Section 2.3.3.6. Direct structure determination from difference Pattersons

The difference Patterson computed with coefficients contains information on the heavy atoms (HH vectors) and the macromolecular structure (HL vectors) (Section 2.3.3.3). If the scaling between the and data sets is not perfect there will also be noise. Rossmann (1961b) was partially successful in determining the low-resolution horse haemoglobin structure by using a series of superpositions based on the known heavy-atom sites. Nevertheless, Patterson superposition methods have not been used for the structure determination of proteins owing to the successful error treatment of the isomorphous replacement method in reciprocal space. However, it is of some interest here for it gives an alternative insight into SIR phasing.

The deconvolution of an arbitrary molecule, represented as `?', from an Patterson, is demonstrated in Fig. 2.3.3.5. The original structure is shown in Fig. 2.3.3.5(a) and the corresponding Patterson in Fig. 2.3.3.5(b). Superposition with respect to one of the heavy-atom sites is shown in Fig. 2.3.3.5(c) and the other in Fig. 2.3.3.5(d). Both Figs. 2.3.3.5(c) and (d) contain a centre of symmetry because the use of only a single HH vector implies a centre of symmetry half way between the two sites. The centre is broken on combining information from all three sites (which together lack a centre of symmetry) by superimposing Figs. 2.3.3.5(c) and (d) to obtain either the original structure (Fig. 2.3.3.5a) or its enantiomorph. Thus it is clear, in principle, that there is sufficient information in a single isomorphous derivative data set, when used in conjunction with a native data set, to solve a structure completely. However, the procedure shown in Fig. 2.3.3.5 does not consider the accumulation of error in the selection of individual images when these intersect with another image. In this sense the reciprocal-space isomorphous replacement technique has greater elegance and provides more insight, whereas the alternative view given by the Patterson method was the original stimulus for the discovery of the SIR phasing technique (Blow & Rossmann, 1961).

Figure 2.3.3.5 | top | pdf | Let (a) be the original structure which contains three heavy atoms ABC in a noncentrosymmetric configuration. Then a Fourier summation, with coefficients, will give the Patterson shown in (b). Displacement of the Patterson by the vector BC and selecting the common patterns yields (c). Similarly, displacement by AC gives (d). Finally, superposition of (c) on (d) gives the original figure or its enantiomorph. This series of steps demonstrates that, in principle, complete structural information is contained in an SIR derivative.

Other Patterson functions for the deconvolution of SIR data have been proposed by Ramachandran & Raman (1959), as well as others. The principles are similar but the coefficients of the functions are optimized to emphasize various aspects of the signal representing the molecular structure.