Abstract
Single-particle diffraction imaging experiments at free-electron lasers (FELs) have a great potential for the structure determination of reproducible biological specimens that cannot be crystallized. One of the challenges in processing the data from such an experiment is to determine the correct orientation of each diffraction pattern from samples randomly injected in the FEL beam. We propose an algorithm (Yefanov et al 2010 Photon Science—HASYLAB Annual Report) that can solve this problem and can be applied to samples from tens of nanometres to microns in size, measured with sub-nanometre resolution in the presence of noise. This is achieved by the simultaneous analysis of a large number of diffraction patterns corresponding to different orientations of the particles. The algorithm’s efficiency is demonstrated for two biological samples, an artificial protein structure without any symmetry and a virus with icosahedral symmetry. Both structures are a few tens of nanometres in size and consist of more than 100 000 non-hydrogen atoms. More than 10 000 diffraction patterns with Poisson noise were simulated and analysed for each structure. Our simulations indicate the possibility of achieving resolution of about 3.3 Å at 3 Å wavelength and incoming flux of 1012 photons per pulse focused to 100×100 nm2.
Highlights
The problem of solving the structure of individual biological specimens to high resolution is critical for many branches of modern life- and bio-science
X-ray crystallography can only be used for molecules that form crystals [2], whereas transmission electron microscopy is limited to structures with a thickness well below one micron [3]
In a typical single particle diffraction imaging experiment, a sample with unknown orientation is injected into the focused coherent x-ray beam of an free-electron lasers (FEL) (Fig. 1,a)
Summary
The problem of solving the structure of individual biological specimens to high resolution is critical for many branches of modern life- and bio-science. One is based on the common arc algorithm [25] originally developed for electron microscopy [26, 27] This algorithm exploits the fact that all two-dimensional (2D) diffraction patterns of reproducible particles in random orientations represent sections by the Ewald sphere of the 3D intensity distribution in reciprocal space. The classification step decreases the achievable resolution and can produce artifacts in the final stage of electron density reconstruction Another method is based on generative topographic mapping and neural networks [29, 30]. To improve the quality of the orientation determination, a 3D angular refinement procedure is applied at the final step This algorithm works well even with a low photon signal down to 0.05 photons per pixel for sampling rate of three at the edge of the detector. The details of the algorithm implementation are presented in the Appendix
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