SOLVAR: Fast covariance-based heterogeneity analysis with pose refinement for cryo-EM

TL;DR

SOLVAR introduces a fast, low-rank covariance estimation method for cryo-EM heterogeneity analysis that also refines particle poses, enabling efficient and accurate structural variability characterization.

Contribution

The paper presents SOLVAR, a novel low-rank covariance estimator that incorporates pose refinement, significantly improving computational efficiency and accuracy in cryo-EM heterogeneity analysis.

Findings

Accurately captures dominant variability components.

Achieves state-of-the-art performance on heterogeneity benchmarks.

Maintains computational efficiency on large datasets.

Abstract

Cryo-electron microscopy (cryo-EM) has emerged as a powerful technique for resolving the three-dimensional structures of macromolecules. A key challenge in cryo-EM is characterizing continuous heterogeneity, where molecules adopt a continuum of conformational states. Covariance-based methods offer a principled approach to modeling structural variability. However, estimating the covariance matrix efficiently remains a challenging computational task. In this paper, we present SOLVAR (Stochastic Optimization for Low-rank Variability Analysis), which leverages a low-rank assumption on the covariance matrix to provide a tractable estimator for its principal components, despite the apparently prohibitive large size of the covariance matrix. Under this low-rank assumption, our estimator can be formulated as an optimization problem that can be solved quickly and accurately. Moreover, our framework enables refinement of the poses of the input particle images, a capability absent from most heterogeneity-analysis methods, and all covariance-based methods. Numerical experiments on both synthetic and experimental datasets demonstrate that the algorithm accurately captures dominant components of variability while maintaining computational efficiency. SOLVAR achieves state-of-the-art performance across multiple datasets in a recent heterogeneity benchmark. The code of the algorithm is freely available at https://github.com/RoeyYadgar/SOLVAR.