title: Efficient estimation of three-dimensional covariance and its application in the analysis of heterogeneous samples in cryo-electron microscopy.
abstract: Single-particle cryogenic electron microscopy (cryo-EM) is a powerful tool for the study of macromolecular structures at high resolution. Classification allows multiple structural states to be extracted and reconstructed from the same sample. One classification approach is via the covariance matrix, which captures the correlation between every pair of voxels. Earlier approaches employ computing-intensive resampling and estimate only the eigenvectors of the matrix, which are then used in a separate fast classification step. We propose an iterative scheme to explicitly estimate the covariance matrix in its entirety. In our approach, the flexibility in choosing the solution domain allows us to examine a part of the molecule in greater detail. Three-dimensional covariance maps obtained in this way from experimental data (cryo-EM images of the eukaryotic pre-initiation complex) prove to be in excellent agreement with conclusions derived by using traditional approaches, revealing in addition the interdependencies of ligand bindings and structural changes.
authors.affiliation: Department of Biochemistry and Molecular Biophysics, Columbia University, 650 West 168 Street, New York, NY 10032, USA.
authors.forename: Hstau Y
authors.initials: HY
authors.lastname: Liao
authors.affiliation: Architecture et Réactivité de l'ARN, Institut de Biologie Moléculaire et Cellulaire, CNRS, Université de Strasbourg, 15 Rue René Descartes, 67084 Strasbourg, France.
authors.forename: Yaser
authors.initials: Y
authors.lastname: Hashem
authors.affiliation: Department of Biochemistry and Molecular Biophysics, Columbia University, 650 West 168 Street, New York, NY 10032, USA; Department of Biological Sciences, Columbia University, 600 Fairchild Center, New York, NY 10027, USA; Department of Biochemistry and Molecular Biophysics, Howard Hughes Medical Institute, Columbia University, 650 West 168 Street, New York, NY 10032, USA. Electronic address: jf2192@cumc.columbia.edu.
authors.forename: Joachim
authors.initials: J
authors.lastname: Frank
mesh_terms: D000704:Analysis of Variance; D020285:Cryoelectron Microscopy / Q000379:methods* / Q000592:standards*; D003627:Data Interpretation, Statistical; D008958:Models, Molecular; D054657:Ribosome Subunits / Q000737:chemistry*