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Physical and Non-Physical Methods of Solving Crystal Structures

Authors Authors and affiliations E. Landree C. Collazo-Davila D. Grozea E. Bengu L. Marks C. This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Marks, L. Plass, R. Gilmore, C. Crystallographica A 52 — Google Scholar. D and Landree, E. Crystallographica A Submitted. Gutowski, M. A: Math.

Goldberg, D. Landree, E and Marks, L. Crystallographica B. Feldhaus 1 , F. Staier 2 , R. Barth 2 , A. Rosenhahn 2 , M. Grunze 2 , T.

Fan, Hai-Fu | TWAS

Nisius 3 , T. Wilhein 3 , D. Stickler 4 , H.

Bragg's Equation For X-Ray Diffraction In Chemistry - Practice Problems

Stillrich 4 , R. Oepen 4 , M. Martins 5 , B. Pfau 6 , C. Eisebitt 6 , B. Faatz 1 , N. Guerassimova 1 , K. Honkavaara 1 , V. Kocharyan 1 , R. Treusch 1 , E. Saldin 1 , S. Schreiber 1 , E. Schneidmiller 1 , M. Yurkov 1 , E. Weckert 1 , and I. Vartanyants 1. Crystallization and radiation damage is presently a bottleneck in protein structure determination.

We propose to use two-dimensional 2D finite crystals and ultrashort Free Electron Laser pulses to reveal the structure of single molecules. This can be especially important for membrane proteins that in general do not form 3D crystals, but easily form 2D crystalline structures.

We have demonstrated single pulse train coherent diffractive imaging for a finite 2D crystalline sample, and conclude that this alternative approach to single molecule imaging is a significant step towards revealing the structure of proteins with sub-nanometer resolution at the newly built XFEL sources. Revealing the structure of protein molecules is mandatory for understanding the structure of larger biological complexes. The major progress in uncovering the structure of proteins in past decades was due to the development of phasing methods [ 1 ] allowing the determination of the structure of complex molecules that crystallize.

One new approach to overcome these difficulties is based on the use of ultrashort pulses of x-ray free-electron lasers XFEL [ 2 ]. This elegant idea is based on measuring a sufficiently sampled diffraction pattern from a single molecule illuminated by an FEL pulse [ 3 ]. However, in spite of the extreme intensity of the FEL pulses, a diffraction pattern from only one molecule will not be sufficient to obtain a high resolution diffraction pattern.

Many reproducible copies will need to be measured to get a sufficient signal to noise ratio for each projection necessary for three-dimensional 3D imaging at sub-nanometer spatial resolution.


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Free-electron lasers are especially well suited for such coherent 2D crystallography. They provide femtosecond coherent pulses with extremely high power.

Only the combination of all of these unique properties will allow the realization of 2D crystallographic x-ray imaging on biological systems. Brilliant, ultrashort pulses could overcome the radiation damage problem [ 3 ] which is a severe limitation of conventional crystallography at 3 rd generation synchrotron sources [ 4 ].

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Higher luminosity and hence improved statistics for such experiments can be obtained by the use of pulse trains that can be provided by FLASH [ 5 ]. We demonstrate finite crystallography by using a micro-structured crystal array that was prepared on a nm thick silicon nitride membrane substrate coated with nm of gold, and nm of palladium.

The finite crystal sample was manufactured by milling holes in the film in a regular array pattern using a Focused Ion Beam FIB. The 'unit cell' of our crystal consists of a large hole of nm diameter representing a 'heavy atom' in conventional crystallography and a smaller hole of nm diameter representing a 'light atom'. The scheme of experiment is shown in Fig. We used a 0. This is an order of magnitude higher than the expected coherent flux of about 3x10 9 photons on the same sample area for the same exposure time at a 3 rd generation synchrotron source.

A typical data set is shown in Fig.

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The diffraction pattern as measured contains signal up to the edge of the detector, which corresponds to a minimum feature size of nm Fig. We note that all expected features of a finite, crystalline structure are observed. The Bragg peaks due to the regular array are clearly seen, as are the oscillations between the Bragg peaks that are the result of the finite extent and coherent illumination of our sample. Also seen is the form factor from the individual elements — the large holes — that can be observed as a radial intensity modulation across the pattern produced.


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  8. The preprocessed data set shown in Fig. A scanning ion micrograph SIM image of the object under investigation is shown in Fig. The initial square support used for reconstruction is indicated by a dashed line in Fig.