Viruses From Structure to Biology

Comments from Gregory Morgan


Genesis of the Caspar-Klug Theory
Sketch of my PhD project

Do not quote without permission

present address:
Gregory J. Morgan
Associate Professor of Philosophy
Stevens Institue of Technology
Castle Point on Hudson
Hoboken, NJ

1. Introduction

I received my PhD dissertation in the history and philosophy of science on the early development of theories of "spherical" virus structure. I had received an NSF grant to help me complete my goal. In Aug 2000 I interviewed most of the major players in the US and UK and I have visited many of the archives that contain relevant material. Naturally, I would love to hear from anyone with similar interests or anyone who has information that would enrich my historical narrative. What follows is a very brief sketch of the historical part of my thesis.

2. A sketch of the case study

In June 1962, Donald Caspar presented a paper, co-authored with Aaron Klug, entitled "Physical Principles in the Construction of Regular Viruses" at the Cold Spring Harbor Symposium on "Basic Mechanisms in Animal Virus Biology" (Casper & Klug, 1962). Among other things, they proposed that spherical virus are shaped like small geodesic domes. The ideas they presented were widely accepted until the early 1980s when the first exception to their theory was discovered (in Caspar's lab).

In 1953, Donald Caspar began his PhD in biophysics at Yale University. His goal was to analyze the rod-shaped Tobacco Mosaic Virus, abbreviated "TMV," using x-ray crystallography. Very roughly, this technique involves passing x-rays through a crystal of virus and then analyzing the diffracted x-rays to infer how the virus is structured. Caspar collected his data over the next year or so. James Watson, of DNA fame, also made a brief foray into TMV research. Watson was interested in RNA and hoped that TMV would allow them to solve the RNA structure since attempts with naked RNA had failed. (TMV contains RNA as its genetic material.) In 1954, he published a paper suggesting that TMV was helical, but he was unable to nail down the number of subunits per turn (Watson, 1954). During a summer meeting at Cold Spring Harbor, Caspar spoke with Watson and Crick. They told him about their ideas regarding spherical virus substructure and symmetry. Briefly, they hypothesized that the small "spherical" viruses must have cubic symmetry. Cubic symmetry involves having at least four 3-fold rotational axes. For example, all of the platonic solids have cubic symmetry. Imagine a cube: if you look down the body-diagonal, you are looking down a 3-fold rotation axis and there are four such axes. In December of 1954, Caspar traveled to Caltech to work with Watson. While there, he analyzed his data on TMV and calculated a cylindrically averaged radial distribution function for TMV. He was also interested in working with spherical viruses but the diffraction equipment at Caltech did not have a sufficiently powerful x-ray source (He would need a rotating copper anode x-ray source).

Rosalind Franklin was also analyzing TMV structure -- she was attempting to calculate a radial distribution function for repolymerized TMV protein without the RNA. Watson and Caspar speculated about the nature of RNA given Caspar's data -- they proposed a 10-12 stranded RNA helix which they both considered rather pretty but speculative. However, they abandoned their pretty idea when further work did not support their model and it was never published. Using Rosalind Franklin's data (i.e., virus without RNA) in conjunction with Caspar's (i.e. virus with RNA), they determined the location of RNA in TMV. Surprisingly, it was not in the core as might be suspected if the protein component of TMV was a "container" for the fragile RNA, but rather 40 Angstroms from the center.

Both Caspar and Watson traveled to England. There Caspar meet Aaron Klug who was a post-doc with Rosalind Franklin. Caspar and Klug discovered that they both wanted to work on spherical viruses and agreed to split up the research. Caspar would work with Tomato Bushy Stunt Virus (BSV) and Klug would work with Turnip Yellow Mosaic Virus (TYMV)--two viruses for which there was some previous work. Results came quickly for Caspar, but they were unexpected. First he obtained 10 "smudges", which surprisingly indicated 5-fold rotational symmetry. He repeated the results and showed that there were "spikes" indicating five fold symmetry. Serendipitously, he had placed the crystal down the five fold axes of the virus. This indicated that the virus has icosahedral symmetry (called 532 symmetry by crystallographers). Of the platonic solids only the icosahedron (20 triangles) and the dodecahedron (12 pentagons) have 532 symmetry. These unexpected results supported Crick and Watson's hypothesis that viruses have cubic symmetry and Caspar showed his results to Crick who happened to be working in the same room. (Icosahedra and dodecahedra possess cubic symmetry as well as five-fold symmetry.) With the knowledge of Caspar's result, Crick and Watson wrote an article for Nature (Crick and Watson, 1956). They argued that "a virus possessing cubic symmetry must necessarily be built from a regular aggregation of smaller asymmetrical building bricks and this can only be done a number of ways." These ways correspond to the three cubic point-groups. A point-group is a mathematical entity consisting of symmetry elements whose axes or planes of symmetry intersect at a point. A virus with the symmetry of a cubic point group is necessarily made up of a multiple of 12 and a maximum of 60 identical subunits.

Caspar's experimental results for tomato bushy stunt virus were published in Nature immediately following Crick and Watson's article (Caspar, 1956). In March of 1956, Crick presented their ideas to a group of animal virologists at a small CIBA conference (Crick and Watson, 1957). He argued that given the size of a small viral genome, and a coding ratio of 3:1, there is not enough information in the viral genome to code for a large number of non-identical subunits. Therefore, Crick concluded, there must be one subunit that is repeated a number of times. His ideas were met with some skepticism among the old-style animal virologists who were not used to thinking in terms of information. In the discussion session following the paper, Caspar illustrated a number of the ideas with ping-pong ball models that he had built. Klug mentioned that he had gotten similar results for Turnip Yellow Mosaic Virus. A week later, at the International Union of Crystallography meeting in Madrid, Caspar presented a paper which combined Crick and Watson's theoretical speculations and his experimental results. The paper entitled "The Molecular Viruses Considered as Point-group Crystals" illustrates how Crick, Watson, and Caspar now thought of viruses as crystals (Caspar, Crick, and Watson, 1956). This analogy allowed them to bring crystallographic concepts to bear upon their subject matter. They imported concepts from the theory of their instruments. They conceived of the virus as made up of identical subunits bonded together in identical ways. Each subunit is equivalent to every other subunit as is true of crystals. The negative analogy, to use the terminology of Mary Hesse, is that virus are spatially bounded, whereas "space-group" crystals potentially extend to infinity (Hesse, 1966). The maximum number of equivalently related subunits in a cubic point-group crystal is 60 -- think of the 20 triangular sides of an icosahedron each divided into three. Crystallographers were reluctant to believe that Caspar had discovered five-fold symmetry. As any of you who have studied crystallography will know, true crystallographic five-fold symmetry is impossible (except as we now know there is a type of five-fold symmetry in some quasi-crystals). At the time, however, crystallographers were suspicious that Caspar had discovered five-fold symmetry even in the virus itself. Klug also presented a paper at the Madrid conference; his paper concerned the Fourier transforms of 23, 432,and 532 point groups (Klug, 1956). However, Caspar and Klug's collaboration would not begin for another two years. In August 1958, Rosalind Franklin was scheduled to talk in Bloomington at a Plant Pathology meeting organized to celebrate the 50th anniversary of the American Phytopathology Society. She most probably would have spoken on her recent work on TMV. Tragically, Rosalind Franklin passed away in April of 1958. Under these unfortunate circumstances, Caspar and Klug began their collaboration. Caspar was invited by the committee to speak in Franklin's place and he co-opted Klug's co-authorship. They wrote a review of the x-ray diffraction of viruses (mainly TMV) which Stanley dedicated to Rosalind Franklin in a tribute published immediately following the paper (Franklin, Caspar, and Klug, 1959).

Klug and his colleague, John Finch, had expanded their research program to include polio as well as TYMV. Buckminster Fuller and his protege, Robert Marks noticed the work on Polio, particularly the similarities between viral structure and Fuller's geodesic domes. Marks corresponded with Klug and Buckminster Fuller met with Klug in London in July of 1959. After obtaining Mark's book, The Dymaxion World of Buckminster Fuller(1960), Caspar and Klug came to the idea of "near-equivalence," later called"quasi-equivalence". This was the idea the viral subunits bind in quasi-equivalent positions. Consider the triangular "subunits" geodesic domes. The subunits lie in (at least) two quasi-equivalent positions, for example those in "pentamers" and those in "hexamers" in a T=3 structure. The relative angles between the neighbors differ slightly for the two types of subunit positions. The important consequence of the idea of subunit binding in "quasi-equivalent" position is that it loosens the constraints up on the number of subunits in the structure. In the "point-crystal" viruses, the maximum number of subunits was 60. With quasi-equivalence, much higher numbers are allowed. The relaxation in the number of allowed subunits was important because in the intervening years there was increasing evidence that many viruses had more than 60 subunits. This evidence came principally from electron microscopy using the new technique of "negative staining" popularized by Robert Horne and Sydney Brenner both of whom also worked in Cambridge (Brenner and Horne, 1959). In 1959, a virologist Peter Wildy worked with Robert Horne and they examined a variety of viruses (see Horne and Wildy, 1961, for a review). However even with "quasi-equivalence" not just any number of subunits are allowed, there are still constraints upon which number of subunits a virus can have.

Caspar began to write a manuscript that explicated the idea of quasi-equivalence. In the meantime, Klug was invited to speak at the 1962 Cold Spring Harbor meeting -- this invitation sparked a further collaborative paper. The collaboration was extremely fruitful and they soon had too much material for one paper. They literally cut up Caspar's original manuscript and reassembled it with new material. The first paper (Caspar and Klug, 1962) would consider the geometrical aspects of virus design and assembly and the second, physical aspects of viral design and assembly. The second paper, although promised in the first, was never published. In the 1962 Cold Spring Harbor paper, Caspar and Klug coin a number of new terms. Icosahedral virus shells can be classified according to their "triangulation number." Roughly, this number represents the number of triangles on any of the faces of the icosahedron. Because only certain triangulation numbers are possible, the Caspar-Klug theory predicts what may occur and what should not be seen in nature. They also introduced the term "self-assembly" which describes how the virus subunits, under the right conditions, assemble correctly into closed shells without any external aid. This new term was introduced with an extension to the crystal analogy:

"Self assembly is a process akin to crystallization and is governed by the laws of statistical mechanics. The protein subunits and the nucleic acid chain spontaneously come together to form a simple virus particle because this is their lowest energy state" (Caspar and Klug (1962), p. 3).

The crystal metaphor of Caspar, Crick, and Watson (1956) was static. Caspar and Klug (1962) now utilize the dynamic nature of crystal growth. This reflects a general trend in their research; as time progressed, Caspar and Klug considered virus production from a more dynamic perspective. As well as importing the idea of viruses as geodesic domes, Caspar and Klug also imported from Fuller the idea of a "tensegrity structure." Although there is some controversy over the origins of the concept, the American sculptor Kenneth Snelson constructed the first tensegrity structure/sculpture in 1948 while he was a student of Buckminster Fuller's at Black Mountain College, North Carolina. There are a number of his sculptures dotted around the country. You might have seen one on the Mall in Washington DC or in the inner harbor of Baltimore. The basic idea of a tensegrity structure is to isolate the components of the structure that are under pressure and those under compression. Tensegrity structures are in equilibrium and will return to the original state after deformation. Fuller popularized Snelson's idea by incorporating it into his "energetic geometry", and often gave people the impression that it was one of his own ideas. Although, in the promised 1963 paper, which was never published, Caspar and Klug write:

"The tensegrity principle provides a very useful analogue approach to model building, since it indicates a way to represent, in a model, the energy distribution in a molecular structure, rather than just the arrangement of matter. This approach is particularly appropriate for the problem of bonding identical units in quasi-equivalent environments. The structure units can be represented by rigid compression members and the bonds by tension members" (Caspar and Klug (unpublished MS dated 8/2/62)). As I mentioned before, tensegrity structures are in equilibrium. From a thermodynamic perspective, this means that they are in an energy well or energy minimum. One of the goals of the unpublished 1963 paper was to demonstrate that the structures predicted from the Caspar-Klug theory are in fact minimum energy structures. Thinking of viruses as tensegrity structures suggests the hypothesis that virus shells will be energy minimum structures.

To summarize, the biophysicist Donald Caspar began his career working on the radial distribution function of TMV. This brought him into professional contact with Jim Watson. Francis Crick and Jim Watson argued from theoretical principles that small spherical viruses, such as Tomato Bushy Stunt Virus, Turnip Yellow Mosaic Virus and Polio Virus would be made up of identical subunits in identical environments. They thought of viruses as "point-crystals." This analogy is not too surprising, as Crick and Watson were practicing crystallographers. The maximum number of subunits that can be arranged in a cubic "point-crystal" virus is 60. However, evidence from electron microscopy and further evidence from biochemistry was that many viruses had more than 60 subunits. After reading Mark's book on Buckminster Fuller, Caspar and Klug developed the idea that virus shells were structured like geodesic domes. Subunits on geodesic domes were not equivalently related, but quasi-equivalently related. If viral subunits are quasi-equivalently related then there can be more than 60 subunits per virus. They also developed the idea of "self assembly" after considering the viral assembly process as a crystallization process. In an unpublished paper, Caspar and Klug develop the idea that viruses are tensegrity structures. Both the crystallization analogy and the tensegrity analogy legitimate further work on the thermodynamics of viral assembly where viral shells are taken to be minimum energy structures. Thus, the early history of the Caspar-Klug theory can be thought of as a succession of macroscopic analogies applied to the microscopic realm.

Select Bibliography

Brenner, S. and Horne, R. (1959) "A Negative Staining Method for High Resolution Electron Microscopy" Biochim. et Biophys. Acta 34, pp. 103-110.

Caspar, D. L. D., (1956) "Structure of Bushy Stunt Virus" Nature 177, pp. 475-7.

Caspar, D. L. D., Crick, F. H. C., and Watson, J. D., (1956) "The Molecular Viruses considered as Point-Group Crystals" International Union of Crystallography Symposium at Madrid, publisher and editor not stated.

Caspar, D. L. D. and Klug, A. (1962) "Physical Principles in the Construction of Regular Viruses" Cold Spring Harbor Symposia on Quantitative Biology XXVII, Cold Spring Harbor Laboratory, New York. pp. 1-24.

Crick, F. H. C. and Watson, J. D. (1956) "Structure of Small Viruses" Nature 177, 473-5.

Crick, F. H. C. and Watson, J. D. (1957) "Virus Structure: General Principles" in G. E. W. Wolstenholme and E. C. P. Millar (eds.) CIBA Foundation Symposium on the Nature of Viruses, Little Brown and Co., Boston, pp. 5-13.

Franklin, R. E., Caspar, D. L. D., and Klug, A. (1959) "The Structure of Viruses as Determined by X-ray Diffraction" in Plant Pathology: Problems and Progress 1908-1958, University of Wisconsin Press, Madison, pp. 447-461.

Horne, R. and Wildy, P. (1961) "Symmetry in Virus Structure" Virology 15, pp. 348-373.

Klug, A. (1956) "The Fourier Transforms of the Cubic Point Groups 23, 432, and 532" International Union of Crystallography Symposium at Madrid, publisher and editor not stated.

Laszlo, P. (1986) "The analogy between Biomolecular Structure and Architecture" in Albert Neuberger and Laurens Van Deenen Comprehensive Biochemistry Volume 34A, Elsevier Amsterdam

Makowski, L. (1998) "Don Caspar, TMV, and Protein-Protein Interactions" Proteins: Structure, Function, and Genetics 30 pp. 109-112.

Marks, R. W. (1960) The Dymaxion World of Buckminster Fuller, Southern Illinois University, Carbondale.

Watson, J. D. (1954) "The Structure of Tobacco Mosaic Virus I: X-ray evidence of a helical arrangement of sub-units around a longitudinal axis" Biochimica et Acta 13, pp 10-19.

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