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The Role of Symmetry in Conformational Changes of Viral Capsids: A Mathematical Approach

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Discrete and Topological Models in Molecular Biology

Part of the book series: Natural Computing Series ((NCS))

Abstract

For many viruses, structural transitions of the viral protein containers, which encapsulate and hence provide protection for the viral genome, form an integral part of their life cycle. We review here two complementary mathematical models for the expansion of an icosahedral viral capsid. The first is based on a geometrical description of the capsid involving a library of point sets obtained by affine extensions of the icosahedral group, and allows us to characterize the space of the possible transition paths between the initial and the final state. In the second approach, the capsid is described as a union of rigid tiles that interact with each other and with the genomic material, placing emphasis on the energetic determinants of the transition event. Both models predict loss of icosahedral symmetry along the transition path, even though the final state is icosahedral.

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Acknowledgements

RT and GI thank the Leverhulme Trust for financial support via a Research Leadership Award. PC and GI acknowledge the Italian PRIN 2009 project “Mathematics and Mechanics of Biological Systems and Soft Tissues”.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino, Italy

    Paolo Cermelli

  2. Department of Mathematics, York Centre for Complex Systems Analysis, University of York, York, UK

    Giuliana Indelicato

  3. Departments of Mathematics and Biology, York Centre for Complex Systems Analysis, University of York, York, UK

    Reidun Twarock

Authors
  1. Paolo Cermelli
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  2. Giuliana Indelicato
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  3. Reidun Twarock
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Correspondence to Paolo Cermelli .

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Editors and Affiliations

  1. Dept. Mathematics & Statistics, University of South Florida, Tampa, Florida, USA

    Nataša Jonoska

  2. Dept. Mathematics & Statistics, University of South Florida, Tampa, Florida, USA

    Masahico Saito

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Cermelli, P., Indelicato, G., Twarock, R. (2014). The Role of Symmetry in Conformational Changes of Viral Capsids: A Mathematical Approach. In: Jonoska, N., Saito, M. (eds) Discrete and Topological Models in Molecular Biology. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40193-0_10

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  • DOI: https://doi.org/10.1007/978-3-642-40193-0_10

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