Journal of Structural Biology 125, 209–215 (1999)Article ID jsbi.1999.4085, available online at http://www.idealibrary.com on

A Strategy for Determining the Orientations of Refractory Particlesfor Reconstruction from Cryo-Electron Micrographs with Particular

Reference to Round, Smooth-Surfaced, Icosahedral VirusesJose R. Caston,*,1 David M. Belnap,* Alasdair C. Steven,* and Benes L. Trus*,†,2

*Laboratory of Structural Biology Research, National Institute of Arthritis, Musculoskeletal and Skin Diseases and †ComputationalBioscience and Engineering Laboratory, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892-5624

Received December 10, 1998, and in revised form January 8, 1999

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Cryo-electron microscopy and three-dimensionalmage reconstruction are powerful tools for analyz-ng icosahedral virus capsids at resolutions thatow extend below 1 nm. However, the validity ofuch density maps depends critically on correctdentification of the viewing geometry of each par-icle in the data set. In some cases—for example,ound capsids with low surface relief—it is difficulto identify orientations by conventional applicationf the two most widely used approaches—‘‘commonines’’ and model-based iterative refinement. We de-cribe here a strategy for determining the orienta-ions of such refractory specimens. The key step iso determine reliable orientations for a base set ofarticles. For each particle, a list of candidate orien-ations is generated by common lines: correct orien-ations are then identified by computing a single-article reconstruction for each candidate and thenystematically matching their reprojections withhe original images by visual criteria and cross-orrelation analysis. This base set yields a first-genera-ion reconstruction that is fed into the model-basedrocedure. This strategy has led to the structuraletermination of two viruses that, in our hands,esisted solution by other means.Key Words: 3D reconstruction; capsid structure;

ommon lines.

INTRODUCTION

All cats look gray in the dark.—Old Spanish proverb

Icosahedral viruses have played a central role inhe development of cryo-electron microscopy (Adrian

1 Current address: Centro Nacional de Biotecnologıa, Unidad deicroscopıa Electronica, Campus Universidad Autonoma, Canto-

lanco 28049 Madrid, Spain.2 To whom correspondence should be addressed at Building

2A, Room 2033, MSC 5624, NIH, Bethesda, MD 20892-5624.

lax: (301) 402-2867. E-mail: TRUS@helix.nih.gov.

209

t al., 1984) and three-dimensional image reconstruc-ion (Baker, 1992; Baker and Johnson, 1997; Chiu,993). Their large sizes and distinctive shapes madehem readily visible in low-contrast cryo-micro-raphs and their high order of symmetry facilitatedeconstruction, and resolutions below 10Å are noweasible (Conway et al., 1997; Bottcher et al., 1997;rus et al., 1997). However, for a reconstruction to bealid, the orientation of each capsid must be cor-ectly identified. Moreover, the resolution of theeconstruction is limited by the precision with whichhe orientation angles are determined, among otheractors. Not all viruses are equally tractable in thisespect. Capsids with planar facets offer the advan-age that their outline varies markedly with viewingirection—hexagonal in a threefold view, pseudo-exagonal in a twofold view, and round in a fivefoldiew, whereas spherical capsids appear round fromny direction. Capsids with large protrusions projectonspicuous features that make them easier to solvehan smooth-surfaced capsids, and capsids contain-ng nucleic acids generate noisier images than emptyapsids and are less easily solved.Nowadays, model-based orientation recognition

Baker and Cheng, 1996) is the method of choice. Itroceeds iteratively: a model is used to generaterojections in all possible directions and these projec-ions are used to sort the original images by ‘‘super-ised classification.’’ An improved model is thenalculated, and this procedure is repeated exhaus-ively. However, to get started, one needs an unbi-sed model of sufficient resolution and discrimina-ory power.

Originally, orientations were determined by the‘common-lines’’method (Crowther, 1971; Fuller, 1987;aker et al., 1988). Common lines are lines in theourier transform of an image of a symmetric par-

icle, along which the values should be identical—at

east for ideal, noise-free, data. Icosahedral symme-

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ry provides 37 pairs of common lines for a singlearticle. ‘‘Cross common lines’’ relate lines in theransforms of different particles. In practice, onccount of noise, one calculates residuals, defined aseighted sums of the discrepancies between all pairsf symmetry-related points. The most likely orienta-ion is the one with the lowest residual. Common-ines has undergone further refinement (e.g., Thu-

an-Commike and Chiu, 1997; Bottcher et al., 1997;ohnson et al., 1994) but has been superceded inany studies by model-based methods. However,

ommon-lines has an advantage that may be ex-loited in the early stages of analysis in that it isotentially capable of determining orientations fromingle images.Here we outline a strategy for solving the struc-

ures of viruses that resist other methods. The key iso establish a small base set of correctly determinedarticles. These yield a first-generation reconstruc-ion that is then fed into the model-based procedure.his approach evolved during our work on L-A—anNA virus of yeast (Fig. 1; Caston et al., 1997; Cheng

t al., 1994)—and has since been applied successfullyo poliovirus (Belnap et al., in preparation). Althoughelated strategies have been developed indepen-ently by others (Baker and Cheng, 1996; Fullert al., 1996; Wikoff et al., 1997), none has beenescribed in detail and we present this report in the

FIG. 1. Cryo-electron micrograph of purified L-A viral par-icles. Empty and RNA-filled particles are clearly distinguished:either particle exhibits conspicuous features in these projec-ions, even though the defocus (,1.67 µm, corresponding to a firstero of the contrast transfer function at (25 Å)21) ) is such as totrongly convey frequencies typical of spacings between protein

ubunits. Bar, 500 Å.

ope that it may help others tackling similarroblems.

STRATEGY

Our method involves five steps: selecting a smallet of images for detailed analysis; determiningossible orientations by common lines; calculatingingle-particle reconstructions (SPRs) for each orien-ation; evaluating the SPRs by comparing theireprojections to the original images; and evaluatingultiparticle reconstructions in the same way.

. Select a Small Set of Promising Particles

Pick out a few (e.g., 5–10) particles that exhibitelatively pronounced features that may be used toiscriminate between candidate orientations. Sucheatures are often most evident around the periph-ry. Determine the centers for particles.

. Determine Possible Orientations

Run a common-lines program (e.g., Fuller et al.,996) to find candidate orientations for each particle.e typically keep the 25 solutions with the lowest

elf-residuals. This ‘‘best list’’ may be reduced byliminating redundant solutions, i.e., orientationshat differ by only 2–3°.

. Calculate Single-Particle Reconstructions

Each candidate orientation is used to compute aPR. We compute SPRs at low resolution (e.g., 40–50); even so, they are usually very noisy. Noise may beeduced somewhat by ‘‘unblobbing’’ (Conway et al.,996) or by setting to background, all densitiesnside and/or outside a certain radius.

. Compare Reprojections of SPRsto the Original Images

SPRs may be used to screen candidate orienta-ions by visual evaluation. It is often possible toliminate some candidates and to promote others byisual comparison between SPR reprojections andhe original images, suitably band-limited (Fig. 2).o rank the surviving candidates, each SPR is pro-

ected according to its input orientation and thenompared to the original cryo-EM image by cross-orrelation (see Eq. (1) ). The orientation with theighest correlation coefficient (CC) is taken as theest orientation for that particle. The comparisonay be confined to its periphery, which often con-

ains relatively pronounced features and where theignal from the edge of the particle is strong.

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211ORIENTATION DETERMINATION FOR REFRACTORY VIRAL PARTICLES

FIG. 2. Analysis of candidate orientations for an image of a Lask. (c) A list of candidate orientations generated by the common

ngles (u, f, and v). The numbers given in parentheses in the fouist,’’ according to its phase residual, given in degrees. (The originaumbers are used to label the corresponding reprojections in (d).eprojection with the masked (b) and unmasked (a) images, respolumn. (d) Shown at the top left is the particle image from (aeprojections of the corresponding SPRs. Upon close visual inspectexagonal profiles in significantly different orientations from the o

eatures (like the striations in (8) or the round-as-opposed-to-hexamage (a, d) and may be rejected for that reason. In terms of both c25) are favored, of which solution (25) eventually prevailed.

-A virion, shown in (a). (b) The same particle after imposing an annular-lines program, FINDVIEW. The orientations are defined by their Eulerrth (residual) column show the ranking of each orientation in the ‘‘bestl list of 25 was reduced to 11 by eliminating redundant solutions.) TheseColumns CC1 and CC2 list the correlation coefficients obtained for eachectively. Rankings by this criterion are shown in parentheses for each) after low-pass filtering at (40 Å)21; the remaining images represention, it emerges that some candidates (e.g., (5), (11), (18), and (23) ) projectriginal image (a) and may thus be eliminated. Others show pronounced

gonal profile of (1), (4), (10), and (22) ) that are not shared by the originalorrelation coefficients (last two columns—cf. Eq. (1) ), solutions (10) and

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here pi is the reprojection image, and qi is the rawltered image.

. Calculate and Evaluate MultiparticleReconstructions (MPRs)

At this point, the only way to further reduce theoise level in the SPR is to combine particles.ccordingly, calculate MPRs from two or more par-

icles, starting with combinations of candidate orien-ations that appear most likely. MPRs should bevaluated by the same criteria as SPRs, in particu-ar, visual and correlation-based comparison of repro-ections with the original, band-limited images.

Once a base set is established, it is fed into atandard application of model-based refinementBaker and Cheng, 1996), progressively drawing inore particles and allowing increasingly precise

ngular refinement. For capsids in the range of0–45 nm in diameter, five or six particles shoulduffice for a base set.

riteria for Correct and Incorrect Solutions

How does one know that a given SPR or MPR isorrect? This is a difficult question: in practice, it isard to completely exorcise intuition, but the follow-

ng guidelines may help. If, on visually comparingurface renderings, one SPR of particle A resemblesne SPR of particle B, both orientations may beorrect since at most one solution in each best list isight. SPRs that depict very smooth, near-sphericalarticles should be treated with caution. Base setarticles should remain stable with one solution andot vacillate between two or more solutions. Addingparticle to a current data set should produce an

verall increase in the correlation coefficients if theewcomer’s orientation is correct. Moreover, theesolution of the resulting MPR should improveSaxton and Baumeister, 1982; Conway et al., 1993).lso, the structure visualized should also be consis-

ent with any a priori information that is available,uch as copy number (or triangulation number—aspar and Klug, 1962) or the oligomeric nature of

he capsomers.

Case History

A cryo-micrograph of L-A virions is shown in Fig.. A set of empty particles was selected and aommon-lines list of the 25 most likely solutions wasbtained for each. After redundant solutions wereliminated, the corresponding SPRs were calculatedo 40-Å resolution and unblobbed. The candidatesere then evaluated, as illustrated for one particle in

igs. 2 and 3. Some orientations (e.g., Nos. 5, 8, and t

1) may be eliminated on grounds of evident visualnconsistency between the SPR reprojection and theriginal image (cf. Fig. 2d). The remaining candi-ates were ranked in terms of their correlationoefficients (Fig. 2c). Although correlation coeffi-ients have limitations—e.g., they may vary onlylightly in value over a set that includes both cor-ectly and incorrectly identified particles—it haseen our experience that solutions that rank high foroth correlation coefficients (total and annular) areften correct. In this case, there are two such solu-ions, Nos. 10 and 25. Of these, No. 25 seems to be aetter visual match and subsequent analysis indi-ated that it was indeed the correct solution. None ofhe 11 candidate SPRs is obviously correct or incor-ect from visual inspection of their surface render-ngs (Fig. 3).

The correct relative handedness of particles whoserientation angles have been established remains toe determined (for determination of absolute handed-ess, see (Belnap et al., 1997) ). In the conventionsed here, there are two possible enantiomorphsorresponding to values of v and v 1 180°, respec-ively, for the third Euler angle. Fixing the firstmage, a second image may be combined with it withither handedness (two solutions). Our strategy is tostablish consistent handedness for a manageablymall set of particles by calculating a MPR for eachermutation of handedness (e.g., eight such MPRsith four particles) and to evaluate them as de-

cribed above. A comparison of three raw imagesith their correct SPR reprojections and reprojec-

ions from the final MPR model illustrates theirutual consistency (Fig. 4). Combining particlesith inconsistent handedness leads to an artifactual

ymmetrization, a general smoothing, and a loss ofynamic power. After enough particles have beenncorporated with consistent handedness to give an

PR with sufficient resolution, it may be relied upono solve additional particles with consistent handed-ess as the data set is expanded via the model-basedpproach.

DISCUSSION

We have outlined a procedure for determining therientations of refractory virus particles (e.g., cap-ids with smooth surfaces, roundish profiles, andlled interiors). Using it, we were able to solve twoiruses that resisted solution by other means: L-ACaston et al., 1997; Cheng et al., 1994) and poliovi-us (Belnap et al., in preparation). We wished toolve the latter virus de novo from cryo-micrographs,ven though a high-resolution crystallographic struc-

ure was available (Hogle et al., 1985). It was solved

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213ORIENTATION DETERMINATION FOR REFRACTORY VIRAL PARTICLES

s outlined above: a two-particle reconstruction cal-ulated to 39-Å resolution led, after numerous cyclesf model-based refinement, to a final 120-particleeconstruction at 22-Å resolution.Use of SPRs was first reported by Fuller and

olleagues (Dokland et al., 1992; Venien-Bryan anduller, 1994; Fuller et al., 1996). It has been ourxperience that reprojections are more useful thanurface renderings for evaluation of SPRs (cf. Figs. 2nd 3) and we are not aware of them having beensed before. For larger viruses, the Fourier–Besseleconstruction method (Crowther, 1971) may notllow SPRs to be calculated to resolutions highnough to allow evaluation, although such SPRsalbeit noisy) can be calculated by back-projectionRadermacher, 1992).

Because it depends on the high order of symmetryf icosahedral particles, which makes it possible toalculate SPRs, the strategy described here does notdapt readily to the analysis of particles with lowerymmetries. Nevertheless, some other approachesre possible and have in common the principle ofeeking to enhance the signal or reduce the noise inhe data set:

(1) The S:N ratio may be enhanced by image

FIG. 3. Surface renderings of 11 SPRs, each corresponding toompared to that of the final, well-defined, density map (top left). Bo which, if any, SPR corresponds to the correct orientation. In thnformative (see Fig. 2).

estorations that combine focal pairs or triplets t

Conway et al., 1997; Trus et al., 1997), thus expand-ng the range of frequencies that are strongly con-eyed. In marginal cases, the resulting improvementay be enough to render the data solvable.

(2) Labeling particles with antibody fragmentsr other bulky ligands will enhance the surfaceelief, so that the various projections are moretrongly differentiated and may be recognized moreasily and with greater precision.

(3) Tomographic reconstructions (Walz et al.,998) produce density maps of individual particles ofny symmetry, although they are limited in resolu-ion by the total electron dose. Such reconstructions,nhanced by aligning and averaging, should serve asvaluable source of starting models (Walz et al.,

997).(4) Negative staining (Kolodziej et al., 1997),

erhaps combined with low-temperature techniquesAdrian et al., 1998), provides specimens with higherontrast and greater radiation resistance that maylso serve as a source of starting models for recon-tructing cryo-electron micrographs.

(5) Angular reconstitution (van Heel, 1987) af-ords another approach. In this case, the S:N isoosted by class averaging after multivariate statis-

didate orientation for the trial particle (as listed in Fig. 2c), aree of their high noise level, these images give no clear indication asect, the corresponding reprojections from the SPRs proved to be

a canecausis resp

ical analysis. This is a powerful method, although

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214 CASTON ET AL.

ts applicability depends, to some extent, on thearticle presenting a limited number of preferentialiews and having enough structural irregularity toenerate images for which reliable classification isossible.It is not evident to us that any single method is

niversally optimal. Rather, each kind of particle is

FIG. 4. Steps in the calculation of an MPR of L-A virus made arom particles 132, 210, and 24. The views are along twofold (leftecond row, band-limited images obtained after low-pass filteririentations (third row) are compared to reprojections (fourth row)

ikely to be most amenable to some particular strat-gy or combination of strategies. As the above listllustrates, there is a fertile range of possible ap-roaches. In three-dimensional analysis of singlearticles, accurate and precise determination of ori-ntations represents what is often technically theost challenging phase of the analysis.

g to the procedure described. (a) Outer surface of a 3PR computedvefold (right) symmetry axes. (b) First row, original images; and(40 Å)21. Reprojections of their SPRs in the assumed viewinged from the 3PR shown in (a).

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215ORIENTATION DETERMINATION FOR REFRACTORY VIRAL PARTICLES

We thank Dr. James Conway for helpful discussions, Dr. Timaker for critically reading the manuscript, and Dr. Reed Wickner

or preparations of L-A virions.

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