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A method is proposed to reconstruct the 3D molecular structure from micrographs collected at just one sample tilt angle in the random conical tilt scheme in cryo-electron microscopy. The method uses autocorrelation analysis on the micrographs to estimate features of the molecule which are invariant under certain nuisance parameters such as the positions of molecular projections in the micrographs. This enables the molecular structure to be reconstructed directly from micrographs, completely circumventing the need for particle picking. Reconstructions are demonstrated with simulated data and the effect of the missing-cone region is investigated. These results show promise to reduce the size limit for single-particle reconstruction in cryo-electron microscopy. 

We consider the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated copies of the target image. Motivated by single-particle cryo-electron microscopy, we focus on the low signal-to-noise regime, where it is difficult to estimate the locations and orientations of the target images in the measurement. Our approach uses autocorrelation analysis to estimate rotationally and translationally invariant features of the target image. We demonstrate that, regardless of the level of noise, our technique can be used to recover the target image when the measurement is sufficiently large. 

In recent years, the success of serial femtosecond crystallography and the paucity of beamtime at X-ray free-electron lasers have motivated the development of serial microcrystallography experiments at storage-ring synchrotron sources. However, especially at storage-ring sources, if a crystal is too small it will have suffered significant radiation damage before diffracting a sufficient number of X-rays into Bragg peaks for peak-indexing software to determine the crystal orientation. As a consequence, the data frames of small crystals often cannot be indexed and are discarded. Introduced here is a method based on the expand–maximize–compress (EMC) algorithm to solve protein structures, specifically from data frames for which indexing methods fail because too few X-rays are diffracted into Bragg peaks. The method is demonstrated on a real serial microcrystallography data set whose signals are too weak to be indexed by conventional methods. In spite of the daunting background scatter from the sample-delivery medium, it was still possible to solve the protein structure at 2.1 Å resolution. The ability of the EMC algorithm to analyze weak data frames will help to reduce sample consumption. It will also allow serial microcrystallography to be performed with crystals that are otherwise too small to be feasibly analyzed at storage-ring sources.