The statistical labeling method in in situ neutron scattering and diffraction measurements on ordered systems

Neutron scattering experiments, combined with selective isotopic labeling and contrast matching, allow in situ shape and distance information about selected particles in a macromolecular complex to be obtained. However, the observed intensities can be distorted by intercomplex interference and by scattering-length-density fluctuations of the (otherwise) contrast-matched matrix. Two methods by which such distortion can be eliminated have been proposed [Hoppe (1973). J. Mol. Biol. 78, 581-585; Pavlov & Serdyuk (1987). J. Appl. Cryst. 20, 105-110] and effectively used for globular particles in solution. A third method, a statistical labeling method, has also been proposed for measuring distances between two identical particles in complexes in solution [Kneale, Baldwin & Bradbury (1977). Q. Rev. Biophys. 10, 485-527]. In the present work, it is shown that this method can be generalized. With reliance in part on this generalization, it is then shown that all of the methods can be generalized to apply to ordered systems having any number of labeled particles. For macromolecular complexes having underlying order but no net orientation, the same distance or shape information can be obtained as with systems having no underlying order. The feasibility of measurements using the statistical labeling method on such an ordered system was demonstrated experimentally. If ordered complexes are oriented, orientational as well as distance or shape information can be obtained about the labeled particles. Possible applications to X-ray crystallography are also discussed.