Dec. 16, 1952

Dear Dr. Pauling

I enclose copies of the radial distribution functions I spoke of in my last letter. For my curves with B=4, each interaction has the shape Z_{i}Z_{j} exp (-5r^{2}) and for B=2, Z_{i}Z_{j} exp (-10r^{2}) (as derived from the part in David Shoemaker's thesis on the shape of peaks in modified Pattersons. I calculated the distances to the closest 0.1 Å, and synthesized the curves at 0.1 Å intervals, up to 9 Å, since I feel interhelical distances may become too important beyond this. I used the coordinates on p. 240 of P.N.A.S. reprint set. Arndt has also recalculated R.D.I.'s for the α-helix, using likewise the 18-residue 5 turn coordinates. I enclose also a tracing of his curves. He used the function Z_{i}Z_{j} x the function: [table of data used in the function]

I include my two smoothing functions for comparison. I don't know what kind of smoothing function you and Dr. Corey used, but I don't see how a difference in them could lead to the big difference between your curves and mine and Arndt's.

Arndt now inverts the R.D.I.'s for the helix and compares scattering curves. He finds that for bovine serum albumin and egg albumin there is quite good agreement with the α-helix, and he still favors BC_{2} over BC_{1}, or a 50-50 mixture is possibly the best of all. He has also calculated curves for α-helices of finite lengths, and thinks "in most of the globular proteins the agreement between model and experiment is best for a length of about 20 residues, the chains in α-keratin probably being longer." I have not yet talked to him about this last point, but the evidence for it cannot be very strong, for using a helix of finite length would merely depress the outer part of the curve gradually, I think. He writes also that he is now writing his work up and will go to press early in January.

I also enclose comparative R.D.I.'s for the α-helix, the 4_{13} (not that I like it structurally, but I wanted to see what effect the extra twist had) and my 3.0_{10}, of which I sent you a drawing last week. I shall do the 4.4_{14} and 4.4_{16} as soon as I hear from Barbara about which is the π. (How does she put "π" between "α" and "γ", by the way?) She does not apparently realize that there are two kinds of helices, and that the α and γ are different kinds.

I'll send the data on the new helices (I have called the 3.0_{10} the ζ-helix [?], as I discovered it before the 4.4_{14} and 4.4_{16}. If Barbara is the 4.4_{16}, then the 4.4_{14} remains to be lettered. It is not as satisfactory as the others, but perhaps it should be called ω, as I am now sure that there are no more, unless the condition of equivalent residues is abandoned). Incidentally, Carlisle still thinks the α-ribbon (2_{7}) explains ribonuclease! But he will not give coordinates of it. Understandably.

Sincerely

Jerry