SubspaceEM: A fast maximum-a-posteriori algorithm for cryo-EM single particle reconstruction.

Single particle reconstruction methods based on the maximum-likelihood principle and the expectation-maximization (E-M) algorithm are popular because of their ability to produce high resolution structures. However, these algorithms are computationally very expensive, requiring a network of computational servers. To overcome this computational bottleneck, we propose a new mathematical framework for accelerating maximum-likelihood reconstructions. The speedup is by orders of magnitude and the proposed algorithm produces similar quality reconstructions compared to the standard maximum-likelihood formulation. Our approach uses subspace approximations of the cryo-electron microscopy (cryo-EM) data and projection images, greatly reducing the number of image transformations and comparisons that are computed. Experiments using simulated and actual cryo-EM data show that speedup in overall execution time compared to traditional maximum-likelihood reconstruction reaches factors of over 300.

[1]  Richard Henderson,et al.  Tilt-Pair Analysis of Images from a Range of Different Specimens in Single-Particle Electron Cryomicroscopy , 2011, Journal of molecular biology.

[2]  Nikolaus Grigorieff,et al.  FREALIGN: high-resolution refinement of single particle structures. , 2007, Journal of structural biology.

[3]  Thomas Walz,et al.  The advent of near-atomic resolution in single-particle electron microscopy. , 2009, Annual review of biochemistry.

[4]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[5]  N. Grigorieff,et al.  Structure of the ribosome with elongation factor G trapped in the pretranslocation state , 2013, Proceedings of the National Academy of Sciences.

[6]  F. Sigworth.  A maximum-likelihood approach to single-particle image refinement. , 1998, Journal of structural biology.

[7]  Z Yin,et al.  An ab initio algorithm for low-resolution 3-D reconstructions from cryoelectron microscopy images. , 2001, Journal of structural biology.

[8]  Hemant D. Tagare,et al.  Fast, Adaptive Expectation-Maximization Alignment for Cryo-EM , 2008, MICCAI.

[9]  Padmaja Natarajan,et al.  A statistical approach to computer processing of cryo-electron microscope images: virion classification and 3-D reconstruction. , 2003, Journal of structural biology.

[10]  Christopher Irving,et al.  A toolbox for ab initio 3-D reconstructions in single-particle electron microscopy. , 2010, Journal of structural biology.

[11]  Sjors H.W. Scheres,et al.  RELION: Implementation of a Bayesian approach to cryo-EM structure determination , 2012, Journal of structural biology.

[12]  Fred J Sigworth,et al.  An adaptive Expectation-Maximization algorithm with GPU implementation for electron cryomicroscopy. , 2010, Journal of structural biology.

[13]  J M Carazo,et al.  XMIPP: a new generation of an open-source image processing package for electron microscopy. , 2004, Journal of structural biology.

[14]  Roberto Marabini,et al.  Maximum-likelihood multi-reference refinement for electron microscopy images. , 2005, Journal of molecular biology.

[15]  Donald A. Jackson,et al.  How many principal components? stopping rules for determining the number of non-trivial axes revisited , 2005, Comput. Stat. Data Anal..

[16]  John E. Johnson,et al.  Exact Reduced-Complexity Maximum Likelihood Reconstruction of Multiple 3-D Objects From Unlabeled Unoriented 2-D Projections and Electron Microscopy of Viruses , 2007, IEEE Transactions on Image Processing.

[17]  José María Carazo,et al.  Fast maximum-likelihood refinement of electron microscopy images , 2005, ECCB/JBI.

[18]  Lori A. Passmore,et al.  Ultrastable gold substrates for electron cryomicroscopy , 2014, Science.

[19]  Shaoxia Chen,et al.  Prevention of overfitting in cryo-EM structure determination , 2012, Nature Methods.

[20]  R. Cattell.  The Scree Test For The Number Of Factors. , 1966, Multivariate behavioral research.

[21]  I. Jolliffe.  Principal Component Analysis , 2002 .

[22]  Sjors H. W. Scheres.  A Bayesian view on cryo-EM structure determination , 2012, ISBI.

[23]  Jose-Maria Carazo,et al.  An introduction to maximum-likelihood methods in cryo-EM. , 2010, Methods in enzymology.

[24]  Alp Kucukelbir,et al.  A Bayesian adaptive basis algorithm for single particle reconstruction. , 2012, Journal of structural biology.

[25]  Conrad C. Huang,et al.  UCSF Chimera—A visualization system for exploratory research and analysis , 2004, J. Comput. Chem..

[26]  R. Henderson,et al.  Optimal determination of particle orientation, absolute hand, and contrast loss in single-particle electron cryomicroscopy. , 2003, Journal of molecular biology.

[27]  John E. Johnson,et al.  Ab initio reconstruction and experimental design for cryo electron microscopy , 2000, IEEE Trans. Inf. Theory.

[28]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[29]  G. Herman,et al.  Disentangling conformational states of macromolecules in 3D-EM through likelihood optimization , 2007, Nature Methods.