234 LETTERS -TO THE EDITORS Ne notice Se taben of anonymous commmuncoations Evidence for the Pauling-Corey «Helix in ' Synthetic Polypeptides . We have calculated, in collaboration with Dr. V. Mpronl the Fourier en (or Soutinaous siuctre of an atom repeated at regular in on an Pan helix. The ies of the transform are wuch that it will be possible to predict the character of X-ray scattering by any structure d on a regular succession of similar groupe of atoms arranged in a helical manner. In particular, the type of X-ray diffraction picture given by the synthetic polypeptide poly-y-methyl-L-glutamate, ‘which has been prepared in a highly crystaliine form by Dr. C. H: Bamford and his colleagues in the Research Laboratories, Courtaulds, Ltd., Maiden- head, is so readily explained on this basis as to leave little doubt that the i e-helix®, or some lose approximation to it, exists in this polypeptide. Pauling and Corey* have already shown this corre- in the equatorial plane ; it is shown here the correspondence extends over the whole of the diffraction pattern. : We quote here the value of the transform which applies when the axial distance between successive turns of the helix is P, the axial distance between the successive atoms lying on the helix is p, and the structure so formed is repeated exactly in an axial distance c. (For the latter condition to be possible, P/p roust be expressible as the ratio of whole numbers.) Tn nis case, the transform is restricted to planes in reciprocal space which are perpendicular to the axis of the helix, and occur at heights { = i/c, where ! is an integer. crystallographic nomenclature, these are the layer lines corresponding to a unit cell of fength c. On the Ith such plane the transform has the value : P (29.7) = f EJn(2nRr) exp [in (4 + =). (1) R,y,%) are the cylindrical co-ordinates of a point in iprocal space, f is the atomic scattering factor, Ja is the Bessel function of,.order n; r is the ius of the helix on which the set of atoms lies, exes in real being chosen so that one atom ies at (r,0,0). For a given value of J, the sum in ion (1) is to be taken over all integer values ich are solutions of the equation, Y n,m "f.- P + p ne’ ~~ 4 rye 7 (2) certain Bessel functions contribute to ble for the sof 1 ethyl. accompanying tal or oase ly-Y- Dee Y'for which Pauling and Cor 8 . and o = 387A. The: first the number, /, of the layer line, while the second gives the orders (n) of the Bessel functions which contribute to it (for si only the lowest two values of » are given for each layer line). Now there is, of course, more than one set of atoms in the polypeptide, but for all of them, P, p and c are the same, although rf is different. The basis of - i t wa - P 3 i -_ a > NATURE February 9, 1952 vou. 169 Value of Lfor the | Lowest two values of | Observed average layer line ‘8 allowed by theory Mae tee ayer 0 e +18 strong 1 -—7 +11 Po] EGE] thee - very 4 +8 —-10 5 +1 -~17 medium 6 —6 +12 7? +5 =—18 8 -8 +0 +16 weak 10 +8 —-16 weak li -—5 +13 12 +6 —32 13 ~-1 $17 very weak 14 -8 + 10 15 +3 18 16 —4 +14 17 +7 =i 18 Qo +18 medium 19 -7 +11 2 +4 -~14 21 ~3 +15 2 +8 -10 23 +1 -17 trace 24 6 + 12 . 25 +5 — 138 26 -8 +16 trace 27 +9 28 +8 - 16 trace Layers not described are absent. * (1012), the refiexion having the smallest value of R, is absent. our prediction is that a reflexion will be absent if the contribution of all seta of atoms to it is very small, and that on the average it will be strong if all sets of atoms make a large contribution. Be © Deepen 7 Ot heer Scone ot higher ce illustrated in the graph, that they remain very small until a certain value of 2rRr is reached, and that this point recedes from the origin as the order increases. Now, whatever the precise form of the chain, the value of r for any atom cannot be greater than about 8 A. because of the packing of the chains. This sets & limit to the value of 2rkr within the part of the transform covered by the observed diffraction picture (R < 0-3 A. for i 3% 0). No set of atoms can make an appreciable contribution to the amplitude of a reflexion occurring on a layer line with which only high-order Bessel functions are associated, because 2xRr comes within the very low part of the ourvo in the graph. . We should therefore predict that layer lines to which only high-order Bessel functions contribute would be weak or absent, and that those to which very low orders contribute would be strong. These predictions are strikingly borne out by the experimental data‘ summarized in the last column of the table. The significant Bessel functions involved in the first twenty-eight layer lines are shown in the second column, and, ae will be seen, only layer lies associated with a function of order 4 or less [. The porch of Ligher-ercer Ecere) fonetions (with J, added dashed) motion. In addition, the theory predicts (as can also be shown by a simpler approach) that meridional re- flexions can occur on layer lines which involve Bessel functions of zero; that is, at reciprocal spacings of multiples of 1/1-5A.-*. This had pre- viously been pointed out by Perutz* when reporting the strong meridional 1-8-A. reflexion. We have therefore no doubt that the structure of poly-y-methyl-L-glutamate is based on a helix of eighteen residues in five turns and 37 A., or a helix which approximates to this very closely. Aa tho structure by Pauling and Corcy' satisfies these conditions and is also stereochemically very satisfactory, it seems to us highly probable that it is rrect 0) 'e . We should like to thank Dr. Bamford and his — colleagues for allowing us to quote their experi- mental results in advance of publication, and Sir Lawrence Bragg and Dr. M. Perutz for the stimulus which their interest in this work has provided. W. Cocuean Crystallographic Laboratory, Cavendish Laboratory, Cambridge. ¥. H. C. Carox Medical Research Council Unit for the Study of the Molecular . Structure of Biological Systems, Cavendish Laboratory, Deo. 14. ‘Cochran, W., Crick, F. H. C., and Vand, V. (to be published). * Fault 4 sine and Corey, R. B., Pro. U.S. Nat. Acad, Set., 87, 241 * Peruts, M. ¥., Nature, 167, 1058 (1961). w H., L., Elliott, A., Hanby, W. E., and Trotter, “LF ee be Scpianed): 235