
project:
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '788183'
  name: Alpha Shape Theory Extended
- _id: 268116B8-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: Z00342
  name: Mathematics, Computer Science
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I02979-N35
  name: Persistence and stability of geometric complexes
publication: Journal of Chemical Information and Modeling
publication_identifier:
  eissn:
  - 1549-960X
  issn:
  - 1549-9596
publication_status: published
publisher: American Chemical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Computing the volume, surface area, mean, and Gaussian curvatures of molecules
  and their derivatives
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: 63
year: '2023'
...