X-ray diffraction and atomic force microscopy analysis of twinned crystals: rhombohedral canavalin

accommodated in both ‘top-up’ and ‘bottom-up’ orientations in a rhombohedral unit cell of the R 3 crystal and explained the presence of a high twin fraction. The large inter-trimer stacking interface of the C 222 1 crystal may account for its relative stability. Atomic force microscopy (AFM) investigations of the growth of three crystal forms of canavalin indicate the rhombohedral form to be unique. Unlike the other two crystal forms, it contains at least an order of magnitude more screw dislocations and stacking faults any other macromolecular crystal yet studied, it of

The structure of canavalin, the vicilin-class storage protein from jack bean, was re®ned to 1.7 A Ê resolution in a highly twinned rhombohedral crystal of space group R3 and unit-cell parameters a = b = c = 83.0 A Ê , = = = 111.1 . The resulting R and R free were 0.176 and 0.245, respectively. The orthorhombic crystal structure (space group C222 1 , unit-cell parameters a = 136.5, b = 150.3, c = 133.4 A Ê ) was also re®ned with threefold non-crystallographic symmetry restraints. R and R free were 0.181 and 0.226, respectively, for 2.6 A Ê resolution data. No signi®cant difference in the protein structure was seen between these two crystal forms, nor between these two and the hexagonal and cubic crystal forms reported elsewhere , Acta Cryst. D49, 478±489; , Plant Physiol. 101, 729±744]. A phosphate ion was identi®ed in the lumen of the C-terminal -barrel. Lattice interactions showed that the trimeric molecule could be well accommodated in both`top-up' and`bottom-up' orientations in a rhombohedral unit cell of the R3 crystal and explained the presence of a high twin fraction. The large inter-trimer stacking interface of the C222 1 crystal may account for its relative stability. Atomic force microscopy (AFM) investigations of the growth of three crystal forms of canavalin indicate the rhombohedral form to be unique. Unlike the other two crystal forms, it contains at least an order of magnitude more screw dislocations and stacking faults than any other macromolecular crystal yet studied, and it alone grows principally by generation of steps from the screw dislocations. The unusually high occurrence of the screw dislocations and stacking faults is attributed to mechanical stress produced by the alternate molecular orientations in the rhombohedral crystals and their organization into discrete domains or blocks. At boundaries of alternate domains, lattice strain is relieved by the formation of the screw dislocations.

Introduction
Crystal twinning is problematic in the structure determination of proteins, especially when phasing is by multiple isomorphous replacement (Yeates, 1997). For merohedrally twinned crystals with low fractions of twinning, it is possible to directly recover the true diffraction intensities. When the twin fraction approaches 0.5, the observed intensities I obs (h 1 ) and I obs (h 2 ) related by hemihedral twinning will become nearly equal and additional symmetry appears in the diffraction pattern. For these nearly perfect twin crystals, direct detwinning of the data is not reliable. The situation is less acute, however, in molecular replacement. Using an accurate starting model, it is still possible to solve and re®ne the crystal structure. Structure determination and re®nement of twinned protein crystals have become of increasing interest as seen, for example, in the papers regarding bacteriorhodopsin (Luecke et al., 1998(Luecke et al., , 1999, cephalosporin synthase (Valegard et al., 1998), cytidylyltransferase (Weber et al., 1999), human lactoferrin (Breyer et al., 1999) and an arginase±boronic acid complex (Cox et al., 1999). A more recent review on this subject can be found in the paper by Yeates & Fam (1999).
Canavalin is the vicilin-class storage protein from jack bean (Canavalia ensiformis) and is a trimer of 142 kDa (Smith et al., 1982;McPherson, 1999). The tertiary structure of canavalin was determined by multiple isomorphous replacement and molecular-replacement methods in four different crystal forms (Ko, Ng, Day et al., 1993;McPherson, 1999). It is similar to phaseolin, another vicilinclass protein from French bean (Phaseolus vulgaris; Lawrence et al., 1990Lawrence et al., , 1994. Both canavalin and phaseolin are trimers with exact threefold symmetry. Each subunit of the trimer, however, is composed of amino-and carboxy-terminal domains. The two domains are structurally very similar and are related to one another by pseudo-dyad axes perpendicular to the threefold axis. Thus, the canavalin molecule has a high degree of quasi-D 3 symmetry. As shown in Fig. 1, each domain is comprised of a`core' -barrel subdomain with an extended helical`loop' subdomain. Within a subunit, the core subdomains are tightly associated through the larger -sheets of A H ABIDGZ; between subunits, the smaller -sheets of JJ H CHEF, and the loop subdomains are involved in the assembly into trimers (Ko et al., 2000).
The structure of canavalin has recently assumed some additional importance, serving, along with that of phaeseolin, as the model structures for the protein superfamily known as cupins. This superfamily now includes a vast array of both plant and animal proteins, some containing metal ions, that catalyze a variety of biochemical reactions. All share the fundamental architecture of the canavalin domain (Dunwell et al., 2000).
The rhombohedral canavalin crystal has special merits in that it appeared ®rst (Sumner & Howell, 1936), grows easily and reproducibly, grew to largest size (Day & McPherson, 1992) and diffracted X-rays to highest resolution (Koszelak et al., 1995). It has provided a model system for a diverse array of crystallization studies (Kuznetsov et al., , 1997Land et al., 1995Land et al., , 1996Land et al., , 1999Malkin et al., 1995Malkin et al., , 1996Malkin et al., , 1999 and has also been a prominent crystal employed in microgravity crystal-growth investigations (Day & McPherson, 1992;Koszelak et al., 1995;. This crystal form displays a high degree of R32 symmetry, but the true space group was identi®ed as R3 (McPherson & Spencer, 1975). It has unit-cell parameters a = b = c = 83.0 A Ê , = = = 111.1 or a = b = 136.9, c = 76.0 A Ê in the equivalent hexagonal cell and contains one canavalin protomer per asymmetric unit.
In earlier lower resolution stages of study, it was disturbing to ®nd that a crude model could be placed in different orientations, including inverting the trimer, and the model would still yield acceptable R values in the low 20s. Ambiguities appeared to be resolved by calculating direct crossrotation functions between the hexagonal crystal form in which the structure had been solved by MIR, and the R3 crystal. This was described in Ko, Ng, Day et al. (1993). Re®nement using higher resolution data, however, yielded only mediocre results. This was particularly perplexing because all of the other crystal forms of canavalin were re®ned successfully and well (Ko et al., 2000). Because of the suspicious behavior of the rhombohedral crystals and their model, further analysis of structure was focused on the other crystal forms of the molecule, particularly the hexagonal form (Ko, Ng, Day et al., 1993).
Here, we show that the rhombohedral crystal form is indeed hemihedrally twinned and that with the inclusion of this feature the structure can be satisfactorily re®ned. The orthorhombic crystal, previously re®ned to 2.6 A Ê resolution (Ko, Ng, Day et al., 1993), belongs to space group C222 1 , has unit-cell parameters a = 136.5, b = 150.3, c = 133.4 A Ê and contains the entire canavalin trimer as its asymmetric unit. This crystal has also been further re®ned and serves as a useful basis of comparison for the rhombohedral crystal form, particularly with regard to the atomic force microscopy investigation described below.
In parallel with our X-ray diffraction studies, we have investigated, by in situ AFM, the growth of three different crystal forms of canavalin: the rhombohedral, hexagonal and orthorhombic crystals (the cubic form was not examined by AFM). While both of the latter forms grow almost exclusively by the mechanism of two-dimensional nucleation, the rhombohedral form does not (Land et al., , 1996(Land et al., , 1999Malkin et al., 1995). Unique among all of the macromolecular and virus crystals we have studied (more than 20 in number), it alone grows principally owing to a vast array of screw dislocations distributed throughout its volume. This has long been a puzzling observation without any apparent explana- A ribbon diagram of the three identical subunits of the canavalin trimer shown here as viewed along the threefold axis. The N-terminal and the C-terminal domains are in red and blue, respectively. Each domain of a subunit can in turn be divided into a -barrel subdomain and a helix± loop±helix subdomain. The former is responsible for intrasubunit domain interactions and the latter for intersubunit contacts. All other components of the molecule, including sheet strands and helices, are according to the nomenclature de®ned in Ko et al. (2000). The phosphate ions in the lumina of the C-terminal barrels are also shown, with bonds in yellow. tion. We suggest, based on the evidence presented here, that the appearance of the screw dislocations and the many accompanying stacking faults may be correlated with the unusual twinning shown by X-ray crystallography. This would be entirely consistent with theory and experience from conventional crystal-growth research.

Materials and methods
Canavalin was prepared as described previously (McPherson & Spencer, 1975;Sumner & Howell, 1936) and large rhombohedral crystals were grown in microgravity experiments on the US Space Shuttle by liquid±liquid diffusion (Koszelak et al., 1995). X-ray data were collected and processed using a San Diego Multiwire Systems detector with a Rigaku RU-200 rotating anode and SDMS software package also as previously described (Ko, Ng, Day et al., 1993). These microgravity-grown crystals extended the effective diffraction resolution from 2.6 A Ê to about 1.7 A Ê . Statistics are found in Table 1. For re®nement of the orthorhombic crystal structure, the data set previously used in structure determination by molecular replacement was retrieved from the Protein Data Bank (PDB code 1cax). It contains 28 836 re¯ections with F > 3' F and extends to 2.6 A Ê resolution. Throughout the re®nement, 8% randomly selected re¯ections from both crystals were set aside for cross validation with R free (Bru È nger, 1992a). The program X-PLOR (Bru È nger, 1992b) was used in initial re®nements, but at later stages CNS (Brunger et al., 1998) was employed. Computation was performed on a Silicon Graphics Octane workstation. Manual rebuilding of the model and addition of solvent molecules were carried out using O (Jones et al., 1991) and analyses of the models employed CNS, CCP4 (Collaborative Computational Project, Number 4, 1994) and PROCHECK (Laskowski et al., 1993). Figures were produced using MOLSCRIPT (Kraulis, 1991) and Raster3D (Merrit & Murphy, 1994).
Re®nement of the rhombohedral canavalin structure was reinitiated using a new model derived from the re®ned cubic crystal (Ko et al., 2000). After appropriate placement of the model in the rhombohedral unit cell, rigid-body re®nement using X-PLOR yielded an R value of 0.32 at 3.0 A Ê resolution. Subsequent re®nement, including addition of solvent molecules, gave marginally acceptable R and R free values of only 0.28 and 0.35, respectively, at 2.0 A Ê resolution. The problem was manifest in the difference Fourier maps which contained unexplained densities outside the protein region. We then found that the entire model could be rotated by 180 about the 100 or 010 axis of the hexagonal unit cell and still yield comparable re®nement results. Both`top-up' and`bottom-up' molecules were evidently present in the rhombohedral crystal, suggesting that the crystal was actually twinned with a high fraction. Further re®nements were unsuccessful until CNS was employed.
Hemihederally twinned crystals consist of a large number of individual domains consisting alternately of molecules in one of two orientations. Thus, every measured re¯ection can be considered a composite of contributions from two separate crystals. Both orientations of the molecule,`top up' and bottom up', contribute to the intensity of each re¯ection in proportion to the degree of twinning.
For crystals where the twinning is disparate, e.g. 20±80%, and the twinning fraction can be accurately determined, then the contributions can be separated and re®nement carried out against partial intensities. When the twinning fraction is near 50%, as it is for canavalin, detwinning the contributions becomes impossible. It is, however, possible to estimate the relative contributions of each twin to the intensity, I, and therefore to re®ne the model of the structure against I.
The intensities, sigmas and R value are calculated for all equivalent re¯ections by I obs h I obs h 1 I obs h 2 a2 fF obs h 1 2 F obs h 2 2 ga2Y A routine for carrying this out has been implemented in CNS. For canavalin, re®nement was carried out in parallel using both the measured R3 intensities and a data set produced by averaging re¯ections according to R32, the apparent space group of a perfect twin, but re-expanded according to R3. The R avg between hemihedrally related intensities was 0.132 for 27 473 independent re¯ections. Model alterations were applied only as a result of the re®nement against the perfect twin data and maps were calculated using only those structure amplitudes. The original strictly R3 data was used for cross validation during re®nement, in addition to the conventional R free based on a sequestered data subset.
Using CNS, the twin fraction of the rhombohedral crystal was estimated to be 0.42±0.44 based on hHi and hH 2 i (Yeates, 1997) or 0.46 based on the initial model. Starting with this model, a minimal R value of 0.215 for all data at 2.0 A Ê resolution was obtained, while the twin fraction converged to 0.426 by optimization with small intervals between 0.3 and 0.5. Initial cycles of re®nement at 2.0 A Ê , including simulated annealing, yielded R and R free values of 0.183 and 0.247.
Addition of water molecules was carried out manually using O in conjunction with the water-pick procedure of CNS. The  Table 1 Data-collection statistics of the rhombohedral canavalin crystals.
Numbers in parentheses refer to the highest resolution shell. ² R merge = hkl j jI ave À I obsYj j/ hkl j I ave , in which I ave is the average intensity of j equivalent re¯ections I obs,j and the sum is over all re¯ections that are equivalent in the unmerged data set. general criteria were a distance of less than 6 A Ê from appropriate protein atoms, a temperature factor of less than 60 A Ê 2 after re®nement and a corresponding density level of more than 2' in the Fourier maps. However, strong densities in the central cavity of the canavalin trimer, near the N-and C-termini or in the vicinity of crystal contact regions were also interpreted as ordered waters with a less stringent distance criterion. At the C-terminus of the C-terminal domain, the density initially interpreted as waters was later shown to correspond to two additional amino-acid residues Gln422 and Pro423. In the lumen of the C-terminal -barrel, density for a cluster of three to four waters was reinterpreted as a phosphate ion. The model was repeatedly checked against omit maps for selected regions which had high temperature factors or real-space R values. Adjustments of protein side chains were made as the re®nement proceeded, while the resolution was gradually increased to 1.7 A Ê .

Space group
Re®nement of the orthorhombic crystal was carried out in parallel with that of the rhombohedral crystal. An initial R value of 0.27 for all re¯ections in the data set was calculated by X-PLOR using a trimer generated from the re®ned protein model of the cubic crystal (Ko et al., 2000), with proper placement in the orthorhombic unit cell and rigid-body minimization of the six domains. In Fourier maps calculated from this initial model, densities for several water molecules were seen clearly, justifying inclusion of a solvent model, even at 2.6 A Ê . Non-crystallographic symmetry (NCS) restraints were imposed on the three protein subunits. Using CNS, maps were also threefold averaged with only limited improvement. In addition to the C-terminal Gln422 and Pro423 of all subunits, another extension of Met331 was identi®ed for the E±F loop of the C-terminal domain in two subunits. A phosphate ion was also clearly seen in the C-terminal barrels of all subunits.
For AFM studies, seed crystals of canavalin were nucleated and grown on glass substrates in 10 ml droplets by a batch method consisting of mixing 40 mg ml À1 of protein dissolved in water with an equal amount of 2 Â Dulbecco's phosphate buffered saline (DPBS). Canavalin crystals of sizes 50±500 mm in the longest dimension were used. The glass substrate with its seed crystals was then immediately transferred to the sealed uid cell of a Nanoscope III atomic force microscope (Digital Instruments, Santa Barbara, CA, USA) and the entire volume of the cell (approximately 50 ml) was ®lled with a 1:1 mixture of protein (4±20 mg ml À1 ) in DPBS. Images were collected in contact mode using oxide-sharpened silicon nitride tips (Park Scienti®c Instruments, Sunnyvale, CA, USA). Cantilevers with nominal force constants of 0.01 N m À1 and forces of 0.3 nN or less were utilized during imaging. When scanning, care was taken to continually adjust the set-point voltage to the lowest value for which tip-to-crystal contact was maintained in order to minimize the force applied to the crystalline surface.

Refinement
To recon®rm the molecular-replacement solution of the rhombohedral crystal, the R values of the protein model were plotted against rotation angle about the threefold axis. This was performed with either top-up or bottom-up models and the results are shown in Fig. 2. The symmetric pro®le was also seen in the cross-rotation function of the rhombohedral and hexagonal crystals (Fig. 5a of Ko, Ng, Day et al., 1993). These plots indicated that only two orientations of the canavalin molecules were present in the rhombohedral crystal. To estimate the precise twin fraction, several cumulative H plots were made and are illustrated in Fig. 3. However, the linear portion of the curve was only seen within a cumulative distribution of 0±0.65; above 0.65 its slope declined rapidly. Depending on the selection of data in the calculation, the linear portion showed a range of slope for twin fraction from 0.43 (all re¯ections) to 0.47 (10% strongest re¯ections). A plausible explanation for the uncertainty of twin fraction was that data from four crystals, possibly twinned to slightly different degrees, were merged to provide the ®nal data set. Ambiguity was removed by using an averaged data set for a perfect twin in re®nement. At the same time, re®nement was also carried out using the original data set with the optimized twin fraction of 0.426.
The re®ned model in the rhombohedral crystal contained 2783 non-H atoms in the 346 residues Asn46±Pro223, Asp246± Glu321 and Gln332±Pro423 plus a phosphate ion and 292 waters. Residues 46±223 and 246±423 comprised the two domains described previously (Ko et al., 2000) in which the omitted loop between strands E and F of the C-terminal barrel (Gln322±Met331) had weak density, probably owing to¯exibility. For the orthorhombic crystal, the re®ned model contained 8356 protein atoms, three phosphate ions and 168 waters. The polypeptide chains of the three canavalin subunits were named A, B and C, which all contained similar residues as in the rhombohedral model, while the residue Gln321 was not observed in the A chain and an additional Met331 was observed for the A and B chains. Statistics of the re®ned models are listed in Table 2.
For the rhombohedral crystal, the R and R free values at 1.7 A Ê were 0.176 and 0.245, respectively, using the averaged data set of perfect twin with F > 2' F cutoff, or 0.181 and 0.248 using all data. If the original data set and a twin fraction of 0.426 were used, the R and R free would be 0.183 and 0.250, respectively, for data with F > 2' F , or 0.189 and 0.252 for all data. The coordinate errors estimated by a Luzzati plot (Luzzati, 1952) using the work and test data sets were 0.24 and 0.25 A Ê , respectively. For the orthorhombic crystal, the R and R free at 2.6 A Ê were 0.181 and 0.226, respectively, and the estimated errors were 0.27 and 0.34 A Ê . In CNS, where domains were restrained separately, the NCS-related atoms deviated by 0.09±0.10 A Ê for the backbone and 0.16±0.19 A Ê for side chains. Superposition of entire subunits using LSQKAB from CCP4 produced differences of 0.23±0.24 and 0.37±0.42 A Ê , respectively, as shown in Table 3. Between the rhombohedral and orthorhombic crystals the coordinate differences for backbone and side-chain atoms were 0.46±0.49 and 1.05±1.07 A Ê , respectively. Similar ranges of 0.32±0.43 and 1.20±1.43 A Ê were obtained if the cubic and hexagonal models (PDB codes 2cau and 2cav) were included in the comparison. In all models, there was only one residue per subunit, Tyr417 (9 = 61 AE 6, 2 = À65 AE 10 ), in the disallowed region of Ramachandran plot de®ned by PROCHECK. Another residue, Ser351 (9 = 75 AE 3 , 2 = À8 AE 4 ), was in the generously allowed region. These residues assumed conformations in a -turn (Tyr417) and a type II turn (Ser351) as described previously (Richardson, 1981;Ko et al., 2000).
In the lumen of the C-terminal -barrel, the phosphate ion made four hydrogen bonds, including a salt bridge, with the side chains of His297, Asn299 and Arg376, as shown in Fig. 4. The phosphate was probably also present in the cubic and hexagonal crystals at the solvent sites of Wat515 and Wat501 (Ko et al., 2000), respectively, but was now identi®ed with certainty in the re®ned subunit models for the rhombohedral and orthorhombic crystals. In retrospect, this phosphate corresponded to the major mercury iodide site of the rhombohedral and hexagonal crystals used in the original structure determination (Ko, Ng, Day et al., 1993). At the equivalent position in the N-terminal domain, another water molecule made hydrogen bonds with His102 and Lys161. However, the volume of density and interatomic distances precluded a phosphate ion.

Figure 3
Cumulative H distribution plot for the twinned rhombohedral crystal of canavalin. Curves I and II were calculated using 16 000 pairs of matched re¯ections having I > 2' and the strongest 1800 re¯ection pairs, respectively. Table 3 Comparison of canavalin models.
The diagonal in bold contains numbers of amino-acid residues in the subunit models. Numbers above and below the diagonal are root-mean-square differences in A Ê for the backbone and side-chain atoms (de®ned in

Solvent and crystal packing
The Matthews coef®cients, or speci®c volumes (V M ; Matthews, 1968), of the hexagonal, rhombohedral, orthorhombic and cubic canavalin crystals were 2.49, 2.78, 2.33 and 2.03 A Ê 3 Da À1 , respectively (Ko, Ng, Day et al., 1993). Solvent models of the cubic and hexagonal crystals were analyzed in a previous paper (Ko et al., 2000). In the newly re®ned models of the rhombohedral and orthorhombic crystals there were 292 and 168 water molecules, respectively. After superposition of the two structures based on backbone atoms, 44 pairs of water molecules per trimer matched with distances less than 1.0 A Ê . The average temperature factor was 23.8 A Ê 2 . Among these, ®ve waters in the rhombohedral crystal were observed at equivalent positions in all three subunits of the orthorhombic crystal and they were also found among the best de®ned waters for the cubic and hexagonal crystal structures. Speci-®cally, waters 542, 549, 550, 759 and 762 in the rhombohedral model were equivalent to 509/556/634, 528/548/617, 523/579/ 616, 522/545/666 and 508/527/561 in the orthorhombic model and 506/504, 505/503, 504/502, 553/537 and 513/511 in the cubic and hexagonal models. They all bound to at least two backbone atoms of the protein. In addition, nine waters in the rhombohedral model were observed at equivalent positions in two subunits of the orthorhombic model and were also observed in either the cubic or hexagonal model or both. In the central cavity, there were 81 waters per trimer in the rhombohedral crystal but only 16 in the orthorhombic crystal.
The packing diagrams of Fig. 5 show that the disk-shaped canavalin trimer can be very well accommodated in the rhombohedral unit cell in either top-up or bottom-up orientation. Inter-trimer contacts between the rims of disks occur at the unit-cell faces. In either orientation, a trimer is in contact with six other trimers. In the top-up orientation there is only one type of interface, the top±bottom contact, which buries 310 A Ê 2 area on the top surface and 371 A Ê 2 on the bottom surface. There were at least 11 amino-acid residues involved on the top and eight on the bottom; all were polar. Interactions included a water-mediated salt bridge between Arg312 and Glu411 and a bidentated salt bridge between Asp344 and Arg392. Two other possible salt bridges of Arg52±Glu407/ Glu408 and Glu314±Lys414 between the trimers were also observed at the crystal contact, but the distances were somewhat long for direct bonding. In the bottom-up orientation there were two types of interface, the top±top contact and the bottom±bottom contact, burying at least 240±250 A Ê 2 area on each contact surface. Precise interfaces could not be determined because the z coordinates of the model were arbitrary; the contact areas were minimized by translation of the bottom-up model along the threefold axis. There were seven and ®ve amino-acid residues, also polar, from each subunit involved in the top±top and the bottom±bottom interfaces, respectively (see Table 4). The close contact between two pairs of twin-dyad symmetry-related side chains, Arg312 in the top± top interface and Lys414 in the bottom±bottom interface, would not be problematic since they were¯exible with room for rotation away from one another. In the`normal' top-up packing, close contacts were also observed between Lys357 and Lys414 at the top±bottom interface. More than 100 water molecules appeared in each crystal contact area.
In the orthorhombic crystal, a canavalin trimer was in contact with seven neighbors through ®ve types of interfaces.
The disk-shaped molecules were stacked with their threefold axes approximately parallel to a (Ko, Ng, Day et al., 1993). Fig. 6 shows a schematic diagram of the crystal packing. The most extensive interface (I) was observed between two trimers related by a twofold axis parallel to b and buried 773 A Ê 2 of surface area on each trimer (see Table 5). There were 22 amino-acid residues and six waters per trimer involved in interface I having dyad symmetry. Three possible salt bridges, ArgA254±AspC128, AspA255±ArgA388 and LysA272±AspC125, occurred at this interface but were not well de®ned, possibly owing to NCS restraints in the re®nement. The second type of interface (II) was between molecules related by screw axes parallel to c and buried 444 A Ê 2 on one trimer and 438 A Ê 2 on the other. The numbers of residues involved were The bound phosphate ion in the C-terminal -barrel. The side chains of His297, Asn299 and Arg376, which make hydrogen bonds with the phosphate, are also shown, as well as sections of the -strands in the background. The model shown here corresponds to the A chain in the orthorhombic crystal. Table 4 Speci®c bonds between canavalin trimers in the R3 crystal. 13 and 11, respectively, plus four ordered waters. The third interface (III) buried 389 and 348 A Ê 2 on two trimers related by a screw axis parallel to b and involved ten and 11 amino-acid residues, respectively, plus three waters. Two other possible salt bridges, ArgC52±GluA213 and LysC55±GluA207, were observed for interface II and another, AspB204±ArgA52, for interface III. The fourth and ®fth types of interface (IV and V) were between molecules related by twofold axes parallel to a [with symmetry operations (x, Ày, Àz) and (x, 1 À y, Àz), respectively]. Interface IV involved eight residues and buried 182 A Ê 2 on each trimer, while interface V involved only two residues and buried 8 A Ê 2 . Fig. 7 presents atomic force micrographs of the surface of a growing orthorhombic crystal of canavalin; they are also typical of those from the prismatic faces of the hexagonal crystal form. Development is characterized by the appearance of two-dimensional nuclei on the surfaces, with subsequent tangential extension by recruitment of molecules into advancing step edges. This is the mechanism that predominates, often exclusively, in the growth of most macromolecular crystals as shown by AFM . While stacking faults in these crystals, and also other types of imperfections, can occasionally be found, they are relatively uncommon.
Figs. 8 and 9 are AFM images of the faces obtained during growth of rhombohedral canavalin crystals. These are quite typical of many images obtained from rhombohedral cana-valin crystals, including those reported by other laboratories (Land et al., , 1996(Land et al., , 1999. Their striking characteristics are the frequent appearance of screw dislocations in many forms, both double and single, left and right handed, and a high frequency of stacking faults and other related imperfections. Together, these dislocations and faults lead to a defect density that is more than an order of magnitude greater than for other macromolecular crystals and several orders of magnitude greater than for conventional crystals .
If one examines the step edges arising from screw dislocations at higher magni®cation, as in Fig. 10, the edges appear extremely irregular and rough. Such roughness is generally ascribed to a high level of impurities (Chernov, 1984   Speci®c bonds between canavalin trimers in the C222 1 crystal. Interface I: molecules related by (1) x, y, z and (2) 1 À x, y, 1 2 À z. Residue 1 in molecule 2 also made equivalent bonds with residue 2 in molecule 1, i.e. the interactions were twofold redundant.  al., 1988;Nakada et al., 1999;McPherson et al., 1996).
Step edges arising from two-dimensional nuclei on the surfaces of hexagonal and orthorhombic crystals have a similar rough appearance, further consistent with impurities as the cause. AFM observations of amorphous material on the surfaces of growing rhombohedral and orthorhombic crystals suggests that the primary impurities may be aggregates of canavalin molecules themselves.

Discussion
The total interface area on a canavalin trimer was larger in the orthorhombic crystal (2 580 A Ê 2 ) than in the rhombohedral (2 043 A Ê 2 ) and the hexagonal (2 340 A Ê 2 ) crystals, but smaller than in the cubic crystal (3 282 A Ê 2 ). Excluding the cubic crystal, which had a very unique arrangement of the canavalin trimers, the other three crystal forms shared a similar arrangement of disk stacking. These crystals were seen to interconvert between one form and another, while the orthorhombic crystal was often the ®nal and most stable form (Ko, Ng, Day et al., 1993). This was consistent with its smaller speci®c volume and lower solvent content, as well as its larger crystal contact surface areas. In particular, interface I covered 773 A Ê 2 per trimer, signi®cantly larger than all other contact interfaces of the canavalin crystals. It was also larger than the average of 280 A Ê 2 and was outside the range of 100±600 A Ê 2 surface area per contact in most crystals (Janin & Rodier, 1995). Through interface I, a pair of dyad-related trimers were bound`bottom-to-bottom' by at least six salt bridges and ten hydrogen bonds. On the`top' side of the trimer there were four`normal' crystal contacts of interfaces II and III, with molecules related by screw axes (Fig. 6). The other two interfaces IV and V were smaller and occurred at the rims of disks. Perhaps the bottom-to-bottom dimer of canavalin trimers forms in solution prior to incorporation into a growing orthorhombic crystal, but there is no evidence otherwise.
Atomic force microscopy investigation of three of the four crystal forms of canavalin provides an interesting correlation. The cubic crystal form has been solved and re®ned by X-ray Figure 7 In (a) is a 20 mm 2 area on the surface of a growing orthorhombic canavalin crystal, as visualized using atomic force microscopy, showing the extensive distribution of two-dimensional nuclei and islands. This image is typical of those from both hexagonal and orthorhombic canavalin crystals and illustrates the dominant, perhaps exclusive, growth mechanism common to these crystals. Also typical is the absence of screw dislocations and the relative scarcity of other types of dislocations or faults. In (b) is a higher magni®cation image of two-dimensional growth islands and step edges.

Figure 6
Schematic diagram of the C222 1 crystal packing, viewed along the crystallographic c axis. The disk-shaped trimers were stacked with the threefold axes almost parallel to the a axis (vertical). The reference molecule had a center of mass at fractional coordinates of approximately (0.36, 0.24, 0.18) and was in contact with seven other molecules through the labelled interfaces I±V. crystallography (Ko et al., 2000), but is dif®cult to obtain reproducibly and has not been studied by AFM. The other three (rhombohedral, hexagonal and orthorhombic) crystal forms, however, have been examined. In addition, crystals of more than two dozen other proteins, viruses and nucleic acids have also been analyzed in our laboratory by AFM and these provide a broader context for the canavalin crystal investigations.
When the surface features and face development of the various crystals are compared, rhombohedral canavalin crystals stand out from all other crystalline macromolecules. Rhombohedral canavalin crystals contain an exceptionally large number of screw dislocations, which provide the major Acta Cryst. AFM images of screw dislocations on surfaces of rhombohedral canavalin crystals at higher resolution. The variety of types of screw dislocations and their modes of interaction are far more diverse than observed on any other protein crystals.

Figure 8
Representative AFM images from surfaces of growing rhombohedral canavalin crystals. In contrast to other forms of canavalin crystals, rhombohedral crystal surfaces display a vast array of screw dislocations frequently interrupted by stacking faults. Virtually no two-dimensional islands are seen, as the screw dislocations provide the sources for new step edges. Images like those shown here are unlike those recorded from all other macromolecular crystals studied using AFM. sources of growth steps for the crystals. The numbers of screw dislocations observed in the rhombohedral crystals, like those in Figs. 8 and 9, not only by us, but also by Land et al. (1995Land et al. ( , 1996Land et al. ( , 1999, is well over an order of magnitude greater than any other macromolecular crystal examined. They also contain an unusually high density of other defects, such as stacking faults . Other crystal forms of canavalin, on the other hand, exhibit virtually no screw dislocations and far fewer defects. Fig. 7, for example, is typical of the surface of a growing orthorhombic canavalin crystal and is also very similar to hexagonal prismatic surfaces. Both the hexagonal and the orthorhombic form grow almost exclusively by the deposition of two-dimensional nuclei on actively growing surfaces. Analysis for the presence of twinning according to Yeates (1997) using X-ray diffraction data show convincingly that about half of the canavalin trimers are`top up', while the other half are`bottom up'. The statistical analysis is consistent with a crystal composed of many domains or blocks that alternate randomly between molecules all in the top-up orientation, with domains composed of molecules all in the bottom-up orientation. Twinning, molecular misorientation and other misalignments create mechanical stress in crystal lattices. In most cases the stress is relieved, depending on the nature of the sources, by the formation of point defects or other crystal faults. For a crystal having ordered domains, half top up and half bottom up, then at domain boundaries where steps merge, stress would accumulate.
It has been well established in conventional crystal growth that stress at domain boundaries is most frequently relieved by the lattice through formation of screw dislocations or stacking faults (Burton et al., 1951;Chernov, 1984;Chernov et al., 1988). If canavalin trimers in the rhombohedral crystals were organized as alternative orientation domains, then the extreme occurrence of screw dislocations observed by AFM might well be anticipated.
Screw dislocations are not common to particular crystal classes or symmetries, as far as we know. They do not occur in other crystal forms of canavalin, which are not twinned as shown by X-ray analysis. Thus, it is not a consequence of some inherent property of the molecule. The only peculiarity of the rhombohedral crystals is their twinned lattice, a feature known in conventional crystals to promote formation of screw dislocations.
The canavalin molecule is unusual because of its disk shape that promotes stacking and its high degree of pseudosymmetry, having almost 32 point-group symmetry. The high pseudo-symmetry is responsible for moderating the differences between the two kinds of domains in the rhombohedral crystals. This is probably a re¯ection of its physiological function, which is to store protein by packing it in seeds in a highly ef®cient fashion. Few simple objects pack more densely than plates into cylindrical stacks. The shape and packing propensity undoubtedly contributes to the ease of its crystallization and to the diversity of its crystal forms.
The rhombohedral crystal form has the highest water content, 56%, of the several crystal forms and makes the least intricate lattice interactions. It is, unless special precautions are taken, also somewhat unstable. Rhombohedral crystals will redissolve only a few days after growth, or dissolve and regrow into alternate forms, or their surfaces give rise directly to other crystals. The excessive dislocation and defect density probably contributes further to the instability. All of the other crystal forms of canavalin are stable once formed. The relaxed Figure 10 High-magni®cation AFM images of 5 mm 2 areas on surfaces of rhombohedral canavalin crystals showing the exceptional irregularity and roughness of the step edges, presumably a consequence of impurities. packing of molecules and higher solvent content combined with molecular properties enable the twinning, which in turn gives rise to the defect structure.
Despite the twinning and the consequent defect density, rhombohedral canavalin crystals grow as large or larger than any other form, more rapidly and reproducibly than any other form, and from more impure preparations than any other form. In addition, when optimized they diffract to almost as high a resolution as the cubic crystals, the best diffracting form. Curiously, the twinning does not in itself appear to limit resolution.
Crystals grown in microgravity ultimately produced the highest resolution best quality diffraction data. Those crystals, however, were no less twinned than crystals grown in laboratories on earth. Similar results regarding the effect of microgravity on the twinning of alcohol dehydrogenase crystals was also reported by Esposito et al. (1998). Thus, gravity seems to play no role in the twinning phenomenon and suggests that crystallization of macromolecules in space will not be a therapy for this problem. On the other hand, mechanical stress produced by twinning may be less in microgravity or be better accommodated and a reduced defect density may result as a consequence.
Defect density may, we believe, have an important effect on diffraction resolution and mosaicity, and a reduction in defect density may explain the improvement in diffraction resolution for the microgravity grown crystals. We have not yet, however, had the opportunity to carry out AFM investigations of rhombohedral canavalin crystals grown in microgravity to evaluate their defect structures and densities.