Three-dimensional diffractive imaging for crystalline monolayers with one-dimensional compact support

John Spence, Uwe Weierstall, T. T. Fricke, R. M. Glaeser, K. H. Downing

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


The use of a compact support constraint along the beam direction is considered as a solution to the phase problem for diffraction by two-dimensional protein crystals. Specifically we apply the iterative Gerchberg-Saxton-Fienup algorithm to simulated three-dimensional transmission electron diffraction data from monolayer organic crystals. We find that oversampling along the reciprocal-lattice rods (relrods) normal to the monolayer alone does not solve the phase problem in this geometry in general. However, based on simulations for a crystalline protein monolayer (lysozyme), we find that convergence is obtained in three dimensions if phases are supplied from a few high resolution electron microscope images recorded at small tilts to the beam direction. In the absence of noise, amplitude-weighted phase residuals of around 5°, and a cross-correlation coefficient of 0.96 between the true and estimated potential are obtained if phases are included from images at tilts of up to 15°. The performance is almost as good in the presence of noise at a level that is comparable to that commonly observed in electron crystallography of proteins. The method should greatly reduce the time and labor needed for data acquisition and analysis in cryo-electron microscopy of organic thin crystals by avoiding the need to record images at high tilt angles.

Original languageEnglish (US)
Pages (from-to)209-218
Number of pages10
JournalJournal of Structural Biology
Issue number1-2
StatePublished - Oct 2003


  • Diffraction
  • Electron crystallography
  • Phase determination
  • Protein structure

ASJC Scopus subject areas

  • Structural Biology


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