Towards the spatial resolution of metalloprotein charge states by detailed modeling of XFEL crystallographic diffraction.

Oxidation states of individual metal atoms within a metalloprotein can be assigned by examining X-ray absorption edges, which shift to higher energy for progressively more positive valence numbers. Indeed, X-ray crystallography is well suited for such a measurement, owing to its ability to spatially resolve the scattering contributions of individual metal atoms that have distinct electronic environments contributing to protein function. However, as the magnitude of the shift is quite small, about +2 eV per valence state for iron, it has only been possible to measure the effect when performed with monochromated X-ray sources at synchrotron facilities with energy resolutions in the range 2-3 × 10-4 (ΔE/E). This paper tests whether X-ray free-electron laser (XFEL) pulses, which have a broader bandpass (ΔE/E = 3 × 10-3) when used without a monochromator, might also be useful for such studies. The program nanoBragg is used to simulate serial femtosecond crystallography (SFX) diffraction images with sufficient granularity to model the XFEL spectrum, the crystal mosaicity and the wavelength-dependent anomalous scattering factors contributed by two differently charged iron centers in the 110-amino-acid protein, ferredoxin. Bayesian methods are then used to deduce, from the simulated data, the most likely X-ray absorption curves for each metal atom in the protein, which agree well with the curves chosen for the simulation. The data analysis relies critically on the ability to measure the incident spectrum for each pulse, and also on the nanoBragg simulator to predict the size, shape and intensity profile of Bragg spots based on an underlying physical model that includes the absorption curves, which are then modified to produce the best agreement with the simulated data. This inference methodology potentially enables the use of SFX diffraction for the study of metalloenzyme mechanisms and, in general, offers a more detailed approach to Bragg spot data reduction

Autoindexing the diffraction patterns from crystals with a pseudotranslation

Lattice patterns containing alternating strong and weak reflections can be identified by a targeted search for the weak signals, permitting a wider range of diffraction patterns to be indexed automatically

SAD phasing of XFEL data depends critically on the error model.

A nonlinear least-squares method for refining a parametric expression describing the estimated errors of reflection intensities in serial crystallographic (SX) data is presented. This approach, which is similar to that used in the rotation method of crystallographic data collection at synchrotrons, propagates error estimates from photon-counting statistics to the merged data. Here, it is demonstrated that the application of this approach to SX data provides better SAD phasing ability, enabling the autobuilding of a protein structure that had previously failed to be built. Estimating the error in the merged reflection intensities requires the understanding and propagation of all of the sources of error arising from the measurements. One type of error, which is well understood, is the counting error introduced when the detector counts X-ray photons. Thus, if other types of random errors (such as readout noise) as well as uncertainties in systematic corrections (such as from X-ray attenuation) are completely understood, they can be propagated along with the counting error, as appropriate. In practice, most software packages propagate as much error as they know how to model and then include error-adjustment terms that scale the error estimates until they explain the variance among the measurements. If this is performed carefully, then during SAD phasing likelihood-based approaches can make optimal use of these error estimates, increasing the chance of a successful structure solution. In serial crystallography, SAD phasing has remained challenging, with the few examples of de novo protein structure solution each requiring many thousands of diffraction patterns. Here, the effects of different methods of treating the error estimates are estimated and it is shown that using a parametric approach that includes terms proportional to the known experimental uncertainty, the reflection intensity and the squared reflection intensity to improve the error estimates can allow SAD phasing even from weak zinc anomalous signal

Robust indexing for automatic data collection

Improved methods for indexing diffraction patterns from macromolecular crystals are presented. The novel procedures include a more robust way to verify the position of the incident X-ray beam on the detector, an algorithm to verify that the deduced lattice basis is consistent with the observations, and an alternative approach to identify the metric symmetry of the lattice

Challenges in solving structures from radiation-damaged tomograms of protein nanocrystals assessed by simulation

Structure-determination methods are needed to resolve the atomic details that underlie protein function. X-ray crystallography has provided most of our knowledge of protein structure, but is constrained by the need for large, well ordered crystals and the loss of phase information. The rapidly developing methods of serial femtosecond crystallography, micro-electron diffraction and single-particle reconstruction circumvent the first of these limitations by enabling data collection from nanocrystals or purified proteins. However, the first two methods also suffer from the phase problem, while many proteins fall below the molecular-weight threshold required for single-particle reconstruction. Cryo-electron tomography of protein nanocrystals has the potential to overcome these obstacles of mainstream structure-determination methods. Here, a data-processing scheme is presented that combines routines from X-ray crystallography and new algorithms that have been developed to solve structures from tomograms of nanocrystals. This pipeline handles image-processing challenges specific to tomographic sampling of periodic specimens and is validated using simulated crystals. The tolerance of this workflow to the effects of radiation damage is also assessed. The simulations indicate a trade-off between a wider tilt range to facilitate merging data from multiple tomograms and a smaller tilt increment to improve phase accuracy. Since phase errors, but not merging errors, can be overcome with additional data sets, these results recommend distributing the dose over a wide angular range rather than using a finer sampling interval to solve the protein structure

Challenges in solving structures from radiation-damaged tomograms of protein nanocrystals assessed by simulation

Structure determination methods are needed to resolve the atomic details that underlie protein function. X-ray crystallography has provided most of our knowledge of protein structure but is constrained by the need for large, well-ordered crystals and the loss of phase information. The rapidly developing methods of serial femtosecond crystallography, micro-electron diffraction, and single-particle reconstruction circumvent the first of these limitations by enabling data collection from nanocrystals or purified proteins. However, the first two methods also suffer from the phase problem, while many proteins fall below the molecular weight threshold required by single-particle reconstruction. Cryo-electron tomography of protein nanocrystals has the potential to overcome these obstacles of mainstream structure determination methods. Here we present a data processing scheme that combines routines from X-ray crystallography and new algorithms we developed to solve structures from tomograms of nanocrystals. This pipeline handles image processing challenges specific to tomographic sampling of periodic specimens and is validated using simulated crystals. We also assess the tolerance of this workflow to the effects of radiation damage. Our simulations indicate a trade-off between a wider tilt-range to facilitate merging data from multiple tomograms and a smaller tilt increment to improve phase accuracy. Since phase errors but not merging errors can be overcome with additional datasets, these results recommend distributing the dose over a wide angular range rather than using a finer sampling interval to solve the protein structure