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Macromolecular diffractive imaging using imperfect crystals


The three-dimensional structures of macromolecules and their complexes are mainly elucidated by X-ray protein crystallography. A major limitation of this method is access to high-quality crystals, which is necessary to ensure X-ray diffraction extends to sufficiently large scattering angles and hence yields information of sufficiently high resolution with which to solve the crystal structure. The observation that crystals with reduced unit-cell volumes and tighter macromolecular packing often produce higher-resolution Bragg peaks1,2 suggests that crystallographic resolution for some macromolecules may be limited not by their heterogeneity, but by a deviation of strict positional ordering of the crystalline lattice. Such displacements of molecules from the ideal lattice give rise to a continuous diffraction pattern that is equal to the incoherent sum of diffraction from rigid individual molecular complexes aligned along several discrete crystallographic orientations and that, consequently, contains more information than Bragg peaks alone3. Although such continuous diffraction patterns have long been observed—and are of interest as a source of information about the dynamics of proteins4—they have not been used for structure determination. Here we show for crystals of the integral membrane protein complex photosystem II that lattice disorder increases the information content and the resolution of the diffraction pattern well beyond the 4.5-ångström limit of measurable Bragg peaks, which allows us to phase5 the pattern directly. Using the molecular envelope conventionally determined at 4.5 ångströms as a constraint, we obtain a static image of the photosystem II dimer at a resolution of 3.5 ångströms. This result shows that continuous diffraction can be used to overcome what have long been supposed to be the resolution limits of macromolecular crystallography, using a method that exploits commonly encountered imperfect crystals and enables model-free phasing6,7.

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Figure 1: Lattice disorder reveals the continuous molecular transform.
Figure 2: Molecular coherent diffraction.
Figure 3: An unbiased size estimate of the rigid structural unit.
Figure 4: Improvement in resolution and quality of electron density.

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Accession codes

Primary accessions

Protein Data Bank

Data deposits

The coordinates of the atomic model obtained by molecular replacement from the Bragg peaks alone, and with the inclusion of continuous diffraction, have been deposited into the Protein Data Bank under accession codes 5E7C and 5E79, respectively.


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We acknowledge support of the Helmholtz Association through project-oriented funds and the Virtual Institute “Dynamic Pathways in Multidimensional Landscapes”; the DFG through the Gottfried Wilhelm Leibniz Program; the European Research Council under the European Union’s Seventh Framework Programme ERC Synergy Grant 609920 “AXSIS” and Marie Curie FP7-PEOPLE-2011-ITN Grant 317079 “Nanomem”; the BMBF through Project 05E13GU1; the Graduate College “GRK 1355” at the University of Hamburg, the International Max Planck Research School UFAST, the BioXFEL Science Technology Center (award 1231306); and the US National Institutes of Health (NIH), National Institute of General Medical Sciences grants R01 GM095583, U54 GM094599, and R01 GM097463. Parts of the sample injector used at the Linac Coherent Light Source (LCLS) for this research was funded by the NIH, P41GM103393, formerly P41RR001209. Use of the LCLS, SLAC National Accelerator Laboratory, is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under contract number DE-AC02-76SF00515.

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Authors and Affiliations



H.N.C. conceived the idea of molecular imaging using imperfect crystals, and developed it with K.A., A.B., O.M.Y., D.O., V.M., K.R.B. and L.G. K.A., A.B., O.M.Y., D.O., L.G. and V.M. carried out the diffractive imaging analysis. P.F. led the photosystem II project. Serial femtosecond crystallography measurements were led by P.F. and A.B. and performed with S.R.-C., J.C., C.K., D.O., M.M., A.S., K.D., D.J., G.N., U.W., Y.Z. and M.S. M.L., A.A., M.S.H., J.S.R., J.E.K. and S.Bo. set up and operated the CXI instrument. S.Ba., R.F., A.B. and M.M. performed on-site data evaluation at LCLS. S.Ba. and R.F. provided the initial search model and carried out model refinement on the image with D.O. Photosystem II was isolated by S.R.-C., J.C., C.E.C., A.S., C.K., A.S., J.-H.Y. and K.D., from which microcrystals were grown by S.R.-C., J.C., C.E.C., A.S. and C.K. Test experiments on crystals were performed by K.D., I.S., P.L.X. and M.M. H.N.C., A.B., K.A., O.M.Y., D.O., L.G., P.F., J.C.H.S., T.A.W., S.Ba. and S.Bo. wrote the manuscript with improvements from all authors.

Corresponding author

Correspondence to Henry N. Chapman.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Model refinement is improved at low resolution.

A plot of the metric Rfree as a function of resolution shell q, showing a marked improvement of the model refined against the 3.5-Å diffractive image. The blue curve shows Rfree prior to the inclusion of the continuous diffraction and the red curve shows Rfree afterwards. Here Rfree is calculated using only Bragg intensities (which were excluded from the refinement) for a resolution below 4.5 Å.

Extended Data Figure 2 Data quality and resolution of Bragg diffraction.

Plot of the reduced Pearson correlation coefficient, CC* (ref. 41), as an estimate of the consistency of the integrated Bragg intensities determined from 25,585 indexed patterns. A value of CC* = 0.5 is reached at q = 0.23 Å−1, or a resolution of 4.3 Å.

Extended Data Figure 3 Strongest continuous diffraction occurs with strongest Bragg diffraction.

a, Two-dimensional histogram of patterns, sorted by the integrated counts in the continuous component of the diffraction pattern (in a q range of 0.22–0.34 Å−1) and the integrated signal in all detected Bragg peaks, for all 25,585 indexed patterns. We chose the 2,848 patterns with the strongest continuous diffraction signal above 17 X-ray counts (purple line) in the q region to generate the 3D continuous pattern shown in Fig. 2c. The featureless background due to scattering from the solvent contributes 10 X-ray counts (blue line). b, The measurement from the liquid jet without crystals. c, d, Two representative patterns with speckle counts above the mean solvent background, but not above the threshold (c), and one of the 2,848 strongest patterns (d), as indicated by the positions of the yellow circles in a.

Extended Data Figure 4 Patterson function of a disordered lattice.

A distorted lattice (left, black circles, with ideal positions in grey), with vectors (red arrows) connecting all lattice points that have difference vectors anak = (1, 1). On the right, the arrows from the left panel are translated in two ways: upper right, the heads and tails are both displaced from their ideal positions; bottom right, the tails are lined up, resulting in the distribution of head positions forming a broader Gaussian. In the limit of a large crystal, the resultant distribution is the autocorrelation of the displacement distribution. This process can be repeated for all difference vectors, leading to equation (3).

Extended Data Figure 5 Continuous diffraction exhibits Wilson statistics.

Histogram of merged continuous intensities in a q range of 0.22–0.25 Å−1. Above a background level of around one photon per pixel per pulse, the logarithm of the histogram follows a linear trend with negative slope, characteristic of the exponential distribution predicted by Wilson statistics43.

Extended Data Figure 6 Central sections of the 3D full-pattern diffraction volume.

ac, Bragg intensities in planes normal to the three orthogonal reciprocal-space axes, qz, qy and qx, respectively, which were arbitrarily chosen to be parallel to the c*, b* and a* axes of the PSII crystal. The 4.5-Å extent of the Bragg peaks is indicated by the red circle. df, Full-pattern diffraction intensities in central sections normal to the same three orthogonal axes as in ac, respectively, obtained from that 2,848 strongest snapshot diffraction patterns. gi, Continuous diffraction intensities calculated for a single PSII dimer using the model refined from the 4.5-Å Bragg data, for the same set of orthogonal planes as in ac, respectively. The intensities were calculated from the incoherent sum of the squared modulus of the 3D molecular transform of a single (uncrystallized) PSII dimer in each of the four orientations of the 222 point group. All panels are plotted on the same scale, with the experimental data (df) extending to q = 0.33 Å−1 at the centre edge. The agreement between each of df with the corresponding panel gi is further evidence that the rigid structural unit is the PSII dimer.

Extended Data Figure 7 Real-space orthogonal slices.

ac, Slices of the observed structure factor (Fo) electron density map, plotted as a grey scale, of a single PSII dimer obtained from the 4.5-Å Bragg intensities following model refinement of that data. Each slice is one pixel thick (1.5 Å) and is normal to the z, y and x real-space axes, respectively (conjugate to qz, qy and qx). df, Slices through the 3D real-space support constraint used to for iterative phasing. The support was generated by blurring the 4.5-Å-resolution electron density map by 2.2 Å and then thresholding to achieve a binary mask. gi, Slices through the 3.5-Å-resolution image obtained by iterative phasing of the continuous diffraction, using the support constraint illustrated in df and Fig. 3d.

Extended Data Figure 8 The continuous pattern is consistent with diffraction from a rigid object in crystallographic orientations.

a, When the continuous diffraction intensities are substituted for intensities averaged over all orientations (that is, constant on surfaces of constant q), iterative phasing using the support constraint of Fig. 3d fails, as indicated by this plot of the FSC as a function of resolution for solutions (green) obtained from two independent phasing trials. The blue curve is the same FSC shown in Fig. 3e for comparison. The iterations never converged, so a phase retrieval transfer function for the control could not be generated. b, Plot of the cross correlation (CC) between the measured diffraction and that calculated from the determined electron density of a dimer, symmetrized by the four crystallographic orientations.

Extended Data Figure 9 Electron density maps of regions of the PSII dimer.

af, Electron density maps based on maximum likelihood structure factors (2mFo-DFc) obtained using the Bragg diffraction (model shaded green, left), the Bragg and continuous diffraction (model shaded blue, middle) and computed from pseudo-crystal refinement (model shaded brown, right). The maps are rendered at various density levels relative to the standard deviation of the overall density. a, b, Non-haem iron coordinated by two His residues from D1 (chain A) and two from D2 (chain D), contoured at 1.5σ (a) and 4σ (b). Neighbouring Tyr and Lys residues are displayed as well. c, Part of an α-helix (chain T), showing that the side chains (for example, Arg and Phe) fit better in the electron density when applying our new method (maps contoured at 1.5σ). d, Helices from chains Y and Z (maps contoured at 1.25σ). The density map shows more details and better agreement to the model when applying the analysis using the Bragg and continuous diffraction. e, Detailed view of a section of chain Z (maps contoured at 1.25σ). Using only the Bragg diffraction, no electron density is visible at this level around the side chains of Trp, Lys and Arg. Again, the model fits better into the map when using the continuous diffraction. f, Two chlorophylls and part of the transmembrane helix of chain C (maps contoured at 1.5σ). g, Matrix of Pearson correlation coefficients of electron density maps obtained from the model presented in ref. 2 (PDB, 3WU2), the model refined from Bragg diffraction and that obtained from the continuous diffraction.

Extended Data Table 1 Data collection, phasing and refinement

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Ayyer, K., Yefanov, O., Oberthür, D. et al. Macromolecular diffractive imaging using imperfect crystals. Nature 530, 202–206 (2016).

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