IN variants and LEDGF(Cterm) constructs alone were expressed and purified as described previously (10, 40). IN and LEDGF constructs were co-expressed from pETDuet (Novagen) in BL21(DE3) cells at 37 °C. LEDGF was inserted into the vector in-frame with a C-terminal Mxe intein (New England Biolabs) containing the chitin binding domain and hexahistidine affinity tags. Proteins were purified using nickel-nitrilotriacetic acid (Qiagen) and chitin (New England Biolabs) resins. Fusion proteins were released by intein cleavage in 50 mm dithiothreitol overnight at 4 °C. Preparations of IN alone were further purified using SP-Sepharose chromatography (GE Healthcare). Proteins were concentrated at 4 °C in YM-3 Centricon (Millipore), and aliquots were flash-frozen in liquid nitrogen for storage at −80 °C. All preparations were stored and analyzed in 20 mm HEPES, pH 7.5, 150–450 mm NaCl, 0.1 mm EDTA, 10 μm ZnOAc₂, and 1–10 mm dithiothreitol. The viscosity of this buffer at 4 and 20 °C was determined using a glass viscometer. Solvent density was determined gravimetrically. Prior to SAXS analyses, proteins were purified by size-exclusion chromatography (SEC) on a S200 10/300GL column, concentrated, and dialyzed. All purified proteins were analyzed by mass spectrometry (matrix-assisted laser desorption ionization time-of-flight) to verify the correct molecular weights of the individual components.

Sedimentation equilibrium ultracentrifugation (SE) experiments were performed at either 4 or 20 °C with an XL-A analytical ultracentrifuge (Beckman Coulter) and a TiAn60 rotor with six-channel charcoal-filled Epon centerpieces and quartz windows. Radial absorption scan data at 280 nm for three protein concentrations were measured at 16 and 18 h for each of three different rotor speeds (12,000, 16,000, and 20,000 rpm). Comparison of radial absorption scans verified that equilibrium had been reached. Data were analyzed using the programs SEDFIT (41) and SEDPHAT (42). Single species or multimer equilibrium models were selected based on the smallest goodness of fit observed, with low and randomly distributed residual errors. An estimated error for the equilibrium constant was determined from a 1,000-iteration Monte Carlo simulation, as implemented in SEDPHAT.

Sedimentation velocity ultracentrifugation experiments were performed at either 4 or 20 °C with an XL-A analytical ultracentrifuge (Beckman) and a TiAn60 rotor with two-channel charcoal-filled Epon centerpieces and quartz windows. Complete sedimentation velocity profiles were collected every 30 s at 45,000 rpm followed by data analysis using the program SEDFIT.

For determination of the Stokes radius (R_S), SEC experiments were performed with a Superdex 200 10/300 GL column (GE Healthcare) at 0.4 ml/min at 20 °C in buffer containing 20 mm HEPES-NaOH, pH 7.5, 150 mm NaCl, 5 mm dithiothreitol, 0.1 mm EDTA, and 10 μm Zn(OAc)₂. The column was calibrated using the following proteins (Bio-Rad): thyroglobulin (670 kDa, R_S = 85 Å), γ-globulin (158 kDa, R_S = 52.2 Å), ovalbumin (44 kDa, R_S = 30.5 Å), myoglobin (17 kDa, R_S = 20.8 Å), and vitamin B₁₂ (1,350 Da). Blue dextran (Sigma) was used to define the void volume of the column.

Absolute molecular weights of LEDGF and IN·LEDGF heteromers were determined using MALS coupled with a TSK3000 or TSK4000 analytical SEC column (TosoHaas, Montgomeryville, PA). The columns were calibrated as described above. The scattered light intensity of the column eluant was recorded at 16 different angles using a DAWN-HELEOS MALS detector (Wyatt Technology Corp.) operating at 658 nm after calibration with RNase A. Protein concentration of the eluant was determined using an in-line Optilab DSP interferometric refractometer (Wyatt Technology Corp.). The weight-averaged molecular weight of species within defined chromatographic peaks was calculated using the ASTRA software version 5.2 (Wyatt Technology Corp.), by construction of Debye plots (KC/Rθ versus sin²[θ/2]) at 1-s data intervals. The weight-averaged molecular weight was then calculated at each point of the chromatographic trace from the Debye plot intercept, and an overall average molecular weight was calculated by averaging across the peak.

X-ray scattering data were measured at three different synchrotron sources as follows: beam line G1 at Cornell University High Energy Synchrotron Source (Ithaca, NY), beam line X21 at the National Synchrotron Light Source (Upton, NY), and beam line BL4-2 at the Stanford Synchrotron Radiation Light Source (Menlo Park, CA). Specific details of the experimental setup and procedures specific to each location are provided in the supplemental material. In all cases, the forward scattering from the samples studied was recorded on a CCD detector and circularly averaged to yield one-dimensional intensity profiles as a function of Q (Q = 4πsinθ/λ, where 2θ is the scattering angle). Samples were centrifuged at 10,000 × g for 10 min at 4 °C before 1–20-s exposures were taken at 20 °C. Scattering from a matching buffer solution was subtracted from the data and corrected for the incident intensity of x-rays. Replicate exposures were examined carefully for evidence of radiation damage by Guinier analysis and Kratky plot analysis. Silver behenate powder was used to locate the beam center and to calibrate the sample-to-detector distance.

All of the preparations analyzed were monodisperse, as evidenced by linearity in the Guinier region of the scattering data and agreement of the I(0) and R_g values determined with inverse Fourier transform analysis by the programs GNOM (43) and AUTOGNOM (44). Molecular mass as derived from I(0) measurements, using the forward scatter from either bovine serum albumin or ovalbumin as a control, was consistent with the molecular masses determined by centrifugation and SEC-MALS. When fitting manually, the maximum diameter of the particle (D_max) was adjusted in 10-Å increments in GNOM to maximize the goodness-of-fit parameter. This analysis also yielded determinations of R_g and I(0). The theoretical SAXS profiles for heteromer models of IN and LEDGF were created using the CRYSOL program (45).

Low resolution shapes were determined from solution scattering data using the programs DAMMIF (46) and GASBOR (47). With GASBOR, the number of dummy residues used in shape reconstruction is prescribed by the user, requiring an understanding of the composition of the particle being modeled. Ten independent calculations were performed for each data set using default parameters. Initially, no symmetry constraints were applied. Calculations were then repeated assuming 2-fold symmetry, if justified by the apparent shape of the particle and improvement in the final χ and normalized spatial discrepancy (NSD) criterion. The models resulting from the independent runs were superimposed by the program SUPCOMB based on the NSD criterion (48). The 10 independent reconstructions were then averaged and filtered to a final consensus model using the DAMAVER suite of programs (49). Consensus models obtained by DAMMIF and GASBOR approaches yielded similar results, unless otherwise noted. Bead models were visualized in PyMOL (50) or converted to meshed envelopes using SITUS (51) and visualized using Chimera (52).

Models of IN(NTD-CCD)₂·LEDGF(IBD)₂ and IN(tetra)₄·LEDGF(IBD)₂ were created by superposition of available crystal structures (Protein Data Bank codes 1K6Y, 2B4J, 3F9K, and 1EX4) in the program PyMOL, followed by energy minimization in the program CNS (53) to relieve bad side-chain contacts. Residues 270–288 from IN and 430–471 from LEDGF are all predicted to be disordered and are missing in our structural models. The program HYDROPRO (54) was used to determine theoretical hydrodynamic properties of these models and of SAXS bead ensembles from their respective atomic coordinates. Sculptor was used to rigid body dock structural models into low resolution envelopes using a feature-based docking algorithm (55).

Biophysical and crystallographic efforts to study HIV IN have been hindered by the poor solubility and yield of recombinant preparations of the full-length protein. Combinations of IN surface mutations and additives such as high salt, glycerol, and the detergent CHAPS have been used extensively to improve the stability and solubility of IN for in vitro experiments (56, 57). We found that by co-expressing truncated and full-length IN variants with LEDGF(IBD) in Escherichia coli, a number of IN:LEDGF(IBD) complexes could be co-purified in the absence of CHAPS or other additives, allowing the protein assemblies to be studied using more physiological buffer conditions.

We evaluated purification of IN complexes containing several of the previously described surface mutations, including IN(F185H), IN(F185K), and IN(tetra) (“tetra” refers to the C56S, F139D, F185H, C280S-substituted protein). IN(tetra) retains the binding and catalytic activities of wild-type IN (58).⁴ Substitutions at Phe-139, and Phe-185 improve solubility (15, 20), whereas the serine substitutions at positions Cys-56 and Cys-280 reduce the formation of oxidative side products that form during purification and storage (20, 59). The proteins and protein-protein complexes were purified using nickel-nitrilotriacetic acid and chitin chromatography, based on a modified self-cleaving intein fused to the C terminus of LEDGF. Only those complexes that were stable to repeated column washes with 300 mm NaCl (used for both resins) were recovered by co-purification. Table 1 summarizes the IN·LEDGF complex constructs that we have attempted to purify using this system.

The smallest IN·LEDGF complex that we considered is the IN(CCD)·LEDGF(IBD) heterotetramer that was successfully crystallized (24). Although both components are produced during co-expression in E. coli, we found that the complex is not sufficiently stable to survive co-purification. Consistent with previous observations (8, 26), when the IN expression construct was extended to include both the NTD and CCD (Fig. 1A), we found that a stable complex could be obtained that was soluble in 0.3 m NaCl, defining a minimal three-domain composition for a stable IN·LEDGF complex under our conditions. This complex was stable to washes with 1 m NaCl and was not disrupted by 10 mm tetraphenylarsonium chloride (data not shown), a compound previously found to bind at the CCD-IBD interface (60). We were also able to obtain soluble complexes of LEDGF(IBD) with several full-length IN variants (Table 1). Interestingly, when we extended the LEDGF construct to include residues 325–530 (Cterm, Fig. 1A), the resulting IN·LEDGF complexes were obtained in higher yield and were highly soluble in 150 mm NaCl. We were not able to co-purify stable complexes of full-length LEDGF with IN for biophysical studies due to their limited solubility.

We used several independent and complementary techniques to characterize the IN·LEDGF assemblies that we obtained from co-expression and co-purification. Our initial goal was to establish the oligomeric state and the protein stoichiometries of the complexes, both of which are crucial to interpretation of small angle x-ray scattering experiments. First we analyzed the complexes using sedimentation equilibrium (SE) ultracentrifugation. In all cases, we observed either a single species for which we were able to determine the molecular weight or we were able to fit the radial distribution curves to a simple monomer-dimer or dimer-tetramer association model. For the association models, we obtained estimates of the molecular weight and the dissociation constant. The results of the SE experiments are summarized in Table 2.

In a second set of experiments, we used SEC coupled with MALS detector to determine the Stokes radius (R_S) of the complex and to obtain an independent measurement of the complex mass. Finally, we used sedimentation velocity (SV) ultracentrifugation to determine sedimentation coefficients for several of the species studied. The measured Stokes radius and sedimentation coefficients then provided a third estimate of the complex mass via the Siegel and Monty equation (61). The results of these experiments for IN, LEDGF, and co-purified IN·LEDGF complexes are summarized in Tables 2 and 3, with representative examples of SE, SEC-MALS, and SV experiments shown in Fig. 1, B–D, respectively. Additional SE and SEC-MALS data are shown in supplemental Figs. 1 and 2, respectively.

The IN(NTD-CCD)·LEDGF(IBD) complex exists as a single species in solution, with a molecular weight consistent with a 2:2 complex (Tables 2 and 3). Thus, two LEDGF(IBD) molecules bind to a dimer of IN(NTD-CCD). This result is consistent with the IN(CCD)·LEDGF(IBD) crystal structure, which reveals two IBDs bound to each IN CCD dimer (24), as well as that observed with the maedi-visna virus IN(NTD-CCD)·LEDGF(IBD) crystal structure (26). However, the 2:2 stoichiometry is not consistent with the crystal structure of HIV-2 IN(NTD-CCD)·LEDGF(IBD), which shows one IBD bound to each IN dimer (26).

In addition to the question of stoichiometry, the arrangement of NTDs in the IN dimer has not been unambiguously demonstrated based on structural data. In the HIV-2 IN(NTD-CCD) structure, two IN dimers are observed in the asymmetric unit, but the linkers connecting the NTDs to the CCDs are disordered (26). Two symmetric NTD arrangements can be considered based on the observed crystal packing (Fig. 2). In one configuration, two NTDs interact with one another and to a CCD dimer surface that is orthogonal to that formed by the IBD interface. In this “apical” arrangement, the 2-fold symmetry axis of the CCD dimer passes through the NTD dimer. In the alternative “lateral” configuration, each NTD interacts with one CCD adjacent to where the IBD binds. This arrangement is similar to the domain organization observed in one-half of the HIV-2 IN(NTD-CCD)·LEDGF(IBD) crystal structure, where the CCD-NTD linker is well ordered. In the other half of that IN dimer, the NTD adopts a different position, and there is no IBD bound. This same lateral arrangement is also observed in the maedi-visna virus IN(NTD-CCD)·LEDGF(IBD) crystal structure (25). The apical arrangement of NTDs has been proposed to occur in the context of a LEDGF-bound IN tetramer (37). The apical and lateral positions for the NTDs are compared in Fig. 2.

To address the question of NTD positions, we analyzed the IN(NTD-CCD)·LEDGF(IBD) complex using SAXS. We measured scattering for three different IN(NTD-CCD) mutants and at several concentrations and obtained similar results in each case (supplemental Table 1). The results of these experiments for IN(C56S, F139D, and F185H) are summarized in Fig. 2. Assuming a 2:2 stoichiometry, we constructed the symmetric IN(NTD-CCD)₂IBD₂ models discussed above and shown in Fig. 2, C and D. The models have similar maximum dimensions (D_max) that correlate well to the D_max of 114 Å experimentally determined from the scattering data.

We generated theoretical scattering profiles for both models and compared them to the experimental data. The model with NTDs in lateral positions shows better agreement with experimental data (χ² = 1.75) than the apical model (χ² = 2.32) (supplemental Fig. 3). This correlation is also mirrored in comparison with P(r) shape functions (Fig. 2B). The P(r) curve is a distribution of inter-atomic distances present in the molecule, so differently shaped molecules give rise to different features in the P(r) function. Because 80 amino acids in the constructs studied here are missing from the crystal structures used to derive the two models, an exact match between calculated and experimental P(r) functions for any model is unlikely. However, the general shape of the function should be similar for a correct model. As shown in Fig. 2B, the shape function associated with the lateral model is most similar to the experimental P(r) but compressed toward smaller interatomic distances due to the smaller size of the complex.

To generate shape reconstructions from the scattering data, we used the DAMMIF and GASBOR programs (see “Experimental Procedures”), which use different but complementary algorithms to generate shape envelopes of the scattering molecule. With a 2-fold symmetry constraint for the overall shape, both approaches reproducibly yielded envelopes with good correlations between experimental and calculated scattering data (sqrt(χ) ∼1.5). The ensemble of envelopes generated from multiple iterations of the reconstruction process also agreed well with one another, with NSD values of ranging from 0.7 to 0.8 for DAMMIF and 1.0 to 1.3 for GASBOR (where a value of unity corresponds to identity between two structures, and values below 1 indicate a high degree of overlap). We obtained similar solution parameters and SAXS results for constructs containing the F185H and F185K solubility mutations (data not shown).

As shown in Fig. 2 and in supplemental Fig. S4, the averaged envelope is an elongated prolate ellipsoid. The hydrodynamic properties calculated for this shape closely resemble those determined experimentally (Table 3). For example, the calculated sedimentation coefficient of 4.6 and the extended ellipsoidal shape of the envelope agree well with the values derived from SV analysis (s_20,w = 4.3), and the calculated R_S of 40 Å agrees well with results derived from SEC (38.5 Å) and DLS (40.8 Å) measurements (data not shown). From a comparison of the two alternative models docked into the SAXS envelope, it is clear that the lateral model (Fig. 2C) captures the overall shape of the IN(NTD-CCD)·IBD complex in solution much better than the apical model (Fig. 2D). These results strongly support the model shown in Fig. 2C, where each NTD of IN interacts with the CCD and IBD, but the NTDs do not interact with one another and do not contribute directly to the dimer interface. The model is also consistent with mutagenesis data that support the IBD·NTD interface observed in the IN(NTD-CCD)·IBD crystal structure (26).

We next examined a series of full-length IN complexes with the LEDGF(IBD). The IN(tetra)·LEDGF(IBD) complex is soluble and monodisperse in buffers containing 300 mm salt, but it differs in two important ways with respect to the truncated IN(NTD-CCD) complexes described above. First, the full-length complex forms tetramers of IN, with a dimer-tetramer K_d ∼9 μm (Tables 2 and 3). Thus, the LEDGF(IBD) is alone capable of stabilizing the tetrameric form of IN, although the comparison to IN oligomerization in the absence of bound IBD is to a protein solution containing 10 mm CHAPS at a lower temperature (Table 2). The second difference is that the IN:IBD stoichiometry is 4:2 in the tetramer, where each CCD dimer binds only one IBD. In this case, experimental determination of the mass of the IN·IBD complex comes from a dimer-tetramer association model fit to the SE data, plus direct MALS analysis of the tetramer species observed on the SEC column (Fig. 1C). The IN(tetra)·IBD complex is stable and is not disrupted by 1 m NaCl (data not shown).

Our interpretation of the 4:2 IN·IBD stoichiometry is that IN tetramerization leads to formation of one pair of high affinity binding sites for the IBD and one pair of low affinity sites, a concept previously proposed based on modeling of available crystallographic structures (37). The IBDs bound to low affinity sites are presumably removed from the IN complex during purification. This conceptual model of the tetramer requires that the complex is at most 2-fold symmetric. To further understand this complex, we used SAXS to determine the shape of the particle in solution.

The IN(tetra)·LEDGF(IBD) heteromer is a well suited for SAXS analysis and interpretation, because it is very soluble and not prone to aggregation, and the component protein domains are represented by available crystal structures. We tested IN(tetra)·LEDGF(IBD) scattering over a range of concentrations well in excess of the dimer-tetramer K_d value to fully populate the tetramer state. Across the range of concentrations examined, the mass of the particle was constant (based on I(0) extrapolation and comparison with scattered bovine serum albumin standards) and consistent with the mass determined by biophysical measurements. The shape parameters (R_g and D_max) derived from x-ray scattering at different concentrations are also consistent, with only a small increasing trend toward higher concentrations (supplemental Table 1).

Shape reconstructions using both the DAMMIF and GASBOR approaches yielded prolate ellipsoids of similar volume and dimension and are consistent with the hydrodynamic properties determined by SV analysis (Fig. 3 and Table 3). Independent reconstructions using DAMMIF showed good agreement, with sqrt(χ) values ranging from 1.8 to 1.9 and NSD values ranging from 0.78 to 0.87, indicating a very stable structural solution (Fig. 3B and supplemental Fig. 4). Although the reconstructions using GASBOR featured similar sqrt(χ) values (1.7 to 1.8), the NSD values were higher, ranging from 1.8 to 2.2. Examination of the individual models showed similar core ellipsoidal shapes, with the most apparent deviations located on the distal ends of each particle, perhaps suggesting inherent disorder within these regions (supplemental Fig. 4). However, the averaged envelope shares the same conserved features observed in all the reconstructions and recapitulates the shape observed in the averaged DAMMIF envelope. The averaged shape obtained from GASBOR also correlates well with measured hydrodynamic properties as follows: calculated versus measured R_S values are 53.3 and 54.9 Å, respectively, and the calculated versus measured sedimentation coefficients are 7.3 and 7.4, respectively.

There are currently no crystal structures of IN tetramers available to provide a basis for modeling the shape of the IN·LEDGF(IBD) complex in solution. However, contacts between neighboring molecules in the crystal structures of IN(NTD-CCD) and IN(CCD-CTD) reveal a number of interactions that could be relevant in the context of an IN tetramer (15, 18). We constructed a series of models based on these contacts, the determined 4:2 IN·IBD stoichiometry, the known binding position of the LEDGF(IBD), and two alternative positions for the NTD. Because the envelope reconstructions and stoichiometry strongly indicate that the complex is at most 2-fold symmetric in solution, we only considered 2-fold symmetric arrangements of the IN and LEDGF domains.

Four models that fit these criteria are shown in Fig. 4A. Models 1 and 2 are derived from crystallographic packing observed in the IN(CCD-CTD) crystal structure (15), where CTD-CCD and CTD-CTD interactions account for nearly all of the contacts between dimers. Models 3 and 4 are derived from the crystallographic packing observed in the IN(NTD-CCD) structure (18), where dimer-dimer contacts are mediated primarily by NTD-CCD interactions. As was the case in the IN(NTD-CCD) crystal structure, there are multiple ways to connect the NTDs to the CCDs in models 3 and 4. In models 1 and 2, however, the domain connectivity is unambiguous, but the complex is distinctly asymmetric with respect to the NTD arrangement.

The differences between models 1 and 2 and between models 3 and 4 involve the location of the bound IBDs. In models 1 and 3, each IBD interacts with one NTD and one CCD of IN, as observed in the IN(NTD-CCD)·LEDGF(IBD) structure (26). In models 2 and 4, the IBD is moved to the alternative location on the CCD dimer, where it binds in the absence of NTD interactions. We attempted to construct models in which both the NTD and the IBD were moved to the alternative surface, but the resulting structures were rejected because distance constraints prevented connection of all four NTDs to a nearby CCD. Models 1 and 3 therefore have IBDs bound in high affinity sites, the most likely arrangement in a 4:2 IN·IBD complex. Models 2 and 4 have IBDs bound at low affinity sites, which as discussed later are likely to be occupied when in complex with the longer LEDGF(Cterm) construct.

To determine whether one or more of the models shown in Fig. 4A is consistent with the SAXS data for the IN(tetra)·LEDGF(IBD) complex, we computed the expected hydrodynamic properties and scattering profiles for each model and compared them with the experimental data (Table 4). Theoretical scattering data for the models agreed reasonably well with the observed I(q) curves (χ² of 2.10, 2.33, 2.08, and 4.41, for models 1–4, respectively, see supplemental Fig. 3). As expected from the ellipsoidal shape of the reconstructed envelopes, the calculated molecular dimensions of model 1 showed the best overall agreement with the parameters derived from SAXS. The most discriminating comparison comes from a P(r) curve analysis (Fig. 4B). Of the four models, the calculated P(r) for model 1 showed the best correlation with the experimental shape function.

To compare more directly the models to the SAXS-derived molecular shape, each of the four candidate models was optimally docked as rigid bodies into the experimental envelope (Fig. 4C). Of the four models, only model 1 (correlation coefficient (cc) = 0.76) provided a solution that properly accounts for the particle volume, with all structural domains contained within the envelope. Despite being derived from the same IN tetramer, model 2 (cc = 0.67) fails to account for the longest dimension of the particle due to the alternative placement of the IBDs, which protrude out of the envelope. Models 3 and 4 (cc = 0.55 and 0.67, respectively) have a more compact, oblate ellipsoidal character in the core tetramer and lead to substantially poorer agreement with the molecular envelope.

Within the constraints of the relatively simple modeling performed here, we conclude that the IN tetramer represented by model 1 best accounts for the experimental solution scattering data. It is important to note, however, that models can be readily scored as unlikely based on their overall three-dimensional shapes, but it is difficult to conclude that any given model is correct based on agreement with the SAXS data alone. Alternative models with similar elongated shapes as that shown for model 1 may also exist.

We next examined complexes containing the LEDGF “Cterm” fragment, which includes the entire C-terminal domain of LEDGF and is therefore larger than the IBD construct by an additional 80 amino acids (Fig. 1A). When we examined complexes containing full-length IN (both wild-type and the tetra mutant) bound to the longer LEDGF(Cterm) construct, we obtained a surprising result. The IN dimer-tetramer equilibrium strongly favors tetramer formation (i.e. the K_d is lower) and the IN:LEDGF stoichiometry is 4:4 (Tables 2 and 3). The additional sequences flanking the IBD in the LEDGF(Cterm) construct apparently enhance binding to IN, allowing all four LEDGF-binding sites in the tetramer to be stably occupied. A comparison of the SV and SEC profiles for these complexes is shown in Fig. 1, C and D. The IN(tetra)·LEDGF(Cterm) complex is exceptionally well behaved, with no evidence for formation of higher order species or aggregates.

The hydrodynamic properties of LEDGF(Cterm) alone indicate that LEDGF(Cterm) exists as a monomeric elongated particle in solution (Tables 2 and 3). The regions flanking the IBD in the LEDGF(Cterm) construct have eluded direct structural analysis (23) and are predicted to be unstructured. Our ability to model the IN(tetra)·LEDGF(Cterm) envelope is therefore limited by the lack of structural information for these additional regions. Nonetheless, we decided to analyze the IN(tetra)-LEDGF(Cterm) tetramer by SAXS. Not only is this complex likely to be more representative of the LEDGF·IN complexes that form in vivo, but a comparison of the molecular shape to that obtained for the IN·LEDGF(IBD) complex could provide information about the location of the additional LEDGF sequences present in the longer construct. Because this complex forms a stable tetramer at micromolar concentrations, we were able to perform the SAXS experiments under conditions where only tetramers exist in solution.

As shown in Fig. 5B and supplemental Table 1, both R_g and D_max values are significantly larger for IN(tetra)· LEDGF(Cterm) than for the same IN tetramer with two bound IBDs. Shape reconstruction using DAMMIF yielded prolate ellipsoids similar to those obtained with IN(tetra)· LEDGF(IBD), but with a larger dimension along the longest axis (223 versus 147 Å). The NSDs of the reconstructions are small (∼0.6), indicating a tight clustering of nearly identical shapes (supplemental Fig. 4). Similar results were obtained with IN(F185H)·LEDGF(Cterm) (data not shown).

A difference envelope generated from the IN(tetra)· LEDGF(IBD) and IN(tetra)·LEDGF(Cterm) shapes computed by DAMMIF at similar nominal resolutions (Q_max = 0.25) is shown in Fig. 5C. This envelope shows regions of protein present in the IN(tetra)·LEDGF(Cterm) structure that are not present in IN(tetra)·LEDGF(IBD). We assume that these difference densities correspond primarily to the two additional molecules of bound LEDGF and the additional residues flanking the LEDGF(IBD). Based on this result, we can infer the locations of the four bound LEDGF molecules.

To construct a model for the IN(tetra)·LEDGF(Cterm) tetramer, we added two additional IBDs to model 1, creating a composite of models 1 and 2. The new IBDs were placed in the “low affinity” sites that do not include binding contributions from an adjacent NTD. Because the sequences flanking the IBDs are missing in this model, the protein inventory is not complete, but the model does serve to identify a plausible arrangement of domains in a 4:4 complex. We then docked the 4:4 IN·IBD model into the IN(tetra)·IBD envelope that we had determined for the 4:2 complex (Fig. 5C). As expected from consideration of model 2, the additional IBDs project out of the envelope. When we superimposed the difference density envelope, we found two distinct lobes of density located at opposite ends of the envelope, adjacent to the high affinity IBDs. Thus, the extension of the maximal dimension of the 4:4 particle as a result of increasing the size of the LEDGF construct can be readily understood in terms of adding additional residues to the IBDs, based on the domain arrangement in model 1. Two additional patches of difference density are located near the central region of the envelope. These regions correspond to the second pair of IBDs that were placed in the lower affinity sites of model 1.