Imaging of single biomolecules

A single shot from the SwissFEL, with 1011 photons focused to 100 × 100 nm2 (= 1013 photons/μm2), corresponds to a bio-material dose of 8 × 109 Gray, i.e., approximately 3 orders of magnitude above the damage threshold. Each shot will therefore require a fresh biomolecule, and since these will have random orientations, the scattering patterns cannot be simply accumulated (see Fig. III.6). How severe is the damage to a biomolecule from a single SwissFEL shot? The irradiation process has been simulated [7] for a lysozyme protein molecule exposed to an XFEL pulse of 3 × 1012 photons with 12 keV energy and focused to a 100 nm diameter spot, with various pulse durations (e.g., see Fig. III.7). The explosion of the molecule begins with primary photoionization (photoelectric and Compton effects), followed by secondary (Auger) ionization. Approximately one in five of these electrons will undergo inelastic scattering, removing an additional outer shell electron; the XFEL pulse causes more than one ionization event per non-hydrogen atom. The resulting positive ions react to the large net positive charge of the molecule and move outward, led by light hydrogen ions and highly-ionized sulphur. If the XFEL pulse is shor ter than approximately 20 fs, the analysis of Neutze et al., suppor ts the view that the ionization and ionic movement incurred during the pulse represent a tolerable per turbation for a structural determination. With innovations in low-charge operation and high electron bunch compression, the SwissFEL will be able to produce such pulses. Individual biomolecules are to be successively introduced into the XFEL beam by a spraying technique, presumably each with a different orientation (see Infobox). Will a sufficient number of scattered photons be detected in a single shot to determine the orientation, such that the data can be accumulated in a 3-d reciprocal space representation? This question has been investigated by simulating the scattering of a single XFEL pulse by small, medium and large biomolecules [8] (see Fig. III.8). For the ferritin complex, no more than 0.01 photons per pixel can be expected in the interesting region of intermediate scattering vector. Can useful structural information be extracted from such sparse data? The answer to this question by Fung et al. [9] is a qualified “yes”. Instead of attempting to determine the molecular orientation from a single exposure, these authors propose a method based on the correlations of a large ensemble of scattering patterns. They define p-space, with a dimension p equal to the number of detector pixels, perhaps 106. Each measured scattering pattern corresponds to a p-dimensional vector in this space – with coordinates given by the photon count in each pixel (see Fig. III.9).
The authors then ask the question: as the scattering molecule is rotated in 3d-space, how does the corresponding p-vector move? Their answer: it will move on a subset of p-space defined by a 3d-manifold, corresponding to the three (Eulerian) orientation angles in 3d-space. Such an embedded-manifold can be described mathematically by a set of coefficients. Using simulated scattering data from a small protein, the authors demonstrate that these coefficients can be reliably determined with statistics corresponding to 0.01 photons/ pixel, effectively solving the classification problem for molecular orientations and hence allowing for data from successive XFEL shots to effectively be accumulated. Although it should be noted that impor tant effects due to background scattering and unknown illumination functions have yet to be considered, this approach may potentially even treat the cases of multiple molecular configurations (for which several 3d-manifolds will exist in p-space) and perhaps even continuous variation between configurations (for which manifolds must be determined with more than 3 dimensions).