3D object reconstruction from random orientations

The featured item this time is “Structure from Fleeting Illumination of Faint Spinning Objects in Flight with Application to Single Molecules” by Russell Fung and co-authors at U Wisconsin Milwaukee.

The promise of solving atomic-resolution 3D structure of biological proteins with X-ray Free Electron Lasers has several obstacles. First one is to have fast enough x-ray pulse to image molecules before it starts to undergo “Coulomb explosion”. But even that is not sufficient to produce atomic-scale structure due to low scattering cross-section of hard x-rays – so the experiment will need to be repeated many (thousands?) times to improve statistics. Luckily, protein molecules are identical, so the fundamental 3D structure of the sample could be considered the same – however, the orientation of protein molecule is going to be different each time.

There are two ways to solve the “random orientation” problem – one is to try to align the molecule, for example with a laser beam. However this has to be done with a very high precision and is difficult to achieve in practice. Another approach is to do experiment thousands of times with random orientations of molecules, catalogue all resulting projections, and then use mathematical algorithms to “fold” the projections into a unique 3D object that is consistent with all resulting projections.

Russel Fung et al. provide an algorithm that does just that – by simulating realistic conditions of 4th generation synchrotron source, X-ray Free Electron Laser, with collection of 100,000 photons, 72,000 repeated diffraction patterns from single shot experiments and scattering rates as low as 0.01 photons per pixel at large wavevectors corresponding to 1.8 Angstrom.

The result of folding using Generative Topographic Mapping for protein chignolin in random orientations is shown in figure above, for 3D movie of this reconstructed molecule see Abbas Ourmazd’s webpage at UW Milwaukee.

Recent Coherent X-ray Literature Round-Up

Electrospray approach to single-particle diffraction at XFEL facilities:

M. Bogan, W. Benner, S. Boutet et al., “Single Particle X-ray Diffractive Imaging,” Nano Letters 8, 310-316 (2008)

A study of SiN etched “logo” pattern x-ray induced destruction, similar to Chapman’s Nature Physics 2006 work (Cowboys holding hands logo, doi:10.1038/nphys461):

A. Barty, S. Boutet, M. J. Bogan et al., “Ultrafast single-shot diffraction imaging of nanoscale dynamics,” Nat Photon 2, 415-419 (2008)

Lens-less imaging of Fresnel Zone Plate using ptychography – scanning coherent diffraction – improvement in resolution and illumination function from FZP reconstruction by Rodenburg et al. PRL 98, 034801 (2007):

P. Thibault, M. Dierolf, A. Menzel et al., “High-Resolution Scanning X-ray Diffraction Microscopy,” Science321, 379-382 (2008)

Tabletop coherent soft x-ray microscopy by UColorado group – an exciting alternative to large XFEL machines:

R. L. Sandberg, C. Song, P. W. Wachulak et al., “High numerical aperture tabletop soft x-ray diffraction microscopy with 70-nm resolution,” Proceedings of the National Academy of Sciences of the United States of America 105, 24-7 (2008)

X-ray holography with 5 reference beams is obviously better than holography with 3 or 1 reference beams. How about 1,000,000 reference beams? This is what can be accomplished with uniformly redundant arrays:

S. Marchesini, S. Boutet, A. E. Sakdinawat et al., “Massively parallel X-ray holography,” Nat Photon 2, 560-563 (2008)

Coherent imaging of 80-100nm particle (in SAXS mode, similar to work by Miao group) with 5nm resolution, but done at 15 keV. Coherent fraction of the beam drops off as lambda^2, and efficiency of area x-ray detectors is substantially reduced at higher energies too. But at higher energies one can capture more of the Q range for the same solid angle defined by scattering geometry. Still, 5 nm number is better resolution that I expected – this should imply there are at least 15-20 highly visible fringes in diffraction pattern, instead of 7 or so. Maybe it’s log scale of intensity that hides extra fringes…

C. G. Schroer, P. Boye, J. M. Feldkamp et al., “Coherent X-Ray Diffraction Imaging with Nanofocused Illumination,” Physical Review Letters 101, 090801-4 (2008)

A review article on coherent x-ray diffractive imaging of small particles:

J. Miao, T. Ishikawa, Q. Shen and T. Earnest, “Extending X-ray crystallography to allow the imaging of noncrystalline materials, cells, and single protein complexes,” Annual Review of Physical Chemistry 59, 387-410 (2008)

First example of x-ray holography in hard x-ray regime. Sample preparation is quite a bit more challenging.

L. Stadler, C. Gutt, T. Autenrieth et al., “Hard X Ray Holographic Diffraction Imaging,” Physical Review Letters 100, 245503-4 (2008)

Pine-tree PbS nanowires, screw dislocations and Eshelby twist

This week’s item is Science Express paper “Dislocation-Driven Nanowire Growth and Eshelby Twist ” by Michael Bierman et al. (doi:10.1126/science.1157131). By growing PbS nanowires using chemical vapor deposition (CVD) they observe hyper-branched structures, similar to the pine trees with a trunk and multiple branches. The spiral growth pattern is due to the existence of a single screw dislocation within the trunk of the nanoscale “pine tree”. The authors test the theory of screw dislocations developed by Eshelby in 1950ies, in particular his prediction of the “Eshelby twist”, an angular twist in the lattice, with twist per unit length proportional to Burgers vector of the dislocation and inversely proportional to the radius of the structure. Because of small radii of the grown PbS nanostructures, nanowires present an excellent testing ground for expected Eshelby twist. The authors find that the fit to Eshelby theory produces Burgers vector on the order of 6 Angstroms, comparable to the expected value of a single unit cell, 5.94 Angstroms.

two PRLs on x-ray phasing

Two new PRLs are dealing with x-ray phasing.

The first paper is de Jonge et al., “Quantitative Phase Imaging with a Scanning Transmission X-Ray Microscope” Phys. Rev. Lett. 100, 163902 (2008). Typically the differential phase contrast measurements become non-trivial for thick specimens, when the adsorption and phase-wrapping effects become significant. This paper resolves this problems when differential phase contrast measurements are done in scanning transmission x-ray microscopy mode (STXM), since the solution is overconstrained, allowing to arrive at unique phase and adsorption values.

The second paper is Johnson et al., “Coherent Diffractive Imaging Using Phase Front Modifications” Phys. Rev. Lett. 100, 155503 (2008).

Since phase is lost during the measurements, it is impossible to simply fourier-transform the coherent x-ray diffraction pattern to obtain a real-space image of an object with nanoscale resolution. There are numerous numerical approaches of phase-retrieval based on oversampling the diffraction pattern. This paper presents an alternative approach of introducing a phase plate, and deconvolving the set of phases resulting from the sample by scanning the phase object around, making the contribution from the phase plate known, and providing information on un-altered phases that would be observed if no phase plate was present. This technique is similar to ptychography, as it provides additional constraints that help arriving at unique solution in a rapidly convergent manner, except it scans the known phase plate, rather than the object being imaged.

3D Neutron Microscopy

This week we highlight a paper in Nature Physics by Nikolay Kardjilov and co-authors “Three-dimensional imaging of magnetic fields with polarized neutrons”.

3D tomography and microscopy with x-rays is nothing new. Neutrons, however, provide the advantage of strong scattering from magnetic spins – but microscopy with neutrons is limited due to lack of focusing optics, low brightness and monochromacity of neutron sources.

Kardjilov and co-authors present a new technique based on observing the rotation of spin polarization of neutrons as they travel through magnetic material. The result is a 3D view of local magnetization with 100-micron spatial resolution. This technique requires highly polarized and monochromatic neutron beams.