¹Verna and Marrs McLean Departmentof Biochemistry and The W. M. Keck Center for Computational Biology, Baylor College of Medicine, One Baylor Plaza, Houston, Texas 77030, USA

² Department of Molecular Physiologyand Biophysics, Baylor College of Medicine, One Baylor Plaza, Houston,Texas 77030, USA

³ Fritz Haber Institute of the Max Planck SocietyFaradayweg 4-6, D-14195 Berlin, Germany

SUMMARY

We exploit the random orientations of ice-embedded molecules imaged in an electron cryomicroscope to determine the three-dimensional structure of the Ca²⁺-release channel from the sarcoplasmic reticulum (SR) in its closed state, without tilting the specimen holder. Our new reconstruction approac hincludes an exhaustive search of all different characteristic projection images in the micrographs and the assignment of Euler angle orientations to these views. The resulting 30 Å three-dimensional map implied reveals a structure in which the transmembrane region exhibits no apparent opening on the SR lumen side. The extended cytoplasmic region has a hollow appearance and consists, in each monomer, of a clamp-shaped and a handle-shaped domain.

Introduction

Electron cryomicroscopy has become a unique tool forstudying the structures of large macromolecular assemblies which cannot be readily approached by X-ray crystallography or NMR ¹. Vitreous ice is a natural, structure-preserving embedding medium for biological samples ^{2, 3} . Because of the inherent simplicity and reproducibility of the procedure,the macromolecules can be prepared in different chemical or functionalstates ⁴ . The reliability of the technique has been illustrated by a number of studies of large oligomeric assemblies in which the X-ray structures of individual components were known ^5,6. One of the powers of electron microscopy of biological samples is its direct retrieval of the structure from the images without the "phase" problem in conventionalcrystallography ⁷. This imaging technique is now well capable of elucidating multi-componentbiological structures at the 10-40 Å resolution level ^8-13.

Here we present a three-dimensional (3D) reconstruction of the Ca²⁺-release channel in its closed state based on 3,000 electron microscopicimages of randomly oriented molecules embedded in vitreous ice. The philosophy behind the angular reconstitution approach ^{14, 15}- used here for the first time to solve a biological structure - is that even untilted specimens ofnon-crystallized macromolecules contain the molecules in a continuum ofdifferent orientations relative to the electron beam. The systematic information extracted from a very large number of electron images of randomly oriented macromolecules should thussuffice to calculate the underlying molecular structure in threedimensions.

Purification and cryo-imaging

The Ca²⁺-release channel was purified from rabbit fast-twitch skeletal muscle using ion-exchange chromatography on DEAE-Trisacryl M and sedimentation on a linear sucrose gradient at high salt concentration (0.3M KCl) ¹⁶. The zwitterionic CHAPS (3-[(3-cholamidopropyl)dimethylammonio]-1-propanesulphonate) detergent was used tosolubilize the heavy SR membranes. Protease inhibitors (200 mM PMSF, 200 mMaminobenzamidine, 2 mg/ml aprotinin, 2 mg/ml pepstatin A, 10 mg/ml soybean trypsin inhibitor) were used throughout the preparation in 10 mM MOPS(pH 7.4). By depleting the Ca²⁺ with 1 mM EGTA in 300 mM KCl,10 mM MOPS (pH 7.4), the Ca²⁺-release channel protein was driven towards its closed state ¹⁷.

The protein solution was vitrified without adding stain or fixative in order to preserve the functional state of the protein during the electronmicroscopic observation. The top row in Figure 1 shows six raw molecularimages of the ice-embedded Ca²⁺-release channel in different orientations taken at a defocusvalue of ~ 2.8 um in a JEOL1200 electron cryomicroscopeoperated at 100 keV ¹⁸. The best 4 micrographs were digitized in a Perkin Elmermicrodensitometer using a step size of 20 um (6.7 Å on the specimen scale). The defocus values of the images were determinedcomputationally from the maxima and minima positions of the contrast transfer function rings seen in power spectra of the images from eachmicrograph. After the micrographs were confirmed to have similar defocus values, they were processed as a single data set following the strategy depicted in Figure 1. All the data processing was performed in the context of the IMAGIC-5 software ¹⁹ on either Silicon Graphics Indigo R4400 or DEC 3000 model 500 AXPworkstations.

Image alignment and characteristic views

The raw images of individual channel proteins are verynoisy and of low contrast (Figure 1, top row). In the angular reconstitution approach ^{14, 15}, one typically works with averages of a statistically significant number of raw molecular images. Average images have a much higher signal-to-noise ratio than the raw images and this reduction of noise facilitatesall further processing. Since, however, it is only useful to average imagescorresponding to the molecule in the same orientation, the initial task inour reconstruction scheme (Figure 1) is to sort the thousands of raw molecular images into homogeneous groups which can be averaged into 'characteristic views' ²⁰ .

Figure 1. Scheme for 3D reconstruction of 100 kVelectron images of ice-embedded Ca2+-release channel taken withdefocus between 2.4 - 2.8 um. The selected 3,000 particle images are aligned by iterativemulti-reference alignment techniques, and sorted into homogeneous classesof similar images by automatic multivariate statistical classificationprocedures 23, 24. All molecular images belonging to the same class are averaged to producenoise-reduced class averages or characteristic views. An Euler angleorientation is assigned to each class average by the angular reconstitutiontechnique. A first 3D reconstruction is computed and used to produce reprojected images, which, in turn, areused as reference images for realignment of the original raw image data setand for improving the accuracy of the Euler angle determinations. Six (leftpanel from top to bottom) of the 150 final class averages with different Euler angles match well with rawimages of the same angular views (top panel from left to right) and thecorresponding reprojections of 3D reconstruction (right panel from top tobottom). A final 3D map is shown as a stereo view at an oblique angle (bottom panel). The solid line arrowsrefer to the directions of image processing steps and the dashed linearrows refer to the examples of image data at different stages ofprocessing and the final 3D structure.

Of the three translational degrees of freedom (x,y,z) themolecules have, only the (x,y) translations in the plane of the grid are of relevance because the microscope projects our molecules alongthe beam direction (z). The molecules also have three rotational degrees offreedom (Euler angles: [[alpha]], [[beta]], [[gamma]]). Whereas one ([[alpha]]) represents only a rotation of the image in the plane of the grid, theremaining two Euler angles ([[beta]], [[gamma]]) correspond to rotations ofthe molecule in directions out of the plane of the grid and lead tofundamentally different projection images.

Correlation function-based alignment procedures have beendesigned to eliminate the translational (x,y) and rotational in-planedifferences ([[alpha]]) between otherwise identicalimages ^{21, 22}. For more complicated data sets in which different ([[beta]],[[gamma]]) projections of a structure are mixed, multi-reference alignment (MRA)procedures have been proposed ²⁰. Such alignments help reduce the number of degrees of freedom or thecomplexity of a data set.

In this study, the selected molecular images were firstcentered by translational alignment relative to the rotationally averagedtotal sum of the images (Figure 1). Multivariate statistical data compression²³ and automatic classification²⁴ procedures were then used to find similar images in similarrotational orientations in a procedure known as "alignment by classification"²⁵. This procedure avoids bias towards any specific reference image andclearly revealed the four-fold symmetry properties of the molecule (resultsnot shown). The class averages resulting from this phase of the analysiswere then used as a set of independent reference images for a conventional, iterative MRA procedure ²⁰. The procedures used so far, however, do not ensure that all referenceimages will share a common 3D origin (x,y,z) and a standard rotationalorientation in terms of the Euler angle [[alpha]]. Thus, the aligned data set - in these early phases of the analysis -remains more complex than necessary. In later phases of the procedures onecan generate sets of reference images which are perfect in terms of their3D consistency and which can be used to optimize the alignment in this sense.

Assignments and reconstruction

A sufficiently large set of good, noise-free 2-dimensional(2D) projection images (characteristic views) of a 3D structure indifferent projection directions suffices to calculate a 3D reconstructionto high resolution ^26,27using appropriate reconstruction schemes for randomly distributedprojection directions, such as the exact-filter back projectionalgorithm ^{28, 29}. However, since we are exploiting the random orientations of particles in the embedding medium rather than actually tilting aspecimen, we originally have no clue about the relative orientations of ourinput 2D projection images. We use the angular reconstitution technique todetermine these Euler angular orientations. The angular reconstitution method is based on the common lineprojection (CLP) theorem ¹⁴, stating that any two 2D projections of a 3D object share at least oneline projection. Our Euler angle determination with CLPs is the real-spaceequivalentof the classical common lines technique, commonly practiced for orientationdetermination of icosahedral virus particle in its 3Dreconstruction ^30-32.

The search for the best relative Euler angles assignmentsfor a set of 2D projection images (class averages) is performed by firstcalculating all possible 1D projections ("sinograms") from each of the 2Dprojection images ¹⁴. For finding common line projections between two 2D projection images,their sinograms are compared line-by-line in so-called sinogram correlationfunctions (Figure 2). For the Ca²⁺-release channel, with four-fold rotational symmetry, there are four CLPsper pair of projections in the sinogram correlation functions. For the bestEuler orientation of the projection, all corresponding peaks in thesinogram correlation functions have the highest value and should be equivalent in height to each other (Figure2). The relative standard deviation of the peak heights among correspondingpeaks serves as a consistency check and may be used to exclude poorprojection images.

Figure 2. Sinograms and Sinogram correlation functions

Left: Self Sinogram Correlation Function (SSCF) between projection imageand itself.

a,b: a projection image (class average) resultingfrom an exhaustive search for all characteristic projection images presentin the data set.

c,d: the "sinogram" of the projection image is thecollection of all line projections through the 2D projection image. Thefirst line projection of a, i.e., the top line of c, by summing all horizontal lines of the image in a.. The secondline of the sinogram is line-projection in a direction of typically 1[[ring]]away from the first projection direction, etc.

e: SSCF of the projection image in a. Eachpoint of the sinogram correlation function is calculated as the correlation(inner product) between two lines of the input sinograms as illustrated by the lay-out ofthe montage. Sinogram correlation functions calculated over 0-360[[ring]], have a two-fold redundancy because any line projection of a 2D image isthe mirror of the line projection in the opposite direction. The four color-coded (dots plus corresponding sinogramlines) symmetry-related peaks in the SSCF thus occur twice at positions corresponding to a 180[[ring]] distance. The SSCF of any 2D projection has an additional diagonalsymmetry as is obvious from this illustration. SSCFs are mainly importantfor the first Euler angle assignments of (highly) symmetric particles.

Right: Cross Sinogram Correlation Function (CSCF) between two projectionimages.

a,b: input projection images (class averages).

c,d: the "sinogram" of the projection images a,b.

e: CSCF of projection images a,b.

The four color-coded dots (plus corresponding sinogramlines) indicate the optimal relative Euler angle orientations of these twoprojections assuming four-fold symmetry. In final phases of the "angular reconstitution" analysis all Euler angleassignments are performed using CSCFs.

The Euler angle determination is done stepwise with an increasing number ofprojection images. First we start with one projection image with a lowrelative standard deviation of the symmetry-related peaks in the SelfSinogram Correlation Function ("SSCF",Figure 2, left panel e). For assigning Euler angles to subsequentprojection images we search for symmetry-related peaks in the SSCF of thenew projections and in the Cross Sinogram Correlation Functions ("CSCF") ofthe oldprojection images (which already have been assigned Euler angleorientations) simultaneously. The search is performed as a complete ("bruteforce") search over all Euler angles corresponding to the asymmetrictriangle for the given point-group symmetry. For the C4 point group symmetry of the Ca²⁺-release channel, theasymmetric "triangle" covers one fourth of the unit sphere: a segment ofthe sphere from the north pole to the south pole spanning 90[[ring]] along theequator. The [[beta]] angle ranges from 0[[ring]] to 180[[ring]], while [[gamma]] ranges from 0[[ring]]to 90[[ring]]. After having assigned Euler orientations to a set of projections, a first3D density distribution of the object is calculated using the exact filterback projection algorithm ^{28, 29}. For our first 3D reconstruction we assigned Euler angles to the 30 bestclass averages taken out of a total of 200 characteristic views which hadresulted from the first rounds of alignments and classification.

3D Alignment Refinement

Once a preliminary 3D reconstruction is available, some essential refinement procedures can be used (Figure 1). First the 3D map isreprojected into a set of Euler directions homogeneously covering theasymmetric triangle. These reprojections are comparable to thecharacteristic views used for computing the first 3Dmap, but are uniformly distributed over the unique part of the unit sphere.These reprojections share the same 3D origin (x,y,z) and are all computedwith the Euler angle a set to zero and thus have a common rotationalorientation in the plane of the grid. In other words, these reprojected images are perfect reference images fornew rounds of multi-reference alignment of the raw images. Rare molecularviews, which were missed in the first round(s) of alignment, will typicallybe picked up in such refinements and will become significant characteristic views in theMSA/classification procedures. The number of reprojections used for thisrealignment is rather high (150 in our study) and in general depends on thecomplexity and on the point group symmetry of the molecule. The re-alignment of the full data with respect to this largenumber of reference images is currently one of the most CPU-intensive partsof our procedures and may take days of CPU on a modern workstation.

Anchor Set Refinement of Euler Angles

A preliminary 3D reconstruction can also be used for a refinement of Eulerangle assignments we call "anchor set refinement" (Figure 1). Reprojectionsfrom a 3D reconstruction are perfectly consistent with each other in thesense that they are ideally centered with respect to a common 3D origin and the symmetry axes for thegiven point group symmetry. Moreover, the reprojections have even lessnoise than the original characteristic views because of the averaging in 3Dspace that takes place during 3D reconstruction. The assignment of Euler angles by using only the CSCFs of agiven class average with respect to the, say 30, reprojected images of theanchor set is thus more sensitive and precise than the Euler-angleassignments of the first round of processing. The standard deviation error values associated with each of the inputprojections will also be more discriminative since there are - perdefinition - no inconsistencies within the anchor set.

Reprojections from an initial 3D structure to aiddetermining particle centers or to find/refine Eulerorientations ³³ have been used quite effectively for analyzing icosahedralparticles ^13,34. The number of reprojections used for a highly symmetrical objectcan be quite small as shown in the study of Crowther et al. who used only 3 reprojections from an initial 3Dmap ³⁴Their technique is the Fourier space equivalent of our real-space anchorset approach. Provided the number of reprojections in the asymmetrictriangle is (very) large, correlation of the images with the reprojectionscan also provide refined orientationinformation ^{13, 15, 33, 35}.

Structure of the channel

Through the iterative refinement steps based onreprojections of previous 3D maps (Figure 1), both the quality of the classaverages and of the 3D reconstruction was improved significantly. The final 3D mapwas computed from 150 class averages (Figure 1) with a sufficiently uniformdistribution of Euler angles to attain 30 Å isotropic resolution. The reprojections of the final reconstruction (Figure 1 left and right panels with 6 corresponding views) comparewell with the corresponding characteristic views produced from the rawimages of single channel proteins (Figure 1 top panel). The validity of the3D structure was confirmed by a 3D Fourier shell correlation between two independent reconstructions ²⁸, each calculated with 1,500 molecular images of the channel protein.

Figure 3. Surface representation of the 3D structureof ice-embedded Ca²⁺-release channel in closed state in (a) bottom view, (b) top view and (c) side view. The volume of the reconstruction at the chosen densitythreshold level corresponds to a mass of 2.4 million daltons assuming aprotein density of 1.35 g/cm3.

The 3D structure of the Ca²⁺ release channelseen from different directions (Figure 3a-c) is strikingly empty whencompared to familiar soluble proteins or to the 3D structure of anegatively stained channel ³⁶. The bottom view of the channel protein (Figure 3a) shows an outersquare and an inner square, which are rotated with respect to each otherover an angle of ~ 40[[ring]]. The top view of the protein (Figure 3b), facing the cytoplasm towards thetransverse tubule, shows a central opening of ~ 50 Å in diameter. Radialchannels found earlier ³⁶ are not seen in our reconstruction. The rim of the central channel forms acontinuous network that extends to the peripheral mass (Figure 1). At thecorners of the peripheral mass is a most characteristic domain shaped likea closed laboratory clamp (single arrow) with four fingers. "Handles" or "bridging domains" (doublearrows) interconnect the four clamps. Each of these features may representdistinct domains of the protein.

The side view (Figure 3c) of the channel protein has amushroom-shape with the length of the stem ~ 65 Å, part of which should contain the membrane-spanning domain of the channelprotein. The flat side of the mushroom stem corresponds to the inner squareshape seen in the bottom view (figure 3a). The number of residues on thelumenal side of the SR membrane is thought to be small ^{37, 38}. The membrane-spanning region of the channel is thus likely to be close to the bottomsurface of the mushroom stem. It has been suggested that themembrane-spanning domain contains either 4 or 10 transmembrane alphahelices per subunit ^{37, 38}. Taking the typical thickness of the membrane to be ~ 45 Å, we have estimated the volume of the membrane-spanning domain close to thebottom of the mushroom stem to be ~ 120,000 ų per subunit.This molecular volume would easily accommodate a bundle of 10 nearlyparallel alpha helices per subunit.

The oblique stereo view (Figure1, bottom panel) illustrates that thebridging domain is connected to the membrane-spanning domain through acolumn of density protruding from the membrane. The rather hollow andpretzel appearance of the putative cytoplasmic portion of the structure may be associated with efficient diffusionpathways for the Ca²⁺ into the cytoplasm and its binding todifferent ligands and modulators. The central cavity seen in the top sidedoes not penetrate through the stemof the mushroom. As would be expected for a closed channel, there is noobvious opening of the Ca²⁺-release channel on the lumenal sideof this membrane protein.

Our analysis has provided the first 3D structure of theCa²⁺-release channel in the absence of Ca²⁺ and the observed features must be related to this specific chemical stateof the channel protein. The angular reconstitution method, used here forthe first time to solve a biological structure, is a powerful 3Dreconstruction approach that can beused, for instance, to map the binding domains for various macromolecularmodulators and sequence-specific antibody fragments. Because of thesimplicity and reproducibility of the associated cryomicroscopy techniques,the angular reconstitutionapproach is particularly well suited for examining different chemical and functionalstates of large oligomers, such as the Ca²⁺-release channel.

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This research has been supported by grants from the NCRR of NIH, W.M.Keck Foundation, and R. Welch Foundation to W.C.; Muscular DystrophyAssociation and NIH to S.L.H.; and DFG to M.v.H. We thank Michael F. Schmidfor helpful comments, Michael Schatz and Ralf Schmidt of Image Science Software GmbH for the IMAGIC Softwaresystem, and Angela Loh of Digital Equipment Corporation for the loan of aDEC Alpha workstation.

Added note: After the submission of this manuscript, a 3Dstructure of calcium-release channel was published by Radermacher, M., et al. Cryo-electron microscopy and three-dimensional reconstruction of thecalcium channel/ryanodine receptor from skeletal muscle. J. Cell Biol.127, 411-423 (1994).

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