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Viruses and the Physics of Soft Condensed Matter

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Viruses and the Physics of Soft Condensed Matter COMMENTARY Viruses and the physics of soft condensed matter Adam Zlotnick* Department of Biochemistry and Molecular Biology, University of Oklahoma Health Sciences Center, Oklahoma City, OK 73190 lmost 50 years ago, Francis Crick and James Watson ob- served that ‘‘almost all small viruses are either spheres or Arods’’ and put forth the hypothesis that such viruses were symmetrical arrays of subunits (1). In the following paper in that issue of Nature, Donald Caspar demonstrated that tomato bushy stunt virus had at least cubic symmetry and provided the first evidence for icosahe- dral symmetry in a biological molecule (2). About half of all virus families share icosahedral geometry, even though they may have nothing else in common. In this issue of PNAS, Zandi et al. (3) have investigated the physical basis for the prevalence of icosahedral symmetry by using a simplest case model: circular elements tiling the sur- face of a more or less spherical solid. The resulting model can produce the complex behavior observed in solution experiments. Their results strongly sup- port a corollary implicit in Crick’s hy- pothesis: the physical properties of icosahedra lead to their prevalence in biology. Here, I will briefly discuss the paper by Zandi et al. and compare it to some recent theoretical and biochemical studies of virus structure and assembly. Icosahedral Symmetry To understand the nature and applica- tion of Zandi et al.’s argument, it is probably best to start with a description of icosahedral symmetry. An icosahe- dron is 20-sided solid, where each facet has threefold symmetry (Fig. 1A). To Fig. 1. Different arrangements of icosahedral symmetry. (A)AT ϭ 1 icosahedron has 20 triangular facets, build an icosahedron out of protein, each of which has threefold symmetry; an icosahedron has 20 ϫ 3 ϭ 60 equivalent asymmetric units. Larger each face must be made of at least three facets can be cut out of hexagonal lattice, resulting in facets where smaller triangles are arranged around local quasi-sixfolds. The area of the larger facet is T ϭ h2 ϩ hk ϩ k2, where h and k are integers (h Ն 1 and proteins, because an individual protein k Ն 0). A T ϭ 3 facet has three smaller triangles and nine subunits, but it still has only three asymmetric cannot have intrinsic threefold symme- units. (B) A selection of cryoelectron microscopy image reconstructions demonstrating different T num- try. In an icosahedron, the proteins are bers: polio (T ϭ 1), small hepatitis B virus (HBV) capsid (T ϭ 3), large HBV capsid (T ϭ 4), bacteriophage HK97 related by exact two-, three-, and five- (T ϭ 7), and herpes simplex virus (T ϭ 16). Bovine papilloma virus, like all papovaviruses, has a T ϭ 7 lattice, fold symmetry axes. It turns out that few but is assembled exclusively from pentamers. An icosahedral facet is highlighted on selected images. spherical viruses are built of 60 subunits [Image in A reproduced with permission from ref. 16 (Copyright 2003, Elsevier Science, Amsterdam).] The (3 ϫ 20), but most viruses are built of T reconstructions in B are courtesy of Alasdair Steven and coworkers (National Institute of Arthritis and multiples of 60, where the T (for trian- Musculoskeletal and Skin Diseases, National Institutes of Health, Bethesda). gulation) number indicates the number of subunits within each of the 60 icosa- Fundamental Models and ably stable capsids (5). When capsomers hedral asymmetric units (4). The term Complex Behavior were allowed to ‘‘equilibrate’’ between quasi-equivalence indicates that the sub- units are in distinct but quasi-equivalent Zandi et al. identified the most stable pentamer and hexamer forms, the most environments. In this manner, some sub- arrangements of circular capsomers on stable species were the series of quasi- units are arranged around icosahedral different sized spheres by Monte Carlo equivalent icosahedra. This is not to say fivefold axes and others are arranged as methods. Capsomers interacted via a that nonicosahedral forms were unsta- hexamers. Quasi-equivalence is readily van der Waals-like force field. This ap- apparent in a virus structure by the proach built on an earlier analysis of the presence of pentameric and hexameric stability of ‘‘tiled’’ spheres, which See companion article on page 15556. groupings of subunits, the capsomers showed that nonicosahedral arrange- *E-mail: [email protected]. (Fig. 1B). ments of capsomers could yield reason- © 2004 by The National Academy of Sciences of the USA www.pnas.org͞cgi͞doi͞10.1073͞pnas.0406935101 PNAS ͉ November 2, 2004 ͉ vol. 101 ͉ no. 44 ͉ 15549–15550 Downloaded by guest on September 30, 2021 ble, but at equilibrium they would be and scaffold proteins. The recently dis- tions (16, 17), but they say little about vanishingly rare. The nonicosahedral covered tape-measure function of a pro- the details of the assembly of single structures are intriguing: they may be a tein in a large bacteriophage (D. Stuart particles. However, course-grained mo- window into the structure of retrovirus and D. Bamford, personal communica- lecular dynamics can provide a detailed provirions, which are heterogeneous in tion) is a biological mechanism for picture of successful assembly of simple size, nonicosahedral, possess local six- maintaining homogeneity that perfectly particles (18) or test proposed mecha- fold symmetry, yet according to Euler’s responds to the mechanism for hetero- nisms for regulating assembly and quasi- theorem still contain 12 fivefolds (6–9). geneity based on theory (13). equivalence (19, 20). Thus, retroviral capsids may represent a Where Zandi et al. considered spheri- What Is the Value of Understanding kinetic trap unable to successfully reor- cal capsomers that conformed to quasi- Virus Stability and Assembly? ganize into an icosahedral isomer. equivalence, Twarock (14) examined Another demonstration of the power alternative tiling strategies. Twarock’s Virus life cycle is regulated at many lev- els. A great deal of effort has been in- of this fundamental model based on alternatives are icosahedral but provide vested in studying regulation at the level primitive capsomers is its response to a clever way of viewing deviations from of viral nucleic acid replication, interfer- perturbation. When the model capsids the ideality of quasi-equivalent predic- ence with cell cycle, synthesis of viral are swollen, capsids may burst along tions, such as those presented by pa- proteins, and so on. A virus capsid must shear lines, reminiscent of maturation povaviruses where pentamers occupy assemble at the right time and place to mutants of Flock House Virus (10). (be ready to) package the right nucleic Pentamers absorbed strain when a cap- acid, it must be able to undergo confor- sid was deformed, suggestive of the be- Assembly mational transitions if required, and it havior of fivefolds in bacteriophages must be able release its nucleic acid. HK97 and P22 as the respective capsids models can be The capsid must be tough and fragile, are stressed (11, 12). the subunits refractory to assembly and The paper by Zandi et al. (3) is part developed that are readily assembled. Part of the key to of a recent burst of activity by physicists these paradoxes is the role of hysteresis and mathematicians in the field of virol- specific for biologically in stability (16, 21) and the recent ob- ogy. A good example of this is the re- servation that hepatitis B virus assembly cent satellite workshop on ‘‘Mathematical observed geometry. may be subject to allosteric regulation Virology,’’ supported by the Isaac New- (22). Studies of assembly models have ton Institute and the London Mathe- also led to the hypothesis that assembly matical Society, organized by Reidun hexavalent lattice points (Fig. 1B). By can be misdirected (16, 19, 23). The re- Twarock. Participants at that workshop using a more detailed geometric descrip- cent discovery of a highly effective mis- ranged from condensed matter physicists tion, assembly models can be developed director for hepatitis B virus (24) is a to structural virologists; some of the that are specific for biologically ob- case of biological experiment replicating fundamental predictions. published work from participants is rele- served geometry. The interplay between theoretical and vant to this discussion. Simple geometric figures are a far cry solution studies is powerful and valu- Nelson and coworkers (13) considered from a detailed virus structure, but are able. Physicists studying soft condensed how a growing sheet, analogous to an perfect for build-up experiments and matter provide a framework that will icosahedral facet, with an intrinsic cur- course-grained simulations of assembly. help interpret and rationalize virological vature would be limited (by accumulated Build-up ‘‘games’’ allow identification of experimental observations. Conversely, strain and statistical factors) to a distri- intermediates along an assembly path virologists provide experimental obser- bution of sizes. Such a distribution can and provide a means for developing vations that are constraints and test the be observed in retroviruses and other master (thermodynamic–kinetic) equa- application of theory. Different scien- pleiomorphic viruses. Most icosahedral tion descriptions of capsid assembly (15, tific approaches reveal new questions viruses are very uniform. In some vi- 16). Thermodynamic–kinetic models and answers that expand our under- ruses, the size distribution may be limited have been very successful in explaining standing of viruses and the means to by the intrinsic curvature of subunits the behavior of in vitro assembly reac- combat them. 1. Crick, F. H. C. & Watson, J. D. (1956) Nature 177, 9. Yeager, M., Wilson-Kubalek, E. M., Weiner, S. G., 17. Casini, G. L., Graham, D., Heine, D., Garcea, 473–475. Brown, P. O. & Rein, A. (1998) Proc. Natl. Acad. R. L. & Wu, D. T. (2004) Virology 325, 320–327. 2. Caspar, D. L. D. (1956) Nature 177, 476–477. Sci.
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