Pseudo-merohedral twinning and noncrystallographic symmetry in orthorhombic crystals of SIVmac239 Nef core domain bound to different-length TCRζ fragments

P212121 crystals of SIV Nef core domain bound to a peptide fragment of the T-cell receptor ζ subunit exhibited noncrystallographic symmetry and nearly perfect pseudo-merohedral twinning simulating tetragonal symmetry. For a different peptide fragment, nontwinned tetragonal crystals were observed but diffracted to lower resolution. The structure was determined after assignment of the top molecular-replacement solutions to various twin or NCS domains followed by refinement under the appropriate twin law.


Introduction
Protein crystallization occurs under supersaturating conditions where protein molecules organize by either noncrystallographic or crystallographic symmetry operations into repeating unit cells that pack to form a crystal lattice. Crystal twinning occurs when two or more crystal packings intersperse in one larger aggregate crystal. This has been reported to occur as a result of polymorphic transformation during physical stress (Yeates, 1997;Govindasamy et al., 2004), but more commonly occurs as a pathology of crystal growth. When the lattices of each crystal packing in the aggregate crystal do not overlap in three dimensions, the crystal exhibits epitaxial, or nonmerohedral, twinning, which can easily be detected by the presence of split reflections in the crystal's X-ray diffraction pattern. However, when the lattice axes of the individual crystals are parallel the crystal is considered to be merohedrally twinned and the X-ray diffraction pattern will not provide any visual cues of crystal twinning. For protein molecules, merohedrally twinned crystals exist predominately as hemihedrally twinned crystals (Yeates, 1997) which contain two distinct twin domains that are related to each other by a twin-law operation. The twin fraction represents the fractional contribution of the less prevalent twin domain. The diffraction pattern of a hemihedrally twinned crystal is therefore the superimposition of two unique diffraction patterns, one from each twin domain, where each reflection intensity is the weighted sum of two twin-related intensities (Grainger, 1969), The individual intensities I(h 1 ) and I(h 2 ) can be solved by combining the linear equations Iðh 2 Þ ¼ ÀI obs ðh 1 Þ þ ð1 À ÞI obs ðh 2 Þ 1 À 2 : As the twin fraction approaches 1/2 the crystal is considered to be perfectly twinned and calculation of the intensities I(h 1 ) and I(h 2 ) begins to fail as the term (1 À 2) begins to approach zero. This complicates the process of twin-related reflection intensity calculation, commonly referred to as detwinning. Structure determination has therefore preferentially been performed for hemihedral crystals that exhibit nonperfect twinning. Less common cases of twinning have been described where a twin-law operation supports a higher Laue symmetry than that of the crystal unit cell (Rudolph et al., 2004). This type of twinning, which is referred to as pseudo-merohedral twinning, can occur in special circumstances such as a monoclinic system where the angle approaches 90 (Larsen et al., 2002) or an orthorhombic system where the unit-cell axes a and b are fortuitously similar in length (a ' b), resulting in the emulation of higher apparent tetragonal symmetry (Brooks et al., 2008). In this report, we describe such a case for crystals of a complex of the Nef (negative factor) protein from simian immunodeficiency virus bound to a fragment of one of Nef's cellular targets, the cytosolic domain of the TCR subunit (TCR).
Nef from human immunodeficiency virus (HIV) or simian immunodeficiency virus (SIV) is a 27-35 kDa viral accessory protein that is dispensable for replication but required for high infectivity and virulence (reviewed in Arien & Verhasselt, 2008). Expressed in abundance early in the viral life cycle, Nef performs a number of functions that can be generalized into three activities: enhancement of viral infectivity, downregulation of surface receptors and modulation of T-cell activation. Notable among Nef's functions is the interaction of Nef with TCR (Sigalov et al., 2008;Fackler et al., 2001;Swigut et al., 2000;Schaefer et al., 2000;Xu et al., 1999;Howe et al., 1998;Bell et al., 1998), the principal signaling component of the T-cell antigen receptor. This interaction has been suggested to play a role in HIV-mediated modulation of membraneproximal T-cell signaling events (Fenard et al., 2005;Thoulouze et al., 2006) and in SIV-mediated downregulation of the T-cell receptor (Schindler et al., 2006;Swigut et al., 2003;Schaefer et al., 2002;Munch et al., 2002;Willard-Gallo et al., 2001). In previous work (Schaefer et al., 2000), SIV and HIV-2 Nef have been shown to bind TCR at two unique sites denoted 'SIV Nef interaction domains' (SNIDs), the first containing elements of immunoreceptor tyrosine activation motif (ITAM) 1 and the second containing elements of ITAM 2. However, the structural features of Nef that determine its specificity for TCR remain unknown.
Nef contains two domains: an unstructured highly variable myristylated N-terminal domain and a C-terminal structured core domain Grzesiek et al., 1997;Lee et al., 1996) that exhibits high sequence conservation among different HIV-1, HIV-2 and SIV isolates. The Nef conserved core domain (Nef core ) has been described to be responsible for the majority of Nef's interactions (Peter, 1998), including the TCR-binding activity of SIV Nef. The core domain of HIV-1 Nef has been shown to be amenable to crystallization Lee et al., 1996;Franken et al., 1997). In this study, we aimed to determine the crystal structure of the Nef-TCR complex by crystallizing complexes of SIVmac239 Nef core with TCR fragment polypeptides containing the putative binding regions.
Here, we describe the crystallization and structure determination of the complexes of SIVmac239 Nef core with two different TCR polypeptides, TCR DP1 and TCR A63-R80 . Structure determination of the SIVmac239 Nef core -TCR DP1 complex was hampered by the poor electron-density maps calculated from the low-resolution diffraction data and phases derived from molecular replacement using the published HIV Nef core-domain structures. Eventually, we were able to determine this structure using the higher resolution SIVmac239 Nef core -TCR A63-R80 complex as a starting model. However, determination of the high-resolution SIVmac239 Nef core -TCR A63-R80 complex structure was hindered by the nearly perfect pseudo-merohedral crystal twinning that was detected on analysis of the intensity statistics. Ultimately, a partially twinned crystal with a twin fraction of 0.426 was used to solve the structure of the SIVmac239 Nef core -TCR A63-R80 complex to 2.05 Å resolution. The structures of the two complexes revealed that crystallization of SIVmac239 Nef core with the shorter TCR polypeptide had reduced the spacegroup symmetry from tetragonal to orthorhombic and introduced noncrystallographic symmetry (NCS). Because the unit-cell axes a and b were still nearly identical in the orthorhombic crystal form, the crystal was prone to twinning. This study presents a unique case in which pseudo-merohedral crystal twinning is the consequence of a reduction in crystal symmetry induced by the truncation of a protein ligand.

Protein expression and purification
The core domain of SIVmac239 Nef with a two-residue linker, GS-Nef (Asp95-Ser235) (Nef core ), was expressed and purified as described by Sigalov et al. (2008). Briefly, Nef was expressed as a 6ÂHis-thioredoxin fusion protein in Escher-research papers ichia coli BL21 (DE3) cells. Following cell lysis, the Nef fusion protein was isolated by Ni-NTA affinity chromatography (Qiagen) under denaturing conditions (8 M urea) and then dialyzed against a nondenaturing buffer containing 20 mM Tris, 150 mM NaCl, 100 mM DTT at pH 8.0. The soluble fusion protein was then subjected to proteolysis with thrombin (MP Biochemicals), resulting in the cleaved Nef core protein. SIVmac239 Nef core was purified by anion-exchange and sizeexclusion chromatography and concentrated to 700 mM by ultrafiltration (Amicon) in PBS.
TCR cyt includes an acid-labile Asp-Pro sequence (Landon, 1977) at positions 93-94. We made use of this to prepare two fragments of TCR cyt , termed DP1 (Leu51-Asp93) and DP2 (Pro94-Arg164). TCR cyt , purified as described by Sigalov et al. (2004), was incubated at 1.3 mg ml À1 (0.1 mM) in 30% acetonitrile, 0.5%(v/v) TFA for 48 h at 323 K. Fragments were isolated by reverse-phase chromatography on a Vydac C18 300 Å pore-size column using an acetonitrile gradient in 0.1% TFA and recovered by lyophilization. Mass spectrometry was used to verify the identity of the fragments and the lack of any additional chemical modification other than the desired amide hydrolysis. All TCR polypeptides were solubilized in 20 mM Tris pH 8.0 to a final concentration of 700 mM. Full-length TCR was expressed and purified as reported previously (Sigalov et al., 2004).

Data collection and processing
16 data sets were collected from various Nef core -TCR crystals, of which three were used for structure determination. One low-resolution data set (3.7 Å ) for the SIVmac239 Nef core -TCR DP1 complex and two high-resolution data sets (1.9 and 2.05 Å ) for the SIVmac239 Nef core -TCR A63-R80 complex were collected from single crystals at the National Synchrotron Light Source (beamline X29) using an ADSC Quantum-315r CCD detector system. The crystal-to-detector distances for the Nef core -TCR DP1 complex and the Nef core -TCR A63-R80 complex crystals were 275 and 250 mm, respectively. The crystals were exposed for 1 s with an oscillation of 1 per image. A total of 180 images were collected for each data set, which were separately indexed, integrated and scaled in HKL-2000 (Otwinowski & Minor, 1997). Detection and analysis of crystal twinning was performed in phenix.xtriage from the PHENIX software package (Adams et al., 2002). Determination of the twin law governing the pseudo-merohedrally twinned SIVmac239 Nef core -TCR A63-R80 crystals was performed following proper assignment of the crystal space group as described below.

Structure determination and refinement
The structures of the SIVmac239 Nef core -TCR A63-R80 and SIVmac239 Nef core -TCR DP1 complexes were determined by molecular replacement. Firstly, the atomic coordinates of the Nef core domain from HIV-1 were extracted from the crystal structures of the unliganded HIV-1 isolate LAI Nef structure (PDB code 1avv; Arold et al., 1997), the HIV-1 isolate LAI Nef-Fyn SH3 domain complex (PDB code 1avz; Arold et al., 1997) and HIV-1 isolate NL4-3 Nef-Fyn SH3 (R96I) domain complex (PDB code 1efn; Lee et al., 1996) and were modified with CHAINSAW (Stein, 2008) to trim the side chains not shared by SIVmac239 Nef (44% sequence identity) to methyl Table 1 Data-collection and refinement statistics (molecular replacement).
Values in parentheses are for the highest resolution shell.
Nef core -TCR DP1 Nef core -TCR A63-R80 , crystal 1 Nef core -TCR A63-R80 , crystal 2 Data collection Space group P4 3 2 1 2 P2 1 2 1 2 1 P2 1 2 1 2 1 Unit-cell parameters a groups. The modified Nef coordinate sets were used as an ensemble search model for molecular replacement in Phaser (Storoni et al., 2004) and single solutions with translationfunction Z scores (TFZ) greater than 6.0 were used as starting models. The structure of the Nef core -TCR A63-R80 complex was solved by multiple rounds of twinned refinement using phenix.refine from the PHENIX software package (Adams et al., 2002) interspersed with rounds of manual model building and fitting of F o À F c and 2F o À F c electron-density maps in Coot (Emsley & Cowtan, 2004). The twin operator (k, h, Àl) was applied during each round of refinement, which included three cycles of individual atomic displacement factor refinement and individual energy-minimization procedures accompanied by refinement of the twin fraction . Water molecules were added to the refined model using both phenix.refine and Coot. The quality of the final refined SIVmac239 Nef core -TCR A63-R80 structure was validated in PROCHECK (Laskowski et al., 1993). The structure of the refined SIVmac239 Nef core -TCR A63-R80 complex was used as a search model to find a molecular-replacement solution for the SIVmac239 Nef core -TCR DP1 data. A single top molecular-replacement solution (TFZ = 10.5, LLG = 266) was found and used as a starting model. The structure of the SIVmac239 Nef core -TCR DP1 structure was solved by refinement consisting of several rounds of individual atomic displacement factor refinement and individual energy-minimization procedures using phenix.refine. Model inspection was performed between each round of refinement and the model was modified in Coot. The final refined structure was validated for acceptable chemical properties with PROCHECK. Final model and refinement statistics for both SIVmac239 Nef core -TCR polypeptide structures are shown in Table 1 and Ramachandran plots generated by RAMPAGE (Lovell et al., 2003) are provided in Supplementary Figs. S1 and S2 1 .

Results and discussion
3.1. Crystallization and data collection of two SIVmac239 Nef core -TCRf polypeptide complexes In order to determine the structure of the Nef-TCR complex, mixtures of the structured core domain of SIVmac239 Nef (Asp95-Ser235) with various polypeptides spanning the putative binding regions of TCR (Schaefer et al., 2000) were screened for crystal formation. Initial crystallization experiments were aimed towards crystallizing the complex of Nef core (SIVmac239, HIV-1 ELI and NL4-3) with the full-length cytoplasmic domain of TCR (TCR cyt ), but these were unsuccessful. Therefore, a polypeptide crystallization screening strategy was employed to identify a minimal TCR polypeptide that bound SIVmac239 Nef core , which exhibited the highest affinity TCR cyt binding among the SIV, HIV-1 and HIV-2 variants tested (SIVmac239, HIV-1 ELI and NL4-3, and HIV-2 ST; unpublished results).
Crystallization efforts focused on TCR fragments that contained the N-terminal of the two SIV-interaction domains (Fig. 1). Of a series of polypeptides spanning TCR cyt , a peptide included in this region, TCR A61-R80 , bound to Nef core from HIV-1, HIV-2 and SIV strains (manuscript in preparation) and the structural information obtained for the higher affinity SIV variant might be relevant for HIV-1 as well as the more homologous HIV-2 Nef proteins. Moreover, TCR DP1 (i.e. the N-terminal acid-cleavage fragment, residues Leu51-Asp93) formed a 1:1 stoichiometric complex with SIVmac239 Nef core (unpublished results), as did intact TCR cyt (Sigalov et al., 2008). Therefore, a series of polypeptides containing the original TCR DP1 polypeptide, the shorter TCR A61-R80 polypeptide and several peptides containing the proposed SNID-1 (Schaefer et al., 2000) sequence were either prepared from full-length TCR cyt (TCR DP1 ) or chemically synthesized (TCR A61-R80 and variants) and used in crystallization experiments with SIVmac239 Nef core .
SIVmac239 Nef core crystallized in complex with TCR DP1 and TCR A63-R80 under similar conditions. Crystals of the SIVmac239 Nef core -TCR DP1 complex grew readily as long tetragonal pyramids (Fig. 2a) but diffracted X-rays to low resolution (3.7 Å ; Fig. 2b) and could not be improved further by optimization of the crystallization conditions. In contrast, crystals of SIVmac239 Nef core bound to TCR A63-R80 adopted a bipyramidal shape (Fig. 2a) and diffracted X-rays to high resolution (1.9-2.05 Å ; Fig. 2b). Neither crystal form exhibited the concave or 're-entrant' features that have been suggested to predict the presence of twinned crystals (Yeates, 1997), nor did their diffraction patterns contain split reflections (Fig. 2c).
3.2. Space-group determination and molecular replacement for SIVmac239 Nef core -TCRf DP1 The low-resolution diffraction data for the SIVmac239 Nef core -TCR DP1 complex were indexed in the tetragonal Laue group 4/mmm (422 point group), with unit-cell parameters a = b = 51.638, c = 189.449 Å and an R merge of 5.1%. The Matthews coefficient V M (Matthews, 1968) was calculated to be 2.86 Å 3 Da À1 (57.1% solvent), indicating the presence of one SIVmac239 Nef core -TCR DP1 heterodimer per asym- TCR polypeptide crystallization screen. The polypeptide sequences are shown with residue position numbers assigned on the left. The boxed region contains the sequence of the first of the two reported SIV Nef interaction domains (Schaefer et al., 2000). The sequence of ITAM 1 is colored red. metric unit. After analysis of the h00, 0k0 and 00l reflection intensities, the space group was further assigned as P4 3 2 1 2 or P4 1 2 1 2 based on the indicated presence of screw axes along a and c. Using an ensemble of HIV-1 Nef core domain structures as a search model, a single molecular-replacement solution (TFZ = 9.4, LLG = 63) was found in space group P4 3 2 1 2. However, model refinement and building were hindered by the poor quality of the A -weighted F o À F c and 2F o À F c electron-density maps, resulting in an R free that could not be reduced below 41%.
3.3. Initial space-group determination and molecular replacement for SIVmac239 Nef core -TCRf A63-R80 Two crystals of SIVmac239 Nef core bound to the shorter TCR A63-R80 polypeptide diffracted X-rays to higher resolution (1.9-2.05 Å ), but spacegroup determination proved to be more complicated than for the P4 3 2 1 2 crystal form of Nef core -TCR DP1 described above. The diffraction patterns that were observed for Nef core -TCR A63-R80 appeared to be consistent with the lattice previously observed for the lower resolution Nef core -TCR DP1 crystals, and the TCR A63-R80 data (crystal 1) were initially indexed in the same tetragonal Laue group 4/mmm (422 point group), with unit-cell parameters a = b = 47.203, c = 182.939 Å . The integration statistics were similar to those observed previously (R merge = 7.6%). Visual inspection of reflection intensities using HKLVIEW (Collaborative Computational Project, Number 4, 1994) and evalution of the R merge and ÁI/(I) statistics confirmed the presence of each of the symmetry elements comprising the 422 point group. All of the unit-cell parameters were reduced by 4-10% compared with the SIVmac239 Nef core -TCR DP1 crystals, which is potentially consistent with the shorter length of the TCR polypeptide ligand. Analysis of the h00 and 0k0 intensities indicated the presence of 2 1 screw axes along a and b. However, 00l intensities were observed for l = 2n, which is consistent with a 4 2 (or 2 1 ) axis along c but inconsistent with a 4 3 axis as observed for the lower resolution tetragonal SIVmac239 Nef core -TCR DP1 data. A search for a molecular-replacement solution for the SIVmac239 Nef core -TCR A63-R80 data in 4 2 2 1 2 or any of the other 422 space groups yielded no solutions. A data set that was collected from a second SIVmac239 Nef core -TCR A63-R80 crystal (crystal 2) resulted in similar difficulties with molecular replacement. The ambiguous space-group assignment and the inability to find a molecular-replacement solution for the SIVmac239 Nef core -TCR A63-R80 complex in the tetragonal  Laue symmetry group suggested the possibility of crystal twinning and required space-group re-evaluation.

Detection and analysis of twinning
A number of statistical methods have been developed to characterize crystal twinning, including the recently developed Padilla-Yeates algorithm for detection of the presence of crystal twinning (Padilla & Yeates, 2003) and the Britton plot for estimation of the twin fraction (Britton, 1972). To assess the twinning of the SIVmac239 Nef core -TCR polypeptide crystals, several analyses of the intensity statistics were performed in phenix.xtriage. Firstly, the second moments of the intensities of acentric data (hI 2 i/h|I| 2 i) were calculated for all three SIVmac239 Nef core -TCR polypeptide complexes. Untwinned and twinned data are expected to have hI 2 i/h|I|   Padilla & Yeates, 2003). The expected plots for untwinned and twinned acentric data (red) and the calculated plots for the SIVmac239 Nef core -TCR polypeptide data (blue) are shown. Middle row, estimation of the twin fraction by Britton plot analysis (Britton, 1972). The percentage of negative intensities after detwinning is plotted as a function of the assumed value of . Overestimation of the twin factor results in an increase in the percentage of negative intensities. The estimated value of is extrapolated from the linear fit (dashed line). Bottom row, estimation of the twin fraction using the H plot (Yeates, 1988  values of 2.0 and 1.5, respectively. The SIVmac239 Nef core -TCR DP1 crystal had an hI 2 i/h|I| 2 i value of 2.106, suggesting the absence of twinning, whereas the SIVmac239 Nef core -TCR A63-R80 crystals had hI 2 i/h|I| 2 i values of 1.676 (crystal 1) and 1.628 (crystal 2), indicating the presence of twinning in both crystals. A more robust method of twin detection that uses cumulative local intensity deviation distribution statistics as determined by the Padilla-Yeates algorithm (Padilla & Yeates, 2003) was also employed. In a plot of the local intensity difference |L| of non-twin-related intensities versus the distribution of the local intensity differences N|L|, the presence of twinning can be deduced by comparing the experimental plots with the expected plots for twinned and untwinned data (Padilla & Yeates, 2003). The SIVmac239 Nef core -TCR DP1 data plot was linear, which is consistent with the expected curve for untwinned data (Fig. 3, top). In contrast, the plots for both SIVmac239 Nef core -TCR A63-R80 crystals 1 and 2 were curved, suggesting the presence of crystal twinning (Fig. 3, top). The L test, which is also based on the local intensity differences of non-twin-related reflection pairs, was additionally employed in order to confirm twinning in the SIVmac239 Nef core -TCR A63-R80 crystals; for untwinned data |L| and mean L 2 are expected to be 1/2 and 1/3, respectively, and for twinned data they are expected to be 3/8 and 1/5, respectively. The SIVmac239 Nef core -TCR DP1 data had calculated |L| and L 2 values of 0.473 and 0.307, which were consistent with an absence of appreciable twinning. The SIVmac239 Nef core -TCR A63-R80 crystals had calculated |L| and L 2 values of 0.402 and 0.229 for crystal 1 and 0.390 and 0.218 for crystal 2, further supporting the presence of crystal twinning. All of the twinning tests suggested that the lowresolution SIVmac239 Nef core -TCR DP1 crystal was not appreciably twinned, whereas the high-resolution SIVmac239 Nef core -TCR A63-R80 crystals were pseudo-merohedrally twinned with a twin fraction near 0.5.
In order to estimate the twin fraction in the two pseudomerohedrally twinned SIVmac239 Nef core -TCR A63-R80 crystals, Britton plot (Britton, 1972) and H-plot (Yeates, 1988) analyses were performed (Fig. 3, middle and bottom). Crystal 1 exhibited near-perfect twinning, with an estimated twin fraction of 0.452 from the Britton plot and of 0.477 from the H plot. In contrast, crystal 2 seemed to be only partially twinned, with estimated twin fractions of 0.344 and 0.356 from the Britton plot and H plot, respectively. These initial estimates of the twin fraction based on statistical analysis of intensities were found to underestimate the actual twin fraction, which refined upwards during structure determination to 0.500 and 0.426 for crystals 1 and 2, respectively (see below).
Because the Laue group 4/mmm does not support merohedral twinning, we explored the possibility that the twinned SIVmac239 Nef core -TCR A63-R80 crystals were orthorhombic crystals that emulated tetragonal symmetry owing to pseudomerohedral crystal twinning. The twinned SIVmac239 Nef core -TCR A63-R80 diffraction data were therefore re-indexed in the orthorhombic point group 222. Twinning in an orthorhombic P2 1 2 1 2 1 crystal. (a) A P4 3 2 1 2 space-group unit cell with one molecule (arrow) per ASU (eight per unit cell) is shown with axes a, b and c labeled. (b) A P2 1 2 1 2 1 space-group unit cell with one molecule per ASU (four per unit cell) is shown (left) with its twin unit cell (right) related by the twin operator (y, x, Àz). (c) A P2 1 2 1 2 1 space-group unit cell with two molecules per ASU (four per unit cell) is shown (left) with its twin unit cell (right) related by the twin operator (y, x, Àz). The ASU is comprised of one blue and one black arrow related by noncrystallographic symmetry.
The reduction in symmetry from a fourfold axis along c in the tetragonal unit cell to a twofold axis in the orthorhombic unit cell, together with an increase in the number of molecules per asymmetric unit, helped us to identify the pseudo-merohedral twin operation (k, h, Àl) that accounted for the apparent fourfold Laue symmetry observed in the diffraction data. Consider a P2 1 2 1 2 1 unit cell with unit-cell length a approximately equal to unit-cell length b (Fig. 4). Pseudomerohedral twinning can exchange the a and b axis under the twin relationship (h, k, l)!(k, h, Àl), resulting in apparent tetragonal symmetry around the c axis (Fig. 4b). The apparent symmetry observed in this case will be indistinguishable from a nontwinned P4 3 2 1 2 (or P4 1 2 1 2) unit cell (Fig. 4a), of which P2 1 2 1 2 1 is a subgroup. Note that in this case the twinned P2 1 2 1 2 1 unit cell is less tightly packed, with one molecule per asymmetric unit (four per unit cell), than the corresponding nontwinned tetragonal P4 3 2 1 2 (or P4 1 2 1 2) cell, with one molecule per asymmetric unit (eight per unit cell). Based on the Matthews coefficient, we expected two molecules per asymmetric unit for the twinned P2 1 2 1 2 1 unit cell. Note that the nontwinned crystals of the SIVmac239 Nef core -TCR DP1 complex, which did adopt true tetragonal symmetry with unitcell parameters similar to those of the twinned P2 1 2 1 2 1 crystal, had a Matthews coefficient consistent with one molecule per asymmetric unit. Because the SIVmac239 Nef core -TCR DP1 and SIVmac239 Nef core -TCR A63-R80 complexes had similar molecular sizes and crystallized in related unit cells with similar lengths and angles we expected similar packing, but this was inconsistent with the different packing expected for the related twinned P2 1 2 1 2 1 and nontwinned P4 3 2 1 2 (or P4 1 2 1 2) unit cells shown in Fig. 4. Noncystallographic symmetry relationships that are similar to crystallographic symmetry operators also can result in observed symmetry that is higher than that actually present in the crystal. For example, breakdown of the crystallographic fourfold axis in a tetragonal cell could result in an orthorhombic cell with pseudo-fourfold symmetry. In this case, the noncrystallographic symmetry relationship is similar to the missing crystallographic operator and the related tetragonal and orthorhombic unit cells would have similar packing (Fig. 4c). This arrangement can be particularly prone to pseudo-merohedral twinning as a result of the similarity of the crystal packing along the a and b unitcell axes (Fig. 4c). We explored this scenario as an explanation for the observed twinning in the P2 1 2 1 2 1 crystals with packing similar to nontwinned P4 3 2 1 2 (or P4 1 2 1 2) crystals.
3.5. Structure determination and refinement of SIVmac239 Nef core -TCRf A63-R80 using twinned data After assignment of the SIVmac239 Nef core -TCR A63-R80 crystal data to the orthorhombic P2 1 2 1 2 1 space group, several strong molecular-replacement solutions were readily found with TFZ scores of 6.1-9.2 using a consensus model derived from unliganded HIV-1 Nef core crystal structures. In principle, molecular-replacement solutions corresponding to both twin 2F o À F c OMIT electron-density maps of the TCR polypeptide. 2F o À F c OMIT electron-density maps contoured at 1 calculated from the detwinned P2 1 2 1 2 1 data of the SIVmac239 Nef core -TCR A63-R80 crystal (a) and the P4 3 2 1 2 data of the SIVmac239 Nef core -TCR DP1 crystal (b) are shown for the region encompassing the TCR polypeptide.

Figure 7
Crystal packing of the P4 3 2 1 2 and P2 1 2 1 2 1 crystal forms. (a) The crystal symmetry organization of the P4 3 2 1 2 crystal form (left) and the P2 1 2 1 2 1 crystal form (right) is shown viewed down the fourfold symmetry axis and the corresponding twofold symmetry axis for the two SIVmac239 Nef core -TCR polypeptide complexes. In (b) the crystal packing along the c axis is shown for both crystal forms. SIVmac239 Nef core and TCR are colored cyan and yellow (left) and magenta and green (right), respectively. orientations and noncrystallographically related molecules are expected. Transformations among these solutions were examined to assign each to a twin or NCS domain (Fig. 5). All solutions could be accounted for using a single NCS transformation, the (k, h, Àl) twinning operator and the P2 1 2 1 2 1 space-group symmetry. Two nearby molecules (A and B) in the same twin domain related by an approximate 90 rotation were selected to comprise the asymmetric unit.
Once the twinning arrangement was properly understood and taken into account, model building and refinement in space group P2 1 2 1 2 1 with two molecules per asymmetric unit was relatively straightforward. The twin operation (k, h, Àl) was factored into each round of twinned refinement in phenix.refine, which included three cycles of individual atomic displacement parameter (B factor) and energy-minimization refinement. The twin fraction was also refined in each round and used to detwin the intensity data in order to generate interpretable 2F o À F c and F o À F c OMIT electron-density maps suitable for manual model building. However, during the first round of refinement, the twin fraction converged to 0.5 for crystal 1 and 0.426 for crystal 2. The calculated 2F o À F c electron-density maps generated by phenix.refine were noticeably less interpretable for crystal 1 than for crystal 2. Therefore, structure determination proceeded with crystal 2 through iterative cycles of twinned refinement interspersed with rounds of model inspection and building. As the model and twin fraction continued to be refined, there was a marked improvement in the quality of the electron-density maps that allowed the building of five additional residues at the N-terminus (Val98-Val102), one residue at the C-terminus (Gly234) and 11 residues in the internal disordered loop (Pro197-Trp207) of Nef; the starting model generated from the published crystal structures of HIV-1 Nef was missing nine residues at the N-terminus, two residues at the C-terminus and 29 residues in the disordered loop. Clear density for the TCR A63-R80 polypeptide ligand was observed and this region was also built into the structure, with 13 of the 16 resolved residues comprising a canonical -helix (Fig. 6). Water molecules were added to the model using the automated waterpicking functions in phenix.refine and Coot. The final structure (crystal 2) contained 120 residues of SIVmac239 Nef, 16 residues of TCR, 116 ordered water molecules and had R work and R free values of 17.0% and 18.4%, respectively (Table 1).
SIVmac239 Nef core -TCR DP1 , the high-resolution SIVmac239 Nef core -TCR A63-R80 structure was used as the starting model for refinement and building. Structure determination by molecular replacement was repeated for the nontwinned SIVmac239 Nef core -TCR DP1 data. A stronger molecularreplacement solution was found (TFZ = 10.5, LLG = 266) but in the same general orientation as that described previously. Refinement of atomic positions and individual B factors was performed in phenix.refine as described above for the twinned crystal, although without the twin-refinement and detwinning steps. The TCR DP1 peptide extends 12 residues futher at the N-terminus and 14 residues further at the C-terminus compared with the TCR A63-R80 polypeptide, but no additional electron density was observed beyond that seen in the SIVmac239 Nef core -TCR A63-R80 complex (Fig. 6), suggesting that both the N-and C-termini of the TCR DP1 fragment were disordered and that no additional Nef contacts were present. The final structure of the SIVmac239 Nef core -TCR DP1 complex contained 111 residues of Nef and 16 residues of TCR and had R work and R free values of 30.1% and 32.9%, respectively (Table 1).
3.7. Analysis of the P2 1 2 1 2 1 and P4 3 2 1 2 crystal forms of the SIVmac239 Nef core -TCRf polypeptide complex As described above, the SIVmac239 Nef core -TCR polypeptide complex crystallized in two related but different crystal lattices depending on the length of the TCR ligand. In the presence of the longer 43-residue TCR DP1 polypeptide SIVmac239 Nef core crystallized in the tetragonal P4 3 2 1 2 space group with one SIVmac239 Nef core -TCR DP1 heterodimer comprising the asymmetric unit. In the presence of the shorter 18-residue TCR A63-R80 polypeptide the complex unexpectedly crystallized in the P2 1 2 1 2 1 space group with severe pseudo-hemihedral twinning. In this crystal form, a rotation axis parallel to c exhibited pseudo-fourfold symmetry that deviated slightly from the crystallographic fourfold screw axis observed in the P4 3 2 1 2 crystal form (Fig. 7). The overall packing of the unit cell was also condensed in the orthorhombic crystal form, as evidenced by an $4 Å ($8%) reduction in the a and b axes and an $6 Å ($3%) shortening of the c axis.
The transformation from the tetragonal to the orthorhombic crystal system was caused by the introduction of noncrystallographic symmetry (NCS) and rearrangement of the hydrogen-bonding network at the crystal contact sites. The P4 3 2 1 2 crystal form contained one molecule per asymmetric unit. The P2 1 2 1 2 1 crystal form contained two molecules per asymmetric unit which were no longer related by a crystallographic twofold symmetry operation (y, x, Àz) but instead by a twofold NCS operation, 0:000 1:000 0:000 1:000 0:000 0:000 0:000 0:000 À1:000 In the tetragonal crystal form the SIVmac239 Nef core -TCR DP1 complex and its symmetry-related partner (y, x, Àz) form an antiparallel dimer similar to the crystallographic dimer described previously for the HIV-1 Nef core . Structural alignment of one SIVmac239 Nef core -TCR A63-R80 complex from the P2 1 2 1 2 1 crystal form with its corresponding molecule in the P4 3 2 1 2 crystallographic dimer reveals that the NCS-related molecule in the orthorhombic crystal form is rotated by $10 from its corresponding molecule in the P4 3 2 1 2 crystal form (Fig. 8). The interface between the two molecules involves the C-terminus of SIVmac239 Nef core and is predominantly occupied by aromatic residues (Tyr113, Tyr221, Phe171, Tyr223 and Tyr226). As shown in Fig. 8(b), SIVmac239 Nef core is rotated as a single rigid body in the orthorhombic crystal form with no significant changes in either main-chain or side-chain geometry, suggesting that the crystallographic Nef core dimer interface is flexible and permissible to variations in crystal packing.
Alternate crystal packing was also observed at the crystal contact of two asymmetric units in the orthorhombic crystal form and the corresponding symmetryrelated molecules (y, x, Àz) and (1/2 + y, 1/2 À x, 1/4 + z) in the tetragonal crystal form. The interface involves three proteins: SIVmac239 Nef core and its bound TCR polypeptide ligand from the symmetry-related molecule Variation in the crystal contact hydrogen-bond network. Overlay of the crystal-packing interface between two asymmetric units of the P2 1 2 1 2 1 crystal lattice (SIVmac239 Nef is shown in magenta and TCR is shown in green) and two symmetry-related molecules (y, x, Àz) and (1/2 + y, 1/2 À x, 1/4 + z) of the P4 3 2 1 2 crystal lattice (SIVmac239 Nef is shown in cyan and TCR is shown in yellow). Alignment was performed by leastsquares methods using one SIVmac239 Nef-TCR polypeptide complex [at the bottom in (a)]. Hydrogen bonds present in the crystal lattices are represented by dashed lines and are colored green and yellow for the P2 1 2 1 2 1 and P4 3 2 1 2 crystal forms, respectively.
Accompanying the transformation is a possible reorganization of the hydrogen-bonding network at the crystal contact site. In the orthorhombic crystal form the TCR A63-R80 polypeptide forms a main-chain hydrogen bond to the neighboring SIVmac239 Nef core protein between the main-chain amide of TCR Tyr64 and the side-chain carbonyl of Nef Gln202 (Fig. 9b). TCR residue Gln65 additionally participates in hydrogen bonding to the main-chain amide and carbonyl of residues Arg103 and Val102, respectively, on its bound SIVmac239 Nef core partner. Interestingly, this interaction orders the proline-rich region in the N-terminus of the bound SIVmac239 Nef core into a polyproline type II (PPII) helix as evidenced by the clearly resolved electron-density maps calculated from the P2 1 2 1 2 1 crystal data for that region. This carries significant functional importance owing to the regulatory role that the PPII helix on HIV-1 Nef has been suggested to play in modulating kinase activity through its interaction with the SH3 domain of the kinase Lee et al., 1996). The PPII helix was found to be disordered in the unliganded HIV-1 Nef core crystals and was only ordered in crystals containing the Fyn SH3 domain. Surprisingly, the hydrogen-bonding network between the TCR polypeptide and its bound SIVmac239 Nef core partner is seemingly absent in the tetragonal crystal form; this explains the lack of electron density calculated from the P4 3 2 1 2 data for the N-terminus of SIVmac239 Nef core since the PPII helix would no longer be expected to be ordered. Instead of participating in a sidechain-main-chain hydrogen bond with its bound partner, residue Gln65 in TCR is translocated in the tetragonal crystal form, bringing it into close enough proximity to residue Gln202 on the neighboring SIVmac239 Nef core protein to participate in a side-chain-side-chain hydrogen bond. The main-chain-main-chain hydrogen bond between the TCR polypeptide and the neighboring SIVmac239 Nef core protein is also lost in the rearranged P4 3 2 1 2 crystal contact interface.
Since the proposed hydrogen bond between Gln65 on TCR and Gln202 on SIVmac239 was formed by TCR and an adjacent SIVmac239 Nef core protein in the crystal lattice and not its interacting SIVmac239 Nef core partner, it is likely to be an artifact of crystallization that was necessary for proper lattice packing in the tetragonal crystal form. Curiously, the more physiologically relevant interaction of Gln65 on TCR with its bound SIVmac239 Nef core partner was restored when the TCR polypeptide was truncated. The loss of the crystal contact hydrogen bond reduced the crystal symmetry to an orthorhombic crystal lattice that was subsequently prone to twinning. This was unexpected owing to the inclusion of a more complete TCR sequence in the tetragonal crystal and represents an interesting scenario in which a protein-ligand interaction was disrupted by a crystal contact interaction that permitted higher order crystal packing.

Conclusions
Crystal twinning can be induced by a number of perturbations, including heavy-metal soaking, ligand binding, selenomethionine substitution, flash-freezing and the introduction of point mutations (Parsons, 2003;Helliwell et al., 2006). The structure determination of the two SIVmac239 Nef core -TCR polypeptide complexes provides a unique example of crystal twinning caused by the modification of peptide-ligand size. Truncation of the TCR polypeptide reduced the crystal symmetry from a tetragonal crystal system to an orthorhombic crystal system and introduced an NCS operation that only deviated slightly from the true fourfold symmetry axis. The pseudo-symmetry in the P2 1 2 1 2 1 crystal made crystal growth highly susceptible to crystal twinning but serendipitously restored a physiologically relevant protein-ligand interaction at the crystal contact interface.