Introduction

Heterogeneous data sets obviously pose a challenge to the single-particle reconstruction approach, as each projection presents only a single aspect of a structure. Biochemical purifications generally result in preparations that have molecules of the same kind; heterogeneity is introduced by the coexistence of ligand-bound with ligand-free forms, or the coexistence of different conformational states that might equilibrate because they are separated by a small energy barrier. In terms of image-processing solutions, the problem posed by partial ligand occupancy is somewhat different than the problem of conformational heterogeneity, so that it is convenient to discuss them separately. We note, however, that there are many cases in which ligand binding induces conformational changes in the target molecule, making it possible to find the solution to one problem by solving the other.

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