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)

sub-picosecond movies of nucleation dynamics

A shortlived SPPS facility is still producing papers – this week it’s the PRL paper by Aaron Lindenberg and some 28 co-authors ” X-Ray Diffuse Scattering Measurements of Nucleation Dynamics at Femtosecond Resolution” Phys. Rev. Lett. 100, 135502 (2008).

This is yet another pump-probe experiment, where pump is a femtosecond laser which ablates/melts a crystal, and a probe is a sub-picosecond x-ray pulse from SPPS. X-ray probe pulse length is still a limiting parameter in overall time resolution of such pump-probe setups. This experiment had a time resolution of 700 fs, but in the near future at XFEL facilities such as LCLS the time resolution will approach tens of femtosecond.

Lindenberg and coworkers were able to look at both high-angle and small-angle diffuse scattering resulting in ablation process in this time-resolved mode. Their data indicates presence of short-lived nanoscale voids (shown in green in the figure on the right) in the liquid state caused by the laser pulse, and these voids merge together to form larger voids over the timescale of 20 ps or so – claims supported by molecular dynamics simulations. While their data was taken in reciprocal space, by recording ensemble-averaged structure factor S(q) at various time delays from the laser pulse, in the future one could envision fully inverting the speckle patterns shown in the figure above, to obtain a real-space images of the nanoscale voids.

Giant molecules or tiny crystals?

Nature Materials has a News and Views article by Ian Robinson titled “Coherent diffraction: Giant molecules or tiny crystals?”, which reviews recent coherent electron diffraction results by Huang et al. featured here earlier. One of the interesting points made in this mini-review is the phase diagram on the left showing a transition from bulk cubic crystal to decahedral and icosahedral structures, including quasi-molten and liquid phases.

Near-Field X-ray Speckle

There is a brand new paper that appeared today in Nature Physics by Cerbino and co-workers that describes a new x-ray coherent technique based on observations of Near-Field Speckle pattern.

Typically x-ray speckles (or visible light speckles) are observed in Fraunhoffer, or far-field diffraction regime, in which parallel beam approximation can be applied.

The other extreme regime is the near-field (aka Fresnel) geometry, where the detector is placed in the relative vicinity of the sample. This regime is often ignored by scientists because of the complicated scattering patterns caused by interference between scattered and transmitted beams.

However, recently it was shown that Fresnel geometry has some advantages – both in terms of performing lensless imaging microscopy: curved wavefronts, resulting from for example focusing Fresnel Zone Plate optics, result in faster convergence of lensless imaging algorythms – see this paper by Williams et al. Phys. Rev. Lett. 97, 025506 (2006) - and now in terms of using near-field x-ray speckle for X-ray Photon Correlation Spectroscopy.

The Near-Field Speckle setup is limited to relatively small Q-range – the example used in the featured paper by Cerbino et. al is covering ultra-small angle scattering range of Q<0.001 inverse nanometers, corresponding to lengthscales on the order of 10 microns. While such low angles are difficult to access with far-field hard x-ray speckle, the same lengthscales can in principle be reached with visible light (laser) speckle – dynamic light scattering techniques. However, one big advantage of x-rays here is their penetrating
ability and no complications due to multiple scattering effects. Therefore, Near Field X-ray Speckle has a lot of potential for use in non-transparent materials and thick specimens where multiple light scattering effects make laser-based measurements difficult.