"Diffraction by helical structures"

Date:
1956-1957
Reference:
PP/CRI/H/2/17
Catalogue details

Licence: In copyright

Credit: "Diffraction by helical structures". Source: Wellcome Collection.

    17/98
    - io - Accordingly if one travels round the n, ÍJ helical yj y iec|: t ioT| . keeping at a constant radiuS| th© variations in projected electron density will, in general, repeat n times in one complete revolution! i.e. tjie pattern will have n-fold rotational symmetry. This pattern can then be considered as made tip of a number of angular Fourier components of frequency 0, ± n t ♦ 2n, — -, ± hn # ——, where h is an integer« How consider one of these angular components, the (hn)*^ 1 , say. It is a two dimensional pattern with (hn)-fold (settlor rotational symmetry t and we shall show below,that its two-dimensional Fourier transform is identical with the term G Im» ht < R >exp[l^A(^-ÍT)] O t that is t with the structure factor on the (ht) th layer line. How since the direction of the \ja,£] helical projection raOjc is determined only by the ratio % (the pitch being ), we thus see that a Fourier analysis of this single projection leads to the whole set of terms Gj mf t 11 being any integer as before. It is in this sense that we may think of the term G im as th ® h th * ifin| U/m««« order of ft- o * If the helical projection has a large ( Mb )-fold . c*« ste *CAit A layer-line h€ will have strong X-ray spots on it. Alternatively if its (h^n)^ angular Fourier component is weak, the X-ray intensities will be weak or absent. Note that it is not necessary to project the whole structure. It is clear from the manner of derivation that one need only project one asymmetric unit along the relevant helix on to plane z «=0 and then operate on this limited projection with an n-fold rotation to produce the entire helical projection. It is the fact that only on© asymnffcric unit needs to be projected that makes the method useful»