Affinity and Kinetic Analysis of Fcγ Receptor IIIa (CD16a) Binding to IgG Ligands*

Binding of pathogen-bound immunoglobulin G (IgG) to cell surface Fc γ receptors (FcγRs) triggers a wide variety of effector functions. The binding kinetics and affinities of IgG-FcγR interactions are hence important parameters for understanding FcγR-mediated immune functions. We have measured the kinetic rates and equilibrium dissociation constants of IgG binding to a soluble FcγRIIIa fused with Ig Fc (sCD16a) using the surface plasmon resonance technique. sCD16a interacted with monomeric human IgG and its subtypes IgG1 and IgG3 as well as rabbit IgG with on-rates of 6.5 × 103, 8.2 × 103, 1.1 × 104 and 1.8 × 104 m–1 s–1, off-rates of 4.7 × 10–3, 5.7 × 10–3, 5.9 × 10–3, and 1.9 × 10–2 s–1, and equilibrium dissociation constants of 0.72, 0.71, 0.56, and 1.1 μm, respectively. The kinetics and affinities measured by surface plasmon resonance agreed with those obtained from real time flow cytometry and competition inhibition binding experiments using cell surface CD16a. These data add to our understanding of IgG-FcγR interactions.

Fc ␥ receptors (Fc␥Rs) 7 are a family of cell surface glycoproteins with varying affinities for the Fc region of immunoglobulins G (IgG). Three classes of human Fc␥Rs have been described: Fc␥RI (CD64), Fc␥RII (CD32), and Fc␥RIII (CD16), which are widely distributed in hematopoietic cell lineages. These include at least 12 different isoforms many of which are polymorphic. For example, CD16 has two isoforms, a and b, that differ by six amino acids in the extracellular domain and the presence (CD16a) or absence (CD16b) of the transmembrane and cytoplasmic domains (1).
The IgG-Fc␥R interaction-mediated binding of antibody-opsonized pathogens to leukocytes is a key event by which antibody effector functions are initiated. Kinetic rates and binding affinity are critical determinants of an IgG-Fc␥R interaction, as they control how likely and how rapidly such binding will occur, how many bonds will be formed, and how long the bonds last. In addition, it has been hypothesized that these parameters are related to the signaling events following the initial binding (2)(3)(4). Using a micropipette method, we have measured the kinetic rates and binding affinities of several IgG-Fc␥R interactions when both interacting molecules are anchored on apposing surfaces. We found that in this assay the half-lives of these IgG-Fc␥R bonds are in the order of seconds (5)(6)(7)(8)(9).
In addition to interaction parameters of surface-linked molecules, the kinetic rates and affinities of Fc␥Rs for soluble IgG are also of interest, because in vivo interactions of immobilized IgG to leukocyte Fc␥Rs are subject to competitive binding of soluble antibodies in sera. Of the three Fc␥Rs, CD64 binds to monomeric IgG with high affinity (K d ϳ tens of nM) (10), CD32 and CD16b are of low affinities (K d , several and several tens of M, respectively) (6,11,12), and CD16a is considered as an intermediate affinity receptor (K d ϳ hundreds of M) for monomeric IgG (6,10,12). In addition to the above results, which were obtained by conventional assays using Fc␥R-expressing cells, there were two studies using the surface plasmon resonance (SPR) technology and soluble Fc␥Rs. Galon et al. (13) reported half-lives of the order of 10 min and equilibrium dissociation constants of several micromolar for sCD16b NA2 binding to human (h) IgG1 and IgG3. By comparison, Maenaka et al. (14) found a much faster off-rate (half-lives of the order of seconds) but similar K d for IgG-sCD16b NA2 binding.
Here, we report kinetic and affinity measurements of a soluble dimeric human Fc␥RIIIa (sCD16a) interacting with various IgG ligands in both monomeric and multimeric forms using SPR. We found that sCD16a interacted with monomeric rabbit (Rb) IgG, hIgG, hIgG1, and hIgG3 with on-rates of 1.8 ϫ 10 4 , 6.5 ϫ 10 3 , 8.2 ϫ 10 3 , and 1.1 ϫ 10 4 M Ϫ1 s Ϫ1 , off-rates of 1.9 ϫ 10 Ϫ2 , 4.7 ϫ 10 Ϫ3 , 5.7 ϫ 10 Ϫ3 , and 5.9 ϫ 10 Ϫ3 s Ϫ1 , and equilibrium dissociation constants of 1.1, 0.72, 0.71, and 0.56 M, respectively. sCD16a bound with aggregated ligands with lower apparent equilibrium dissociation constants and slower apparent off-rates. To ensure that the relatively slow kinetics is not artifactual, various controls were performed in both the experiment and analysis steps. The slow kinetics was not found to be artifacts because of the mass transport limitation, ligand aggregation, or dimeric binding of the sCD16a molecule. The kinetic rates and affinities were also measured by real-time flow cytometry and a competition inhibition binding experiment using CD16 expressed on the cell surface, which were found to be in agreement with those obtained by SPR.

EXPERIMENTAL PROCEDURES
Cells, Soluble CD16a, and Antibodies-Chinese hamster ovary (CHO) cells transfected to express human CD16a TM , CD16b NA1 , CD16b NA2 , and B7-1 GPI as well as untransfected CHO cells were cultured as previously described (15,16). sCD16 was generated by attaching the extracellular domain of CD16a to the Fc domain of IgG1. The mutated IgG1 CH2-CH3 Fc domains were obtained from Dr. Peter Linsley, Bristol-Meyers Squibb, as the hB7-1-Ig construct and the extracellular domain of hCD16a was cloned in the place of hB7-1 as described (17). Mutations in the Fc domain of hCD16a-Ig are L267F, L268E, G270A, and A363T (numbered as in accession number AAH69020.1). These mutations were shown to abolish the binding of Fc␥Rs (18,19). The anti-CD16 nonblocking monoclonal antibody (mAb) 214.1 (murine IgG1) was a generous gift from Dr. Howard Fleit (State University of New York, Long Island). The anti-CD16 adhesion blockade mAb CLBFcgran-1 (murine IgG2a) was purified in house from hybridomas as previously described (20). Cleavage of CLBFcgran-1 into Fab fragments was done by Lampire (Pipersville, PA). The rabbit anti-mouse Fc polyclonal antibody was purchased from BIAcore (Piscataway, NJ). Total hIgG and subtypes (hIgG1, hIgG2, and hIgG3) as well as RbIgG were purchased from Sigma, except hIgG1 used for the real time flow cytometry experiment, which was a generous gift from Dr. Adrian Whitty (Biogen Inc., Boston, MA). Fab of CLBFcgran-1 and hIgG1 was labeled with fluorescein isothiocyanate (Molecular Probes, Eugene, OR) following the manufacturer's instructions.
Size Exclusion Chromatography-Monomeric and multimeric IgG ligands were separated by size exclusion chromatography. 7.5 g of Sephadex G-200 (Amersham Biosciences) was swelled in 200 ml of PBS/EDTA (containing 5 mM EDTA, pH 7.4) at 90°C for 5 h and then cooled at 4°C overnight. The supernatant was decanted and the gel was resuspended in 150 ml of PBS/EDTA and poured into a column. Two columns were used, with respective diameters of 1.7 and 1.0 cm and respective volumes of 150 and 103 ml (Bio-Rad). The columns were rinsed with 300 ml of PBS/EDTA at 0.3 ml/min between each run. Two sets of gel filtration standards were used to calibrate the columns. The first set included 4 mg each in 1 ml of PBS/EDTA of cytochrome c (molecular mass 12 kDa), blue dextran (2,000 kDa), and BSA (88 kDa) (Sigma). The second set included 2.5 mg of thyroglobulin (670 kDa), 2.5 mg of bovine ␥-globulin (158 kDa), 2.5 mg of chicken ovalbumin (44 kDa), 1.25 mg of equine myoglobin (17 kDa), and 0.25 mg of vitamin B12 (1.4 kDa). After adding 5-20 mg of IgG in 1 ml of PBS/EDTA, the column was connected to a 1-liter reservoir of PBS/EDTA. Setting the flow rate at 0.25-0.75 ml/min, the effluent was collected sequentially in fractions of 1.5 ml each. The optical density at 280 nm was measured to monitor the protein concentration in each fraction.
Monomeric or multimeric IgG fractions were used immediately after separation, either directly or further diluted to lower concentrations for SPR or real time flow cytometry experiments. In some cases where higher concentrations were desired, chromatographed IgG was reconcentrated by using protein concentrators (Amicon, Beverly, MA). The concentrations of monomeric and multimeric IgG were determined by a protein estimation kit (Bio-Rad).
SPR Measurement-SPR experiments were conducted in a BIAcore TM 1000 instrument using CM5 sensor chips (BIAcore) at 25°C. Samples were prepared in PBS/EDTA and perfused over the sensor chip at 30 l/min (unless otherwise stated) for kinetic measurements. For other control experiments, the flow rate was 5 l/min. The running buffer was BIA-certified HBS buffer (10 mM HEPES, pH 7.4, 150 mM NaCl, 3.4 mM EDTA, 0.005% Surfactant p20) filtered and degassed using 0.2-m bottle top filter (Millipore, Bedford, MA).
Several approaches were tried in preliminary experiments to immobilize sCD16a on the sensor chip, including the standard amine coupling procedure to coat either sCD16a directly or a nonblocking anti-CD16 mAb 214.1, which in turn captured sCD16a. Unfortunately, the former adversely affected the ability of sCD16a to bind ligands and the latter did not allow satisfactory regeneration of the sensor chip. The approach that worked best with our reagents appeared to be coupling first a rabbit anti-mouse Fc antibody to the sensor chip with the amine coupling procedure then binding mAb 214.1, followed by capturing sCD16a. This approach also ensured the consistent orientation of the sCD16a molecule on the sensor chip. The sensor chip could be regenerated with three washes of 10 l of 1 M formic acid (Sigma), which completely removed noncovalently bound sCD16a and 214.1 without impairing the reactivity of the anti-mouse Fc antibody. The binding of mAb 214.1 was Ն95% of the initial level after 40 times of regeneration. Using the full rabbit anti-mouse Fc antibody yielded negligible sCD16a binding to its Fc region, as confirmed by a control experiment in which sCD16a was injected over the sensor chip coupled with the full rabbit anti-mouse Fc antibody alone without mAb 214.1 followed by subsequent injection of IgG ligands.
The kinetic rates of IgG-sCD16a binding were derived by globally fitting the Langmuir (1:1) model (cf. Equations 1 and 2) to the family of association and dissociation curves collected at different ligand concentrations, using BIAevaluation 3.0 software provided by the manufacturer. The affinity of CLBFcgran-1 Fab-sCD16a binding was derived by Scatchard analysis.
Kinetic Measurement of Cell Surface CD16 by Real Time Flow Cytometry-5 ϫ 10 6 cells were washed three times in 5 ml of binding buffer (RPMI, 1% IgG-free BSA, 0.02% sodium azide). Cells were resuspended in 0.5 ml of binding buffer and transferred to a tube. Fluorescein isothiocyanate-labeled ligands in binding buffer were added and quickly mixed with the cells to obtain 2.5 ϫ 10 6 cells/ml cell concentration and the desired final ligand concentration. A range of ligand concentrations was selected based on separate affinity measurements using other techniques, such that the receptors could be saturated at high concentrations yet the ligands would not be depleted in low concentrations. To assay for association, the sample was immediately run in a FACS Vantage machine (BD Biosciences) and a total of 15 fluorescence intensity histograms were measured sequentially in predetermined time points over a 12-min period. The earliest time point a histogram could be measured was ϳ10 s. Each histogram included Ͼ2,000 events and took ϳ2 s to acquire. The sample was vortexed between two consecutive time points to ensure cells and ligands were well mixed. The right-shift of the histogram toward higher fluorescence intensity was monitored in real time.
To assay for dissociation, the remaining sample from the association assay was incubated for another 20 min to ensure equilibrium was achieved. 1 ml of the sample was centrifuged, the supernatant was decanted, and the tube was vortexed to disperse the cell pellet. 2 ml of plain medium was added to resuspend the cells. The sample was immediately run in the FACS machine to measure another 15 fluorescence intensity histograms sequentially in predetermined time points over a 12-min period.
The background-subtracted mean fluorescence intensity (MFI) versus time data of the association and dissociation assays were, respectively, fit to equations, where k on and k off are the respective on-and off-rates and t is time. The concentration of bound ligands C is proportional to the measured MFI. Neglecting depletion due to binding, the free ligand concentration L is assumed to be the same as that added to the reaction mixture. R T is the concentration of total receptors. The proportionality constant accounts for the difference between the equilibrium MFI from the association assay and the initial MFI from the dissociation assay. The standard free energy of binding, ⌬G°(kcal mol Ϫ1 ), was calculated from the K d measured at various temperatures, ⌬G°ϭ RTln(K d ), where R is the universal gas constant (1.987 ϫ 10 Ϫ3 kcal mol Ϫ1 K Ϫ1 ), T is the absolute temperature, and K d is expressed as mole liter Ϫ1 .
Affinity Measurement for Cell Surface CD16-The affinities of CLBFcgran-1 Fab for CHO cell CD16a TM , CD16b NA1 , and CD16b NA2 were determined by Scatchard analysis. The affinities of monomeric IgG to CD16 were measured by a competitive inhibition binding assay as previously described (6). Briefly, CHO cells were grown in flasks until near confluence. Cells were rinsed once in PBS and then removed from the flask using PBS/EDTA. After washing, they were resuspended at 10 6 cells/ml in PBS/EDTA and added to V-bottom 96-well plates at 100 l/well. The wells were precoated with 1% IgG-free BSA (Sigma) in PBS by incubating at room temperature for 2 h. They were rinsed with PBS/EDTA and kept on ice until the cells were added. After adding cells, the plates were spun at 2000 rpm for 2 min. The supernatant was removed and 50 l of IgG in PBS/ EDTA at the titrated concentrations were added to each well with mixing. Then, 50 l of 125 I-CLBFcgran-1 Fab in PBS/ EDTA at a concentration of 0.25-0.50 g/ml was added to each well, followed by a 45-min incubation on a shaker at 5°C. After washing 3 times, the cell pellets were removed and counted in a ␥ counter.
In the presence of increasing concentrations of the low affinity ligand (IgG, concentration c l l ), the binding of the high affinity ligand ( 125 I-CLBFcgran-1 Fab, concentration c l h ) to the cell surface receptor (CD16) is gradually reduced, or displaced. The displaced fraction, defined as the bound fraction ( f ) of CLBFcgran-1 normalized by the value when no IgG was present ( f 0 ), can be expressed by Equation 3.
Because the affinity to CD16 of 125 I-CLBFcgran-1 Fab (K a h ) and the receptor concentration (c r ) were predetermined from a separate experiment by Scatchard analysis, the only unknown in Equation 3 is the affinity of IgG (K a l ). Therefore, K a l can be calculated from a single measurement of F without the experimental displacement curve to include data at the IC 50 point. To increase the accuracy of the K a l value, however, the predicted displaced fraction (Equation 3) was nonlinearly fit to the entire f/f 0 versus c l l data set. Fig. 1, monomeric hIgG did not bind to a CM5 chip surface only coated with rabbit anti-mouse Fc antibody and mAb 214.1. However, after further functionalization with sCD16a, a similar injection of monomeric hIgG resulted in a time-dependent binding of 370 resonance units in 150 s. Switching the perfusate from hIgG solution to plain buffer resulted in dissociation of the bound hIgG. The chip was regenerated by washing off the 214.1-sCD16a-HIgG complex with three injections of 1 M for- mic acid at 2 min each, and then re-capturing mAb 214.1 and sCD16a. Binding resulted when the saturating concentration of CLBFcgran-1 Fab (anti-CD16 blocking mAb) was injected; however, subsequent injection of monomeric hIgG did not yield further binding (not shown), indicating nearly complete blockade of the sCD16a sites for hIgG binding. These results indicate that the binding of hIgG to the surface coated with sCD16a was mediated by the specific hIgG-sCD16a interaction.

Demonstration of Binding Specificity-As shown in
Separation of Monomeric and Multimeric IgG-The presence of multimers in commercial IgG even after high speed centrifugation was revealed by size exclusion chromatography as exemplified in Fig. 2A for RbIgG. Results for hIgG, hIgG1, and hIgG3 were similar (data not shown). The first peak, which appeared at fraction 28, was eluted at nearly the same time as the peak fraction of blue dextran (indicated by arrow). Blue dextran has a molecular mass (2,000 kDa) much higher than that of monomeric IgG (ϳ150 kDa) and was excluded by Sephadex G-200. This suggests that the first peak represents multimeric RbIgG. A second peak of RbIgG, which appeared at fraction 40, was eluted before BSA (peaked at fraction 51). The relative elution volumes (V e /V o ) of cytochrome c, BSA, and IgG (2nd peak, assumed to be monomeric) are plotted against their molecular weights in Fig. 2B and compared with published results (21). Good agreement is seen between our data and those of Andrews (21), indicating that the second IgG peak in Fig. 2A indeed represents monomers. The small difference in the relative volume of cytochrome c between the results of Andrews (21) and ours may be attributed to the difference in how long the column had been used, which was noted to influence the relative position of low molecular weight protein. As shown in Fig. 2A, the multimeric RbIgG comprised a significant fraction of RbIgG from the commercial source, which would have adversely affected the SPR measurement if not removed.
To determine whether the chromatographed IgG would form aggregates in experiments where reconcentrated IgG was used, the monomeric RbIgG fractions were pooled, reconcentrated to 5 mg/ml, and passed through the column again in the time scale of SPR experiments. It is evident from Fig. 2A that only a single, symmetric peak of monomeric IgG was seen, apparently free of any detectable multimers. This suggests that re-aggregation of IgG is a relatively slow process and did not occur under our experimental conditions, which is consistent with a previous report (12).
Kinetics of Monomeric IgG-sCD16a Interactions-Monomeric IgG solutions of increasing concentrations were perfused over the sCD16a-derivitized sensor chip and the interaction time courses were measured, as exemplified in Fig. 3. It can be seen that both the association and dissociation were relatively slow, requiring a few minutes to achieve equilibrium or reach half-dissociation. It is also apparent that RbIgG bound to and dissociated from sCD16a faster than human IgGs.
sCD16a was immobilized to the sensor chip via a nonblocking anti-CD16 mAb 214.1, which in turn was captured by a rabbit anti-mouse Fc antibody. Although at rates much slower than those of IgG ligands dissociating from sCD16a, sCD6a and 214.1 also dissociated from their respective capturing antibodies over time, manifested as a negatively drifting baseline. To correct for this effect, the curve resulting from an injection of plain buffer alone, in which the slow dissociation of 214.1 and sCD16a was monitored, was subtracted from all the measured binding curves. The refraction index difference between protein samples and the running buffer, manifested as an instantaneous resonance unit change, was also determined in a control experiment (on the same rabbit anti-mouse Fc antibody-coated chip but without sCD16a immobilization) and subtracted from raw data in all sensorgrams presented here.
A Langmuir (1:1) model was fit simultaneously to the entire family of data curves in both association and dissociation phases. Such a global fitting procedure accentuates deviation at any one concentration but ensures more robust kinetic constants overall (22). The kinetic rates so evaluated are summarized in Table 1; and the model predictions based on these parameters are exemplified in Fig. 4 along with the data. It can be seen that the model fits both the association and dissociation data of the hIgG-sCD16a interaction reasonably well. Similarly good fits were obtained for the hIgG1-and RbIgG-sCD16a interactions (data not shown). By comparison, the fit for the hIgG3-sCD16a interaction is not as good (data not shown). Despite its low concentration in serum (23), hIgG3 is known to comprise at least 12 allotypes (24). In this study, no attempt was made to further separate the various hIgG3 allotypes from the purchased heterogeneous mixture, which, we believe, is the reason why the homogeneous Langmuir model does not fit the hIgG3-sCD16a interaction data well.
Kinetics of Multimeric IgG-sCD16a Interactions-Compared with monomers, multimeric IgG dissociated from sCD16a much more slowly and required much lower concentrations to achieve the same level of binding, indicating a much higher avidity (Fig. 5). For the purpose of comparing our results with data in the literature, the same Langmuir model was used to fit the association and dissociation curves of IgG multimers. The kinetic mechanism for binding of multimeric ligands must not be 1:1; as such, a more involved model is needed to extract the intrinsic kinetic constants. Fitting the simple Langmuir model   Table 1. RU, resonance units.  to the multimeric ligand binding data returns the apparent rates of a surrogate monomeric ligand whose kinetics would generate approximately the same time courses as the multimeric ligand. The apparent on-and off-rates so obtained nevertheless reveal the much higher binding capacities of the IgG multimers than those of the IgG monomers. The apparent rates obtained from the multimeric ligand experiments are listed in Table 1.
Affinity of mAb CLBFcgran-1 Fab-sCD16a Interactions-It should be instructive to compare receptor-ligand and antibodyantigen interactions. CLBFcgran-1 Fab solutions at various concentrations were perfused over a sCD16a-derivitized surface. It is evident from Fig. 6A that CLBFcgran-1 Fab bound sCD16a with a much higher affinity and a much slower off-rate than any of the sCD16a ligands tested.
Antibody typically binds to antigen with a rather high onrate. In such a case mass transfer may be the limiting step (4); fitting a transient model to the association and dissociation time courses would likely yield erroneous results. To circumvent this problem, Scatchard analysis (Fig. 6B) was used to derive the binding affinity of CLBFcgran-1 Fab for sCD16a. The estimated equilibrium dissociation constant is in the order of nanomolar (Table 2). In comparison, the K d values for IgG-sCD16a interactions are in the order of micromolar.
The sCD16a-IgG Binding Kinetics Were Not Affected by the Injection Time-The presence of a significant amount of multimers in the chromatographed IgG could give rise to a multiexponential appearance in both association and dissociation sensorgrams. Such a diagnostic feature was not observed (e.g. Fig.  3). However, this effect could be amplified by the long injection time because multimeric ligands would continue to bind the receptors after the binding of monomeric ligands had achieved equilibrium (25). Also, due to their high avidity, multimers, even if only present in undetectable amounts in the monomer solution, might gradually replace the bound monomers, thus giving rise to an artifactually slow dissociation. The longer the injection time, the slower the dissociation, as the bound multimers would accumulate on the sensor surface over time (25). To address these issues, chromatographed hIgG of various concentrations were perfused over immobilized sCD16a in an experiment with long injection time and low flow rate (10 min and 5 l/min, respectively) to amplify the multimeric effect, if any. Again, multiexponential appearance was not observed (Fig. 7). The kinetic rates so obtained (k on ϭ 6.47 ϫ 10 3 M Ϫ1 s Ϫ1 and k off ϭ 4.52 ϫ 10 Ϫ3 s Ϫ1 from the data exemplified in Fig. 7) were compared with those listed in Table 1, which were evaluated from experiments that minimize the multimeric effect by using a short injection time and fast flow rate (2.5 min and 30 l/min, respectively). The lack of dependence of kinetic rates on the injection time and flow rate, as shown by the excellent agreement between the two sets of values, suggests a minimal (if any) role of the effect in question.
The sCD16a-IgG Binding Kinetics Were Not Affected by Reconcentrating the Chromatographed IgG-Due to their limited quantities, the fractions of chromatographed hIgG1 and hIgG3 were reconcentrated in a protein concentrator before kinetic measurements. It has been reported that in this step some monomeric ligands may form multimeric aggregates (which might escape detection by chromatography), which may in turn affect the subsequent kinetic measurement (25). To address this issue, chromatographed hIgG was reconcentrated to a nearly 2-fold higher concentration (0.7 mg/ml) than those normally used in kinetic measurements, which was then used in an experiment with long injection time and slow flow rate (10 min and 5 l/min, respectively) to favor multimeric binding. Again, multiexponential appearance was not observed (Fig. 8).
The on-and off-rates (6.12 ϫ 10 3 M Ϫ1 s Ϫ1 and 4.56 ϫ 10 Ϫ3 s Ϫ1 , respectively) so obtained are similar to those measured from experiments using chromatographed hIgG without reconcentration and with short injection time and fast flow rate (Table 1). This suggests that reconcentrating the chromatographed IgG did not have much of an adverse effect on the kinetic measurement.  (Table 2). RU, resonance units. Binding to Partially Blocked sCD16a Resulted in Similar Kinetic Rates as Unblocked sCD16a-To test whether the two binding sites of the dimeric sCD16a molecule would work cooperatively to produce higher binding and slower dissociation, the active sites of immobilized sCD16a were partially blocked by injection of a sub-saturating concentration of CLBFcgran-1 Fab to reduce the maximum ligand binding capacity by 70%. Monomeric hIgG solutions at various concen-trations were then injected to the sensor chip, as shown in Fig.  9. The globally fitted on-and off-rates (6.41 ϫ 10 3 M Ϫ1 s Ϫ1 and 4.43 ϫ 10 Ϫ3 s Ϫ1 , respectively) are very similar to those obtained from experiments using unblocked sCD16a (Table 1), suggesting the lack of cooperation between the two binding sites of the dimeric sCD16a.
CD16a TM on CHO Cell Surface Had Similar Binding Kinetics and Affinities to sCD16a on Sensor Chip-Two sets of experiments were performed to test whether sCD16a-Ig coupled on sensor chip has binding characteristics comparable with CD16a TM anchored on the cell surface. In the first set, the binding kinetics of monomeric hIgG1 for the CHO cell CD16 TM were measured by real time flow cytometry. Fig. 10A shows association time courses of CHO cells transfected to express CD16a TM due to binding of four concentrations of chromatographed fluorescein isothiocyanate-conjugated hIgG1 (closed symbols). Fig. 10B shows the corresponding dissociation time courses. The low affinity of CD16a TM -hIgG1 binding (K d in M range) required submilligram per ml concentrations of hIgG1 to achieve appreciable binding, which resulted in high nonspecific MFI of B7-1 GPI -expressing CHO cells. The nonspecific MFI was especially high in the association assays, which also increased with increasing hIgG1 concentration (open symbols in Fig. 10A). This was due to the presence of a high concentration of fluorescence molecules in the binding buffer, as their removal in the dissociation assay greatly reduced the nonspecific MFI signals, suggesting that such signals were not caused by hIgG1 binding that could last more than 10 s, the time for the first data point.
Specific binding curves were obtained by subtracting MFI of B7-1 GPI -expressing CHO cells from that of CD16a TM -expressing CHO cells measured at matched hIgG1 concentrations at   matched time points (Fig. 10, C and D). Equations 1 and 2 were simultaneously fit (curves) to the corresponding association (Fig. 10C) and dissociation (Fig. 10D) data (points) for each hIgG1 concentration with a set of model parameters (k on , k off , R T , and ). Unlike the fitting of SPR data, an additional param-eter was introduced because the equilibrium MFI level from the association assay did not match the initial MFI level of the dissociation assay (Fig. 10, C and D). Similar to the analysis of SPR data, only the first 240 s in the dissociation data that follow single exponential decay were used in the fitting to minimize the potential impact of possible rebinding on the best-fit parameters. The individually fitted observed rate k obs ϭ k on L ϩ k off was found to increase linearly with the concentration of hIgG1 (Fig. 10E), as predicted by Equation 1. The y axis intercept, the slope, and their ratio provide respective global estimates for off-rate (k off ϭ 6.6 ϫ 10 Ϫ3 s Ϫ1 ), on-rate (k on ϭ 2.6 ϫ 10 4 M Ϫ1 s Ϫ1 ), and equilibrium dissociation constant (K d ϭ 0.25 M), which are comparable with their averaged values from the four individual fits Experiments were performed at 0, 15, 20, and 37°C and the kinetic parameters so evaluated are plotted in Fig. 11. It is evident that they are comparable with those of the sCD16a-hIgG1 binding measured by SPR (Table 1). The standard free energy of binding at these temperatures were also calculated (Fig.  11D). The dependence of ⌬G 0 on T was found to agree qualitatively with published results (14,26).
To obtain independent confirmation of some of the above results, the affinities of CLBFcgran-1 Fab and monomeric IgG ligands for CHO cell surface CD16 isoforms were measured in the second set of experiments. Fig. 12 shows Scatchard analyses of the binding of 125 I-labeled CLBFcgran-1 Fab to CD16a TM , CD16b NA1 , and CD16b NA2 . The estimated affinities are listed in Table 2. Fig. 13 shows the displacement curves of monomeric hIgG and RbIgG for three CD16 membrane isoforms. The affinities, estimated from fitting Equation 3 to the data (6), are summarized in Table 2. It is evident that for all three cases tested (CLBFcgran-1 Fab, RbIgG, and hIgG), the affinities of CD16a TM expressed on CHO cells are in reasonable agreement with those of sCD16a immobi- assays. The MFI were plotted against time at which samples were run (closed black symbols). CHO cells transfected by the same procedure but to express a different molecule, B7-1 GPI , were mixed with matched concentrations of the same ligands and analyzed at the same time points to provide a control for nonspecific background binding (open symbols). The time courses for specific binding (closed gray symbols), obtained by subtracting MFI of B7-1 GPI -expressing CHO cells from that of CD16a TM -expressing CHO cells at matched ligand concentrations, were fitted by Equations 1 and 2 simultaneously for the respective association data (C) and dissociation data (D) for each ligand concentration. E, the rate parameter, k obs ϭ k on L ϩ k off , that best fit a pair of individual association and dissociation data curves in C and D is plotted against the concentration of hIgG1, L. According to Equation 1, the slope and the y axis intercept are, respectively, equal to k on and k off . lized on the BIAcore sensor chip. It should also be noted that CD16a TM bound hIgG and RbIgG with much higher affinities than did CD16b NA1 and CD16b NA2 . CD16b NA1 and CD16b NA2 have similar affinities for hIgG and RbIgG.

DISCUSSION
The primary goal of the present work was to determine the kinetic rates of IgG-sCD16a interactions in solution. Whereas the increasingly popular SPR technology makes these measurements seemingly easy, careful studies have revealed several sources of potential artifacts that may be equally easily produced by the misuse of this technique (27). We therefore felt obliged to ask: are the kinetic rates measured in the present work intrinsic to monomeric IgG-sCD16a interactions? To address this question rigorously, several tests were performed to systematically rule out potential artifacts in SPR measurements. Possible sources of the artifacts include mass transport limitation (27), the presence of multimers due to reaggregation of the monomers either spontaneously or during the process of re-concentration (25), the cooperation between the two binding sites of the dimeric sCD16a, the use of inappropriate kinetic model, heterogeneity of the reactants, and problems in receptor immobilization (27). These are discussed below.
Mass Transport Was Not Limiting in the IgG-sCD16a Interactions-Otherwise, the association phase would have been slowed down by the limited supply of ligands and rebinding would have been significant during the dissociation phase, leading to underestimated off-rates. The criterion for a transport-limited reaction in the SPR measurement is the ratio of rate of mass transport to that of intrinsic molecular reaction, Q, such that when Q Ͼ Ͼ 1, the reaction is not considered to be transport-limited. Q ϭ mtc/k on R max , where R max is the maximum ligand binding capacity of the receptor-coated surface and mtc is the mass transport coefficient. Based on the analysis of convective and diffusive mass transport for the following, where b, l, and h are the respective width, length, and height of the flow cell, f is the flow rate, and MW is the molecular weight of the ligand. To examine whether the reactions in our experiments were transport limited, the Q values were calculated and listed in Table 3. As can be seen, even at the low flow rate, the Q values were 1-2 orders of magnitude greater than unity for all FIGURE 11. Temperature dependence of CD16a TM -hIgG1 binding. The kinetic on-rate (A), off-rate (B), equilibrium dissociation constant (C), and standard free energy of binding (D) of CD16a TM -hIgG1 binding were plotted against temperature at which they were measured by real time flow cytometry. Data are presented as mean Ϯ S.E. estimated from two to four curves. Fab to CD16a TM , CD16b NA1 , and CD16b NA2 on the CHO cell surface was determined by radioimmunoassay. Specific CLBFcgran-1 Fab-CD16 binding was obtained by subtracting from the total binding to CD16-expressing CHO cells the background binding of the same concentrations of mAb to plain CHO cells. The concentration of the specifically bound mAb divided by that of the free mAb was plotted against the concentration of the bound mAb. A straight line was fit to each set of data (points) and the equilibrium dissociation constant of mAb for CD16 was calculated from the negative reciprocal slope of the line ( Table 2). The experiment was done in triplicate and repeated twice with similar results.
IgG ligands tested. This indicates a much faster mass transport than intrinsic reaction, which minimizes the potential for the limited mass transport to yield artifactually slow off-rates. The insensitivity of estimated kinetic rates to the flow rate (k on ϭ 6.47 and 6.51 ϫ 10 3 M Ϫ1 s Ϫ1 and k off ϭ 4.52 and 4.71 ϫ 10 Ϫ3 s Ϫ1 for f ϭ 5 l/min and 30 l/min, respectively) and to the amount of immobilized sCD16a (k on ϭ 6.41 and 6.51 ϫ 10 3 M Ϫ1 s Ϫ1 and k off ϭ 4.43 and 4.71 ϫ 10 Ϫ3 s Ϫ1 for R max ϭ 51 and 212 resonance units, respectively) provided further evidence for the lack of influence of mass transport on our SPR measurements. Despite the fact that mass transport limitation was not expected to be a problem, precautions were taken in both experimental design and data analysis. The amount of sCD16a immobilized on the sensor chip was kept low (Ͻ300 resonance units). The flow rate (30 l/min) used for the kinetic measurements was the fastest allowable in our BIAcore instrument. Only the data in the first 60 s immediately after switching to the plain buffer was used for the dissociation analysis to minimize any possible rebinding effect. Because of these precautions and the large Q values, it is unlikely that the measured off-rates are influenced by the mass transport limitation.
The antibody-antigen interaction between CLBFcgran-1 Fab and sCD16a was more likely limited by mass transport. As such, the kinetic rates estimated from fitting the sensorgrams in Fig. 6A (k on ϭ 6.7 ϫ 10 5 M Ϫ1 s Ϫ1 and k off ϭ 7.6 ϫ 10 Ϫ4 s Ϫ1 ) may be apparent rather than intrinsic constants. However, due to the low (nanomolar) concentrations needed for the SPR measurements, aggregation is not expected to be a problem, and the affinity measured via Scatchard analysis should thus be reliable.

The Kinetic Rates of Monomeric IgG-sCD16a Interactions Were Not Affected by the Possible Presence of Multimers-Gel
filtration was used to separate monomers and multimers from commercial IgG. Had the chromotographed IgG reaggregated quickly, however, the monomeric IgG used in SPR measurement might have contained multimers of a significant amount to slow down the dissociation and led to underestimated offrates. To test this possibility, monomeric IgG diluted by chromatography was re-concentrated to 5 mg/ml (ϳ7 times higher than the highest concentration used in the SPR measurement) and passed through the gel filtration column again in the time scale of the SPR experiment (ϳ4 h). As can be seen from Fig. 2A, the reconcentrated IgG eluted as a single symmetric peak at the same position as that of the monomeric IgG in the previous gel filtration experiment. Thus, multimers were not detected in the second gel filtration. This result is in agreement with a previous report, which showed that monomeric IgG remained monomeric in solution for at least 48 h (12). Despite this evidence, low IgG concentrations (Յ0.7 mg/ml) were nevertheless used in the SPR experiments, which were performed immediately after gel filtration. These precautions ensured that the amount of re-aggregated IgG (if any) would always be below the detection limit of size exclusion chromatography.
To test whether the undetectable trace amount of multimeric ligands (if any) would result in artifactually slow apparent off-rates, SPR experiments were performed with different flow rates and injection times. It has been reported that when monomeric ligands were contaminated with multimers, longer injection time would result in more multimeric binding (25). Using multimeric ligands, we also found greater binding of largersized aggregated IgG with longer injection times (data not shown). However, a 4-fold prolonged injection time did not cause any change in the kinetic rates of monomeric IgG-sCD16a binding (Fig. 7). The same result was found even when reconcentrated IgG was used (Fig. 8). Thus, either the kinetic rates were the same for both multimeric and monomeric interactions, or the multimer contamination was too high or too low for the kinetic rates to be sensitive to the further accumulation of multimers over time. The first two possibilities can be ruled out. Kinetic measurements of multimeric binding revealed their faster on-rates and slower off-rates (Table 1). Gel filtration experiments were unable to detect any multimer contamination in the monomer solution ( Fig. 2A). Thus, even if trace amounts of multimers had existed in the chromatographed IgG, its concentration would have been too low to affect the kinetic rates of the monomeric IgG-sCD16a interactions. The lack of influence of aggregated ligands in our system is probably due to the low concentrations of monomeric ligands used in the SPR experiments (Յ0.7 mg/ml). In the experiment of Maenaka et al. (14), by comparison, the ligand concentrations used were as high as 11.5 mg/ml.
Dimeric sCD16a Likely Has Similar Ligand Binding Kinetics as Monomeric Molecule-It is possible that two IgG molecules that are bound to the same sCD16a dimer associate to form a stable complex, which delays dissociation. Also, the dimeric sCD16a molecule may favor rebinding because there are two sites available for capturing the dissociated IgG instead of one, again resulting in an apparently slow off-rate. To address this  Table 2). The experiment was done in triplicate and repeated three times with similar results. issue, sCD16a was partially blocked in an experiment by a subsaturating concentration of Fab fragment of CLBFcgran-1, an anti-CD16 adhesion blockade mAb (Fig. 9), which binds to an epitope near the ligand binding site (28). Assuming equal and independent binding of CLBFcgran-1 Fab to every antigen epitope regardless of whether the other epitope on the same sCD16a dimer is free or occupied, it can be estimated that when 70% of Fc binding sites was blocked, only Ͻ18% of those sCD16a dimers that have at least one site unblocked would have both sites available for IgG binding. In other words, Ͼ82% of functional sCD16a molecules only have a single site for IgG binding. Should the dimeric sCD16a cause slow dissociation, a much faster off-rate would have been predicted in this partially blocked configuration. That the kinetic rates in this experiment were found very similar to those measured using unblocked sCD16a (k on ϭ 6.41 and 6.51 ϫ 10 3 M Ϫ1 s Ϫ1 and k off ϭ 4.43 and 4.71 ϫ 10 Ϫ3 s Ϫ1 for experiments using partially blocked and unblocked sCD16a, respectively) suggests that the dimeric nature of sCD16a did not alter the kinetics of its monovalent interaction with ligands. Binding Stoichiometry, Kinetic Mechanism, Receptor Orientation, Decaying Surface, and Ligand Heterogeneity-The present work used a Langmuir model to fit all the SPR data to estimate kinetic rates. The 1:1 stoichiometry for the IgG-sCD16a interaction is supported by a previous analytical centrifugation measurement (26) and by a hIgG1-sCD16 co-crystal structural model (29,30). As possible kinetic mechanisms, we tested both a single-step model, A ϩ B ϭ C, and a two-step model, A ϩ B ϭ AB ϭ C, where A, B, AB, and C denote, respectively, IgG, sCD16a, intermediate IgG-sCD16a complex, and stable IgG-sCD16a complex. Although using the two-step model resulted in slightly better fits to the data, the improvement was too small and the data were insufficient to warrant the more complicated model with two more freely adjustable parameters.
The presentation of surface molecule is known to affect SPR measurements; but the two-step procedure with capturing antibodies likely resulted in proper and uniform orientation of the immobilized sCD16a for ligand binding. However, immobilizing sCD16a this way yielded a decaying surface for ligand binding, because over time sCD16a dissociated from 214.1, which also dissociated from the rabbit anti-mouse Fc antibody. Although more rigorous treatment of the decaying surface is possible (31), the much slower dissociation of antibody-antigen interactions than that of IgG-sCD16a interactions allows simply subtracting the negatively drifting baseline to be an adequate correction for the effect of the antibody-antigen dissociation on the measured kinetic rates of the IgG-sCD16a binding.
The IgG ligands tested in the present work are heterogeneous even for those of single isotypes. For example, hIgG3 comprises at least 12 allotypes (24). Ligand heterogeneity appeared to affect the ability of the Langmuir model to fit the data of hIgG3 but not hIgG1, RbIgG, or hIgG. Total human IgG in serum is known to consist of four isotypes, with relative abundance of 60, 30, 6, and 3% for hIgG1-4, respectively (32). Preliminary experiments suggests that hIgG2 binds sCD16a with an affinity 15-20 times lower than that of hIgG1 (data not shown). The predominance of hIgG1 may explain why the Langmuir model appears to work in the case of hIgG despite its heterogeneity.
Comparison with Other Experiments-Having ascertained that intrinsic monomeric IgG-sCD16a interactions have indeed been measured, the next questions are, does sCD16a retain the binding characteristics of cell surface CD16a? How are our results compared with results from other studies? These are legitimate questions because sCD16a, which was made by fusing the extracellular domain of CD16a with the Fc fragment of hIgG1 (17), lacks the transmembrane and cytoplasmic domains and the associated ␥ and/or signaling subunits. Furthermore, the secreted sCD16a was purified by affinity chromatography and then immobilized on the biosensor chip via nonblocking antibody. Both the membrane anchor (6) and the ␥ chain (10) have been shown to alter kinetic rates/binding affinity.
To address the first question, two sets of independent binding studies were performed using CD16-expressing CHO cells. Real-time flow cytometry kinetic analysis yielded off-rates very similar to that measured by SPR, whereas the on-rates and hence dissociation constant from the two experiments differed by a few fold. Scatchard analysis showed that CLBFcgran-1 Fab bound to CHO cell CD16a TM with a K d ϳ 2-fold of the value estimated in the SPR measurement using sCD16a. The K d values of CD16a TM for monomeric hIgG and RbIgG measured from the competitive inhibition binding experiments were also ϳ2-fold of those of the sCD16a for the respective ligands via SPR measurement. These data are consistent with the results of a separate study of ours, which showed that the effect of CD16 anchor on its on-rate (but not the off-rate) depended on the nature of the anchor regardless of whether CD16 was on the cell surface or extracted from the cell and then immobilized on a surface. 8 Given the different conditions between the CHO cell CD16a TM experiment and the sCD16a experiment, it is difficult to further interpret the small differences in the binding parameters. Thus, sCD16a on the biosensor chip bound IgG ligands and a mAb with affinities and/or off-rate similar to those of CD16a TM on the CHO cell membrane.
A previous SPR study of hIgG1 and hIgG3 binding to sCD16b NA2 (a monomer) reported 2-5-fold slower off-rates (0.98 and 2.63 ϫ 10 Ϫ3 s Ϫ1 , respectively) and similar (0.76 M for hIgG1) or 7-fold larger (3.8 M for hIgG3) equilibrium dissociation constants (13) compared with the values found here for the hIgG1-and hIgG3-sCD16a interactions (Table 1). By comparison, our competitive inhibition binding experiments using chromatographed ligands found that CHO cells CD16b NA1 and CD16b NA2 bound IgG (from both human and rabbit species) with K d values several tens fold greater than those of CHO cell CD16a TM (Table 2). On the other hand, a more recent SPR study using an inverted configuration (i.e. perfusing monomeric sCD16b NA2 over immobilized IgG) found much faster off-rates (half-life of a few seconds) (14). No resolution has been found at this point, and further studies are required to address these discrepancies.
We previously measured the kinetic rates of CHO cell CD16a TM and CD16a GPI , and CHO cell and K562 cell CD16b NA2 interacting with IgG coupled to the red blood cell surface using a micropipette technique (6 -9). The off-rates for the hIgG-CD16a TM and RbIgG-CD16a TM (on CHO cells) and hIgG1-CD16b NA2 (on CHO and K562 cells) interactions were 0.34, 0.24, 0.70, and 0.50 s Ϫ1 , respectively. Although the solution (i.e. the so-called three-dimensional interaction) and surface (i.e. the so-called two-dimensional interaction) binding off-rates have the same unit of s Ϫ1 , they have been theorized as physically distinct quantities (33). A major physical difference between the two-and three-dimensional binding is that, instead of approaching one another by free diffusion in the three-dimensional case, molecules in two-dimensional interactions are brought together (and apart) by cells to which they are anchored. Cells are 1,000 times the size of the molecules; and thereby their motions dictate the transport of the reacting molecules prior (and post) to their intrinsic binding (34,35). The difference between the three-dimensional k off values measured via the SPR technique and the two-dimensional k off values measured by the micropipette technique has been highlighted in a recent study (36). The present study has provided another such example. These examples provide a starting point for studying the relationship between two-and three-dimensional kinetic parameters.