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

Kaushik S Hatti,Airlie J Mccoy,Randy J Read

doi:10.1107/s2059798321004538

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.

Highlights

The anomalous differences between Bijvoet pairs of reflections can be exploited for phasing in crystallography
In our previous work on the LLGI intensity-based likelihood target (Read & McCoy, 2016), we showed that a log-likelihood-gain score that accounts exactly for the effect of Gaussian measurement errors on intensities can be approximated extremely well with a target computed via the Rice function, in which the intensity and its standard deviation are transformed into an effective amplitude and a Luzzati-style weighting term approximating the effect of the scalar measurement error as an error in the complex plane
The method to determine substructure content was tested on a database of SAD data sets provided by collaborators or downloaded from the Worldwide Protein Data Bank. 124 data sets were kindly provided by Zbigniew Dauter, most of which have been discussed earlier (Banumathi et al, 2004; Dauter et al, 2002; Wang et al, 2006). 162 data sets were collated by Tom Terwilliger from JCSG experiments and have been discussed earlier (Bunkoczi et al, 2015)

Summary

Introduction

The anomalous differences between Bijvoet pairs of reflections can be exploited for phasing in crystallography. Planning the experiment benefits from estimating the achievable anomalous difference, considering the number of anomalous scatterer sites that might be present and the precision with which the intensities are measured (Terwilliger et al, 2016a). Both SHELXD (Schneider & Sheldrick, 2002) and AutoSol (Terwilliger et al, 2009), the experimental phasing suite in Phenix (Liebschner et al, 2019), require a prior estimate of how many anomalous scatterers are expected in the substructure. For soaking experiments with heavy metals or halides, initial estimates of the number of sites depend on rules of thumb that are typically

Methods

Results

Conclusion