Locating the anomalous scatterers within a crystal using dual-wavelength X-ray diffraction measurements

A simple algebraic expression is used to calculate the structure-factor amplitudes of the anomalous scatterers within a protein crystal, using X-ray diffraction measurements made at two wavelengths and given a single type of anomalous scatterer within the crystal. The expression is exact and is readily derived from the standard algebraic equations for analyzing multi-wavelength anomalous diffraction data. Evaluation of the expression requires estimates for (lambda)f' and (lambda)f", the real and imaginary components of the anomalous scattering, respectively. When these are not known at the wavelengths in question, a statistical procedure is suggested, applicable when the crystal space group has centrosymmetric projections, which allows the expression to be used regardless. The method may provide a useful alternative to existing procedures when (lambda)f' and (lambda)f" are unknown or when data have been measured at a limited number of wavelengths.