Three-dimensional Crystals of Ca2 -ATPase from ... · ging electron diffraction data from tilt...

$: Three-dimensional Crystals of Ca2 -ATPase from ... · ging electron diffraction data from tilt series. We have applied this method to thin, monoclinic crystals of Ca2⁄-ATPase from$
Three-dimensional Crystals of Ca2�-ATPase fromSarcoplasmic Reticulum: Merging Electron DiffractionTilt Series and Imaging the (h, k, 0) Projection

Dan Shi, Michael R. Lewis, Howard S. Young and David L. Stokes*

Skirball Institute ofBiomolecular MedicineDepartment of Cell BiologyNYU School of Medicine540 First Avenue, New YorkNY 10016, USA

Electron crystallography offers an increasingly viable alternative to X-raycrystallography for structure determination, especially for membrane pro-teins. The methodology has been developed and successfully applied to2D crystals; however, well-ordered thin, 3D crystals are often producedduring crystallization trials and generally discarded due to complexitiesin structure analysis. To cope with these complexities, we have devel-oped a general method for determining unit cell geometry and for mer-ging electron diffraction data from tilt series. We have applied thismethod to thin, monoclinic crystals of Ca2�-ATPase from sarcoplasmicreticulum, thus characterizing the unit cell and generating a 3D set ofelectron diffraction amplitudes to 8 AÊ resolution with tilt angles up to30�. The indexing of data from the tilt series has been veri®ed by an anal-ysis of Laue zones near the (h, k, 0) projection and the unit cell geometryis consistent with low-angle X-ray scattering from these crystals. Basedon this unit cell geometry, we have systematically tilted crystals to recordimages of the (h, k, 0) projection. After averaging the correspondingphases to 8 AÊ resolution, an (h, k, 0) projection map has been calculatedby combining image phases with electron diffraction amplitudes. Thismap contains discrete densities that most likely correspond to Ca2�-ATPase dimers, unlike previous maps of untilted crystals in which mol-ecules from successive layers are not aligned. Comparison with a projec-tion structure from tubular crystals reveals differences that are likely dueto the conformational change accompanying calcium binding to Ca2�-ATPase.

# 1998 Academic Press

Keywords: electron microscopy; Ca2�-ATPase; sarcoplasmic reticulum;crystallography; ion transport*Corresponding author

Introduction

Over the last decade, there has been considerableprogress in the methods of electron crystallographyand, as a result, there has recently been dramaticsuccess in structure determination from two-dimensional (2D) crystals at atomic resolution(Henderson et al., 1990; Kimura et al., 1997;KuÈ hlbrandt et al., 1994; Nogales et al., 1998). Thesemethods are particularly well suited for membraneproteins, because they are naturally constrained tothe 2D surface of the membrane. Given theextreme dif®culty in growing large, three-dimen-

sional (3D) crystals of membrane proteins suitablefor X-ray crystallography, electron crystallographyof 2D crystals may offer the best hope for obtainingthe atomic structure of many membrane proteins.

Thin, 3D crystals represent an alternative crystalmorphology that is frequently obtained duringcrystallization trials, but is seldom employed forstructure determination. Often, these platelets cor-respond to type I (Michel, 1983) or multilamellarcrystals in which each layer resembles a 2D crystal.Because they are usually composed of a smallnumber of layers, such crystals are unsuitable forX-ray crystallography and the few attempts at elec-tron crystallographic structure determination havesooner or later been abandoned, due to the extracomplications in characterizing the unit cell and inmanaging the data. In particular, the geometry oflamellar stacking must be accurately determined

E-mail address of the corresponding author:[email protected]

Abbreviations used: 2D, two-dimensional; 3D, three-dimensional.

Article No. mb982283 J. Mol. Biol. (1998) 284, 1547±1564

0022±2836/98/501547±18 $30.00/0 # 1998 Academic Press

and, in the worst cases, this stacking turns out tobe irregular. As in any 3D crystal, the number oflayers is variable, but with a small number of unitcells the sampling function is strongly dependenton the precise thickness. On the other hand, theincreased number of unit cells and the extra crys-talline constraints imposed by stacking often resultin much stronger diffraction from thin, 3D crystalsrelative to 2D crystals.

Ca2�-ATPase from skeletal sarcoplasmic reticu-lum offers a good example of thin, 3D crystals(Taylor et al., 1988) and produces electron diffrac-tion to �3.5 AÊ resolution (Shi et al., 1995). Therequirement for saturating concentrations of cal-cium suggest that Ca2�-ATPase adopts the confor-mation known as E1 �Ca2 in these crystals (Stokes& Lacapere, 1994), in which calcium binding totransport sites has activated the nucleotide site forphosphorylation by ATP (MacLennan et al., 1997).Thus, these crystals represent one of the key con-formational intermediates that couples ATPhydrolysis to calcium transport and a structuralcomparison with Ca2�-ATPase in the absence ofcalcium (E2 conformation) would be very informa-tive. Indeed, this E2 conformation is most likelyrepresented by a recent structure at 8 AÊ resolution(Zhang et al., 1998). This structure was determinedfrom 2D crystals within the sarcoplasmic reticulummembrane that, in favorable conditions, producelong, thin tubules with helical symmetry(Toyoshima et al., 1993). The resulting helicalreconstruction revealed the arrangement of trans-membrane and stalk helices and suggested a par-ticular path for calcium during active transport.Thus, structure determination of the E1 confor-mation from thin, 3D crystals has the potentialboth to improve this resolution and to reveal theconformational dynamics that couple this transportto ATP hydrolysis.

So far, these 3D crystals have been shown tocomprise an ordered stack of lamellae, which con-form to the C2 space group (Stokes & Green,1990b; Taylor et al., 1988). The individual lamellaeconsist of a mixed bilayer of lipid and detergentwith Ca2�-ATPase molecules protruding from bothsides of this bilayer (Figure 1a). Lamellar stackingis mediated by the cytoplasmic domains of Ca2�-ATPase and attempts to produce 2D crystals havefailed (Misra et al., 1991; Shi et al., 1995); in fact,these attempts provide circumstantial evidencethat stacking is essential to crystal nucleation. Sym-metry and unit cell dimensions within the lamellarplane have been documented in images and inelectron diffraction patterns from thin, plate-likecrystals (a � 166.4 AÊ and b � 55.7 AÊ ), whereassmall, cylindrical crystals grown under slightlydifferent conditions have been used to measureunit cell dimensions normal to the lamellae(Cheong et al., 1996; Ogawa et al., 1998). Unlikelarge, thin plate-like crystals, these small cylindri-cal crystals lie with the lamellar plane perpendicu-lar to the carbon support, thus offering a directview of the lamellar axis. However, the stacking of

lamellae was observed to change in response togrowth conditions, leaving considerable doubtwhether these observations were relevant to plate-like crystals.

Here, we have recorded tilt series of electron dif-fraction from the large, plate-like crystals and havedeveloped methods for determining the unit cellgeometry. These methods are analogous to deter-mining the space group from X-ray oscillationphotographs, though with several unique practical

Figure 1. Unit cell geometry for multilamellar crystalsof Ca2�-ATPase. a, Packing diagram showing a centeredlattice in the plane of the lamellae and a 2-fold axis par-allel to b. Molecules protrude from both surfaces of thelamellae and mediate their stacking. The values for cand b correspond to crystal form I found in the currentstudy (Table 1). The orientation of molecules in the dia-gram is consistent with previous work (Cheong et al.,1996) and with the (h, k, 0) projection map in Figure 9.b, Our coordinate system is de®ned with the (x-y) planecoincident with the a-b (lamellar) plane of untilted crys-tals and with the z axis parallel to the electron beam.Because the angle b 6� 90�, c and a* axes are inclinedrelative to z and x axes, respectively. The 2-fold axisconstrains b and b* to be colinear. c, Fourier intensitiesalong the c* axis are sampled by sinc functions, whichdepend on the number of lamellae (i.e. the number ofunit cells along the c axis). The three sinc functionsshown correspond to 3, 6, and 20 unit cells as indicated.

1548 3D Crystals of Ca2�-ATPase

constraints. Electron diffraction data were then suc-cessfully combined to 8 AÊ resolution with �30� ofmaximum tilt. This appears to be the ®rst time that3D electron diffraction data have been mergedfrom a 3D protein crystal. Finally, our knowledgeof the unit cell was used to obtain images of the(h, k, 0) projection. Phases from these images havebeen combined with electron diffraction ampli-tudes to generate the ®rst true (h, k, 0) projectionmap of these multilamellar Ca2�-ATPase crystals.These data provide a solid foundation for deter-mining the 3D structure of Ca2�-ATPase in the cal-cium-bound conformation.

Results

Previous work (Stokes & Green, 1990a,b; Tayloret al., 1988) showed the space group of these multi-lamellar Ca2�-ATPase crystals to be C2, which hasa centered lattice within the plane of the lamellae(bilayer) and a 2-fold rotation axis relating mol-ecules above and below this plane (Figure 1). Crys-tal axes a and b lie in the plane separated by 90�;the 2-fold axis is along b, which constrains theangle a (between b and c) to be 90�. However, theangle b (between a and c) is unconstrained and, insmall cylindrical crystals, we previously measuredb as either 95� or 98� with corresponding lengthsof c equal to 184.7 or 161.0 AÊ , depending on theconditions of crystallization (Cheong et al., 1996).Given this sensitivity of lamellar stacking to crys-tallization conditions, our ®rst goal in the currentwork (Figure 2) was to determine the stacking geo-metry for the large, thin plate-like crystals. For this

analysis, we used the geometrical convention thatthe a-b (lamellar) plane in an untilted crystal is par-allel to the x-y plane and that the electron beamde®nes the z axis (Figure 1b).

Determination of unit cell parameters fromelectron diffraction tilt series

The reciprocal lattice is characterized by thethree unit cell vectors a*, b* and c*, which can becalculated after determining the 3D coordinates ofthree or more Fourier re¯ections. For this calcu-lation, these re¯ections cannot be coplanar, so apriori we know that the crystal must be tilted; how-ever, the sampling of Fourier data from thin, 3Dcrystals along c* is not discrete and must be expli-citly taken into account. In particular, diffractionfrom thick, 3D crystals produces a 3D lattice of dis-crete re¯ections and diffraction from 2D crystalsproduces a 2D array of lattice lines with continu-ous Fourier amplitude (Amos et al., 1982). Thin, 3Dcrystals fall in between these extremes and producelattice lines comprising a series of Bragg re¯ectionsthat are convoluted with sinc functions (Figure 1c):sin(npx)/npx where n corresponds to the numberof unit cells along the c axis and x is the distancefrom the Bragg re¯ection. As a result, the width ofthese re¯ections along c* is inversely proportionalto the number of unit cells along the c axis (two-®ve in our case), ultimately producing a discrete3D lattice as n becomes large. The considerablewidth of these re¯ections means that their cen-troids cannot be accurately determined from asingle tilt. We therefore collected tilt series of elec-

Figure 2. Processing scheme for electron diffraction tilt series. Program names are shown in upper case letters andnew programs are indicated by an asterisk. The three branches are taken at different points during the analysis. Theleft-hand branch is initially used to determine the unit cell parameters of the crystal. Based on these parameters, themiddle branch produces a merged set of electron diffraction amplitudes, which allow re®nement of c* and b and the®tting of curves to the data. Based on these curves, the right-hand branch is used iteratively to re®ne various par-ameters for individual diffraction patterns and to include future data. The ultimate goal is a set of structure factors,Fh,k,l, as shown at the lower right.

3D Crystals of Ca2�-ATPase 1549

tron diffraction (Figure 3), in order to provide suf®-cient sampling along the lattice lines to identifyre¯ections and to allow ®tting of a reciprocal lat-tice.

In particular, 10-12 diffraction patterns weretaken of each crystal clustered around three tiltangles: e.g. ÿ25�, 0�, and �25� with maximal tiltangles of �30�. In order to obtain so many patternsfrom a single crystal, we used very low electrondoses, which limited the resolution to 8 AÊ . Knowl-edge of the tilt angle and tilt axis is required to cal-culate the 3D location of individual re¯ections andwe devised a geometrical analysis for determiningthese parameters for each diffraction pattern in theseries. Initially, we located the tilt axis by identify-ing invariant diffraction spots while tilting thin,aluminum crystals. However, the tilt axis rotateswith small changes in lens currents and the absol-ute crystal tilt includes a random component dueto bending of the copper grid and to lack of carbon®lm ¯atness. Our geometrical analysis thereforere®ned this initial estimate of the tilt axis and ulti-mately determined the absolute orientation of indi-vidual diffraction patterns in our ®xed coordinatesystem; this analysis depended on the relativeangles between successive diffraction patterns,which are accurately provided by the microscope.To start, the tilt series was placed in an arbitrarycoordinate system in which the ®rst diffraction pat-tern, at about ÿ30�, de®ned the x-y plane and aninitial value for the tilt axis was used to positionthe subsequent patterns (Figure 4a). So assembled,the 2D coordinates of (1,0) and (0,1) re¯ectionsfrom each pattern could be converted into 3D vec-tors. The direction of the c* axis was then de®nedby a line running through all the 3D vectorsderived from the (1,0) and (0,1) re¯ections; i.e. thered lines in Figure 4 de®ned as:

c� �Xn

i�0

Xn

j�i

�~a�i ÿ ~a�j � � �~b�i ÿ ~b�j �

where cÃ* is a 3D vector approximating the direc-tion of ~c�; ~a�i and ~b�i are 3D vectors for the (1,0) and(0,1) re¯ections on the ith ®lm. A least squaresresidual was calculated from the distance betweenthe 3D vectors and c� (Figure 4b) and used tore®ne orientations of the tilt axis and c�. To con-form to our geometrical convention (Figure 1b), theentire tilt series was then rotated until cÃ* was par-allel to z, thus producing absolute orientations foreach of the individual diffraction patterns in Four-ier space (Figure 4c) and values for the effective tiltangles and tilt axes to be used later during datamerging.

Based on these absolute orientations, diffractionamplitudes along all of the lattice lines wereplotted as a function of c*. For example, the ampli-tudes along three lattice lines are shown inFigure 3g. At this point, the values along theabscissa are arbitrary, because the orientation ofthe (h, k, 0) plane has not been determined. Ampli-tudes of re¯ections near the tilt axis (circles and tri-

angles in Figure 3a-e) are relatively constantthroughout this tilt series, whereas amplitudes ofthe boxed re¯ection, which is far from the tilt axis,change dramatically and appear to sample twoadjacent lattice points along c*. The distancebetween such peaks suggests that c* has a lengthof �1/160 AÊ . Figure 5 shows a more complete plotwith amplitudes along nine lattice lines measuredfrom all 12 patterns within the tilt series; the indi-ces of these lattice lines were (h, 3), where thevalue for h is shown along one axis of the plot. Thelattice line at h � 7 is close to the tilt axis and there-fore its amplitude does not change much. In con-trast, the lattice lines at h � ÿ 1 and h � 15 are farfrom the tilt axis and appear to sample three differ-ent re¯ections along c*. The rationale for collectingclosely spaced diffraction patterns in three widelyspaced groups should now be apparent: (1) the lar-ger angle between groups provides long differencevectors for accurate determination of cÃ*; (2) anglesnear 0� are required because lattice foreshorteningat ÿ25� is the same as at �25� leading to ambigu-ities in the tilt axis; (3) the small angles within thegroups sample the lattice lines at small intervals,which accurately de®ne the location of manypeaks.

The positions of the peaks along the latticelines were then ®t with a 3D reciprocal lattice,thus de®ning the geometry of the 3D unit cell(Figure 5b). Generally, 80-100 such peaks werede®ned manually for each tilt series and peakpositions were determined by ®tting sinc func-tions to the observed amplitudes. The 3D recipro-cal lattice was de®ned by vectors for a*, b* andc*, which were normalized to b* � 1/55.7 AÊ asobserved in untilted diffraction patterns; anglesfor a, b and g were unconstrained during the ®t.We found that the 3D unit cells fell into twogroups with different values for b (Table 1). Bothgroups appear to belong to the C2 space group,because a and g were 90�, and a and b wereinvariant. These two crystal forms were observedon the same microscope grid and therefore co-existed in the same crystallization solution,although particular crystallization batches favoredone crystal form over the other. Comparing theseunit cell dimensions with those previously deter-mined for small cylindrical crystals (Cheong et al.,1996) suggests that the unit cell with b � 98� isthe same as that for small cylindrical crystalsgrown in 5% glycerol; however, cylindrical crys-tals grown in 20% glycerol have a much longer caxis and therefore appear distinct.

Low-angle X-ray diffraction

To verify the lamellar spacing by an independentmeans, we prepared pellets of these crystals andrecorded X-ray diffraction at low scattering angles.Due to their anisotropic shape, crystals tended toalign with their lamellar plane perpendicular to thelong axis of the X-ray capillary. As a result, wewere able to distinguish diffraction normal to the


Figure 3. Electron diffraction patterns from a tilt series. a-e, Five out of 12 patterns from this tilt series are shown,which were taken near a tilt angle of 25�; precise tilt angles are shown at the lower right of each pattern, which camefrom our geometrical analysis of the tilt series in Figure 4. The orientation of the tilt axis is shown in a and happensto intersect the (ÿ2,4) re¯ection (circle). Laue zones are visible in all of the patterns, though they are rather closetogether in d and e. f, 2D representation of the reciprocal lattice, in which re¯ections are broad along c* and discretein the a*-b* plane (abscissa). Oblique lines represent diffraction planes from tilted crystals and the intersection of theselines with the reciprocal lattice gives rise to the Laue zones (shaded boxes). g, Amplitudes of the three marked re¯ec-tions in a-e plotted as a function of c*. The (ÿ2,4) re¯ection (circle) is on the tilt axis and its amplitude does notchange with tilt, whereas the (14,0) re¯ection (box) is far from the tilt axis and appears to sample two peaks along c*over the 7� of tilt shown. The l indices along the abscissa were assigned after ®tting a reciprocal lattice to all the datafrom the tilt series (Figure 5) and are con®rmed by an analysis of the Laue zones in a-e (see the text).

lamellae (i.e. along c*) from that in the a*-b* plane.Figure 6 shows an X-ray diffraction patterntogether with integrated intensities from the meri-dian and the equator. Five orders of a 155.9 AÊ

repeat are clearly visible along the meridian, whichcorresponds to the distance between lamellae. Thisdistance is consistent with a mixture of the twocrystal forms, which would have interlamellar dis-tances of 160.0 and 152.1 AÊ (1/csinb) according toour analysis of electron diffraction. Theoretically,these lamellar re¯ections should be split to re¯ectthe two different spacings, but the observed peaksare too broad to detect such splitting. Two weakerre¯ections are visible along the equator corre-

sponding to 53.2 and 39.3 AÊ spacing. The 53.2 AÊ

spacing matches the (1,1) re¯ection and the 39.3 AÊ

re¯ection matches the (3,1) or (4,0) re¯ections asmeasured by electron microscopy at 52.8 AÊ , 39.4 AÊ

and 41.7 AÊ , respectively. The relative weakness ofthe equatorial diffraction can be explained by theazimuthal disorder of crystals in the pellet, suchthat only a small fraction of crystals are properlyoriented to contribute to these re¯ections.

Analysis of Laue zones

Additional veri®cation of the angle b can beobtained from the presence of Laue zones near the

Figure 4. Geometrical analysis of tilt series. a, Individual diffraction planes from the tilt series are initially orientedwith the ®rst plane aligned to the x-y plane (actually at about ÿ30� according to the goiniometer). Orientation ofother planes are based on an initial estimate of the tilt axis and the relative tilt as read from the goiniometer. The redlines correspond to a vector (cÃ*) ®t to the 3D coordinates of (1,0) and (0,1) re¯ections from individual patterns andare labelled as a* and b*, respectively. b, The tilt axis was re®ned by minimizing the distance between cÃ* and the cal-culated 3D coordinates of these (1,0) and (0,1) re¯ections. This ®t is shown for two values of the tilt axis (25� apart)and the continuous line obviously ®ts much better to the circles than the dotted line to the squares. c, Based on thebest tilt axis, the absolute orientations of the diffraction planes were obtained by rotating the entire tilt series to aligncÃ* with the z axis as in Figure 1b.


(h, k, 0) projection. Laue zones are bands of re¯ec-tions (e.g. Figure 3a), where a 2D plane intersectssuccessive layers in the 3D reciprocal lattice. InFigure 3f, the oblique lines correspond to diffrac-tion planes at two discrete tilt angles and theshaded boxes represent the intersection of theseplanes with a 3D reciprocal lattice, which has beenconvoluted with sinc functions along c*. Theshaded boxes produce the bands of re¯ections and,at higher tilt angles, the zones become closertogether and narrower until they eventually pro-duce an apparent continuum of re¯ections. Thus,Laue zones are most prominent near the a*-b*plane (h, k, 0 projection), or possibly near otherprincipal projections. In addition, crystal thicknesscan be judged by the width of the Laue zones (Shiet al., 1995), which re¯ects the width of the sincfunctions (Figure 1c).

These Laue zones are present in all the patternsin Figure 3, though most clearly visible in Figure 3aand b. Figure 3a appears to be closest to the(h, k, 0) projection and, because the central zonecorresponding to l � 0 includes the a* axis, it con-tains re¯ections of the type (h, 0, 0). According toour geometrical analysis of this entire tilt series,the a* axis on this pattern is 18.9� away from thex-y (untilted) plane, which is perfectly consistentwith b* � 71.8� considering the slight misalignmentapparent in this pattern. Furthermore, the (0,4) and(ÿ2,4) re¯ections (circles and triangles, respect-ively) are very near the tilt axis and can beassigned an index of l � 1 for all ®ve patterns. Incontrast, the (14,0) re¯ection (square) moves froml � 0 in Figure 3a to l � 1 in Figure 3c to l � 2 inFigure 3e, as indicated along the abscissa inFigure 3g. These assignments were compared withthe reciprocal lattice that was independently ®t topeaks from this tilt series (e.g. Figure 5b) andfound to be completely consistent.

Merging and refinement of electron diffractiontilt series

After grouping data from the two crystal forms(b � 108� and b � 98�) and determining theirrespective unit cell parameters, we could proceedwith making a 3D data set. In particular, data fromeach tilt series were positioned in 3D using theabsolute orientations deduced for individual pat-terns (Figure 4b). We used a modi®ed version ofthe standard merging program, which accountedfor b 6� 90� and which compensated for the sincfunction sampling along c* during scaling. Also,only data within the central peak of the sinc func-tion were used for scaling, which depended on thenumber of unit cells along c (Figure 1c). This num-ber ranged from two to ®ve unit cells and was esti-mated from the shape of peaks along the latticelines from individual tilt series (Figure 5) and fromthe residual obtained during this merging. Two lat-tice lines from crystals with b � 108� are shown inFigure 7a and c and the observed amplitudesclearly de®ne peaks spaced at regular intervals

Figure 5. Fitting a reciprocal lattice to data from indi-vidual tilt series. After determining the absolute orien-tations of tilt series (Figure 4), amplitudes along latticelines were plotted, peaks were identi®ed and ®t withsinc functions. Nine lattice lines are plotted correspond-ing to (h, 3), with h shown along the x axis, and peakcentroids are marked with a vertical line. Initially, thelocation of the (h, k, 0) plane is undetermined and, as aresult, the coordinate along the c* axis is relative.b, The reciprocal lattice is characterized by the unit cellvectors (~a�; ~b� ~c�), which are determined by a leastsquares ®t to the 3D positions of 80-100 peak centroids.The resulting lattice is shown in grey along the x-yplane and each of the peak centroids can be seen tointersect one of its vertices. Thus the l index of eachpeak is determined as well as the orientation of the(h, k, 0) plane.


along c*, which occur at the lattice positions pre-dicted by the results in Table 1. The length of c*and the angle of b were then re®ned by ®tting

these data with a series of Gaussian functions cen-tered at the reciprocal lattice positions along c* andapproximating the falloff of a three-unit cell sinc

Table 1. Crystal lattice parameters

a (AÊ ) b (AÊ ) c (AÊ ) a (�) b (�) g (�) No. tilt series

Type I Averagea 167.0 55.7 161.4 90.0 108.1 90.0 10Refinedb ± ± 159.9 ± 108.2 ± 25

Type II Average 165.8 55.7 161.8 89.9 97.9 90.0 7Refined ± ± 161.6 ± 98.0 ± 15

a Average of lattice parameters ®t to individual tilt series.b Values for c and b were re®ned after merging data from all tilt series together (LATTICEREFINE in Figure 2).

Figure 6. Low-angle, X-ray diffraction from crystal pellets. Intensity was integrated along 25� arcs centered on themeridian (vertical plot at the left) and equator (horizontal plot along the bottom). The meridional axis shows a set ofregularly spaced re¯ections with a spacing of 1/155.9 AÊ , which corresponds to the distance between lamellae. Theequator shows weaker re¯ections at spacings of 53.2 and 39.3, which correspond to in-plane diffraction from the (1,1)re¯ection and from the (3,1) and (4,0) re¯ections, respectively.


function (see Materials and Methods); Table 1shows that c* and b changed very little during thisre®nement. The ®tted Gaussian functions werethen used to re®ne tilt angles, tilt axes, scale andtemperature factors for individual patterns, whichwere then remerged and ®tted with sinc functions,thus producing an obvious improvement in theoverall ®t (Figure 7b and d). R-factors were used to

quantify these improvements (Table 2) and werecalculated both with and without applyingGaussian weights (see Materials and Methods). Ingeneral, the Gaussian functions served to empha-size data near the reciprocal lattice positions and toeliminate subsidiary peaks, thus minimizing thein¯uence of variable crystal thickness duringmerging.

Table 2. R-factors for merging electron diffraction tilt series

Merged with C2 symmetry Merged with P1 symmetryFriedel Rcurve

a Rcurve Rsymmc

symmetry Unweighted Weightedb Unweighted Weighted Data Curve

Initial 0.14 0.89 0.48 0.81 0.44 0.41 0.28Round 1d 0.14 0.51 0.27 0.53 0.27 0.23 0.24Round 2d 0.14 0.48 0.25 0.47 0.24 0.20 0.24

a R factor of individual data against the sum of sinc functions.b The weighted R-factor is described in Materials and Methods.c Symmetry-related R-factor was calculated by comparing either individual amplitudes at analogous positions along the lattice

lines (data) or by comparing the sinc function coef®cients after ®tting curves to the data (curves).d After re®ning tilt angle, tilt axis, scale and temperature factor using ANGLEREFINE.

Figure 7. Merged electron diffraction data before and after re®nement. a and c, Fitting sinc functions to electrondiffraction intensities along the (4,4) and (13,3) lattice lines, which were merged according to orientational parametersfrom the geometrical analysis in Figure 4. The xs correspond to the average intensity of Friedel-related re¯ections andthe vertical bar corresponds to the difference between these intensities. b and d, Fitting of sinc functions after re®ningtilt axis, tilt angle, scale and temperature factor for individual patterns (ANGLEREFINE in Figure 2). The ®t is clearlyimproved and is re¯ected in the smaller R-factors in Table 2.


Finally, the expected 2-fold symmetry was testedby merging these diffraction data in the P1 spacegroup and then by comparing data from the 2-foldrelated lattice lines. The symmetry-related R-factors(Rsym) are comparable to the merging R-factors(Rcurve), indicating that these data are indeed con-sistent with the C2 space group (Table 2).

(h, k, 0) projection map

The (h, k, 0) projection from 3D crystals rep-resents the natural choice for a phase referencefor merging phases from images of tilted crystals.Unlike 2D crystallography, in which untiltedcrystals provide this phase reference, the (h, k, 0)

Figure 8. Computed Fourier transforms and ®ltered images near the (h, k, 0) projection. a and b, A crystal verynear the (h, k, 0) projection produces an isotropic distribution of re¯ections and no evidence of Laue zones. c and d,A crystal tilted by �1� relative to the (h, k, 0) projection. Although no Laue zones are visible in the transform, Fourieramplitudes fall off in one direction and the tilt angle was estimated by simulating the distribution of these ampli-tudes. This very slight tilt makes a clear impact on the ®ltered image. Nevertheless, phases from the re¯ections withinthe central zone can be assigned as l � 0 and can therefore contribute to an averaged (h, k, 0) projection map. Thecircled re¯ections are at �10.5 AÊ resolution.


projection comes from 3D crystals tilted at a par-ticular angle about a particular axis, whichdepends on the geometry of the 3D unit cell.Based on the above analysis of electron diffrac-tion tilt series, either an 8� or 18� tilt (dependingon the angle b) about the b axis will provide thisprincipal projection for our monoclinic Ca2�-ATPase crystals. Unfortunately, a double-tiltholder with cryo-transfer capabilities does notexist and we were therefore forced to search forcrystals with their b axes fortuitously alignedwith the ®xed tilt axis of the goiniometer, beforeseeking the appropriate tilt angle (�/ÿ 8 or�/ÿ18�). Electron diffraction was used for thissearch and alignment procedure and, in the pro-cess, a limited electron diffraction tilt series wasobtained before imaging the crystal. The datafrom these tilt series were used to verify theorientation of the imaged crystal and, by com-parison with the re®ned curves (Figure 7), to beabsolutely certain of the angle b. The latter waseasy, given that peaks from the two unit cells donot occur in the same locations in reciprocalspace. Crystals with b � 98� were scarce in thepreparations used for this imaging and we weretherefore successful in locating the (h, k, 0) projec-tion only from crystals with b � 108�.

The resulting images were all within a fewdegrees of the (h, k, 0) projection, but we found thedistribution of amplitudes to be exquisitely sensi-tive to the precise tilt angle and axis. The imageclosest to the (h, k, 0) projection is compared inFigure 8 with an image inclined �1� relative to(h, k, 0). Precise values for tilt angles and tilt axeswere determined by simulating the distribution ofamplitudes from the images and then phase originswere determined by comparing only re¯ectionsclose to the (h, k, 0) plane. Averaging phases from20 images resulted in an overall merging phaseresidual of �10� and a symmetry-related phaseresidual of 20� (Table 3). We then calculated an(h, k, 0) projection map (Figure 9a) by combiningthe electron diffraction amplitudes, taken from the®tted curves, with these averaged phases at 8 AÊ

resolution. Although overlap of molecules is inevi-table in projection, the (h, k, 0) projection mapappears to contain discrete densities, which areprobably dimers related by the crystallographic

2-fold axis. Half of each density has been shadedto yield approximate molecular dimensions of33 AÊ � 53 AÊ , which are generally consistent withour knowledge of the 3D structure of the moleculefrom tubular crystals (Toyoshima et al., 1993;Zhang et al., 1998).

Discussion

Previous electron microscopic studies of thin3D crystals

Here, we have presented methodology for ana-lyzing thin, 3D crystals by electron crystallographyand have successfully applied it to monoclinic crys-tals of Ca2�-ATPase. From a theoretical point ofview, the methods are highly analogous to thoseused every day by X-ray crystallographers andinvolve three steps: (1) determining the orientationof individual diffraction patterns; (2) ®tting a reci-procal lattice to observed re¯ections (i.e. indexingthe patterns); and (3) merging individual diffrac-tion patterns into a 3D data set consisting of dis-crete structure factors at reciprocal lattice positions.Despite this theoretical simplicity and numerousexamples of thin, 3D crystals, successful mergingof electron diffraction from such crystals has notpreviously been reported.

Nevertheless, previous electron microscopic ana-lyses of 3D crystals have demonstrated tremen-dous creativity. Two prominent examples aregp32*I (Grant et al., 1991) and crotoxin (Jeng &Chiu, 1983); in both cases, the unit cells consist ofseveral discrete molecular layers and the majorityof crystals were discovered to comprise less than afull unit cell. As a consequence, the symmetry ofany given crystal depends on its particular thick-ness (e.g. 1/4, 1/2, 3/4, or one unit cell) and a var-iety of methods were devised to classify crystalsprior to merging data. In the case of crotoxin, thispractical hurdle of classi®cation has so far provedinsurmountable. In the case of gp32*I, however, a3D reconstruction was determined from a subclassof negatively stained crystals containing half a unitcell (or 3/2 or 5/2) using standard methods for 2Dcrystals. The original crystals of light harvestingcomplex turned out to be stacks of 2D crystalswith random translations between the individual

Table 3. Phase statistics for (h, k, 0) projection

Resolution C2 symmetry P1 symmetry(AÊ ) Total reflections Unique reflections jmerge(

�)a Unique reflections jmerge(�)a jsymm(�)b

100-20 330 11 1.73 17 2.00 3.6920-14.1 237 8 2.69 15 3.21 8.0814.1-11.5 195 10 4.39 18 4.87 30.7811.5-10 183 11 5.94 21 8.34 25.1410-8.9 88 8 7.86 14 9.75 15.628.9-8.2 48 7 16.33 12 20.35 21.828.2-7.6 29 6 26.11 9 31.81 40.8Total 1124 67 9.86 111 10.34 20.03

a Phase residual weighted according to the signal-to-noise ratio (IQ) of individual re¯ections.b Unweighted phase residual comparing symmetry-related phases after averaging with P1 symmetry.


layers (KuÈ hlbrandt, 1988). In effect, these were nottruly 3D crystals, but a unique analysis was devel-oped to determine the relative shifts between thelayers. After compensating for the resulting MoireÂ

patterns, a projection map was calculated at 7 AÊ

resolution.Another novel approach was taken with insect

¯ight muscle (Taylor & Crowther, 1992), which

Figure 9. Comparison of the (h, k, 0) projection map with that from untilted crystals. a, The averaged (h, k, 0) pro-jection map obtained from this work by combining image phases with amplitudes from merged electron diffractioncurves. Distinct densities are observed, which we believe correspond to crystallographic dimers of Ca2�-ATPase andshading distinguishes the core regions of individual molecules. The projection of the structure from tubular crystals(Zhang et al., 1998) is overlaid at the top margin, showing the probable disposition of the molecules in the dimer;differences in density distribution within the projected molecules are likely to represent the conformational changethat accompanies calcium binding to Ca2�-ATPase. b, A previously published projection map from untilted, 3D crys-tals (Stokes & Green, 1990a), which has no clear molecular boundaries. Both maps contain two centered unit cellsand each unit cell contains four molecules. c, A packing diagram to explain the different density distributions inthese two maps. When projected along the c axis, densities from molecules in successive lamellae are superimposed,giving rise to the distinct densities seen in a. Projection from untilted crystals produces a systematic overlap of mol-ecules, which accounts for the more continuous density distribution in the corresponding projection map.


represents a veritable 3D crystal of actin and myo-sin. Early work had identi®ed two principal projec-tions of these crystals and had calculated 3D mapsfrom tilt series of sectioned material (Taylor et al.,1984); these sections had to be accurately cut paral-lel to the ®lament (i.e. crystal) axes and normal tothe principal projections. The novel approachemployed slightly oblique sections that progress-ively revealed different regions of the unit cell andprovided a full set of 3D data from a single micro-graph, thus avoiding all the problems with align-ing data from a tilt series. Sectioning was also usedfor thick 3D crystals of myosin S1, whose unit cellparameters had previously been determined byX-ray crystallography. A 3D structure was thencalculated from six tilt series about two of thesecrystal axes at 25 AÊ resolution (Winkelmann, 1991).

Catalase was the ®rst 3D crystal studied by elec-tron microscopy and has become a standard testspecimen due to its well de®ned unit cell and wellordered lattice. The molecular packing was theprincipal issue for many years and was initiallydetermined for the orthorhombic crystal form bysimulating the projection of a multilamellar crystalbased on that of a single layer (Unwin, 1975). Pack-ing normal to the lamellar plane was directlyobserved after sectioning the copper grids onwhich negatively stained crystals had beenadsorbed (Jesior, 1982). Molecular packing of thetrigonal crystal form was later deduced from(h, k, 0) and (0, k l) projections obtained by section-ing these thicker crystals (Akey et al., 1984). Thesesamples were unsuitable for 3D reconstruction,due to differential shrinkage during specimenpreparation and imaging. Ultimately, the atomicstructures of catalase and myosin S1 were deter-mined by X-ray crystallography, making furtherefforts by electron microscopy unnecessary, butcatalase is still being used as a test specimen todevelop electron crystallographic methods analo-gous to those presented here (Schroeder et al.,personal communication).

Generally speaking, the eccentricities of each 3Dcrystal form have precluded a uni®ed strategy forelectron crystallography; nevertheless, there arenumerous, more tractable crystals with orderedstacking and uncleavable unit cells that couldbene®t from a systematic approach to structuredetermination. A few recent examples are �29phage connector (Valpuesta et al., 1994), DNAplate crystals (Downing, 1984), cytochrome b6f(Mosser et al., 1997) and Na�/K�-ATPase (Taylor& Varga, 1994). Most of these crystals have beenshown to diffract to high resolution, presumablyhelped by the added constraints of a 3D unit celland the increased number of molecules in the crys-tals. However, the analyses to date have all endedwith projection maps of untilted crystals. Webelieve that our methodology should be generallyapplicable to thin, 3D crystals and thus representsa valuable supplement to existing methods forstructure determination by electron microscopy.

Data collection and analysis strategy

It is informative to compare our method withestablished methods used by X-ray crystallogra-phers and by electron microscopists studyingeither 2D protein crystals or thin, 3D crystals ofinorganic materials. All crystallographic methodsshare a common theoretical background, but mustaccommodate a variety of practical constraintsassociated with particular crystal morphologiesand radiation sources. Thin, 3D crystals used bymaterial scientists are morphologically most similarto our crystals, but the radiation insensitivity oftheir specimens allows material scientists to huntfor the principal zones of their crystal usingdouble-tilt holders. Also, the simplicity of the mol-ecules often allows structure modeling based on alimited set of Fourier data (e.g. diffraction intensi-ties only). Furthermore, the much smaller unit cellsizes mean that there are numerous unit cells evenin very thin crystals, thus producing well-de®nedre¯ections along all three crystal axes.

X-ray crystallographers bene®t from largercrystals which contain many more molecules, thusproducing sharp re¯ections and withstandingrelatively large doses of radiation; as a result, oscil-lation photography can be employed aboutselected axes to record intensities of the Fouriercomponents. Although modern, motorized electronmicroscope stages might be programmed to act asan oscillation camera, the high rate of radiationdamage by electrons would severely limit therange of oscillation data one could record from anindividual crystal; furthermore, the axis of oscil-lation cannot be controlled with available, ®xed-axis goiniometers. Nevertheless, each of our tiltseries represents a set of ``stills'' at de®ned inter-vals and it may be possible to adapt autoindexingprograms for determination of unit cell parametersby X-ray crystallography (Otwinowski & Minor,1997), though some modi®cation might be necess-ary for the severe anisotropy in the shape of ourre¯ections.

Electron microscopists have been highly success-ful in structure determination from 2D crystals dueto extensive efforts in developing the necessarymethodologies (Baldwin & Henderson, 1984;Downing, 1991; Henderson et al., 1986). 2D crystalsymmetry is constrained to a small number ofplane groups and out-of-plane diffraction alwaysconsists of a set of lattice lines running normal tothe crystal plane; thus, there has been no need toconsider unit cell parameters normal to the crystalplane. Amplitudes vary relatively slowly alongthese lines, and the orientation of tilted crystals cantherefore be determined with suf®cient accuracyfrom the foreshortening of the reciprocal lattice(Shaw & Hills, 1981). Thin, 3D crystals could, inprinciple, be analyzed by these same methods, butvery dense sampling of lattice lines would berequired to follow the more rapidly changingamplitudes; also, only a subset of crystals with aspeci®ed thickness (i.e. number of unit cells) could


be included. To avoid this labor-intensiveapproach, which relies on accurate determinationof crystal thickness, we have concentrated only onintensities near the reciprocal lattice positions andultimately will compensate for the differentnumbers of layers composing individual crystals.Thus, like X-ray crystallographers, our 3D data setconsists of discrete structure factors (Fh,k,l) at reci-procal lattice positions, rather than continuousFourier data along lattice lines.

Crystal thickness

In previous studies of thin, 3D crystals, both byourselves (Shi et al., 1995) and by others (Leapmanet al., 1993; Rez et al., 1992), much effort has beenmade to account for the thickness of crystals. Thisis because the sampling of Fourier data along c* isvery much dependent on this thickness, especiallywith a small number of unit cells along this axis.Here, however, we have con®ned ourselves to thethinnest crystals, which contain �2-5 unit cells, buthave not explicitly accounted for variability duringdata merging. Rather, a weighting scheme wasused during merging of diffraction data thatemphasized the ®t near the reciprocal lattice pos-itions and de-emphasized the ®t in between thesepositions. If scaled appropriately, amplitudes at thereciprocal lattice positions are independent ofthickness, even though the distribution of ampli-tudes between lattice positions varies. Thus, wehave built imprecision into the shape of the ®ttedcurves, while focussing on the coef®cient thatre¯ects the amplitude at the reciprocal latticeposition: i.e. jFh,k,lj. The curves used for the re®ne-ments (Figure 7) correspond to three unit cells, butfuture re®nement will include crystal thickness,together with tilt angle, tilt axis, scale and tempera-ture factors, as a ®tting parameter. It seems reason-able to allow non-integral numbers of unit cells toaccommodate disorder either in stacking or oncrystal surfaces; such an empirical use of crystalthickness to merge data would be analogous to thewidespread use of temperature factor to accountfor a variety of different kinds of disorder.

Similarly, we anticipate that crystal thicknesswill not pose major dif®culties during the mergingof image phases into a 3D data set. The phaseorigin normal to the crystal plane is not explicitlyspeci®ed during the merging of phase data fromsingle-layered, 2D crystals yet this phase origininevitably ends up in the middle of the recon-structed unit cell (i.e. at z � 0). During merging, aphase shift (±��a, ��b) is applied to each re¯ec-tion (h, k) as h��a �k��b. If the image is tilted,the re¯ection (h, k) also has a component of z* (orc*) and the phase shift therefore includes a corre-sponding component ��z, which ultimately con-strains the phase origin at z � 0. For multilamellarcrystals, the middle of three unit cells (z � 0) differsfrom the middle of four unit cells (z � c/2) by halfa unit cell and we envision two possible strategiesto combine data from even and odd numbers of

unit cells. The simplest is to search over a widerrange of phase shifts, to obtain a suf®ciently largez* component. However, it may prove morepractical to explicitly apply a phase shift of p tore¯ections with odd l, which will effectively shiftthe phase origin by half a unit cell along c. Com-parison of phase residuals with and without thisadditional phase shift could actually be used todistinguish crystals with even and odd numbers ofunit cells, much as inversion of axes is currentlyused to distinguish crystals that are upside down.

Our current resolution is limited to 8 AÊ primar-ily due to the low electron dose required to record10-12 electron diffraction patterns from an individ-ual crystal. Now that we have accurate unit cellparameters and a set of reference curves, we canincrease the dose and can record fewer diffractionpatterns at higher resolution. However, increasedcrystal thickness means that several additional fac-tors need to be considered when incorporating thehigher resolution data. Based on the distribution ofdiffraction amplitudes from tilt series and on thewidth of Laue zones, our crystals appear tocomprise between two and ®ve unit cells, whichcorresponds to a thickness between 300 and 750 AÊ .Both multiple and inelastic scattering increase withspecimen thickness and could potentially haveadverse effects on our data. However, recent stu-dies of electron energy loss have determined amean free path for inelastic scattering in ice of2000 AÊ at 120 kV (Grimm et al., 1996); the meanfree path for elastic scattering is two to three timeslonger than for inelastic scattering (Angert et al.,1996) and the use of 200 kV will increase this®gure by a factor of 1.3. Thus, our thin, 3D crystalssuffer from an increased background from inelasticscattering, which reduces the signal-to-noise ratiopredominantly at low resolution, but should notgenerate signi®cant amounts of multiple elasticscattering. Perhaps more serious is the increasedrange of defocus in images. For a 500-AÊ thick crys-tal with a mean defocus of 5000 AÊ at 200 kV, thecontrast transfer function from the top of the crys-tal will become completely out-of-phase with thatfrom the bottom at �3.6 AÊ resolution, and the sig-nal at 5 AÊ resolution would be reduced by a factorof 0.7. Another way to consider this problem isthrough the curvature of the Ewald sphere; thedifference between two Friedel-related rays isaccentuated in a thick structure due to the morerapid variation of structure factors along c*. Tocope with this problem, electron diffraction ampli-tudes, jFh,kj and jFÿh, ÿ kj could be treated indepen-dently and assigned to their proper respectivelocations along the lattice lines. In the case ofimages, a large tilt angle causes re¯ections to split,re¯ecting the slightly different scattering angle forthe Friedel-related rays. Normally, application ofthe tilted contrast transfer function (TTF;Henderson et al., 1986) recombines these rays, butthey could also be handled independently as longas the signal-to-noise ratio was not limiting.


A higher accelerating voltage (e.g. 300 kV) wouldameliorate all of these thickness-related problems.

(h, k, 0) projection

By taking into account the angle b, we havebeen able to obtain images that correspond to the(h, k, 0) projection. Previous publications usednegatively stained, small cylindrical crystals toestimate that b was close to 90� and assumedthat projections of untilted crystals were close tothe (h, k, 0) projection (Stokes & Green, 1990a,b);we can now say that the previous maps do notin fact correspond to this principal projection.Although the presence of cm symmetry wasoffered in support of the (h, k, 0) projection, cmsymmetry is actually obtained whenever thetilt axis is aligned with the b* axis, becauseFh,k,l � Fÿh,k, ÿ l in the C2 space group; fortuitously,untilted crystals have this symmetry regardless ofb because b* always lies in the untilted plane (x-yor a-b plane in Figure 1b). Of course, not everycrystal was perfectly untilted, but the presence ofcmm symmetry in diffraction amplitudes and cmsymmetry in phases were the primary criteria forincluding images in previous projection maps,which speci®cally selected crystals with b* in thex-y plane. Some of these crystals may have beentilted about their b axis, but would have been dis-carded due to their high phase residuals duringmerging. Thus, previously published maps almostcertainly correspond to the projection of untiltedCa2�-ATPase crystals, but not to the (h, k, 0) projec-tion.

A comparison of the current (h, k, 0) projectionmap and a previous untilted projection map isshown in Figure 9. The (h, k, 0) projection mapshows isolated densities that plausibly correspondto dimers of Ca2�-ATPase, whereas the previousmap contains density that is continuous along botha and b axes. The molecular packing diagram inFigure 9c shows how these different patterns ofdensity arise: projection along the c axis tends toseparate molecules above the bilayer from thoseunderneath, whereas projection normal to thebilayer produces a systematic overlap of densities.In fact, the particular arrangement of molecules inthe diagram is consistent with previous images ofnegatively stained crystals (Stokes & Green,1990b), of freeze-dried, shadowed crystals and ofthe (h, 0, l) projection from frozen-hydrated cylind-rical crystals (Cheong et al., 1996; Ogawa et al.,1998), all of which suggest that the cytoplasmic``nose'' points along the a axis. The (h, 0, l) projec-tion map also reveals the relative positions ofmolecules above and below the bilayer, which,prior to the a axis inversion applied by Cheonget al. (Figure 3b of Cheong et al., 1996), is consistentwith Figure 9c. The unit cell dimensions of cylind-rical crystals grown in 5% glycerol indicate thatthey are probably isomorphic to our crystal type II,with b � 98� (Table 1), whereas our (h, k, 0) projec-tion map is from the more dominant crystal type I

with b � 108�. However, the angle b is the onlydifference between these crystal types and molecu-lar packing within the lamellae appears to bepreserved in all multilamellar crystal forms studiedso far.

Thus, the strong densities in the (h, k, 0) projec-tion map most likely correspond to the core ofindividual Ca2�-ATPase molecules, which runsfrom the cytoplasmic to the lumenal ends of themolecule and which would include contributionsfrom the cytoplasmic, stalk, transmembrane, andlumenal domains. The overlapping densities withinthe dimer most likely correspond to the nose ofCa2�-ATPase, which is hypothesized to undergomajor conformational changes upon bindingcalcium (Ogawa et al., 1998). These features areillustrated at the top of Figure 9a, where the projec-tion of the 8AÊ structure from tubular crystals(Zhang et al., 1998) has been superimposed on eachmember of the crystallographic dimer. The projec-tions have an innately different appearance due tothe character of the data used for reconstruction,namely a resolution-dependent fade-out of Fourierpower in the image data used for the previous heli-cal reconstruction which is not present in the elec-tron diffraction amplitudes used in the currentstudy. Nevertheless, this comparison illustratesthat the dimensions and basic molecular shape arepreserved, but that the detailed distribution ofdensity within the molecule is somewhat different.Such differences are expected when comparingstructures from these two crystal forms, given thatthey represent enzymatic states before and afterbinding calcium at transport sites (Stokes &Lacapere, 1994). The conformational change thataccompanies this calcium binding is thought toinvolve a redistribution of density within the cyto-plasmic domain. In particular, the strong arc ofdensity at the outer margins of the dimer probablyre¯ects the inclination of the stalk away from thenose, which has been suggested both by projectionmaps from cylindrical crystals of Ca2�-ATPase(Cheong et al., 1996; Ogawa et al., 1998) and bycomparison of 3D structures for Ca2�-ATPase andH�-ATPase (D.L.S., Zhang, Auer & KuÈ hlbrandt,unpublished observations). This rearrangement ofthe cytoplasmic domain provides a physical mech-anism by which the cytoplasmic, ATP-binding siteis activated in response to cation binding withinthe membrane domain and is likely to be central tothe mechanism of energy coupling for the wholefamily of P-type ion pumps. Using our (h, k, 0)phase data as a reference, we are currently mer-ging phase data from tilted crystals and, using ourreference curves of electron diffraction, we areincorporating diffraction amplitudes at higher tiltangles and higher resolution. These additional datashould provide a proper 3D structure from thesethin, 3D crystals of Ca2�-ATPase and thus revealthe details of this critical conformational change inthree dimensions.


Materials and Methods

Crystallization

Sarcoplasmic reticulum was prepared from the whitemuscle of rabbit hind leg (Eletr & Inesi, 1972) and puri-®ed by Reactive Red af®nity chromatography as pre-viously described (Stokes & Green, 1990b).Crystallization was carried out by dialysis of the eluantagainst 100 mM KCl, 20 mM Mes (pH 6.0), 10 mMCaCl2, 3 mM MgCl2, 20% (v/v) glycerol, 0.1 mg/mlC12E8, 5 mM DTT. During crystallization, the tempera-ture was varied between 4 and 25�C, usually initiatingnucleation for two to three days at the higher tempera-ture and then switching to the lower temperature forseveral weeks. Alternatively, crystals were nucleated atlow temperature, brought to the higher temperature for�seven days and then returned to the lower tempera-ture, or simply left at low temperature for their entirenucleation and growth period. These different tempera-ture regimens were designed to produce the largest,thinnest, most uniform crystals possible (Shi et al., 1995).

Electron microscopy and image analysis

Frozen-hydrated crystals were prepared for electronmicroscopy ®rst by gently centrifuging crystals(1000 rpm), by removing the supernatant and by resus-pending in a glycerol-free solution containing 100 mMKCl, 1 mM CaCl2, 1 mM MgCl2, 20 mM Mes (pH 6.0).An optimal crystal concentration was determined byexamining air-dried samples in the electron microscope.Then, 5 ml was put on a perforated carbon ®lm that hadbeen treated by glow discharge in amyl amine vaporand, after blotting excess solution from the opposite sideof the carbon ®lm, the samples were plunged into anethane slush and stored in liquid N2.

Samples were examined in a Philips CM200 FEG elec-tron microscope (Philips Electronic Instruments, Eindho-ven NL) either with Gatan 626DH (Gatan Corp,Pleasanton, CA) or Oxford CT3500 (Oxford Instruments,Oxford, UK) cryoholders. Low dose conditions wereused to collect both electron diffraction patterns andimages and the actual dose was determined with aGatan 794 slow-scan CCD camera, which had been cali-brated by ®lm density and by a picoammeter to respondwith 24 counts for each electron. Electron diffraction pat-terns were recorded on this CCD camera at a cameralength of 1.9 m and a dose of �0.1 electrons/AÊ 2. Gener-ally, a 25-100 mm2 area on the crystal was illuminatedand a tilt series was recorded consisting of 10-12 tiltangles ranging from ÿ30� to �30�. Initially, we recordedsuch tilt series on ®lm and digitized the ®lms with amicrodensitometer, but the inef®ciency of such a processand inaccuracy in ®lm orientation during digitizationmade the CCD camera indispensable.

A ¯ow chart summarizing the individual steps in ouranalysis of electron diffraction patterns is shown inFigure 2. Each individual diffraction pattern was ®rstprocessed with standard MRC programs (Baldwin &Henderson, 1984) to subtract background (BACKAUTO),to re®ne lattice parameters and to integrate spot intensi-ties (PICKAUTO); we found the CCD to respond linearlyto electrons up to 14,000 counts and modi®ed the dose-response curve for PICKAUTO accordingly. We devel-oped our own program (CSTARFIT) for determiningcrystal orientation based on lattice parameters from thetilt series; values from lattice foreshortening (Shaw &Hills, 1981) were not accurate enough, especially at low

tilt angles. As described in Results, peaks along the c*axis were identi®ed in these individual merged data setsand their centroid positions were used for least-squaresdetermination of a reciprocal lattice (LATTICEFIT).Thus, each tilt series provided an independent estimateof unit cell parameters. Based on orientations fromCSTARFIT and on the average lattice parameters, aslightly modi®ed version of the program MERGEDIFFwas used to merge data from all the tilt series (MERGE-DIFF3D). This merged data set was used to re®ne thelength of the c* axis (LATTICEREFINE) and then curveswere ®t to these data, using the MRC program SYNCFITthat had been modi®ed to ®t non-overlapping sinc func-tions at reciprocal lattice positions instead of the over-lapping sinc functions used for 2D crystals(SYNCFIT3D). In order to re®ne tilt angles, tilt axes,scale and temperature factors of individual diffractionpatterns, a new program (ANGLEREFINE) ®t the datawith a sum of Gaussian functions:X

i

Ii expÿ13n�z� ÿ zo�

i �2jc�j2

� �;

where n is the number of unit cells (assumed to be threeat this stage), zo*

i is the coordinate of the ith Bragg re¯ec-tion with intensity Ii and jc*j is the length of the recipro-cal lattice vector. Each Gaussian term mimicked thecentral peak of a sinc function for n unit cells (seeFigure 1c), thus eliminating subsidiary peaks from there®nement and emphasizing data near the reciprocal lat-tice positions. Finally, data was merged again, curveswere re®tted with sinc functions, and an R-factor wascalculated with and without applying a Gaussianweight:

R �

Xi

wijAe�ÿBD2�Iobsi ÿ Icurve�z�i �jX

i

wiIcurve�z�i �

;

where Iobsi is the ith observed intensity, Icurve is the corre-

sponding intensity from the curve at the reciprocal coor-dinate z*i (calculated from the tilt angle and tilt axis), A isthe scale factor, B is the temperature factor, D is the dis-tance from the reciprocal space origin, wi is a Gaussianweight:

wi � expÿ13n�z� ÿ zo��2

jc�j2� �

as described above. In addition to merging data with C2symmetry, P1 symmetry was used to verify the 2-foldsymmetry expected in this diffraction data.

In order to record images of the (h, k, 0) projection,electron diffraction was used to identify suitable crystalsand the appropriate tilt angles. Speci®cally, diffractionwas recorded from untilted crystals to determine theirorientation. For those with their b axis within 10� of thephysical tilt axis of the goiniometer, further diffractionpatterns were recorded at ÿ18, ÿ8, �8 and �18� and theangle nearest the (h, k, 0) projection was identi®ed by thepresence of Laue zones. Several more closely spaced pat-terns were then recorded to get as close as possible tothe (h, k, 0) projection and to provide a tilt series of dif-fraction data, which was later used to verify the crystalform and orientation (see Results). The total accumulateddose was <1 electron/AÊ 2. Several ¯ood-beam imageswere then recorded at different positions along the crys-tal, either on the CCD or on ®lm at 68,000� magni®-cation with a dose of �10 electrons/AÊ 2. Suitable areas on


®lms were identi®ed by optical diffraction and2048 � 2048 pixel areas were digitized at 13 mm intervalswith a PDS 1010GM densitometer (Orbital Sciences,Pomona, CA). Standard MRC programs were used tocorrect crystal distortions, to extract phases from theimages and to correct for the contrast transfer function(Henderson et al., 1986). Although the best images wereclose enough to the (h, k, 0) projection that no Lauezones were visible, the tilt axis and angle were estimatedfrom asymmetry in the distribution of strong re¯ections.The standard MRC phase origin re®nement and mergingprogram (ORIGTILT) was modi®ed slightly for thesemultilamellar crystals. Similar to MERGDIFF3D, onlydata within the central sinc function peak at each Braggre¯ection were considered, which required an estimateof the number of unit cells composing the crystal(Figure 1c). Average phases for the (h, k, 0) projectionwere determined by a weighted addition of phases forre¯ections with c* <0.001 AÊ ÿ1; i.e. within the peak for the(h, k, 0) re¯ection. As for analysis of 2D crystals, thisweight depended on the signal-to-noise ratio (IQ) of agiven re¯ection (Henderson et al., 1986). Amplitudesfrom the sinc function coef®cients of the merged electrondiffraction curves were combined with these averagedphases to produce the (h, k, 0) projection map.

Low-angle X-ray diffraction

Crystal pellets were prepared for low-angle X-ray dif-fraction by allowing 100 mg of crystallized protein tonaturally sediment in their mother liquor within 1 mmglass, X-ray capillaries. After removing excess solution,capillaries were sealed with wax, were mounted on agoiniometer and were kept at 4�C. X-ray diffraction wasrecorded on ®lm with CuKa X-rays generated from aRigaku RU-2000 (Rigaku USA, Danvers, MA) rotatinganode selected with a graphite monochromator and a0.4 mm collimator at a camera length of �480 mm.Helium-®lled beam tunnels were used to reduce back-ground scattering and exposure times were 12-24 hours.Films were digitized with a PDS 1010GM microdensit-ometer at 50 mm intervals and positions of re¯ectionswere measured after integration of patterns along 25�arcs centered on either the meridian or the equator.

Acknowledgments

This work was funded by the grant AR40997 from theNIH.

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Edited by W. Baumeister

(Received 4 June 1998; received in revised form 25 September 1998; accepted 25 September 1998)


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