Billy K. Poon

Shapes and vorticities of superfluid helium nanodroplets

X-raying superfluid helium droplets When physicists rotate the superfluid 4He, it develops a regular array of tiny whirlpools, called vortices. The same phenomenon should occur in helium droplets half a micrometer in size, but studying individual droplets is tricky. Gomez et al. used x-ray diffraction to deduce the shape of individual rotating droplets and image the resulting vortex patterns, which confirmed the superfluidity of the droplets. They found that superfluid droplets can host a surprising number of vortices and can rotate faster than normal droplets without disintegrating. Science, this issue p. 906 Vortex lattices inside individual helium droplets are imaged using x-ray diffraction. Helium nanodroplets are considered ideal model systems to explore quantum hydrodynamics in self-contained, isolated superfluids. However, exploring the dynamic properties of individual droplets is experimentally challenging. In this work, we used single-shot femtosecond x-ray coherent diffractive imaging to investigate the rotation of single, isolated superfluid helium-4 droplets containing ~108 to 1011 atoms. The formation of quantum vortex lattices inside the droplets is confirmed by observing characteristic Bragg patterns from xenon clusters trapped in the vortex cores. The vortex densities are up to five orders of magnitude larger than those observed in bulk liquid helium. The droplets exhibit large centrifugal deformations but retain axially symmetric shapes at angular velocities well beyond the stability range of viscous classical droplets.

Polder maps: improving OMIT maps by excluding bulk solvent

Residual OMIT maps can be improved by the selective exclusion of bulk solvent from the OMIT region.

Three-dimensional single-particle imaging using angular correlations from X-ray laser data

Femtosecond X-ray pulses from X-ray free-electron laser sources make it feasible to conduct room-temperature solution scattering experiments far below molecular rotational diffusion timescales. Owing to the ultra-short duration of each snapshot in these fluctuation scattering experiments, the particles are effectively frozen in space during the X-ray exposure. In contrast to standard small-angle scattering experiments, the resulting scattering patterns are anisotropic. The intensity fluctuations observed in the diffraction images can be used to obtain structural information embedded in the average angular correlation of the Fourier transform of the scattering species, of which standard small-angle scattering data are a subset. The additional information contained in the data of these fluctuation scattering experiments can be used to determine the structure of macromolecules in solution without imposing symmetry or spatial restraints during model reconstruction, reducing ambiguities normally observed in solution scattering studies. In this communication, a method that utilizes fluctuation X-ray scattering data to determine low-resolution solution structures is presented. The method is validated with theoretical data calculated from several representative molecules and applied to the reconstruction of nanoparticles from experimental data collected at the Linac Coherent Light Source.

Autoindexing with outlier rejection and identification of superimposed lattices

After autoindexing, Bragg spot candidates that do not fit on the model lattice can be identified, providing a potentially useful measure of sample quality and giving an avenue for indexing a second lattice, if one is present.

Structure determination of Pt-coated Au dumbbells via fluctuation X-ray scattering

A fluctuation X-ray scattering experiment has been carried out on platinum-coated gold nanoparticles randomly oriented on a substrate. A complete algorithm for determining the electron density of an individual particle from diffraction patterns of many particles randomly oriented about a single axis is demonstrated. This algorithm operates on angular correlations among the measured intensity distributions and recovers the angular correlation functions of a single particle from measured diffraction patterns. Taking advantage of the cylindrical symmetry of the nanoparticles, a cylindrical slice model is proposed to reconstruct the structure of the nanoparticles by fitting the experimental ring angular auto-correlation and small-angle scattering data obtained from many scattering patterns. The physical meaning of the refined structure is discussed in terms of their statistical distributions of the shape and electron density profile.

Real-space refinement in PHENIX for cryo-EM and crystallography

A description is provided of the implementation of real-space refinement in the phenix.real_space_refine program from the PHENIX suite and its application to the re-refinement of cryo-EM-derived models.

Computation of fluctuation scattering profiles via three-dimensional Zernike polynomials

Ultrashort X-ray pulses from free-electron laser X-ray sources make it feasible to conduct small- and wide-angle scattering experiments on biomolecular samples in solution at sub-picosecond timescales. During these so-called fluctuation scattering experiments, the absence of rotational averaging, typically induced by Brownian motion in classic solution-scattering experiments, increases the information content of the data. In order to perform shape reconstruction or structure refinement from such data, it is essential to compute the theoretical profiles from three-dimensional models. Based on the three-dimensional Zernike polynomial expansion models, a fast method to compute the theoretical fluctuation scattering profiles has been derived. The theoretical profiles have been validated against simulated results obtained from 300 000 scattering patterns for several representative biomolecular species.

Detection and correction of underassigned rotational symmetry prior to structure deposition

An X-ray structural model can be reassigned to a higher symmetry space group using the presented framework if its noncrystallographic symmetry operators are close to being exact crystallographic relationships. About 2% of structures in the Protein Data Bank can be reclassified in this way.

Interactive Comparison and Remediation of Collections of Macromolecular Structures

Often similar structures need to be compared to reveal local differences throughout the entire model or between related copies within the model. Therefore, a program to compare multiple structures and enable correction any differences not supported by the density map was written within the Phenix framework (Adams et al., Acta Cryst 2010; D66:213–221). This program, called Structure Comparison, can also be used for structures with multiple copies of the same protein chain in the asymmetric unit, that is, as a result of non‐crystallographic symmetry (NCS). Structure Comparison was designed to interface with Coot(Emsley et al., Acta Cryst 2010; D66:486–501) and PyMOL(DeLano, PyMOL 0.99; 2002) to facilitate comparison of large numbers of related structures. Structure Comparison analyzes collections of protein structures using several metrics, such as the rotamer conformation of equivalent residues, displays the results in tabular form and allows superimposed protein chains and density maps to be quickly inspected and edited (via the tools in Coot) for consistency, completeness and correctness.

Free-electron laser data for multiple-particle fluctuation scattering analysis

Fluctuation X-ray scattering (FXS) is an emerging experimental technique in which solution scattering data are collected using X-ray exposures below rotational diffusion times, resulting in angularly anisotropic X-ray snapshots that provide several orders of magnitude more information than traditional solution scattering data. Such experiments can be performed using the ultrashort X-ray pulses provided by a free-electron laser source, allowing one to collect a large number of diffraction patterns in a relatively short time. Here, we describe a test data set for FXS, obtained at the Linac Coherent Light Source, consisting of close to 100 000 multi-particle diffraction patterns originating from approximately 50 to 200 Paramecium Bursaria Chlorella virus particles per snapshot. In addition to the raw data, a selection of high-quality pre-processed diffraction patterns and a reference SAXS profile are provided.