Affinities between the Binding Partners of the HIV-1 Integrase Dimer-Lens Epithelium-derived Growth Factor (IN Dimer-LEDGF) Complex

The interaction between lens epithelium-derived growth factor/transcriptional co-activator p75 (LEDGF) and human immunodeficiency virus type 1 (HIV-1) integrase (IN) is essential for HIV-1 replication. Homogeneous time-resolved fluorescence resonance energy transfer assays were developed to characterize HIV-1 integrase dimerization and the interaction between LEDGF and IN dimers. Using these assays in an equilibrium end point dose-response format with mathematical modeling, we determined the dissociation constants of IN dimers (Kdimer = 67.8 pm) and of LEDGF from IN dimers (Kd = 10.9 nm). When used in a kinetic format, the assays allowed the determination of the on- and off-rate constants for these same interactions. Integrase dimerization had a kon of 0.1247 nm−1·min−1 and a koff of 0.0080 min−1 resulting in a Kdimer of 64.5 pm. LEDGF binding to IN dimers had a kon of 0.0285 nm−1·min−1 and a koff of 0.2340 min−1 resulting in a Kd of 8.2 nm. These binding assays can also be used in an equilibrium end point competition format. In this format, the IN catalytic core domain produced a Ki of 15.2 nm while competing for integrase dimerization, confirming the very tight interaction of IN with itself. In the same format, LEDGF produced a Ki value of 35 nm when competing for LEDGF binding to IN dimers. In summary, this study describes a methodology combining homogeneous time-resolved fluorescence resonance energy transfer and mathematical modeling to derive the affinities between IN monomers and between LEDGF and IN dimers. This study revealed the significantly tighter nature of the IN-IN dimer compared with the IN-LEDGF interaction.

Targeting the viral integration process with small molecules as a strategy to inhibit HIV-1 2 replication has recently yielded an important new class of antiviral drugs. One integrase strand transfer inhibitor (INSTI), raltegravir (MK-0518), has been approved by the Food and Drug Administration for treatment of HIV-1 infection, and a second drug, elvitegravir (GS-9137), is in late stage clinical development. Based on binding experiments (1) and molecular modeling (2), strand transfer inhibitors are thought to interact with a pocket in the active site of integrase that is formed after 3Ј-processing of the viral DNA ends. INSTIs thus prevent the integrase-viral DNA complex from engaging host target DNA. More recently, a second site on integrase that represents the binding site for the cellular cofactor LEDGF was demonstrated to be a viable and attractive target for antiviral drug discovery (3)(4)(5). A small molecule inhibitor targeting this second site may retain activity against viral mutants resistant to INSTIs and complement the antiviral activity of INSTIs, akin to non-nucleoside reverse transcriptase inhibitors with nucleoside reverse transcriptase inhibitors. Hence, compounds that interact with the LEDGF binding pocket on IN could be used in combination with INSTIs to decrease the likelihood of resistance emergence.
The cellular cofactor LEDGF has been identified as the dominant binding partner of HIV-1 integrase in human cells (6 -10). LEDGF interacts with integrase primarily through an ϳ80amino acid domain termed the integrase binding domain (IBD) (11). A solution structure of the IBD has been derived (12). In addition, several co-crystal structures involving IBD and IN domains have been solved and include the following: IBD bound to a dimer of HIV-1 integrase catalytic core domain (CCD), IBD bound to an HIV-2 two-domain integrase (N-terminal domain (NTD) and catalytic core domain), and IBD bound to a maedi-visna virus two-domain (NTD ϩ CCD) integrase (13)(14)(15). Several lines of evidence point to the requirement of LEDGF for HIV-1 replication as a viral cofactor as follows. 1) Mutations in integrase that preserve the catalytic activity of the enzyme but cause defects in viral replication also disrupt integrase interaction with LEDGF (16 -18). 2) Suppression of LEDGF expression mediated by small interfering RNA alters the choice of target sites for HIV integration (19) and inhibits HIV replication (20,21). 3) Mouse embryonic fibroblasts knocked out genetically for LEDGF resist infection by vesicular stomatitis virus glycoprotein G-pseudotyped HIV-1 vectors and suppress gene-specific integration (22). 4) Overexpression of the IBD in target cells inhibits HIV replication through a dominant negative mechanism (23). 5) Serial passaging of HIV-1 in cell lines overexpressing IBD selected for mutant viruses that can overcome IBD-mediated inhibition and whose integrase are mutated to bind LEDGF with higher affinity than IBD (24). Together, these lines of evidence validate the disruption of the integrase-LEDGF interaction as a strategy with therapeutic potential.
Despite an abundance of structural information about the interaction of integrase with the IBD of LEDGF, precise determination of the equilibrium and kinetic binding constants between integrase monomers and between integrase and LEDGF is lacking. To characterize these interactions in detail, we developed a novel methodology that combines homogeneous time-resolved fluorescence resonance energy transfer assays and mathematical modeling. This methodology enabled the precise determination, for the first time, of the equilibrium constants and kinetic constants of integrase dimer formation and integrase-LEDGF association. These assays can also be used in an equilibrium end point competition binding format to study inhibitors of integrase dimerization or of integrase-LEDGF interaction.

EXPERIMENTAL PROCEDURES
Peptides-All the peptides used in this study were customsynthesized and purified to Ͼ90% purity using the services of Anaspec Inc. (San Jose, CA).
Construction of LEDGF Expression Vectors-Isolation of the LEDGF cDNA and the construction of pLEDGF-6His, a plasmid expressing a C-terminally His 6 -tagged LEDGF protein, have been described previously (25). All subsequent LEDGF variants were created using pLEDGF-6His as the starting plasmid. Plasmid pLEDGF, containing native LEDGF, was constructed by substituting a C-terminal 472-bp fragment of pLEDGF-6His with the corresponding fragment lacking the His 6 tag. The two PCR amplification primers used for this construction were as follows: Stu5p-LEDGF1126, 5Ј-CATT-GAGGCCTTGGATG-3Ј, and Hind3p-LEDGF1593, 5Ј-TTT-AAGCTTTTAGTTATCTAGTGTAGAATCC-3Ј. Plasmid pLEDGF-FLAG containing a C-terminally FLAG-tagged LEDGF was constructed by substituting the same 472-bp fragment of pLEDGF-6His with one containing a FLAG epitope using the two PCR amplification primers as follows: Stu5p-LEDGF1126, 5Ј-CATTGAGGCCTTGGATG-3Ј, and Hind3pCFLAG LEDGF, 5Ј-AAGCTTTATTTGTCATCA-TCGTCTTTGTAGTCGCTGCCGTTATCTAGTGTAGA-ATCCTTC-3Ј. After PCR amplification, the amplification products were purified using the QIAquick PCR purification kit (catalogue number 28104, Qiagen, Valencia, CA) and digested with StuI and HindIII. The double-digested PCR products were purified on a 1% agarose gel and subcloned into pLEDGF75-6His in which the StuI and HindIII cut fragment has been removed. The construct was introduced into Escherichia coli BL21 (DE3) (catalogue number C6000-03, Invitrogen) for protein expression.
Construction of C-terminally FLAG-tagged Integrase Expression Vector-The N-terminally His 6 -tagged integrase (6His-IN) has been described previously (2). For C-terminally FLAGtagged IN (IN-FLAG) expression, the sequence of wild-type IN was cloned as an N-terminal His 8 -tagged and C-terminal FLAG-tagged protein. The N-terminal His 8 tag serves as an affinity purification handle that was subsequently cleaved off by rTEV protease to generate IN-FLAG. The cloning primers are as follows: NdeI5pIN, 5Ј-GGCCATATGTTTTTAGATGGA-ATAG-3Ј, and HindIII3pFLAGIN, 5Ј-AAGCTTTATTTGTC-ATCATCGTCTTTGTAGTCGCTGCCATCCTCATCCTG-TCTACTTGC-3Ј. The integrase sequence was amplified from pET3a-6HisIN as described previously (2). After amplification, the amplification products were purified using the QIAquick PCR purification kit (catalogue number 28104, Qiagen, Valencia, CA) and digested with NdeI and HindIII. The NdeI and HindIII cut inserts were purified on a 1% agarose gel and cloned into the NdeI and HindIII sites of the modified pET28a vector that encodes two more histidine residue and an rTEV recognition site (catalogue number V351-20, Invitrogen). The construct is named p8His-Tev-IN-FLAG. The construct was introduced into BL21(DE3) One Shot cells (catalogue number C6000-03, Invitrogen) for protein expression.
Construction of INCCD(F185K) Expression Vector-The integrase catalytic core domain (INCCD), residues 50 -212 of IN, with a single solubility mutation (F185K) was cloned as an N-terminally His 6 -tagged protein in the plasmid p6His-INCCD(F185K). For production of untagged INCCD, the INCCD was cloned downstream of a thrombin cleavage site preceded by a His 6 tag in pET28a to generate the construct p6His-IIa-INCCD(F185K). The cloning primers for this construct are as follows: NdeINCore5p, 5Ј-TTTCATATGCATGG-ACAAGTAGACTG-3Ј, and H3INCore3p, 5Ј-TTTAAGCTT-TTATTCTTTAGTTTGTATG-3Ј. After PCR amplification using p6His-INCCD(F185K) as template, the amplification product was purified using the QIAquick PCR purification kit (catalogue number 28104, Qiagen, Valencia, CA) and digested with NdeI and HindIII. The double-digested product was purified on a 1% agarose gel and subcloned into the NdeI and HindIII sites of the pET28a (catalogue number 69864, EMD BioSciences, La Jolla, CA). Both constructs were introduced into E. coli BL21-(DE3) (catalogue number 70235-3, EMD Bio-Sciences) for protein expression.
Expression of Recombinant Proteins-BL21(DE3) E. coli transformed with the various expression constructs were grown overnight at 37°C with shaking at 250 rpm. These overnight cultures were used to inoculate 6 liters of L-broth containing ampicillin (kanamycin for p8His-Tev-IN-FLAG) at an initial density of 0.05 A 600 /ml. The cultures were grown at 37°C and 250 rpm until they reached a density of A 600 ϭ 0.8 -1.0, which took ϳ3-4 h. Protein expression was then induced by addition of isopropyl 1-thio-␤-D-galactopyranoside to a final concentration of 1 mM. The cultures were kept at 30°C and 250 rpm for an additional 3 h before the cells were pelleted and stored at Ϫ80°C. Sixteen grams of cell pellet were lysed in 200 ml of Lysis Buffer by passing three times through a microfluidizer. Lysis Buffer A (25 mM Tris, pH 7.0) was used for LEDGF, Lysis Buffer B (20 mM Tris, pH 7.8, 200 mM NaCl, 1 mM EDTA, 10 mM ␤-mercaptoethanol) for MBP-IBD, Lysis Buffer C (20 mM HEPES, pH 7.0, 500 mM NaCl, 5 mM ␤-mercaptoethanol) for INCCD, and Lysis Buffer D (50 mM Tris, pH 8.0, 10 mM MgCl 2 , 2 mM ␤-mercaptoethanol) for 8His-Tev-IN-FLAG. The homogenate was centrifuged at 33,000 ϫ g for 60 min at 4°C. For most proteins, supernatant (S1) was saved for protein purification using a three-column method.
Purification of Native LEDGF and LEDGF-FLAG-The supernatant (S1) derived from the centrifugation of cell homogenates (see above) was loaded at 5 ml/min to an XK 26 ϫ 20 column (catalogue number 17-0510-10, GE Healthcare) containing 20 ml of Q-Sepharose-HP that was pre-equilibrated in Buffer A (10 mM sodium phosphate, pH 7.0, 10% glycerol, 1 mM DTT) to eliminate nonspecific bacterial protein. The flowthrough from the Q-Sepharose-HP column was loaded directly onto a 5-ml heparin column. Nonspecific proteins were washed away with 8 -10 column volumes of Buffer A at 5 ml/min. LEDGF or LEDGF-FLAG were next eluted with a 100-ml NaCl gradient (0 -1000 mM) with a slope of 10 mM/ml. Three milliliter fractions were collected during the elution. The protein peak fractions were analyzed on a NuPAGE TM 4 -12% BisTris gel (catalogue number NP0322BOX, Invitrogen) in MES buffer. Fractions containing the ϳ60.0or 61.2-kDa LEDGF or LEDGF-FLAG band were pooled, diluted 15-fold with Buffer A to ϳ10 mM NaCl, adjusted to pH 7.0, and filtered to remove any precipitate. The diluted and filtered sample was loaded at 5 ml/min onto a 5-ml cation exchange HiTrap SP-HP column (catalogue number 17-1152-01, GE Healthcare) pre-equilibrated in Buffer A. The column was then washed with Buffer A until the base line was reached and eluted at 3 ml/min with a 125-ml NaCl gradient (0 -1000 mM) with a slope of 8 mM/ml. Two and a half-milliliter fractions were collected during the elution. The protein peak fractions were analyzed on a NuPAGE TM 4 -12% BisTris gel in MES buffer. The fractions containing the LEDGF or LEDGF-FLAG band were pooled and concentrated using Centriprep-30 (catalogue number 4322, Millipore, Billerica, MA) to a final volume of ϳ1 ml. The concentrated sample was then loaded into a 1-ml loop and injected into a 100-ml Shodex gel filtration column (catalogue number KW2003, Showa Denko KK, Japan) pre-equilibrated in Gel Filtration Buffer (10 mM NaPO 4 , pH 7.0, 10% glycerol, 300 mM NaCl, 1 mM DTT). One-milliliter fractions were collected and analyzed on a NuPAGE TM 4 -12% BisTris gel in MES buffer. Peak fractions were pooled, and protein concentration was determined. The material was aliquoted, quickly frozen in liq-uid nitrogen, and stored at Ϫ80°C. Purity of LEDGF was determined to be Ͼ90% by SDS-PAGE.
Purification of MBP-IBD-(347-471)-WT and MBP-IBD-(347-471)-2Mut-The supernatant (S1) derived from the centrifugation of cell homogenates (see above) was loaded at 3 ml/min onto a 10-ml amylose resin high flow column (catalogue number E8022S, New England Biolabs, Beverly, MA) preequilibrated in Buffer A (20 mM Tris, pH 7.8, 200 mM NaCl, 1 mM EDTA, 1 mM DTT). After washing off nonspecific proteins from the column at 3 ml/min with 8 -10 column volumes of Buffer A, MBP-IBD-(347-471) was eluted with Buffer B (20 mM Tris, pH 7.8, 200 mM NaCl, 1 mM EDTA, 10 mM maltose, 1 mM DTT). Three milliliter fractions were collected during elution. The protein peak fractions were analyzed on a NuPAGE TM 4 -12% BisTris gel (catalogue number NP0322BOX, Invitrogen) in MES buffer. The fractions containing the ϳ58-kDa MBP-IBD-(347-471) band were pooled and dialyzed overnight against Buffer C (25 mM Tris, pH 8.0, 50 mM NaCl, 1 mM DTT). The dialyzed sample was diluted five time with Buffer D (25 mM Tris, pH 9.0, 2 mM DTT), filtered, and loaded onto an anion exchange column, QHP-HiTrap (catalogue number 17-1154-01, GE Healthcare), pre-equilibrated in Buffer D. The column was then washed with 25 ml of Buffer D until base line was reached and eluted at 5 ml/min with a 125-ml NaCl gradient (0 -1000 mM) with a slope of 8 mM/ml. Three milliliter fractions were collected during the elution. The protein peak fractions were analyzed on a NuPAGE TM 4 -12% BisTris gel in MES buffer. The fractions corresponding to 100 mM NaCl containing the MBP-IBD-(347-471) band were pooled and concentrated using Centriprep-30 (catalogue number 4322, Millipore, Billerica, MA) to a final volume of ϳ1 ml. The concentrated sample was then loaded into a 1-ml loop and injected into a 100-ml Shodex gel filtration column (catalogue number KW2003, Showa Denko KK, Japan) pre-equilibrated in Gel Filtration Buffer (50 mM Tris, pH 7.2, 500 mM NaCl, 10% glycerol, 1 mM DTT). One-milliliter fractions were collected and analyzed on a NuPAGE TM 4 -12% BisTris gel in MES buffer. Fractions corresponding to the first half of the elution peak containing the ϳ58-kDa MBP-IBD-(347-471) were pooled, determined for protein concentration using the Bradford method, quickly frozen in liquid nitrogen, and stored at Ϫ80°C.
Purification an equal volume of Adjustment Buffer (62.5 mM Tris, pH 8.0, 12.5 mM MgCl 2 , 10 mM CHAPS, 40 mM imidazole, 20% glycerol, 2.5 mM ␤-mercaptoethanol). This diluted S2 fraction was then loaded at 5 ml/min onto a 5-ml HisTrap HP column (catalogue number 17-5248-02, Amersham Biosciences) pre-equilibrated in Ni Buffer A (50 mM Tris, pH 8.0, 600 mM NaCl, 10 mM MgCl 2 , 20 mM imidazole, 10% glycerol, 10 mM CHAPS, 2 mM ␤-mercaptoethanol). After washing off nonspecific proteins from the column at 5 ml/min with 8 -10 column volumes of Ni Buffer A, 8His-Tev-IN-FLAG was eluted with 25 column volumes of an imidazole gradient of (20 -500 mM) with a slope of 3.84 mM/ml. Three-milliliter fractions were collected during the elution. The protein peak fractions were analyzed on a NuPAGE TM 4 -12% BisTris gel (catalogue number NP0322BOX, Invitrogen) in MES buffer. The fractions corresponding to 200 -400 mM imidazole (60 ml) containing the ϳ35.9-kDa 8His-Tev-IN-FLAG were pooled and dialyzed overnight in 2 liters of Ni Buffer A without imidazole at 4°C. After dialysis, 13 ml of this pool (ϳ45 mg) was digested for 4 h with 2.6 mg of rTEV protease at room temperature and for an additional 2 h with an additional 1.7 mg of rTEV protease. The digested protein was loaded on a 1-ml Ni HiTrap column (catalogue number 17-5247-01, Amersham Biosciences) to remove the His 8 tag and any uncleaved protein. One-third of the flow-through was concentrated using Amicon Ultra-15 Centrifugal Filter Unit with Ultracel-10 membrane (catalogue number UFC901024, Millipore, Billerica, MA) to a final volume of ϳ1 ml. The concentrated sample was loaded into a 1-ml loop and injected into a 100-ml Shodex gel filtration column (catalogue number KW2003, Showa Denko KK, Japan) pre-equilibrated in Gel Filtration Buffer (50 mM Tris, pH 8.0, 600 mM NaCl, 10 mM MgCl 2 , 10% glycerol, 10 mM CHAPS, 2 mM ␤-mercaptoethanol). One-milliliter fractions were collected and analyzed on a NuPAGE TM 4 -12% BisTris gel in MES buffer. Three peak fractions were pooled, quickly frozen in liquid nitrogen, and then stored at Ϫ80°C. The yield of IN-FLAG was 0.1 mg/g of bacterial pellet. Protein purity based on SDS-PAGE analysis was Ͼ90%. The final protein preparation had a concentration of 0.14 mg/ml.
HTRF-based IN-LEDGF Interaction Assay-An assay was devised to measure the interaction between HIV-1 integrase and LEDGF using a homogeneous time-resolved fluorescence resonance energy transfer format (HTRF). In this assay, we make use of an integrase that is N-terminally tagged with hexahistidine (6His-IN) and a LEDGF that is C-terminally tagged with the FLAG epitope (LEDGF-FLAG). Anti-6His-XL665 and anti-FLAG-EuCryptate antibodies (catalogue numbers 61HISXLA and 61FG2KLA, Cisbio-US, Inc., Bedford, MA), which bind, respectively, to the His 6 and FLAG tags, were added to allow fluorescence resonance energy transfer when LEDGF interacted with integrase ( Fig. 1). To test competitors in this assay, 6His-IN, LEDGF-FLAG, and competitor were mixed in 60 l of binding buffer (25 mM Tris, pH 7.4, 150 mM NaCl, 2 mM MgCl 2 , 0.1% Nonidet P-40, and 1 mg/ml bovine serum albumin) in a well of a 96-well halfarea white flat bottom plate (catalogue number 3693, Corning Glass). Fifteen microliters of antibody conjugates in binding buffer were then added to start equilibrium binding. The equilibrium binding mixture contained 10 nM 6His-IN, 10 nM LEDGF-FLAG, serial 2.2-fold dilutions of the competitor, 0.45 nM anti-FLAG-EuCryptate, and 10 nM anti-6His-XL665 in binding buffer. After 6 h of incubation at 4°C, KF was added to a final concentration of 100 mM in each well to prevent quenching of europium fluorescence before reading. The plate was read in an Envision 2102 multilabel reader (PerkinElmer Life Sciences) using 320-nm excitation filter UV2 (TRF), 590-nm emission filter 1, and 665-nm emission filter 2 with dichroic mirror D400. Raw counts (in counts/s) at 665 and 620 nm were collected, and the signal was calculated as the ratio of (cps 665:620 nm) ϫ 10,000. The signal for the competitor dose response was analyzed by curve fitting with Equation 1 after conversion of the data to % uninhibited to determine the 50% inhibitory concentration (IC 50 ). The on-rate constants are k 1 to k 7 . The off-rate constants are k Ϫ1 to k Ϫ7 . At the concentrations of integrase used in our experiments, the presence of integrase tetramer is negligible (Ͻ0.068% of total integrase); hence, the formation of integrase tetramer was omitted for simplicity. Because the co-crystal structure of integrase CCD and LEDGF IBD showed that the IBD can bind to either of two symmetric pockets formed by the integrase CCD dimer (13), it was assumed in this model that the binding of LEDGF (or competitors) to integrase minimally requires an integrase dimer. Scheme 1 can be written as a system of nine differential equations (see Equation 3).
In this model, the integrase dimer dissociation constant is K dimer ϭ k Ϫ1 /k 1 . For simplicity, we assume that the dissociation constant of LEDGF from integrase is K d ϭ k Ϫ2 /k 2 ϭ k Ϫ3 /k 3 ϭ k Ϫ6 /k 6 , and the dissociation constant of the competitor from integrase is K i ϭ k Ϫ4 /k 4 ϭ k Ϫ5 /k 5 ϭ k Ϫ7 /k 7 . System III can be solved numerically using a general purpose differential equation solver ( .
According to this model, the only species detectable by HTRF is the integrase heterodimer AB. To simulate a binding curve of AB as a function of input B ϭ 6His-IN for a given value of K dimer , the initial concentrations were set as follows: The mathematical models for Schemes 3 and 4 are shown as systems of differential Equations 5 and 6, respectively. SCHEME 2 SCHEME 3 SCHEME 4

Binding Affinities in the Integrase-LEDGF Complex
Again, in both Schemes 3 and 4, AB is the only species detectable by HTRF. In both Schemes 3 and 4, the integrase dimer dissociation constant, K dimer ϭ K AA ϭ K BB ϭ K AB ϭ k Ϫ1 /k 1 , has been determined separately using Scheme 2. When using competitor (C) capable of self-dimerization such as a nontagged integrase CCD, it was assumed that the K i ϭ K CC ϭ K AC ϭ To simulate a competition binding curve of AB as a function of input C for given values of K dimer and K i , the initial concentrations were set as follows: When using a competitor C incapable of self-dimerization such as an integrase dimer interfacial peptide, it was assumed that the K i ϭ K AC ϭ K BC ϭ k Ϫ3 /k 3 . Simulation of a competition binding curve of AB as a function of input C was done in a way similar to that of a competitor C capable of self-dimerization using Scheme 4 and system VI. Fig. 1. To maximize the HTRF signal, two different pairs of antibody conjugates were tested with the 6His-IN/LEDGF-FLAG and 6His-IN/IN-FLAG binding partner pairs. The anti-FLAG-EuCryptate/anti-6His-XL665 antibody conjugate pair is referred to as the A1/A2 pair and the anti-FLAG-XL665/anti-6His-EuCryptate antibody conjugate pair is referred to as the B1/B2 pair. Different concentrations of mixtures of 6His-IN and LEDGF-FLAG at a 1:1 molar ratio were tested against fixed concentrations of either A1/A2 or B1/B2 ( Fig. 2A). From 0 to 13 nM 6His-IN/ LEDGF-FLAG, a binding partner dose response can be seen with increasing HTRF signal. At concentrations higher than 13 nM, the binding partners diluted the antibodies, and the HTRF signal gradually decreased. The A1/A2 antibody pair produced the stronger signal and was used for all subsequent IN-LEDGF HTRF assays. For the 6His-IN/IN-FLAG HTRF, a stronger dose response was also seen with the A1/A2 antibody pair (Fig. 2B). Because the A1/A2 antibody pair produced stronger signals in both IN-LEDGF and IN-IN HTRF assays, we tested this antibody pair against two false-positive control peptides ( Fig. 1  and Fig. 2C). Each peptide is an ␣-helical segment bearing an N-terminal His 6 and a C-terminal FLAG tag. While the 6His(AQ)FLAG peptide contains an artificial stretch of six AQ repeats, the 6His(INC)FLAG peptide contains a known ␣-helical segment from integrase (amino acids 211-222 of integrase). Both peptides displayed a dose response with increasing HTRF signals up to 9 nM peptide and gradual antibody dilution at higher peptide concentrations. A mixture of 6His-IN/LEDGF-FLAG (both proteins at 13 nM) was used as a positive control. Either peptide at 13 nM gave an HTRF signal that is ϳ7-fold higher than the 13 nM IN/LEDGF mixture. In competition binding studies involving the IN-LEDGF interaction, the 6His(AQ)FLAG peptide was chosen (used at 5 nM) as a control to verify that a competitor specifically disrupts the IN-LEDGF interaction.

Affinity of Integrase Monomer-Monomer Interaction Can Affect the Apparent Dissociation Constant of LEDGF and of Its
Competitors from Integrase Dimer-We first simulated the integrase-binding dose response to LEDGF according to Scheme 1 by testing the effect of different integrase dimer dissociation constants, K dimer (Fig. 3A). We have used a K d ϭ 10 nM for this simulation because the K d of IN-LEDGF was previously reported to be ϳ10 nM (28). In Fig. 3A, the curve with open circles is derived from Equation 7 describing a classical ligandreceptor system using K d ϭ 10 nM and [R] tot ϭ 10 nM, NOVEMBER 27, 2009 • VOLUME 284 • NUMBER 48 where [L] tot is the total concentration of ligands in nanomolars; [R] tot is the total concentration of binding sites; [RL] is the concentration of receptor-ligand complex; and K d is the affinity of the receptor-ligand interaction. In the simulation of the IN-LEDGF interaction according to Scheme 1 and system III, the receptor is LEDGF-FLAG and the ligand is 6His-IN, which needs to dimerize before it can interact with LEDGF. Like the classical binding curve, all the curves simulated with a K d ϭ 10 nM according to Scheme 1 eventually plateau at 10 nM (i.e. the concentration of LEDGF-FLAG) but deviate significantly from it as the integrase dimer dissociation constant K dimer increases (Fig. 3A). If Equation 7 for classical binding were used to analyze these simulated IN-LEDGF binding curves, only an apparent dissociation constant (K d,app ) could be determined, but it can deviate significantly from the K d of 10 nM used for the simulation if K dimer becomes Ͼ0.25 nM (Fig. 3A). The integrase dimer dissociation constant has not been determined previously, but an upper limit of 44 -168 nM was provided by the affinity of an integrase dimer interfacial peptide (27 (Fig. 3B). Unlike the classical competition dose-response curves, as the competitor concentration increased, the signal initially increased and reached a peak and then decreased to zero as competitor concentration was further increased. According to modeling, the shape of these curves results from two simultaneous phenomena as follows: 1) binding of competitor to one of the two binding sites on the unbound integrase dimer, shifting the integrase equilibrium from monomer to dimer and thereby facilitating the occupation of the second binding site by LEDGF resulting in a signal increase; and 2) with increasing competitor concentration, displacement of bound LEDGF eventually becomes predominant, resulting in a signal decrease. The magnitude of K dimer for integrase and K i for the competitor can both affect the balance between these two phenomena. When simulation was performed with increasingly higher affinities for monomer-monomer interaction (i.e. smaller and smaller K dimer ), the characteristic peak gradually disappears when K dimer decreases below 25 nM (Fig. 3B, red curves). The reason is that with a decreasing K dimer , which results in more stable dimers, the monomer pool becomes so small that any further shift toward dimer by addition of a competitor becomes insignificant. When the affinity of the competitor increases (i.e. decreasing K i ), displacement of LEDGF by the competitor becomes more and more effective relative to its ability to shift the equilibrium from monomer to dimer, also resulting in a gradual decrease of the peak (Fig.  3B, compare solid line to short dashed line of the same color).

Binding Affinities in the Integrase-LEDGF Complex
Finally, for a competitor of a given K i , the IC 50 value of the competition dose-response curve will increase with increasing K dimer . For example, with K i ϭ 25 nM, the IC 50 values of the competition dose-response curves are 168, 363, and 997 nM for K dimer values of 25, 80, and 250 nM, respectively (Fig. 3B, long  dashed lines). The reason for the IC 50 increase with larger K dimer values is that with weaker integrase monomer-monomer interactions, more competitors are initially spent in shifting monomers to dimers before they are effectively used to displace LEDGF.
Determination of the Affinity of the Antibody Conjugates for the His 6 and FLAG Tags-Because signal generation in the assay depends not only on the association of the binding partners, IN and LEDGF, but also on the affinity of the antibody conjugates for their epitopes, we determined the affinity of all four antibody conjugates (Fig. 4). The dose responses were analyzed with the classical binding model described by Equation 8, which is a modified version of Equation 7, where the concentration of receptor-ligand complex [RL] is converted into the units of the HTRF signal (i.e. ratio of 665:620 nm) by the conversion factor, s expressed in ratio/nM, and R m ϭ s[R] tot is the plateau of the binding curve.
It was determined that the anti-6His-XL665 antibody conjugate A2 has a K d of 19 pM for the His 6 tag, and the anti-FLAG-EuCryptate antibody conjugate A1 has a K d of 376 pM for the FLAG tag (Fig. 4A). The K d values of antibody conjugates B1 and B2 were similarly determined with the anti-His 6 conjugate displaying again the higher affinity (Fig. 4B). Simulation showed that with A2 set to 65.6 nM and an affinity of 20 -200 pM for the His 6 tag, antibody-bound 6His-IN increases linearly with increasing input 6His-IN in the range of 0 -65 nM (i.e. the dose range used in our experiments) (Fig. 4C). This means that the specific activity of labeling 6His-IN with antibody does not change within the dose range used, and therefore the K d determination of the binding partners will not be affected. The affinity of the anti-FLAG-EuCryptate is somewhat weaker, but this does not pose a concern because LEDGF-FLAG and IN-FLAG are always used at a fixed concentration. to determine the corresponding EC 50 (Fig. 5B). The EC 50 values thus determined can be correlated with the K dimer values using parabolic interpolation. Once the successive quadratic functions fitting three points at a time were determined by curve fitting (Fig. 5C, solid line), the quadratic function describing the curve segment bracketing the experimental EC 50 value of 5.3 nM was used to convert this value into a K dimer of 67.8 pM. Using this value of K dimer , we calculated that in an equilibrium solution of 10 nM integrase (monomer concentration), ϳ89% of integrase is in dimeric form. Simulation indicates that a 20 -200 pM affinity for the XL665 conjugates ensures that the antibody-bound integrase increases linearly with increasing integrase concentrations in the dose range used for subsequent dissociation constant determinations (Fig. 5A and Fig. 6A).

Nanomolar Affinity of LEDGF Interaction with Integrase Dimer-
Having determined the integrase dimer dissociation constant, K dimer , the K d value of LEDGF from integrase dimer was determined experimentally by fixing [LEDGF-FLAG] at 10 nM while varying [6His-IN] (Fig. 6A). Having established that the integrase monomer-monomer interaction is very tight and that the great majority of integrase is present in dimeric form, we first analyzed our binding data with Equation 7 for classical binding. Fitting Equation 7 to the data yielded an apparent K d of 11.6 nM for the interaction of LEDGF with integrase dimers. To determine the real K d , we first fit Equation 2 to the data to determine an EC 50 of 19.2 nM. Next, we used parabolic interpolation to establish a correlation between K d and EC 50 by simulating a family of binding curves corresponding to different K d values according to Scheme 1 and Equation 3 while fixing K dimer at the value of 67.8 pM, which was determined above (Fig. 6B). Using the result of parabolic interpolation (Fig. 6C), the EC 50 of 18.8 nM was converted to a real K d of 10.9 nM. Because the integrase monomermonomer interaction is very tight, the apparent K d of 11.6 nM determined from the classical binding equation is very close to the real K d determined according to Scheme 1.

Kinetics of IN-LEDGF and IN-IN
Associations-By monitoring the kinetics of 6His-IN and LEDGF-FLAG association (Fig. 7A) in our HTRF assay format, we were able to determine the on-rate (k on ϭ k 2 ϭ k 3 ) and off-rate constants (k off ϭ k Ϫ2 ϭ k Ϫ3 ) for LEDGF-FLAG binding to 6His-IN dimer (see Scheme 1) by assuming we have the same integrase dimer dissociation constant of 67.8 pM, which was determined previously. The k on for LEDGF binding to IN dimer was measured at 0.0285 nM Ϫ1 ⅐min Ϫ1 and the k off at 0.234 min Ϫ1 . These on-and off-rate constants are in ranges comparable with those observed with anti-carbohydrate antibodies determined by surface plasmon resonance spec-troscopy (29). The dissociation constant of LEDGF from integrase dimer calculated from the ratio of k off /k on is 8.2 nM, which is comparable with the K d value we determined above using equilibrium end point dose-response analysis (Fig. 6A). From the off-rate constant of LEDGF dissociating from the IN dimer, we calculated a half-life for the IN-LEDGF complex of ϳ3 min. Similarly, by monitoring the kinetics of 6His-IN and IN-FLAG association (Fig. 7B), we determined the on-and off-rate constants, k 1 and k Ϫ1 , for integrase monomer-monomer association (see Scheme 2). The on-rate constant k 1 is 0.1247 nM Ϫ1 ⅐min Ϫ1 , which is ϳ4.4-fold larger than that of LEDGF binding to integrase dimer. The off-rate constant k Ϫ1 is 0.0080 min Ϫ1 , which is ϳ29-fold smaller than that of LEDGF binding to integrase dimer. The ratio of k off /k on , which yields an integrase dimer dissociation constant of 64.5 pM, is comparable with the K dimer we previously determined using equilibrium end point dose-response analysis (Fig. 5A). From the off-rate constant of integrase monomers, we calculated a half-life for integrase dimer of ϳ87 min.
Peptides and Small Molecules Are Capable of Displacing LEDGF from Integrase-We tested in our HTRF-based IN-LEDGF interaction assay various competitors that included a tag-free native LEDGF, an MBP-IBD fusion, and a mutated version of MBP-IBD, where Ile-365 and Asp-366 previously identified as hot spot contact residues with integrase have been mutated (Fig. 8A) (12). Native LEDGF produced an IC 50 of 91 nM, and wild-type and mutant MBP-IBDs displayed IC 50 values of 565 nM and 10.2 M, respectively. Using Equation 3 represented by Scheme 1 and a method similar to that described in Fig. 6, B and C, the three IC 50 values generated from competition binding were converted to K i values of 35 and 218 nM and 3.9 M for native LEDGF, wild-type, and double mutant MBP-IBDs, respectively. Three peptides, LEDGF-(354 -378), LEDGF-(360 -370), and LEDGF-(400 -413) derived from the IBD of LEDGF (30) were also tested in the HTRF IN-LEDGF interaction assay. All three peptides competed with LEDGF-FLAG binding to IN (Fig. 8B). LEDGF-(354 -378) showed the strongest competition among the three peptides with an IC 50 of 2.0 M (K i ϭ 0.78 M), followed by LEDGF-(360 -370) with an IC 50 of 11.9 M (K i ϭ 4.6 M), whereas LEDGF-(400 -413) was much less potent. Tetraphenylarsonium chloride (TPAsCl) has been shown to co-crystallize with integrase at a site of IN dimer interface now identified as the LEDGF binding pocket (31); hence, we decided to test whether it competes with LEDGF binding to integrase in the IN-LEDGF interaction assay. TPAsCl competed with LEDGF and produced an IC 50 of 400 M (K i ϭ 167 M) (Fig. 8B). To determine whether the inhibition observed in this assay with the three peptides and TPAsCl was specific for the IN-LEDGF interaction, each peptide and the small molecule were tested against the 6His(AQ)FLAG peptide, showing no decrease in the HTRF signal (data not shown). In terms of additional negative controls to help assess the specificity of the TPAsCl inhibitory effect, three small molecule HIV antiviral drugs zidovudine, raltegravir, and tenofovir were also tested in the assay and displayed IC 50 values that were at least 10-fold higher than that of TPAsCl (Table 1).
Additional LEDGF-derived peptides with point mutations that diminish the ability of LEDGF to interact with integrase and LEDGF-derived peptides that were engineered with internal disulfide bonds to allow circularization were also tested ( Table 1). The LEDGF-(354 -378 IN)-peptide, which contains mutation D366N, was less effective by ϳ9.4-fold at competing with LEDGF compared with the wild-type peptide LEDGF-(354 -378). Peptide LEDGF-(354 -378-AD) which contains the I365A mutation displayed an ϳ14.5-fold lower potency compared with wild-type peptide. The inhibitory potency of peptide LEDGF-(354 -378-AN), which contains the double mutation D366N/I365A, was comparable with either mutation alone indicating that the individual mutations maximally compromise the interaction of the peptide with integrase. A six amino acid circular peptide, LEDGF(363CG-368C), containing the critical integrase binding dipeptide ID motif, retained significant potency with an IC 50 of 26 M, whereas the ID or VD dipeptides by themselves were essentially inactive with IC 50 values of ϳ2 mM. Three linear peptides derived from LEDGF, together with circularized versions of these peptides, were tested in the IN-LEDGF interaction assay. The circular versions seemed to be more potent in this assay compared with the linear forms (Table 1). In particular, LEDGF(363SG-368S) was not inhibitory, suggesting that circularization of the hexapeptide facilitated binding by possibly pre-organizing the ID dipeptidebinding motif into a preferred conformation. To determine whether the potency of the circular peptide LEDGF(363CG-368C) was dependent on the presence of the key ID residues required for binding to integrase, a peptide in which ID was replaced with AN was tested. This mutant peptide termed LEDGF(363CG-368 AN) displayed a Ͼ40-fold decrease in competition potency (Table 1).
Finally, to assess whether the greater flexibility provided by the glycine residue in LEDGF(363CG-368C) was responsible for the higher binding affinity of this peptide or whether the charge and longer side chain of the naturally occurring lysine residue in LEDGF(363CK-368C) was the cause of decreased potency, glycine was substituted with alanine yielding peptide LEDGF(363CA-368C). LEDGF(363CA-368C) displayed comparable affinity to LEDGF(363CK-368C), suggesting that the flexibility provided by the glycine may be responsible for the greater affinity. Another possibility that we cannot reject at this time is that the increased flexibility of the LEDGF(363CG-368C) peptide may allow it to either bind differently within the same pocket as LEDGF(363CA-368C) or to a different site entirely resulting in increased ability to disrupt the IN-LEDGF interaction.

INCCD and Peptides Derived from the IN Dimer Interface Disrupt
Integrase Dimers-Two peptides, INH1 and INH5, derived from the ␣-1 and ␣-5 helices located at the integrase dimer interface were previously shown to perturb the integrase oligomer equilibrium in favor of monomer species and to inhibit integrase catalytic function (27). We sought to test these two peptides in our IN dimerization HTRF assay to determine whether they can prevent the formation of the 6His-IN-IN-FLAG heterodimer. In addition, we used INSC3G, a scrambled version of INH5, into which three glycine residues were introduced to break the ␣-helicity as a negative control. As a positive control, we used the integrase catalytic core domain, INCCD (F185K) containing the solubility mutation F185K. INCCD(F185K) inhibited the formation of 6His-IN-IN-FLAG heterodimers with an IC 50 of 2.5 M (Fig. 9A). Using Equation 5 represented by Scheme 3 and a method similar to that described in Fig. 6, B and C, this IC 50 value was converted to a K i value of 15.2 nM. A possible reason why the IC 50 of INCCD is ϳ164-fold larger than the K i value is that INCCD not only competes against integrase heterodimer formation, which generates the signal, but it also competes against integrase homodimer formation, which cannot be directly detected, and finally it forms self-dimers that are inactive as competitors. represented by Scheme 4 and a method similar to that described in Fig. 6, B

DISCUSSION
In this study, we describe HTRFbased assays coupled with mathematical models to study the interaction of integrase with itself and with LEDGF. Unlike the AlphaScreen TM method previously used to investigate the IN-LEDGF interaction (4), the HTRF method is suitable for both equilibrium end point and real time kinetic analyses. Because our system involves at least four different interactions (i.e. anti-6His-6His, anti-FLAG-FLAG, 6His-IN-6His-IN, and 6His-IN-LEDGF-FLAG), we systematically determined the dissociation constants of these four interactions. We started with the determination of the affinity of the antibody conjugates for their respective epitopes (i.e. 6His tag or FLAG tag) because these affinities dictate whether corrections to the We next studied the interaction of integrase monomers to form an integrase dimer. According to the co-crystal structure of INCCD bound to the IBD of LEDGF, the IN dimer corresponds to the minimal oligomeric form of integrase that serves as a binding partner for LEDGF (13). The dissociation constant of an integrase tetramer into two integrase dimers has been determined previously to be ϳ22 M using sedimentation equilibrium (26), but the dissociation constant of integrase dimer has never been reported to our knowledge. The closest upper estimate  is 224-fold larger than the K dimer , while the most potent peptide derived from the integrase dimer interface showed a K i 27,000-fold larger than the K dimer .
According to the co-crystal structure of integrase CCD and IBD, the interaction between integrase and LEDGF involves an integrase dimer with two symmetrical binding pockets formed at the dimer interface that can accommodate two molecules of LEDGF (13). This binding interaction cannot be a priori analyzed with the classical binding model of one receptor and one ligand without potentially grossly overestimating the K d . With the knowledge of the integrase dimer dissociation constant, we used a binding model involving an obligate dimer with two symmetrical binding sites to analyze the equilibrium binding dose response of integrase to LEDGF. By this method, we determined that the K d value of the LEDGF interaction with integrase is 10.9 nM. Because the integrase dimer is a very tight complex, the binding of LEDGF to integrase practically behaved according to the classical one receptor, one ligand binding model. This explains why the apparent K d of 11.6 nM is comparable with the real K d . By monitoring and analyzing the time course of the IN-LEDGF association, we determined a very similar K d value of 8.2 nM with a IN-LEDGF complex half-life of ϳ3 min. A previous deletion study revealed that in addition to the primary LEDGF binding determinant present in the integrase CCD dimer interface, the NTD of integrase also contributes to the binding affinity (7). More recent studies showed that LEDGF and IBD can promote detectable integrase tetramer formation at integrase concentrations of 1-14 M (30, 37), and it was proposed that the integrase tetramer has two low affinity and two high affinity binding sites for the IBD of LEDGF (37). According to molecular modeling, although the two low affinity binding sites are present in the integrase dimer, the two high affinity sites involving additional NTD contacts can only be realized in the context of the integrase tetramer (37). Under the much lower integrase concentrations used in our study, it is unlikely that there is significant formation of integrase tetramers, even in the presence of LEDGF. In support of this, the K d value for the 6His-INCCD (lacking the additional NTD contacts) and LEDGF-FLAG interaction was similar to that of 6His-IN interacting with LEDGF-FLAG (data not shown), suggesting that the K d we determined in this study is that of the low affinity binding site.
Using the HTRF IN-LEDGF interaction assay in competition binding mode, we determined the IC 50 and K i values of variants of LEDGF and LEDGF-derived peptides. As expected, the K i value of native LEDGF determined in competition binding is comparable with the K d value of the 6His-IN and LEDGF-FLAG interaction as determined by direct binding. Consistent with previous results using the pulldown assay (12), the double mutation I365A/D366N in the binding loop of IBD decreased its affinity for integrase by ϳ18-fold relative to wild type in our HTRF assay. Recently, three peptides derived from the LEDGF IBD were shown to inhibit integrase activity by shifting integrase oligomer equilibrium toward tetramers (30). The K i values (0.8 -4.6 M) for two of these peptides (i.e. LEDGF-(354 -378) and LEDGF-(360 -370)) as determined in our competition binding assay correspond to the same range as the K d values previously determined by direct binding using fluorescence anisotropy (30). More recently, a shorter version of peptide LEDGF-(354 -378), termed LEDGF-(355-377), was shown to disrupt the IN-LEDGF interaction with an IC 50 of 25 M in mathematical modeling to characterize the four major equilibrium binding constants involved in this assay system. This study is the first to determine the very tight picomolar interaction between the subunits of the integrase homodimer and the first to derive the affinity of LEDGF for integrase by using a model of ligand binding to an obligate dimer. The novel methodologies described in this study should be applicable to many other complex protein-protein interactions. FIGURE 10. CCD dimer interface and salt bridge location. A, dimer structure of integrase CCD. B, close-up view of four salt bridges at the core of the CCD dimer interface. The integrase CCD dimer interface has a large shared surface area consistent with nanomolar affinities. In addition, ion pairs forming four buried salt bridges may be giving increased affinity and stability resulting in the observed subnanomolar dimer dissociation constant. The structure shown is based on Protein Data Bank code 2B4J (13).