  The three-dimensional structure of a protein plays a key role in determining
its function. Methods like AlphaFold have revolutionized protein structure
prediction based only on the amino-acid sequence. However, proteins often
appear in multiple different conformations, and it is highly relevant to
resolve the full conformational distribution. Single-particle cryo-electron
microscopy (cryo EM) is a powerful tool for capturing a large number of images
of a given protein, frequently in different conformations (referred to as
particles). The images are, however, very noisy projections of the protein, and
traditional methods for cryo EM reconstruction are limited to recovering a
single, or a few, conformations. In this paper, we introduce cryoSPHERE, a deep
learning method that takes as input a nominal protein structure, e.g. from
AlphaFold, learns how to divide it into segments, and how to move these as
approximately rigid bodies to fit the different conformations present in the
cryo EM dataset. This formulation is shown to provide enough constraints to
recover meaningful reconstructions of single protein structures. This is
illustrated in three examples where we show consistent improvements over the
current state-of-the-art for heterogeneous reconstruction.
