Ways & Means 741
High-resolution icosahedral reconstruction: fulfilling the promiseof cryo-electron microscopyErika J Mancini, Felix de Haas and Stephen D Fuller*
Address: The Structural Biology Programme, European MolecularBiology Laboratory, Meyerhofstrabe 1, Postfach 10.2209, 69117Heidelberg, Federal Republic of Germany.
*Corresponding author.E-mail: fuller@EMBL-Heidelberg.DE
Structure 15 June 1997, 5:741750http://biomednet.com/elecref/0969212600500741
Current Biology Ltd ISSN 0969-2126
SummaryTwo recent papers have defined the secondary structureof the hepatitis B virus capsid using a combination of cryo-electron microscopy and icosahedral image reconstruction.These two papers do more than reveal a new fold for avirus protein; they herald a new era in which image recon-struction of single particles will provide reliable high-reso-lution structural information. In revealing the promise ofthese techniques to the structural biology community,their two papers should play a seminal role for single parti-cle work, similar to that of the work of Unwin and Hen-derson  on bacteriorhodopsin in revealing the potentialof electron microscopy of membrane protein crystals.Indeed, the success of these single particle methods owesmuch to the development of high-resolution techniquesfor two-dimensional crystals. This review will summarizesome of the history of icosahedral reconstruction fromcryo-electron micrographs, compare the two differentapproaches used to obtain the recent results and outlinesome of the challenges and promises for the future.
IntroductionIcosahedral reconstruction is a type of single particleimage reconstruction in which the process of combiningimages of individual particles in random orientations toyield a structure is aided by the icosahedral symmetry ofthe particle. In this way, the progress made in icosahedralreconstruction provides a glimpse of the future of othersingle particle methods which do not rely upon the sym-metry of the structure and have recently achieved break-throughs of their own [2,3]. In all cases, the quality of thefinal structure is determined by the precision and accuracyof the alignment of the individual views, rather than bythe presence of order in the arrangement of individual par-ticles. The two papers which breached the 10 barrier forthe resolution of such a reconstruction both used the samewell-defined N-terminal fragment (residues 1149) of thehepatitis B capsid (HBc) in their studies. This fragment ofthe HBc assembles upon expression in Escherichia coli toyield T=4 (360 diameter) and T=3 (320 diameter)capsids. The structure of this capsid had been determined
initially by Crowther et al.  to 30 and has been shownto be conserved in different constructs of varying length,including those corresponding to hepdnaviruses of otherspecies [5,6]. This set the stage for the higher resolutionwork [7,8] described below. A third paper reports a 9 map of a larger particle, the 600 diameter bovine papillo-mavirus , using an overall strategy similar to that ofConway et al. .
Overview of the methodThe use of icosahedral reconstruction in combination withcryo-electron microscopy is the marriage of two comple-mentary developments [10,11]. Crowther introduced theuse of common lines as a method for determining the ori-entation (Euler angles ,,) and phase origin (x,y) of anicosahedral particle [12,13]. Once their orientations areestablished, the images of separate particles in differentorientations are combined by considering them as separateviews of the same structure. This is done using the projec-tion theorem for Fourier transforms and the 60-fold (532)symmetry of the structure. Each individual particle trans-form is placed into the three-dimensional transform in its60 equivalent positions. The assembled data from all par-ticles is then used to calculate the coefficients of a seriesof expansion functions with 52 symmetry by linear leastsquares. This series is subsequently inverted to producethe density sampled in Cartesian coordinates. The eigen-values for the linear least squares determination of thecoefficients of the expansion functions reveal how wellthese coefficients, and hence the final map, are deter-mined. Eigenvalues of 1 indicate that the ensemble ofparticle data has determined the reconstruction whilelarger values indicate that it is overdetermined so that thecoefficients are determined by averaging. This entire pro-cedure rests on the twin assumptions of icosahedral sym-metry in the particle and the constancy of the structurefrom particle to particle. These are very dubious assump-tions when data from negatively stained samples are usedas virions are often distorted by the staining process. Cryo-electron microscopy makes these assumptions more reli-able by eliminating the stain  and preserving theparticle in water . Typically, a drop of virus suspensionis placed on a microscope grid which is covered by a holeycarbon film. The grid is blotted to produce a very thin(~1000) layer of the sample across the holes of thecarbon film. This thin layer is rapidly cooled by plunginginto a bath of ethane slush held in a container of liquidnitrogen [10,14]. The very rapid cooling causes the forma-tion of a vitrified sample which provides an aqueous envi-ronment to preserve the sample. Indeed, a number ofdynamic particles, including microtubules  and
membrane viruses [18,19], can be visualized in an intactform only by cryo-electron microscopy.
This preservation, however, comes with a cost; cryo-elec-tron micrographs have substantially lower contrast thannegatively stained ones and are substantially morecomplex because the entire particle, including its interiorstructures, is seen in projection. The contrast in the imagecomes primarily from defocus phase contrast, whichaccentuates certain resolution ranges in the image andsuppresses others. This effect must be corrected (videinfra) in the final structure. In the first work with nega-tively stained material [13,20], the orientation of the indi-vidual particles was determined by eye and then theseorientations refined using their common lines phase resid-uals. Identification of the view by eye is possible for rela-tively few orientations of an unstained virus particle invitrified water. A modification of the original common
lines residual which is appropriately weighted for thedegeneracy of the lines near symmetry axes allows the ori-entation to be determined computationally . Thedetermination of orientation as the one with the lowestweighted common lines residual is the approach used atthe beginning of the solution of a new structure . Itsadvantage is that the only assumption made concerningthe particle is that it is icosahedrally symmetric. Unfortu-nately, the reliability of this approach is compromised bythe low signal-to-noise ratio in the images and the possi-bility of variation within the population of particles .Consequently, as soon as an initial reconstruction has beencalculated and seen to be reliable by comparing recon-structions derived from independent sets of particles,model-based methods are used to refine the orientations[4,21]. The implementation of model-based methods con-verted icosahedral reconstruction from an intricate puzzleto be solved by intuition and perseverance to a reliablemethod for structure determination. These methods alsomake it practical to screen, and hence include, largernumbers of particles into a reconstruction and conse-quently to increase the signal-to-noise ratio and resolutionof the final map.
The history of the field can be summarized in a revealingchart (Fig. 1) of the increase in resolution of representa-tive, published structures over time. The chart shows agradual increase in resolution from worse than 30 toaround 20 as the advent of model-based orientationmethods allowed inclusion of increased numbers of parti-cles. The second marked increase in resolution, which cul-minated in the two HBc structures, has a second cause: theuse of data from field emission gun (FEG) equippedmicroscopes. The higher coherence of these sources pro-duces an image with more contrast at high resolution .The effect is synergistic for icosahedral reconstructionbecause the effectiveness of averaging, and hence thequality of the map which is used for further alignment, isdependent upon the precision of alignment. More strengthin the higher resolution data of an image allows more accu-rate alignment and hence allows the averaging of higherresolution data. Reconstructions performed with such highquality data (indicated by m in Fig. 1) result in a higherresolution for the same number of images. Indeed, one canextrapolate from the least squares fit to the progress ofreconstructions which relied upon conventional illumina-tion (Fig. 1) that without the use of FEG microscopederived data the 10 barrier would have been crossed inthe next millennium and require many more images.
Just combine lots of images and you see helicesA crystallographer colleague summed up a widespreadimpression of the recent advances in resolution in a strik-ing way. His comment was that he hoped that the twopapers would inspire electron microscopists to be morebold in interpreting their data and in using larger and larger
742 Structure 1997, Vol 5 No 6
Improving resolution of reconstructions. The improvement in theresolution of published icosahedral reconstructions from cryo-electronmicrographs. (a) The reported resolution as a function of the date ofpublication. (b) The number of particles included in the reconstructionsshown in (a). The least squares fitted line indicates the improvingresolution of reconstructions from cryo-electron micrograph data takenusing conventional illumination (l). Reconstructions from datacollected with field emission gun (FEG) illumination (m) yield higherresolution for the same number of particles. The reconstructionsshown [4,69,18,19,26,3234,5580] were chosen to berepresentative rather than exhaustive. Some reconstructions combineimages of the same particles at different defocuses to produce thefinal structure but all are displayed as the number of particles.
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data sets. It was a satisfying feeling to realize that our fieldhad become so respectable that the X-ray crystallographersnow thought that we were afflicted with caution. However,the comment misses two important features of reconstruc-tion from cryo-electron micrographs. It is not only thenumber of particles used in the reconstruction but theimproved ability to orient them accurately with high preci-sion that has led to the increase in resolution. Hence, themethod of orientation is critical. Particles must also beselected carefully. Most biological specimens show hetero-geneity. A major advantage of electron microscopy is thatone can consider each particle separately and so excludethose which should not contribute to the average. TheHBc case is an extreme one as the preparation containsboth T=3 and T=4 particles which must be treated sepa-rately . In a sense the quality of the reconstruction isoften a function of the fraction of particles excluded as wellas the number of particles included in the final map.
An essential distinction between single particle methodsand crystallographic ones is that there is no truly objectivemeasure of the quality of the data, such as the strength of areflection, except for the quality of the final structure. Onecan measure the optical quality of an image objectively byexamining its optical or computed transform, but this isonly a limit on the quality of the data contained within it.Images which pass this criterion must then be examinedby eye to exclude particles which fail the o test (i.e.resemble any letter of the alphabet but o) and which showcrisp features. This initial screening produces the data set(e.g. in the two recent papers 6650 particles from 34 micro-graphs  or 2040 from two micrographs of the same field imaged at two different defocuses) for which orienta-tions must be determined.
The two groups used different model-based methods fordetermining the orientations of the particles in their dataset, on the basis of the previously determined low-resolu-tion structures of the assembled HBc protein expressed inE. coli [4,6]: Bttcher et al.  used refinement of the crosscommon lines (ccl) residual while Conway et al.  usedthe polar Fourier transform (pft) method  (Fig. 2).
The 532 symmetry of the particle gives rise to two types ofcommon lines in the Fourier transform of the image: thosewithin a single image transform and those between imagetransforms. The transform of a single image contains 37pairs of common lines. The positions of these lines dependupon the orientation of the view relative to the icosahedralsymmetry axes. The calculation of the weighted phaseresidual between these pairs is the basis of the orientationmethod for individual images described above [11,20,23].The transforms of any pair of differently oriented particlesshare 60 pairs of ccl which each must have identical valuesand whose position in each can be calculated from therelative orientation of the particles. The ccl residual
method calculates the positions of the ccl between thetransforms of the image and those of a set of projections ofthe current best map. The power of the method over theuse of individual image transforms arises from the largenumber and even distribution of the ccl as well as from theuse of an averaged model structure. The authors mini-mized this ccl phase residual by varying the orientationsand phase origins of the individual particle transforms rela-tive to six transforms of the best current map. The refine-ment of orientations was carried out to increasingresolution as Fourier shell correlation  demonstratedthe improved quality of the map. Particles from eachmicrograph were refined separately and used to generatereconstructions which were contrast transfer function(CTF) weighted and summed (vide infra) to produce aCTF corrected, average reconstruction at each stage of therefinement (Fig. 2a).
Conway et al.  utilized the pft method (Fig. 2b) forrefinement . This widely used method proceeds inseveral stages to convert the five-dimensional (,,,x,y)search to a two-dimensional (,) one. Firstly, an averagedprojection of the current best map is used to find the bestcenter for each image by cross correlation. Then projec-tions of the map for different values of and are interpo-lated onto polar coordinates (r,) and Fourier transformedalong the angular () axis. One-dimensional cross correla-tion along this axis with pfts of the image are used to findmodel projection which most closely matches the image.The cross-correlation value reveals the quality of thematch whi...