  Aligning electron density maps from Cryogenic electron microscopy (cryo-EM)
is a first key step for studying multiple conformations of a biomolecule. As
this step remains costly and challenging, with standard alignment tools being
potentially stuck in local minima, we propose here a new procedure, called
AlignOT, which relies on the use of computational optimal transport (OT) to
align EM maps in 3D space. By embedding a fast estimation of OT maps within a
stochastic gradient descent algorithm, our method searches for a rotation that
minimizes the Wasserstein distance between two maps, represented as point
clouds. We quantify the impact of various parameters on the precision and
accuracy of the alignment, and show that AlignOT can outperform the standard
local alignment methods, with an increased range of rotation angles leading to
proper alignment. We further benchmark AlignOT on various pairs of experimental
maps, which account for different types of conformational heterogeneities and
geometric properties. As our experiments show good performance, we anticipate
that our method can be broadly applied to align 3D EM maps.
