Single-particle imaging without symmetry constraints at an X-ray free-electron laser

Abstract

The analysis of a single-particle imaging (SPI) experiment performed at the AMO beamline at LCLS as part of the SPI initiative is presented here. A workflow for the three-dimensional virus reconstruction of the PR772 bacteriophage from measured single-particle data is developed. It consists of several well defined steps including single-hit diffraction data classification, refined filtering of the classified data, reconstruction of three-dimensional scattered intensity from the experimental diffraction patterns by orientation determination and a final three-dimensional reconstruction of the virus electron density without symmetry constraints. The analysis developed here revealed and quantified nanoscale features of the PR772 virus measured in this experiment, with the obtained resolution better than 10 nm, with a clear indication that the structure was compressed in one direction and, as such, deviates from ideal icosahedral symmetry.

Keywords: XFELs; single-particle imaging; three-dimensional virus reconstructions.

Figure 1

Workflow of the SPI experiment towards single-particle reconstruction: (a) single-hit classification of the initial data, (b) refined filtering of the classified data, (c) orientation determination, (d) particle reconstruction using phase retrieval.

Figure 2

(a)–(c) Typical diffraction patterns collected during the SPI experiment with (a) typical candidates for weak single hits, (b) strong single hits and (c) multiple hits (all diffraction patterns are shown on a logarithmic scale). (d) Histogram of diffraction images as a function of the integrated intensity. Three dashed threshold lines mark the transient region between weak and strong hits passing our intensity filter. Diffraction patterns in (a) and (c) belong to blue and red regions in (d), respectively. The diffraction pattern in (b) belongs to the central region in (d).

Figure 3

Projection of feature vectors onto the PCA plane. Each dot corresponds to a diffraction pattern. The green empty dots represent diffractions patterns of Set_44k and the yellow dots represent single hits of Set_14k. The manually classified patterns are marked by red (single hits) and blue dots (multiple hits).

Figure 4

(a)–(c) FV densities on PCA planes for different intensity thresholds (number of hits in Table 1 ▸). (d)–(f) Projection view of the PCA densities with manually classified single-hit patterns shown as red dots. Blue and yellow dots correspond to the same selections as in Fig. 3 ▸. The black contour level corresponds to 3.3% of the maximum value of the PCA density (selected hits in Table 1 ▸). For low-intensity thresholds, the black contour contains a region that is not clearly represented by the manual single hit selection (a), (d) and (b), (e). The manual hit selection is most precisely matched by data Set_10k ^PCA within the contour line for an intensity threshold at 2 × 10⁵ ph in (c) and (f).

Figure 5

Power spectral density (PSD) for distinct data sets obtained at different stages of particle-size filtering. (a) PSDs for the data Set_10k ^PCA of diffraction patterns. (b) PSDs after the size-distribution filtering for Set_8k ^PCA. (c) PSDs after using a restricted fit quality range for Set_7k ^PCA. (d) Histogram of positions of the first minimum from data Set_10k ^PCA used for the size filtering. Diffraction patterns inside the blue box (±1 r.m.s. around the mean value) were selected for further analysis. (e) Histogram of the PSD fit quality χ. Diffraction patterns inside the blue box ( r.m.s. around the mean value) were selected for further analysis.

Figure 6

(a) Data workflow and filtering stages. The red box indicates the data selection provided by Reddy et al. (2017 ▸) and the green boxes show the selection from the PCA technique. (b) Schematic of data set relations with the intersection shown in blue.

Figure 7

Correlation maps of the amplitudes for even order difference spectra Fourier components. (a) Set_14k and (b) Set_8k ^excluded have very similar features which suggests that Set_8k ^excluded with presumably non-single hits dominates the properties of Set_14k. (c) Set_7k ^PCA consists of the PCA single-hit selection and shows more pronounced features.

Figure 8

Comparative analysis of different pairs of the selected data sets by the Fourier quadrant correlation (FQC) approach.

Figure 9

(a)–(c) Three-dimensional intensity distribution from data Set_14k (a), data Set_7k ^PCA (b), and data Set_7k ^PCA (c) with background subtraction. All three intensity distributions are shown in a logarithmic scale in different orientations. (d)–(f) Line profiles along the red and black lines shown in (a)–(c) for three data sets. Note that the data sets in (a) and (b) are not aligned because of the non-deterministic iterative orientation determination.

Figure 10

PR772 virus electron-density reconstruction obtained from different data selections. (a)–(c) Isosurface at 10% of the maximum electron density. (d)–(f) Isosurface at 10%, 82% and 89% of the maximum electron density. (g)–(i) Slices through the particle center in the x–y plane. Low-density site in (i) is marked by a black arrow. Black scale bar denotes 50 nm.

Figure 11

Line scans from facet to facet (top row) and from vertex to vertex (bottom row) in different directions for the selected data set (Set_7k ^PCA) without (a)–(d) and with (e)–(h) background subtraction. The horizontal dotted lines in (b), (d), (f) and (h) indicate 10% of the maximum density used for size analysis.

Figure 12

(a) Phase-retrieval transfer function (PRTF) and (b) Fourier-shell correlation (FSC) of data Set_7k ^PCA with background subtraction. Red dots correspond to the determined resolution.