Automatic recovery of missing amplitudes and phases in tilt-limited electron crystallography of two-dimensional crystals

Bryant R. Gipson, Daniel J. Masiel, Nigel D. Browning, John Spence, Kaoru Mitsuoka, and Henning Stahlberg
Phys. Rev. E 84, 011916 – Published 22 July 2011
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Abstract

Electron crystallography of 2D protein crystals provides a powerful tool for the determination of membrane protein structure. In this method, data is acquired in the Fourier domain as randomly sampled, uncoupled, amplitudes and phases. Due to physical constraints on specimen tilting, those Fourier data show a vast un-sampled “missing cone” of information, producing resolution loss in the direction perpendicular to the membrane plane. Based on the flexible language of projection onto sets, we provide a full solution for these problems with a projective constraint optimization algorithm that, for sufficiently oversampled data, produces complete recovery of unmeasured data in the missing cone. We apply this method to an experimental data set of Bacteriorhodopsin and show that, in addition to producing superior results compared to traditional reconstruction methods, full, reproducible, recovery of the missing cone from noisy data is possible. Finally, we present an automatic implementation of the refinement routine as open source, freely distributed, software that will be included in our 2dx software package.

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  • Received 27 February 2011

DOI:https://doi.org/10.1103/PhysRevE.84.011916

©2011 American Physical Society

Authors & Affiliations

Bryant R. Gipson1,*, Daniel J. Masiel2, Nigel D. Browning2, John Spence3, Kaoru Mitsuoka4, and Henning Stahlberg1,†

  • 1Center for Cellular Imaging and Nano Analytics (C-CINA), Biozentrum, University Basel, WRO-1058 Mattenstrasse 26, CH-4058 Basel, Switzerland
  • 2Department of Chemical Engineering and Materials Sciences, University of California at Davis, Davis, California 95616, USA
  • 3Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
  • 4Biomedicinal Information Research Center (BIRC), National Institute of Advanced Industrial Science and Technology (AIST), 2-3-26, Aomi, Koto-ku, Tokyo 135-0064, Japan

  • *Present address: Department of Computer Sciences, Duncan Hall, Rice University, Houston, TX 77030, USA; bryant.gipson@rice.edu
  • henning.stahlberg@unibas.ch

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Issue

Vol. 84, Iss. 1 — July 2011

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