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Credit: Dissertation in Draft: Chapter III. Source: Wellcome Collection.
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![—»■ TUE BT l R^CTtyRE---0!P--8 J iHy rH«¥î©-PO-LY-PBλ®I»B»-ï- reflexions to which a number of sets may contribute are likely to be strong. The contribution of the jth set of atoms is of course the sum over a few values of n of terms of the form (f), so that, if the values of J n (2nRr) are very small for all values of r which occur in the structure, the corresponding reflexion must be absent. When this quantity is large for many of the values of r which we might expect to be present, the corresponding reflexion is not necessarily strong, as the phase part of the expression (f) may effect a cancellation when the contributions from all sets are summed. On the average, however, such reflexions will be strong. We assume, therefore, that poly-y-methyl -l -glu- tamate is based on the «-helix proposed by Pauling & Corey, so that the structure of one infinite chain can be produced from one residue by the operation of a non-integer screw of 100° and 1-5 Â. We now use the property of Bessel functions, illustrated in Fig.% that for small values of the argument 2nRr, the function J n (2jiRr) is very small when n is large. The greater the value of n, the greater 2 nRr can be before J n (2nRr) becomes appreciable. Now, whatever the precise form of the side groups, no atom can lie further than about 8 Á from the axis of the helices if reasonable bond lengths are assumed. For any set of atoms making up the main chain (including the /9-carbon atom)—and this accounts for half the total— r is not greater that 3-3 Á, according to Pauling & Corey (1951). The part of the transform covered by the observed diffraction data does not extend beyond R = 0-35  _1 (I =j= 0), so that in considering the contribution of any set of atoms of the main chain to any reflexion, a value of 2jiRr greater than 7-2 will not occur. Even when the contributions of atoms of the side groups are considered, 2 nRr will not exceed 11\The implications of this can be seen by considering the reflexions on the first layer, which are contributed to by Besselfunctions of order 7 and 11. For the reflexion (1011), R = 0-097  1 , and J 7 (2nRr) is quite negligible for r < 7 Á. Only the outermost atoms of the side groups could contribute weakly to this reflexion. A similar calculation shows that the con tribution of atoms of the main chain to any reflexions on this layer for which R < 0-35 Á -1 is always very small, although atoms of the side group could make a small contribution. No reflexions are observed ex perimentally on this layer. Intensities on the second layer depend on J 4 (2nRr), so that low-order re flexions are again likely to be weak, and the main contributors to reflexions (1122) and (2022) must be the atoms of the side groups. The third layer involves J s (2nRr), and we might expect to find some reflexions on it, while on the fourth the intensities depend on J a (2nRr), so we would expect nothing except possibly at comparatively large values of R. On the other hand, I = 5 is contributed to by J x {2nRr), and many sets of atoms can make large contributions. In short, we can make the general prediction that 'layer lines to which only high-order Bessel functions contribute will be weak or absent, and those to which low-orders 'contribute will be strong' (Cochran & Crick, 1952). The experimental data of Bamford et al. (1952)^agree with this prediction in a striking manner, no reflexion t appearing on any layer line unless a Bessel function 1 Uz ~ of order 4 or less is involved. In fact the agreement is ! ' too good, and suggests that the upper limit to the value of 2 nRr is more nearly 7 than 17; that is, that the effect of the atoms of the side groups is in some way reduced. This could be due to the side groups having a greater amplitude of thermal vibration, or being more disordered, than the atoms of the main chain. On the other hand, the assumption that the side groups are all equivalent, i.e. that both the main chain and side grouris have an 18-fold screw axis, may not be correct. E*a<, i A (p u Có'fkkífc (äö^requiref only that every third side group should be equivalent. If all are equivalent, their relationship to neighbouring parts of their own chain is the same for each, but their relationship to neighbouring parts of adjacent chains falls into three different types. Thus there is no compelling reason for all the side groups to have the same orientation relative to the main chain. The evidence thus suggests very strongly that the main chain of poly-y-methyl -l -glutamate is based on the «-helix, or a very similar helix, but it is not possible by this rather general approach to decide whether the side groups also conform strictly to this arrangement. TV'S U u-, wwc. ¿ieRil ¿v. Ci. < A-v SC- • Keierences Ambrose, E .J. & Elliott, A. (1951). Proc. Roy. Soc. , K, 205, 47. Êamford, C. B,, Brown, L., ElIiott, A., Hanby, W.E. & Trotter, I. F. (1952). Natur p., Land. 169, '357. Bamford, C. H., Hahby, W. E. & happçyf F. (1951). Proc. Roy. Soc. A, 205, 30. Cochran, W. & Crick, F. H. C. (] &52). Nature, Lond. 169, 234. Paulino, L. <fc Corey, R. B,yfl951). Proc.,Nat. Acad. Sci., Wash. 37, 241. Pauling, L., Corey, R.BC & BransqîC H. R. (1951). Próc. Nat. Acad. Sciï, Wash. 3 7,, ,205. Perutz, M. F. (1951). Nature, Lond. 167, ip53.](https://iiif.wellcomecollection.org/image/b1817467x_PP_CRI_F_1_3_0005.jp2/full/800%2C/0/default.jpg)
