title: Directly reconstructing principal components of heterogeneous particles from cryo-EM images.
abstract: Structural heterogeneity of particles can be investigated by their three-dimensional principal components. This paper addresses the question of whether, and with what algorithm, the three-dimensional principal components can be directly recovered from cryo-EM images. The first part of the paper extends the Fourier slice theorem to covariance functions showing that the three-dimensional covariance, and hence the principal components, of a heterogeneous particle can indeed be recovered from two-dimensional cryo-EM images. The second part of the paper proposes a practical algorithm for reconstructing the principal components directly from cryo-EM images without the intermediate step of calculating covariances. This algorithm is based on maximizing the posterior likelihood using the Expectation-Maximization algorithm. The last part of the paper applies this algorithm to simulated data and to two real cryo-EM data sets: a data set of the 70S ribosome with and without Elongation Factor-G (EF-G), and a data set of the influenza virus RNA dependent RNA Polymerase (RdRP). The first principal component of the 70S ribosome data set reveals the expected conformational changes of the ribosome as the EF-G binds and unbinds. The first principal component of the RdRP data set reveals a conformational change in the two dimers of the RdRP.
authors.affiliation: Dept. of Diagnostic Radiology, Yale University, CT 06520, United States; Dept. of Biomedical Engineering, Yale University, CT 06520, United States. Electronic address: hemant.tagare@yale.edu.
authors.forename: Hemant D
authors.initials: HD
authors.lastname: Tagare
authors.affiliation: Data Science Institute, Columbia University, NY 10027, United States; Dept. of Computer Science, Columbia University, NY 10027, United States.
authors.forename: Alp
authors.initials: A
authors.lastname: Kucukelbir
authors.affiliation: Dept. of Cellular and Molecular Physiology, Yale University, CT 06520, United States; Dept. of Biomedical Engineering, Yale University, CT 06520, United States.
authors.forename: Fred J
authors.initials: FJ
authors.lastname: Sigworth
authors.affiliation: Center for Struct. Biol., School of Life Sciences, Tsinghua University, Beijing 100084, China.
authors.forename: Hongwei
authors.initials: H
authors.lastname: Wang
authors.affiliation: Dept. of Mathematics, University of Florida, FL 32611-8105, United States.
authors.forename: Murali
authors.initials: M
authors.lastname: Rao
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D020285:Cryoelectron Microscopy; D009980:Influenza A virus / Q000201:enzymology; D016013:Likelihood Functions; D008958:Models, Molecular; D025341:Principal Component Analysis; D017510:Protein Folding; D017434:Protein Structure, Tertiary; D012324:RNA-Dependent RNA Polymerase / Q000737:chemistry* / Q000648:ultrastructure; D012270:Ribosomes / Q000737:chemistry* / Q000648:ultrastructure
chemical_list: D012324:RNA-Dependent RNA Polymerase
keywords: EM algorithm; Heterogeneity; Maximum-likelihood; Principal components; Single particle reconstruction