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New insights into viral architecture via affine extended symmetry groups

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New insights into viral architecture via affine extended symmetry groups. / Keef, T.; Twarock, R.

In: Computational and Mathematical Methods in Medicine, Vol. 9, No. 3-4, 01.09.2008, p. 221-229.

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Harvard

Keef, T & Twarock, R 2008, 'New insights into viral architecture via affine extended symmetry groups', Computational and Mathematical Methods in Medicine, vol. 9, no. 3-4, pp. 221-229. https://doi.org/10.1080/17486700802168163

APA

Keef, T., & Twarock, R. (2008). New insights into viral architecture via affine extended symmetry groups. Computational and Mathematical Methods in Medicine, 9(3-4), 221-229. https://doi.org/10.1080/17486700802168163

Vancouver

Keef T, Twarock R. New insights into viral architecture via affine extended symmetry groups. Computational and Mathematical Methods in Medicine. 2008 Sep 1;9(3-4):221-229. https://doi.org/10.1080/17486700802168163

Author

Keef, T. ; Twarock, R. / New insights into viral architecture via affine extended symmetry groups. In: Computational and Mathematical Methods in Medicine. 2008 ; Vol. 9, No. 3-4. pp. 221-229.

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@article{287dac04025f4671bad430a4e1489193,
title = "New insights into viral architecture via affine extended symmetry groups",
abstract = "Since the seminal work of Caspar and Klug on the structure of the protein containers that encapsulate and hence protect the viral genome, it has been recognized that icosahedral symmetry is crucial for the structural organization of viruses. In particular, icosahedral symmetry has been invoked in order to predict the surface structures of viral capsids in terms of tessellations or tilings that schematically encode the locations of the protein subunits in the capsids. Whilst this approach is capable of predicting the relative locations of the proteins in the capsids, a prediction on the relative sizes of different virus particles in a family cannot be made. Moreover, information on the full 3D structure of viral particles, including the tertiary structures of the capsid proteins and the organization of the viral genome within the capsid are inaccessible with their approach. We develop here a mathematical framework based on affine extensions of the icosahedral group that allows us to address these issues. In particular, we show that the relative radii of viruses in the family of Polyomaviridae and the material boundaries in simple RNA viruses can be determined with our approach. The results complement Caspar and Klug's theory of quasi-equivalence and provide details on virus structure that have not been accessible with previous methods, implying that icosahedral symmetry is more important for virus architecture than previously appreciated.",
keywords = "viral capsids, affine extensions, icosahedral symmetry, tilings, STRONGLY CORRELATED STRUCTURE, 3-DIMENSIONAL STRUCTURE, COXETER GROUPS, RESOLUTION, PROTEINS, VIRUSES, BACTERIOPHAGE-MS2, RNA, VP1",
author = "T. Keef and R. Twarock",
year = "2008",
month = sep,
day = "1",
doi = "10.1080/17486700802168163",
language = "English",
volume = "9",
pages = "221--229",
journal = "Computational and Mathematical Methods in Medicine",
issn = "1748-670X",
publisher = "Hindawi Publishing Corporation",
number = "3-4",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - New insights into viral architecture via affine extended symmetry groups

AU - Keef, T.

AU - Twarock, R.

PY - 2008/9/1

Y1 - 2008/9/1

N2 - Since the seminal work of Caspar and Klug on the structure of the protein containers that encapsulate and hence protect the viral genome, it has been recognized that icosahedral symmetry is crucial for the structural organization of viruses. In particular, icosahedral symmetry has been invoked in order to predict the surface structures of viral capsids in terms of tessellations or tilings that schematically encode the locations of the protein subunits in the capsids. Whilst this approach is capable of predicting the relative locations of the proteins in the capsids, a prediction on the relative sizes of different virus particles in a family cannot be made. Moreover, information on the full 3D structure of viral particles, including the tertiary structures of the capsid proteins and the organization of the viral genome within the capsid are inaccessible with their approach. We develop here a mathematical framework based on affine extensions of the icosahedral group that allows us to address these issues. In particular, we show that the relative radii of viruses in the family of Polyomaviridae and the material boundaries in simple RNA viruses can be determined with our approach. The results complement Caspar and Klug's theory of quasi-equivalence and provide details on virus structure that have not been accessible with previous methods, implying that icosahedral symmetry is more important for virus architecture than previously appreciated.

AB - Since the seminal work of Caspar and Klug on the structure of the protein containers that encapsulate and hence protect the viral genome, it has been recognized that icosahedral symmetry is crucial for the structural organization of viruses. In particular, icosahedral symmetry has been invoked in order to predict the surface structures of viral capsids in terms of tessellations or tilings that schematically encode the locations of the protein subunits in the capsids. Whilst this approach is capable of predicting the relative locations of the proteins in the capsids, a prediction on the relative sizes of different virus particles in a family cannot be made. Moreover, information on the full 3D structure of viral particles, including the tertiary structures of the capsid proteins and the organization of the viral genome within the capsid are inaccessible with their approach. We develop here a mathematical framework based on affine extensions of the icosahedral group that allows us to address these issues. In particular, we show that the relative radii of viruses in the family of Polyomaviridae and the material boundaries in simple RNA viruses can be determined with our approach. The results complement Caspar and Klug's theory of quasi-equivalence and provide details on virus structure that have not been accessible with previous methods, implying that icosahedral symmetry is more important for virus architecture than previously appreciated.

KW - viral capsids

KW - affine extensions

KW - icosahedral symmetry

KW - tilings

KW - STRONGLY CORRELATED STRUCTURE

KW - 3-DIMENSIONAL STRUCTURE

KW - COXETER GROUPS

KW - RESOLUTION

KW - PROTEINS

KW - VIRUSES

KW - BACTERIOPHAGE-MS2

KW - RNA

KW - VP1

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U2 - 10.1080/17486700802168163

DO - 10.1080/17486700802168163

M3 - Article

VL - 9

SP - 221

EP - 229

JO - Computational and Mathematical Methods in Medicine

JF - Computational and Mathematical Methods in Medicine

SN - 1748-670X

IS - 3-4

ER -