In this letter Klug discussed virus structure and possible symmetries in the arrangements of subunits of protein, which together
with RNA make up the polio virus Klug was examining. (Other viruses have DNA as their genetic material.) Crick had become
interested in the study of virus structure in the mid-1950s as a way of understanding the structure and transcription of RNA.
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1959-02-13 (February 13, 1959)
Original Repository: Wellcome Library for the History and Understanding of Medicine. Francis Harry Compton Crick Papers
I enclose a copy of our polio paper for any comments you might have before we submit it for publication - to Nature, most
probably. I would be particularly grateful for your opinion of the general disussion at the end. I feel it is now appropriate
to draw attention to the occurrence of icosahedral symmetry in 5 viruses (although I haven't mentioned Bea's result
I am now trying to see whether it is possible to classify the ways in which a large virus like Tipula IV might be built up
out of sub-units, a problem you suggested some time ago. It seems to me that one must start off with a "point-group core",
like a small virus and then try to make a "crystal" of it, by adding more sub-units to try to achieve close packing.
In this way, starting off from the three Archimedean semi-regular solids with 60 vertices, one can arrive at 3 families of
truncated icosahedron; small rhomb-icosadodecahedron; snub dodecahedron
I can see why the virus should have plane faces if one invokes the equivalent of surface energy in a crystal (density of packing
perhaps? in view of our ignorance of the exact forces). But what I cannot see is what there is to determine the uniformity
of size, if the nucleic acid is all in the core and there are no other components.
Incidentally I have found a fair amount of mathematical literature on external problems concerning points arranged on a sphere
(densest packing, nimumum density for convering). There are a lot of gaps in the subject and some of the results are really
only very plausible rather than proved, but what does seem clear, is that the solution of an extremal problem is nearly always
the regular or semi-regular polyhedron, for the appropriate number of points. The maximisation or minimisation (of some relevant
quantity) is nearly always more favourable for arrangements where symmetry is possible than for those in which it is not.
These results are, what one might have guessed. But it does seem, though this point is not made explicit anywhere, that among
the class of symmetric arrangements, those with icosahedral symmetry are the best. This is the basis of the statement made
in the last paragraph of the enclosed paper.
Would you please also show the paper to Jim, if he wishes to see it.