Expectation-maximization for structure determination directly from cryo-EM micrographs

Abstract

A single-particle cryo-electron microscopy (cryo-EM) measurement, called a micrograph, consists of multiple two-dimensional tomographic projections of a three-dimensional (3-D) molecular structure at unknown locations, taken under unknown viewing directions. All existing cryo-EM algorithmic pipelines first locate and extract the projection images, and then reconstruct the structure from the extracted images. However, if the molecular structure is small, the signal-to-noise ratio (SNR) of the data is very low, making it challenging to accurately detect projection images within the micrograph. Consequently, all standard techniques fail in low-SNR regimes. To recover molecular structures from measurements of low SNR, and in particular small molecular structures, we devise an approximate expectation-maximization algorithm to estimate the 3-D structure directly from the micrograph, bypassing the need to locate the projection images. We corroborate our computational scheme with numerical experiments and present successful structure recoveries from simulated noisy measurements.

Figures (10)

• Figure 1: Three simulated micrographs at different SNRs. Each measurement contains $T = 9$ projections of the target volume. We focus on the low SNR regime, where the 2-D locations and 3-D rotations of the projection images cannot be estimated reliably.
• Figure 2: An illustration of the patch generation model described in \ref{['eq:patch']}.
• Figure 3: Results for estimating the TRPV1 structure directly from a micrograph. The micrograph was generated from volumes of original size, and then downsampled such that each projection is of size $17^2$ (Method 1).
• Figure 4: Results for estimating the TRPV1 structure directly from a micrograph. The micrograph was generated from volumes downsampled to size $17^3$ (Method 2).
• Figure 5: Resolution progression across iterations for the estimation of the TRPV1 volume using Method 2. Resolution is defined as ${{k}}$ at which the FSC with the ground truth crosses $0.5$. Colors indicate the maximal spherical harmonic frequency: blue ($\ell_{\text{max}}=6$), orange ($\ell_{\text{max}}=10$), red ($\ell_{\text{max}}=14$). Higher values of ${{k}}$ correspond to finer resolved detail.