The most notable of these limitations arises from the restricted X-ray intensity from synchrotrons, such that statistically meaningful signal cannot be obtained during exposures shorter than the time for rotational diffusion on a length scale smaller than the desired resolution. Although Kam originally proposed his method for solution X-ray scattering, it has never been realized in this form owing to limitations of previously available X-ray sources. He demonstrated that averaging angular autocorrelation functions of individual 2D diffraction patterns yields the autocorrelation function of the 3D diffraction volume for a single particle, and this function can be related to the expansion coefficients of the diffraction volume in spherical harmonics 12. Instead of orientation classification of diffraction patterns, Kam proposed the simple averaging method that overcomes these constraints, and also reduces the vast data amount to a single compact 3D array. They generally require each diffraction pattern to be generated by a single particle, posing practical constraints on the experiment. The corresponding algorithms are based on expectation maximization (EM) 9 or dimensionality reduction 10, 11. A weak signal dictates the necessity to use a complete data set of diffraction patterns from particles in random orientations to construct a 3D diffraction volume. For most systems of practical interest, such as protein complexes, the experiment will be characterized by the small number of scattered photons, immersed in the high background noise, and uncertain number of particles in each shot. The next aim is experimental determination of three-dimensional (3D) structure from non-crystalline single particles using LCLS single-shot diffraction 3. Resolution in reconstructions of two-dimensional (2D) electron density projections for a large submicron virus 6, soot and other aerosols 7, 8 from single-shot LCLS diffraction patterns ranges from 24 to 41 nm. In the single-shot diffraction serial nanocrystallography experiments at the Linac Coherent Light Source (LCLS), structure factors for lysozyme have been measured to 1.9 Å resolution 5. Owing to the extreme brevity and high fluence of the FEL pulses, even though a radiation dose at the target far exceeds the ‘safe dose’ radiation limit for conventional macromolecular crystallography 2, diffraction is recorded before the onset of the structural damage processes 3, 4. The advent of X-ray free-electron lasers (FELs) promises to eliminate the resolution limitation imposed on imaging of biological materials by radiation damage 1. This method may be applied to the structural determination of biological macromolecules in solution. The correlation analysis avoids the need for orientation determination entirely. Our demonstration uses unsupported test particles created via aerosol self-assembly, and composed of two polystyrene spheres of equal diameter. Here we report the first application of a three-dimensional spatial frequency correlation analysis to carry out this synthesis from noisy single-particle femtosecond X-ray diffraction patterns of nearly identical samples in random and unknown orientations, collected at the Linac Coherent Light Source. As signal strength diminishes for small particles, the synthesis of a three-dimensional diffraction volume requires simultaneous involvement of all data. The ultra-short, ultra-bright X-ray pulses provide snapshots of the randomly oriented particles frozen in time, and terminate before the onset of structural damage. Nature Communications volume 3, Article number: 1276 ( 2012)ĭiffractive imaging with free-electron lasers allows structure determination from ensembles of weakly scattering identical nanoparticles. Single-particle structure determination by correlations of snapshot X-ray diffraction patterns
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