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 ZiZj exp (-5r2) and for B=2, ZiZj exp (-10r2) (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
ZiZj 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 BC2 over BC1, 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 413 (not that I like it structurally, but I wanted to see what effect the extra twist
had) and my 3.010, of which I sent you a drawing last week. I shall do the 4.414 and 4.416 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 3.010 the ζ-helix [?], as I discovered it before the 4.414 and 4.416. If Barbara is the 4.416, then the 4.414 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
(27) explains ribonuclease! But he will not give coordinates of it. Understandably.