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SummaryWe present the codimensional principal component analysis (PCA), a novel and straightforward method for resolving sample heterogeneity within a set of cryo-EM 2D projection images of macromolecular assemblies. The method employs PCA of resampled 3D structures computed using subsets of 2D data obtained with a novel hypergeometric sampling scheme. PCA provides us with a small subset of dominating “eigenvolumes” of the system, whose reprojections are compared with experimental projection data to yield their factorial coordinates constructed in a common framework of the 3D space of the macromolecule. Codimensional PCA is unique in the dramatic reduction of dimensionality of the problem, which facilitates rapid determination of both the plausible number of conformers in the sample and their 3D structures. We applied the codimensional PCA to a complex data set of Thermus thermophilus 70S ribosome, and we identified four major conformational states and visualized high mobility of the stalk base region.

Summary The structure of the endosomal-associated protein, Hrs, has been determined with cryo-electron microscopy. Hrs interacts with a number of proteins, including SNAP-25 and STAM1, forming a complex that binds ubiquitin moieties. Analytical ultracentrifugation studies revealed that Hrs exists as a hexamer. The symmetry and the structure of the hexameric form of Hrs were determined with the single-particle reconstruction method. Hrs comprises three antiparallel dimers with a central core and distinct caps on either end. Crystal structures of VHS and FYVE domains fit into the Hrs end caps in the EM density map. Thus, the location of domains that interact with the endosomal membrane, the VHS, FYVE, and C-terminal domains, facilitates the anchorage of Hrs to the membrane, initiating the functional processes of Hrs on the endosome. Based on our model, the Hrs hexamer interacts with the membrane and acts as a "master molecule" that presents multiple sites for protein binding.

Background: This study addresses the general problem of dividing a density map of a nucleic-acid–protein complex obtained by cryo-electron microscopy (cryo-EM) or X-ray crystallography into its two components. When the resolution of the density map approaches ∼3 A it is generally possible to interpret its shape (i.e., the envelope obtained for a standard choice of threshold) in terms of molecular structure, and assign protein and nucleic acid elements on the basis of their known sequences. The interpretation of low-resolution maps in terms of proteins and nucleic acid elements of known structure is of increasing importance in the study of large macromolecular complexes, but such analyses are difficult. Results: Here we show that it is possible to separate proteins from nucleic acids in a cryo-EM density map, even at 11.5 A resolution. This is achieved by analysing the (continuous-valued) densities using the difference in scattering density between protein and nucleic acids, the contiguity constraints that the image of any nucleic acid molecule must obey, and the knowledge of the molecular volumes of all proteins. Conclusions: The new method, when applied to an 11.5 A cryo-EM map of the Escherichia coli 70S ribosome, reproduces boundary assignments between rRNA and proteins made from higher-resolution X-ray maps of the ribosomal subunits with a high degree of accuracy. Plausible predictions for the positions of as yet unassigned proteins and RNA components are also possible. One of the conclusions derived from this separation is that 23S rRNA is solely responsible for the catalysis of peptide bond formation. Application of the separation method to any nucleoprotein complex appears feasible.

Macromolecular structure determination by cryo-electron microscopy (EM) and single particle analysis are based on the assumption that imaged molecules have identical structure. With the increased size of processed datasets it becomes apparent that many complexes coexist in a mixture of conformational states or contain flexible regions. As the cryo-EM data is collected in form of projections of imaged molecules, the information about variability of reconstructed density maps is not directly available. To address this problem, we describe a new implementation of the bootstrap resampling technique that yields estimates of voxel-by-voxel variance of a structure reconstructed from the set of its projections. We introduced a novel highly efficient reconstruction algorithm that is based on direct Fourier inversion and which incorporates correction for the transfer function of the microscope, thus extending the resolution limits of variance estimation. We also describe a validation method to determine the number of resampled volumes required to achieve stable estimate of the variance. The proposed bootstrap method was applied to a dataset of 70S ribosome complexed with tRNA and the elongation factor G. The variance map revealed regions of high variability: the L1 protein, the EF-G and the 30S head and the ratchet-like subunit rearrangement. The proposed method of variance estimation opens new possibilities for single particle analysis, by extending applicability of the technique to heterogeneous datasets of macromolecules, and to complexes with significant conformational variability.

Summary Identification of homogeneous subsets of images in a macromolecular electron microscopy (EM) image data set is a critical step in single-particle analysis. The task is handled by iterative algorithms, whose performance is compromised by the compounded limitations of image alignment and K-means clustering. Here we describe an approach, iterative stable alignment and clustering (ISAC) that, relying on a new clustering method and on the concepts of stability and reproducibility, can extract validated, homogeneous subsets of images. ISAC requires only a small number of simple parameters and, with minimal human intervention, can eliminate bias from two-dimensional image clustering and maximize the quality of group averages that can be used for ab initio three-dimensional structural determination and analysis of macromolecular conformational variability. Repeated testing of the stability and reproducibility of a solution within ISAC eliminates heterogeneous or incorrect classes and introduces critical validation to the process of EM image clustering.