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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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The construction of Δψ. As stated in the text, the sign of the rotation Δψ bringing Q onto the Ewald sphere is considered to be negative if Q is outside the sphere (as shown) or positive if it is inside.
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fig3: The construction of Δψ. As stated in the text, the sign of the rotation Δψ bringing Q onto the Ewald sphere is considered to be negative if Q is outside the sphere (as shown) or positive if it is inside.

Mentions: To prevent divergence while numerically optimizing the crystal orientation from still shots, we have followed the example of other authors (Jones et al., 1977 ▶, Kabsch, 2014 ▶) by introducing an additional restraint that keeps model spots as close to the diffracting condition as possible (Fig. 2 ▶). For each observed Bragg spot, we define Δψcalc as the magnitude of the rotation that most directly brings the modeled spot centroid from an approximate to an exact diffraction condition (Fig. 3 ▶). The model is then optimized using the new least-squares minimization targetIn the hybrid target (2), rcalc has a direct dependence on Rz, while Δψcalc depends on Rx and Ry; therefore, all three misorientation angles can be properly optimized. It is important to note the distinction between Δψcalc and the similar angle Δϕ used in synchrotron experiments, which represents the difference in goniometer rotation angle ϕ between the observed and modeled spot centroids. The still shots discussed here do not employ a goniometer spindle, so instead of bringing the reciprocal-lattice point into a reflecting condition by an angular rotation Δϕ around a physical spindle, we simply construct a rotation axis (different for each Bragg spot; Fig. 3 ▶) that brings the model centroid into the reflection condition with the smallest possible angle Δψcalc.


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)

The construction of Δψ. As stated in the text, the sign of the rotation Δψ bringing Q onto the Ewald sphere is considered to be negative if Q is outside the sphere (as shown) or positive if it is inside.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig3: The construction of Δψ. As stated in the text, the sign of the rotation Δψ bringing Q onto the Ewald sphere is considered to be negative if Q is outside the sphere (as shown) or positive if it is inside.
Mentions: To prevent divergence while numerically optimizing the crystal orientation from still shots, we have followed the example of other authors (Jones et al., 1977 ▶, Kabsch, 2014 ▶) by introducing an additional restraint that keeps model spots as close to the diffracting condition as possible (Fig. 2 ▶). For each observed Bragg spot, we define Δψcalc as the magnitude of the rotation that most directly brings the modeled spot centroid from an approximate to an exact diffraction condition (Fig. 3 ▶). The model is then optimized using the new least-squares minimization targetIn the hybrid target (2), rcalc has a direct dependence on Rz, while Δψcalc depends on Rx and Ry; therefore, all three misorientation angles can be properly optimized. It is important to note the distinction between Δψcalc and the similar angle Δϕ used in synchrotron experiments, which represents the difference in goniometer rotation angle ϕ between the observed and modeled spot centroids. The still shots discussed here do not employ a goniometer spindle, so instead of bringing the reciprocal-lattice point into a reflecting condition by an angular rotation Δϕ around a physical spindle, we simply construct a rotation axis (different for each Bragg spot; Fig. 3 ▶) that brings the model centroid into the reflection condition with the smallest possible angle Δψcalc.

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