Structure from fleeting illumination of faint spinning objects in flight

Abstract

There are many instances when the structure of a weakly-scattering spinning object in flight must be determined to high resolution. Examples range from comets to nanoparticles and single molecules. The latter two instances are the subject of intense current interest. Substantial progress has recently been made in illuminating spinning single particles in flight with powerful X-ray bursts to determine their structure 1,2 , with the ultimate goal of determining the structure of single molecules 3,4,5,6,7 . However, proposals to reconstruct the molecular structure from diffraction "snapshots" of unknown orientation require ~1000x more signal than available from next-generation sources 8 . Using a new approach, we demonstrate the recovery of the structure of a weakly scattering macromolecule at the anticipated next-generation X-ray source intensities. Our work closes a critical gap in determining the structure of single molecules and nanoparticles by X-ray methods, and opens the way to reconstructing the structure of spinning, or randomly-oriented objects at extremely low signal levels. Other potential applications include low-dose electron microscopy, ultra-low-signal tomography of non-stationary objects without orientational information, and the study of heavenly bodies.

In-plane rotation classification for coherent X-ray imaging of single biomolecules

“…This property could be used in conjunction with the manifold method described in [22]. A hyper-space constructed from the radial distribution shall exhibit a 2-manifold depending only on α and β .…”

“…Whether a certain class belongs to an out-of-plane orientation of the reference molecule in the same conformation or an orientation class of the molecule in a different conformation can be addressed in the next step of the classification. One possible method for such purpose is the manifold method [22]. A general heterogeneous sample may not be solely classified by means of the low-angle scattering data, large-angle-scattering may have to be additionally included in the classification algorithm.…”

“…Because of the extremely low signal-to-noise level, this method is not applicable in current x-ray diffraction experiments. Current classification work on X-ray diffraction data [21,22] is primarily focused on the direct 2D diffraction patterns. We propose to compress the diffraction data by radial and azimuthal integrals, so that the orientation information can…”

“…If we can relax the requirement on the sensitivity of the classification, we can achieve 92% accuracy for the class size of 3 • and 97% accuracy for 5 • . In this way we can break the data set into smaller groups and use more sophisticated algorithms such as described in [21] or [22] to find additional information. Research in this direction is underway.…”

“…Thus the classification schemes based on large-angle-scattering-data are not currently practical. Recently there are two interesting developments where ExpectationMaximization algorithms is utilized for classification [21,22]. The signal level for successful classifications is much reduced.…”