research papers
Structure-factor amplitude reconstruction from serial femtosecond crystallography of two-dimensional membrane-protein crystals
aPaul Scherrer Institute, 5232 Villigen PSI, Switzerland, bCenter for Free-Electron Laser Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany, cLawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, USA, dLinac Coherent Light Source, 2575 Sand Hill Road, Menlo Park, CA 94025, USA, eNational Science Foundation BioXFEL Science and Technology Center, 700 Ellicott Street, Buffalo, NY 14203, USA, and fNSLS-II, Brookhaven National Laboratory, PO Box 5000, Upton, NY 11973, USA
*Correspondence e-mail: bill.pedrini@psi.ch
Serial femtosecond crystallography of two-dimensional membrane-protein crystals at X-ray free-electron lasers has the potential to address the dynamics of functionally relevant large-scale motions, which can be sterically hindered in three-dimensional crystals and suppressed in cryocooled samples. In previous work, diffraction data limited to a two-dimensional reciprocal-space slice were evaluated and it was demonstrated that the low intensity of the diffraction signal can be overcome by collecting highly redundant data, thus enhancing the achievable resolution. Here, the application of a newly developed method to analyze diffraction data covering three reciprocal-space dimensions, extracting the reciprocal-space map of the structure-factor amplitudes, is presented. Despite the low resolution and completeness of the data set, it is shown by
that the reconstructed amplitudes carry meaningful structural information. Therefore, it appears that these intrinsic limitations in resolution and completeness from two-dimensional crystal diffraction may be overcome by collecting highly redundant data along the three reciprocal-space axes, thus allowing the measurement of large-scale dynamics in pump–probe experiments.Keywords: free-electron lasers; serial femtosecond crystallography; membrane proteins; two-dimensional crystals.
1. Introduction
The ultrashort and ultrabright pulses provided by hard X-ray free-electron lasers (XFELs) have enabled innovative experimental investigation methods to address new scientific problems. In the field of macromolecular crystallography, which traditionally uses three-dimensional crystals as samples, the femtosecond et al., 2011; Barty et al., 2011; Nass et al., 2015), making measurements at room temperature and/or with smaller and smaller crystals (to the submicrometre range) possible (Gati et al., 2017). On the other hand, structural dynamics at 1–3 Å resolution that can be triggered externally, such as side-chain movements or cofactor isomerizations, become accessible on the femtoscond time scale by pump–probe experiments (Kern et al., 2014; Kupitz et al., 2014; Tenboer et al., 2014; Barends et al., 2015; Nango et al., 2016; Nogly et al., 2016; Young et al., 2016; Suga et al., 2017) and on the millisecond timescale by mix-and-inject experiments (Stagno et al., 2016; Olmos et al., 2018). Because each crystal is destroyed by the interaction with the X-ray pulse, the single-shot diffraction data have to be recorded from a large number of crystals to achieve sufficient completeness and redundancy. This data-acquisition strategy is called serial femtosecond crystallography (SFX). The crystals are delivered to the beam within a running liquid or viscous jet (Chapman et al., 2011; Boutet et al., 2012; Weierstall et al., 2014) or by a solid support that is scanned through the beam (Hunter et al., 2014; Cohen et al., 2014; Roedig et al., 2017). From the data-analysis point of view, the main challenge to be solved was the merging of diffraction patterns from crystals of different sizes and in random orientations illuminated by X-ray pulses of variable intensity and wavelength (White et al., 2012; Sauter et al., 2013; Neutze et al., 2015; Schlichting, 2015).
on one hand allows most radiation damage to be outrun (LombConformational changes at larger length scales of 3–6 Å are more challenging for investigation with three-dimensional crystals because the motions may be sterically hindered (Kühlbrandt, 2000). If available, two-dimensional crystals represent an opportunity because of the looser intermolecular contacts owing to the single layer of molecules. Membrane proteins are definitely the most relevant candidates (Stahlberg et al., 2001) because their function typically involves such structural modifications (see, for example, Subramaniam & Henderson, 2000) and because the arrangement in two dimensions more closely mimics the environment on the cell membrane. When the relevant structural modifications take place on submillisecond timescales, investigations by and electron diffraction on samples whose dynamics have been frozen by flash-cooling are difficult (Subramaniam & Henderson, 1999). This opens a niche for SFX on two-dimensional crystals in pump–probe mode.
The diffraction signal of two-dimensional crystals is markedly lower than for analogous three-dimensional crystals with the same dimensions because the diffracting volume is orders of magnitude smaller and the reciprocal-space region that generates the diffraction is not concentrated in Bragg points but is diluted over one-dimensional Bragg rods. Because of the weak signal and the ill-effects of radiation damage, measuring high-resolution diffraction data from two-dimensional protein crystals at a continuous X-ray source is extremely challenging. Data collection at an XFEL represents a viable alternative (Frank et al., 2014; Pedrini et al., 2014). In recent work, we showed that the signal-to-noise ratio of the diffracted intensities is substantially enhanced by summing equivalent portions of images across the data set (Casadei et al., 2018). In this way, the resolution of a highly redundant data set collected in November 2013 from two-dimensional bacteriorhodopsin crystals at zero tilt angle, i.e. with the incoming X-ray beam perpendicular to the crystal plane, could be extended from about 6 Å to the detector edge at 4 Å.
With zero-tilt data only a reciprocal-space slice is sampled, corresponding to two points on each Bragg rod. During the same November 2013 beamtime, we also collected data at a few different nonzero tilt angles, which cover three dimensions in et al., 2008) indicate that, despite their low completeness and the limited resolution of about 6 Å, the experimental data contain meaningful structural information. The measures required to improve the data quality, which are crucial to follow structural dynamics in future pump–probe experiments, are then discussed.
and led to a genuine three-dimensional data set. We report here on the application of a novel method to merge the diffraction images and determine the structure-factor amplitudes along the Bragg rods. These were then phased by The composite OMIT maps (Terwilliger2. Results
2.1. Bragg rod intensity reconstruction
Sets of 1000 diffraction images of two-dimensional bacteriorhodopsin D96N mutant crystals were collected at the CXI experimental station of the LCLS free-electron laser at three different tilt angles η = 5, 15 and 20°. The diffraction images were analyzed assuming p3 symmetry (planar 13) of the crystal (Henderson et al., 1990), with two unit-cell vectors of equal length a forming an angle γ of 120°. The corresponding two-dimensional reciprocal-space is spanned by two vectors of length 2π/a forming an angle of 60°. With the further assumption that Friedel symmetry of the diffraction intensity is valid, it follows that the of the structure-factor amplitudes, and thus of the diffracted intensity, is S6.
The data-analysis pipeline to calculate the structure-factor amplitudes consists of eight subsequent steps, which are schematized in Fig. 1. Because it presents a number of novel aspects with respect to that applied previously to untilted data (Casadei et al., 2018), the pipeline is outlined below in some detail and for each step the obtained outcome is mentioned explicitly.
|
2.2. Density maps from molecular replacement
Although the data set was of low completeness, the experimental structure-factor amplitudes Fo{(h,k)}(l) and the corresponding error estimates were used as input for and subsequent rigid-body (see Section 4). The bacteriorhodopsin structure obtained by and diffraction, available as entry 1fbb in the Protein Data Bank (Berman et al., 2003), was used as a starting model.
Owing to the bias introduced by the use of model phases, molecular-replacement maps are not to be considered representative of the information content of the data. To assess this content, we calculated the composite OMIT map (see Section 4), which is shown in Fig. 4 for two different views of the molecule. The map shows that the data contain information about the position and orientation of the α-helices in the structure. Although the presence of a missing cone of data in the qrod direction leads to real-space features which are elongated along the z axis, at sufficiently high contour levels only density overlapping with the expected positions of helices is present in the maps. These conclusions also emerge from the `single-helices' OMIT maps (see Section 4) shown in Supplementary Fig. S3. Furthermore, the findings are reproduced by the molecular-replacement procedure from the intensities sampled at δqrod = 2π/2d and δqrod = (1/4)2π/2d (see Supplementary Figs. S4 and S5).
3. Discussion
We present a protocol which allowed a three-dimensional X-ray diffraction data set from two-dimensional protein crystals to be analysed. The three-dimensionality of the data set in
is a consequence of the tilting of the membrane supporting the samples with respect to the X-ray beam. These data differ from electron diffraction data in that the cannot be considered to be flat, even at low resolution, and in that each lattice diffraction pattern is a snapshot from one crystal, independent of any other pattern and not, for example, a representative in a tilt series from the same crystal. These differences triggered the development of a novel method which combines approaches from traditional X-ray crystallography (lattice identification, lattice-parameter and Bayesian estimates of unique intensities, amplitudes and their error), three-dimensional SFX (merging of images from individual crystals affected by indexing ambiguity and intensity scaling) and two-dimensional electron diffraction (intensity modeling along Bragg rods). Applying this method, we reconstructed the diffraction intensities along Bragg rods in from which the structure-factor amplitudes were extracted and their phases were determined by The electron-density composite OMIT maps show that despite their low completeness and resolution, the data are meaningful.The completeness is enhanced by recording data sets at higher tilt angles, which in general increases the qrod coverage of the Bragg rods (see Supplementary Fig. S2). As a concrete example, with a tilt of 40° the completeness for the same down to the same resolution range increases to 68.9%. Increasing the tilt angle unfortunately leads to an increased background because of the longer path of the X-ray beam inside the sample support. The image-summing approach presented in previous work (Casadei et al., 2018), which aims to extend the achievable resolution by enhancing the signal-to-noise ratio, can be generalized straightforwardly. Obviously, to achieve the same improvement, for each qrod bin of a tilted data set the same redundancy as an untilted data set has to be achieved, boosting the amount of required sample and the data-collection time by orders of magnitude. In this regard, the new high-speed scanning stage that has recently been commissioned at the CXI station opens new perspectives (Roedig et al., 2017).
In agreement with the results from pioneering two-dimensional electron diffraction work (Unwin & Henderson, 1975), we observe that the intensities decay in an anisotropic fashion with increasing resolution. We quantify this effect by modeling the ratio |Fo|2/|Fm,iso|2, with model amplitudes Fm,iso calculated in the same way as above from the 1fbb model but without anisotropic B factors (see Section 4), with a two-dimensional Gaussian function:
The fit is shown in Fig. 5, and the values of the obtained fit parameters δB2D = −0.27 Å2 and δBrod = 6.70 Å2 indicated that the experimental intensities decay remarkably faster in the qrod direction than in the in-plane direction. We carried out the same treatment using observed and model structure factors from PDB entry 5b6v (Nango et al., 2016), a structure of bR from three-dimensional SFX. In this case the fit parameters were refined to δB2D = 0.39 Å 2 and δBrod = 0.51 Å2, showing that anisotropic effects are negligible with three-dimensional crystals. The large decay rate of two-dimensional crystal intensities along qrod hints at increased disorder in the real-space out-of-plane direction as expected for a single-layer arrangement. Such an increase can be quantified by observing that the difference between experimental and model mean-square out-of-plane displacements amounts to approximately 6.7 Å2.
In conclusion, we have shown that the structure-factor amplitudes derived from the two-dimensional SFX data contain meaningful and structural information, and have made the point that the completeness and resolution limitations are overcome by enhancing the redundancy in the data collection. It therefore appears that with the present status of XFELs, three-dimensional difference electron-density maps at a few ångströms resolution can be determined between protein molecules with different configurations in two-dimensional crystals. Of particular interest are large-scale configuration changes on this length scale that are sterically hindered in three-dimensional crystals. If these movements are triggered by optical stimuli, two-dimensional SFX data sets can be measured at different delays between the exciting laser pulse and the X-ray probing pulse, in a fashion that is nowadays standard in three-dimensional SFX (Standfuss & Spence, 2017).
4. Methods
4.1. Sample preparation
Purple membrane was isolated from Halobacterium salinarum expressing the gene for the D96N bacteriorhodopsin mutant (bR-D96N) and detergent-stabilized two-dimensional crystal suspensions were prepared using previously described procedures (Frank et al., 2014; Pedrini et al., 2014). The two-dimensional crystals were washed with 6 mM octylglucoside, suspended in 0.5%(w/v) glucose to a final protein concentration of 0.4 mg ml−1 and subsequently applied onto the sample carrier for X-ray diffraction data collection.
Silicon chips with areas of 25 × 25 and 12.5 × 25 mm2 with 200 µm thickness, produced by Silson Inc., were used as sample carriers. The chips had a 44 × 44 or 22 × 44 array of 100 × 100 µm windows of 20 nm thick Si3N4. A total of about 20 µl bR-D96N two-dimensional crystal suspension was deposited onto the silicon chip and allowed to dry in air. The resulting glucose layer served to protect the protein sample from dehydration.
4.2. Experimental setup and data collection
The X-ray diffraction measurements were carried out using the 0.1 µm focus setup of the CXI experimental station (Liang et al., 2015) at the Linac Coherent Light Source. The beam size was estimated to be below 200 nm full width at half maximum (FWHM). The photon energy was set to 8.5 keV (1.5 Å), the pulse energy was approximately 2 mJ and the pulse length was approximately 35 fs FWHM.
The chips covered with two-dimensional bR-D96N crystals were mounted on a metallic frame that was fixed to the sample stages inside the vacuum experimental chamber. The sample stages were scanned in steps at a rate of about 1.5 s−1. The silicon frames were kept in a nonperpendicular configuration with respect to the X-ray beam, with tilt angles of 5, 15 and 20° about the x axis (Fig. 2). Diffraction patterns were recorded using a 2.3 megapixel Cornell–SLAC pixel-array detector, which was positioned 285 mm downstream of the sample in the same vacuum chamber (Blaj et al., 2015).
4.3. Software
Unless specified otherwise, the processing was performed using dedicated algorithms written in the Python 2.7 language, which are available on request.
4.4. Peak indexing
The geometry of the diffraction experiment using two-dimensional crystals is schematized in Figs. 2(c) and 2(d), where z denotes the direction of the incoming X-ray beam and η denotes the sample-support tilt angle about the x axis. The reciprocal-space plane spanned by the reciprocal basis vectors a* and b* can alternatively be described using the orthonormal vectors and , with
The in-plane component of the momentum-transfer vector q = kf − ki is
and forms an azimuthal angle α with the axis given by
where φ is the random in-plane orientation of the two-dimensional crystal and a*qy, 0 and b*qy, 0 are the components of a* and b* along when the two-dimensional crystal is in the reference in-plane orientation. The transferred wavevector is
with
where q = 2π/λ. By squaring kf and solving for qrod one obtains
By considering
and replacing with the values from (8), the following expression for the azimuth detector coordinate of the diffraction spot is obtained,
where
The radial coordinate of the diffraction spot is
where D is the detector distance and is the scattering angle given by
2.5. Re-indexing
The task is determining lattice-specific re-indexing transformations Ti (with i = 0, 1, 2, 3) that make the assignment of reciprocal-space indices coherent across the data set. The set of possible transformations is
A lattice is randomly extracted from the data set and used as a reference R. The transformation TLR required to re-index lattice L and make it compatible with R is established based on the calculation of intensity correlation coefficients. This determination of TLR is accepted if the expression
equals the identity for at least 70% of a large number (∼100) of randomly selected lattices L′. The procedure is repeated using different reference lattices and the consistency of the results is checked.
The transformation required to re-index L1 and make it compatible with L2 is determined by calculating a between intensities from the two lattices in each of the four different indexing scenarios. The largest coefficient is considered to be representative of the correct transformation. The intensity CCi related to the transformation Ti is calculated by matching every spot (h, k, qrod) in L1 to any of the following p3-symmetry equivalent spots in L2,
where T indicates the transpose, and their Friedel mates. Importantly, in the general tilt case it is necessary to allow ≃ qrod and to set an upper limit on the absolute qrod difference of matched spots.
2.6. Evaluation of data quality
A merging residual was calculated in three-dimensional resolution bins,
where the sum extends over all Bragg lines {(h, k)} and observations i within the resolution bin (Baldwin & Henderson, 1984). A half-data-set CC1/2 was calculated per resolution bin as follows. Observations in each qrod bin of width π/(2d) were split randomly into two groups of (approximately) equal size and the linear between half-data-set averages was calculated. The random splitting was repeated ten times and the average was considered. The value of CC* was calculated according to the definition in Karplus & Diederichs (2012). The global CC1/2 and CC* values were calculated as the weighted averages of individual bin values, with weights based on the number of unique reflections. Signal-to-noise ratios were calculated as three-dimensional resolution-bin averages of ratios between Bayesian estimates of intensities and their standard deviations for unique reflections. Completeness values in three-dimensional resolution bins were calculated as the ratio between the number of reciprocal-space points sampled by two-dimensional crystal diffraction with tilt angle 20°, considering δqrod = π/2d, and the number of points within the corresponding spherical shell.
2.7. Molecular replacement
Bayesian estimates of unique reflection structure-factor amplitudes Fo and their errors were converted to MTZ format using the CCP4 program F2MTZ (Winn et al., 2011). The data were phased by in Phaser (McCoy et al., 2007) using the structural model 1fbb (Subramaniam & Henderson, 2000) from the Protein Data Bank (Berman et al., 2003). The solution was rigid-body refined in PHENIX (Adams et al., 2010) to obtain model structure-factor amplitudes and phases (Fc, φc). To verify that the model was not biased by the phases from we calculated composite OMIT electron-density maps (Terwilliger et al., 2008) using the PHENIX software suite. We also carried out the standard procedure of removing a portion of the model, in this case a sequence of 20 amino acids, and using structure-factor amplitudes and phases (Fc,OMIT, φc,OMIT) determined from the truncation of the complete model. The Fourier coefficients of the OMIT maps (mFo − DFc,OMIT)exp(iφc,OMIT), where m are the Sim weights and D are the Luzzati factors (Read, 1986), are conceived so that any feature accounted for in the data, but absent in the model, is represented by a region of positive electron density in the map.
APPENDIX A
Derivation of the intensity model
We show that the summation in (3) represents an appropriate model for intensities in the qrod direction because of the finite thickness d of the molecule monolayer. The diffracted intensity is the square amplitude of the Fourier transform of the charge density,
This is equivalent to the expression
P is the charge-density autocorrelation, qz is the reciprocal-space coordinate along the direction of the Bragg lines, x and y are fractional coordinates in terms of the real-space crystallographic vectors a and b, and z is the real-space coordinate in the direction perpendicular to the plane spanned by a and b. It should be emphasized that since the monolayer has a finite thickness d, the extent of the autocorrelation function is limited to |z| ≤ d. The autocorrelation function can be expressed by means of a discrete sum
where the sampling points {qz,i} along Bragg lines are equally spaced by 1/(2d) as defined by Shannon's sampling theorem. Including (19) in (18) gives
Considering that
and
the following expression for intensity is obtained,
leading to
The integral term in (24) is the Fourier transform of a step function extending from −d to +d, namely a sinc function
(25) corresponds to (3), where the factor 2π is included in the definition of qrod.
Supporting information
Supplementary Figures and Table. DOI: https://doi.org/10.1107/S2052252518014641/ec5011sup1.pdf
Acknowledgements
We thank Rafael Abela, Gebhard Schertler, John Spence, Geoffrey Feld and Richard Kirian for discussions and support of this work. CMC thanks Tim Gruene for fruitful discussion.
Funding information
This work was performed in part under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and supported by LLNL Lab-directed Research and Development (LDRD) project 12-ERD-031 and NIH grant 1R01GM117342-01. This work was supported in part by National Science Foundation grant 1231306 to M. Messerschmidt. Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. This research was supported in part by resources of the National Synchrotron Light Source II, a US Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DE-SC0012704.
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