Indexing amyloid peptide diffraction from serial femtosecond crystallography: new algorithms for sparse patterns

Abstract

Still diffraction patterns from peptide nanocrystals with small unit cells are challenging to index using conventional methods owing to the limited number of spots and the lack of crystal orientation information for individual images. New indexing algorithms have been developed as part of the Computational Crystallography Toolbox (cctbx) to overcome these challenges. Accurate unit-cell information derived from an aggregate data set from thousands of diffraction patterns can be used to determine a crystal orientation matrix for individual images with as few as five reflections. These algorithms are potentially applicable not only to amyloid peptides but also to any set of diffraction patterns with sparse properties, such as low-resolution virus structures or high-throughput screening of still images captured by raster-scanning at synchrotron sources. As a proof of concept for this technique, successful integration of X-ray free-electron laser (XFEL) data to 2.5 Å resolution for the amyloid segment GNNQQNY from the Sup35 yeast prion is presented.

Keywords: Sup35 yeast prion; XFEL; crystallography; indexing methods.

Figure 1

Example GNNQQNY diffraction patterns at different detector distances (111 and 166 mm). (a) One of the clearer GNNQQNY images, with obvious periodicity. Note the spot pathologies, including split spots and streaked spots. (b) Typical GNNQQNY image with few spots visible. Both (a) and (b) are indexable with cctbx.small_cell.

Figure 2

Derivation of unit-cell parameters from a powder pattern. (a) GNNQQNY maximum-value composite image from 32 178 diffraction patterns. Powder rings are visible in the composite. (b) Unit cell from the published GNNQQNY structure (PDB entry 1yjp). Calculated powder rings are overlaid in red. (c) Radial averaging trace from the composite pattern displayed in Rex.cell. Peaks used for indexing are marked in green. (d) As (b) with the corrected Rex.cell-derived unit cell.

Figure 3

Indexing a single still shot. Two spots are shown from Fig. 1 ▶(a). Predicted powder rings are overlaid in red. Rings that overlap a spot represent potential Miller indices for that spot. The index of the spot in the upper left corner is ambiguous owing to its proximity to two closely spaced powder rings. The pair of spots in the lower right corner illustrates an ambiguity likely owing to crystal splitting.

Figure 4

Resolving indexing ambiguities in the diffraction pattern from Fig. 1 ▶(b) using a maximum clique. (a) Calculation of d ₁, the observed distance in reciprocal space between two reflections. A reference reflection A and a candidate reflection B are projected back on to the Ewald sphere from their positions on the detector. Inset: the distance between the reflections A and B is measured in reciprocal space. (b) Calculation of d ₂, the predicted distance in reciprocal space. Given the reference reflection A and its candidate index (1, 0, 1), there are four possible symmetry operators applicable to reflection B and its candidate index (4, 1, 1). Two of them are not correct, as the predicted distances d ₂ do not match the observed distance d ₁. (c) Complete graph from Fig. 1 ▶(b). Each node represents a single reflection paired with a candidate Miller index and one of four symmetry operators of the reciprocal-lattice point group. The boxes are labeled first with an arbitrary identification of the spot (a spot ID) and then with the Miller index being examined. For example, the central spot is spot number 4, with index (−4, 0, −2). The nodes are colored by degree (number of connections), with green representing many connections and red representing one. Edges represent spot connections (see text). (d) Plotting the eight reflections from the correct maximum clique in (c) in reciprocal space. The plotted reflections form a right-handed basis and intersect the Ewald sphere.

Figure 5

GNNQQNY needle crystals preferentially orient in the sample-delivery stream. (a) Optical microscope image of GNNQQNY needle crystals. (b) The basis vectors of GNNQQNY crystals indexed by cctbx.small_cell in this work are displayed in reciprocal space. a*, b* and c* are displayed in red, green and blue, respectively. Axes are in units of reciprocal ångströms. Two views of the same set of vectors are displayed from different angles. Needle crystals in the injection stream tend to align along the x* axis, which is orthogonal to the beam. The real-space b axis corresponds to the length of the needle crystals and is coaxial with the direction of the hydrogen bonds formed between strands of the β-sheet.

Figure 6

Refined GNNQQNY map from 232 images indexed by cctbx.small_cell. The GNNQQYNY peptide is shown in cyan. Blue density is the 2F _o − F _c map contoured at 1.5σ; F _o − F _c difference density is shown in red (negative) and green (positive) contoured at 3.0σ. The unit cell is drawn in yellow. This image was rendered using Coot (Emsley et al., 2010 ▶).