Protein nanocrystals and 2d-crystals
With its extremely high peak flux and small focus spot, the SwissFEL will allow coherent diffraction measurements on 3d-nanocrystals of protein, which are individually injected into the X-ray beam (see Infobox). The growth of protein crystals is a complex and poorly understood process, and different molecular systems show different behaviors. In general, however, as a crystal grows, it tends to accumulate defects such as stacking faults. These defects often limit the maximum size of good-quality crystals. It is believed that many interesting protein species may only form good crystals with sub-μm dimensions (see Fig. III.4).
Fig. III.4. Examples of micrometer and sub-micrometer crystals of
the protein lysozyme . The scale bar at bottom left is 2 μm.
Scattering from a crystal has the great advantage over a single-molecule experiment that a large number of identically-oriented unit cells contribute coherently to the scattering signal. In a per fect infinite crystal, this leads to sharp Bragg reflections corresponding to particular scattering vectors, with the peak intensity in each Bragg peak propor tional to the square of the number of unit cells in the crystal. As mentioned earlier, since there is no scattering intensity between the peaks, oversampling for an infinite crystal is not possible, thus complicating the phase-retrieval process. The use of nanocrystals, for which (weak) continuous coherent scattering features connect the Bragg peaks, provides additional information useful for phasing.
An innovative method, developed at PSI, of using coherent diffraction features to solve the phase problem is ptychographic diffraction (from the Greek for “folding”) . In ptychography, a small-spot coherent X-ray beam is scanned across a large, non-periodic sample, and a series of coherent scattering patterns is collected. The speckle size is determined by the inverse of the spot size rather than by the sample dimensions. Overlapping the scanned spots allows one to incorporate the speckles into the phase-retrieval process, in spite of the large sample size. By this method, the complex transmission function of a region of interest within an extended sample can be uniquely reconstructed, along with the detailed illumination function . In an extension of ptychography to 2d-crystal diffraction with the SwissFEL, a large (i.e., several μm) 2d-crystal is illuminated at randomly chosen positions with the tightly-focused (100 nm) coherent XFEL beam. The resulting scattering is a convolution of crystalline Bragg peaks and finite-aper ture coherent scattering features (see Fig. III.5). Each exposure represents a different alignment between the periodic lattice and the illumination function describing the spot, and although it locally destroys the sample, successive exposures from undamaged regions of the sample provide partially-redundant information. Kewish et al. have demonstrated that this multiple exposure method aids in solving the phase problem and hence facilitates the recovery of the projected high-resolution structure of a membrane protein. By repeated scans at different tilt angles of the 2d-crystal, it will be possible to obtain the 3d-protein structure.
Fig. III.5. Simulated ptychographic diffraction  of a 2d-crystal of the membrane protein aquaporin-1. The projected
electron density (above) is sampled with an XFEL pulse (1012 photons at 12 keV, focused to a spot
100 nm in diameter), producing the simulated scattering pattern shown below. Note the coherent diffraction
features between the Bragg peaks (insets).