3D alignment of cryogenic electron microscopy density maps by minimizing their Wasserstein distance

Aligning electron density maps of multiple conformations of a biomolecule from Cryogenic electron microscopy (cryo-EM) is a first key step to study conformational heterogeneity. As this step remains challenging, with standard alignment tools being potentially stuck in local minima, we propose here a new procedure, 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 show that our method outperforms standard methods on experimental data, with an increased range of rotation angles leading to proper alignment, suggesting that it can be further applied to align 3D EM maps.