International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by M. G. Rossmann and E. Arnold © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. F. ch. 19.4, p. 442
Section 19.4.4.1. Theory and background
aDepartment of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT 06520, USA, and bDepartments of Chemistry and Molecular Biophysics and Biochemistry, Yale University, New Haven, CT 06520, USA |
By measuring distances between chemically specified points in a macromolecule or macromolecular complex, useful information may be obtained concerning its structure. In the case of a complex with many subunits, successive inter-subunit distance measurements can be combined by triangulation to generate a three-dimensional map specifying the relative positions of subunits and, perhaps, their individual radii of gyration. The only uncertainty is the handedness if more than three distances are combined. A number of approaches exist for making distance measurements, including NMR, fluorescence and electron-microscope techniques in which labelling is employed. Neutron scattering provides a particularly simple approach to such measurements in a conceptual sense. If we consider two labelled centres in a large macromolecule or complex, the interference of the scattering from the two labelled positions, , can be separated from the scattering of the rest of the complex by measuring the scattering of the unlabelled complex, I(Q), the two singly labelled complexes,
and
, and the doubly labelled complex,
, as they are related by
Using the Debye relationship, it can be shown that the cross term will have the approximate form
where the interference intensity results from the correlation between radiation scattered from sites 1 and 2, with scattering strengths
and
. It is a damped sinusoidal fringe with a periodicity reciprocally related to the separation between the scattering regions. If the scattering regions are very small compared with the object, there will be nodes at equal intervals in Q; if they are not,
will be a sum of all cross correlations of label positions in the two regions.