Elucidation of Crystal Packing by X-ray Diffraction and Freeze-etching Electron Microscopy. Studies on GTP Cyclohydrolase I ofEscherichia coli

J. Mol. Biol. (1995) 253, 208–218

Elucidation of Crystal Packing by X-ray Diffractionand Freeze-etching Electron Microscopy. Studies onGTP Cyclohydrolase I of Escherichia coli

Winfried Meining 1, Adelbert Bacher 1*, Luis Bachmann 1

Cornelia Schmid 1, Sevil Weinkauf 1, Robert Huber 2 and Herbert Nar 2

A monoclinic crystal modification of GTP cyclohydrolase I (space group P21,1Department of Chemistrya = 204.2 Å, b = 210.4 Å, c = 71.8 Å, a = g = 90 °, b = 95.8 °) was studied byTechnical University offreeze-etching electron microscopy and by Patterson correlation techniques.Munich, Lichtenbergstr. 4The freeze-etched samples were either shadowed with Pt/C or decoratedD-85747 Garching, Federal

Republic of Germany with monolayers of gold, silver or platinum.Correlation averaged electron micrographs of decoration replicas indicated2Max-Planck-Institut fur 5-fold molecular symmetry. In conjunction with the molecular mass of the

Biochemie, Am Klopferspitz active GTP cyclohydrolase I enzyme complex of about 210,000 Da, which hadD-82152 Martinrsied, Federal been reported in the literature, and a molecular mass of the protomers ofRepublic of Germany 24,700 Da, the electron microscopic observation suggests that the enzyme is

a decamer with 5-fold symmetry. The processed images of decorated crystalsurfaces also showed that the four protein multimers in the crystal unit cellare related by 4-fold pseudosymmetry. A Patterson analysis of the X-ray datashowed two non-crystallographic 5-fold axes, inclined at 12 ° to each other,thus confirming and extending the electron microscopic findings.Additionally, local 2-fold axes were found in planes perpendicular to the5-fold particle axes. Thus, the combined X-ray and electron microscope dataindicate that GTP cyclohydrolase I is a decamer with D5 symmetry.

A procedure for hkl assignments of the crystal planes observed in electronmicrographs was developed. On this basis, it was possible to determine theapproximate molecular positions in the ab plane. Independent informationon the crystal packing was obtained by single isomorphous replacement andelectron density averaging. The 5-fold averaged 6 Å electron density showsthat the GTP cyclohydrolase I decamer is torus-shaped with an approximatediameter of 100 Å and a thickness of 65 Å.

The study demonstrates that the combination of freeze-etching electronmicroscopy with Patterson analysis of X-ray data is a powerful approach forthe solution of complex crystallographic problems. The procedure for thisanalysis as well as possible pitfalls are discussed in detail.

7 1995 Academic Press Limited

*Corresponding author Keywords: GTP cyclohydrolase I; X-ray crystallography; electronmicroscopy; metal decoration; crystal packing

Introduction

GTP cyclohydrolase I catalyzes the first committedstep in the biosynthetic pathways of tetra-hydrofo-late (Brown & Williamson, 1987; Matthews et al.,1995), tetrahydrobiopterin (Nichol et al., 1985) andtetrahydromethanopterin (Eisenreich & Bacher,1994). The vitamin, folic acid, is bio-synthesized inplants and microorganisms with the exception ofmethanogenic bacteria, which utilize tetrahy-dromethanopterin instead of tetrahydrofolate as thecarrier of 1-carbon fragments. Animals are unable to

synthesize folic acid, but they utilize GTP cyclo-hydrolase I for the biosynthesis of tetrahydro-biopterin, which serves as cofactor for the hydroxyl-ation of aromatic amino acids and thus plays a centralrole in the biosynthesis of catecholamine-typeneurotransmitters. The rare genetic deficiencies ofGTP cyclohydrolase I result in severe neurologicdisorder. More recent studies have shown thattetrahydrobiopterin is involved in the cytokine-mediated proliferation of T-lymphocytes (Ziegler &Schwulera, 1989).

The evolution of GTP cyclohydrolase I has been

0022–2836/95/410208–11 $12.00/0 7 1995 Academic Press Limited

Elucidation of Crystal Packing 209

rather conservative. The proteins of Escherichia coliand man share 81 identical amino acid residues (37%)and 27 (12%) conservative replacements (Togari et al.,1992; Schmid et al., 1993). Thus, it appears likely thatthey have similar three-dimensional structures.

The GTP cyclohydrolase I of E. coli was firstpurified to homogeneity by Yim & Brown (1976),who reported a molecular mass of 210 kDa andproposed an octamer structure. More recently, theprimary structure of the E. coli enzyme has beendetermined by sequencing of the cognate gene, folE,which is located at 2251 kb on the E. coli chromosome(Schmid et al., 1993; Ritz et al., 1993). In line with thepredicted primary structure, the mass of theprotomer was determined as 24699.5 Da by massspectrometry.

GTP cyclohydrolase I of E. coli has beencrystallized from citrate buffer (Schmid et al., 1993;Meining et al., 1994). The monoclinic crystals havethe space group P21 (a = 204.2 A, b = 210.4 A,c = 71.8 A, a = g = 90°, b = 95.8°) and diffract X-raysto a resolution of 3 A.

Studies with the lumazine synthase/riboflavinsynthase complex of Bacillus subtilis have shown thatthe elucidation of complex crystal packing problemscan be assisted by freeze-etching electron mi-croscopy (Bacher et al., 1992). In this technique, smallcrystals are frozen in their growth buffer, and crystalsurfaces are exposed by sublimation of water at− 100°C in a high vacuum. The crystal surfaces arethen replicated by shadowing with Pt/C or bydecoration with very thin deposits of a heavy metal.These very thin vacuum deposits, e.g. of silver, goldor platinum, are not continuous films but consist ofmicrocrystals of the respective metal. The formationof the metal clusters occurs preferentially at locationspredetermined by local surface properties of thesubstrate (Bassett, 1958; Bethge & Heydenreich,1987). In the case of protein molecules with intrinsicsymmetry properties, this so-called decorationtechnique allows the determination of the relativetranslational and rotational position of the differentparticles in the crystal lattice (Weinkauf et al., 1991;Weinkauf & Bachmann, 1992; Bacher et al., 1992).

We describe the analysis of the crystal packing inmonoclinic crystals of GTP cyclohydrolase I by thecombination of X-ray diffraction analysis andfreeze-etching electron microscopy. A rationalprocedure for the efficient application of the methodis discussed in detail.

Results

Non-crystallographic symmetries derived byelectron microscopy

Monoclinic crystals of GTP cyclohydrolase Igrown in 0.4 M citrate buffer appear as rectangularplates or cubes (Figure 1). Figure 2 shows afreeze-etched crystal plane shadowed with Pt/C.Similar crystal planes decorated with gold or silverare shown in Figure 3a and b. Because the directions

Figure 1. Crystals of GTP cyclohydrolase I grown fromcitrate buffer as used for freeze etching.

of metal evaporation and observation coincide, thecontrast in these micrographs is very low. Averagedimages of crystal planes decorated with gold,platinum or silver are shown in Figure 4.

The different metals do not decorate the samesurface features of the molecules, a phenomenon thathas been observed with other proteins (Weinkaufet al., 1991; Weinkauf & Bachmann, 1992;Rubenkamm et al., 1995). The decoration patterns ofgold (Figure 4a) and platinum (Figure 4c) arecharacterized by a ring-shaped arrangement of fivemetal maxima, suggesting a 5-fold rotationalsymmetry of the molecule as highlighted by theoverlays in Figure 4b and d. The asymmetry of themotifs can be explained by a relatively highshadowing contribution, which might be due to aninclination of the particles in the crystal plane and toa deviation of the evaporation angle from 90°C. Atfirst sight, the 5-fold motifs on silver-decoratedcrystals are primarily indicated by the metalaccumulated on the periphery of the molecules(Figure 4e and f). As shown below and in Figure 5,a quantitative analysis reveals that the silver

Figure 2. Freeze-etched ab plane of a GTP cyclohydro-lase I crystal grown from citrate buffer, shadowed withPt/C at 45° incidence. Inset, optical transform.

Elucidation of Crystal Packing210

Figure 3. Freeze-etched surface of crystals grown fromcitrate buffer decorated (a) with 2 A gold and (b) with 4 Asilver.

Figure 5. Rotational correlation analysis of the particlesA, B, C and D of the averaged silver decoration image inFigure 4e, using the metal distribution at the central partsof the molecules. A circular mask of the particle A with40 A diameter was rotated in steps of 1° and comparedwith unrotated masked particles A, B, C and D. The plotshows the correlation coefficient as a function of therotation angle.

distribution at the centre of the particles also revealsthe 5-fold symmetry of the particles as well as theirrotational position.

The observed decoration patterns can be accom-modated with a pentamer or a decamer structure ofthe particle with C5 or D5 symmetry, respectively.However, in conjunction with the molecular mass ofthe active enzyme complex of about 210,000 kDa,which had been reported by Yim & Brown (1976),

and a molecular mass of the promoter of 24,700 Daas determined by mass spectrometry (Schmid et al.,1993), the decamer structure is more plausible. Theobserved 5-fold symmetry is clearly at odds with anearlier model: based on gel filtration and electrophor-etic studies, it was proposed that GTP cyclohydro-lase is a tetramer of dimers (Yim & Brown, 1976).

Figure 4. a, Correlation average of the gold decorated crystal plane shown in Figure 3a; b, same as a with a superimposedmask, indicating 5-fold symmetry and dimensions of the particles and the pseudo 4-fold symmetry axis (r); c and d,correlation average of a platinum-decorated crystal surface; e and f, correlation average of the silver-decorated crystalsurface shown in Figure 3b.

Elucidation of Crystal Packing 211

Figure 6. Patterson self-rotation function with k = 180°computed with data from 20 A to 6 A and Patterson vectorlength of 15 to 50 A. The angle conventions used for therotation functions are as follows: c is the angle from they-axis, 8 is the angle from the x-axis, b is along y. A seriesof peaks is found in the range −6° < 8 < 6° (i.e. close to orin the ab plane) with peak heights of 40 to 60% of thecrystallographic b-axis. Although the function is smearedout in this region it indicates intervals of 9° betweenmaxima. This is to be expected for a superposition ofparticle 2-folds of two crystallographically related GTPcyclohydrolase I decamers and local axes relatingindividual monomers between the two decamers.

Figure 7. Plot of the Patterson self-rotation function as afunction of the rotation angle k at (c = 90°, 8 = 90°), i.e.half-way between the orientations of the GTP cyclohydro-lase I particle 5-fold axes. The peak pattern with a repeatof 18° is indicative of a particle 5-fold axis roughly parallelwith a local 4-fold symmetry element.

and f this putative 4-fold axis is marked by adiamond.

In order to verify the non-crystallographicsymmetry elements derived from the electronmicrographs, a Patterson self-correlation analysiswas initiated.

Patterson analysis

Patterson space rotation functions were calculatedwith native data at 6 A resolution. For allcalculations, Patterson vector lengths of 15 to 50 Awere used. The upper limit for the vector lengths waschosen on the basis of the metric information on theparticle dimensions obtained by electron mi-croscopy. Calculations with reduced vector lengthsresulted in noisier rotation functions. A search forlocal 5-fold symmetry gave a high signal at (c = 90°,8 = 90°), i.e. perpendicular to the ab plane, whichactually consisted of two peaks at (c = 90°, 8 = 84°)and (c = 90°, 8 = 96°).

A search for 2-fold local symmetry axes resulted ina series of unresolved peaks between −10° < 8 < 10°with maxima at (8 = 0°), (8 = 6°) and (8 = 174°), i.e.in planes perpendicular to the local 5-fold axes. Weinterpreted these as both particle 2-folds and localsymmetry elements between monomers in crystallo-graphically independent and related GTP cyclohy-drolase I particles (Figure 6). A plot of the Pattersoncorrelation value at (c = 90°, 8 = 90°) as a function ofthe rotation angle k shows a peak pattern with arepeat of 18° (i.e. 20-fold symmetry) indicative ofparticle 5-fold axes roughly parallel with a local4-fold symmetry element (Figure 7).

These crystallographic results confirm the obser-vations made by the electron microscope; namely,

Closer inspection of the averaged images revealsthat the centres of four 5-fold motifs, designated asA through D, are located close to the corners of asquare with a side-length of 111 A. This arrangementsuggests a local 4-fold symmetry, provided that theorientation of the particles A through D also followsthe 4-fold symmetry. To determine the relativeorientations of the particles A through D, a rotationalcorrelation analysis was applied in steps of 1° usinga circular mask of 40 A diameter. Figure 5 shows thedependence of the correlation coefficient on therotation angle. Without imposing a rotationalsymmetry, the plot shows five steps at intervals ofabout 72°C, which is a strong indication of a 5-foldparticle symmetry. The presence of a local,non-crystallographic 4-fold symmetry axis modu-lated by a 5-fold particle symmetry would lead to anapparent local 20-fold symmetry with a rotationalrepeat of 18°. A Fourier transform of the rotationalcorrelation resulted in rotational transpositions of18.6° between A and B, 10.5° between B and C, 18.4°between D and C and 24.5° between C and A.Although these values do not exactly reflect therotational repeat of 18°, they still support thepresence of a local, non-crystallographic 4-fold orpseudo 4-fold symmetry axis relating the particlesA through D. The deviation might again be dueto an inclination between the local 4-fold andmolecular 5-fold axes and/or to a deviation ofthe angle of observation from 90°. In Figure 4b, d

Elucidation of Crystal Packing212

Figure 8. a, An illustration of the orientation of the twoGTP cyclohydrolase I decamers in the asymmetric unit.The local 5-fold axes are inclined by 6° (D8C) and −6° (D8A)with respect to the normal to the ab-plane; b, the projectionof the monoclinic unit cell showing the orientations andpositions of the four GTP cyclohydrolase I decamers (Athrough D) with respect to the crystallographic axes (fordetails see Discussion).

of the riboflavin synthase complex (Ladenstein et al.,1986), but rather difficult with monoclinic crystals ofthe same protein (Bacher et al., 1992).

In principle, two-dimensional lattice parametersof crystal planes observed in electron micrographscan be determined by optical diffraction. These datamay be used for the assignment of hkl indices bycomparison with the cell constants obtained fromX-ray analysis. However, this task can be hamperedby the limited accuracy of the electron microscopicdata and by problems related to the latticeparameters and morphology of the crystals. Theseproblems will be discussed in the following.

The magnification of the microscope must bedetermined with great accuracy. In the presentstudy, we used Pt/C replicas of hexagonal crystalsof the lumazine synthase/riboflavin synthasecomplex of B. subtilis with cell dimensionsa = b = 156.4 A, c = 298.5 A, a = b = 90°, g = 120° asstandard (Ladenstein et al., 1986). The crystals havethe shape of hexagonal prisms, and only 40015 and41005 planes are observed in freeze-fracturereplicas (Bachmann et al., 1989; Weinkauf et al.,1991). Micrographs of this standard were taken atthe beginning and at the end of each workingsession. The specimens were observed at theeucentric position, and the lens current wasmonitored. Using this procedure, lattice lengthsand angles obtained from the optical transformscould be determined with an accuracy of 22% and21.5, respectively.

The two-dimensional lattice constants will bedistorted by parallax effects if the area of the replicaunder study is not orthogonal to the electron beam.This parallax distortion can be eliminated byevaluation of tilt-series of the crystal plane and thecorrect lattice constants can be calculated. However,it turned out that in almost all cases, crystal planessubject to parallax distortion, either decorated orshadowed, can already be recognized duringelectron microscopic observation. Moreover, itappears that the replica is flattened duringprocessing by the influence of surface tension whenfloated on water. Thus, in line with our earlierobservations, the parallax distortion is hardly aproblem.

In crystals, different planes may have very similarlattice parameters and thus cannot be indexed purelyon the basis of their metric properties. A computerprogram developed by W. Meining was used tocalculate the two-dimensional lattice parameters ofall non-symmetry-equivalent crystal planes of GTPcyclohydrolase I from their hkl indices. It turns outthat a considerable number of crystal planes havelattice dimensions similar to the electron micro-graphs shown in Figure 2 through 4 (Table 1). Thus,due to the limited accuracy of the electronmicroscopic analysis, the hkl assignment of theseplanes is non-trivial. However, it is unlikely that allthe surfaces shown in Table 3, would actually beobserved in freeze-etched crystals because the set ofobserved crystal planes will be determined by theexternal habitus of the crystals used.

that GTP cyclohydrolase I is a decamer with D5

symmetry and that the four enzyme particles in thecrystal unit cell are related by a pseudo 4-fold axis.Further, the rotation function analysis showed theexact orientation of the particle axes and indicatedthat the two enzyme complexes in the asymmetricunit are inclined to each other by 12° in the ac-plane(Figure 8a).

Assigning Miller indices to crystal planes onelectron micrographs

From the electron microscopic data and the X-rayresults, it was obvious that the packing of themolecules in the large crystal cell of the monoclinicmodification is quite complex. Whereas the X-raydata yielded the rotational parameters of the crystal,the particle positions could not be determined untila suitable heavy-metal derivative became available.Thus, an alternative approach was tried to obtain theapproximate translational positions and orientationsof the particles from the decoration averages. Thisrequires the unequivocal assignment of the hklindices of the observed planes.

The problems of assigning Miller indices to crystalplanes observed by freeze-etching electron mi-croscopy has been addressed in earlier studies.Briefly, this task was simple with hexagonal crystals

Elucidation of Crystal Packing 213

Table 1. Calculated and observed two-dimensional lattice parameters of symmetry-equivalentplanes of space group P21

Type I II III

4hkl5 40015 4101�5 41015 40115 4111�5 41115 41105 41005 401054h�k�l�5 401�1�5 41�1�1�5 41�1�1�5 41�1�0�5 401�05u (A) 210.4 210.2 223.9 222.2 222.2 223.9 293.4 210.4 204.2v (A) calc 204.2 210.4 210.4 204.2 210.2 222.2 71.8 71.8 71.88 (°) 90.0 90.0 90.0 91.9 94.6 97.8 94.0 90.0 95.8u (A) 208 282 193v (A) obs 202 69 698 (°) 90 90 94

Sets of symmetry-equivalent planes are described as 4hkl5. Plane sets denoted with 4h�k�l�5 have the samelattice parameters as 4hkl5 sets, but are not symmetry-equivalent to them. u, v and 8 obs. represent meanvalues of lattice parameters derived from different electron micrographs.

In order to estimate the number of differentcrystal planes observed by freeze-etching, weperformed a systematic metric analysis of allelectron micrographs. In this analysis, the two-di-mensional lattice lengths were selected from thediffractogram in such a way that the products of thecell vector lengths became minimal, i.e. the crystalplanes were all considered as primitive lattices.The longer vector was assigned to a coordinate u,and the shorter vector was assigned to a coordinatev. The angle 8 was then measured from u to v. Thedimensions of all crystal planes studied aresummarized in Figure 9. The data form threedistinct clusters. Each of the clusters could representeither one specific crystal plane or a set of planeswith closely similar dimensions.

The crystal planes shown in Figures 2 through 4belong to cluster I in Figure 9. This cluster couldrepresent 40015 planes, but the assignment is notunequivocal. In order to check whether 40015 planesactually form surfaces of the crystals, large crystalsof GRP cyclohydrolase I were mounted in the X-raydiffraction camera in such a way that one surfaceplane was orthogonal to the X-ray beam, and the hklindices of the respective plane were then determinedfrom the diffraction pattern. This approach showedthat 40015 planes did indeed represent growthsurfaces. Thus, we concluded that the planes inFigures 2 through 4 represent 40015 planes with highprobability.

Cluster II in Figure 9 represents diagonal planes.An example is shown in Figure 10. It appears likelythat this micrograph represents a 41105 or a 41�105plane. Cluster III in Figure 9 may represent 41005and/or 40105 planes.

Determination of molecule positions from theelectron microscopic data

An attempt was made to extract the x,y positionsof the molecules in the crystallographic cell byanalysing averaged micrographs of decorated crystalplanes. The assignment of the two-dimensionallattice vectors u, v to the crystallographic axes inFigure 4 is non-trivial, since the values differ only by3% (a = 204.2 A, b = 210.4 A) and thus cannot bedistinguished on the basis of vector lengths.However, from Patterson analysis it is known that the5-fold axes of the two cyclohydrolase decamers in theasymmetric unit are inclined against the direction ofthe crystallographic a axis by 84° and 96° (Figure 8a).Thus, the distances of the molecules on the electronmicrographs must alternate along the a axis due to aparallax effect, as replicas do not show the centres ofthe molecules but their surfaces. No parallax effectoccurs along the b axis. Therefore, distance of themolecules in direction of b should not alternate (i.e.the distance between any two adjacent moleculesshould be b/2) on the electron micrographs. Thisbehavior was indeed observed on a platinum-decorated replica (Figure 11); the mean variation ofthe particles distance was 10 A along the u axis and2 A along v. Making use of the parallax effect itwas thus possible to assign the u and v axes tothe crystallographic axes a and b, respectively(Figure 11).

The translational positions of the molecules in themonoclinic cell were then determined from theelectron micrographs by the following procedure.Since the directions of the axes observed on theelectron micrographs are not known, there exist four

Table 2. Averaged translational parameters of particles in correlation averagesof gold, silver and platinum decorated planes of types I (all data in A) andx,y positions obtained from SIR

Metal xA yA xB yB xC yC xD yD

Au 16 0.0 −16 105 118 27 87 132I Ag 16 0.0 −16 105 119 25 86 130

Pt 16 0.0 −16 105 118 26 87 131X-ray 16.7 0.0 −16.7 105.1 119.3 26.1 85.5 131.2

For comparison of electron microscope data with X-ray data, all y coordinates of eachline were diminished by yA .

Elucidation of Crystal Packing214

Table 3. Data collection statisticsNumber of Unique Resolution Completeness Number of Phasing power

Derivative measurements reflections (A) overall/last shell (%) RM RF sites (20.0–6.0 A)

Native 23,487 10,022 6.0 60/30 10.3 4.0TABR 21,933 9599 6.0 56/16 11.6 4.4 4 1.84

Overall figure-of-merit (20.0–6.0 A) = 0.52.Derivative soaking conditions: TABR: 5 mM, Ta6 Br14, 30 minutes.RM = S=Ih − �Ih�=/S�Ih�; RF:RM after independent averaging of Friedel pairs.Phasing power: �FH �/E, where �FH� = S( f2

H/n)1/2 is the root-mean-square heavy-atom structure factor amplitude.E = S[(FPHC − FPH)2/n]1/2 is the residual lack of closure error with FPH being the structure factor amplitude and FPHC = FP + FH the

calculated structure factor of the derivative.

possibilities for the assignment of the directions. Foreach of the assignments the common centre of themolecules related by the (pseudo) 4-fold symmetry(A through D, Figure 4b, d and f) were calculated. Arectangular fractional coordinate system was definedwhere the axes afr and bfr corresponded to thecrystallographic a and b axes and were scaled inunits of the lattice vectors observed by electronmicroscopy. The four different sets of the moleculepositions on the decoration image were transferredinto the fractional coordinate system, in such a waythat the centres of the four 5-fold motifs A throughD were set to x = 1/4 and y = 1/4 as shown in Figure12. The setting y = 1/4 is arbitrary and is chosen inthe sense of a best alignment. Because of the parallaxeffect described above, the centres of the 5-foldmotifs scatter significantly along the afr axis.Positions resulting from a change of the a-axis to thereversed a-axis represent the centre of the 5-foldmotif on the reverse side of the molecules. Theaverage of these observed positions therefore leads tothe x,y coordinates of the decamer centres, which arelisted in Table 2. The decamer positions obtainedfrom platinum and gold decorations are also given inTable 2. In all cases, the values from electronmicroscopy agree with the X-ray data within 21.5 A.An illustration of the monoclinic unit cell demon-strating the particle positions and orientations withrespect to the crystallographic axes is shown inFigure 8b.

The 6 A structure of GTP cyclohydrolase I bySIR-phasing and averaging

A screening for potential heavy-atom derivativesfor cyclohydrolase was unsuccessful. Probably, thiswas due to a slight non-isomorphism of the citratecrystal form dealt with herein. Thus, a new strategywas employed in which native and derivative data setwere collected from the same crystal specimen. Afterthe native data were collected, the crystal was keptin the capillary and soaked with a solution of Ta6Br14

in mother liquor, the most promising candidate toresult in strong binding to the crystalline proteinmatrix. Subsequently, the derivative data set wascollected. A difference Patterson function calculatedwith these data was readily interpreted guided byknowledge of the data from electron microscopy.

It turned out that the Ta6Br14 cluster binds in thecentre of each of the four GTP cyclohydrolase Ipentamers in the asymmetric unit. The vectorsbetween the two cluster sites belonging to each of thetwo independent decamers have the expectedorientations of the 5-fold particle axes previouslyfound in the self-rotation analysis, i.e. (c = 90°,8 = 84°) and (c = 90°, 8 = 96°). An electron densitycomputed with SIR phases at 6 A resolution wasvery noisy, but showed a clear contrast aftersolvent flattening. As expected, the density for theprotein was apparent within a radius of about 50 Aaround the heavy-atom binding sites. Moreover, a

Figure 9. Distribution of latticeparameters u, v and 8, observed onfreeze-etched replicas. For eachlattice determined from the micro-graphs a couple of lattice vectorswas calculated so that the productsof the vector lengths became mini-mal. The longer vector was assignedto a coordinate u, and the shortervector was assigned to a coordinate v.The angle 8 was then measured fromu to v. The parameters of all crystalplanes studied are summarized inTable 3. The data form three distinctclusters I, II and III. Each of the

clusters could represent either one specific crystal plane or a set of planes with closely similar dimensions. Figures 2through 4 were taken from crystal planes belonging to group I.

Elucidation of Crystal Packing 215

Figure 10. Freeze-etched plane of GTP cyclohydrolase Icrystals grown from citrate buffer, shadowed with Pt/C at45° incidence. The crystal plane belongs to the group IIshown at Figure 9 and Table 1, respectively. Figure 12. Centres of 5-fold motifs from platinum

decoration in Figure 4b. As the axis directions are notknown, four sets of positions result. The positions arealigned so that the average of the centres of the four 5-foldmotifs are set to x = y = 1/4.

quantitative analysis of the correlation of the densitypattern around the centre of gravity of each pair ofcluster sites revealed strong 5-fold and 2-foldsymmetry.

The exact position of the local symmetry elementswas determined by real space rotational andtranslation functions. Subsequently, the electrondensity was cyclically averaged using two cylindricalenvelopes with 52 A radius centred at the resultantdecamer centres of symmetry (x = 16.7 A, y = 0.4 A,z = 35.7 A) and (x = 119.3 A, y = 26.5 A, z =35.9 A), respectively.

The two decamers were treated independentlyusing only the 5-fold axes for averaging, the 2-foldsbeing used as a control during the averaging cycles.The R-factor obtained after back-transformation ofthe electron density was 48% at the beginning and22% at the end of the averaging procedure. Thecorrelation values for the local 2-fold symmetry axeswas 30% in the SIR map and 55% in the cyclically5-fold averaged map. A plot of a section of theaveraged electron density viewed in projection ontothe ab crystal plane is shown in Figure 13a. It clearlyshows the arrangement of the GTP cyclohydrolase Ienzyme complexes in the unit cell. The electrondensity indicates that the cyclohydrolase decamer isa torus with a height of 65 A and a diameter of 100 A.

Discussion

Freeze-etching electron microscopy in combi-nation with heavy-metal decoration has been utilizedearlier to support the X-ray diffraction analysis of theriboflavin synthase complex of B. subtilis (Bacheret al., 1992) and of proteasomes from Thermoplasmaacidophilum (Puhler et al., 1992) which were both inthe MDa range. Here, we describe for the first timethe successful application of the method to a smallerprotein (Mr = 247 × 103). Moreover, this is the firstcase where the method has been applied to aprotein whose quaternary structure was completelyunknown.

The combination of freeze-etching electron mi-croscopy and Patterson methods has been used todetermine the non-crystallographic symmetry prop-erties of E. coli GTP cyclohydrolase I crystals, and amodel of the crystal packing has been developed.This approach depends critically on the interaction

Figure 11. Averaged platinum-decorated ab plane asshown in Figure 4b. Assignment of crystallographic axes.Due to the parallax effect induced by the inclination of the5-fold molecule axes, the molecules distance must alternatealong the a axis, while being constant along b. On analysedmicrographs of platinum-decorated ab planes the corre-sponding mean distances were Du1 = 110 A, Du2 = 95 A,Dv1 = Dv2 = 105 A. Therefore, the vector u was assigned toa and the vector v to b. The distance alternation along ainduced by the b axis being a 2-fold screw axis amounts ofless than 1 A and can thus be ignored.

Elucidation of Crystal Packing216

Figure 13. a, Electron density of five sections plotted parallel to the ab plane (y horizontal). Four unit cells are depicted.The initial SIR-map was averaged using the particle 5-folds, backtransformed and a new map calculated. After 20 of suchaveraging cycles, the map shown was obtained. It clearly shows the arrangement of the four GTP cyclohydrolase I decamersper unit cell and their relative rotations within the ab plane; b, average of a gold-decorated ab plane as shown in Fig-ure 4a, superimposed with the electron density (c).

between crystallographers and electron micro-scopists as can be seen from the following summaryof the experimental process.

The cell dimensions of the monoclinic crystalmodification were determined earlier by Schmidet al. (1993). Initial decoration studies indicated thepresence of 5-fold particle symmetry, suggesting thatthe protein complex could have D5 symmetry(pentamer of dimers). Moreover, the micrographssuggested that four particles in the crystal cell couldbe related by 4-fold pseudosymmetry.

A Patterson search was initiated to verify the D5

symmetry hypothesis, using vector lengths withinthe suggested decamer radius of 50 A. It revealed thepresence of two 5-fold axes with an inclination of 12°between them and two corresponding sets ofnon-crystallographic 2-folds in the plane perpen-dicular to the particle 5-folds. These data confirmedthe notion that GTP cyclohydrolase I exists as a D5

decamer and, moreover, showed that two decamersare present in different orientations in the asymmet-ric unit. This relative spatial arrangement leadsfurthermore to the presence of a 4-fold pseudosym-metry, which was suggested by the decorationimages and confirmed by the Patterson analysis.

Since both electron microscopic and X-raycrystallographic arguments supported the assign-ment of the planes shown in Figures 2 through 4 asab planes, both x,y positions of the molecule centresand the approximate orientations of the 2-fold and5-fold molecular local axes could be estimated fromthat plane. The data obtained by analysing thedecoration motifs of different metals deviated notmore than 1.5 A from the X-ray values.

An independent crystallographic analysis of aheavy-atom derivative provided coordinates of fourbinding sites, which were, based on the availableinformation, identified as the centres of the fourpentamers in the asymmetric unit. The quality of theSIR electron density map was subsequently muchimproved by molecular averaging. The resultantelectron density map viewed in projection onto the

ab crystal plane is in agreement with the decorationimage obtained by electron microscopy (Figure 13band c).

The results of this study suggest that freeze-fracture electron microscopy can be more generallyapplied to assist the X-ray structure determination incases where phase determination by multipleisomorphous replacement is difficult or impossible.We have previously summarized the experimentalapproach. This description can now be modified toincorporate the more recent methodical advances.Briefly, the following approach is proposed.

The cell dimensions must be determined by X-raydiffraction analysis. This information should be usedto calculate the two-dimensional lattice parametersof all crystal planes with hkl indices up to at least 3.

Microcrystals should be prepared, and decorationand shadowing images should be obtained withcareful control of the microscope magnification.

The two-dimensional lattice constants of all goodmicrographs should be determined by opticaldiffraction analysis and should be subjected to aformal analysis of data clustering (see Figure 9). Thisshould establish the minimum number of non-equiv-alent crystal planes that can be observed byfreeze-etching electron microscopy.

The observed lattice data should be matchedagainst the table of lattice dimensions calculatedfrom the cell constants determined by X-raycrystallography. X-ray diffraction of crystalsmounted with one plane orthogonal to the beam canhelp to check the plausibility of these results.

Symmetry elements observed in decorationimages should be compared with the results ofPatterson analysis of the X-ray diffraction data.

Following the localization of the crystal axis in themicrographs, the approximate translational positionof molecules in the crystal cell can be obtained infavorable cases.

The accumulated information may at that stage beused for phasing crystallographic structure factoramplitudes at low resolution, provided that a

Elucidation of Crystal Packing 217

reasonable estimate for a molecular envelope (shapeand size of the particles) can be made. From there,phase extension will be necessary to arrive at anelectron density map at higher resolution. Thisprocess can, in principle, be based on various densitymodification routines or direct methods. Molecularaveraging, however, is at present the most powerfultechnique for phase extension in cases of homo-multimeric protein complexes.

Materials and Methods

Protein

GTP cyclohydrolase I was overexpressed in therecombinant E. coli strain JM83 (Schmid et al., 1993).The strain harbors the plasmid vector pUC13 with thestructural gene for GTP cyclohydrolase I under the controlof its own promoter. The protein was purified from thecrude extract by ammonium sulfate precipitation andaffinity chromatography with GTP-Sepharose 4B (Yim &Brown, 1976).

Crystallization

Crystals were grown by the vapor diffusion method insitting drops at 20°C from a solution containing 5 mg ofenzyme per ml in 0.27 M sodium citrate (pH 7.4), 6.25 mMpotassium phosphate, 1.5 mM EDTA and 0.01% (w/v)sodium azide (Schmid et al., 1993). The reservoir contained0.41 M sodium citrate, 6.25 mM potassium phosphate,1.5 mM EDTA and 0.01% sodium azide.

Electron microscopy and image processing

Suspensions containing small crystals of GTP cyclo-hydrolase I (E100 mm) were pooled, washed with 0.5 Mcitrate (pH 7.4) and frozen on standard specimen mountsby immersion into liquid nitrogen. The frozen sampleswere fractured in a Balzers BAF400 freeze-etching unit,deep-etched at − 100°C, and either shadowed in theconventional way with Pt/C at 45° incidence or decoratedwith one to two monolayers of silver, gold or platinum atnormal incidence. The carbon-backed replicas werethawed, floated on water, mounted on grids, andinvestigated with a JEOL JEM 100 CX electron microscopeat a magnification of 33,000 × . The magnification wascalibrated using freeze-etched replicas of crystals withknown lattice parameters. Only electron micrographs ofcrystal surfaces exposed by deep-etching were used for adetailed analysis. Mechanically fractured crystal planeswere not suitable.

Standard correlation averaging was applied to thedigitized micrographs (1024 × 1024 pixels) without impos-ing any rotational symmetry (Saxton & Baumeister, 1982).The lattice parameters were determined either from opticaldiffractograms or from power spectra. Details of thespecimen preparation and image processing procedureshave been described (Bachmann et al., 1989; Weinkauf et al.,1991; Rubenkamm et al., 1995).

X-ray intensity data collection

X-ray intensity data of GTP cyclohydrolase I crystalswere measured at 4°C on a FAST area detector system(Enraf-Nonius, Delft) mounted on a Rigaku RU200 rotating

anode generator. Data sets were collected by rotating thecrystal by 90° around the crystal c-axis. A native data setas well as a Ta6Br14 derivative data set were collected fromthe same crystal to a resolution of 6 A. Data were scaledand reduced with the programs MADNES (Messer-schmidt & Pflugrath, 1987) and ABSCOR (Messerschmidtet al., 1990). All further crystallographic computing wasperformed with PROTEIN (Steigemann, 1974). Heavy-atom positions were determined from difference Pattersonfunctions and refined in PROTEIN. Data collection andsingle isomorphous replacement (SIR) phasing statisticsare summarized in Table 3. The electron density mapcomputed with SIR phases was averaged using theprogram package MAIN (Turk, 1992).

AcknowledgementsThis work was supported by the Deutsche Forschungs-

gemeinschaft and Fonds der Chemischen Industrie. Wethank Angelika Kohnle for expert help with thepreparation of the manuscript.

ReferencesBacher, A., Weinkauf, S., Bachmann, L., Ritsert, K.,

Baumeister, W., Huber, R. & Ladenstein, R. (1992).Electron microscopy of decorated crystals for thedetermination of crystallographic rotation and trans-lation parameters in large protein complexes. J. Mol.Biol. 225, 1065–1073.

Bachmann, L., Weinkauf, S., Baumeister, W., Wildhaber, I.& Bacher, A. (1989). Electron microscopy ofsubnanometer surface features on metal-decoratedprotein crystals. J. Mol. Biol. 207, 575–584.

Bassett, G. A. (1958). A new technique for decoration ofcleavage and slip steps on ionic crystal surfaces. Phil.Mag. ser. 8, 3, 1042–1045.

Bethge, H. & Heydenreich, J. (1987). Editors of ElectronMicroscopy in Solid State Physics. Elsevier, Amsterdam.

Brown, G. M. & Williamson, J M. (1987). Biosynthesis offolic acid, riboflavin, thiamine, and panthotenic acid.In Escherichia coli and Salmonella typhimurium:Cellular and Molecular Biology (Neidhardt F. C., ed.),vol. 1, pp. 521–538, American Society for Micro-biology, Washington, DC.

Eisenreich, W. & Bacher, A. (1994). Biosynthesis ofmethanopterin in Methanobacterium thermoauto-trophicum. Pteridines, 5, 8–17.

Ladenstein, R., Meyer, B., Huber, R., Labischinski, H.,Bartels, K., Bartunik, H. D., Bachmann, L., Ludwig,H. C. & Bacher, A. (1986). Heavy riboflavin synthasefrom Bacillus subtilis. Particle dimensions, crystalpacking and molecular symmetry. J. Mol. Biol. 187,87–100.

Matthews, R. G., Green, J. M. & Nichols, B. P. (1995). InEscherichia coli and Salmonella typhimurium:Cellular and Molecular Biology (Neidhardt, F. C., ed.),American Society for Microbiology, Washington, DC.In the press.

Meining, W., Schmid, C., Nar, H., Weinkauf, S. & Bacher,A. (1994). The crystal packing of GTP cyclohydrolaseI from Escherichia coli: a combined study by electronmicroscopy and X-ray analysis. Electron Microscopy 94,Proc. 12th Int. Congr. Electron Microscopy, ICEM 13-Paris, Les editions de physique, France, pp. 961–962.

Messerschmidt, A. & Pflugrath, J. (1987). Crystalorientation and X-ray pattern prediction routines for

Elucidation of Crystal Packing218

area-detector diffractometer systems in macro-molecular crystallography. J. Appl. Crystallog. 20,306–315.

Messerschmidt, A., Schneider, M. & Huber, R. (1990).ABSCOR: a scaling and absorption correctionprogram for the FAST area detector. J. Appl. Crystallog.23, 436–439.

Nichol, C. A., Smith, G. K. & Duch, D. S. (1985).Biosynthesis and metabolism of tetrahydropterin andmolybodopterin. Annu. Rev. Biochem. 54, 729–764.

Puhler, G., Weinkauf, S., Bachmann, L., Muller, S., Engel,A., Hegerl, R. & Baumeister, W. (1992). Subunitstoichiometry and three-dimensional arrangement inproteasomes from Thermoplasma acidophilum. EMBO J.11, 1606–1616.

Ritz, H., Keller, G., Ritcher, G., Katzenmeier, G. &Bacher, A. (1993). Location of the gene coding for GTPcyclohydrolase I on the physical map of Escherichia coli.J. Bacteriol. 175, 1553.

Rubenkamm, E., Braun, N., Bachmann, L., Bacher, A.,Brandt, J., Baumeister, W. & Weinkauf, S. (1995).Quantitative evaluation of heavy metal decoration onprotein molecules: contrast, specificity and resolution.Ultramicroscopy, in the press.

Saxton, W. O. & Baumeister, W. (1982). The correlationaveraging of a regularly arranged bacterial cellenvelope protein. J. Microsc. 127, 127–138.

Schmid, C., Meining, W., Weinkauf, S., Bachmann, L., Ritz,H., Eberhardt, S., Gimbel, W., Werner, Th., Lahm, H.W., Nar, H. & Bacher, A. (1993). Studies on GTP

cyclohydrolase I of Escherichia coli. Chemistry andBiology of Pteridines and Folates (Ayling, J. E., Nair, M.G. & Baugh, Ch. M., ed), pp. 157–162, Plenum Press,New York and London.

Steigemann, W. (1974). Die Entwicklung und Anwendungvon Rechenverfahren und Rechenprogrammen zurStrukturanalyse von Proteinen. Thesis, TechnicalUniversity, Munich.

Togari, A., Ichinose, H., Matsumoto, Sh., Fujita, K. andNagatsu, T. (1992). Multiple mRNA forms of humanGTP cyclohydrolase I. Biochem. Biophys. Res. Commun.187, 359–365.

Turk, D. (1992). Weiterentwicklung eines Programms furMolekulgraphik und Elektronendichte-Manipula-tionen. Thesis, Technical University, Munich.

Weinkauf, S. & Bachmann, L. (1992). Metal decoration ofbiomacromolecules and molecular assemblies: areview. Ultramicroscopy 46, 113–134.

Weinkauf, S., Bacher, A., Baumeister, W., Ladenstein, R.,Huber, R. & Bachmann, L. (1991). Correlation of metaldecoration and topochemistry on protein surfaces.J. Mol. Biol. 221, 637–645.

Yim, J. J. & Brown, G. M. (1976). Characteristics ofguanosine triphosphate cyclohydrolase I purifiedfrom Escherichia coli. J. Biol. Chem. 251, 5087–5094.

Ziegler, I. & Schwulera, U. (1989). Modulation ofinterleukin 2 high-affinity binding by lymphocytederived tetrahydrobiopterin: pterins as potentialparticipants in the control of interleukin 2 receptorassembly. J. Cell. Biochem. 41, 103–112.

Edited by T. Richmond

(Received 24 March 1995; accepted 25 July 1995)