Alignment of Partially Overlapping Cryo-EM Maps Using Unbalanced Gromov-Wasserstein Divergence

Aligning EM density maps and fitting atomic models are essential steps in single-particle cryogenic electron microscopy (cryo-em), with recent methods leveraging various algorithms and machine learning tools. As aligning maps remains challenging in the presence of a map that only partially fits the other (e.g., one subunit), we here propose a procedure, em partial alignment with optimal transport (EMPOT), for partial alignment of three-dimensional (3D) maps. EMPOT finds a coupling between 3D point-cloud representations, which is associated with their so-called unbalanced Gromov Wasserstein divergence, and uses this coupling to find an optimal rigid body transformation. On running and benchmarking our method with experimental maps and structures, we show that EMPOT outperforms standard methods for aligning density maps and fitting atomic models to a density map, suggesting potential applications of partial optimal transport for improving cryo-em pipelines.