Toward single particle reconstruction without particle picking: Breaking the detection limit

Abstract

Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. In a cryo-EM experiment, the microscope produces images called micrographs. Projections of the molecule of interest are embedded in the micrographs at unknown locations, and under unknown viewing directions. Standard imaging techniques rst locate these projections (detection) and then reconstruct the 3-D structure from them. Unfortunately, high noise levels hinder detection. When reliable detection is rendered impossible, the standard techniques fail. This is a problem especially for small molecules, which can be particularly hard to detect. In this paper, we propose a radically dierent approach: we contend that the structure could, in principle, be reconstructed directly from the micrographs, without intermediate detection. As a result, even small molecules should be within reach for cryo-EM. To support this claim, we setup a simplied mathematical model and demonstrate how our autocorrelation analysis technique allows to go directly from the micrographs to the sought signals. This involves only one pass over the micrographs, which is desirable for large experiments. We show numerical results and discuss challenges that lay ahead to turn this proof-of-concept into a competitive alternative to state-of-the-art algorithms.

Image Recovery from Rotational And Translational Invariants

“…The estimation problem described in Section I-A is a simplified version of the cryo-EM reconstruction problem: the tomographic projection operator is omitted and we observe the same 2-D image multiple times with random in-plane rotations. This image recovery problem is an instance of the multi-target detection statistical model, in which a set of signals appear multiple times at unknown locations in a noisy measurement [3], [4], [13]. Here, we extend previous works by taking in-plane rotations into account, which forms an important step towards the analysis of the full cryo-EM problem.…”

“…This difficulty of detection in turn sets a lower bound on the usable molecule size in the current analysis workflow of cryo-EM data [9]. To circumvent this fundamental barrier, recent papers [3], [4] suggest to directly estimate the 3-D structure from the micrograph, without an intermediate detection stage; this approach was inspired by Kam [11] who introduced autocorrelation analysis to cryo-EM.…”

“…and that the rotations in the measurement are chosen uniformly at random. Under these assumptions it is straightforward to show, see for example [3], that if p/m 2 → γ, then…”

Single-Particle Cryo-Electron Microscopy: Mathematical Theory, Computational Challenges, and Opportunities

“…Therefore, the MTD model paves the way to fully model the cryo-EM problem, including most of its important features [21]. In particular, MTD provides a mathematical and computational framework for reconstructing φ directly from micrographs, without intermediate particle picking [20]. A full analysis of this model is still lacking.…”

“…The logic is simple: small molecules induce low contrast, and thus low SNR on the micrograph, which in turn hinders detection (particle picking) [42]. A recent paper contends this belief and suggests that it is possible, at least in principle, to reconstruct structures directly from the micrograph, without particle picking and at any SNR level, given enough data [20].…”