Three-dimensional electron microscopy (3D-EM) is a powerful tool for visualizing complex macromolecules. In the so-called single particle reconstruction problem we assume that we have multiple identical copies of the same macromolecule and the task is the reconstruction of the common structure. It is often the case, however, that the macromolecule to be reconstructed has multiple not-exactly identical conformations and so the set of projection images from which we need to reconstruct is a heterogeneous mixture of projections of more than one conformation. For high resolution 3D-EM, the effect of this is quite dramatic and severely limits the achievable resolution. In this talk a combinatorial method is described for partitioning such heterogeneous projection data sets into homogeneous components, each of which consists of projections of mostly one conformation. The method operates directly on the 2D projection images, and it does not require reference images or the performance of 3D reconstructions. It is demonstrated that the approach can be successfully applied to noisy data.
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