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

HIV/SIV Nef mediates many cellular processes through interactions with various cytoplasmic and membrane-associated host proteins, including the signalling ζ subunit of the T-­cell receptor (TCRζ). Here, the crystallization strategy, methods and refinement procedures used to solve the structures of the core domain of the SIVmac239 isolate of Nef (Nef_core) in complex with two different TCRζ fragments are described. The structure of SIVmac239 Nef_core bound to the longer TCRζ polypeptide (Leu51–Asp93) was determined to 3.7 Å resolution (R_work = 28.7%) in the tetragonal space group P4₃2₁2. The structure of SIVmac239 Nef_core in complex with the shorter TCRζ polypeptide (Ala63–Arg80) was determined to 2.05 Å resolution (R_work = 17.0%), but only after the detection of nearly perfect pseudo-merohedral crystal twinning and proper assignment of the orthorhombic space group P2₁2₁2₁. The reduction in crystal space-group symmetry induced by the truncated TCRζ polypeptide appears to be caused by the rearrangement of crystal-contact hydrogen-bonding networks and the substitution of crystallographic symmetry operations by similar noncrystallographic symmetry (NCS) operations. The combination of NCS rotations that were nearly parallel to the twin operation (k, h, −l) and a and b unit-cell parameters that were nearly identical predisposed the P2₁2₁2₁ crystal form to pseudo-merohedral twinning.

1. 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 α 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(h₁) and I(h₂) can be solved by combining the linear equations

As the twin fraction α approaches 1/2 the crystal is considered to be perfectly twinned and calculation of the intensities I(h₁) and I(h₂) begins to fail as the term (1 − 2α) 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 β 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 ζ subunit (TCRζ).

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 TCRζ (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 membrane-proximal 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 TCRζ 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 TCRζ remain unknown.

Nef contains two domains: an unstructured highly variable myristylated N-terminal domain and a C-terminal structured core domain (Arold et al., 1997; 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 TCRζ-binding activity of SIV Nef. The core domain of HIV-1 Nef has been shown to be amenable to crystallization (Arold et al., 1997; Lee et al., 1996; Franken et al., 1997). In this study, we aimed to determine the crystal structure of the Nef–TCRζ complex by crystallizing complexes of SIVmac239 Nef_core with TCRζ 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 TCRζ polypeptides, TCRζ_DP1 and TCRζ_A63–R80. Structure determination of the SIVmac239 Nef_core–TCRζ_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–TCRζ_A63–R80 complex as a starting model. However, determination of the high-resolution SIVmac239 Nef_core–TCRζ_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–TCRζ_A63–R80 complex to 2.05 Å resolution. The structures of the two complexes revealed that crystallization of SIVmac239 Nef_core with the shorter TCRζ polypeptide had reduced the space-group 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.

2. Materials and methods

2.1. 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 6×His-thioredoxin fusion protein in Escherichia 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 µM 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 size-exclusion chromatography and concentrated to 700 µM by ultrafiltration (Amicon) in PBS.

TCRζ_cyt includes an acid-labile Asp-Pro sequence (Landon, 1977) at positions 93–94. We made use of this to prepare two fragments of TCRζ_cyt, termed DP1 (Leu51–Asp93) and DP2 (Pro94–Arg164). TCRζ_cyt, purified as described by Sigalov et al. (2004), was incubated at 1.3 mg ml⁻¹ (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 TCRζ polypeptides were solubilized in 20 mM Tris pH 8.0 to a final concentration of 700 µM. Full-length TCRζ was expressed and purified as reported previously (Sigalov et al., 2004).

2.2. Crystallization

Crystals of SIVmac239 Nef_core in complex with the TCRζ polypeptides TCRζ_DP1 and TCRζ_A63–R80 were grown at 277 K using the hanging-drop vapor-diffusion method (McPherson, 1982). Crystals of the Nef_core–TCRζ_DP1 complex were grown in a 2 µl hanging drop by mixing 0.5 µl SIVmac239 Nef_core (700 µM), 0.5 µl TCRζ_DP1 (700 µM) and 1 µl crystallization buffer (15% PEG 3350, 150 mM KF, 100 mM HEPES pH 8.2). Crystals of the Nef_core–TCRζ_A63–R80 complex were grown in a 3 µl hanging drop by mixing 1 µl SIVmac239 Nef_core (700 µM), 1 µl TCRζ_A63–R80 (700 µM) and 1 µl crystallization buffer (10–15% PEG 3350, 200 mM NH₄F, 100 mM HEPES pH 7.4–7.5). The hanging drops were suspended on siliconized glass cover slips over 1 ml crystallization buffer in 24-well plates (Vydax). Crystals of the Nef_core–TCRζ polypeptide complexes grew to maximal size (750 × 150 × 150 µm) in 3–7 d. Prior to X-ray diffraction experiments, the Nef_core–TCRζ_DP1 and Nef_core–TCRζ_A63–R80 crystals were transferred into cryoprotectant solutions containing 20–25% ethylene glycol in their respective crystallization buffers and then flash-cooled in liquid nitrogen.

2.3. Data collection and processing

16 data sets were collected from various Nef_core–TCRζ crystals, of which three were used for structure determination. One low-resolution data set (3.7 Å) for the SIVmac239 Nef_core–TCRζ_DP1 complex and two high-resolution data sets (1.9 and 2.05 Å) for the SIVmac239 Nef_core–TCRζ_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–TCRζ_DP1 complex and the Nef_core–TCRζ_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–TCRζ_A63–R80 crystals was performed following proper assignment of the crystal space group as described below.

2.4. Structure determination and refinement

The structures of the SIVmac239 Nef_core–TCRζ_A63–R80 and SIVmac239 Nef_core–TCRζ_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 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 translation-function Z scores (TFZ) greater than 6.0 were used as starting models. The structure of the Nef_core–TCRζ_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 − F_c and 2F_o − F_c electron-density maps in Coot (Emsley & Cowtan, 2004). The twin operator (k, h, −l) 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 α. Water molecules were added to the refined model using both phenix.refine and Coot. The quality of the final refined SIVmac239 Nef_core–TCRζ_A63–R80 structure was validated in PROCHECK (Las­kowski et al., 1993).

The structure of the refined SIVmac239 Nef_core–TCRζ_A63–R80 complex was used as a search model to find a molecular-replacement solution for the SIVmac239 Nef_core–TCRζ_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–TCRζ_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–TCRζ polypeptide structures are shown in Table 1 and Ramachandran plots generated by RAMPAGE (Lovell et al., 2003) are provided in Supplementary Figs. S1 and S2¹.

Table 1
Data-collection and refinement statistics (molecular replacement)

Values in parentheses are for the highest resolution shell.

	Nefcore–TCRζDP1	Nefcore–TCRζA63–R80, crystal 1	Nefcore–TCRζA63–R80, crystal 2
Data collection
Space group	P43212	P212121	P212121
Unit-cell parameters
a (Å)	51.64	47.19	47.42
b (Å)	51.64	47.24	47.42
c (Å)	189.45	182.99	183.52
α = β = γ (°)	90	90	90
Resolution (Å)	50–3.70 (3.83–3.70)	50–1.93 (2.02–1.93)	30–2.05 (2.12–2.05)
Rmerge	0.051 (0.393)	0.083 (0.513)	0.084 (0.498)
I/σ(I)	12.8 (2.1)	9.7 (2.4)	9.6 (2.5)
Completeness (%)	99.4 (100.0)	99.5 (98.8)	99.1 (96.5)
Redundancy	12.6 (12.7)	6.9 (5.9)	6.8 (5.2)
Twin fraction (k, h, −l)	N/A	0.500	0.426
Refinement
Resolution (Å)	36–3.70		27–2.05
Total reflections	2923		25896
Rwork/Rfree	0.301/0.329		0.170/0.184
No. of atoms
Protein	1054		2223
Water	N/A		116
NCS deviations (Å)	N/A		0.326
Average B factors (Å^2)
SIVmac239 Nefcore	204.63		46.0
TCRζ polypeptide	219.51		49.2
Waters	N/A		45.2
R.m.s. deviations
Bond lengths (Å)	0.003		0.003
Bond angles (°)	0.565		0.564
PDB code	3ioz		3ik5

3. Results and discussion

3.1. Crystallization and data collection of two SIVmac239 Nef_core–TCRζ polypeptide complexes

In order to determine the structure of the Nef–TCRζ complex, mixtures of the structured core domain of SIVmac239 Nef (Asp95–Ser235) with various polypeptides spanning the putative binding regions of TCRζ (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 TCRζ (TCRζ_cyt), but these were unsuccessful. Therefore, a polypeptide crystallization screening strategy was employed to identify a minimal TCRζ poly­peptide that bound SIVmac239 Nef_core, which exhibited the highest affinity TCRζ_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 TCRζ fragments that contained the N-terminal of the two SIV-interaction domains (Fig. 1). Of a series of polypeptides spanning TCRζ_cyt, a peptide included in this region, TCRζ_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, TCRζ_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 TCRζ_cyt (Sigalov et al., 2008). Therefore, a series of polypeptides containing the original TCRζ_DP1 polypeptide, the shorter TCRζ_A61–R80 polypeptide and several peptides containing the proposed SNID-1 (Schaefer et al., 2000) sequence were either prepared from full-length TCRζ_cyt (TCRζ_DP1) or chemically synthesized (TCRζ_A61–R80 and variants) and used in crystallization experiments with SIVmac239 Nef_core.

Figure 1 TCRζ 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.

SIVmac239 Nef_core crystallized in complex with TCRζ_DP1 and TCRζ_A63–R80 under similar conditions. Crystals of the SIVmac239 Nef_core–TCRζ_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 TCRζ_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).

Figure 2 Crystallization and diffraction. (a) Crystals of the SIVmac239 Nefcore–TCRζDP1 and SIVmac239 Nefcore–TCRζA63–R80 complexes. Both crystals grew to 750 × 150 × 150 µm at 277 K. (b) Diffraction patterns of crystals of the SIVmac239 Nefcore–TCRζ polypeptide complexes collected on beamline X29 at the National Light Synchrotron Light Source, Brookhaven National Laboratory. (c) Enlarged view of the diffraction patterns. The diffraction-pattern spot profiles are singular, with no evidence of split spots.

3.2. Space-group determination and molecular replacement for SIVmac239 Nef_core–TCRζ_DP1

The low-resolution diffraction data for the SIVmac239 Nef_core–TCRζ_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 ų Da⁻¹ (57.1% solvent), indicating the presence of one SIVmac239 Nef_core–TCRζ_DP1 heterodimer per asymmetric unit. After analysis of the h00, 0k0 and 00l reflection intensities, the space group was further assigned as P4₃2₁2 or P4₁2₁2 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 P4₃2₁2. However, model refinement and building were hindered by the poor quality of the σ_A-weighted F_o − F_c and 2F_o − 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–TCRζ_A63–R80

Two crystals of SIVmac239 Nef_core bound to the shorter TCRζ_A63–R80 polypeptide diffracted X-rays to higher resolution (1.9–2.05 Å), but space-group determination proved to be more complicated than for the P4₃2₁2 crystal form of Nef_core–TCRζ_DP1 described above. The diffraction patterns that were observed for Nef_core–TCRζ_A63–R80 appeared to be consistent with the lattice previously observed for the lower resolution Nef_core–TCRζ_DP1 crystals, and the TCRζ_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 ΔI/σ(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–TCRζ_DP1 crystals, which is potentially consistent with the shorter length of the TCRζ polypeptide ligand. Analysis of the h00 and 0k0 intensities indicated the presence of 2₁ screw axes along a and b. However, 00l intensities were observed for l = 2n, which is consistent with a 4₂ (or 2₁) axis along c but inconsistent with a 4₃ axis as observed for the lower resolution tetragonal SIVmac239 Nef_core–TCRζ_DP1 data. A search for a molecular-replacement solution for the SIVmac239 Nef_core–TCRζ_A63–R80 data in 4₂2₁2 or any of the other 422 space groups yielded no solutions. A data set that was collected from a second SIVmac239 Nef_core–TCRζ_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–TCRζ_A63–R80 complex in the tetragonal Laue symmetry group suggested the possibility of crystal twinning and required space-group re-evaluation.

3.4. 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 α (Britton, 1972). To assess the twinning of the SIVmac239 Nef_core–TCRζ polypeptide crystals, several analyses of the intensity statistics were per­formed in phenix.xtriage. Firstly, the second moments of the intensities of acentric data (〈I²〉/〈|I|²〉) were calculated for all three SIVmac239 Nef_core–TCRζ polypeptide complexes. Un­twinned and twinned data are expected to have 〈I²〉/〈|I|²〉 values of 2.0 and 1.5, respectively. The SIVmac239 Nef_core–TCRζ_DP1 crystal had an 〈I²〉/〈|I|²〉 value of 2.106, suggesting the absence of twinning, whereas the SIVmac239 Nef_core–TCRζ_A63–R80 crystals had 〈I²〉/〈|I|²〉 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–TCRζ_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–TCRζ_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–TCRζ_A63–R80 crystals; for untwinned data |L| and mean L² 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–TCRζ_DP1 data had calculated |L| and L² values of 0.473 and 0.307, which were consistent with an absence of appreciable twinning. The SIVmac239 Nef_core–TCRζ_A63–R80 crystals had calculated |L| and L² 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 low-resolution SIVmac239 Nef_core–TCRζ_DP1 crystal was not appreciably twinned, whereas the high-resolution SIVmac239 Nef_core–TCRζ_A63–R80 crystals were pseudo-merohedrally twinned with a twin fraction near 0.5.

Figure 3 Detection of twinning and estimation of the twin fraction α. Top row, cumulative intensity difference plot of the intensity difference of local pairs of intensities that are not twin-related |L| {L = [I(h1) − I(h2)]/[I(h1) + I(h2)]} against the cumulative probability distribution N(L) of the parameter L (Padilla & Yeates, 2003). The expected plots for untwinned and twinned acentric data (red) and the calculated plots for the SIVmac239 Nefcore–TCRζ polypeptide data (blue) are shown. Middle row, estimation of the twin fraction α by Britton plot analysis (Britton, 1972). The percentage of negative intensities after detwinning is plotted as a function of the assumed value of α. Overestimation of the twin factor α results in an increase in the percentage of negative intensities. The estimated value of α is extrapolated from the linear fit (dashed line). Bottom row, estimation of the twin fraction α using the H plot (Yeates, 1988). The cumulative fractional intensity difference of acentric twin-related intensities H {H = |I(h1) − I(h2)|/[I(h1) + I(h2)]} is plotted against H. The initial slope (dashed line) of the distribution is a measure of α. The expected slopes for the indicated twin fractions 0.0–0.4 are shown (dotted lines).

In order to estimate the twin fraction α in the two pseudo-merohedrally twinned SIVmac239 Nef_core–TCRζ_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–TCRζ_A63–R80 crystals were orthorhombic crystals that emulated tetragonal symmetry owing to pseudo-merohedral crystal twinning. The twinned SIVmac239 Nef_core–TCRζ_A63–R80 diffraction data were therefore re-indexed in the orthorhombic point group 222. The unit-cell parameters a and b that are constrained to be equal in point group 422 (Laue group 4/mmm) refined to slightly different values of a = 47.197 and b = 47.208 Å for crystal 1 and a = 47.417 and b = 47.421 Å for crystal 2, with no significant changes in R_merge values (Table 1). Inspection of the h00, 0k0 and 00l intensities indicated the presence of 2₁ screw axes along each axis, suggesting a P2₁2₁2₁ crystal space group. The Matthews coefficient V_M (Matthews, 1968) was calculated to be 2.64 ų Da⁻¹ (53.42% solvent) for crystal 1 and 2.64 ų Da⁻¹ (53.99% solvent) for crystal 2, which is consistent with two SIVmac239 Nef_core–TCRζ_A63–R80 heterodimers comprising the asymmetric unit.

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, −l) that accounted for the apparent fourfold Laue symmetry observed in the diffraction data. Consider a P2₁2₁2₁ unit cell with unit-cell length a approximately equal to unit-cell length b (Fig. 4). Pseudo-merohedral twinning can exchange the a and b axis under the twin relationship (h, k, l)→(k, h, −l), resulting in apparent tetragonal symmetry around the c axis (Fig. 4b). The apparent symmetry observed in this case will be indistinguishable from a nontwinned P4₃2₁2 (or P4₁2₁2) unit cell (Fig. 4a), of which P2₁2₁2₁ is a subgroup. Note that in this case the twinned P2₁2₁2₁ unit cell is less tightly packed, with one molecule per asymmetric unit (four per unit cell), than the corresponding nontwinned tetragonal P4₃2₁2 (or P4₁2₁2) 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 P2₁2₁2₁ unit cell. Note that the nontwinned crystals of the SIVmac239 Nef_core–TCRζ_DP1 complex, which did adopt true tetragonal symmetry with unit-cell parameters similar to those of the twinned P2₁2₁2₁ crystal, had a Matthews coefficient consistent with one molecule per asymmetric unit. Because the SIVmac239 Nef_core–TCRζ_DP1 and SIVmac239 Nef_core–TCRζ_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 P2₁2₁2₁ and nontwinned P4₃2₁2 (or P4₁2₁2) 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 unit-cell axes (Fig. 4c). We explored this scenario as an explanation for the observed twinning in the P2₁2₁2₁ crystals with packing similar to nontwinned P4₃2₁2 (or P4₁2₁2) crystals.

Figure 4 Twinning in an orthorhombic P212121 crystal. (a) A P43212 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 P212121 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, −z). (c) A P212121 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, −z). The ASU is comprised of one blue and one black arrow related by noncrystallographic symmetry.

3.5. Structure determination and refinement of SIVmac239 Nef_core–TCRζ_A63–R80 using twinned data

After assignment of the SIVmac239 Nef_core–TCRζ_A63–R80 crystal data to the orthorhombic P2₁2₁2₁ 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 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, −l) twinning operator and the P2₁2₁2₁ 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.

Figure 5 Molecular-replacement solutions. Five molecular-replacement solutions (A–E) are shown with their translation-function Z (TFZ) scores denoted. The relationships and rotation matrices relating the molecular-replacement solutions are shown.

Once the twinning arrangement was properly understood and taken into account, model building and refinement in space group P2₁2₁2₁ with two molecules per asymmetric unit was relatively straightforward. The twin operation (k, h, −l) 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 α was also refined in each round and used to detwin the intensity data in order to generate interpretable 2F_o − F_c and F_o − 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 − 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 TCRζ_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 α-helix (Fig. 6). Water molecules were added to the model using the automated water-picking functions in phenix.refine and Coot. The final structure (crystal 2) contained 120 residues of SIVmac239 Nef, 16 residues of TCRζ, 116 ordered water molecules and had R_work and R_free values of 17.0% and 18.4%, respectively (Table 1).

Figure 6 2Fo − Fc OMIT electron-density maps of the TCRζ polypeptide. 2Fo − Fc OMIT electron-density maps contoured at 1σ calculated from the detwinned P212121 data of the SIVmac239 Nefcore–TCRζA63–R80 crystal (a) and the P43212 data of the SIVmac239 Nefcore–TCRζDP1 crystal (b) are shown for the region encompassing the TCRζ polypeptide.

3.6. Structure determination and refinement of SIVmac239 Nef_core–TCRζ_DP1

With a high-resolution structure for SIVmac239 Nef_core–TCRζ_A63–R80 structure in hand, we returned to the low-resolution nontwinned SIVmac239 Nef_core–TCRζ_DP1 P4₃2₁2 data set. In order to determine the low-resolution structure of SIVmac239 Nef_core–TCRζ_DP1, the high-resolution SIVmac239 Nef_core–TCRζ_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–TCRζ_DP1 data. A stronger molecular-replacement 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 TCRζ_DP1 peptide extends 12 residues futher at the N-terminus and 14 residues further at the C-­terminus compared with the TCRζ_A63–R80 polypeptide, but no additional electron density was observed beyond that seen in the SIVmac239 Nef_core–TCRζ_A63–R80 complex (Fig. 6), suggesting that both the N- and C-termini of the TCRζ_DP1 fragment were disordered and that no additional Nef contacts were present. The final structure of the SIVmac239 Nef_core–TCRζ_DP1 complex contained 111 residues of Nef and 16 residues of TCRζ and had R_work and R_free values of 30.1% and 32.9%, respectively (Table 1).

3.7. Analysis of the P2₁2₁2₁ and P4₃2₁2 crystal forms of the SIVmac239 Nef_core–TCRζ polypeptide complex

As described above, the SIVmac239 Nef_core–TCRζ polypeptide complex crystallized in two related but different crystal lattices depending on the length of the TCRζ ligand. In the presence of the longer 43-residue TCRζ_DP1 polypeptide SIVmac239 Nef_core crystallized in the tetragonal P4₃2₁2 space group with one SIVmac239 Nef_core–TCRζ_DP1 heterodimer comprising the asymmetric unit. In the presence of the shorter 18-residue TCRζ_A63–R80 polypeptide the complex unexpectedly crystallized in the P2₁2₁2₁ 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 P4₃2₁2 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.

Figure 7 Crystal packing of the P43212 and P212121 crystal forms. (a) The crystal symmetry organization of the P43212 crystal form (left) and the P212121 crystal form (right) is shown viewed down the fourfold symmetry axis and the corresponding twofold symmetry axis for the two SIVmac239 Nefcore–TCRζ polypeptide complexes. In (b) the crystal packing along the c axis is shown for both crystal forms. SIVmac239 Nefcore and TCRζ are colored cyan and yellow (left) and magenta and green (right), respectively.

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 P4₃2₁2 crystal form contained one molecule per asymmetric unit. The P2₁2₁2₁ crystal form contained two molecules per asymmetric unit which were no longer related by a crystallo­graphic twofold symmetry operation (y, x, −z) but instead by a twofold NCS operation,

In the tetragonal crystal form the SIVmac239 Nef_core–TCRζ_DP1 complex and its symmetry-related partner (y, x, −z) form an antiparallel dimer similar to the crystallographic dimer described previously for the HIV-1 Nef_core (Arold et al., 1997). Structural alignment of one SIVmac239 Nef_core–TCRζ_A63–R80 complex from the P2₁2₁2₁ crystal form with its corresponding molecule in the P4₃2₁2 crystallographic dimer reveals that the NCS-related molecule in the orthorhombic crystal form is rotated by ∼10° from its corresponding molecule in the P4₃2₁2 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.

Figure 8 SIVmac239 Nefcore dimer interface in the P43212 and P212121 crystal forms. (a) Overlay of the two molecules in the asymmetric unit of the P212121 crystal (magenta/green) and two symmetry-related molecules [(x, y, z), (y, x, −z)] in the P43212 crystal (cyan/yellow). The SIVmac239 Nefcore is colored magenta (P212121 crystal) or cyan (P43212 crystal) and the TCRζ polypeptide is colored green (P212121 crystal) or yellow (P43212 crystal). The structures of the lower SIVmac239 Nefcore–TCRζ polypeptide complexes were aligned by least-squares methods. The relative 10° counterclockwise rotation of the top P212121 crystal SIVmac239 Nefcore–TCRζ polypeptide complex is depicted. (b, c) Detailed view of the SIVmac239 Nefcore dimer interface in the P212121 (magenta) and P43212 (blue) crystals. The aligned lower SIVmac239 Nefcore–TCRζ polypeptide complex is colored grey and the side chains of residues involved in the interface are shown as stick models. (b) P212121 crystal form (cyan) is highlighted. (c) P43212 crystal form (magenta) is highlighted.

Alternate crystal packing was also observed at the crystal con­tact of two asymmetric units in the orthorhombic crystal form and the corresponding symmetry-related molecules (y, x, −z) and (1/2 + y, 1/2 − x, 1/4 + z) in the tetragonal crystal form. The interface involves three proteins: SIVmac239 Nef_core and its bound TCRζ polypeptide ligand from the symmetry-related molecule (1/2 + y, 1/2 − x, 1/4 + z) and SIVmac239 Nef_core from the symmetry-related molecule (y, x, −z) (Fig. 9a). Interestingly, the N-terminus of the TCRζ polypeptide abuts the neighboring SIVmac239 Nef_core protein, suggesting that the length of the N-terminal sequence of the TCRζ polypeptide ligand directs the space group in which the SIVmac239 Nef_core–TCRζ polypeptide complex crystals grow. Superimposition of the TCRζ polypeptide helix from the symmetry-related molecule (1/2 + y, 1/2 − x, 1/4 + z) with its corresponding partner in the P2₁2₁2₁ crystal form reveals that the neighboring SIVmac239 Nef_core protein is rotated ∼4.5° inwards towards the pseudo-fourfold symmetry axis in the P2₁2₁2₁ crystal form (Fig. 9a).

Figure 9 Variation in the crystal contact hydrogen-bond network. Overlay of the crystal-packing interface between two asymmetric units of the P212121 crystal lattice (SIVmac239 Nef is shown in magenta and TCRζ is shown in green) and two symmetry-related molecules (y, x, −z) and (1/2 + y, 1/2 − x, 1/4 + z) of the P43212 crystal lattice (SIVmac239 Nef is shown in cyan and TCRζ is shown in yellow). Alignment was performed by least-squares methods using one SIVmac239 Nef–TCRζ 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 P212121 and P43212 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 TCRζ_A63–R80 polypeptide forms a main-chain hydrogen bond to the neighboring SIVmac239 Nef_core protein between the main-chain amide of TCRζ Tyr64 and the side-chain carbonyl of Nef Gln202 (Fig. 9b). TCRζ 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 P2₁2₁2₁ 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 (Arold et al., 1997; 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 TCRζ 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 P4₃2₁2 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 side-chain–main-chain hydrogen bond with its bound partner, residue Gln65 in TCRζ 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 TCRζ polypeptide and the neighboring SIVmac239 Nef_core protein is also lost in the rearranged P4₃2₁2 crystal contact interface.

Since the proposed hydrogen bond between Gln65 on TCRζ and Gln202 on SIVmac239 was formed by TCRζ 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 TCRζ with its bound SIVmac239 Nef_core partner was restored when the TCRζ 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 TCRζ 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.

4. 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–TCRζ polypeptide complexes provides a unique example of crystal twinning caused by the modification of peptide-ligand size. Truncation of the TCRζ 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 P2₁2₁2₁ crystal made crystal growth highly susceptible to crystal twinning but serendipitously restored a physiologically relevant protein–ligand interaction at the crystal contact interface.

Footnotes

¹Supplementary material has been deposited in the IUCr electronic archive (Reference: YT5020). Services for accessing this material are described at the back of the journal.