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Maximum Entropy and Bayesian Methods of Solving the Phase Problem in Electron Diffraction

Published online by Cambridge University Press:  02 July 2020

C.J. Gilmore
C.J. Gilmore*
Affiliation:
Department of Chemistry, University of Glasgow, Glasgow, G12 8QQ, Scotland, UK
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Extract

The phasing of electron diffraction data poses considerable problems for traditional direct or heavy atom crystallographic methods since the data are incomplete or at less than atomic resolution (i.e. 1.1Å), and subject to errors arising from dynamical scattering effects. The Bricogne formalism for phasing diffraction data using maximum entropy (ME) and Bayesian methods has proved especially useful in these situations1 since this formalism is stable irrespective of data resolution and completeness, and is robust with respect to errors on the measured diffraction intensities.

Successes with this formalism this include a wide range of structures:

  1. (1) The ab initio phasing of diketopiperazine C4H6N2O2 (Fig 1).

  2. (2) The structure solution of CuCl2.3Cu(OH)2 (Fig 2).

  3. (3) The ab initio phasing of two 2-D membrane data sets at ca. 6Å resolution without the use of image phases (Halorhodopsin and Omp F Porin4 - Figs 3 and 4). In addition, we have had some success in phasing the 3-D data of bacteriorhodopsin at 6Å.

Type
Electron Crystallography; The Electron Phase Problem
Information
Microscopy and Microanalysis , Volume 3 , Issue S2: Proceedings: Microscopy & Microanalysis '97, Microscopy Society of America 55th Annual Meeting, Microbeam Analysis Society 31st Annual Meeting, Histochemical Society 48th Annual Meeting, Cleveland, Ohio, August 10-14, 1997 , August 1997 , pp. 1021 - 1022
Copyright
Copyright © Microscopy Society of America 1997

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References

1.Bricogne, G. (1984). Acta Cryst. A40, 410–445.10.1107/S0108767384000866CrossRefGoogle Scholar
2.Bricogne, G. and Gilmore, C.J., Acta Cryst (1990), A46, 284–297.10.1107/S0108767389012882CrossRefGoogle Scholar
3.Gilmore, C.J., Shankland, K. and Bricogne, G.Proc. Roy. Soc. Series A, (1993), 442, 97–111.Google Scholar
4.Gilmore, C.J., Nicholson, W.V. and Dorset, D.L. (1996). Acta Cryst. A52, 937–946.10.1107/S0108767396008744CrossRefGoogle Scholar
5.Voigt Martin, I.G., Yan, D.H., Gilmore, C.J. and Bricogne, G.Acta Cryst, (1995), A51, 849–868.10.1107/S0108767395004557CrossRefGoogle Scholar
6.Voigt-Martin, LG., Zhang, Z.H., Kolbe, U. and Gilmore, C.J., Ultramicroscopy (1997) accepted.Google Scholar
7.Gilmore, C.J., Marks, L. D., Grozea, D., Collazo, C., Landree, E. and Twesten, R., Surface Science (1997) accepted.Google Scholar