Liao, H.Y., Hashem, Y. and Frank, J. (2015) Efficient Estimation of Three-Dimensional Covariance and Its Application in the Analysis of Heterogeneous Samples in Cryo-Electron Microscopy. Structure, 23, 1129-1137.
http://dx.doi.org/10.1016/j.str.2015.04.004

has been cited by the following article:

• TITLE: Structure Sorting of Multiple Macromolecular States in Heterogeneous Cryo-EM Samples by 3D Multivariate Statistical Analysis

  AUTHORS: Bruno P. Klaholz

  KEYWORDS: Heterogeneity, Structural Biology, Cryo Electron Microscopy, Particle Sorting, Multiple States, Macromolecular Complexes, Resampling, Jackknifing, Bootstrapping, Multivariate Statistical Analysis, 3D MSA, 3D-SC, Ribosome, RNA Polymerase

  JOURNAL NAME: Open Journal of Statistics, Vol.5 No.7, December 30, 2015

  ABSTRACT: Heterogeneity of biological samples is usually considered a major obstacle for three-dimensional (3D) structure determination of macromolecular complexes. Heterogeneity may occur at the level of composition or conformational variability of complexes and affects most 3D structure determination methods that rely on signal averaging. Here, an approach is described that allows sorting structural states based on a 3D statistical approach, the 3D sampling and classification (3D-SC) of 3D structures derived from single particles imaged by cryo electron microscopy (cryo-EM). The method is based on jackknifing & bootstrapping of 3D sub-ensembles and 3D multivariate statistical analysis followed by 3D classification. The robustness of the statistical sorting procedure is corroborated using model data from an RNA polymerase structure and experimental data from a ribosome complex. It allows resolving multiple states within heterogeneous complexes that thus become amendable for a structural analysis despite of their highly flexible nature. The method has important implications for high-resolution structural studies and allows describing structure ensembles to provide insights into the dynamics of multi-component macromolecular assemblies.