  We describe a new generation of algorithms capable of mapping the structure
and conformations of macromolecules and their complexes from large ensembles of
heterogeneous snapshots, and demonstrate the feasibility of determining both
discrete and continuous macromolecular conformational spectra. These algorithms
naturally incorporate conformational heterogeneity without resort to sorting
and classification, or prior knowledge of the type of heterogeneity present.
They are applicable to single-particle diffraction and image datasets produced
by X-ray lasers and cryo-electron microscopy, respectively, and particularly
suitable for systems not easily amenable to purification or crystallization.
