Maximum entropy methods in electron crystallography

Gilmore, C. J.

doi:10.1002/(sici)1097-0029(19990715)46:2<117::aid-jemt5>3.0.co;2-q

Cited by 12 publications

(7 citation statements)

References 46 publications

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“…Conventional direct methods are well established (Schenk, 1992;Giacovazzo, 1998) and have been applied previously with electron diffraction data (Nicolopoulos et al, 1995;Dorset, 1996Dorset, , 2003aGilmore, 1999;Weirich, 2001Weirich, , 2003Hovmö ller et al, 2002;Dorset et al, 2005). In almost all cases, the effects of dynamical diffraction have either been ignored or taken (often without a priori justification) as small.…”

Section: Discussionmentioning

confidence: 99%

“…Fortunately, these are not in general what we referred to earlier as the 'structure-defining reflections'. Provided that one uses code that is capable of handling unknown reflections such as EDM (Kilaas et al, 2005), a feasible-set approach or maximum entropy (Gilmore, 1999), one can simply remove these from the data set (Own et al, 2006a). An exception to this is the case of large-framework structures for which low-index reflections might be structure-defining.…”

Section: Figure 11mentioning

confidence: 99%

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Precession electron diffraction 1: multislice simulation

Own¹,

Marks²,

Sinkler³

2006

Acta Cryst Sect A

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Precession electron diffraction (PED) is a method that considerably reduces dynamical effects in electron diffraction data, potentially enabling more straightforward solution of structures using the transmission electron microscope. This study focuses upon the characterization of PED data in an effort to improve the understanding of how experimental parameters affect it in order to predict favorable conditions. A method for generating simulated PED data by the multislice method is presented and tested. Data simulated for a wide range of experimental parameters are analyzed and compared to experimental data for the (Ga,In)(2)SnO(4) (GITO) and ZSM-5 zeolite (MFI) systems. Intensity deviations between normalized simulated and kinematical data sets, which are bipolar for dynamical diffraction data, become unipolar for PED data. Three-dimensional difference plots between PED and kinematical data sets show that PED data are most kinematical for small thicknesses, and as thickness increases deviations are minimized by increasing the precession cone semi-angle phi. Lorentz geometry and multibeam dynamical effects explain why the largest deviations cluster about the transmitted beam, and one-dimensional diffraction is pointed out as a strong mechanism for deviation along systematic rows. R factors for the experimental data sets are calculated, demonstrating that PED data are less sensitive to thickness variation. This error metric was also used to determine the experimental specimen thickness. R(1) (unrefined) was found to be about 12 and 15% for GITO and MFI, respectively.

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Section: Discussionmentioning

confidence: 99%

Section: Figure 11mentioning

confidence: 99%

Precession electron diffraction 1: multislice simulation

Own¹,

Marks²,

Sinkler³

2006

Acta Cryst Sect A

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“…Although not considered in this study, another powerful FOM to be considered in a complete evaluation is the maximum entropy criterion, already proven to be useful in several ab initio protein determinations (Gilmore, 1999).…”

Section: Discussionmentioning

confidence: 99%

“…Analysis of such zones by maximum entropy and likelihood has also be quite successful (Gilmore, Nicholson, Dorset, 1996;Gilmore, 1999). More recently, maximum likelihood has been used to justify the hypothesis of non-crystallographic five-fold symmetry in the cholera toxin structure (Gilmore, 1999).…”

Section: Introductionmentioning

confidence: 99%

Direct structure analysis in protein electron crystallography via the density histogram: deoxycholate-treated purple membrane

Dorset¹

2000

Zeitschrift Für Kristallographie - Crystalline Materials

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The crystal structure of bacteriorhodopsin in purple membrane treated with sodium deoxycholate (plane group p3, a 57.3 A) was solved ab initio in projection from previously published electron diffraction amplitudes to 6.2 A by direct methods for crystallographic phase determination. The best solution from the Sayre equation was identified by minimizing the skew properties of the cross-correlation of the experimental density histogram with the expected histogram. After Fourier refinement, the overall mean phase error is 43.3 for all 35 unique reflections or 16.9 for the 14 most intense maxima. For six clearly identified helix sites, the mean deviation of positions, when compared to the original model, was 0.7 A

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“…The likelihood function measures how well the observed amplitudes in set {K} match those which are predicted from extrapolation. For full details in an electron crystallography environment see Gilmore (1996Gilmore ( , 1998bGilmore ( , 1999 and Gilmore, Shankland and Bricogne (1993). The maximum entropy formalism is incorporated into a computer program MICE (Gilmore and Bricogne, 1997) which is used in all the following examples.…”

Section: Maximum Entropymentioning

confidence: 99%

Nanocrystals: Solving Crystal Structures Using Electron Crystallography

Gilmore¹

2003

Crystallography Reviews

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Electron crystallography uses the electron microscope to generate diffraction patterns or high resolution images which can be used to solve crystal structures from nano-sized crystallites. The diffraction data collected are subject to systematic errors in intensity arising from n-beam dynamical scattering, secondary scattering, sample bending and radiation damage, but nonetheless the technique yields structural information when all other diffraction methods fail. Solving such structures can be routine especially from inorganic materials and intermetallic compounds, but, in general, the process can be difficult as can the validation of the proposed model. Direct methods, maximum entropy, Patterson techniques, model building and the use of image data can all be employed, and structures of high complexity can be solved and refined in favourable cases. Even low resolution protein data can be analysed in this way, and it is an important tool in surface crystallography.

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Maximum entropy methods in electron crystallography

Cited by 12 publications

References 46 publications

Precession electron diffraction 1: multislice simulation

Precession electron diffraction 1: multislice simulation

Direct structure analysis in protein electron crystallography via the density histogram: deoxycholate-treated purple membrane

Nanocrystals: Solving Crystal Structures Using Electron Crystallography

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