PROJECT SUMMARY Single-particle electron cryomicroscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. In addition, cryo-EM produces images of individual molecules, and therefore has the potential to resolve conformational changes. The proposal aims to develop new algorithms and software for extending the application of cryo-EM to molecules that are either too small or too flexible to be mapped by existing computational tools for cryo-EM. This extension requires solving two of the most challenging computational problems posed by cryo-EM. First, mapping the structural variability of macromolecules is widely recognized as the main computational challenge in cryo-EM. Structural variations are of great significance to biologists, as they provide insight into the functioning of molecular machines. Existing computational tools are limited to a small number of distinct conformations, and therefore are incapable of tackling highly mobile biomolecules with multiple, continuous spectra of conformational changes. The first area of investigation in this project is the development of a computational framework to analyze continuous variability. The proposed approach is based on a new mathematical representation of continuously changing structures and its efficient estimation using Markov chain Monte Carlo (MCMC) algorithms. MCMC algorithms have found great success in many other scientific disciplines, yet they have been mostly overlooked for cryo-EM single particle analysis. Second, a major limiting factor for present cryo-EM studies is the molecule size. Images of small molecules (below ~50kDa) have too little signal to allow existing methods to provide valid 3-D reconstructions. It is commonly believed that cryo-EM cannot be used for molecules that are too small to be reliably detected and picked from micrographs. Challenging that widespread belief, the second area of investigation focuses on developing a groundbreaking approach for reconstructing small molecules directly from micrographs without particle picking. The new approach is based on autocorrelation analysis and completely bypasses particle picking and orientation assignment and requires just one pass over the data. The single-pass approach opens new possibilities for real-time processing during data acquisition.