  Cryogenic electron microscopy (cryo-EM) provides a unique opportunity to
study the structural heterogeneity of biomolecules. Being able to explain this
heterogeneity with atomic models would help our understanding of their
functional mechanisms but the size and ruggedness of the structural space (the
space of atomic 3D cartesian coordinates) presents an immense challenge. Here,
we describe a heterogeneous reconstruction method based on an atomistic
representation whose deformation is reduced to a handful of collective motions
through normal mode analysis. Our implementation uses an autoencoder. The
encoder jointly estimates the amplitude of motion along the normal modes and
the 2D shift between the center of the image and the center of the molecule .
The physics-based decoder aggregates a representation of the heterogeneity
readily interpretable at the atomic level. We illustrate our method on 3
synthetic datasets corresponding to different distributions along a simulated
trajectory of adenylate kinase transitioning from its open to its closed
structures. We show for each distribution that our approach is able to
recapitulate the intermediate atomic models with atomic-level accuracy.
