EMPOT: partial alignment of density maps and rigid body fitting using unbalanced Gromov-Wasserstein divergence

TL;DR

EMPOT introduces a novel partial alignment method for cryo-EM density maps using unbalanced Gromov-Wasserstein divergence, improving subunit alignment and atomic model fitting in cryo-EM analysis.

Contribution

The paper presents EMPOT, a new partial alignment technique leveraging optimal transport for better cryo-EM map and model fitting, especially with incomplete data.

Findings

EMPOT outperforms standard methods in aligning protein subunits.

EMPOT improves atomic model fitting to density maps.

Benchmark results demonstrate EMPOT's effectiveness on experimental data.

Abstract

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 new procedure, EMPOT (EM Partial alignment with Optimal Transport), for partial alignment of 3D maps. EMPOT first finds a coupling between 3D point-cloud representations, which is associated with their so-called unbalanced Gromov Wasserstein divergence, and second, uses this coupling to find an optimal rigid body transformation. Upon running and benchmarking our method with experimental maps and structures, we show that EMPOT outperforms standard methods for aligning subunits of a protein complex and fitting atomic models to a density map, suggesting potential applications of Partial Optimal Transport for improving Cryo-EM pipelines.