Sparse and Steerable Representations for 3D Electron Cryomicroscopy.

摘要

Electron cryomicroscopy (CRYO-EM) is used to study the 3D structure of macromolecular complexes. CRYO-EM works by preparing a solution on a grid with many copies of the complex. Rapidly freezing the grid traps the complexes in their native states. Transmission electron microscopy (TEM) images of the grid reveal noisy 2D projections of the complex at unknown angles. The goal of CRYO-EM is to estimate the highest resolution 3D structure possible, from these randomly oriented and noisy 2D projection images.;We propose a sparse representation for 3D structures. Traditional estimation methods use the Fourier basis to represent structures. We develop a flexible algorithm that uses sparsity to adaptively choose a basis based on the data. The method works in a Bayesian maximum-a-posteriori (MAP) framework and considerably improves structure resolution and signal-to-noise ratio (SNR). Moreover, the algorithm automatically masks the structure, thereby separating the surrounding ice. This eliminates the need for any additional masking.;Resolution is typically assumed to be uniform across the entire structure. This may not always be true, due to structural flexibility and image processing errors. We propose a definition of local resolution using steerable local-sinusoid features. At each point in the noisy volume, a likelihood-ratio hypothesis test detects the presence of a local-sinusoid at a given P-value. We define the local resolution as the smallest scale at which the local-sinusoid is detectable, while controlling for false discoveries. An efficient algorithm, called ResMap, implements this theory. By evaluating the local resolution of structures from the near-atomic to the nanometer range, we report variable resolution across 4 to 40 Angstroms.