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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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Probability of the observation Δψi given the model Δψmodel.
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fig4: Probability of the observation Δψi given the model Δψmodel.

Mentions: What is the likelihood P(data, i; model) of observing the angular offset Δψi given the model? According to the paradigm of (17), there is 100% likelihood thator, stated in other terms, the likelihood is a top-hat function (Fig. 4 ▶), It is clear that there is an optimal solution in which the Δψmodel envelope (see §3) is just large enough to include the observations. If /Δψmodel/ is too small, some observations will fall outside the envelope and the probability of the data Pi will be zero. Conversely, if /Δψmodel/ is too large, the probability (22) again approaches zero asymptotically. A potential problem is that the top-hat function (22) is not continuous and cannot be differentiated at the boundaries Δψmodel, so it is not suitable for iterative parameter-optimization techniques. We therefore modify the equation to include sigmoidal functions f and g that smoothly model the step-up and step-down discontinuities in the top-hat, respectively,


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)

Probability of the observation Δψi given the model Δψmodel.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig4: Probability of the observation Δψi given the model Δψmodel.
Mentions: What is the likelihood P(data, i; model) of observing the angular offset Δψi given the model? According to the paradigm of (17), there is 100% likelihood thator, stated in other terms, the likelihood is a top-hat function (Fig. 4 ▶), It is clear that there is an optimal solution in which the Δψmodel envelope (see §3) is just large enough to include the observations. If /Δψmodel/ is too small, some observations will fall outside the envelope and the probability of the data Pi will be zero. Conversely, if /Δψmodel/ is too large, the probability (22) again approaches zero asymptotically. A potential problem is that the top-hat function (22) is not continuous and cannot be differentiated at the boundaries Δψmodel, so it is not suitable for iterative parameter-optimization techniques. We therefore modify the equation to include sigmoidal functions f and g that smoothly model the step-up and step-down discontinuities in the top-hat, respectively,

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