Structure of the insect troponin complex

Structure of the Insect Troponin Complex

hocerus indicus asynchro-

Article No. jmbi.1998.2414 available online at http://www.idealibrary.com on J. Mol. Biol. (1999) 285, 1845±1856

Thomas Wendt and Kevin Leonard*

Structural Biology and Isolated troponin-tropomyosin complex from Let
Biocomputing ProgrammeEuropean Molecular Biology
nous ¯ight muscle forms paracrystals on a positively charged lipid mono-

Laboratory, Meyerhofstrasse 1D-69117 Heidelberg, Germany

*Corresponding author

Introduction

FL 32306-4380, USA.Abbreviations used: DPR, differen

FSC, Fourier shell correlation; IFM,Tm, tropomyosin; Tn, troponin; TnCTnH, troponin H; TnI, troponin I; T2D, two-dimensional; 3D, three-dim

E-mail address of the [email protected]

0022-2836/99/041845±12 $30.00/0

layer. Single particle analysis was carried out on individual complexesselected from electron micrographs of negatively stained paracrystals. Bya combination of correlation and classi®cation techniques, different aver-age projections of the object were obtained. An initial three-dimensionalmodel was calculated by determining the Euler angles for the differentviews using a common line approach. This starting model was then usedas a reference for the further three-dimensional re®nement of the modelusing the original data set. The re®ned model of the troponin complexhas a diameter of approximately 90 AÊ and a volume corresponding witha molecular mass of about 120 kDa for the globular domain. The resol-ution of the reconstruction was determined to be 32 AÊ using the differen-tial phase residual method and 26 AÊ using the Fourier shell correlationcriterion.

# 1999 Academic Press

Keywords: troponin; 3D reconstruction; insect ¯ight muscle; electronmicroscopy

EF-hand motifs. The two domains have differentaf®nities for calcium.

Muscle contraction is regulated by the calcium-sensitive troponin-tropomyosin complex boundperiodically to the thin ®lament. Tropomyosin(Tm) is a coiled-coil dimer of about 400 AÊ in lengthwith a diameter of 25 AÊ (Phillips et al., 1986) towhich the globular troponin (Tn) complex isattached. In vertebrate striated muscle, the tropo-nin complex is a 79 kDa heterotrimer of the Ca2�-binding subunit troponin C (TnC), the inhibitorysubunit troponin I (TnI) and the tropomyosin bind-ing subunit troponin T (TnT). The structure of the18 kDa TnC has been solved by X-ray crystallogra-phy (Herzberg et al., 1985) to a resolution of 2.8 AÊ .The 75 AÊ long dumbell-shaped molecule hasamino and carboxy-terminal globular domains con-nected by a long a-helix. Each domain containstwo binding sites for divalent cations formed by

Present address: T. Wendt, Institute of MolecularBiophysics, Florida State University, Tallahassee

tial phase residual;insect ¯ight muscle;, troponin C;

nT, troponin T;ensional.ng author:

Data obtained from cross-linking experimentsand deletion mutations of TnC and TnI (Farah et al.,1994), as well as data from small-angle X-ray andneutron scattering experiments (Olah & Trewhella,1994) showed that the elongated part of TnI(24 kDa) binds to the central helix of the TnC sub-unit and that TnI interacts with the actin ®lament.The structure of the TnT subunit (37 kDa) has beendetermined by low-resolution rotary shadowing tobe a 160 AÊ long and 20 AÊ wide rod that attachesthe globular troponin complex to tropomyosin(Flicker et al., 1982). The study of the whole tropo-nin complex by rotary shadowing revealed a bipar-tite structure with a total length of 265 AÊ , whereTnI and TnC form a globular domain and TnTforms a long tail-like structure. The X-ray structureof glutaraldehyde-treated tropomyosin-troponinco-crystals has been described by White et al.(1987). They showed that the amino-terminal endof the TnT tail spans the head-to-tail overlap regionof Tm, and that the globular Tn-domain is locatedabout two-thirds away from that region on Tm.Density corresponding with the globular region ofthe complex was very weak and could not beresolved in detail. At present there is no three-dimensional (3D) structure available for the wholevertebrate troponin-tropomyosin complex that

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could contribute to the understanding of how acto-myosin interaction is regulated.

In insect asynchronous ¯ight muscle (IFM), the

techniques makes it possible to determine the 3Dstructure of macromolecules that are randomly

Figure 1. Troponin-tropomyosin paracrystals formedon a lipid monolayer using a uranyl acetate negativestain. In this loosely packed region, there are well-separ-ated globular troponin complexes aligned at 40 nmintervals along (barely visible) tropomyosin ®laments.A small amount of F-actin contamination can also beseen at the centre of the image.

1846 3D Reconstruction of Troponin Complex

troponin complex also consists of three subunits(Bullard et al., 1988). Biochemical studies have beencarried out on the giant water bug Lethocerus andsequence data are available for Drosophila. InsectTnC shows a high degree of similarity in molecularmass and sequence to the vertebrate component.The TnT subunit has an additional sequence at theC terminus. The extra sequence in TnT may beresponsible for the different arrangement of theglobular troponin complex on Tm, i.e. moved froma central position to the end of the Tm molecule asshown by rotary shadowing of the whole insectregulatory complex (Wendt et al., 1997). In contrastwith vertebrate troponin, the inhibitory subunit(TnI) is not detectable in Lethocerus ¯ight muscle.Instead there is a large troponin H component(TnH) of apparent molecular mass 80 kDa whichhas sequence in common with the hydrophobicproline-rich extension found in Drosophila TnH(Karlik & Fyrberg, 1986).

Despite the differences in molecular mass andamino acid composition of the troponin com-ponents, the calcium sensitivity and other bio-chemical features of the Tn complex in insect ¯ightmuscle are similar to those in vertebrate. Animportant step towards a complete understandingof muscle function is the structural determinationof the protein components. The structures of themain components, actin and myosin, have nowbeen solved to high resolution, but that of thewhole troponin regulatory complex still remainsunsolved. The greater molecular mass of the IFMtroponin complex (148 kDa) results in distinct pro-jections with a periodicity of 387 AÊ along the insectthin ®lament (Bullard et al., 1988), which exactlymatch the helical repeat of the actin ®lament. Thismatch to the helical repeat means that a straight-forward helical 3D reconstruction showing tropo-nin is not possible, but the increased size oftroponin facilitates structural investigation byother methods.

The formation of two-dimensional (2D) paracrys-tals bound to lipid monolayers has been reportedin numerous examples over the past 15 years, andimage reconstructions with a resolution approach-ing 20 AÊ in negative stain have been obtained(Uzgiris & Kornberg, 1983; Mosser & Brisson,1991). Troponin-tropomyosin paracrystals havebeen obtained by this method (Wendt et. al., 1997),but they are not well enough ordered to applyelectron crystallography techniques.

An alternative approach for disordered samplesis single particle analysis using a large number ofindividual images of the object. This has been usedfor large symmetric or asymmetric macromolecularassemblies such as the Escherichia coli ribosomestructure solved to 23 AÊ resolution (Stark et al.,1995) and keyhole limpet hemocyanin type 1(Orlova et al., 1997) that was recently solved to15 AÊ resolution. The use of angular reconstitution

oriented on a support ®lm or in the frozenhydrated state (Vainstain & Goncharov, 1986;Goncharov & Gelfand, 1986; van Heel, 1987;Penczeck et al., 1994). This so-called common lineapproach is a standard method used for virusreconstructions (Crowther et al., 1970) but has beenextended to non-symmetric objects. The power ofthis technique has been demonstrated recently bythe 3D reconstruction of the calcium release chan-nel using angular reconstitution techniques(Serysheva et al., 1995). This agrees in all major fea-tures, within the resolution limits, with the recon-struction obtained by the conical tilt method(Radermacher et al., 1994). Here, we have used anangular reconstitution approach to obtain a 3Dreconstruction of the troponin part of troponin-tropomyosin bound to positively charged lipidmonolayers.

Results

Particle selection and alignment

Particles were selected from areas of paracrystalswhere there was a low density of complex withless lateral interaction and clear separationbetween troponin molecules (Figure 1). The tropo-myosin ®laments are faintly visible runningbetween the globular troponin molecules. The 2Dalignment and classi®cation procedure on a set of1142 selected particles (hereinafter referred to as``molecular images''; Figure 2(a)) revealed ®vestable class averages (Figure 2(b)) composed ofabout 100 molecular images each with animproved signal-to-noise ratio. Figure 2(e) is a mapof the multivariate statistical analysis showing theseparation of three of the classes. There is no sym-

metry apparent in the averages and they appear torepresent different projections of the same struc-ture. The class averages were, therefore, treated as

described in Methods. The combination ofaverages 2, 4 and 5 was chosen to create an initialmodel by weighted back-projection.

Figure 2. (a) Representative mol-ecular images that were used forthe 2D classi®cation and averagingprocedure and later for the re®ne-ment of the 3D reconstruction.(b) The 2D average projections ofthe ®ve dominant classes. (c) The®rst re®ned 3D model ®ltered to aresolution of 30 AÊ and brought intothe same orientations as the 2Daverages. (d) The reprojections ofthe un®ltered 3D model that corre-spond with the 2D averages in (b).The graph in (e) represents a mapof the multivariate statistical anal-ysis showing the separation ofthree of the image classes indicatedby the symbols @, # and *. Theanalysis was based on four factors.Here, we are limited in a 2D rep-resentation to two factors and onlythree of the ®ve classes can beseen.

3D Reconstruction of Troponin Complex 1847

being angular projections of the globular troponinhead as it freely rotates around the axis of tropo-myosin bound to the lipid monolayer.

Three-dimensional reconstruction

Sinograms were calculated for the class averages(Figure 3(a)) and the cross-correlation maximum(Table 1) was determined for each pair from thesine-correlation plot representing the common lineorientation (Figure 3(b)). Since there is no sym-metry apparent in the projection, there were onlytwo maxima present, separated by 180 �. The Eulerangles (Table 2) were calculated for three selectedclass averages using equations (1) and (2) as

Euler angles were assigned to the molecularimages by correlating them with evenly distributedreprojections of the initial model and a re®nedmodel was obtained after weighted back-projec-tion. This was repeated until the model did notchange any further, which typically occured aftertwo cycles. The 2D averages were then aligned onthe re®ned model, and a further initial model wascreated that served as reference. The followingre®nement was repeated three times and a shiftcorrection was additionally applied. A ®nal assign-ment of Euler angles for the 2D averages gaveapproximately the same values as initially assigned(Table 2). The re®ned model (Figure 2(c)) wasreprojected at angles corresponding with the orien-

tation of the 2D averages. The resulting images(Figure 2(d)) ®tted well with the original class

jections (Figure 4(c)) were created to obtain a set ofimages that were comparable with the situation of

Figure 3. (a) The three selectedclass averages that were used toreconstruct an initial 3D model andthe corresponding sinograms forthe full angular range. (b) The sine-correlation plot between the ®rsttwo sinograms. The position ofmaximal correlation between thetwo sinograms is equivalent to thecommon line orientation of thesetwo class averages.


averages (Figure 2(b)).In order to test the ®delity of the angular recon-

stitution procedure used, a simple model was cre-ated consisting of ®ve spheres as shown inFigure 4(a). Three reprojections of this test model(Figure 4(b)) were selected, the Euler angles weredetermined by the common line approach, and aninitial model was calculated as before. Noisy repro-

Table 1. Orientation of the common lines determinedfrom the sine correlation plots

Class 1 2 3 4 5

1 24 21 22 222 33 32 32 263 209 209 30 234 56 57 235 545 67 53 246 60

the molecular images of the troponin particles withrespect to the signal-to-noise ratio. These imageswere aligned on the initial model and a re®nedmodel was obtained (Figure 4(d)) using the sameprocedures as before. This re®ned model showsthe same features as the test model, and the corre-sponding reprojections (Figure 4(e)) of the re®nedmodel agree with the selected projections that wereused for the angular reconstitution procedure.

In order to test the effect of the starting model,we used a ``bad'' initial model where the Eulerangles were not assigned correctly to the classaverages. The same 3D re®nement procedure wasrepeated and resulted in a re®ned model(Figure 5(b)) that was very similar to the oneobtained before (Figure 5(a)). The cross-resolutionbetween the two reconstructions was determinedto be 45 AÊ using the differential phase residual cri-

terion (DPR), allowing a maximum phase residualof 45 �. The resolution of the two independentreconstructions was determined to be 32 AÊ . The

visualize the part that corresponds with proteinmass, and no obvious channels or grooves appear.At this threshold level, the molecular mass of the

Table 2. Euler angle assignment

Euler angles start Euler angles refinedd b Phi Theta Psi Phi Theta Psi

2 6.0 58.4 0.0 0.0 0.0 72.0 10.0 279.84 3.0 25.2 57.0 96.0 ÿ32.0 40.0 105.0 320.15 7.0 96.3 53.0 ÿ25.0 ÿ26.0 38.7 147.5 317.2

The difference angles (d) are used to calculate the tilt angles (b). An initial model is calculated using the ®rst set of Euler angles.The 2D averages are aligned on the re®ned model showing that the difference between the initial set of Euler angles and the re®nedangles is minimal.


resolution determination using the Fourier shellcorrelation (FSC) criterion gave a resolution ofabout 26 AÊ for the individual reconstructions(Table 3).

The threshold of the reconstruction was chosenso that the noise level was reduced just enough to

Figure 4. Overview of the 3D reconstruction pro-cedure on the test model. The test model consisting of®ve different sized spheres is shown in (a). This modelwas projected in different views covering the entire 3Dspace and the three selected projections shown in (b)were used to create an intial model after Euler angleswere assigned using the angular reconstitution tech-nique. The same projections are shown in (c) after theaddition of noise. The model shown in (d) was obtainedafter 3D re®nement using noisy images (as shown in(c)), and reprojections of the model corresponding withthe initial three selected ones are shown in (e).

reconstruction was estimated from the volume ofthe model to be about 120 kDa.

Determination of the tropomyosin position

We believe that the Tm ®lament is rather ¯exibleand is dif®cult to visualise as a clear ``tail'' struc-ture in the class averages. In an attempt to improvethis feature, a new set of 14 averages was createdthat was evenly distributed over the 3D model(Figure 6(a)). The graph represents the distributionof the out of plane angles for the molecular imagesof the previous re®nement. Images clusteringaround the marked positions were aligned on thecorresponding reprojections, classi®ed and aver-aged (Figure 6(b)). Euler angles were assigned tothe averages and an initial model was calculatedand re®ned. The re®ned model (Figure 6(c)) has aresolution of 32 AÊ , as well as a cross-resolution of32 AÊ to the previous model obtained from the``good'' initial model (Table 3), and shows aslightly extended and more de®ned protrusion(arrows).

Since the orientation of the Tm rods relative tothe troponin is known (Figure 1), this informationcan be used to help de®ne the Tm attachment pos-ition. For each particle image, a blank image of thesame size was created and two high-density mar-ker points added at the positions where the axis ofthe Tm ®lament would intersect the edges of theparticle. Back-projection of these arti®cial imagesusing the same Euler angles as found for the corre-sponding molecular images gave two clusters ofdensity at opposite sides of the 3D model(Figure 6(d)). One cluster corresponds in positionwith the protrusion seen in the troponin recon-struction above. This may, therefore, be the regionwhere the TnT tail and the proximal end of the Tmrod enter the globular Tn domain.

Further evidence for the Tm position comes fromthe orientation of the common lines in the 2D classaverages. If, as is likely, a simple rotation of thecomplex about the axis of tropomyosin bound tothe lipid monolayer is taking place, the commonline directions should correspond with the tropo-myosin direction. If the 2D averages are orientedso that the common lines are along the vertical axis(Figure 7(a)), then the corresponding orientationsof the model ``rotate'' about that axis (Figure 7(b)).

Alignment of the troponin reconstruction onthe thin filament

Troponin model obtained from the low dosedata set

Figure 5. Comparison between reconstructions obtained from different initial models. Three-dimensional modelswere ®ltered to a resolution of 30 AÊ and are shown in six different views along the three axes. A re®ned structure isshown in (a) that was obtained from an initial model with correctly assigned Euler angles. (b) A re®ned structureobtained from a different starting model where the Euler angles were initially not correctly assigned to the 2Daverages.


Because the periodicity of the troponin repeatin insect ¯ight muscle exactly matches the actinhelical repeat, troponin complexes are arrangedat 38 nm intervals, with the same motif appear-ing every 76 nm along the ®lament axis. This,together with the greater molecular mass of theTn complex, results in images of negativelystained IFM thin ®laments showing clear Tn pro-trusions lying in the same orientation on thesupport ®lm (Bullard et al., 1988). A total of 90single repeats of isolated insect thin ®lamentswere selected from micrographs taken at a mag-ni®cation of 70,000� and 55 repeats at 55,000�.Images taken at each magni®cation and theircorresponding mirror images were subjected to a2D alignment and classi®cation procedure withthe class average of one cycle serving as refer-ence for the following one. The ®nal averages®ltered to a resolution of 30 AÊ are shown inFigure 7(c). The circled areas were used as thereference for the correlation with reprojectionsobtained from the troponin 3D reconstruction.The reprojection giving the best correlation isshown below each ®lament image. The corre-sponding 3D surface representations of the tro-ponin reconstruction (Figure 7(d)) shows theposition of the 55,000� average in relation tothe thin ®lament axis.

Table 3. Resolution of the individual reconstructions and cusing the DPR criterion with a threshold of 45 �

Model I (AÊ ) Model II (AÊ ) Model III (AÊ )

Model I 31.7 (27.6) 45.1 (24.8) 31.7 (21.6)Model II 31.7 (25.7) 41.3 (30.4)Model III 31.7 (24.8)

The resolution limits using the FSC method are given in parenthes®dence limit) was used. The molecular mass (M) of the reconstructiothe threshold used to view it. Model I is the reconstruction obtaineobtained from the bad initial model. Model III represents the ®nal m

The quality of the troponin reconstruction wasfurther assessed using a data set obtained fromlow-dose electron micrographs of troponin para-crystals that were negatively stained with 0.75 %uranyl formate. The noise level in the molecularimages taken under low dose conditions was muchhigher and the negative stain shell was much ®nercompared with the original data set. This resultedin a reduced contrast and higher noise level, whichis re¯ected in the reconstruction as well. Startingwith different reference models obtained from theoriginal data set and scaled to the same size, there®ned reconstructions are very similar. The modelin Figure 8(b) used a reference model derived fromthe 14 evenly distributed averages, and the recon-struction in Figure 8(c) was obtained using the®nal model shown in Figures 6(c) and 8(a) as refer-ence.

The resolution of the reconstruction shown inFigure 8(c) was determined to be 28 AÊ using theDPR criterion; it is shown here ®ltered to the sameresolution (30 AÊ ) as the previous ones for bettercomparison.

Discussion

Since it was not possible to improve the orderof the troposin-tropomyosin paracrystals bound

ross-resolution between the reconstructions determined

M (kDa) Projected size (pixel) Projected size (AÊ )

128 37 � 46 85 � 105119 39 � 44 90 � 101122 39 � 46 90 � 105

es. For the FSC method, the default Spider threshold (99 % con-ns was determined from the volume of the un®ltered model at

d from the good initial model and model II represents the oneodel.

to lipid monolayers (Wendt et al. 1997), singleparticle analysis has been used here. Tm is

Euler angle psi (rotation around the new Z-axisafter tilting) clusters at around 340 �. This

Figure 6. The graph in (a) shows the distribution of the angles theta and psi of the 1142 molecular images from there®ned model (Figure 2(c)). The 14 2D averages shown in (b) were obtained after images close to the 14 positionsmarked in (a) were subjected to a 2D alignment and classi®cation procedure. The re®ned 3D model (c) was obtainedafter an initial model was created from the 14 new averages and the re®nement procedure was applied. The arrowspoint to a protruding stalk which may be the position of the Tm tail. In (d), markers which have been added toblank images, in the Tm direction of the paracrystals, are seen to cluster around the position of the stalk.


known to have a regular distribution of positivelyand negatively charged regions, and appears tobind electrostatically to the positively chargedlipid monolayer. Once Tm is bound, the globulartroponin complex may then interact non-speci®-cally with the monolayer and accommodate anyorientation by rotating freely around the Tm ®la-ment axis. This is re¯ected in the distribution ofthe tilt angles (theta and psi) assigned to the mol-ecular images (Figure 6(a)). While the azimuthalangle (in plane angle, phi) and the tilt angletheta (out of plane angle) are variable, the third

suggests that the particles are not completely ran-domly adsorbed to the supporting monolayer,but are tilting around a common axis.

In the original 2D average projections(Figure 2(b)), the directions of the common lines(Figure 7(a)); Table 1) fall within a very narrowangular range. For isotropically oriented particles,the orientation of the common lines should be ran-domly distributed. This restriction of the commonline direction again points to a rotational tilt of theglobular domain of the troponin complex aroundthe Tm axis. The direction of the common lines

also enables us to estimate the attachment point ofthe globular Tn complex on the Tm ®lament(Figure 7(b)). The advantage of the lipid monolayer

ent in the graph shown in Figure 6(a). Theassignment of Euler angles was carried out to 5 �

Figure 7. (a) The initial class averages as shown in Figure 2(b) are shown again, but rotated so that the (marked)common lines are now approximately oriented on the y-axis. All four common lines per class average were added tothe projections. (b) The ®nal model is shown in the orientations that correspond with the 2D averages in (a). The 3Dmodel rotates about the common line direction which corresponds with the tropomyosin axis on the lipid monolayer.(c) Alignment of the troponin reconstruction on 2D thin ®lament averages. The orientation was determined by corre-lating the circled areas with reprojections of the ®nal Tn model at the same scale. The left-hand 2D average wasobtained from 55 selected repeats of micrographs taken at 55,000� magni®cation, the right-hand average from 90repeats taken at 70,000� magni®cation. The averages are scaled to the same size and ®ltered to a resolution of 30 AÊ .The reprojections of the troponin reconstruction giving the best correlation are shown below. (d) The 3D model isshown in the orientations that correspond to the side view (") , the top view (*) and the bottom view ().


method is that it allows free rotation of individualTn complexes about the tropomyosin axis, thusgenerating many projected views, and therebyremoving the necessity for tilting the specimens toobtain 3D information.

The 2D alignment and classi®cation of individ-ual Tn-Tm particles revealed ®ve stable classaverages corresponding with different views of acommon 3D structure. These were used to recon-struct a 3D model using an angular reconstitutionprocedure. The initial model was re®ned by align-ing the molecular images which resulted in anintermediate reconstruction showing characteristicfeatures. After assignment of the Euler angles, aweighting function was applied in order to takeinto account the uneven distribution of the molecu-lar images over the entire 3D range which is appar-

accuracy in the initial cycles of re®nement, and to2.5 � accuracy and including a shift correction forthe molecular images in the ®nal cycle. However,this improved accuracy did not change the modelsigni®cantly.

During the re®nement of the 3D structure, thecombination of alignment of the molecular imagesand alignment of the ®ve 2D class averages servedto overcome local minima in the re®nement. Whenstarting with a good initial model, the Euler angleassignment did not change signi®cantly for the 2Daverages and, therefore, the intermediate modelwas obtained after two cycles of re®nement. This isre¯ected in the Euler angle assignment for the 2Daverages of the initial model and the re®nedmodel, as shown in Table 3, where the assignmentdid not change signi®cantly (less than 20 �) duringthe re®nement.

The ®nal reconstruction has an irregular spheroi-dal shape with an approximate diameter of about

kers into blank images is more clearly de®ned inthe ®nal reconstruction and slightly extended.

Figure 8. Re®ned modelsobtained from the low-dose dataset using different referencemodels. (a) The ®nal reconstructionobtained from the high-dose dataset which served as reference forthe model shown in (c). The modelin (b) was obtained after alignmentof the molecular images on the bet-ter de®ned initial model createdfrom 14 averages.


90 AÊ . At the chosen density cut-off, the calculatedvolume agrees with that expected for the globulardomain of the troponin complex (TnH, TnC andparts of TnT and Tm would give a total of approxi-mately 120 kDa). The size of the reconstructionwould easily accommodate the vertebrate TnCsubunit, which has a maximum dimension ofabout 75 AÊ (Herzberg et al., 1985).

In order to determine the approximate TnT-tail-tropomyosin position, two marker spots, giving thedirection of the paracrystal lattice, were added toopposite sides of blank images. These were thenback-projected using the Euler angles assigned forthe re®ned reconstruction as shown in Figure 6(d).This spot insertion procedure gives an error ofabout 20 � for the Tm direction, and there is also anambiguity in deciding which ``pole'' of the modelcorresponds to the TnT-Tm exit position. One of thetwo marker clusters co-localizes well with a pro-truding region of the reconstruction which we havetentatively identi®ed with the TnT-Tm position.

In most work using angular reconstitution (forexample, Serysheva et al., 1995), the 3D reconstruc-tion was carried out by the alignment of large setsof molecular images on a reference model, in orderto assign the Euler angles for back-projecting thepreceding model. Recently, van Heel and co-workers (Schatz et al., 1995) described a differentmethod. By creating a large number of 2D averagesand back-projecting those, they obtained a modelof the Lumbricus terrestris hemoglobin at 30 AÊ res-olution. Since the signal is strongly increased in the2D averages, the 3D model is not so much in¯u-enced by the noise component. This is particularlyimportant for cryo-electron microscopy images dueto their low signal-to-noise ratio.

Here, we have tried to ®nd a compromisebetween the two situations. In the ®nal re®nementprocedure we created a set of 14 averages that werealigned on the latest model to assign the Eulerangles. The ®nal model again shows the same fea-tures, but certain regions were more pronouncedthan before. The approximate Tm-region as deter-mined before by the insertion of extra density mar-

The limiting resolution of the re®ned reconstruc-tions (Table 3), the two intermediate ones obtainedfrom the good (Figure 5(a)) and the bad initialmodel (Figure 5(b)) and the ®nal reconstruction(Figure 6(c)), was determined to be 32 AÊ using theDPR criterion by allowing a maximum phaseresidual of 45 �. Using the FSC method, a resol-ution of about 26 AÊ was calculated.

The second data set, collected under low-doseconditions and less defocus, revealed molecularimages with increased noise and resulted in amodel with slightly better resolution (28 AÊ ). Fil-tered to the same resolution, the re®ned modelobtained from the low-dose data set agrees in allmajor features with the normal dose reconstruction.

In the case of the Tn-Tm complex, the small sizemakes it preferable to use negatively stained speci-mens in order to obtain suf®cient contrast, both forthe selection of the particles as well as for the 2Dand 3D alignment. Even though one cannotexclude negative stain artefacts, the main effect,that of ¯attening of the stain shell, does not affectthe reconstruction. A reduction only in the heightof the object adsorbed to the support when irra-diated with electrons (Berriman & Leonard, 1986)would have little effect on the projected density.The 3D reconstruction carried out here uses onlydata from zero-tilt projections of an object almostrandomly oriented about one axis. Flatteningwould thus have a very limited in¯uence on thestructure of the 3D model obtained.

It is obviously important to ®t the Tn reconstruc-tion to the thin ®lament. We have attempted to dothis by matching our model to thin ®lament aver-age 2D projections and by taking into account thelikely direction of the Tm tail in the reconstruction.The angular reconstitution method used here doesnot establish the absolute hand of the model, so itwas necessary to dock both the model and its mir-ror image on the thin ®lament, where the hand ofthe actin helix is known. If we take into accountthe likely direction of the Tm tail in the troponincomplex, only the docking shown in Figure 9 ®tswell to the ®lament. In this model, the Tm position

in the troponin reconstruction aligns with the tro-pomyosin ®lament seen on Tm decorated F-actin

Methods

Figure 9. The 3D model docked on an actin-tropo-myosin ®lament (adapted from the model by Lehmanet al., 1994) using the orientation shown in Figure 7.Two troponin complexes are shown adjacent to succes-sive actin molecules on opposing sides of the ®lament,as is observed in isolated insect thin ®laments (Bullardet al, 1988). The arrow marks the path of tropomyosinalong the actin helix. The scale bar represents 10 nm.


(Lehman et al, 1994). A solvent-exposed extensionis also visible which could represent the hydro-phobic TnH extension (Bullard et al., 1988) andmay form a connection to other muscle com-ponents (Reedy et al., 1994).

We have concentrated here on the insect thin®lament. In the vertebrate thin ®lament, the actin®lament and the Tn complex are both helicallyarranged but with very different periodicities. In anormal helical reconstruction the troponin densityis averaged out. It would be necessary to obtainimages of vertebrate thin ®laments that are per-fectly preserved over several micrometers length inorder to have the complete 3D information for theTn complex. The choice of insect thin ®lamentswith their slightly different organization combinedwith single repeat analysis, therefore, seems to be amuch easier way to address the problem. To obtaina 3D reconstruction of troponin on insect thin ®la-ments, tilted views would be needed. This couldbe done by collecting thin ®lament data in the fro-zen-hydrated state and then carrying out a 3D ®tof the model we have obtained here with the ®la-ment. It may also be possible to increase the resol-ution of the Tn model by using data obtained fromMg-induced paracrystals of Tm-Tn (Wendt et al.,1997) imaged in the frozen hydrated state andcombining them with the 3D reconstructionobtained here.

Preparation of paracrystals and electron microscopy

Paracrystals of the isolated Tn-Tm complex weregrown on positively charged lipid monolayers andnegatively stained as described (Wendt et al., 1997). Forthe initial data set, normal dose micrographs of Tn-Tmparacrystals stained with 1 % (w/v) uranyl acetatewere used. Electron micrographs were taken at a mag-ni®cation of 43,000� in a Philips 400T electron micro-scope at an acceleration voltage of 80 kV and digitizedon a Perkin Elmer microdensitometer with a pixel sizeof 10 mm (2.3 AÊ ). At a later stage, the 3D reconstruc-tion was repeated on particles selected from micro-graphs of paracrystals stained with 0.75 % uranylformate and taken under low dose conditions (approxi-mately 10 eÿ/AÊ 2) at 0.7 mm underfocus on a PhilipsCM20 at 160 kV acceleration voltage and a magni®-cation of 50,000�. They were digitized with a pixelsize of 14 mm (2.8 AÊ ) on a Zeiss SCAI scanner.

Single particle analysis andtwo-dimensional alignment

Single particle analysis of the troponin-tropomyosincomplex was performed using SPIDER software (Franket al., 1981). Digitized micrographs were converted intoSPIDER format and images were displayed on a graphicworkstation using the SPIDER image viewer WEB(Frank et al., 1996). Areas of paracrystals with a low den-sity of complex and less lateral interaction between tro-ponin molecules were used. Single particles wereselected interactively ensuring that particles were clearlyseparated from neighbouring molecules.

A set of 1142 images, each 64 � 64 pixels, was cen-tered, normalized to an average pixel density of 1, androtationally and translationally aligned with respect to arandomly selected reference image using correlationtechniques (Frank et al., 1978). Images were sorted intohomogeneous classes by a multivariate statistical classi®-cation procedure (van Heel & Frank, 1981) and classaverages were created. These served as the reference forsubsequent 2D alignment and classi®cation steps untilstable classes were obtained.

Angular reconstitution

Five different class averages were used to reconstructan initial 3D model by the angular reconstitution tech-nique (Serysheva et al., 1995). A sinogram was createdfor each class average by calculating all possible 1D pro-jections in 1 deg. increments from each of the 2D averageprojections. Sinograms were correlated line-by-line andthe cross-correlation value was plotted (sinecorr) toidentify the maximum cross-correlation value. The corre-sponding rotation angles represent the orientation of thecommon line. A matrix method as well as a trigono-metric method for calculating the Euler angles from thecommon line directions has been described byGoncharov and co-workers (Vainstain & Goncharov,1986, Goncharov & Gelfand, 1986).

We used a similar trigonometric method to calculateEuler angles for three average projections. The differenceangles d1, d2, d3 between the orientation of the twocommon lines (CL12-CL13; CL21-CL23; CL31-CL32) in eachimage were calculated. By assigning the Euler angles ofthe ®rst average projection to phi, theta, psi � 0, the tilt

angle theta was calculated for the other two average pro-jections using the equations:

The resolution of the re®ned model was calculatedusing the DPR with a 45 � cut-off (Penczek et al., 1994)


cos b2 � 1=2�sin d3=2�2 � �sin d1=2�2 ÿ �sin d2=2�2

2�sin d1=2��sin d3=2� �1�

cos b3 � 1=2�sin d1=2�2 � �sin d2=2�2 ÿ �sin d3=2�2

2�sin d1=2��sin d2=2� �2�

The second average was set to phi � (CL21),theta � (180 � ÿ b2), psi � ÿ (CL12) and the third tophi � (CL31), theta � ÿ (b3), psi � ÿ (CL13).

Testing the angular reconstitution scheme

The common line procedure was tested using a modelconsisting of ®ve different-sized spheres. Three projec-tions of this test model were selected and the corre-sponding sinograms created. The Euler angles werecalculated from the orientation of the common lines andan initial model was back projected and further re®nedusing the same procedures as before. A set of 869 homo-geneously distributed reprojections of the test model wasused as molecular images and random noise from nega-tively stained carbon ®lm was added to obtain compar-able data to the experimental situation. These noisyimages were aligned on the reference model and back-projected after Euler angles had been assigned asdescribed in the following section.

Three-dimensional reconstruction

An initial model was obtained by weighted back-pro-jection which served as a starting 3D reference forfurther 3D re®nement (Radermacher, 1992). The re®ne-ment procedure consisted of two cycles of 3D alignmentand weighted back-projection of the experimental imageset; the 3D model from the ®rst cycle served as referencemodel for the following re®nement. Euler angles wereassigned to the molecular images by comparing themwith homogeneously angular distributed reprojections ofthe 3D map. This was repeated for several cycles untilno detectable changes occurred in the reconstruction andthe Euler angle assignment was constant within 5 � for atleast 75 % of the images. Removing those images whoseangle changed by more than 5 � did not signi®cantlychange the reconstruction.

All ®ve 2D averages were then aligned on reprojec-tions of that intermediate model and back-projected inorder to create a re®ned initial model. Molecular imageswere aligned on that model and back-projected asdescribed. This created a further starting model that wasre®ned using the same procedure, including a 2D shiftcorrection for the particle images in the ®nal cycle.

The combination of 3D alignment of the originalimages followed by alignment of the 2D averages andcreation of a new initial model served to overcome localminima in the re®nement or wrong determination of theEuler angles in the initial steps. A good initial model isde®ned as one in which the corresponding reprojectionsof the model ®t well to the 2D average projections usedto create it, while a bad initial model would be onewhere the match is worse. Starting with a bad initialmodel, the combination of alignment of molecularimages and 2D averages had to be repeated more oftenuntil a stable model was obtained which shows all themajor features of the previous (better) one.

and the FSC method (Saxton & Baumeister, 1982). Themolecular mass of the reconstruction was estimated fromthe volume at the threshold used to view the model,assuming that 1 AÊ 3 corresponds with 0.85 Da.

Reconstruction of the Tn complex with a low-dosedata set

The 3D re®nement procedure was repeated on asecond data set, which was obtained from low-dosemicrographs of negatively stained paracrystals of thepuri®ed troponin complex. These were stained with0.75 % uranyl formate which gives a ®ner grain. Singleparticles were selected from the digitized images andcentered as described. Euler angles were assigned to theselected 716 images using different reference modelsscaled to the same size. The reference models used werethe initial model created from the new set of 14 2Daverages and the re®ned model. After Euler angles wereassigned to the low-dose molecular images, a new recon-struction was calculated by weighted back-projectionand re®ned. Since the noise level was much higher inthese molecular images and the negative stain shell wasmuch ®ner than before, the reconstruction had to bemasked at an appropriate radius in order to visualize themodel above the background.

Alignment of the Tn reconstruction on thin filaments

Isolated thin ®laments were negatively stained usingthe Valentine method as described (Bullard et al., 1988).Filament images (taken at magni®cations of 55,000� and70,000�) were digitized on a Zeiss SCAI scanner at14 mm pixel size, which corresponds with 0.25 and0.20 nm, respectively. Two-dimensional alignment andclassi®cation of selected repeats showing the troponincomplex (2562 pixels) was performed as described above.Adjacent troponin complexes in L. indicus ¯ight muscleappear slightly staggered on each side of the thin ®la-ment. Therefore, the selected images as well as their mir-ror versions were aligned and subjected to multivariatestatistical analysis and classi®cation. Two independentclass averages were calculated from the images belong-ing to the largest class of each set of images taken atdifferent magni®cation. The re®ned troponin model wasprojected in different views, and the reprojections werecorrelated with a reference that was obtained after scal-ing the 2D average of IFM thin ®laments to the samesize.

Docking of the model on the thin ®lament was carriedout interactively in 3D using the program AVS on a Sili-con Graphics O2 workstation. The helical reconstructionof actin-tropomyosin was carried out using layer-linedata provided by Dr W. Lehman (Boston University).

Acknowledgments

We thank Dr W. Lehman for kindly providing hisdata for the F-actin tropomyosin reconstruction used inFigure 9, Dr B. Bullard for her expertise in insect ¯ightmuscle biochemistry, and Dr M. Radermacher for helpfuldiscussions on the single particle analysis.

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Edited by M. F. Moody

(Received 30 July 1998; received in revised form 12 November 1998; accepted 16 November 1998)

Structure of the insect troponin complex

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