Computational Methods for Three-Dimensional Microscopy Reconstruction

After providing a brief general background, this introduction comprises a chapter-by-chapter overview of the rest of this book.

The specification of the information on the three-dimensional orientation of an image with respect to a given coordinate system is at the heart of our ability to reconstruct a three-dimensional object from sets of its two-dimensional projection images. Transferring this information from one package to another is important to structural biologists wanting to get the best from each software suite. In this chapter, we review in depth the main considerations and implications associated with the unambiguous specification of geometrical specifications, in this way paving the way to the future specifications of standards in the field of three-dimensional electron microscopy. This is the case of EMX in which affine transformations have been adopted as the means to communicate geometrical information.

Cryo-electron microscopy combined with single-particle reconstruction is a promising technique for solving the high-resolution structure of macromolecular complexes, even in the presence of conformational or compositional heterogeneity. However, the usual workflow leading to one or several structures is mired in subjective decisions that must be made by an expert. One problem, in particular, has been the difficulty finding algorithms capable of automatically selecting and verifying individual views of a macromolecular complex from the electron micrograph, due to the extremely low signal-to-noise ratio and the presence of contaminants. We present a novel machine-learning algorithm that overcomes these problems. The performance of the algorithm is demonstrated with electron micrographs of ribosomes.

Over the past three decades, cryogenic electron microscopy (cryo-EM) and single-particle reconstruction (SPR) techniques have evolved into a powerful toolbox for determining biological macromolecular structures. In its original form, the SPR requires a homogeneous sample, i.e., all the projection images represent identical copies of the macromolecules (Frank, Three-dimensional electron microscopy of macromolecular assemblies: visualization of biological molecules in their native state, Oxford University Press, Oxford, 2006). Recent developments in computational classification methods have made it possible to determine multiple conformations/structures of the macromolecules from cryo-EM data obtained from a single biological sample (Agirrezabala et al., Proc Natl Acad Sci 109:6094–6099, 2012; Fischer et al., Nature 466:329–333, 2010; Scheres, J Struct Biol 180:519–530, 2012). However, the existing classification methods involve different amounts of arbitrary decisions, which may lead to ambiguities of the classification results. In this work, we propose a quantitative way of analyzing the results obtained with iterative classification of cryo-EM data. Based on the logs of iterative particle classification, this analysis can provide quantitative criteria for determining the iteration of convergence and the number of distinguishable conformations/structures in a heterogeneous cryo-EM data set. To show its applicability, we tailored this analysis to the classification results of the program RELION (Scheres, Methods Enzymol 482:295–320, 2010; Scheres, J Mol Biol 415:406–418, 2011) using both benchmark and experimental data sets of ribosomes.

Influenza is a rapidly changing virus that appears seasonally in the human population. Every year a new strain of the influenza virus appears with the potential to cause a serious global pandemic. Knowledge of the structure and density of the surface proteins is of critical importance in a vaccine candidate. Reconstruction techniques from a series of tilted electron-tomographic projection images provide quantification of surface proteins. Two major categories of reconstruction techniques are transform methods such as weighted backprojection (WBP) and series expansion methods such as the algebraic reconstruction techniques (ART) and the simultaneous iterative reconstruction technique (SIRT). Series expansion methods aim at estimating the object to be reconstructed by a linear combination of some fixed basis functions and they typically estimate the coefficients in such an expansion by an iterative algorithm. The choice of the set of basis functions greatly influences the result of a series expansion method. It has been demonstrated repeatedly that using spherically symmetric basis functions (blobs), instead of the more traditional voxels, results in reconstructions of superior quality, provided that the free parameters that occur in the definition of the family of blobs are appropriately tuned. In this chapter, it is demonstrated that, with the recommended data-processing steps performed on the projection images prior to reconstruction, series expansion methods such as ART (with its free parameters appropriately tuned) will provide 3D reconstructions of viruses from tomographic tilt series that allow reliable quantification of the surface proteins and that the same is not achieved using WBP.

We discuss and illustrate defocus-gradient and attenuation effects that are part of the image formation models of microscopy of biological specimens. We demonstrate how they affect the projection data and in turn the 3D reconstructions. Biologically meaningful results can be obtained ignoring both of these effects, but using image processing techniques to incorporate corrections for them into reconstruction methods provides more accurate reconstructions, with potential for creating higher-resolution models of the biological specimens.

An understanding of the three-dimensional structure of a macromolecular complex is essential to fully understand its function. This chapter introduces the reader to the concept of a component tree, which is a compact representation of the structural properties of a multidimensional image (such as a molecular density map of a biological specimen), and then presents ongoing research on the use of such component trees in interactive tools for exploring biological structures. Component trees capture essential structural information about a biological specimen, irrespective of the process that was used to obtain an image of the specimen and the resolution of that image. We present various scenarios in which component trees can help in the exploration of the structure of a macromolecular complex. In addition, we discuss ideas for a docking methodology that uses component trees.