3D atomic structure from a single X-ray free electron laser pulse.

X-ray Free Electron Lasers (XFEL) are cutting-edge pulsed x-ray sources, whose extraordinary pulse parameters promise to unlock unique applications. Several new methods have been developed at XFELs; however, no methods are known, which allow ab initio atomic level structure determination using only a single XFEL pulse. Here, we present experimental results, demonstrating the determination of the 3D atomic structure from data obtained during a single 25 fs XFEL pulse. Parallel measurement of hundreds of Bragg reflections was done by collecting Kossel line patterns of GaAs and GaP. To the best of our knowledge with these measurements, we reached the ultimate temporal limit of the x-ray structure solution possible today. These measurements open the way for obtaining crystalline structures during non-repeatable fast processes, such as structural transformations. For example, the atomic structure of matter at extremely non-ambient conditions or transient structures formed in irreversible physical, chemical, or biological processes may be captured in a single shot measurement during the transformation. It would also facilitate time resolved pump-probe structural studies making them significantly shorter than traditional serial crystallography.

Comparison of EMC and CM methods for orienting diffraction images in single-particle imaging experiments.

In single-particle imaging (SPI) experiments, diffraction patterns of identical particles are recorded. The particles are injected into the X-ray free-electron laser (XFEL) beam in random orientations. The crucial step of the data processing of SPI is finding the orientations of the recorded diffraction patterns in reciprocal space and reconstructing the 3D intensity distribution. Here, two orientation methods are compared: the expansion maximization compression (EMC) algorithm and the correlation maximization (CM) algorithm. To investigate the efficiency, reliability and accuracy of the methods at various XFEL pulse fluences, simulated diffraction patterns of biological molecules are used.

Incorporating particle symmetry into orientation determination in single-particle imaging.

In coherent-diffraction-imaging experiments X-ray diffraction patterns of identical particles are recorded. The particles are injected into the X-ray free-electron laser (XFEL) beam in random orientations. If the particle has symmetry, finding the orientation of a pattern can be ambiguous. With some modifications, the correlation-maximization method can find the relative orientations of the diffraction patterns for the case of symmetric particles as well. After convergence, the correlation maps show the symmetry of the particle and can be used to determine the symmetry elements and their orientations. The C factor, slightly modified for the symmetric case, can indicate the consistency of the assembled three-dimensional intensity distribution.

Coherent diffraction imaging: consistency of the assembled three-dimensional distribution.

The short pulses of X-ray free-electron lasers can produce diffraction patterns with structural information before radiation damage destroys the particle. From the recorded diffraction patterns the structure of particles or molecules can be determined on the nano- or even atomic scale. In a coherent diffraction imaging experiment thousands of diffraction patterns of identical particles are recorded and assembled into a three-dimensional distribution which is subsequently used to solve the structure of the particle. It is essential to know, but not always obvious, that the assembled three-dimensional reciprocal-space intensity distribution is really consistent with the measured diffraction patterns. This paper shows that, with the use of correlation maps and a single parameter calculated from them, the consistency of the three-dimensional distribution can be reliably validated.

Selection and orientation of different particles in single particle imaging.

The short pulses of X-ray free electron lasers can produce diffraction patterns with structural information before radiation damage destroys the particle. The particles are injected into the beam in random orientations and they should be identical. However, in real experimental conditions it is not always possible to have identical particles. In this paper we show that the correlation maximization method, developed earlier, is able to select identical particles from a mixture and find their orientations simultaneously.

Atomic structure of a single large biomolecule from diffraction patterns of random orientations.

The short and intense pulses of the new X-ray free electron lasers, now operational or under construction, may make possible diffraction experiments on single molecule-sized objects with high resolution, before radiation damage destroys the sample. In a single molecule imaging (SMI) experiment thousands of diffraction patterns of single molecules with random orientations are recorded. One of the most challenging problems of SMI is how to assemble these noisy patterns of unknown orientations into a consistent single set of diffraction data. Here we present a new method which can solve the orientation problem of SMI efficiently even for large biological molecules and in the presence of noise. We show on simulated diffraction patterns of a large protein molecule, how the orientations of the patterns can be found and the structure to atomic resolution can be solved. The concept of our algorithm could be also applied to experiments where images of an object are recorded in unknown orientations and/or positions like in cryoEM or tomography.

Common arc method for diffraction pattern orientation.

Very short pulses of X-ray free-electron lasers opened the way to obtaining diffraction signal from single particles beyond the radiation dose limit. For three-dimensional structure reconstruction many patterns are recorded in the object's unknown orientation. A method is described for the orientation of continuous diffraction patterns of non-periodic objects, utilizing intensity correlations in the curved intersections of the corresponding Ewald spheres, and hence named the common arc orientation method. The present implementation of the algorithm optionally takes into account Friedel's law, handles missing data and is capable of determining the point group of symmetric objects. Its performance is demonstrated on simulated diffraction data sets and verification of the results indicates a high orientation accuracy even at low signal levels. The common arc method fills a gap in the wide palette of orientation methods.