Orientation Reconstruction of Proteins using Coulomb Explosions

Abstract

We solve the orientation recovery of a tumbling protein in the gas phase from single-event measurements of the spatial positions of its ions after an X-ray laser induced explosion. We simulate diffracted X-ray signal and ion dynamics under experimental conditions and compare our method to conventional orientation recovery in single-particle imaging with X-ray free-electron lasers using only diffraction data. We reconstruct 3D diffraction intensities using orientations recovered from the ion signatures and retrieve the electron density with established phase-retrieval algorithms. We test our orientation recovery procedure on 56 proteins ranging from 14 to 52 kDa (1800 to 6500 atoms), achieving roughly an angular error of around 5°. The resulting 3D electron-density reconstructions are compared to ground-truth volumes simulated at the same nominal resolution, and achieve the resolution at the edge of the detector in conditions similar to current single-particle imaging setups. We investigate the reconstruction quality and demonstrate that ion data can be used for reliable orientation recovery of particles in single-particle imaging, achieving orientation on par or better than currently used recovery techniques. This work shows the potential of ion detection for retrieving additional information from the sample fragmentation, and boost single particle imaging with X-ray lasers in the cases where the diffraction signal is a limiting factor.

Figures (4)

• Figure 1: Randomly oriented proteins are hit by an X-ray laser to produce single-shot diffraction patterns and ion explosion footprints. Patterns and footprints corresponding to each concurrent event are paired; we find the orientations of explosion footprints by mapping and assembling them on a spherical surface. These orientations are then applied on the diffraction patterns for reconstructing the 3D diffraction intensities space. Using phase retrieval algorithms we then reconstruct electron densities.
• Figure 2: Mapping and assembling the explosion and diffraction volume. We map the simulated Coulomb explosion footprints onto a sphere with radius equal to the distance from the interaction region. After finding the relative orientation of the sample from the ion maps we can retrieve the electron density in 3D using diffraction intensities. a) Example of a binned simulated explosion footprint for an 80mm MCP located at 10 mm from the interaction region. b) Spherical projection of a single event, plotted using Mollweide view (non-integer intensities in the spherical projection arise from binning and Gaussian filtering). c) Spherical map of the full explosion estimated from the predicted orientations. d) Spherical map of the full explosion simulated from the sum of all the measurements when applying the exact orientations of the sample. e) Orthogonal slices (XY, XZ, YZ) through the assembled diffraction volume. Color bar indicates number of photons (log scale).
• Figure 3: Benchmark of the orientation recovery algorithm against a) number of atoms, b) number of explosion footprints, c) solid angle covered by the detector, and d) detection coefficient (the chance that an ion that hit the detector is recorded). Rotation errors (degrees) are shown on the y-axis (log-scale), the benchmarks are carried out on the four representative proteins ordered by increasing molecular mass. In cases a),c),and d) the number of explosion footprints is 200.
• Figure 4: SPI data analysis using diffraction patterns. a) Orientation error as a function of EMC iteration using 400 diffraction patterns for four representative proteins. Orientation errors are reported modulo $D_2$ (crystallographic $222$). b) Fourier shell correlation (FSC) plot. The dashed orange line indicates the 1/2-bit FSC threshold, and the vertical dashed lines mark respectively the edge and the corner resolutions (3.1 nm and 2.2 nm). The achieved reconstruction resolutions, determined from the 1/2-bit FSC criterion, are $24.3\,\text{\AA}$ for 2BBR, $19.0\,\text{\AA}$ for 2OL6, $22.2\,\text{\AA}$ for 8QDD, and $30.0\,\text{\AA}$ for 1KIJ. All reconstructions achieve a resolution better than the edge resolution limit of $30.1\,\text{\AA}$. c) Representative reconstructed 3D volumes with embedded protein models. The density map was visualized in ChimeraX using an isosurface threshold of 15% of the map intensity range meng2023ucsf.