Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes

Amit Moscovich, Amit Halevi, Joakim Andén, Amit Singer

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


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.

Original languageEnglish (US)
Article number024003
JournalInverse Problems
Issue number2
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Signal Processing
  • Applied Mathematics
  • Computer Science Applications
  • Mathematical Physics


  • Diffusion maps
  • Heterogeneity
  • Laplacian eigenmaps
  • Manifold learning
  • Molecular conformation space
  • Single particle electron cryomicroscopy
  • Tomographic reconstruction


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