A Ginzburg–Landau model for the expansion of a dodecahedral viral capsid

Zappa, Emilio; Indelicato, Giuliana; Albano, Alberto; Cermelli, Paolo

doi:10.1016/j.ijnonlinmec.2013.03.003

Cited by 6 publications

(11 citation statements)

References 18 publications

(37 reference statements)

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“…For example, it provides a framework for the analysis of conformational changes in viral capsid, which are structural rearrangements of the capsid proteins that are important for larger classes of viruses to become infective. Specifically, such structural transitions can be modeled with a crystallographic approach, using a generalisation of the concept of Bain strain for multi-dimensional lattices [41] or in the framework of the Ginzburg-Landau theory of phase transitions [28]. Our work opens up a new avenue for a description of such structural transitions in terms of Hamiltonians that are formulated in terms of the six-dimensional symmetry groups that induce the three-dimensional structures of the virus in projection.…”

Section: Resultsmentioning

confidence: 99%

“…However, these results provide for the first time a finite group structure, albeit in a higher dimensional space, underlying the geometry of the multiple layers of material in a virus. This has important consequences for the modelling of physical properties; specifically, conformational changes of viral capsids, which are important for the virus to become infective, can be modeled in the framework of the Ginzburg-Landau theory of phase transitions [28], via the formulation of an energy function invariant under the generators of the symmetry group of the capsid.…”

Section: Introductionmentioning

confidence: 99%

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Orbits of crystallographic embedding of non-crystallographic groups and applications to virology

2015

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The architecture of infinite structures with non-crystallographic symmetries can be modelled via aperiodic tilings, but a systematic construction method for finite structures with non-crystallographic symmetry at different radial levels is still lacking. This paper presents a group theoretical method for the construction of finite nested point sets with non-crystallographic symmetry. Akin to the construction of quasicrystals, a non-crystallographic group G is embedded into the point group P of a higher-dimensional lattice and the chains of all G-containing subgroups are constructed. The orbits of lattice points under such subgroups are determined, and it is shown that their projection into a lower-dimensional G-invariant subspace consists of nested point sets with G-symmetry at each radial level. The number of different radial levels is bounded by the index of G in the subgroup of P. In the case of icosahedral symmetry, all subgroup chains are determined explicitly and it is illustrated that these point sets in projection provide blueprints that approximate the organization of simple viral capsids, encoding information on the structural organization of capsid proteins and the genomic material collectively, based on two case studies. Contrary to the affine extensions previously introduced, these orbits endow virus architecture with an underlying finite group structure, which lends itself better to the modelling of dynamic properties than its infinite-dimensional counterpart.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Orbits of crystallographic embedding of non-crystallographic groups and applications to virology

2015

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“…Notice that, by construction, the energy is invariant under the action of the symmetry group of the capsid [31]. Writing, with a slight abuse of notation, ρ(H 3 ) ⊂ GL(12, R) simply as H 3 , this means that…”

Section: Energymentioning

confidence: 99%

Minimum energy paths for conformational changes of viral capsids

2017

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In this work we study conformational changes of viral capsids using techniques of large deviations theory for stochastic differential equations. The viral capsid is a model of a complex system in which many units-the proteins forming the capsomers-interact by weak forces to form a structure with exceptional mechanical resistance. The destabilization of such a structure is interesting both, per se, since it is related either to infection or maturation processes and because it yields insights into the stability of complex structures in which the constitutive elements interact by weak attractive forces. We focus here on a simplified model of a dodecahedral viral capsid and assume that the capsomers are rigid plaquettes with one degree of freedom each. We compute the most probable transition path from the closed capsid to the final configuration using minimum energy paths and discuss the stability of intermediate states.

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“…During this period the structure of the capsid-RNA complex has been derived by X-ray diffraction: by Golmohammadi et al (1993) Also analyzed were the asymmetric properties of MS2 occurring in the assembly, during maturation and in the expansion phase (Stockley et al, 2005;Toropova et al, 2008;Dykeman et al, 2010;Zappa et al, 2013). Note that the present approach allows the indexing of asymmetric units as well.…”

Section: Figure 12mentioning

confidence: 99%

Symmetry-adapted digital modeling III. Coarse-grained icosahedral viruses

Janner

2016

Acta Cryst Sect A

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Considered is the coarse-grained modeling of icosahedral viruses in terms of a three-dimensional lattice (the digital modeling lattice) selected among the projected points in space of a six-dimensional icosahedral lattice. Backbone atomic positions (Cα's for the residues of the capsid and phosphorus atoms P for the genome nucleotides) are then indexed by their nearest lattice point. This leads to a fine-grained lattice point characterization of the full viral chains in the backbone approximation (denoted as digital modeling). Coarse-grained models then follow by a proper selection of the indexed backbone positions, where for each chain one can choose the desired coarseness. This approach is applied to three viruses, the Satellite tobacco mosaic virus, the bacteriophage MS2 and the Pariacoto virus, on the basis of structural data from the Brookhaven Protein Data Bank. In each case the various stages of the procedure are illustrated for a given coarse-grained model and the corresponding indexed positions are listed. Alternative coarse-grained models have been derived and compared. Comments on related results and approaches, found among the very large set of publications in this field, conclude this article.

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A Ginzburg–Landau model for the expansion of a dodecahedral viral capsid

Cited by 6 publications

References 18 publications

Orbits of crystallographic embedding of non-crystallographic groups and applications to virology

Orbits of crystallographic embedding of non-crystallographic groups and applications to virology

Minimum energy paths for conformational changes of viral capsids

Symmetry-adapted digital modeling III. Coarse-grained icosahedral viruses

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