On the Poincaré series of $H^*(BL(2,2^n),\mathbb{Z}/2)$

Chapman, G. R.

doi:10.5565/publmat_30186_02

Cited by 7 publications

(9 citation statements)

References 8 publications

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“…Other alignment methods, such as static electric or magnetic fields, or flow alignment have been considered and demonstrated (Bras et al, 1998;Koch et al, 1988), as well as employed in the field of birefringence measurements (Fredericq & Houssier, 1973). These alignment techniques may also be helpful to avoid the problem of orientation classification of diffraction patterns from single molecules in random orientations, which is the main difficulty arising for single molecule imaging using pulsed X-ray freeelectron lasers (Chapman et al, 2006a;Huldt et al, 2003). The motion of the molecules does not affect the diffraction pattern if the illuminating wavefield is approximately planar, so that if there is, for example, one molecule in the beam at any instant, the method is equivalent to diffraction from a single stationary molecule.…”

Section: Introductionmentioning

confidence: 99%

Dose, exposure time and resolution in serial X-ray crystallography

Starodub

Rez

Hembree

et al. 2007

J Synchrotron Radiat

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The resolution of X-ray diffraction microscopy is limited by the maximum dose that can be delivered prior to sample damage. In the proposed Serial Crystallography method, the damage problem is addressed by distributing the total dose over many identical hydrated macromolecules running continuously in a single-file train across a continuous X-ray beam, and resolution is then limited only by the available molecular and X-ray fluxes and molecular alignment. Orientation of the diffracting molecules is achieved by laser alignment. We evaluate the incident X-ray fluence (energy/area) required to obtain a given resolution from (1) an analytical model, giving the count rate at the maximum scattering angle for a model protein, (2) explicit simulation of diffraction patterns for a GroEL-GroES protein complex, and (3) the frequency cut off of the transfer function following iterative solution of the phase problem, and reconstruction of an electron density map in the projection approximation. These calculations include counting shot noise and multiple starts of the phasing algorithm. The results indicate counting time and the number of proteins needed within the beam at any instant for a given resolution and X-ray flux. We confirm an inverse fourth power dependence of exposure time on resolution, with important implications for all coherent Xray imaging. We find that multiple single-file protein beams will be needed for subnanometer resolution on current third generation synchrotrons, but not on fourth generation designs, where reconstruction of secondary protein structure at a resolution of 7 Å should be possible with short (below 100 s) exposures.

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Section: Introductionmentioning

confidence: 99%

Dose, exposure time and resolution in serial X-ray crystallography

Starodub

Rez

Hembree

et al. 2007

J Synchrotron Radiat

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“…We note that the absorbed dose per PSI crystal for a single 70 fs shot is significantly larger (about 405 MGy) than the recommended safe dose limit of 30 MGy for cryo-cooled protein crystals at a third-generation light source (Owen et al, 2006). The initial analysis of the PSI nanocrystal diffraction data described recently by Chapman et al (2011) demonstrates an apparent lack of radiation damage to a detectorlimited resolution of 0.9 nm when using 70 fs pulses or shorter, despite the subsequent destruction of the nanocrystals by the photoelectron cascade following termination of the XFEL pulse (Chapman et al, 2006).…”

Section: Figurementioning

confidence: 97%

“…A recent review of this approach for diffractive imaging, holography and crystallography is given elsewhere (Chapman, 2009). Experiments at the FLASH vacuum ultraviolet free-electron laser (FEL) confirmed this idea at resolution lengths greater than 6 nm (Chapman et al, 2006). However, until now, it had not been demonstrated that quantitative high-quality diffraction data can be extracted from the scattering of intense femtosecond X-ray pulses focused onto a protein nanocrystal or single particle, which would greatly enhance the prospects for structure determination using submicron crystals and for timeresolved crystallography.…”

Section: Introductionmentioning

confidence: 99%

Structure-factor analysis of femtosecond microdiffraction patterns from protein nanocrystals

Kirian

White

Holton

et al. 2011

Acta Crystallogr A Found Crystallogr

134

130

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A complete set of structure factors has been extracted from hundreds of thousands of femtosecond single-shot X-ray microdiffraction patterns taken from randomly oriented nanocrystals. The method of Monte Carlo integration over crystallite size and orientation was applied to experimental data from Photosystem I nanocrystals. This arrives at structure factors from many partial reflections without prior knowledge of the particle-size distribution. The data were collected at the Linac Coherent Light Source (the first hard-X-ray laser user facility), to which was fitted a hydrated protein nanocrystal injector jet, according to the method of serial crystallography. The data are single 'still' diffraction snapshots, each from a different nanocrystal with sizes ranging between 100 nm and 2 mm, so the angular width of Bragg peaks was dominated by crystal-size effects. These results were compared with single-crystal data recorded from large crystals of Photosystem I at the Advanced Light Source and the quality of the data was found to be similar. The implications for improving the efficiency of data collection by allowing the use of very small crystals, for radiation-damage reduction and for time-resolved diffraction studies at room temperature are discussed.

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“…Several XFELs have become operational since then and most of the technical problems were overcome. In recent publications (Chapman et al, 2006;Seibert et al, 2011;Martin et al, 2011), successful two-dimensional reconstructions of particles from XFEL experimental data were presented. Diffraction of an XFEL beam by nanocrystals demonstrated that three-dimensional atomic resolution structure of a protein can be determined from such experiments (Chapman et al, 2011;Boutet et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

Incorporating particle symmetry into orientation determination in single-particle imaging

Tegze

Bortel

2018

Acta Cryst Sect A

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In coherent-diffraction-imaging experiments X-ray diffraction patterns of identical particles are recorded. The particles are injected into the X-ray free-electron laser (XFEL) beam in random orientations. If the particle has symmetry, finding the orientation of a pattern can be ambiguous. With some modifications, the correlation-maximization method can find the relative orientations of the diffraction patterns for the case of symmetric particles as well. After convergence, the correlation maps show the symmetry of the particle and can be used to determine the symmetry elements and their orientations. The C factor, slightly modified for the symmetric case, can indicate the consistency of the assembled three-dimensional intensity distribution.

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On the Poincaré series of $H^*(BL(2,2^n),\mathbb{Z}/2)$

Cited by 7 publications

References 8 publications

Dose, exposure time and resolution in serial X-ray crystallography

Dose, exposure time and resolution in serial X-ray crystallography

Structure-factor analysis of femtosecond microdiffraction patterns from protein nanocrystals

Incorporating particle symmetry into orientation determination in single-particle imaging

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