Using SAD data in Phaser

Abstract

Phaser is a program that implements likelihood-based methods to solve macromolecular crystal structures, currently by molecular replacement or single-wavelength anomalous diffraction (SAD). SAD phasing is based on a likelihood target derived from the joint probability distribution of observed and calculated pairs of Friedel-related structure factors. This target combines information from the total structure factor (primarily non-anomalous scattering) and the difference between the Friedel mates (anomalous scattering). Phasing starts from a substructure, which is usually but not necessarily a set of anomalous scatterers. The substructure can also be a protein model, such as one obtained by molecular replacement. Additional atoms are found using a log-likelihood gradient map, which shows the sites where the addition of scattering from a particular atom type would improve the likelihood score. An automated completion algorithm adds new sites, choosing optionally among different atom types, adds anisotropic B-factor parameters if appropriate and deletes atoms that refine to low occupancy. Log-likelihood gradient maps can also identify which atoms in a refined protein structure are anomalous scatterers, such as metal or halide ions. These maps are more sensitive than conventional model-phased anomalous difference Fouriers and the iterative completion algorithm is able to find a significantly larger number of convincing sites.

Figure 1

Physics of the SAD experiment. (a) Four normal atoms and one anomalous scatterer are shown relative to a pair of Bragg planes. Incident and diffracted X-rays for measurement of diffraction from the top of the Bragg planes (the ‘plus’ hand of a pair of measurements) are shown as black arrows, while red arrows show incident and diffracted X-rays for measurement of diffraction from the same Bragg planes but from the bottom of the planes (the ‘minus’ hand). (b) For the ‘plus’ hand, the phase of the contribution from the normal scatterers varies from 0 for atoms on the bottom plane to 2π for atoms on the top plane. Arrows representing their contributions to diffraction are shown by arrows in colours matching the atoms in (a). The anomalous scatterer has a large normal component, but because of the phase lag there is a small component perpendicular to the normal component, rotated in the counterclockwise direction. For the ‘minus’ hand, the phase of the contribution from normal scatterers has the opposite sign, varying from 0 for the top plane to 2π for the bottom plane, so their contributions (shown with red arrows) are mirrored across the horizontal axis. The normal contribution from the anomalous scatterer is also mirrored, but the phase lag again leads to a perpendicular component rotated counterclockwise, thus breaking the mirror symmetry. (c) The contributions for the ‘minus’ hand are reflected across the horizontal axis (giving the complex conjugate of the structure factor), showing more clearly how the anomalous scattering component of the anomalous scatterer breaks the symmetry, leading to different intensities depending on whether diffraction is measured from above or below the Bragg planes.

Figure 2

The conventional Harker construction for SAD phasing. The total structure factors for F ⁺ and F ⁻* (the complex conjugate of F ⁻) are sums of complex numbers (which can be represented as vectors) with common components. In the Harker construction we represent F ⁺ as the vector sum of the imaginary contribution from the anomalous scatterers (F _H ⁺′′), the real contribution from the anomalous scatterers (F _H + F _H′) and the unknown contribution from the rest of the protein (F _P, represented with two possibilities in solid and dashed arrows). Since the amplitude of the total structure factor, |F _o ⁺|, is known, the F _P vector must end up on the blue circle, which is centred on the tail of the F _H ⁺′′ vector and has a radius of |F _o ⁺|. Similarly, F ⁻* is represented as a vector sum, starting with its imaginary contribution from the anomalous scatterers (F _H ⁻′′) and then sharing the remaining real scattering components. The red circle, which is centred on the tail of the F _H ⁻′′ vector and with a radius of |F _o ⁺|, crosses the blue circle at the two possible values for F _P; the shorter of the two possible vectors is more probable. If the structure factor will be used for a map containing the anomalous scatterers, the origin of the Harker construction is taken at the base of the vector for the real contribution from the anomalous scatterers, indicated by a cross.

Figure 3

The probabilistic Harker construction for SAD phasing. For this figure, the base of the F _H ⁺′′ vector is chosen as the origin. Uncertainty in the anomalous scatterer model will lead to uncertainty in the scale and orientation of the set of black, red and blue vectors representing the real and imaginary contributions of the anomalous scatterers to F ⁺ and F ⁻*. This leads to uncertainty in the position of the red circle, which is represented as a circular distribution of red shading. The contribution of errors in the measurement of the observed |F _o ⁺| and |F _o ⁻| can be represented as a further increase in the width of the red distribution.

Figure 4

Log-likelihood gradient (LLG) maps, contoured at +6 (cyan contours) and −6 (magenta contours) times the r.m.s. deviation of the LLG map; this figure was prepared using CCP4mg (Potterton et al., 2004 ▶). (a) Using data from a bromide soak of the human acyl protein thioesterase I (Devedjiev et al., 2000 ▶), the program HySS (Grosse-Kunstleve & Adams, 2003 ▶) found a substructure of 21 bromide ions. After refinement in Phaser (in which the occupancies refined close to zero for six of the sites), an LLG map was computed. Density is shown for the top two sites in the context of the final protein model, which was not consulted in the calculation. At the convergence of LLG completion, the substructure contained 40 sites. (b) A model of the four Yb atoms in the Yb-substituted mannose-binding protein (Burling et al., 1996 ▶) was refined in Phaser with isotropic B factors before computing an LLG map, which illustrates the positive and negative features that indicate anisotropic motion.

Figure 5

Breakdown of Friedel’s law applied to scattering contribution of mixed anomalous substructure. (a) shows that Friedel’s law is obeyed for the plus and minus hands of partial structure factors obtained by adding the contributions of two atoms that have the same ratio of real to imaginary scattering. In contrast, (b) shows that Friedel’s law breaks down for the plus and minus hands of partial structure factors obtained by adding the contributions of atoms that differ in their ratio of real to imaginary scattering.