Likelihood-based estimation of substructure content from single-wavelength anomalous diffraction (SAD) intensity data

Abstract

SAD phasing can be challenging when the signal-to-noise ratio is low. In such cases, having an accurate estimate of the substructure content can determine whether or not the substructure of anomalous scatterer positions can successfully be determined. Here, a likelihood-based target function is proposed to accurately estimate the strength of the anomalous scattering contribution directly from the measured intensities, determining a complex correlation parameter relating the Bijvoet mates as a function of resolution. This gives a novel measure of the intrinsic anomalous signal. The SAD likelihood target function also accounts for correlated errors in the measurement of intensities from Bijvoet mates, which can arise from the effects of radiation damage. When the anomalous signal is assumed to come primarily from a substructure comprising one anomalous scatterer with a known value of f′′ and when the protein composition of the crystal is estimated correctly, the refined complex correlation parameters can be interpreted in terms of the atomic content of the primary anomalous scatterer before the substructure is known. The maximum-likelihood estimation of substructure content was tested on a curated database of 357 SAD cases with useful anomalous signal. The prior estimates of substructure content are highly correlated to the content determined by phasing calculations, with a correlation coefficient (on a log–log basis) of 0.72.

Multivariate estimation of substructure amplitudes for a single-wavelength anomalous diffraction experiment

“…The refinement of these parameters turned out to have a large radius of convergence, and better results were obtained when refined values were used compared with when unrefined values. We have previously discussed the procedure (Pannu, 2007) and a similar approach was recently reported by Hatti et al (2021). After the refinement, the |F a | values are estimated using equation (1).…”