POLYTECHNIC INSTITUTE OF BROOKLYN 99

LIVINGSTON STREET BROOKLYN 2, NEW YORK

January 26, 1953

Prof. Linus Pauling

Gates and Crellin Laboratories of Chemistry

California Institute of Technology

Pasadena 4, California

Dear Professor Pauling,

I was very interested in your ingeneous cable model of the structure of proteins
which appear in Nature. Would you kindly send me two reprints of this paper and
reprints of further work on this subject?

Since there will no doubt be many attempts to verify your model
experimentally, I think it is very important that the anticipated inter-
ferences be calculated exactly. Dr. D. P. Riley and myself have calcu-
lated the equatorial intensities for an aggregate of seven rods (your
AB_{6} model) in Acta Crystallographica 5 272 (1952) which we have applied
to our scattering data for desoxyribose nucleic acid (Biochim. Biophys.
Acta 7 526 (1951)). Judging from your earlier paper with Corey, I
imagine you calculated the form factor for equatorial spacing ( 1 + 6J_{0}(X)) by treating the A_{6} ring of rods as a shell about the central B rod. However, our detailed analysis
of the problem gives for the normalized
intensity

1/49 [7 + 24 J_{0}(x) + 6J_{0} (2x) + 12 J_{0}( √3x) (1)

This quantity in turn should be multiplied by the normalized intensity for a solid
rod (a fair approximation to your helix) namely by

[2J_{1} (x) / k^{R}]^{2} (2)

If the rods are in contact x = (4Л/λ)ρ sinθ .

If the rods are not in contact (lateral swelling as seems to be the case for collagen,
for example) then x in expression (1) above becomes

(4Л/λ)γ

ρ sinθ where γ is the "degree of swelling" while x remains unchanged in expression
(2) if, as is usually the case, the interatomic distances in the rod remain unchanged
on swelling.

Prof. Pauling
January 26, 1953

For your AB_{6} model where the rods are in contact (Y= i.o) we obtain maxima at x=(0), 3.8, and
6.0 (for infinite two-dimensional array there should be a sharp maximum at x=7.2).
Taking your rod as 10 A_{0} then there should be maxima in intensity along the
equator at sinθ / γ = (0), 0.030, 0.048 reciprocal Angstroms corresponding to
Bragg spacings (first order) of 16.5 and 10.4 Angstroms. For comparison, an
infinite lattice of hexagonally close-packed rods of diameter 10 Å gives a spacing
at 8.8 Angstroms.

You suggest in your paper that there may be overlapping in the X-ray diffraction diagrams
of α-keratin at low angles. I am planning to do small angle experiments with keratin
to look for fine structure along the equator. I think such work is important to
understand the gross structure of proteins of the kind you discuss in your paper.
It would be nice if your model of the seven strand cable is correct. Riley and I
postulated a nearly similar arrangement for deoxyribose nucleic acid. It is conceivable
that the protein cables could fit alongside of or be intermingled with the nucleic
acid cables to form nucleoproteins - but I guess I'm off in the realm of fantasy.

Sincerely and with best personal [sic] regards to you and Professor Corey

Gerald Oster

GO:mf