Solution NMR Structure of the Barrier-to-Autointegration Factor-Emerin Complex*

The barrier-to-autointegration factor BAF binds to the LEM domain (EmLEM) of the nuclear envelope protein emerin and plays an essential role in the nuclear architecture of metazoan cells. In addition, the BAF2 dimer bridges and compacts double-stranded DNA nonspecifically via two symmetry-related DNA binding sites. In this article we present biophysical and structural studies on a complex of BAF2 and EmLEM. Light scattering, analytical ultracentrifugation, and NMR indicate a stoichiometry of one molecule of EmLEM bound per BAF2 dimer. The equilibrium dissociation constant (Kd) for the interaction of the BAF2 dimer and EmLEM, determined by isothermal titration calorimetry, is 0.59 ± 0.03 μm. Z-exchange spectroscopy between corresponding cross-peaks of the magnetically non-equivalent subunits of the BAF2 dimer in the complex yields a dissociation rate constant of 78 ± 2s-1. The solution NMR structure of the BAF2-EmLEM complex reveals that the LEM and DNA binding sites on BAF2 are non-overlapping and that both subunits of the BAF2 dimer contribute approximately equally to the EmLEM binding site. The relevance of the implications of the structural and biophysical data on the complex in the context of the interaction between the BAF2 dimer and EmLEM at the nuclear envelope is discussed.

the LEM (LAP2, Emerin, MAN1) family of nuclear proteins, and its loss is associated with the X-linked recessive form of Emery-Dreifuss muscular dystrophy (6). Emerin is a multidomain protein comprising an N-terminal globular LEM domain (Em LEM ) of ϳ50 residues (7), followed by two polyserine segments separated by a hydrophobic nuclear localization signal, and a C-terminal transmembrane region. Em LEM comprises three helices (8) and is very similar in structure to the LEM domain of the related nuclear envelope protein LAP2 (9). BAF binds to Em LEM (as well as to the LEM domain of LAP2; Ref. 9) and is required for assembly of emerin at the nuclear envelope (10). BAF prevents autointegration of Moloney murine leukemia virus pre-integration complexes in vitro (1), and BAF and emerin have been reported to promote engagement of the HIV-1 pre-integration complex with chromatin prior to integration (11). To further our understanding of the interaction between BAF and the LEM domain of emerin we have characterized the stoichiometry of the complex by NMR, light scattering, and analytical ultracentrifugation; determined the equilibrium constant by isothermal titration calorimetry (ITC) and the dissociation rate constant by z-exchange spectroscopy; and solved the three-dimensional structure of the complex in solution by multidimensional heteronuclear NMR spectroscopy.

EXPERIMENTAL PROCEDURES
Protein Expression and Purification-The LEM domain (residues 1-47) of human emerin (7), Em LEM , was subcloned into a modified pET-32a vector (12) to form a thioredoxin fusion protein with a His 6 tag and expressed in Escherichia coli strain BL21(DE3) (Novagen, La Jolla, CA). The construct was verified by DNA sequencing. E. coli transformed with the Em LEM vector was grown on either Luria Bertini or minimal medium (with 15 NH 4 Cl and 13 C 6 -glucose as the nitrogen and carbon sources, respectively), induced with 1 mM isopropyl D-thiogalactopyranoside at A 600 ϳ 0.8, and harvested by centrifugation 3 h following induction. After harvesting, the cell pellet was resuspended in 50 ml (per liter of culture) of 50 mM Tris, pH 7.4, 100 mM NaCl, 10 mM imidazole, and 1 mM phenylmethylsulfonyl fluoride. The suspension was lysed by three passages through a microfluidizer and centrifuged at 10,000 ϫ g for 20 min. The supernatant fraction was loaded onto a HisTrap HP column (5 ml; Amersham Biosciences), and the fusion protein was eluted with a 100-ml gradient of imidazole (25-500 mM). The fusion protein was then dialyzed against 20 mM Tris, pH 8.0, and 200 mM NaCl, and digested with thrombin (10 NIH units/mg of protein). Thrombin was removed by passage over a benzami-dine-Sepharose column (1 ml; Amersham Biosciences), followed by the addition of 1 mM phenylmethylsulfonyl fluoride. The cleaved His 6 -thioredoxin was removed by loading the digested proteins over a HisTrap HP column. Em LEM was further purified by a Sephadex-75 gel filtration column (Amersham Biosciences) equilibrated with 50 mM potassium phosphate, pH 6.5, and 0.01% (w/v) sodium azide. This buffer was used for NMR studies on free Em LEM .
Light Scattering-Static light scattering data were obtained using an analytical Superdex-75 column (1.0 ϫ 30 cm; GE Healthcare) with in-line multiangle light scattering (DAWN EOS, Wyatt Technology, Inc., Santa Barbara, CA) and refractive index detectors (OPTILAB DSP, Wyatt Technology Inc.). 145 g of BAF 2 dimer mixed with or without Em LEM in 125 l of 50 mM potassium phosphate, pH 6.5, 200 mM NaCl was applied to the pre-equilibrated Superdex-75 column (1 ϫ 30 cm; GE Healthcare) at a flow rate of 0.5 ml/min at room temperature and eluted in the same buffer.
Analytical Ultracentrifugation-Protein stocks purified in 50 mM potassium phosphate, pH 6.5, 200 mM NaCl, and 5 mM 2-mercaptoethanol were used to prepare the samples for sedimentation equilibrium experiments. Samples of the purified complex (eluted in a single peak by gel filtration chromatography) were studied at a loading concentration of 12 M. Different stoichiometric BAF 2 dimer to Em LEM mixtures were prepared at 3:1, 2:1, 1:1, 1:2, and 1:3 ratios and nominal BAF 2 concentrations of 20 M. The 2:1, 1:1, and 1:2 mixtures were also studied at nominal BAF 2 concentrations of 13 M. All samples were kept at 4°C and loaded into pre-chilled cells.
Sedimentation equilibrium experiments were conducted at 4°C on a Beckman Optima XL-A analytical ultracentrifuge. Samples of the complex and various BAF 2 /Em LEM mixtures were studied at rotor speeds of 16,000, 20,000, 24,000, and 28,000 rpm. Data were acquired using 6-hole cells as an average of 4 absorbance measurements at 280 nm and a radial spacing of 0.001 cm. Sedimentation equilibrium was achieved within 48 h. Data collected at different speeds and different loading concentrations were analyzed globally in terms of various species analysis models using SEDPHAT 4.1b (13) to obtain the buoyant molecular mass M(1 Ϫ v). A solution density of 1.01310 cm 3 /g was measured at 20°C on a Mettler-Toledo DE51 density meter and corrected to a value of 1.0149 cm 3 /g at 4°C, which is the value used experimentally. Partial specific volumes (v) for BAF and Em LEM (at 4°C) were calculated based on the amino acid composition using SEDNTERP: the values are 0.7287 and 0.7184 cm 3 /g, respectively.
Isothermal Titration Calorimetry-ITC was performed using a high-precision VP-ITC calorimetry system (Microcal Inc.). BAF 2 dimer and Em LEM were dialyzed against degassed 25 mM Tris-HCl buffer, pH 6.5, and 0.2 M NaCl prior to the experi-ment. BAF 2 dimer (31 M) in the calorimetric cell at 30°C was titrated with Em LEM (at a concentration of 854 M in the injection syringe). Analysis of the data were performed using the Origin software provided with the instrument.
NMR Spectroscopy-Spectra were recorded at 30°C on Bruker DMX500, DRX600, DRX750, and DRX800 spectrometers. Spectra were processed using the program NMRPipe (15), and analyzed using the programs PIPP, CAPP, and STAPP (16). Sequential assignment of 1 H, 15 N, and 13 C resonances was achieved by means of through-bond heteronuclear scalar correlations along the protein backbone and side chains (17,18) using three-dimensional HNCOCACB, HNCACB, (H)C(CO)NH TOCSY, H(CCO)NH-TOCSY, and CCH-COSY experiments. Interproton distance restraints were derived from three-dimensional 15 N-and 13 C-separated NOE experiments. Stereospecific assignments of valine and leucine methyl groups were obtained from a 1 H-13 C HSQC correlation spectrum recorded on 10% 13 C-labeled protein (19). Side chain rotamers were derived from 3 J NCЈ (aromatic, methyl, and methylene) and 3 J CC (aromatic, methyl, and methylene) scalar couplings measured by quantitative J correlation spectroscopy (20), in combination with data from a short mixing time (40 ms) three-dimensional 13 C-separated NOE spectrum recorded in H 2 O (21). Intermolecular interproton distance restraints were derived from three-dimensional 12 C-filtered/ 13 C-separated NOE experiments recorded on complexes comprising either U-15 N/ 13 C or U-15 N/ 13 C/ 2 H/ [methyl-1 H]Val/Leu/Ile BAF 2 dimer complexed to unlabeled Em LEM , or U-15 N/ 13 C-labeled Em LEM complexed to unlabeled BAF 2 dimer. Residual dipolar couplings (RDCs) were measured by taking the difference in J couplings between aligned (ϳ15 and ϳ11 mg/ml phage pf1 (22) for free Em LEM and the BAF 2 -EM LEM complex, respectively) and isotropic media using well established procedures (23). For free Em LEM , 1 D NH , 1 D NCЈ , and 2 D HNCЈ RDCs were obtained. For the BAF 2 -Em LEM complex 1 D NH RDCs were measured on complexes of 15 N/ 13 C-labeled BAF 2 dimer and unlabeled Em LEM , and 15 N/ 13 C-labeled Em LEM and unlabeled BAF 2 dimer (note only 1 D NH RDCs are required for the structure determination of the complex because the backbones of the two proteins are treated as rigid bodies, see below; Ref. 24). The magnitudes of the axial (D a NH ) and rhombic () components of the alignment tensor for free Em LEM were obtained from a histogram of the distribution of the normalized RDCs (25). For the complex, D a NH and were obtained by singular value decomposition using the coordinates of the free proteins (23).
Z-exchange spectroscopy was carried out using the pulse sequence described previously (26,27) using U-15 N/ 13 C/ 2 H/ [methyl-1 H]Val/Leu/Ile-labeled BAF 2 in the presence of 2, 3, and 4 eq of unlabeled Em LEM . The auto-and exchange-peak intensities as a function of mixing time were fitted by numerically integrating the appropriate McConnell (28) differential equations and optimizing the unknown parameters (dissociation rate constant, spin-lattice relaxation rate, and scale factors) using the program FACSIMILE (29), as described previously (27,30).
Structure Calculations-Interproton distance restraints were derived from the NOE spectra and classified into generous approximate distance ranges corresponding to strong, medium, weak, and very weak NOE cross-peak intensities (21).
Nonstereospecifically assigned methyl, methylene, and aromatic protons and ambiguous intermolecular NOEs were represented by a (⌺r Ϫ6 ) Ϫ1/6 sum (31). / torsion angle restraints for free Em LEM were derived from backbone (N, CЈ, C␣, C␤, H␣) chemical shifts using the program TALOS (32). Side chain torsion angle restraints were derived from 3 J heteronuclear couplings and short mixing time NOE experiments using standard procedures (21). The minimum range for the torsion angle restraints was Ϯ20°.
All structure calculations were carried out using Xplor-NIH (33,34) and the IVM (35) module for torsion angle and rigid body dynamics. The structure of the free Em LEM domain was calculated by simulated annealing in torsion angle space (35). The structure determination of the BAF 2 -Em LEM complex was carried out using conjoined rigid body/torsion angle dynamics (24,35). The target function for simulated annealing comprises: square-well potentials for interproton distance and torsion angle restraints (36), harmonic potentials for 13 C␣/ 13 C␤ chemical shift restraints (37), RDC restraints (38), and covalent geometry; and a quartic van der Waals repulsion potential (39), a multidimensional torsion angle data base potential of mean force (40), a backbone hydrogen bonding data base potential of mean force (41), and a radius of gyration term (42) to represent the non-bonded contacts. The radius of gyration term represents a weak overall packing potential and the target value is given by 2.2N 0.38 , where N is the overall number of residues (42).
Structures were displayed using the VMD-XPLOR software (43). Reweighted atomic probability density maps used to represent the conformational space sampled by the interfacial side chains within the complex were calculated and displayed as described previously (44).

RESULTS AND DISCUSSION
Structure Determination of the Free Em LEM Domain-The structure of the free Em LEM domain was determined on the basis of 820 experimental NMR restraints, including 110 backbone RDCs. A summary of the structural statistics is provided in Table 1, a stereoview of the superposition of the ensemble of 180 simulated annealing structures is shown in Fig. 1A, and a ribbon diagram is provided in Fig. 1B. The structure comprises a 3-10 helix (residues 2-6) and two ␣-helices (residues 9 -19 and 28 -46) oriented at an angle of 43°to one another. The structure of Em LEM is very similar to our previously published structure of the BAF binding LEM domain of LAP2 (9) with a C␣ atomic r.m.s. difference of 1.3 Å for 44 atoms (residues 2-46 of Em LEM and 111-154 of LAP2; percentage sequence identity of 36%). The C␣ atomic r.m.s. difference between the current Em LEM structure and the NMR structure previously published by Wolff et al. (8) is 2.4 Å for residues 2-46 and 1.5 Å for residues 3-44. Although the fold and topology of the two Em LEM structures are obviously the same, there are clearly differences in detail, which are significant when one wants to use the coordinates of the free Em LEM domain to solve the structure of the BAF 2 -EM Lem complex using conjoined rigid body/torsion angle dynamics. In this regard, we note that the agreement of the Em LEM coordinates of Wolff et al. (8) with the 1 D NH RDCs measured for Em LEM both free and bound to the BAF 2 dimer is rather poor with RDC R-factors (46) of 49 and 61%, respectively, determined by singular value decomposition. In contrast, the present structure of the Em LEM domains agrees extremely well with the 1 D NH RDCs measured on the BAF 2 -Em LEM complex with an RDC R-factor of 14.8%. The latter value is comparable with the value one would expect for a 1.5-2-Å resolution crystal structure (23,47,48) (Note that the overall orientation of the alignment tensors of free Em LEM and the BAF 2 -EM LEM complex differ by 128°; hence the RDCs measured for Em LEM in the BAF 2 -Em LEM complex provide a good cross-validation measure of the quality of the coordinates of free Em LEM .) Stoichiometry of the BAF 2 -EM LEM Complex by NMR-The BAF 2 -Em LEM complex is in slow exchange on the chemical shift scale and portions of the 1 H-15 N HSQC spectra recorded as a function of various ratios of Em LEM to BAF 2 dimer are shown in Fig. 2A. The binding of Em LEM to the BAF 2 dimer disrupts the symmetry of the dimer such that the chemical shifts of many equivalent residues of the two subunits (about 55% of the 1 H-15 N cross-peaks for BAF) are no longer identical in the com- a There are 460 interproton distance restraints comprising 9 intra-residue restraints, and 160 Ͻ ͉i Ϫ j͉ ϭ 1 sequential, 189 Ͻ 1 ͉i Ϫ j͉ Յ 5 medium range and 102 ͉i Ϫ j͉ Ͼ 5 long range inter-residue restraints. In addition there are 58 distance restraints for 29 backbone hydrogen bonds that were added during the final stages of refinement. b The torsion angle restraints comprise 46 , 45 , 32 1 , and 6 2 angles. c The RDC R-factor, which scales between 0 and 100%, is defined as the ratio of the r.m.s. deviation between observed and calculated values to the expected r.m.s. deviation if the vectors were randomly distributed, given by ͓2D a 2 (4 ϩ 3 2 )/5͔ 1/2 , where D a is the magnitude of the principal component of the alignment tensor and the rhombicity (46). The value of D a NH and , derived from the distribution of normalized RDCs (25), are 13.2 Hz and 0.60 Hz, respectively. d Calculated with the program PROCHECK (45). The dihedral angle G factors for /, 1 / 2 , 1 , and 3 / 4 are 0.64 Ϯ 0.04, 0.39 Ϯ 0.12, 0.21 Ϯ 0.15, and 0.10 Ϯ 0.21, respectively. The WHATIF second generation packing score is 1.83; a value greater than 0 is considered to represent a high quality structure (14). e The precision of the coordinates is defined as the average atomic r.m.s. difference between the individual 180 simulated annealing structures and the corresponding mean coordinates best-fitted to the backbone atoms of residues 2-46. (Residues 1 and 47 at the N and C termini, respectively, are disordered.) plex. Under the conditions of the NMR experiment (concentration of BAF 2 dimer of ϳ130 M), binding of Em LEM is stoichiometric with one molecule of Em LEM bound per BAF 2 dimer (Fig. 2B). Increasing the ratio of Em LEM to BAF 2 dimer above 1:1 results in no change in the intensity of the bound BAF 2 cross-peaks (Fig. 2, A and B).
Because a single molecule of Em LEM binds to the BAF 2 dimer, the chemical environments of the two subunits of BAF 2 are necessarily no longer identical. The backbone of the two subunits of BAF 2 , however, remains identical within coordinate errors as judged from RDC measurements (i.e. the values of the 1 D NH RDCs for the two subunits of BAF 2 are identical in the complex). It should also be noted that if two molecules of Em LEM bound the BAF 2 dimer symmetrically, the chemical environment and hence the chemical shifts of the two subunits of BAF 2 would be identical in the complex.

Stoichiometry of the BAF 2 -EM LEM
Complex by Light Scattering-The calculated molecular mass of the BAF 2 dimer and the EM LEM domains are 20,116 and 5,572 Da, respectively. The BAF 2 dimer elutes as a single peak with a molecular mass of 21.3 Ϯ 0.2 kDa determined from light scattering and the refractive index data (Fig. 3A). A 1:1 mixture of BAF 2 dimer and Em LEM results in a shift of the BAF 2 peak to a lower retention volume with a molecular mass of 25.9 Ϯ 0.2 kDa (Fig. 3B). Increasing the ratio of Em LEM to BAF 2 does not change the position of the latter peak and the molecular mass obtained at a ratio of BAF 2 dimer to Em LEM of 1:2, 1:3, and 1:4 is 24.7 Ϯ 0.2, 24.8 Ϯ 0.2, and 27.4 Ϯ 0.2 kDa, respectively. The peak eluting at ϳ15.4 ml with a molecular mass of 6.48 Ϯ 0.02, 6.45 Ϯ 0.01, and 6.76 Ϯ 0.01 kDa shown in Fig. 3, C-E, respectively, corresponds to free Em LEM . These results clearly indicate that the BAF 2 -Em LEM complex comprises one BAF 2 dimer and one molecule of Em LEM . The concentration of complex upon elution is ϳ12 M. The observation that the position of the peak corresponding to the complex does not change upon increasing concentration of Em LEM indicates that the equilibrium dissociation constant for the complex is Յ1 M.
Stoichiometry of the BAF 2 -EM LEM Complex by Analytical Ultracentrifugation-Sedimentation equilibrium experiments on the BAF 2 -Em LEM complex purified by size-exclusion gel filtration chromatography were carried out at rotor speeds of 16,000 to 28,000 rpm and analyzed in terms of a single ideal solute. Excellent data fits were obtained (Fig. 4) returning a molecular mass of 26.8 Ϯ 0.4 kDa. Based on the amino acid sequence and solution density, the BAF 2 dimer and Em LEM monomer have calculated molecular masses of 20,116 and 5,572 Da, respectively, indicating that the complex has a 2:1 BAF:Em LEM stoichiometry (n ϭ 1.04 Ϯ 0.02): that is one molecule of Em LEM for two subunits of BAF monomer. To confirm the stoichiometry of the complex, sedimentation equilibrium experiments were carried out on a 1:1 loading mixture of BAF 2 dimer and Em LEM at concentrations of 13 and 20 M BAF 2 dimer. A global data analysis in terms of a single ideal solute returned excellent fits with an experimental molecular mass of 25.8 Ϯ 0.3 kDa (Fig. 4), confirming the formation of a 2:1 BAF: Em LEM complex (n ϭ 1.00 Ϯ 0.01). To show that these species only form a 2:1 BAF:Em LEM complex, various BAF 2 dimer and Em LEM mixtures were studied. In the presence of excess BAF 2 , namely the 3:1 and 2:1 BAF 2 :Em LEM loading ratios, free BAF 2 dimer (molecular mass of 20,116 Da) and the 2:1 BAF:Em LEM complex (molecular mass of 25,688 Da) are the only species expected. As the molecular masses are too similar to distinguish by sedimentation equilibrium, a mixture of these two species represents a so-called paucidisperse system and an analysis in terms of a single ideal solute should return a weight average molecular mass. The 3:1 BAF 2 dimer to Em LEM loading mixture returns a weight average molecular mass of 22.2 Ϯ 0.2 kDa with excellent data fits (data not shown), consistent with the formation of the 2:1 BAF-Em LEM complex. Such a loading mixture is expected to return a weight average molecular mass of 22,147 Da if the 2:1 BAF-Em LEM complex were formed. If the BAF-Em LEM complex had a 2:2 stoichiometry (i.e. one Em LEM molecule per BAF subunit), a weight average molecular mass of 24,334 Da would be expected. Data collected for the 2:1 BAF 2 /Em LEM loading mixture were also consistent with a 2:1 BAF-Em LEM complex stoichiometry, within the error of the method.
Sedimentation equilibrium experiments carried out in the presence of excess Em LEM , namely 1:2 and 1:3 BAF 2 dimer to Em LEM mixtures, could not be modeled adequately in terms of a single ideal solute. Accordingly, data were analyzed in terms of two ideal solutes, of which one represents the free Em LEM domain. Fixing the molecular mass of the smaller species to 5,572 Da, a 1:2 BAF 2 dimer to Em LEM mixture returns a molecular mass of 27.0 Ϯ 0.95 kDa for the second species with excellent data fits (data not shown). These data are consistent with the sole formation of a 2:1 BAF-Em LEM complex (n ϭ 1.05 Ϯ 0.04). A 1:3 BAF 2 dimer to Em LEM mixture containing 18.4 M BAF 2 dimer and 55.2 M Em LEM returns a molecular mass of 29.2 Ϯ 1.5 kDa (n ϭ 1.14 Ϯ 0.06) (data not shown). Thus the stoichiometry of the BAF 2 -Em LEM complex, comprising one molecule of Em LEM bound per BAF 2 dimer, is unambiguously confirmed by three independent techniques covering a range of concentrations and molar ratios.
Equilibrium and Kinetic Characteristics of the BAF 2 -EM LEM Complex-ITC was used to determine the equilibrium and thermodynamic properties of the interaction of Em LEM with the BAF 2 dimer. The experimental ITC binding curve obtained upon addition of Em LEM to a 31 M solution of BAF 2 dimer is shown in Fig. 5A. A best-fit to the experimental ITC data with a stoichiometry of one Em LEM molecule bound per BAF 2 dimer yields an equilibrium dissociation constant (K d ) of 0.59 Ϯ 0.03 M, corresponding to a binding free energy (⌬G) of Ϫ8.63 Ϯ 0.03 kcal mol Ϫ1 , and an enthalpy (⌬H) of Ϫ5.70 Ϯ 0.05 kcal mol Ϫ1 . Thus, the interaction of Em LEM with BAF 2 is entropically favored with ⌬S ϭ 9.7 cal mol Ϫ1 K Ϫ1 , where ⌬S ϭ (⌬H Ϫ ⌬G)/T, and T is the temperature in Kelvin. The increase in entropy upon complex formation arises from the hydrophobic effect (49) as a consequence of the displacement of ordered water at the binding interfaces of the two proteins, and suggests that the interaction between Em LEM and BAF 2 is predominantly stabilized by hydrophobic interactions.
The kinetics of the interaction of unlabeled Em LEM and U-15 N/ 13 C/ 2 H/[methyl-1 H]Val/Leu/Ile BAF 2 were studied by z-exchange spectroscopy (26,27), which revealed the presence of chemical exchange cross-peaks between the two sets of shifts for the BAF 2 dimer in the BAF 2 -Em LEM complex (Fig. 5B). This arises from the fact that Em LEM can bind to the BAF 2 dimer in two chemically equivalent ways related by a 180°rotation about the C 2 symmetry axis of the BAF 2 dimer (Fig. 6). Thus crosspeaks corresponding to the two magnetically inequivalent subunits of BAF 2 in the complex are simply interchanged in the two bound states. The exchange process occurs via dissociation followed by reassociation (and note both orientations are equally probable because the two possible complexes are chemically equivalent) (Fig. 5C). The McConnell (28) differential equations describing the evolution of magnetization as a function of mixing time for the scheme shown in Fig. 5C are as follows, where M F is the magnetization of free BAF 2 , and M B and M BЈ are the magnetizations for the two species of BAF 2 in the complex related by the 180°rotation of bound Em LEM ; k on and k off are the association and dissociation rate constants, respectively; F and B are the spin-lattice relaxation rates for BAF 2 in the free and bound states, respectively; [Em LEM ] free is the concentration of free Em LEM ; and k on [Em LEM ] free is a pseudo-first order rate constant because the concentration of free Em LEM is not perturbed during the experiment. The intensity of a given auto-peak and its associated exchange-peaks as a function of mixing time are obtained by numerical integration of Equations 1-3 with the magnetization of the species corresponding to the auto-peak set to 1 and the magnetization of the species corresponding to the exchange-peaks set to zero.  Sedimentation equilibrium profiles obtained for the purified BAF 2 -Em LEM complex (left) and a 1:1 BAF 2 /Em LEM mixture (right) shown in terms of A 280 versus the radius r for data collected at a loading concentration of 12 M complex (left) and 13 M BAF 2 (right). Data were collected at 4°C and 16,000 (green), 20,000 (blue), 24,000 (yellow), and 28,000 (red) rpm. For clarity, alternate data points have been omitted. In both cases data were analyzed in terms of a single ideal solute to return a molecular mass consistent with that of a 2:1 BAF-Em LEM complex (i.e. one molecule of Em LEM per BAF 2 dimer). Best single ideal solute fits are shown as black lines through the experimental points. The corresponding distributions of the residuals are shown in the plots above. The data set shown for the 1:1 mixture was analyzed globally along with a similar sample having 20 M BAF 2 dimer. Z-exchange experiments were carried out at three different concentrations of free Em LEM , 0.39, 0.68, and 0.89 mM. The evolution of the intensities of the normalized auto-and exchange-peaks as a function of mixing time was found to be concentration independent (Fig.  5D). This is as expected because k on ⅐[Em LEM ] free Ͼ Ͼ k off , so that the apparent rate of interconversion between the magnetizations M B and M BЈ is k off /2 in each direction. Note also that the calculated maximum magnetization of the exchangepeak for M F is less than 10 Ϫ3 , and hence no exchange-peak corresponding to free BAF 2 is observed. Simultaneous best-fitting of the time courses of the intensities of the auto-and exchange-peaks (Fig. 5D) yields a value of k off ϭ 78 Ϯ 2 s Ϫ1 . Given the value of K d determined by ITC, the association rate constant (k on ) is calculated to be ϳ1.3 ϫ 10 8 M Ϫ1 s Ϫ1 , typical of a diffusion-controlled protein-protein association reaction (50).
It should be noted that the exchange process observed by z-exchange spectroscopy is a phenomenon that can only be observed by NMR and is of no functional significance because the two binding orientations are chemically equivalent and therefore functionally identical. (It is, of course, of biophysical significance because it enables one to determine the value of the dissociation rate constant.) The existence of the exchange process does, however, have implications for the NMR structure determination of the complex. In particular, all intermolecular NOEs must be treated as ambiguous (⌺r Ϫ6 ) Ϫ1/6 sums (31) because no distinction can be made a priori as to which BAF subunit is involved in a given intermolecular NOE. This situation is exactly analogous to the situation that pertains to the ␦ and ⑀ protons of Phe and Tyr residues undergoing 180°ring flips. It should also be noted that because of chemical exchange between the two binding orientations (related by a 180°r otation), an NOE cross-peak from a residue of Em LEM to a residue on The best-fit curve to a one site binding equilibrium is shown as a solid line and yields a value of K d ϭ 0.59 Ϯ 0.03 M. B, because one molecule of Em LEM binds to the BAF 2 dimer, the chemical environments of equivalent residues from the two subunits of BAF are no longer identical and display different chemical shifts, as illustrated for Gly 47 . Z-exchange spectroscopy reveals the presence of exchange cross-peaks (indicated by ex) between equivalent residues in addition to the auto-peaks (labeled as G47 and g47Ј). This arises from the fact that Em LEM can bind to the BAF 2 dimer in two chemically equivalent ways related by a 180°rotation (see Fig. 6). C, kinetic scheme describing the magnetization transfer involving dissociation and reassociation of Em LEM to BAF 2 in two chemically equivalent orientations. Cross-peaks corresponding to the two magnetically inequivalent subunits of BAF 2 in the complex are simply interchanged in the two bound states. M F is the magnetization of free BAF 2 ; M B and M BЈ are the magnetizations of the two bound states of BAF 2 related by the 180°rotation of Em LEM ; k on and k off are the association and dissociation rate constants, and [Em LEM ] F is the concentration of free Em LEM ; F and B are the spin-lattice relaxation rates for free and bound BAF 2 and for simplicity are considered equal because F cannot be determined from the present data. one subunit of BAF will be transferred by chemical exchange to the corresponding residue on the other BAF subunit. This is clearly evident in some of the strips taken from a three-dimensional 12 C-filtered/ 13 C-separated NOE spectrum shown in Fig.  5E.
Structure Determination of the BAF 2 -Em LEM Complex-The structure of the BAF 2 -Em LEM complex was solved by conjoined rigid body/torsion angle dynamics (24,35) on the basis of 308 experimental NMR restraints including 140 backbone 1 D NH RDCs that yield precise and accurate orientational restraints related to the relative positions of BAF 2 and Em LEM within the complex, and 31 intermolecular interproton distance restraints derived from three-dimensional 12 C-filtered/ 13 C-separated NOE spectroscopy that provide translational, as well as orientational, information. In these calculations the backbone and non-interfacial side chains for the two proteins are treated as rigid bodies, whereas the interfacial side chains are given full torsional degrees of freedom (24,35): the backbone of the BAF 2 dimer is held fixed, Em LEM is free to rotate and translate, and the single RDC alignment tensor is free to rotate.   ͉i Ϫ j͉ ϭ 1 sequential, 13 1 Ͻ ͉i Ϫ j͉ Յ 5 medium range and 4 ͉i Ϫ j͉ Ͼ 5 long range inter-residue), and 61 intramolecular distances related to the interfacial side-chains of Em LEM (3 intra-residue, and 22 sequential, 29 medium range and 7 long range inter-residue). b The torsion angles comprise 13 ϫ 2 1 and 4 ϫ 2 2 for the BAF 2 dimer, and 11 1 and 1 2 for Em LEM . c The values of D a NH and are 10.4 and 0.5 Hz, respectively. Note that the RDR R-factors (46) reported in the table are obtained using a single alignment tensor for the complex. The RDC R-factors for BAF and Em LEM obtained by singular value decomposition to the coordinates of the two proteins individually (i.e. with independent alignment tensors for the two proteins) are 15.2 and 14.8%, respectively, with correlation coefficients of 0.97. d The intermolecular repulsion energy is given by the value of the quartic van der Waals repulsion term calculated with a force constant of 4 kcal mol Ϫ1 Å Ϫ4 and a van der Waals radius scale factor of 0.78. The intermolecular Lennard-Jones van der Waals interaction energy is calculated using the CHARMM19/20 parameters and is not included in the target function used to calculate the structures. The percentage of residues present in the most favorable region of the Ramachandran map for the NMR structure of free BAF is 89.5%. e Defined as the average r.m.s. difference between the final 180 conjoined rigid body/torsion angle dynamics simulated annealing structures and the mean coordinate positions.
The value quoted for the complete backbone provides only a measure of the precision with which the orientation and translation of the BAF 2 dimer and the Em LEM domain have been determined relative to each other and does not take into account the accuracy of the NMR coordinates of free BAF 2 and Em LEM . The excellent agreement of the RDCs measured on the complex with the coordinates of free BAF 2 and Em LEM , however, indicates good accuracy (23,47,48). 48). The RDC R-factors for BAF 2 and Em LEM in the refined complex (that is using a single alignment tensor for the whole complex) are the same as those obtained by singular value decomposition fitting to the coordinates of the two proteins individually. A table of structural statistics for the BAF 2 -Em LEM complex is provided in Table 2. A superposition of the backbone for an ensemble of 180 simulated annealing structures is shown in Fig. 7A, and reweighted atomic probability density maps for the interfacial side chains, derived from the ensemble, are shown in Fig. 7, B and C. The BAF-Emerin Interface-The interaction surface between the BAF 2 dimer and Em LEM is formed by a convex protrusion on Em LEM comprising helix ␣1, the subsequent loop, and the N-terminal end of ␣2; and a deep concave cleft on the BAF 2 dimer comprising the C-terminal end of ␣2, the subsequent hairpin turn and ␣3 of the red subunit of BAF, and the hairpin turn between ␣2 and ␣3, the C-terminal end of ␣3, and the central portion of ␣4 of the blue subunit of BAF (Fig. 8A). (For clarity we distinguish the two subunits of BAF by color coding.) There is no overlap between the single Em LEM binding site and the two symmetry related DNA binding sites on the BAF 2 dimer. The latter comprises the N terminus of ␣1, the 3-10 helix/turn/␣2 motif, and the N-terminal portion of ␣5. 969 Å 2 of accessible surface area are buried at the interface of which 462 Å 2 originates from BAF 2 and 507 Å 2 from Em LEM . The loop connecting helices ␣1 and ␣2 of Em LEM interact with the red subunit of BAF, whereas ␣1 and the following loop interact with the blue subunit. The binding surfaces on both BAF 2 and Em LEM consist of a central hydrophobic portion surrounded by a rim of polar and charged residues (Fig. 8B), typical of many protein-protein complexes (47). The key hydrophobic interactions involve Val 51 , Leu 52 , Leu 58 , val 51 , phe 39 , and gly 38 of BAF (where lowercase letters indicate residues from the blue subunit) and Leu 23 , Gly 24 , Phe 25 , and Val 26 of Em LEM (italics denote residues of Em LEM ). The preponderance of hydrophobic interactions at the interface and the displacement of ordered water from these hydrophobic surfaces upon binding accounts for the positive entropic change upon complex formation observed by ITC. Key electrostatic interactions occur between Arg 37 , Glu 61 , and Asp 65 of the red subunit of BAF and Asp 9 , Lys 38 , and Lys 36 , respectively, of Em LEM (Fig. 7B) and between glu 36 of the blue subunit of BAF and Arg 17 of Em LEM , and possibly the hydroxyl groups of Thr 10 and Thr 13 via water-mediated interactions as well (Fig. 6C). Additional electrostatic interactions include possible water bridged contacts between Gln 48 of the red subunit of BAF and the hydroxyl groups of Ser 29 and Thr 30 of Em LEM (Fig. 7B). Trp 62 of the red subunit of BAF is principally involved in hydrophobic contacts with Thr 30 and Leu 33 (Fig. 7B), and trp 62 of the blue subunit with Val 27 (Fig. 7C). The observed interactions between BAF and Em LEM are fully consistent with mutagenesis data that showed that the G24A/P25A/V26A/V27A, T30A/ FIGURE 7. Stereoviews of the NMR structure of the BAF 2 -Em LEM complex. A, superposition of the backbone (N, C␣, CЈ) atoms) of 180 simulated annealing structures (Em LEM , green, and the two subunits of the BAF 2 dimer shown in red and blue). Reweighted atomic probability density maps (drawn at a value of 25% maximum and calculated from the final 180 simulated annealing structures) for the interfacial side chains, illustrating the interactions between Em LEM (gray mesh) and the red (B) and blue (C) subunits of the BAF 2 dimer (red meshes). The backbone (with the same color scheme as in A) is represented by flat ribbons. The side chains of the restrained regularized mean coordinates are color coded according to atom type (carbon, gray; oxygen, red; and nitrogen, blue).
R31A, and Y34A/E35A/K36A/K37A mutations significantly reduce binding of emerin to BAF (52). (Note that a fourth emerin mutation that disrupts BAF binding, E11A/L12A (52), does not involve the interaction surface but is predicted to destabilize the Em LEM core through the introduction of a cavity as a consequence of the replacement of a leucine by the much smaller alanine side chain.) Modulation of the Interaction of BAF with LEM Domain Proteins-The structure of the BAF 2 -Em LEM complex reported here, together with the structure of BAF 2 in complex with DNA (5), places constraints on how the interaction of BAF with LEM domain proteins is regulated. BAF and LEM domain proteins function as part of large nucleoprotein networks; attempts to fish out interacting partners of BAF and LEM domain proteins by biochemical techniques yields numerous proteins, most of which presumably interact indirectly. 3 LAP2 was first identified as a BAF-interacting protein in a yeast two-hybrid screen, and deletion analysis mapped a region encompassing the LEM domain to be sufficient for this interaction (53). The structure of the BAF 2 -Em LEM complex establishes the basis of this interaction. In in vitro binding studies, the LAP2 constant region has a higher affinity for BAF bound to DNA than for BAF alone and this was taken as evidence for a conformational change in BAF upon DNA binding (54). It is now clear that no conformational changes in BAF occur upon binding either DNA or the LEM domain. Alternative explanations for the higher affinity of the LAP2 constant domain for BAF bound to DNA include the possible interaction of regions outside of the LEM domain with DNA or stabilization of the complex through binding of multiple units of BAF to DNA. Modulation of the BAF-LEM interaction by regions outside the LEM domain is also suggested by the different affinities of various LAP2 isoforms for BAF (54). In addition, studies of the behavior of fluorescently labeled BAF and emerin in cells also suggest modulation of the BAF-LEM interaction (55). A direct interaction between BAF and emerin at the nuclear envelope was demonstrated by FRET analysis. However, fluorescence recovery after photobleaching experiments showed that whereas BAF was highly mobile at the nuclear envelope, emerin was much less mobile. On the basis of these results a "touch and go" model was proposed in which BAF binds emerin frequently but transiently during interphase. This association of BAF and emerin agrees nicely with the transient interaction (k off ϳ 78 s Ϫ1 ) we observe by NMR between BAF and the LEM domain of emerin. In contrast, BAF associates much more stably with LEM domain proteins at the "core" region of telophase chromosomes (55). This stable interaction cannot be accounted for by the interaction of BAF with the LEM domain alone, which is transient, and additional protein factors are likely involved.
Concluding Remarks-The structures of the BAF 2 -Em LEM and BAF 2 -DNA 2 (5) complexes provides a structural basis for how BAF both bridges DNA and binds nuclear membrane proteins that contain the LEM domain. The BAF dimer is required for DNA bridging, but binding of the BAF dimer to a single LEM domain ensures that each BAF dimer 3 R. Craigie, unpublished data.  Fig. 7A) also illustrating the position of the two DNA duplexes observed in the crystal structure of the BAF 2 -DNA 2 complex (5). B, surface representations illustrating the binding surfaces involved in the BAF 2 -Em LEM complex. The binding surface on BAF 2 is shown on the left panel and on Em LEM on the right panel. The binding surfaces are color coded with hydrophobic residues in green, polar residues in light blue, positively charged residues in dark blue, and negatively charged residues in red. The relevant portions of the interacting partner are shown as gold tubes. The surface of the non-interacting residues of the BAF 2 dimer is shown in dark gray for the red subunit and light gray for the blue subunit (as depicted in A). Residues of the blue subunit of BAF 2 are labeled in lowercase, and residues of Em LEM in italics. The view in the right-hand panel is related to that in the left-hand panel by a 180°rotation about an axis parallel to the printed lines on the page.