2020Moscovich DiffusionMaps

Citation

A. Moscovich, A. Halevi, J. Andén, A. Singer, "Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes", Inverse Problems, 36 (2) 024003 (2020).

Abstract

Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and deform. Traditional reconstruction methods fail in these cases, resulting in smeared reconstructions of the moving parts. This poses a major obstacle for structural biologists, who need high-resolution reconstructions of entire macromolecules, moving parts included. To address this challenge, we present a new method for the reconstruction of macromolecules exhibiting continuous heterogeneity. The proposed method uses projection images from multiple viewing directions to construct a graph Laplacian through which the manifold of three-dimensional conformations is analyzed. The 3D molecular structures are then expanded in a basis of Laplacian eigenvectors, using a novel generalized tomographic reconstruction algorithm to compute the expansion coefficients. These coefficients, which we name spectral volumes, provide a high-resolution visualization of the molecular dynamics. We provide a theoretical analysis and evaluate the method empirically on several simulated data sets.

Keywords

Single particle electron cryomicroscopy, heterogeneity, tomographic reconstruction, molecular conformation space, manifold learning, Laplacian eigenmaps, diffusion maps

Links

https://iopscience.iop.org/article/10.1088/1361-6420/ab4f55