"The treatment of errors in the isomporphous replacement method"

Date:
[1958]
Reference:
PP/CRI/H/2/28
Catalogue details

Licence: In copyright

Credit: "The treatment of errors in the isomporphous replacement method". Source: Wellcome Collection.

    9/13
    r%- £- + ¿£fo. F. -V 2-i- H 3C + 3C* (20) The rfc^fetáre probability N' fai 7 of a given phase is — ^ LJUilaJ!- M Ü' «- (21) V , ÌAA'U^.C i XÒS iaa ^ tX, ^U-Ol /s. frttCtV j* - j This is inconvenient to handle analytically, and a graphical method has been developed which can be used very rapidly. This consists of two rulers:, hinged together, each of which carries a cursor. One cursor is piv#ted at the centre of the coordinate system j the length of the attached ruler represents F • The length of the other eepresents Ft+ , and its cursor carries a scale graduated directly in units of /^7« ( A variety of scales is made for different values of^E>). The vectorJ¿ is represented by laying a marker on the baseboard. The probability of any phase may be estimated by setting F to the appropriate phase and reading off the value of ^^from the cursor when the triangle is closed. This is proportional to Figure é> illustrates the way these values of may be used to calculate the relative probabilities of various phases. JL single isomorphous replacement gives an ambiguous result for the phase, fwn» ir , ni ve-*re-r^á a«ys iiiaBfepwfees how this ambiguity may be resolved by the use of a further member of the isomorphous series for which the vectorhas a different phase. The probabilities may be multiplied together to give a joint probability curve. When this product has been taken over all pairs of compounds in the isomorphous series, the curve gives all available information about the phase of the reflexion This phase probability curve may be used to plot a probability map on an Argand diagram as previously described, (figure ?)• (ïhe breadth of the annular region is again as in the centrosymmetric case). In order to obtain the best Fourier, we need a way of finding the centroid of such a probability map. We also need a method of estimating the radius of gyration,