Quantitative symmetry and chirality-A fast computational algorithm for large structures: Proteins, macromolecules, nanotubes, and unit cells

Symmetry is one of the most fundamental properties of nature and is used to understand and investigate physical properties. Classically, symmetry is treated as a binary qualitative property, although other physical properties are quantitative. Using the continuous symmetry measure (CSM) methodology...

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Bibliographic Details
Published in:Journal of computational chemistry Vol. 32; no. 12; pp. 2526 - 2538
Main Authors: Dryzun, Chaim, Zait, Amir, Avnir, David
Format: Journal Article
Language:English
Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.09.2011
Wiley Subscription Services, Inc
Subjects:
Algorithms
Analytical chemistry
chirality
chirality measure
Macromolecular Substances - chemistry
Molecular Structure
Molecules
nanotube chirality
Nanotubes
Nanotubes - chemistry
Proteins
Proteins - chemistry
proteins symmetry
Stereoisomerism
supramolecular structures
symmetry
symmetry measure
unit cells chirality
ISSN:0192-8651, 1096-987X, 1096-987X
Online Access:Get full text
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Summary:Symmetry is one of the most fundamental properties of nature and is used to understand and investigate physical properties. Classically, symmetry is treated as a binary qualitative property, although other physical properties are quantitative. Using the continuous symmetry measure (CSM) methodology one can quantify symmetry and correlate it quantitatively to physical, chemical, and biological properties. The exact analytical procedures for calculating the CSM are computationally expensive and the calculation time grows rapidly as the structure contains more atoms. In this article, we present a new method for calculating the CSM and the related continuous chirality measure (CCM) for large systems. The new method is much faster than the full analytical procedures and it reduces the calculation time dependency from N! to N2, where N is the number of atoms in the structure. We evaluate the cost of the applied approximations, estimate the error of the method, and show that deviations from the analytical solutions are within an error of 2%, and in many cases even less. The method is applicable at the moment for the cyclic symmetry point groups— Ci, Cs, Cn, and Sn, and therefore it can be used also for chirality measures, which are the minimal of the Sn measures. We demonstrate the application of the method for large structures across chemistry: proteins, macromolecules, nanotubes, and large unit cells of crystals. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011
Bibliography:istex:B534690EB2DF33FA88CFDB89CEDEFBAFBBE74FB8
ArticleID:JCC21828
The Israel Science Foundation - No. 307/08
ark:/67375/WNG-5D5KSZKX-1
The German-Israel Binational Foundation - No. 983/2007
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ISSN:0192-8651
1096-987X
1096-987X
DOI:10.1002/jcc.21828