Enabling X-ray free electron laser crystallography for challenging biological systems from a limited number of crystals
- Stanford University, United States
- Janelia Research Campus, United States
- Lawrence Berkeley National Laboratory, United States
- Howard Hughes Medical Institute, Stanford University, United States
Figures
Figure 1
Geometry of the diffraction experiment and calculation of the Ewald-offset distance, rh.
(A) A reciprocal lattice point intersects the Ewald sphere. The inset shows the coordinate system used in cctbx.xfel and prime. The vector S0 represents the direction of the incident beam (–z-axis) …
Figure 2
Post-refinement protocol.
The flowchart illustrates the iterative post-refinement protocol, broken up into ‘microcycles’ that refine groups of parameters iteratively (blue boxes), and ‘macrocycles’. At the beginning of first …
Figure 3
Post-refinement during the first macrocycle of post-refinement for myoglobin.
Shown are the values of the refined parameters and target functions during the first macrocycle of post-refinement for a representative diffraction image of the myoglobin XFEL diffraction data set. …
Figure 4
Convergence of post-refinement after five macrocycles for myoglobin.
The plots illustrate the convergence of post-refined parameters, target functions, and quality indicators during post-refinement over five macrocycles. A subset of 100 randomly selected diffraction …
Figure 5
Merging statistics for myoglobin.
(A) Percent completeness and (B) average number of observations plotted as a function of resolution for the myoblogin XFEL diffraction data set consisting of all 757 diffraction images (Table 1) and …
Figure 6
Impact of post-refinement and number of images on electron density and model quality for myoglobin.
(A) Difference Fourier (mFo-DFc) omit maps around the heme group (which was omitted from molecular replacement and atomic model refinement) for the averaged merged, the mean-scaled …
Figure 7
Quality of synchrotron vs. post-refined XFEL diffraction data sets for myoglobin.
Difference Fourier (mFo-DFo) omit maps at 1.35 Å around the heme group (which was omitted from molecular replacement and model refinement), generated from (A) the synchrotron diffraction data and …
Figure 8
Impact of post-refinement on the hydrogenase diffraction data set.
(A) Difference Fourier (mFo-DFc) omit maps of one of the four Fe-S clusters (which were omitted in molecular replacement and atomic model refinement) for the averaged merged and the post-refined …
Figure 9
Impact of post-refinement on the anomalous signal in the thermolysin diffraction dataset.
Anomalous difference Fourier maps for the averaged merged (A, C) or the post-refined (B, D) thermolysin XFEL diffraction data sets consisting of all 12,692 diffraction images (A, B—Table 1) and a …
Figure 10
Impact of post-refinement on the quality of electron density maps and models of thermolysin.
(A) Difference Fourier (mFo-DFc) maps revealing a Leu–Lys dipeptide near the zinc site for the averaged merged and the post-refined thermolysin XFEL diffraction data sets consisting of all 12,692 …
Figure 11
Convergence of structure refinements for the post-refined thermolysin XFEL data set at 2.6 Å resolution, using increasing numbers of diffraction images.
(A) Average number of observations per unique hkl. (B) CC1/2 for merged subsets using 2000–12,000 images (100% completeness for all subsets). (C) Peak height (σ) in the omit map for the largest …
Figure 12
Distribution of the Ewald sphere offset rh.
The histogram shows the distribution of rh calculated after post-refinement for myoglobin using 757 diffraction images. The number of observations after applying the reflection selection criteria …
Figure 13
The Ewald-offset correction function.
(A) Ewald-offset correction Eoc (Equation 14) viewed as a function of the reciprocal-lattice radius (rs) and the offset distance (rh). (B) A slice through Eoc at rs = 0.003, comparing Eoc (Equation …
Figure 14
Geometry of the incident and diffracted beam for polarization correction.
The diagram shows a reflection on a plane formed by its reciprocal-space vector and the -z-axis at angle . This reflection is affected by the polarization of the incoming primary beam in both the …
Tables
Table 1
XFEL diffraction data sets used in this study
| Myoglobin | Clostridium pasteurianum hydrogenase | Thermolysin | |
|---|---|---|---|
| Space group | P6 | P42212 | P6122 |
| Resolution used (Å) | 20.0–1.35 | 45.0–1.60 | 50.0–2.10 |
| Unit cell dimensions (Å) | a = b = 90.8, c = 45.6 | a = b = 111.2, c = 103.8 | a = b = 92.7, c = 130.5 |
| No. of unique reflections | 46,555 | 85,273 | 19,995 |
| No. of images* indexed | 757 | 177 | 12,692 |
| No. of images with spots to resolution used | 307 | 75 | 1957 |
| Average no. of spots on an image (to resolution used) | 1628 | 3640 | 352 |
| Energy spectrum | SASE† | SASE† | SASE† |
| Detector | Rayonix MX325HE | Rayonix MX325HE | CSPAD‡ |
| Sample delivery method | fixed target | fixed target | Electrospun jet |
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*
This is the number of images indexed using cctbx.xfel program, and in the case of thermolysin it is the number of images indexed for one of the two wavelengths.
-
†
SASE: self-amplified spontaneous emission.
-
‡
CSPAD: Cornell-SLAC pixel array detector.
Table 2
Statistics of post-refinement and atomic model refinement for myoglobin
| No. images | 100 | 757 | ||||
| Resolutiona (Å) | 20.0–1.35 (1.40–1.35) | 20.0–1.35 (1.40–1.35) | ||||
| Completenessa (%) | 80.0 (22.2) | 97.7 (79.8) | ||||
| Average no. observations per unique hkla | 4.0 (1.2) | 25.7 (2.0) | ||||
| Averaged-merged | Mean-scaled partiality corrected | Post-refined | Averaged merged | Mean-scaled partiality corrected | Post-refined | |
| Post-refinement parametersb | ||||||
| Linear scale factor G0 | 1.00 (0.00) | 2.79 (5.02) | 1.00 (1.04) | 1.00 (0.00) | 2.19 (3.83) | 0.89 (1.07) |
| B | 0.0 (0.0) | 0.0 (0.0) | 3.2 (7.8) | 0.0 (0.0) | 0.0 (0.0) | 6.2 (8.3) |
| γ0 (Å−1) | NA | 0.00135 (0.00028) | 0.00128 (0.00022) | NA | 0.00147 (0.00042) | 0.00132 (0.00034) |
| γy (Å−1) | NA | 0.00 (0.00) | 0.00007 (0.00080) | NA | 0.00 (0.00) | 0.00007 (0.00009) |
| γx (Å−1) | NA | 0.00 (0.00) | 0.00010 (0.00011) | NA | 0.00 (0.00) | 0.00008 (0.00010) |
| γe (Å−1) | NA | 0.00200 (0.00) | 0.00344 (0.00266) | NA | 0.00200 (0.00) | 0.00423 (0.00323) |
| Unit cell | ||||||
| a (Å): | 90.4 (0.4) | 90.4 (0.4) | 90.5 (0.4) | 90.4 (0.4) | 90.4 (0.4) | 90.5 (0.3) |
| c (Å) | 45.3 (0.4) | 45.3 (0.4) | 45.3 (0.3) | 45.3 (0.3) | 45.3 (0.3) | 45.3 (0.3) |
| Average Tpr Start/End | NA | NA | 19.39 (7.68)/7.17 (3.38) | NA | NA | 19.83 (7.54)/6.02 (2.59) |
| Average Txy (mm2) Start/End | NA | NA | 169.74 (132.56)/132.02 (104.08) | NA | NA | 170.66 (144.52)/133.42 (109.58) |
| CC1/2 (%) | 81.3 | 79.6 | 86.5 | 91.8 | 95.7 | 98.2 |
| Molecular replacement scoresc | ||||||
| LLG | 2837. | 5043. | 5291. | 8264. | 8364. | 9320. |
| TFZ | 10.5 | 13.0 | 13.4 | 13.7 | 13.8 | 14.0 |
| Structure-refinement parameters | ||||||
| R (%) | 39.4 | 28.0 | 23.5 | 21.1 | 20.3 | 17.8 |
| Rfree (%) | 42.1 | 29.4 | 24.8 | 23.1 | 22.5 | 19.7 |
| Bond r.m.s.d. | 0.006 | 0.006 | 0.004 | 0.006 | 0.006 | 0.006 |
| Angle r.m.s.d. | 1.14 | 0.98 | 0.79 | 1.03 | 1.35 | 0.86 |
| Ramachandran statistics | ||||||
| Favored (%) | 98.0 | 98.0 | 98.0 | 98.0 | 98.0 | 98.0 |
| Outliers (%) | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
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a
Values in parentheses correspond to highest resolution shell.
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b
Post-refined parameters are shown as the mean value, with the standard deviation in parentheses.
-
c
Molecular replacement scores reported by Phaser (McCoy et al., 2007): log-likelihood gain (LLG) and translation function (TFZ).
Table 3
Statistics of post-refinement and atomic model refinement for hydrogenase
| No. images | 100 | 177 | ||
| Resolutiona (Å) | 45.0–1.60 (1.66–1.60) | 45.0–1.60 (1.66–1.60) | ||
| Completenessa (%) | 83.0 (47.7) | 91.2 (63.5) | ||
| Average no. observations per unique hkla | 4.4 (1.7) | 7.13 (2.3) | ||
| Averaged-merged | Post-refined | Averaged-merged | Post-refined | |
| Post-refinement parametersb | ||||
| Linear scale factor G0 | 1.00 (0.00) | 0.56 (1.27) | 1.00 (0.00) | 0.53 (1.22) |
| B | 0.0 (0.0) | 10.0 (7.0) | 0.0 (0.0) | 10.5 (6.9) |
| γ0 (Å−1) | NA | 0.00132 (0.00042) | NA | 0.00126 (0.00041) |
| γy (Å−1) | NA | 0.00002 (0.00004) | NA | 0.00002 (0.00004) |
| γx (Å−1) | NA | 0.00008 (0.00009) | NA | 0.00008 (0.00011) |
| γe (Å−1) | NA | 0.00269 (0.00138) | NA | 0.00288 (0.00160) |
| Unit cell | ||||
| a (Å): | 110.1 (0.4) | 110.4 (0.3) | 110.1 (0.4) | 110.3 (0.4) |
| c (Å) | 103.1 (0.4) | 103.1 (0.2) | 103.0 (0.4) | 103.0 (0.2) |
| Average Tpr Start/End | NA | 28.20 (10.86)/5.92 (2.35) | NA | 26.47 (12.70)/5.22 (2.72) |
| Average Txy (mm2) Start/End | NA | 623.36 (314.57)/381.23 (198.44) | NA | 564.30 (267.45)/ 372.28 (202.28) |
| CC1/2 (%) | 62.0 | 77.3 | 71.7 | 84.8 |
| Molecular replacement scoresc | ||||
| LLG | 53,352. | 9612. | 7229. | 11774. |
| TFZ | 69.2 | 75.9 | 75.0 | 79.0 |
| Structure-refinement parameters | ||||
| R (%) | 33.4 | 25.3 | 29.1 | 22.0 |
| Rfree (%) | 36.7 | 28.9 | 31.3 | 25.0 |
| Bond r.m.s.d. | 0.006 | 0.007 | 0.007 | 0.007 |
| Angle r.m.s.d. | 1.43 | 1.50 | 1.68 | 1.97 |
| Ramachandran statistics | ||||
| Favored (%) | 96.3 | 97.0 | 97.0 | 96.7 |
| Outliers (%) | 0.0 | 0.0 | 0.0 | 0.0 |
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a
Values in parentheses correspond to highest resolution shell.
-
b
Post-refined parameters are shown as the mean value, with the standard deviation in parentheses.
-
c
Molecular replacement scores reported by Phaser (McCoy et al., 2007): log-likelihood gain (LLG) and translation function (TFZ).
Table 4
Statistics of post-refinement and atomic model refinement for thermolysin
| No. images | 2000 | 12,692 | ||
| Resolutiona (Å) | 50.0–2.10 (2.18–2.10) | 50.0–2.10 (2.18–2.10) | ||
| Completenessa (%) | 81.3 (24.3) | 96.5 (74.8) | ||
| Average no. observations per unique hkla | 32.8 (1.2) | 176.6 (2.4) | ||
| Averaged-merged | Post-refined | Averaged-merged | Post-refined | |
| Post-refinement parametersb | ||||
| Linear scale factor G0 | 1.00 (0.00) | 1.65 (1.66) | 1.00 (0.00) | 2.26 (75.12) |
| B | 0.0 (0.0) | 23.0 (33.8) | 0.0 (0.0) | 30.1 (59.8) |
| γ0 (Å−1) | NA | 0.00052 (0.00040) | NA | 0.00051 (0.00039) |
| γy (Å−1) | NA | 0.00001 (0.00003) | NA | 0.00001 (0.00003) |
| γx (Å−1) | NA | 0.00002 (0.00004) | NA | 0.00002 (0.00004) |
| γe (Å−1) | NA | 0.00110 (0.00129) | NA | 0.00103 (0.00128) |
| Unit cell | ||||
| a (Å): | 92.9 (0.3) | 92.9 (0.2) | 92.9 (0.3) | 92.9 (0.3) |
| c (Å) | 130.5 (0.5) | 130.4 (0.4) | 130.5 (0.5) | 130.4 (0.4) |
| Average Tpr Start/End | NA | 1.15 (0.49)/0.55 (0.23) | NA | 1.15 (0.52)/0.28 (0.13) |
| Average Txy (mm2) Start/End | NA | 168.13 (117.29)/167.72 (106.14) | NA | 169.01 (122.20)/170.00 (122.57) |
| CC1/2 (%) | 77.7 | 93.5 | 94.3 | 98.8 |
| Molecular replacement scoresc | ||||
| LLG | 3590. | 4491. | 5477. | 6022. |
| TFZ | 8.9 | 9.7 | 24.1 | 24.6 |
| Structure-refinement parameters | ||||
| R (%) | 25.2 | 19.5 | 20.7 | 18.4 |
| Rfree (%) | 29.1 | 24.0 | 23.9 | 21.1 |
| Bond r.m.s.d. | 0.004 | 0.002 | 0.002 | 0.002 |
| Angle r.m.s.d. | 0.75 | 0.58 | 0.59 | 0.62 |
| Ramachandran statistics | ||||
| Favored (%) | 95.9 | 94.6 | 95.2 | 94.9 |
| Outliers (%) | 0.0 | 0.0 | 0.0 | 0.0 |
| Zinc peak height | ||||
| Zn(1) (σ) | 14.0 | 16.0 | 14.3 | 20.9 |
| Zn(2) (σ) | 3.6 | 5.1 | 7.7 | 7.1 |
| Average peak height for calcium ions (σ) | 9.7 | 11.3 | 14.2 | 16.1 |
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a
Values in parentheses correspond to highest resolution shell.
-
b
Post-refined parameters are shown as the mean value, with the standard deviation in parentheses.
-
c
Molecular replacement scores reported by Phaser (McCoy et al., 2007): log-likelihood gain (LLG) and translation function (TFZ).
