Compressive auto-indexing in femtosecond nanocrystallography

Ultrafast nanocrystallography has the potential to revolutionize biology by enabling structural elucidation of proteins for which it is possible to grow crystals with 10 or fewer unit cells on the side. The success of nanocrystallography depends on robust orientation-determination procedures that allow us to average diffraction data from multiple nanocrystals to produce a three dimensional (3D) diffraction data volume with a high signal-to-noise ratio. Such a 3D diffraction volume can then be phased using standard crystallographic techniques. "Indexing" algorithms used in crystallography enable orientation determination of diffraction data from a single crystal when a relatively large number of reflections are recorded. Here we show that it is possible to obtain the exact lattice geometry from a smaller number of measurements than standard approaches using a basis pursuit solver.Comment: Spence Festschrift on Ultramicroscop

Direct Phasing of Finite Crystals Illuminated with a Free-Electron Laser

abstract: It has been suggested that the extended intensity profiles surrounding Bragg reflections that arise when a series of finite crystals of varying size and shape are illuminated by the intense, coherent illumination of an x-ray free-electron laser may enable the crystal’s unit-cell electron density to be obtained ab initio via well-established iterative phasing algorithms. Such a technique could have a significant impact on the field of biological structure determination since it avoids the need for a priori information from similar known structures, multiple measurements near resonant atomic absorption energies, isomorphic derivative crystals, or atomic-resolution data. Here, we demonstrate this phasing technique on diffraction patterns recorded from artificial two-dimensional microcrystals using the seeded soft x-ray free-electron laser FERMI. We show that the technique is effective when the illuminating wavefront has nonuniform phase and amplitude, and when the diffraction intensities cannot be measured uniformly throughout reciprocal space because of a limited signal-to-noise ratio

Three-Dimensional Reconstruction of the Giant Mimivirus Particle with an X-Ray Free-Electron Laser

Citation: Ekeberg, T., Svenda, M., Abergel, C., Maia, F., Seltzer, V., Claverie, J. M., . . . Hajdu, J. (2015). Three-Dimensional Reconstruction of the Giant Mimivirus Particle with an X-Ray Free-Electron Laser. Physical Review Letters, 114(9), 6. doi:10.1103/PhysRevLett.114.098102We present a proof-of-concept three-dimensional reconstruction of the giant mimivirus particle from experimentally measured diffraction patterns from an x-ray free-electron laser. Three-dimensional imaging requires the assembly of many two-dimensional patterns into an internally consistent Fourier volume. Since each particle is randomly oriented when exposed to the x-ray pulse, relative orientations have to be retrieved from the diffraction data alone. We achieve this with a modified version of the expand, maximize and compress algorithm and validate our result using new methods.Additional Authors: Andersson, I.;Loh, N. D.;Martin, A. V.;Chapman, H.;Bostedt, C.;Bozek, J. D.;Ferguson, K. R.;Krzywinski, J.;Epp, S. W.;Rolles, D.;Rudenko, A.;Hartmann, R.;Kimmel, N.;Hajdu, J

The development and applications of ultrafast electron nanocrystallography

We review the development of ultrafast electron nanocrystallography as a method for investigating structural dynamics for nanoscale materials and interfaces. Its sensitivity and resolution are demonstrated in the studies of surface melting of gold nanocrystals, nonequilibrium transformation of graphite into reversible diamond-like intermediates, and molecular scale charge dynamics, showing a versatility for not only determining the structures, but also the charge and energy redistribution at interfaces. A quantitative scheme for three-dimensional retrieval of atomic structures is demonstrated with few-particle (< 1000) sensitivity, establishing this nanocrystallographic method as a tool for directly visualizing dynamics within isolated nanomaterials with atomic scale spatio-temporal resolution.Comment: 33 pages, 17 figures (Review article, 2008 conference of ultrafast electron microscopy conference and ultrafast sciences

Single molecule imaging with longer x-ray laser pulses

During the last five years, serial femtosecond crystallography using x-ray laser pulses has developed into a powerful technique for determining the atomic structures of protein molecules from micrometer and sub-micrometer sized crystals. One of the key reasons for this success is the "self-gating" pulse effect, whereby the x-ray laser pulses do not need to outrun all radiation damage processes. Instead, x-ray induced damage terminates the Bragg diffraction prior to the pulse completing its passage through the sample, as if the Bragg diffraction was generated by a shorter pulse of equal intensity. As a result, serial femtosecond crystallography does not need to be performed with pulses as short as 5--10 fs, as once thought, but can succeed for pulses 50--100 fs in duration. We show here that a similar gating effect applies to single molecule diffraction with respect to spatially uncorrelated damage processes like ionization and ion diffusion. The effect is clearly seen in calculations of the diffraction contrast, by calculating the diffraction of average structure separately to the diffraction from statistical fluctuations of the structure due to damage ("damage noise"). Our results suggest that sub-nanometer single molecule imaging with 30--50 fs pulses, like those produced at currently operating facilities, should not yet be ruled out. The theory we present opens up new experimental avenues to measure the impact of damage on single particle diffraction, which is needed to test damage models and to identify optimal imaging conditions.Comment: 23 pages; 5 figure

Fourier Phase Retrieval with a Single Mask by Douglas-Rachford Algorithm

Douglas-Rachford (DR) algorithm is analyzed for Fourier phase retrieval with a single random phase mask. Local, geometric convergence to a unique fixed point is proved with numerical demonstration of global convergence

Three-Dimensional Reconstruction of the Giant Mimivirus Particle with an X-Ray Free-Electron Laser

Citation: Ekeberg, T., Svenda, M., Abergel, C., Maia, F., Seltzer, V., Claverie, J. M., . . . Hajdu, J. (2015). Three-Dimensional Reconstruction of the Giant Mimivirus Particle with an X-Ray Free-Electron Laser. Physical Review Letters, 114(9), 6. doi:10.1103/PhysRevLett.114.098102We present a proof-of-concept three-dimensional reconstruction of the giant mimivirus particle from experimentally measured diffraction patterns from an x-ray free-electron laser. Three-dimensional imaging requires the assembly of many two-dimensional patterns into an internally consistent Fourier volume. Since each particle is randomly oriented when exposed to the x-ray pulse, relative orientations have to be retrieved from the diffraction data alone. We achieve this with a modified version of the expand, maximize and compress algorithm and validate our result using new methods.Additional Authors: Andersson, I.;Loh, N. D.;Martin, A. V.;Chapman, H.;Bostedt, C.;Bozek, J. D.;Ferguson, K. R.;Krzywinski, J.;Epp, S. W.;Rolles, D.;Rudenko, A.;Hartmann, R.;Kimmel, N.;Hajdu, J

Three-dimensional reconstruction of the giant mimivirus particle with an X-ray free-electron laser

10.1103/PhysRevLett.114.098102Physical Review Letters114909810