Veit Elser

Biological imaging by soft x-ray diffraction microscopy

We have used the method of x-ray diffraction microscopy to image the complex-valued exit wave of an intact and unstained yeast cell. The images of the freeze-dried cell, obtained by using 750-eV x-rays from different angular orientations, portray several of the cells major internal components to 30-nm resolution. The good agreement among the independently recovered structures demonstrates the accuracy of the imaging technique. To obtain the best possible reconstructions, we have implemented procedures for handling noisy and incomplete diffraction data, and we propose a method for determining the reconstructed resolution. This work represents a previously uncharacterized application of x-ray diffraction microscopy to a specimen of this complexity and provides confidence in the feasibility of the ultimate goal of imaging biological specimens at 10-nm resolution in three dimensions.

The diffraction pattern of projected structures

A method for calculating the properties of structures obtained by projection is developed and applied to a three-dimensional generalization of the Penrose tiling. The diffraction pattern is shown in general to consist of a dense set of delta-function peaks. For the Penrose model the pattern in addition has the symmetry of the icosahedron.

Quasicrystal structure of (Al, Zn)49Mg32

Abstract We express the cubic (Al, Zn)49Mg32 structure as a periodic packing of the rhombohedra1 cells from the three-dimensional Penrose tiling, decorated by atoms. This decoration is extended to the aperiodic quasicrystal packing of the same cells to give a hypothetical structure for the recently discovered icosahedral phase with the same composition. This is the first structure of a real system which is related both to quasicrystals and to Frank-Kasper icosahedral close packings.

Time-resolved protein nanocrystallography using an X-ray free-electron laser

We demonstrate the use of an X-ray free electron laser synchronized with an optical pump laser to obtain X-ray diffraction snapshots from the photoactivated states of large membrane protein complexes in the form of nanocrystals flowing in a liquid jet. Light-induced changes of Photosystem I-Ferredoxin co-crystals were observed at time delays of 5 to 10 µs after excitation. The result correlates with the microsecond kinetics of electron transfer from Photosystem I to ferredoxin. The undocking process that follows the electron transfer leads to large rearrangements in the crystals that will terminally lead to the disintegration of the crystals. We describe the experimental setup and obtain the first time-resolved femtosecond serial X-ray crystallography results from an irreversible photo-chemical reaction at the Linac Coherent Light Source. This technique opens the door to time-resolved structural studies of reaction dynamics in biological systems.

Reconstruction algorithm for single-particle diffraction imaging experiments.

We introduce the EMC algorithm for reconstructing a particles three-dimensional (3D) diffraction intensity from very many photon shot-noise limited two-dimensional measurements, when the particle orientation in each measurement is unknown. The algorithm combines a maximization step (M) of the intensitys likelihood function, with expansion (E) and compression (C) steps that map the 3D intensity model to a redundant tomographic representation and back again. After a few iterations of the EMC update rule, the reconstructed intensity is given to the difference-map algorithm for reconstruction of the particle contrast. We demonstrate reconstructions with simulated data and investigate the effects of particle complexity, number of measurements, and the number of photons per measurement. The relatively transparent scaling behavior of our algorithm provides an estimate of the data processing resources required for future single-particle imaging experiments.

Hierarchical Porous Polymer Scaffolds from Block Copolymers

A Complicated Scaffold, Simply Materials with tailored pore structures can be useful as catalysis supports and for lightweight materials. When preparing medical scaffolds, restrictive preparation conditions have to be met, which can prohibit multistep preparation procedures. Sai et al. (p. 530) describe a method for making porous polymers containing both relatively large (several microns) interconnecting pores and a second population of ∼ tens of nanometer pores. The process exploits spinodal decomposition of a block copolymer blended with small-molecule additives and requires a simple washing step with water, methanol, or ethanol. Spinodal decomposition of block copolymers and oligomeric additives produces three-dimensional hierarchical porous polymers. Hierarchical porous polymer materials are of increasing importance because of their potential application in catalysis, separation technology, or bioengineering. Examples for their synthesis exist, but there is a need for a facile yet versatile conceptual approach to such hierarchical scaffolds and quantitative characterization of their nonperiodic pore systems. Here, we introduce a synthesis method combining well-established concepts of macroscale spinodal decomposition and nanoscale block copolymer self-assembly with porosity formation on both length scales via rinsing with protic solvents. We used scanning electron microscopy, small-angle x-ray scattering, transmission electron tomography, and nanoscale x-ray computed tomography for quantitative pore-structure characterization. The method was demonstrated for AB- and ABC-type block copolymers, and resulting materials were used as scaffolds for calcite crystal growth.

Searching with iterated maps

In many problems that require extensive searching, the solution can be described as satisfying two competing constraints, where satisfying each independently does not pose a challenge. As an alternative to tree-based and stochastic searching, for these problems we propose using an iterated map built from the projections to the two constraint sets. Algorithms of this kind have been the method of choice in a large variety of signal-processing applications; we show here that the scope of these algorithms is surprisingly broad, with applications as diverse as protein folding and Sudoku.

Cryptotomography: reconstructing 3D Fourier intensities from randomly oriented single-shot diffraction patterns

We reconstructed the 3D Fourier intensity distribution of monodisperse prolate nanoparticles using single-shot 2D coherent diffraction patterns collected at DESYs FLASH facility when a bright, coherent, ultrafast x-ray pulse intercepted individual particles of random, unmeasured orientations. This first experimental demonstration of cryptotomography extended the expansion-maximization-compression framework to accommodate unmeasured fluctuations in photon fluence and loss of data due to saturation or background scatter. This work is an important step towards realizing single-shot diffraction imaging of single biomolecules.

Reconstruction of a yeast cell from X-ray diffraction data

Details are provided of the algorithm used for the reconstruction of yeast cell images in the recent demonstration of diffraction microscopy by Shapiro, Thibault, Beetz, Elser, Howells, Jacobsen, Kirz, Lima, Miao, Nieman & Sayre [Proc. Natl Acad. Sci. USA (2005), 102, 15343-15346]. Two refinements of the iterative constraint-based scheme are developed to address the current experimental realities of this imaging technique, which include missing central data and noise. A constrained power operator is defined whose eigenmodes allow the identification of a small number of degrees of freedom in the reconstruction that are negligibly constrained as a result of the missing data. To achieve reproducibility in the algorithms output, a special intervention is required for these modes. Weak incompatibility of the constraints caused by noise in both direct and Fourier space leads to residual phase fluctuations. This problem is addressed by supplementing the algorithm with an averaging method. The effect of averaging may be interpreted in terms of an effective modulation transfer function, as used in optics, to quantify the resolution. The reconstruction details are prefaced with simulations of wave propagation through a model yeast cell. These show that the yeast cell is a strong-phase-contrast object for the conditions in the experiment.

Solution of the crystallographic phase problem by iterated projections

An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual reciprocal-space formulations of atomicity. The new algorithm implements atomicity constraints in real space, as well as intensity constraints in reciprocal space, by projections that restore each constraint with the minimal modification of the scattering density. To recover the true density, the two projections are combined into a single operation, the difference map, which is iterated until the magnitude of the density modification becomes acceptably small. The resulting density, when acted upon by a single additional operation, is by construction a density that satisfies both intensity and atomicity constraints. Numerical experiments have yielded solutions for atomic resolution X-ray data sets with over 400 non-hydrogen atoms, as well as for neutron data, where positivity of the density cannot be invoked.