The method presented here refines molecular conformations directly against projections of single particles measured by electron microscopy. By optimizing the orientation of the projection at the same time as the conformation, the method is well-suited to twodimensional class averages from cryoelectron microscopy. Such direct use of two-dimensional images circumvents the need for a three-dimensional density map, which may be difficult to reconstruct from projections due to structural heterogeneity or preferred orientations of the sample on the grid. Our refinement protocol exploits Natural Move Monte Carlo to model a macromolecule as a small number of segments connected by flexible loops, on multiple scales. After tests on artificial data from lysozyme, we applied the method to the Methonococcus maripaludis chaperonin. We successfully refined its conformation from a closed-state initial model to an open-state final model using just one class-averaged projection. We also used Natural Moves to iteratively refine against heterogeneous projection images of Methonococcus maripaludis chaperonin in a mix of open and closed states. Our results suggest a general method for electron microscopy refinement specially suited to macromolecules with significant conformational flexibility. The algorithm is available in the program Methodologies for Optimization and Sampling In Computational Studies.2D projection | structure refinement | stochastic optimization R ecent advances in single-particle cryoelectron microscopy, or cryo-EM, have enabled 3D structure determination of macromolecules to near-atomic resolution without crystallization, provided that the sample particles are homogeneous and adopt the same conformation (1-6). However, macromolecules are generally flexible in solution and can adopt multiple conformations in order to carry out their functions. Therefore, their cryo-EM images usually represent a heterogeneous mixture of macromolecular conformations. As a result, the power of single particle cryo-EM is limited, in that the reconstruction of a highresolution 3D density map requires hundreds of thousands to millions of particle images of the same conformation.Supervised classification (7) and maximum-likelihood methods (8) have been used to identify multiple structures from samples in which macromolecules experience moderate conformational fluctuations or exist in a small number of discrete structural states. Other approaches based on statistical bootstrapping (9, 10) have been used to separate different substrate-binding modes of macromolecules or to define flexible fragments within a molecular complex. However, these single-particle image processing techniques are severely limited when there are large conformational changes or nondiscrete conformational states (11, 12) that prevent correct determination of the orientation parameters for each raw particle image. Various computational techniques have been developed to model large conformational changes by flexible-fitting of a molecular model into the density map of a...