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Improved crystal orientation and physical properties from single-shot XFEL stills.

Sauter NK, Hattne J, Brewster AS, Echols N, Zwart PH, Adams PD - Acta Crystallogr. D Biol. Crystallogr. (2014)

Bottom Line: This hinders the ability to recover accurate structure factors from experiments that are dependent on single-shot exposures, such as femtosecond diffract-and-destroy protocols at X-ray free-electron lasers (XFELs).Here, additional methods are introduced to optimally model the diffraction.This approach reduces the experimental uncertainties in noisy XFEL data, improving the crystallographic R factors and sharpening anomalous differences that are near the level of the noise.

View Article: PubMed Central - HTML - PubMed

Affiliation: Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.

ABSTRACT
X-ray diffraction patterns from still crystals are inherently difficult to process because the crystal orientation is not uniquely determined by measuring the Bragg spot positions. Only one of the three rotational degrees of freedom is directly coupled to spot positions; the other two rotations move Bragg spots in and out of the reflecting condition but do not change the direction of the diffracted rays. This hinders the ability to recover accurate structure factors from experiments that are dependent on single-shot exposures, such as femtosecond diffract-and-destroy protocols at X-ray free-electron lasers (XFELs). Here, additional methods are introduced to optimally model the diffraction. The best orientation is obtained by requiring, for the brightest observed spots, that each reciprocal-lattice point be placed into the exact reflecting condition implied by Bragg's law with a minimal rotation. This approach reduces the experimental uncertainties in noisy XFEL data, improving the crystallographic R factors and sharpening anomalous differences that are near the level of the noise.

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Two methods for fitting the mosaicity and mosaic block size. Δψ values for bright spots from a single thermolysin still image (blue circles) are plotted as a function of the diffraction angle 2θ, which is inversely related to the resolution d by Bragg’s law. A wider spread of Δψ values is observed at low 2θ. The best integrated intensities are obtained by finding the function Δψmodel (green curve) that minimally envelopes the spots. (16) breaks Δψmodel into a resolution-dependent term containing the effective mosaic block size Deff (inner red curve) and a peripheral zone of constant width determined by the effective mosaic spread η. Alternate algorithms determine these parameters either by (a) least-squares fit of the /Δψ/max values determined for resolution bins or (b) maximum-likelihood treatment of all of the data. Approach (b) consistently gives more realistic fits with smaller η and larger Deff values. Plots reflect refinement results from protocol 6 (Table 2 ▶).
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fig7: Two methods for fitting the mosaicity and mosaic block size. Δψ values for bright spots from a single thermolysin still image (blue circles) are plotted as a function of the diffraction angle 2θ, which is inversely related to the resolution d by Bragg’s law. A wider spread of Δψ values is observed at low 2θ. The best integrated intensities are obtained by finding the function Δψmodel (green curve) that minimally envelopes the spots. (16) breaks Δψmodel into a resolution-dependent term containing the effective mosaic block size Deff (inner red curve) and a peripheral zone of constant width determined by the effective mosaic spread η. Alternate algorithms determine these parameters either by (a) least-squares fit of the /Δψ/max values determined for resolution bins or (b) maximum-likelihood treatment of all of the data. Approach (b) consistently gives more realistic fits with smaller η and larger Deff values. Plots reflect refinement results from protocol 6 (Table 2 ▶).

Mentions: Once the crystal orientation has been refined as above, the residual values of Δψ clearly show the mosaic structure of crystals when plotted against the diffraction angle (Fig. 7 ▶). The average block sizes of the mosaic domain Deff are reflected in the wide spread of Δψ residuals observed at low resolution (14), while the narrow taper at high resolution is a measure of the effective mosaicity angle η (13). Indeed, it is critical to derive correct values for these parameters when modeling an image; an overall envelope Δψmodel that is too narrow will fail to include real Bragg spot signals, while an overly wide envelope will falsely predict Bragg spots, thus mixing Gaussian noise into the average structure factors. Of the two methods evaluated for determining η and Deff, the maximum-likelihood approach (Fig. 7 ▶b) consistently outperformed the least-squares method (Fig. 7 ▶a) and was ultimately adopted for all of the data presented in Tables 1 ▶ and 2 ▶. This judgment was based on lower η for the simulated PSI data set (which ideally should be 0°), a lower percentage of negative measurements for both data sets, better structure-factor quality tests, better crystallographic R factors for the thermolysin structure refinement and higher significance levels for the Zn2+ anomalous peak (data not shown).


Improved crystal orientation and physical properties from single-shot XFEL stills.

Sauter NK, Hattne J, Brewster AS, Echols N, Zwart PH, Adams PD - Acta Crystallogr. D Biol. Crystallogr. (2014)

Two methods for fitting the mosaicity and mosaic block size. Δψ values for bright spots from a single thermolysin still image (blue circles) are plotted as a function of the diffraction angle 2θ, which is inversely related to the resolution d by Bragg’s law. A wider spread of Δψ values is observed at low 2θ. The best integrated intensities are obtained by finding the function Δψmodel (green curve) that minimally envelopes the spots. (16) breaks Δψmodel into a resolution-dependent term containing the effective mosaic block size Deff (inner red curve) and a peripheral zone of constant width determined by the effective mosaic spread η. Alternate algorithms determine these parameters either by (a) least-squares fit of the /Δψ/max values determined for resolution bins or (b) maximum-likelihood treatment of all of the data. Approach (b) consistently gives more realistic fits with smaller η and larger Deff values. Plots reflect refinement results from protocol 6 (Table 2 ▶).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4257623&req=5

fig7: Two methods for fitting the mosaicity and mosaic block size. Δψ values for bright spots from a single thermolysin still image (blue circles) are plotted as a function of the diffraction angle 2θ, which is inversely related to the resolution d by Bragg’s law. A wider spread of Δψ values is observed at low 2θ. The best integrated intensities are obtained by finding the function Δψmodel (green curve) that minimally envelopes the spots. (16) breaks Δψmodel into a resolution-dependent term containing the effective mosaic block size Deff (inner red curve) and a peripheral zone of constant width determined by the effective mosaic spread η. Alternate algorithms determine these parameters either by (a) least-squares fit of the /Δψ/max values determined for resolution bins or (b) maximum-likelihood treatment of all of the data. Approach (b) consistently gives more realistic fits with smaller η and larger Deff values. Plots reflect refinement results from protocol 6 (Table 2 ▶).
Mentions: Once the crystal orientation has been refined as above, the residual values of Δψ clearly show the mosaic structure of crystals when plotted against the diffraction angle (Fig. 7 ▶). The average block sizes of the mosaic domain Deff are reflected in the wide spread of Δψ residuals observed at low resolution (14), while the narrow taper at high resolution is a measure of the effective mosaicity angle η (13). Indeed, it is critical to derive correct values for these parameters when modeling an image; an overall envelope Δψmodel that is too narrow will fail to include real Bragg spot signals, while an overly wide envelope will falsely predict Bragg spots, thus mixing Gaussian noise into the average structure factors. Of the two methods evaluated for determining η and Deff, the maximum-likelihood approach (Fig. 7 ▶b) consistently outperformed the least-squares method (Fig. 7 ▶a) and was ultimately adopted for all of the data presented in Tables 1 ▶ and 2 ▶. This judgment was based on lower η for the simulated PSI data set (which ideally should be 0°), a lower percentage of negative measurements for both data sets, better structure-factor quality tests, better crystallographic R factors for the thermolysin structure refinement and higher significance levels for the Zn2+ anomalous peak (data not shown).

Bottom Line: This hinders the ability to recover accurate structure factors from experiments that are dependent on single-shot exposures, such as femtosecond diffract-and-destroy protocols at X-ray free-electron lasers (XFELs).Here, additional methods are introduced to optimally model the diffraction.This approach reduces the experimental uncertainties in noisy XFEL data, improving the crystallographic R factors and sharpening anomalous differences that are near the level of the noise.

View Article: PubMed Central - HTML - PubMed

Affiliation: Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.

ABSTRACT
X-ray diffraction patterns from still crystals are inherently difficult to process because the crystal orientation is not uniquely determined by measuring the Bragg spot positions. Only one of the three rotational degrees of freedom is directly coupled to spot positions; the other two rotations move Bragg spots in and out of the reflecting condition but do not change the direction of the diffracted rays. This hinders the ability to recover accurate structure factors from experiments that are dependent on single-shot exposures, such as femtosecond diffract-and-destroy protocols at X-ray free-electron lasers (XFELs). Here, additional methods are introduced to optimally model the diffraction. The best orientation is obtained by requiring, for the brightest observed spots, that each reciprocal-lattice point be placed into the exact reflecting condition implied by Bragg's law with a minimal rotation. This approach reduces the experimental uncertainties in noisy XFEL data, improving the crystallographic R factors and sharpening anomalous differences that are near the level of the noise.

Show MeSH
Related in: MedlinePlus