---
_id: '4011'
abstract:
- lang: eng
text: The size and shape of macromolecules such as proteins and nucleic acids play
an important role in their functions. Prior efforts to quantify these properties
have been based on various discretization or tessellation procedures involving
analytical or numerical computations. In this article, we present an analytically
exact method for computing the metric properties of macromolecules based on the
alpha shape theory. This method uses the duality between alpha complex and the
weighted Voronoi decomposition of a molecule. We describe the intuitive ideas
and concepts behind the alpha shape theory and the algorithm for computing areas
and volumes of macromolecules. We apply our method to compute areas and volumes
of a number of protein systems. We also discuss several difficulties commonly
encountered in molecular shape computations and outline methods to overcome these
problems. (C) 1998 Wiley-Liss, Inc.
acknowledgement: We thank Michael Facello for the torus area formula and suggestion
regarding computation of MS model from SA model. We thank Nataraj Akkiraju, Patrick
Moran, and Marcus Wagner for interesting discussionson the topic of this article
and for help in the generationof two- and three-dimensional illustrations. We thank
NSF Meta Center Allocation for providing computational resources. The software
VOLBL is available at:http://alpha.ncsa.uiuc.edu/alpha.
article_processing_charge: No
article_type: original
author:
- first_name: Jie
full_name: Liang, Jie
last_name: Liang
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ping
full_name: Fu, Ping
last_name: Fu
- first_name: Pamidighantam
full_name: Sudhakar, Pamidighantam
last_name: Sudhakar
- first_name: Shankar
full_name: Subramaniam, Shankar
last_name: Subramaniam
citation:
ama: 'Liang J, Edelsbrunner H, Fu P, Sudhakar P, Subramaniam S. Analytical shape
computation of macromolecules: I. molecular area and volume through alpha shape.
Proteins: Structure, Function and Bioinformatics. 1998;33(1):1-17. doi:10.1002/(SICI)1097-0134(19981001)33:1<1::AID-PROT1>3.0.CO;2-O'
apa: 'Liang, J., Edelsbrunner, H., Fu, P., Sudhakar, P., & Subramaniam, S. (1998).
Analytical shape computation of macromolecules: I. molecular area and volume through
alpha shape. Proteins: Structure, Function and Bioinformatics. Wiley-Blackwell.
https://doi.org/10.1002/(SICI)1097-0134(19981001)33:1<1::AID-PROT1>3.0.CO;2-O'
chicago: 'Liang, Jie, Herbert Edelsbrunner, Ping Fu, Pamidighantam Sudhakar, and
Shankar Subramaniam. “Analytical Shape Computation of Macromolecules: I. Molecular
Area and Volume through Alpha Shape.” Proteins: Structure, Function and Bioinformatics.
Wiley-Blackwell, 1998. https://doi.org/10.1002/(SICI)1097-0134(19981001)33:1<1::AID-PROT1>3.0.CO;2-O.'
ieee: 'J. Liang, H. Edelsbrunner, P. Fu, P. Sudhakar, and S. Subramaniam, “Analytical
shape computation of macromolecules: I. molecular area and volume through alpha
shape,” Proteins: Structure, Function and Bioinformatics, vol. 33, no.
1. Wiley-Blackwell, pp. 1–17, 1998.'
ista: 'Liang J, Edelsbrunner H, Fu P, Sudhakar P, Subramaniam S. 1998. Analytical
shape computation of macromolecules: I. molecular area and volume through alpha
shape. Proteins: Structure, Function and Bioinformatics. 33(1), 1–17.'
mla: 'Liang, Jie, et al. “Analytical Shape Computation of Macromolecules: I. Molecular
Area and Volume through Alpha Shape.” Proteins: Structure, Function and Bioinformatics,
vol. 33, no. 1, Wiley-Blackwell, 1998, pp. 1–17, doi:10.1002/(SICI)1097-0134(19981001)33:1<1::AID-PROT1>3.0.CO;2-O.'
short: 'J. Liang, H. Edelsbrunner, P. Fu, P. Sudhakar, S. Subramaniam, Proteins:
Structure, Function and Bioinformatics 33 (1998) 1–17.'
date_created: 2018-12-11T12:06:25Z
date_published: 1998-10-01T00:00:00Z
date_updated: 2022-08-25T13:32:59Z
day: '01'
doi: 10.1002/(SICI)1097-0134(19981001)33:1<1::AID-PROT1>3.0.CO;2-O
extern: '1'
intvolume: ' 33'
issue: '1'
language:
- iso: eng
month: '10'
oa_version: None
page: 1 - 17
publication: 'Proteins: Structure, Function and Bioinformatics'
publication_identifier:
issn:
- 0887-3585
publication_status: published
publisher: Wiley-Blackwell
publist_id: '2112'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Analytical shape computation of macromolecules: I. molecular area and volume
through alpha shape'
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 33
year: '1998'
...
---
_id: '4012'
abstract:
- lang: eng
text: The structures of proteins are well-packed, yet they contain numerous cavities
which play key roles in accommodating small molecules, or enabling conformational
changes. From high-resolution structures it is possible to identify these cavities.
We have developed a precise algorithm based on alpha shapes for measuring space-filling-based
molecular models (such as van der Waals, solvent accessible, and molecular surface
descriptions). We applied this method for accurate computation of the surface
area and volume of cavities in several proteins. In addition, all of the atoms/residues
Lining the cavities are identified, We use this method to study the structure
and the stability of proteins, as well as to locate cavities that could contain
structural water molecules in the proton transport pathway in the membrane protein
bacteriorhodopsin.
acknowledgement: The software for constructing weighted Delaunay complexes and the
alpha shape filters was written by Ernst Mücke and Michael Facello. We thank them
forcreating reliable and robust software so that wecan build on their results. The
authors thank NSF Meta Center Allocation for providing computational resources.
The software VOLBL is part of the standard distribution of the alpha shapes software,
andis available at http://alpha.ncsa.uiuc.edu/alpha.
article_processing_charge: No
article_type: original
author:
- first_name: Jie
full_name: Liang, Jie
last_name: Liang
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ping
full_name: Fu, Ping
last_name: Fu
- first_name: Pamidighantam
full_name: Sudhakar, Pamidighantam
last_name: Sudhakar
- first_name: Shankar
full_name: Subramaniam, Shankar
last_name: Subramaniam
citation:
ama: 'Liang J, Edelsbrunner H, Fu P, Sudhakar P, Subramaniam S. Analytical shape
computation of macromolecules: II. Inaccessible cavities in proteins. Proteins:
Structure, Function and Bioinformatics. 1998;33(1):18-29. doi:10.1002/(SICI)1097-0134(19981001)33:1<18::AID-PROT2>3.0.CO;2-H'
apa: 'Liang, J., Edelsbrunner, H., Fu, P., Sudhakar, P., & Subramaniam, S. (1998).
Analytical shape computation of macromolecules: II. Inaccessible cavities in proteins.
Proteins: Structure, Function and Bioinformatics. Wiley-Blackwell. https://doi.org/10.1002/(SICI)1097-0134(19981001)33:1<18::AID-PROT2>3.0.CO;2-H'
chicago: 'Liang, Jie, Herbert Edelsbrunner, Ping Fu, Pamidighantam Sudhakar, and
Shankar Subramaniam. “Analytical Shape Computation of Macromolecules: II. Inaccessible
Cavities in Proteins.” Proteins: Structure, Function and Bioinformatics.
Wiley-Blackwell, 1998. https://doi.org/10.1002/(SICI)1097-0134(19981001)33:1<18::AID-PROT2>3.0.CO;2-H.'
ieee: 'J. Liang, H. Edelsbrunner, P. Fu, P. Sudhakar, and S. Subramaniam, “Analytical
shape computation of macromolecules: II. Inaccessible cavities in proteins,” Proteins:
Structure, Function and Bioinformatics, vol. 33, no. 1. Wiley-Blackwell, pp.
18–29, 1998.'
ista: 'Liang J, Edelsbrunner H, Fu P, Sudhakar P, Subramaniam S. 1998. Analytical
shape computation of macromolecules: II. Inaccessible cavities in proteins. Proteins:
Structure, Function and Bioinformatics. 33(1), 18–29.'
mla: 'Liang, Jie, et al. “Analytical Shape Computation of Macromolecules: II. Inaccessible
Cavities in Proteins.” Proteins: Structure, Function and Bioinformatics,
vol. 33, no. 1, Wiley-Blackwell, 1998, pp. 18–29, doi:10.1002/(SICI)1097-0134(19981001)33:1<18::AID-PROT2>3.0.CO;2-H.'
short: 'J. Liang, H. Edelsbrunner, P. Fu, P. Sudhakar, S. Subramaniam, Proteins:
Structure, Function and Bioinformatics 33 (1998) 18–29.'
date_created: 2018-12-11T12:06:26Z
date_published: 1998-10-01T00:00:00Z
date_updated: 2022-08-25T13:35:41Z
day: '01'
doi: 10.1002/(SICI)1097-0134(19981001)33:1<18::AID-PROT2>3.0.CO;2-H
extern: '1'
intvolume: ' 33'
issue: '1'
language:
- iso: eng
month: '10'
oa_version: None
page: 18 - 29
publication: 'Proteins: Structure, Function and Bioinformatics'
publication_identifier:
issn:
- 0887-3585
publication_status: published
publisher: Wiley-Blackwell
publist_id: '2113'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Analytical shape computation of macromolecules: II. Inaccessible cavities
in proteins'
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 33
year: '1998'
...