No statistical methods were used to predetermine sample size. The experiments were not randomized and the investigators were not blinded to allocation during experiments and outcome assessment.
All the crystals of Ca2+-ATPase were prepared by microdialysis as described4, 14, 20, 22. Solvent was exchanged by placing the dialysis buttons into buffers containing appropriate amounts of contrast medium. The density of the buffer was also measured directly. For higher (>40%) concentrations of iohexol (available as Histodenz from Sigma-Aldrich; also called Nycodenz), dialysis was prolonged for at least 48 h. Crystals were picked up by nylon loops and flash frozen with cold nitrogen gas in a cold room. They were stored in liquid nitrogen until use.
All the data were collected at BL41XU, SPring-8, with optics optimized for small-angle X-ray diffraction. Specimens were cooled to 100 K or 40 K at a later stage. The detectors used were R-AXIS V imaging plate detector with 400 × 400 mm plate size (RIGAKU), a Q315 CCD detector (ADSC) and a PILATUS3 6M detector (DECTRIS). The camera distance was fixed to 600 mm, with a He path of 450 mm. A beam stop of 1 mm diameter was placed on the polyimide film at the downstream end of the He path. As a result, reflections with 200 Å to 3.2 Å Bragg spacing can be recorded (Extended Data Fig. 1e). Even with a dynamic range of 20 bits, at least two exposures were necessary to record the strongest reflections without saturating the detector with high-resolution reflections. For collecting data, a wavelength of 1 Å or 1.5 Å was used. The iodine atom in iohexol is expected to have an f ″ of 3.3 (at 1 Å) or 6.5 e− (at 1.5 Å), giving rise to a useful anomalous signal.
Diffraction intensities were integrated and merged with Denzo and Scalepack33. Statistics for the merged datasets are listed in Supplementary Tables 3–7.
The starting point for solvent contrast modulation is a set of crystals soaked in buffers containing different concentrations (ξ %) of contrast modulation medium. In these crystals, the electron density ρ at a point (x, y, z) can be separated into two parts: a constant part (the protein and the bilayer) and a variable part (solvent), the electron density of which changes linearly with ξ. The variable part can be expressed using solvent exchange probability P (x, y, z) and the mean solvent density , resulting in
where indicates the normalized structure factor for the solvent with unit electron density (that is, 1 e− per Å3; Extended Data Fig. 1f).
What we can measure for the nth dataset with an iohexol concentration of ξ is
where Δθ (h, k, l) is the angle between the vectors representing |F (h, k, l)| and (Extended Data Fig. 1f). Thus, for any reflection, diffraction intensity should vary as a quadratic function of solvent electron density34(Extended Data Fig. 2a), and we can use , the best estimate of in a least squares sense, for further calculation instead of . As a special case, the amplitude of any centric reflection should vary linearly with solvent electron density (Extended Data Fig. 2b).
As this is a linear equation, the amplitudes of the centric reflections can be used for refining the average solvent density .
In any case, as is known, at least three measurements of diffraction intensities at different ξ are required to obtain |F (h, k, l)|, and Δθ (h, k, l). Nevertheless, as Δθ is not directly related to F , F or (Extended Data Fig. 1f), we need an initial set of phases for F (or, in reality, initial model for ρ )35. Yet, once density maps at two different ξ (usually 0% and maximum concentration) are generated, phases can be substantially refined by posing restraints on P (Extended Data Fig. 1h).
Consistency among datasets at different ξ are maximized both in real and reciprocal space. In reciprocal space, as already described, should change as a quadratic function of ξ (equation (2); Extended Data Fig. 2a), if scaled properly. Systematic errors can arise from errors in abscissa (solvent electron density ) and ordinate (scaling factor K and overall temperature factor B). Initially, K and B of each dataset (at ξ ) are determined by rigid body refinement of the atomic model treating the entire molecule as one segment. They are applied to raw diffraction amplitudes to place on an absolute scale, as in
K and ξ can be optimized in the subsequent steps by minimizing the residual R (Extended Data Fig. 2c)
Nevertheless, restraint in real space through P (x, y, z) is much more direct and powerful. Therefore, we first calculate
(6)and uses only the phase part of this to calculate as
As the average of ρ , , must be zero if F (0, 0, 0) is not incorporated, has to be obtained separately, by bringing the density inside the protein ρ (x, y, z) to that expected from the atomic model. Therefore, is calculated as
in which the summation is taken over all grid points (x, y, z) within the van der Waals radius of a protein atom and N is the total number of grid points. It is then added to ρ at each point in the electron density map.
P (x, y, z) and ρ (x, y, z), that is, ρ (x, y, z) at zero solvent density, can be obtained by linear least squares method, as at point (x, y, z) is a linear function of (Fig. 1a). Because the solvent density can actually be changed only within a narrow range (0.35–0.45 e− per Å3) and far from 0 (Fig. 1a), the error in ρ (x, y, z) could be substantial. Yet, as strong restraints can be placed on ρ (x, y, z) and P (x, y, z) (Extended Data Fig. 1h), these parameters can be largely improved. First, P (x, y, z) is smoothed as in conventional solvent flattening (smoothing radius is set equal to the resolution of the diffraction data).
Then (Extended Data Fig. 1h), (i) for any point in the solvent region, that is, >40 Å from the bilayer centre and >5.2 Å from the protein surface, P (x, y, z) is set to 1 and ρ (x, y, z) to zero (solvent flattening); the same rule applies to any point with P (x, y, z) ≥ 1. (ii) For any point within the van der Waals radius from a protein atom, P (x, y, z) is set to 0 and ρ (x, y, z) to the density calculated from the atomic model (protein flattening). (iii) For any other points in the interface area (outside of the solvent and more distant from a protein atom than the van der Waals radius; light green area in Extended Data Fig. 1h): if P (x, y, z) ≥ 1, P (x, y, z) is set to 1 and ρ (x, y, z) to zero; if P (x, y, z) ≤ 0, P (x, y, z) is set to 0, and if 0 < P (x, y, z) < 1, P (x, y, z) is not modified. Then, ρ (x, y, z) is updated as in
where N is the number of datasets. As a result, equation (1) no longer holds. The parameter should be updated first, as it must be constant independent of (x, y, z). For this purpose, a weighted average residual for was calculated over points that satisfy 0.1 < P (x, y, z) < 1.0, as in
Then we calculated again, as in equation (6), using updated P (x, y, z), ρ (x, y, z) and . For calculating new density maps, the phase part of and the amplitude part of were used after a proper scaling of . For this purpose, the scaling parameters (that is, K and B in equation (4)) were refined by minimizing the residual as defined by
After ten inner cycles of refinement essentially in real space, we went back to reciprocal space to refine with updated . For this purpose, K and B in equation (4) were refined (using instead of ) by minimizing the residual as defined by
with new . We then repeated these refinement cycles until R no longer decreased (30 outer cycles; altogether 300 cycles of refinement; Extended Data Fig. 2d, e).
The protein in the same state is assumed to have an identical structure irrespective of the iohexol concentration. In reality, as the unit cell dimensions vary depending on the concentration of the contrast medium, the protein structure may also change accordingly. In fact, the diagonal of the unit cell changed from 261.7 Å (0% iohexol) to 267.8 Å (80%) for the E1⋅AlF −⋅ADP⋅2Ca2+ crystals. In other crystal forms, they changed from 247.6 Å (0%) to 248.5 Å (70%) for the E1⋅2Ca2+ crystal, 272.7 Å (0%) to 276.1 Å (70%) for the E2⋅AlF −(TG) crystals of C2 symmetry, 204.0 Å (0%) to 204.5 Å (70%) for the E2⋅AlF −(TG) crystals of P2 2 2 symmetry, and 600.8 Å (0%) to 595.5 Å (75%) for the E2(TG) crystals.
To find an atomic model that best fits all datasets of different contrast medium concentrations, rigid body refinement treating the whole ATPase molecule as one segment was done exhaustively using reflections from 15 Å to the highest resolution. First, the starting protein atomic model was fully refined (up to ‘grouped B-factor’) using CNS24 for a particular crystal at ξ% iohexol. Then, rigid body refinement was carried out, using this atomic model as the template, against all the other diffraction datasets in the same state but at different concentrations of iohexol. The starting atomic models used were: 1SU4 (E1⋅2Ca2+), 2ZBD (E1⋅AlF −⋅ADP⋅2Ca2+), 2ZBG (E2⋅AlF −(TG) C2 symmetry), 1XP5 (E2⋅AlF −(TG) P4 2 2 symmetry) and 2AGV (E2(TG)) (Supplementary Table 1). An average of the R-factors taken over all iohexol concentrations was assigned as the ‘average’ R-factor of that particular crystal. Finally, the atomic model of the smallest ‘average R-factor’ was chosen for the common protein atomic model (Supplementary Tables 3–7). In all cases, the atomic model at an intermediate concentration of iohexol yielded the best results. Any diffraction dataset, whose R-factor exceeded 0.35 in the individual rigid body refinement was discarded at this stage.
The electron density profile of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) bilayer from small-angle X-ray scattering32 was used as an initial model for the lipid bilayer (Extended Data Fig. 8a). That is, the peak height was set to 0.44 e− per Å3 and that of the acyl chain to 0.23 e− per Å3; the solvent part was set to that calculated from the composition of the solvent (0.35 to 0.45 e− per Å3).
We examined the effects of errors in peak-to-peak distances and peak heights on the final refined structure. In addition to the standard 40 Å, the peak-to-peak distance was varied between 30 and 50 Å (Extended Data Fig. 8b). The profiles of the final models for the bilayer after refinements were very much the same, converging to a unique structure (Extended Data Fig. 8c). Also the height of the density peak was changed to 0.40 e− per Å3 from 0.44 e− per Å3, the figure obtained by small-angle X-ray scattering32, but the final profile of the bilayer was virtually the same.
In the crystals of C2 symmetry, because of the presence of a twofold axis (that is, b-axis) that goes through the centre of the bilayer, the lipid bilayer has to be parallel to the ab plane of the crystal. However, in the case of the E2⋅AlF −(TG) crystal of P2 2 2 symmetry and E2(TG) crystals of P4 2 2 symmetry, a slanted bilayer is allowed. Due to crystal symmetry, such a plane can be represented by an equation c = (a + b)tan(θ), where θ is the angle between the plane and the crystal ab plane. At first, we calculated a plane that approximates positions of the residues that may anchor phospholipids (or more precisely, the Trp NE1, Tyr OH, Lys NZ and Arg NH1 atoms) for each leaflet, and the plane running through the middle of the two planes was defined as the centre of the lipid bilayer. Such calculation showed that the bilayer plane is inclined by θ = 11.3° (E2⋅AlF −(TG) or 2.9° (E2(TG)), which indeed yielded the smallest R-factors (Extended Data Fig. 8d). The angle of the bilayer plane calculated from the positions of the phosphate in the contrast modulation map after refinement was 12.4° for the E2⋅AlF −(TG) crystals, irrespective of the angle assumed in the initial one-dimensional model, provided that it was less than 16.7°. Nevertheless, as described, the R-factor varied considerably, and each leaflet tended to split into two if started from 0°.
As seen from the formulation, phase information obtained by contrast modulation (that is, Δθ ) is used only for separating solvent and protein + lipid parts (that is, F and F ; equation (2)) and does not appear explicitly afterwards. Once a real space model is obtained, however, the consistency between the calculated and the experimentally obtained phase (that is, ΔΔθ ) must be examined and may be used for map calculation as a weighting factor. For this purpose, we define a kind of figure of merit (FOM) (Extended Data Fig. 2g) as
Although the anomalous signal from heavy atoms in the solvent contains phase information, it cannot be used for obtaining phases in a form suitable for calculation of electron density35, 36. Yet, at least in principle, it provides a useful means for cross-validation of the phase information. For this purpose, R (lack of closure between the sum of ) defined as
where the Bijvoet difference ΔF represents |F (h, k, l) − F (−h, −k, −l)|, was calculated (Extended Data Fig. 2f).
As the anomalous signal is multiplied by |F |, R is a useful measure only when the content of contrast medium is very high (>60%). This is because the anomalous signal is so weak, as heavy atoms are scattered in a large solvent volume, not localized to well defined positions in the crystal lattice.
Atomic models of a part of phospholipid (from the head to the carbonyl groups) were refined by simulated annealing with CNS24 based on the electron density maps calculated using structure factors obtained by contrast modulation (that is, ) after phase combination with those derived from atomic models. This was necessary to avoid problems arising from the CNS mask37 that defines the boundary between the protein (+ lipid) and solvent. The weights for the phases derived from contrast modulation were chosen so that it is 1 for the reflections at the Bragg spacing (d) of 15 Å or larger, and 0.0112e0.3d for those at d < 15 Å (0.05 at d = 5 Å). This is because phase difference rapidly increases from d = 10 Å towards a larger spacing (Extended Data Fig. 2h), whereas the contribution from the bilayer becomes very small at d = 5 Å (approximately 5% of the total amplitude; Extended Data Fig. 1g). The phases at 15 Å or lower resolution were derived entirely from contrast modulation. The atomic model was finally refined with CNS24 and Phenix38. Structure figures were prepared with Pymol (Pymol version1.7 Schrodinger LLC) and videos were prepared with Molscript39.
To evaluate the impact on the R-factors of the atomic model for the bilayer in the crystal (Extended Data Fig. 2i), atomic models for the acyl chains are needed. They were taken from those in 100-ns molecular dynamics simulations, as they could not be built into the contrast modulation electron density maps. Here the molecular dynamics model was aligned using that of Ca2+-ATPase and the portions of the acyl chains that do not overlap with the protein or head groups were cut out and incorporated into the model of the crystal structure. The temperature factors of the acyl chain atoms were set to 999, which is the largest number allowed in a PDB file. Here, in addition to the hard mask that CNS24 generates for non-solvent part, a soft mask similar to that used in solvent flattening40 was also tried (Extended Data Fig. 2i). In the best case, that is, E2(TG), a combined atomic model decreased the R-factor nearly 60% in the lowest resolution region (Extended Data Fig. 2i).
Starting atomic models were derived from the PDB entries 1SU4 (E1⋅2Ca2+), 2ZBD (E1~P⋅ADP⋅2Ca2+), 2ZBG (E2~P) and 2AGV (E2). The inhibitor (thapsigargin (TG)) in the entry was removed and the first-layer lipids modelled in this study were incorporated. Ca2+-ATPase was embedded in a fully hydrated DOPC bilayer, solvated and ionized using VMD41. The four protein structures were oriented in the membrane so that the planes that approximate the positions of the phosphorous atoms become horizontal in each crystal form as in Fig. 3. The positions and the orientations of Ca2+-ATPase were slightly different from those predicted27. All-atom molecular dynamics simulations of the Ca2+-ATPase in a box of 136 × 136 × 180 Å with explicit solvent and 471–475 phospholipids were performed for 100 ns in the NPT ensemble as described previously42 using NAMD2.8 (ref. 43). Protein atoms were restrained with a harmonic potential of 10.0 kcal mol−1 Å−2. CHARMM36 (ref. 44) force-field parameters were used for phospholipids and CHARMM27 (ref. 45) for the protein and ions, and TIP3P for water. The number of molecules and other parameters are listed in Supplementary Table 8.
Atomic coordinates and structure factors for the reported crystal structures are deposited in the Protein Data Bank under accession numbers 5XA7 (E1⋅2Ca2+), 5XA8 (E1⋅AlF −⋅ADP⋅2Ca2+), 5XA9 (E2⋅AlF −(TG); C2 symmetry), 5XAA (E2⋅AlF −(TG); P2 2 2 symmetry), and 5XAB (E2(TG)).