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.

Cryo-electron microscopy (cryo-EM) is an imaging modality that provides unique insights into the dynamics of proteins and other building blocks of life. The algorithmic challenge of jointly estimating the poses, 3D structure, and conformational heterogeneity of a biomolecule from millions of noisy and randomly oriented 2D projections in a computationally efficient manner, however, remains unsolved. Our method, cryoFIRE, performs ab initio heterogeneous reconstruction with unknown poses in an amortized framework, thereby avoiding the computationally expensive step of pose search while enabling the analysis of conformational heterogeneity. Poses and conformation are jointly estimated by an encoder while a physics-based decoder aggregates the images into an implicit neural representation of the conformational space. We show that our method can provide one order of magnitude speedup on datasets containing millions of images, without any loss of accuracy. We validate that the joint estimation of poses and conformations can be amortized over the size of the dataset. For the first time, we prove that an amortized method can extract interpretable dynamic information from experimental datasets.

MOTIVATION: Cryogenic electron microscopy (cryo-EM) offers the unique potential to capture conformational heterogeneity, by solving multiple three-dimensional classes that co-exist within a single cryo-EM image dataset. To investigate the extent and implications of such heterogeneity, we propose to use an optimal-transport-based metric to interpolate barycenters between EM maps and produce morphing trajectories. RESULTS: While standard linear interpolation mostly fails to produce realistic transitions, our method yields continuous trajectories that displace densities to morph one map into the other, instead of blending them. AVAILABILITY AND IMPLEMENTATION: Our method is implemented as a plug-in for ChimeraX called MorphOT, which allows the use of both CPU or GPU resources. The code is publicly available on GitHub (https://github.com/kdd-ubc/MorphOT.git), with documentation containing tutorial and datasets. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.