Multivalent DNP-BSA is commonly used to cross-link anti-DNP IgE bound to FcεRI to stimulate cellular responses, although key features of the binding process are unknown. Fluorescence quenching can be used to study the kinetics of DNP-BSA binding to FITC-IgE. We observe that DNP-BSA binds more slowly to IgE than does an equimolar amount of a monovalent DNP ligand, suggesting that the average effective number of DNP groups per BSA is less than one. The binding data are well described by a transient hapten exposure model in which most of the DNP groups are unavailable for binding but have some probability of becoming exposed and available for binding during the time of the binding measurement. Additional experiments indicate that, for suboptimal to optimal concentrations of DNP-BSA, most of the FITC fluorescence quenching on the cell surface is due to cross-linking events. With these concentrations at 15°C, the kinetics of FITC fluorescence quenching by DNP-BSA correlates with the kinetics of DNP-BSA-stimulated tyrosine phosphorylation of FcεRI. At 35°C, the phosphorylation kinetics are biphasic during the time period in which cross-linking continues to increase. Our results establish a quantitative relationship between the timecourse for cross-linking by multivalent Ag and FcεRI-mediated signaling, and they provide the means to predict the kinetics of cross-linking under a wide variety of conditions.

Antigen-mediated aggregation of immunoreceptors initiates signal transduction leading to cellular activation, and this has been best characterized for FcεRI, the high affinity receptor for IgE (1). RBL-2H3 mast cells, which express ∼3 × 105 FcεRI/cell, often serve as a model system for examining this process in detail. Monomeric IgE binding to FcεRI does not stimulate a cellular response but does create a bivalent cell surface receptor for Ag with the specificity of the IgE. Binding of monovalent ligand to IgE-FcεRI causes no response. However, aggregation of IgE-FcεRI by multivalent Ag generates a complex cascade of cellular responses, including tyrosine phosphorylation of multiple proteins, inositol phosphate production, Ca2+ mobilization, and protein kinase C activation, culminating in degranulation and secretion of mediators of allergy and inflammation (2). Steady progress has been made in elucidating the binding properties of bivalent ligands, particularly from studies with the symmetric bivalent ligand, N,N′-bis(ε-N-(2,4-DNP)aminocaproyl-l-tyrosine)- cystine ((DCT)2-cys)3 (3). However, synthetic bivalent ligands, such as (DCT)2-cys, typically stimulate only weak cellular responses (4, 5). Multivalent ligands, such as BSA conjugated with multiple DNP groups (DNP-BSA), are used extensively in experimental studies to stimulate strong cellular responses (1, 3), but the features of Ag binding that are critical for signaling have not been fully defined.

A major reason that DNP-BSA binding and cross-linking have not been examined in detail previously is the complexity encountered in describing these processes. Whereas bivalent ligands are limited to forming linear or cyclic complexes with bivalent IgE, multivalent ligands can also form a variety of complicated branched structures (6, 7). We have initiated a detailed study of multivalent ligand binding to surface IgE by using a simple mathematical model to analyze the observed kinetics of DNP-BSA binding to IgE-FcεRI. We find that these data can be explained by a transient hapten exposure model, in which individual DNP groups are mostly inaccessible for binding to IgE but transiently become exposed, allowing binding and cross-linking to proceed.

Protein tyrosine phosphorylation is known to be a primary signaling event for FcεRI and other members of the multichain immune recognition receptor family (8, 9). As established in RBL-2H3 cells, tyrosine phosphorylation of FcεRI β and γ subunits is the earliest detectable cytoplasmic signaling event resulting from Ag-mediated aggregation of IgE-FcεRI (10). Therefore, we compared the kinetics of DNP-BSA binding to, and cross-linking of, IgE-FcεRI with those of DNP-BSA-stimulated tyrosine phosphorylation of FcεRI to relate these two processes directly.

FITC was obtained from Molecular Probes (Eugene, OR). The protein-reactive carbocyanine dye Cy3 was purchased from Biological Detection Systems (Pittsburgh, PA). Monoclonal mouse IgE specific for DNP (11) was purified (12) and modified with FITC (13) as previously described. The monovalent DNP ligand {ε-[(2,4 DNP)amino]caproyl}-l-tyrosine (DCT) was purchased from Biosearch (San Rafael, CA). BSA, conjugated with an average of 15 DNP groups (DNP-BSA), and bovine γ-globulin (BGG), conjugated with an average of 25 DNP groups (DNP-BGG), were prepared as previously described (14). DNP-BSA was chromatographed on a Sepharose 12 HPLC gel filtration column (Phamacia Fine Chemicals, Piscataway, NJ) to remove trace amounts of aggregates. Conjugation of DNP-BSA with Cy3 (yielding 2.4 DNP groups per Cy3 bound) was conducted as recommended by the Cy3 manufacturer. Concentrations of BSA and BGG were determined by absorption at 280 nm using extinction coefficients of 0.69 ml/(mg · cm) and 1.4 ml/(mg · cm), respectively; absorption by DNP and Cy3 at this wavelength was corrected. ImmunoPure Immobilized Protein A was purchased from Pierce Chemical Co. (Rockford, IL). Polyclonal rabbit anti-IgE was purified by affinity chromatography (15). Horseradish peroxidase-conjugated mouse mAb 4G10 and recombinant Ab RC20H, both specific for phosphotyrosine, were purchased from Upstate Biotechnology (Lake Placid, NY) and Transduction Laboratories (Lexington, KY), respectively.

RBL-2H3 cells (16) were grown in stationary culture and harvested as described (17), then resuspended in buffered saline solution (BSS: 135 mM NaCl, 5 mM KCl, 20 mM HEPES, 1.8 mM CaCl2, 1 mM MgCl2, 1.8 mM glucose, 0.1% gelatin, pH 7.4). For spectrofluorometric measurements, suspended cells (∼1 × 107 cells/ml) were mixed with a three- to fivefold molar excess of FITC-anti-DNP-IgE over FcεRI and rotated at 37°C for 75 min to saturate FcεRI, then washed three times with BSS. For tyrosine phosphorylation experiments, cells were sensitized overnight or for 75 min at 37°C with three- to fivefold excess of anti-DNP-IgE over FcεRI. For flow cytometric measurements, cells were sensitized with three- to fivefold excess of unlabeled anti-DNP-IgE over FcεRI. Cells were resuspended in BSS at 1 to 2 × 106 cells/ml for all experiments.

Steady state fluorescence measurements were made with an SLM 8000 fluorescence spectrophotometer (SLM, Urbana, IL) operated in ratio mode. For each experiment 1.3 to 2.0 ml RBL-2H3 cells saturated with FITC-IgE were stirred continuously in a 10×10×40-mm acrylic cuvette and thermostatically controlled at 15°C or 35°C as indicated. FITC was excited at 495 nm, and emission was monitored at 520 nm. Indicated concentrations of DNP-BSA or DNP-BGG solution were added, and the FITC quenching was monitored. Dissociation was induced by adding a large excess of DCT and monitored by the partial recovery of FITC that occurs when DCT replaces DNP-BSA in the FITC-IgE combining sites, causing less fluorescence quenching per site (18). The data were collected at 1-s intervals with an AST386 computer (AST Products, Billerica, MA). For experiments at 35°C, 2 μM cytochalasin D, which is known to inhibit aggregation-dependent internalization (19), was added to the cells before the addition of DNP-BSA. This prevents additional fluorescence quenching resulting from the acidic environment encountered by internalized FITC. Independent experiments showed that cytochalasin D has no significant effects on the kinetics of DNP-BSA binding and cross-linking (Ref. 20 and data not shown).

Cell-associated Cy3 fluorescence was measured by a Coulter Epics Profile flow cytometer (Coulter Electronics, Hialeah, FL). Excitation was provided by an air-cooled argon ion laser with spectral lines at 458 nm, 488 nm, and 514 nm (intensities at 458 nm and 514 nm are about 20% of that at 488 nm). Emitted light was passed through a 457- to 515-nm laser blocking glass interference filter, followed by a 550-nm dichroic short pass glass filter. The reflected light then passed through a 590-nm long pass glass filter and was detected as Cy3 fluorescence. For each experiment, 1 ml of RBL-2H3 cells saturated with unlabeled IgE was maintained at 15°C, and the cells were gently agitated occasionally to maintain suspension.

IgE-saturated cells were stirred in a 25-ml Celstir spinner flask (Wheaton, Millville, NJ) and maintained at 15°C or 35°C while indicated concentrations of DNP-BSA were added to stimulate the cells. Cells (750 μl) were removed from the flask at indicated times and mixed with an equal volume of ice-cold 2× lysis buffer (20 mM Tris, 2 mM Na3VO4, 30 mM Na4P2O7, 10 mM glycerolphosphate, 0.04 U/ml aprotinin, 0.02% NaN3, 6 mM EDTA, 2 mM 4-(2-aminoethyl)-benzenesulfonylfluoride (Calbiochem, La Jolla, CA), pH 8.0) containing 0.13% TX-100. This was followed by addition of 10 μM DCT to dissociate bound DNP-BSA, incubation on ice for 10 min, then centrifugation at 14,000 × g for 5 min at 4°C in a Hermle Z 230 MR microfuge (B. Hermle, AG, Gosheim, Germany) to sediment the nuclei. The supernatants were incubated with 1 μg/ml polyclonal rabbit anti-IgE on ice for 1 h, followed by rotating with 35 μl protein A beads at 4°C for 1 h to immunoprecipitate the IgE-FcεRI. The beads were washed once in lysis buffer containing 0.06% TX-100 followed by another wash with lysis buffer without detergent, then boiled in 33 μl sample buffer (10% glycerol, 1% SDS, 0.05 M Tris, pH 6.8) for 3 min, followed by centrifugation, removal of the supernatant, and reextraction of the beads with the same volume of sample buffer. Proteins in the combined sample buffer supernatants were separated by SDS-PAGE under nonreducing conditions, then transferred to immobilon-polyvinylidene difluoride (PVDF) (Millipore, Bedford, MA) using a semidry transfer apparatus (Integrated Separation Systems, Hyde Park, MA). Membranes were blocked with 5% BSA then probed with horseradish peroxidase-conjugated anti-phosphotyrosine Abs (4G10 or RC20H). Blots were developed using ECL chemiluminescence and Hyperfilm-ECL (Amersham, Arlington Heights, IL). In most of these experiments, the only bands detected with apparent molecular mass less than 200 kDa were tyrosine-phosphorylated FcεRI β and γ, as previously identified (21). Densitometry was performed with a Quick Scan Flur-Vis Densitometer (Helena Laboratories, Beaumont, TX). Peak intensities were integrated after subtracting the background.

Time-dependent tyrosine phosphorylation of the β subunit of FcεRI was plotted together with the time-dependent quenching of FITC-IgE fluorescence obtained under the same conditions of DNP-BSA binding and stimulation. The relative tyrosine phosphorylation obtained at 15°C was scaled to maximize overlap with the fluorescence-quenching curves at the longer time points measured. Tyrosine phosphorylation data obtained under the same stimulating conditions for three separate experiments were included in this analysis. Unlike the phosphorylation data, which are subject to scatter, the fluorescence-quenching curves are highly reproducible. Therefore, a single fluorescence-quenching curve is compared with the combined phosphorylation data.

Two models were used to analyze DNP-BSA binding data, a monovalent ligand model and a transient hapten exposure model. For both models, we make the following simplifying assumptions: 1) all the Fab binding sites have the same intrinsic binding properties; 2) all the DNP groups conjugated to BSA fall into two categories: they are either not available for binding (buried DNP) or available for binding and have the same intrinsic binding properties (exposed DNP); 3) FITC fluorescence quenching is proportional to the Fab binding site occupancy, i.e., the fluorescence quenching per Fab site bound remains the same regardless of whether the Fab site is occupied by monovalently bound DNP-BSA or by DNP-BSA that bridges two or more Fab sites.

FIGURE 2.

Analysis of DNP-BSA (B) and DCT (C) binding to cell-bound FITC-IgE with monovalent ligand model (A). The small open and closed circles in the schematic diagrams in A represent the DNP groups on BSA unavailable and available for binding, respectively. Data for DNP-BSA and DCT binding to cell-bound IgE (in B and C) are the same as those shown in Figure 1. The solid lines represent best fits with the monovalent ligand model (Eqs. 1–4FD1FD2FD3FD4). The values for the fitting parameters derived are: (B) k+1 = 1.1 × 106 M−1 · s−1, k−1 = 5.4 × 10−3 s−1; (C) k+1 = 2.0 × 107 M−1 · s−1, k−1 = 1.1 × 10−2 s−1.

FIGURE 2.

Analysis of DNP-BSA (B) and DCT (C) binding to cell-bound FITC-IgE with monovalent ligand model (A). The small open and closed circles in the schematic diagrams in A represent the DNP groups on BSA unavailable and available for binding, respectively. Data for DNP-BSA and DCT binding to cell-bound IgE (in B and C) are the same as those shown in Figure 1. The solid lines represent best fits with the monovalent ligand model (Eqs. 1–4FD1FD2FD3FD4). The values for the fitting parameters derived are: (B) k+1 = 1.1 × 106 M−1 · s−1, k−1 = 5.4 × 10−3 s−1; (C) k+1 = 2.0 × 107 M−1 · s−1, k−1 = 1.1 × 10−2 s−1.

Close modal

This model further assumes that each BSA has a single exposed DNP group. The rate of binding is described by the following differential equation:

\[\mathit{d}\mathrm{{[}}\mathit{Y}\mathrm{{]}/}\mathit{dt\ {=}\ k}_{\mathrm{{+}1}}\mathrm{{[}}\mathit{R}\mathrm{{]}{[}}\mathit{C}\mathrm{{]}\ -\ }\mathit{k}_{\mathrm{-1}}\mathrm{{[}}\mathit{Y}\mathrm{{]},}\]

where [C] and [R] are the molar concentrations of nonbound DNP-BSA and IgE Fab sites, respectively, and [Y] is the molar concentration of bound DNP-Fab complexes. k+1 and k−1 are the rate constants for the reversible binding of a DNP-group to a Fab site. The conservation equations for total Fab sites ([R]total) and total DNP-BSA ([C]total) are

\[{[}\mathit{R}\mathrm{{]}}_{\mathrm{total}}\mathrm{\ {=}\ {[}}\mathit{R}\mathrm{{]}\ {+}\ {[}}\mathit{Y}\mathrm{{]},}\]
\[{[}\mathit{C}\mathrm{{]}}_{\mathrm{total}}\mathrm{\ {=}\ {[}}\mathit{C}\mathrm{{]}\ {+}\ {[}}\mathit{Y}\mathrm{{]}.}\]

Substituting for [C] and [R] into Eq. 1 we obtain a single equation for [Y], which we solve numerically. We note that an analytic solution could also have been used.

We define fb=[Y]/[R]total as the fraction of Fab sites in the bound state at a time t after DNP-BSA is added to the FITC-IgE-saturated cells. fb is related to the experimentally measured fluorescence by the expression

\[\mathit{f}_{\mathrm{b}}\mathrm{\ {=}\ (}\mathit{F}_{\mathrm{max}}\mathrm{\ -\ }\mathit{F}\mathrm{)/(}\mathit{F}_{\mathrm{max}}\mathrm{\ -\ }\mathit{F}_{\mathrm{min}}\mathrm{),}\]

where F is the relative fluorescence at time t, Fmax is the relative fluorescence of FITC-IgE-saturated cells before addition of DNP-BSA, and Fmin is the relative fluorescence when all the Fab sites are saturated with DNP-BSA.

FIGURE 3.

Analysis of DNP-BSA binding to (C) and dissociation from (B) cell-bound FITC-IgE with the slow hapten exposure model (A). The small open and closed circles in the schematic diagrams in (A) represent the DNP groups on BSA unavailable and available for binding, respectively. Data for DNP-BSA binding to cell-bound IgE (in B and C) are the same as those shown in Figure 1. The solid lines through the data points represent best fits with this model (Eqs. 5–22FD5FD6FD7FD8FD9FD10FD11FD12AFD13FD14FD15FD16FD17FD18FD19FD20FD21FD22A). Values for the fitting parameters are: (B) k−1 = k−2 = 8.5 × 10−3 s−1; (C) k+1 = 9.2 × 106 M−1 · s−1; k+2[R]total = 1.1 × 10−1 s−1, k−1 = k−2 = 1.2 × 10−2 s−1; λ+ = 9.1 × 10−5 s−1 and λ = 7.5 × 10−4 s−1.

FIGURE 3.

Analysis of DNP-BSA binding to (C) and dissociation from (B) cell-bound FITC-IgE with the slow hapten exposure model (A). The small open and closed circles in the schematic diagrams in (A) represent the DNP groups on BSA unavailable and available for binding, respectively. Data for DNP-BSA binding to cell-bound IgE (in B and C) are the same as those shown in Figure 1. The solid lines through the data points represent best fits with this model (Eqs. 5–22FD5FD6FD7FD8FD9FD10FD11FD12AFD13FD14FD15FD16FD17FD18FD19FD20FD21FD22A). Values for the fitting parameters are: (B) k−1 = k−2 = 8.5 × 10−3 s−1; (C) k+1 = 9.2 × 106 M−1 · s−1; k+2[R]total = 1.1 × 10−1 s−1, k−1 = k−2 = 1.2 × 10−2 s−1; λ+ = 9.1 × 10−5 s−1 and λ = 7.5 × 10−4 s−1.

Close modal

This model postulates that most of the DNP groups on BSA are buried at any time. However, in any time interval, the DNP groups have some probability of becoming exposed and available for binding to IgE. The binding stabilizes the exposed state. The simplest form of this model is considered here, and we make the following two additional assumptions: 1) the exposure and burying of DNP on BSA can be described by fixed rate constants, λ+ and λ, respectively; and 2) the maximal DNP groups per BSA that can become exposed (n) is 2. (It is straightforward to generalize assumption 2 and take n to be any value less than or equal to the total number of DNP per BSA.) We assign the rate constants k+1 and k−1 for a free ligand (with one or two exposed DNP groups) binding reversibly to a free Fab site, and the rate constants k+2,2D and k−2 for a ligand (with one exposed DNP bound and the other exposed DNP free) binding reversibly to a free Fab site, where k+2,2D is a two dimensional rate constant. In the fitting program, we use the spatially dimensionless parameter k+2[R]total, where [R]total is three dimensional molar concentration of total Fab sites, and k+2 is the apparent three dimensional cross-linking rate constant corresponding to the same amount of Fab sites as that on the cell surface but spread uniformly over available three dimensional space. Because k+2 and [R]total have units of M−1 · s−1 and M, respectively, k+2[R]total has units of s−1. By dividing k+2[R]total by rt, the total Fab site density on the cell surface (in units of sites/cm2), we get k+2,2D.

Five differential equations describe DNP-BSA binding and cross-linking in this model (when n = 2), and there are two conservation equations for total Fab sites ([Ctotal]) and total DNP-BSA ([Rtotal]) (See Fig. 3 A):

\[\mathit{d}\mathrm{{[}}\mathit{C}_{\mathrm{1}}\mathrm{{]}/}\mathit{dt}\mathrm{\ {=}\ 2{\lambda}}_{\mathrm{{+}}}\mathrm{{[}}\mathit{C}_{\mathrm{0}}\mathrm{{]}\ -\ {\lambda}}_{\mathrm{-}}\mathrm{{[}}\mathit{C}_{\mathrm{1}}\mathrm{{]}\ {+}\ 2{\lambda}}_{\mathrm{-}}\mathrm{{[}}\mathit{C}_{\mathrm{2}}\mathrm{{]}\ }\]
\[-\ {\lambda}_{{+}}{[}\mathit{C}_{\mathrm{1}}\mathrm{{]}\ {+}\ }\mathit{k}_{\mathrm{-1}}\mathrm{{[}}\mathit{Y}_{\mathit{a}}\mathrm{{]}\ -\ }\mathit{k}_{\mathrm{{+}1}}\mathrm{{[}}\mathit{C}_{\mathrm{1}}\mathrm{{]}{[}}\mathit{R}\mathrm{{]},}\]
\[\mathit{d}\mathrm{{[}}\mathit{C}_{\mathrm{2}}\mathrm{{]}/}\mathit{dt}\mathrm{\ {=}\ {\lambda}}_{\mathrm{{+}}}\mathrm{{[}}\mathit{C}_{\mathrm{1}}\mathrm{{]}\ -\ 2{\lambda}}_{\mathrm{-}}\mathrm{{[}}\mathit{C}_{\mathrm{2}}\mathrm{{]}\ {+}\ }\mathit{k}_{\mathrm{-1}}\mathrm{{[}}\mathit{Y}_{\mathit{b}}\mathrm{{]}\ -\ 2}\mathit{k}_{\mathrm{{+}1}}\mathrm{{[}}\mathit{C}_{\mathrm{2}}\mathrm{{]}{[}}\mathit{R}\mathrm{{]},}\]
\[\mathit{d}\mathrm{{[}}\mathit{Y}_{\mathit{a}}\mathrm{{]}/}\mathit{dt}\mathrm{\ {=}\ }\mathit{k}_{\mathrm{{+}1}}\mathrm{{[}}\mathit{C}_{\mathrm{1}}\mathrm{{]}{[}}\mathit{R}\mathrm{{]}\ -\ }\mathit{k}_{\mathrm{-1}}\mathrm{{[}}\mathit{Y}_{\mathit{a}}\mathrm{{]}\ {+}\ {\lambda}}_{\mathrm{-}}\mathrm{{[}}\mathit{Y}_{\mathit{b}}\mathrm{{]}\ -\ {\lambda}}_{\mathrm{{+}}}\mathrm{{[}}\mathit{Y}_{\mathit{a}}\mathrm{{]},}\]
\[\mathit{d}\mathrm{{[}}\mathit{Y}_{\mathit{b}}\mathrm{{]}/}\mathit{dt}\mathrm{\ {=}\ {\lambda}}_{\mathrm{{+}}}\mathrm{{[}}\mathit{Y}_{\mathit{a}}\mathrm{{]}\ -\ {\lambda}}_{\mathrm{-}}\mathrm{{[}}\mathit{Y}_{\mathit{b}}\mathrm{{]}\ {+}\ 2}\mathit{k}_{\mathrm{{+}1}}\mathrm{{[}}\mathit{C}_{\mathrm{2}}\mathrm{{]}{[}}\mathit{R}\mathrm{{]}}\]
\[-\ \mathit{k}_{\mathrm{-1}}\mathrm{{[}}\mathit{Y}_{\mathit{b}}\mathrm{{]}\ {+}\ 2}\mathit{k}_{\mathrm{-2}}\mathrm{{[}}\mathit{Y}_{\mathit{c}}\mathrm{{]}\ -\ }\mathit{k}_{\mathrm{{+}2}}\mathrm{{[}}\mathit{Y}_{\mathit{b}}\mathrm{{]}{[}}\mathit{R}\mathrm{{]},}\]
\[\mathit{d}\mathrm{{[}}\mathit{Y}_{\mathit{c}}\mathrm{{]}/}\mathit{dt}\mathrm{\ {=}\ }\mathit{k}_{\mathrm{{+}2}}\mathrm{{[}}\mathit{Y}_{\mathit{b}}\mathrm{{]}{[}}\mathit{R}\mathrm{{]}\ -\ 2}\mathit{k}_{\mathrm{-2}}\mathrm{{[}}\mathit{Y}_{\mathit{c}}\mathrm{{]},}\]
\[{[}\mathit{C}\mathrm{{]}}_{\mathrm{total}}\mathrm{\ {=}\ {[}}\mathit{C}_{\mathrm{0}}\mathrm{{]}\ {+}\ {[}}\mathit{C}_{\mathrm{1}}\mathrm{{]}\ {+}\ {[}}\mathit{C}_{\mathrm{2}}\mathrm{{]}\ {+}\ {[}}\mathit{Y}_{\mathit{a}}\mathrm{{]}\ {+}\ {[}}\mathit{Y}_{\mathit{b}}\mathrm{{]}\ {+}\ {[}}\mathit{Y}_{\mathit{c}}\mathrm{{]},}\]
\[{[}\mathit{R}\mathrm{{]}}_{\mathrm{total}}\mathrm{\ {=}\ {[}}\mathit{R}\mathrm{{]}\ {+}\ {[}}\mathit{Y}_{\mathit{a}}\mathrm{{]}\ {+}\ {[}}\mathit{Y}_{\mathit{b}}\mathrm{{]}\ {+}\ 2{[}}\mathit{Y}_{\mathit{c}}\mathrm{{]}.}\]

[C0], [C1], and [C2] are the molar concentrations of free DNP-BSA with 0, 1, and 2 exposed DNP groups, respectively. [Ya] and [Yc] are the molar concentrations of bound DNP-BSA to IgE on the cell surface, with one and two DNP groups bound, respectively; these species contain no exposed DNP groups that are not bound. [Yb] is the molar concentration of bound DNP-BSA with one DNP group bound to IgE and one exposed DNP group that is not bound. In this model fb=([Ya]+[Yb]+2[Yc])/[R]total, and it is related to the experimentally measured fluorescence by Eq. 4.

Based on the conservation equations and the equilibrium constant for the hapten exposure step, λ = λ+, we derive the following equations, which determine the initial distribution of the Ag species, with 0, 1, or 2 exposed haptens.

\[{[}\mathit{C}_{\mathrm{0}}\mathrm{{]}}_{\mathrm{t{=}0}}\mathrm{\ {=}\ }\ \frac{\mathrm{{[}}\mathit{C}\mathrm{{]}}_{\mathrm{total}}}{\mathrm{(1\ {+}\ {\lambda})}^{\mathrm{2}}}\mathrm{\ ,}\]
\[{[}\mathit{C}_{\mathrm{1}}\mathrm{{]}}_{\mathrm{t{=}0}}\mathrm{\ {=}\ }\ \frac{\mathrm{2{\lambda}{[}}\mathit{C}\mathrm{{]}}_{\mathrm{total}}}{\mathrm{(1\ {+}\ {\lambda})}^{\mathrm{2}}}\mathrm{\ ,}\]
\[{[}\mathit{C}_{\mathrm{2}}\mathrm{{]}}_{\mathrm{t{=}0}}\mathrm{\ {=}\ }\ \frac{\mathrm{{\lambda}}^{\mathrm{2}}\mathrm{{[}}\mathit{C}\mathrm{{]}}_{\mathrm{total}}}{\mathrm{(1\ {+}\ {\lambda})}^{\mathrm{2}}}\mathrm{\ .}\]

Correspondingly, the average number of exposed hapten per Ag before the encounter of the FITC-IgE (Dav) is given by

\[\mathit{D}_{\mathrm{av}}\mathrm{\ {=}\ }\ \frac{\mathrm{{[}}\mathit{C}_{\mathrm{1}}\mathrm{{]}}_{\mathrm{t{=}0}}\mathrm{\ {+}\ 2{[}}\mathit{C}_{\mathrm{2}}\mathrm{{]}}_{\mathrm{t{=}0}}}{\mathrm{{[}}\mathit{C}_{\mathrm{0}}\mathrm{{]}}_{\mathrm{t{=}0}}\mathrm{\ {+}\ {[}}\mathit{C}_{\mathrm{1}}\mathrm{{]}}_{\mathrm{t{=}0}}\mathrm{\ {+}\ {[}}\mathit{C}_{\mathrm{2}}\mathrm{{]}}_{\mathrm{t{=}0}}}\mathrm{\ {=}\ }\ \frac{\mathrm{2{\lambda}}}{\mathrm{(1\ {+}\ {\lambda})}}\mathrm{\ .}\]

In general, for any n, Dav =nλ/(1 + λ).

If, at t=tz, a large excess of DCT is added to dissociate DNP-BSA, free Fab sites fill up quickly with DCT, and [R] ≃ 0. Then Eqs. 7–9 become

\[\mathit{d}\mathrm{{[}}\mathit{Y}_{\mathit{a}}\mathrm{{]}/}\mathit{dt}\mathrm{\ {=}\ -}\mathit{k}_{\mathrm{-1}}\mathrm{{[}}\mathit{Y}_{\mathit{a}}\mathrm{{]}\ {+}\ {\lambda}}_{\mathrm{-}}\mathrm{{[}}\mathit{Y}_{\mathit{b}}\mathrm{{]}\ -\ {\lambda}}_{\mathrm{{+}}}\mathrm{{[}}\mathit{Y}_{\mathit{a}}\mathrm{{]},\ }\]
\[\mathit{d}\mathrm{{[}}\mathit{Y}_{\mathit{b}}\mathrm{{]}/}\mathit{dt}\mathrm{\ {=}\ {\lambda}}_{\mathrm{{+}}}\mathrm{{[}}\mathit{Y}_{\mathit{a}}\mathrm{{]}\ -\ {\lambda}}_{\mathrm{-}}\mathrm{{[}}\mathit{Y}_{\mathit{b}}\mathrm{{]}\ -\ }\mathit{k}_{\mathrm{-1}}\mathrm{{[}}\mathit{Y}_{\mathit{b}}\mathrm{{]}\ {+}\ 2}\mathit{k}_{\mathrm{-2}}\mathrm{{[}}\mathit{Y}_{\mathit{c}}\mathrm{{]},}\]
\[\mathit{d}\mathrm{{[}}\mathit{Y}_{\mathit{c}}\mathrm{{]}/}\mathit{dt}\mathrm{\ {=}\ -2}\mathit{k}_{\mathrm{-2}}\mathrm{{[}}\mathit{Y}_{\mathit{c}}\mathrm{{]}.}\]

If we set [Yab]=[Ya]+[Yb], and add Eq. 14 to Eq. 15, we get

\[\mathit{d}\mathrm{{[}}\mathit{Y}_{\mathit{ab}}\mathrm{{]}/}\mathit{dt}\mathrm{\ {=}\ -}\mathit{k}_{\mathrm{-1}}\mathrm{{[}}\mathit{Y}_{\mathit{ab}}\mathrm{{]}\ {+}\ 2}\mathit{k}_{\mathrm{-2}}\mathrm{{[}}\mathit{Y}_{\mathit{c}}\mathrm{{]}}\]

Eqs. 16, and 17 can be integrated to yield

\[{[}\mathit{Y}_{\mathit{ab}}\mathrm{{]}\ {=}\ {[}}\mathit{Y}_{\mathit{ab}}\mathrm{{]}}_{\mathrm{t{=}t}_{\mathrm{z}}}\mathit{e}^{\mathrm{-k}_{\mathrm{-1}}\mathrm{(t-t}_{\mathrm{z}}\mathrm{)}}\mathrm{\ {+}\ }\ \frac{\mathrm{2}\mathit{k}_{\mathrm{-2}}\mathrm{{[}}\mathit{Y}_{\mathit{c}}\mathrm{{]}}_{\mathrm{t{=}t}_{\mathrm{z}}}}{\mathrm{2}\mathit{k}_{\mathrm{-2}}\mathrm{\ -\ }\mathit{k}_{\mathrm{-1}}}\mathrm{\ }\mathit{e}^{\mathrm{-k}_{\mathrm{-1}}\mathrm{(t-t}_{\mathrm{z}}\mathrm{)}}\mathrm{\ -\ }\mathit{e}^{\mathrm{-2k}_{\mathrm{-2}}\mathrm{(t-t}_{\mathrm{z}}\mathrm{)}}\mathrm{,}\]
\[{[}\mathit{Y}_{\mathit{c}}\mathrm{{]}\ {=}\ {[}}\mathit{Y}_{\mathit{c}}\mathrm{{]}}_{\mathrm{t{=}t}_{\mathrm{z}}}\mathit{e}^{\mathrm{-2k}_{\mathrm{-2}}\mathrm{(t-t}_{\mathrm{z}}\mathrm{)}}\mathrm{,}\]

where [Yab]t=tz and [Yc]t=tz are the concentrations of DNP-BSA singly and doubly bound to cell surface IgE, respectively, immediately after DCT is added. Note that for DCT-induced dissociation (Eqs. 18, and 19) the exponential decay constants depend only on k-1 and k-2. Thus, in the dissociation phase the dynamics of DNP exposure on the Ag surface plays no role.

We define f as the fraction of Fab sites originally bound to DNP-BSA at tz that are still bound at subsequent time t,

\[\mathit{f}\mathrm{\ {=}\ }\ \frac{\mathrm{{[}}\mathit{Y}_{\mathit{ab}}\mathrm{{]}\ {+}\ 2{[}}\mathit{Y}_{\mathit{c}}\mathrm{{]}}}{\mathrm{{[}}\mathit{Y}_{\mathit{ab}}\mathrm{{]}}_{\mathrm{t{=}t}_{\mathrm{z}}}\mathrm{\ {+}\ 2{[}}\mathit{Y}_{\mathit{c}}\mathrm{{]}}_{\mathrm{t{=}t}_{\mathrm{z}}}}\mathrm{\ .}\]

f is related to the experimentally measured fluorescence by

\[\mathit{f}\mathrm{\ {=}\ (}\mathit{F}\mathrm{^{{^\prime}}}_{\mathrm{max}}\mathrm{\ -\ }\mathit{F}\mathrm{)/(}\mathit{F}\mathrm{^{{^\prime}}}_{\mathrm{max}}\mathrm{\ -\ }\mathit{F}\mathrm{^{{^\prime}}}_{\mathrm{min}}\mathrm{),}\]

where Fmax is the value of the relative fluorescence after dissociation has gone to completion and Fmin is the value of the relative fluorescence immediately after addition of DCT. Substituting Eqs. 18, and 19 into Eq. 20, we obtain

\[\mathit{F\ {=}\ F}\mathrm{^{{^\prime}}}_{\mathrm{min}}\mathrm{\ -\ (}\mathit{F}\mathrm{^{{^\prime}}}_{\mathrm{max}}\mathrm{\ -\ }\mathit{F}\mathrm{^{{^\prime}}}_{\mathrm{min}}\mathrm{)(}\mathit{A}_{\mathrm{i}}\mathit{e}^{\mathrm{-k}_{\mathrm{-1}}\mathrm{(t-t}_{\mathrm{z}}\mathrm{)}}\mathrm{\ {+}\ (1-}\mathit{A}_{\mathrm{i}}\mathrm{)}\mathit{e}^{\mathrm{-2k}_{\mathrm{-2}}\mathrm{(t-t}_{\mathrm{z}}\mathrm{)}}\mathrm{,}\]
\[\mathit{A}_{\mathrm{i}}\mathrm{\ {=}\ 1\ {+}\ }\mathit{{\bar}a}\mathrm{\ }\ \frac{\mathit{k}_{\mathrm{-1}}\mathrm{\ -\ }\mathit{k}_{\mathrm{-2}}}{\mathrm{2}\mathit{k}_{\mathrm{-2}}\mathrm{\ -\ }\mathit{k}_{\mathrm{-1}}}\mathrm{\ ,}\]
\[\mathit{{\bar}a}\mathrm{\ {=}\ }\ \frac{\mathrm{2{[}}\mathit{Y}_{\mathit{c}}\mathrm{{]}}}{\mathrm{{[}}\mathit{Y}_{\mathit{ab}}\mathrm{{]}}_{\mathrm{t{=}t}_{\mathrm{z}}}\mathrm{\ {+}\ 2{[}}\mathit{Y}_{\mathit{c}}\mathrm{{]}}_{\mathrm{t{=}t}_{\mathrm{z}}}}\mathrm{\ ,}\]

i.e., the fluorescence recovery can be fit by a double exponential equation. If k-1 = k-2, then Ai = 1, and F in Eq. 22aFD22A reduces to a single exponential equation.

The parameter estimates of Fmax, Fmin, Fmax, Fmin, k+1, k+2,2D, k−1, k−2, λ+, and λ were obtained with a subroutine, DNLSI, from the Common Los Alamos Software Library, which is based on a finite difference, Levenberg-Marquardt algorithm for solving nonlinear least-squares problems. For fitting both models to the association data, the differential equations Eq. 1 and Eqs. 5–9FD5FD6FD7FD8FD9 were numerically solved with a standard algorithm. The dissociation data were fit with the exponential equation Eq. 22aFD22A. The zero time point for binding was determined by the addition of DNP-BSA or DNP-BGG; tz for the induced dissociation of DNP-BSA or DNP-BGG was determined by the addition of DCT; [R]total was calculated by multiplying measured cell density (cells/ml) by 2× the estimated number of FcεRI on the cell surface (3 × 105/cell) and converting to molar concentration; [C]total was determined by absorption spectroscopy measurements of the stock ligand solutions as described above.

We examined DNP-BSA binding to FITC-labeled anti-DNP IgE in solution or bound to FcεRI on RBL cells with our previously established fluorescence quenching method (13). Figure 1 shows a kinetic quenching curve for cells saturated with FITC-IgE after addition of DNP-BSA at 15°C. Binding was evaluated at this temperature to avoid complications due to cross-linking-dependent internalization of IgE-receptor complexes (22). Although maximal quenching varies somewhat with the levels of FITC and DNP conjugations, these quenching curves are very reproducible for the same preparations of DNP-BSA and FITC-IgE. The saturation level of fluorescence quenching remains the same (∼35% of the total fluorescence) for DNP-BSA additions ranging from concentrations where cross-linking dominates to conditions where monovalent binding dominates (22), and this supports our assumption that the FITC fluorescence quenching is proportional to the fraction of Fab binding sites occupied by DNP groups. We monitored the dissociation of DNP-BSA by adding an excess of monovalent DCT, which quenches FITC-IgE fluorescence less than DNP-BSA; fluorescence recovery occurs as DNP from DCT replaces DNP from DNP-BSA in the Fab site.

FIGURE 1.

Binding of monovalent DCT (inset) and multivalent DNP-BSA to cell-bound FITC-anti-DNP-IgE, and dissociation of DNP-BSA in the presence of large excess of DCT at 15°C. DNP-BSA (11 nM; DNP:BSA = 15) or DCT (5.6 nM) were added to FITC-IgE-saturated RBL cells (1 × 106 cells/ml; 0.5 nM FITC-IgE) at the arrows. At t = 2093 s, 77 μM DCT was added to the DNP-BSA-containing sample (arrowhead); the quenching occurring immediately after this addition is due to filling of unoccupied IgE combining sites, inner filter effect, and a small dilution effect. The partial FITC fluorescence recovery indicates the dissociation of DNP-BSA, which cannot rebind in the presence of sufficiently excess DCT. The dashed line represents the level of relative fluorescence observed for a separate but identical sample of cells to which 77 mM DCT was added to saturate the FITC-IgE.

FIGURE 1.

Binding of monovalent DCT (inset) and multivalent DNP-BSA to cell-bound FITC-anti-DNP-IgE, and dissociation of DNP-BSA in the presence of large excess of DCT at 15°C. DNP-BSA (11 nM; DNP:BSA = 15) or DCT (5.6 nM) were added to FITC-IgE-saturated RBL cells (1 × 106 cells/ml; 0.5 nM FITC-IgE) at the arrows. At t = 2093 s, 77 μM DCT was added to the DNP-BSA-containing sample (arrowhead); the quenching occurring immediately after this addition is due to filling of unoccupied IgE combining sites, inner filter effect, and a small dilution effect. The partial FITC fluorescence recovery indicates the dissociation of DNP-BSA, which cannot rebind in the presence of sufficiently excess DCT. The dashed line represents the level of relative fluorescence observed for a separate but identical sample of cells to which 77 mM DCT was added to saturate the FITC-IgE.

Close modal

Fluorescence quenching caused by binding and cross-linking of DNP-BSA to cell-bound FITC-IgE (Fig. 1) is surprisingly slow compared with that observed when similar amounts of DCT are added (Fig. 1, inset). For this experiment the DCT concentration was 5.6 nM and the DNP-BSA concentration was 11 nM (corresponding to 165 nM DNP groups). These results raise the possibility that the effective number of DNP groups available for binding on BSA is relatively small. Because DNP-BSA triggers cellular responses, we know that a signficant fraction of these ligands can cross-link IgE, i.e., are effectively multivalent. However, for comparison purposes we began our analysis of the DNP-BSA binding data with a monovalent ligand model (Eqs. 1–4FD1FD2FD3FD4 and Fig. 2,A). The data from Figure 1 for DNP-BSA binding to cell-bound FITC-IgE were analyzed with this model as illustrated in Figure 2,B. In the analysis, the effective DNP concentration was assumed to be the same as the DNP-BSA concentration (11 nM). We see that the monovalent ligand model predicts faster leveling off of fluorescence quenching than the experimental data (Fig. 2,B). As expected, the binding of monovalent ligand DCT to cell-bound FITC-IgE (Fig. 1, inset) is well fit with the monovalent ligand model (Fig. 2 C). Furthermore, this analysis of DCT binding yields association and dissociation rate constants (k+1 ∼ 2 × 107 M−1 · s−1, k−1 ∼ 1 × 10−2 s−1) that are consistent with those determined previously for DCT binding to cell-bound IgE (23).

Variations of this simple model also do not fit the DNP-BSA binding data. In particular, a bivalent model, which assumes that there are two effective DNP groups per BSA that can cross-link IgE, predicts even faster binding (data not shown). This shows that expanding the monovalent ligand model to higher effective valency does not improve the fit to the data. On the other hand, simply reducing the average effective valency to less than one without including a cross-linking step in the model also fails to fit the data (data not shown). We confirmed that this DNP-BSA preparation is a potent stimulus for RBL cellular degranulation (∼50% β-hexosaminidase release at 0.2–1.1 nM DNP-BSA for adherent RBL cells), verifying productive cross-linking of IgE-FcεRI by this ligand.

We developed this model (Eqs. 5–22FD5FD6FD7FD8FD9FD10FD11FD12AFD12BFD12CFD13FD14FD15FD16FD17FD18FD19FD20FD21FD22AFD22BFD22C; Fig. 3,A) to take into account both the low effective valency of DNP-BSA and its capacity for cross-linking on the cell surface. With it we analyzed the DNP-BSA binding and dissociation data shown in Figure 1. Figure 3,B shows that DCT-induced DNP-BSA dissociation from cell-bound FITC-IgE is fit by a single exponential indicating k−1 = k−2 (Eqs. 14–22FD14FD15FD16FD17FD18FD19FD20FD21FD22A). Consequently, we set k−1 = k−2 as an adjustable parameter in fitting the forward binding. As shown in Figure 3 C, this model readily fits the kinetics of DNP-BSA binding to the cell-bound IgE and yields values of k+1 ∼ 1 × 107 M−1 · s−1, k+2[R]total ∼ 1 × 10−1 s−1, k−1 = k−2 ∼ 1 × 10−2 s−1, and λ = λ+ ∼ 1 × 10−1. The molar concentration of total Fab is 1 nM, yielding the apparent three dimensional k+2 ∼ 1 × 108 M−1 · s−1, which is about 10-fold higher than k+1. This indicates that the cross-linking step is accelerated, presumably due to the high local concentration of IgE confined to the cell surface.

We tested whether this transient hapten exposure model is consistent with binding of DNP-BSA to cell-bound IgE over a range of concentrations corresponding to biologic responses, i.e., 1 to 11 nM DNP-BSA. For all of these experiments, a similar amount of FITC-IgE quenching (∼35%) is achieved when binding reaches saturation. We find that these binding data are all well fit, and values for parameters derived from the best fits of representative data are listed in Table I. Also included in this table is the lumped parameter nk+1λ/(1+λ) for n = 2 which corresponds to the initial rate of DNP-BSA binding to IgE. The dissociation data were consistently well fit with a single exponential, and the values for k−1 = k−2 derived from various Ag concentrations are in good agreement. Furthermore, values for k−1 = k−2 derived from fits of the association data are consistent with those derived from fitting the dissociation data. For the data summarized in Table I, the arithmetic average of the parameter estimates for DNP-BSA are k+1 = 8.0 × 106 M−1 · s−1, k+2[R]total = 1.1 × 10−1 s −1, k−1 = k−2 = 9.4 × 10−3 s−1, λ = λ+ = 1.6 × 10−1, and 2k+1λ/(1+λ) = 2.1 M−1 s−1. Notably, the estimates of k+1 and k−1 derived from DNP-BSA binding are comparable to those derived from DCT binding (Table I and 23 , indicating that the slower binding of DNP-BSA compared with DCT is not because DNP groups on BSA intrinsically bind significantly slower to IgE than does DCT or that the binding of DNP-BSA is diffusion limited. The model implies that the DNP groups on BSA are not readily available for binding because of their low exposure probability as indicated by values for λ and Dav that are less than 1 (see below). Uncertainties in the absolute values for the various parameters derived with this model are considered in the Discussion.

Table I.

Parameter values derived from fitting of binding data for DNP ligands and anti-DNP IgE on RBL cellsa

Binding Experimentk+1 (106 M−1 · s−1)k−1 = k−2 (10−3 s−1)k+2[R]total (10−2 s−1)λ (10−1)2k+1λ/(1+λ) (107 M−1 · s−1)
Association:DNP-BSA (11 nM) 9.2 ± 0.2 11.5 ± 0.1 11.1 ± 1.6 1.2 ± 0.1 2.0 ± 0.1 
Association: DNP-BSA (5.5 nM) 8.6 ± 0.5 10.0 ± 0.1 12.6 ± 1.8 1.4 ± 0.0 2.2 ± 0.2 
Association: DNP-BSA (2.2 nM) 8.2 ± 0.0 9.7 ± 0.0 11.0 ± 0.0 1.6 ± 0.0 2.3 ± 0.1 
Association: DNP-BSA (1.1 nM) 5.8 ± 0.0 6.2 ± 0.1 7.3 ± 0.1 2.3 ± 0.0 2.2 ± 0.1 
Dissociation: DNP-BSA (11 nM) NAb 8.5 ± 0.2 NA NA NA 
Dissociation: DNP-BSA (5.5 nM) NA 9.3 ± 0.2 NA NA NA 
Dissociation: DNP-BSA (2.2 nM) NA 8.5 ± 0.2 NA NA NA 
Dissociation: DNP-BSA (1.1 nM) NA 9.0 ± 0.2 NA NA NA 
Association: DNP-BGG (0.66 nM) 8.12 ± 0.2 6.3 ± 0.2 18.1 ± 1.1 5.9 ± 0.2 6.0 ± 0.4 
Dissociation: DNP-BGG (0.66 nM) NA 11.4 ± 0.2 NA NA NA 
Association: DCT (5.6 nM) 20.0 ± 0.4 10.5 ± 0.2 NA NA NA 
Binding Experimentk+1 (106 M−1 · s−1)k−1 = k−2 (10−3 s−1)k+2[R]total (10−2 s−1)λ (10−1)2k+1λ/(1+λ) (107 M−1 · s−1)
Association:DNP-BSA (11 nM) 9.2 ± 0.2 11.5 ± 0.1 11.1 ± 1.6 1.2 ± 0.1 2.0 ± 0.1 
Association: DNP-BSA (5.5 nM) 8.6 ± 0.5 10.0 ± 0.1 12.6 ± 1.8 1.4 ± 0.0 2.2 ± 0.2 
Association: DNP-BSA (2.2 nM) 8.2 ± 0.0 9.7 ± 0.0 11.0 ± 0.0 1.6 ± 0.0 2.3 ± 0.1 
Association: DNP-BSA (1.1 nM) 5.8 ± 0.0 6.2 ± 0.1 7.3 ± 0.1 2.3 ± 0.0 2.2 ± 0.1 
Dissociation: DNP-BSA (11 nM) NAb 8.5 ± 0.2 NA NA NA 
Dissociation: DNP-BSA (5.5 nM) NA 9.3 ± 0.2 NA NA NA 
Dissociation: DNP-BSA (2.2 nM) NA 8.5 ± 0.2 NA NA NA 
Dissociation: DNP-BSA (1.1 nM) NA 9.0 ± 0.2 NA NA NA 
Association: DNP-BGG (0.66 nM) 8.12 ± 0.2 6.3 ± 0.2 18.1 ± 1.1 5.9 ± 0.2 6.0 ± 0.4 
Dissociation: DNP-BGG (0.66 nM) NA 11.4 ± 0.2 NA NA NA 
Association: DCT (5.6 nM) 20.0 ± 0.4 10.5 ± 0.2 NA NA NA 
a

RBL cells (∼106/ml) were saturated with IgE (∼0.5 nM bulk concentration). Standard errors are bootstrap estimates. The standard error in the values for Fmax and Fmin (not included here) were always less than 0.2% of the parameter values. The arithmatic average of the parameter values for DNP-BSA are k+1 = (8.0 ± 1.5) × 106 M−1 · s−1, k+2[R]total = (1.1 ± 0.2) × 10−1 s−1, k−1 = k−2 = (9.4 ± 2.2) × 10−3 s−1, λ = (1.6 ± 0.5) × 10−1, and 2k+1λ/(1 + λ) = 2.2 ± 0.1.

b

NA, not applicable.

DNP-BGG is also commonly used experimentally as an Ag, therefore, we compared its binding properties with those of DNP-BSA. Figure 4 shows binding of 0.66 nM of DNP-BGG and 1.1 nM of DNP-BSA to two identical samples of RBL-2H3 cells saturated with FITC-IgE (∼0.5 nM bulk IgE). Because the degree of modification for DNP-BGG and DNP-BSA are 25 and 15, respectively, the bulk DNP concentrations for the two Ags are the same under these conditions. FITC-IgE combining sites are occupied faster by DNP-BGG than by DNP-BSA although still substantially slower than by the monovalent ligand DCT (Fig. 1 and data not shown). As with DNP-BSA, DCT-induced dissociation of DNP-BGG is well-fit with a single exponential (data not shown), and the derived dissociation rate constants are similar to those for DNP-BSA and DCT (Table I). Binding of DNP-BGG can also be fit with the transient hapten exposure model as shown in Figure 4. As indicated for these and other representative data presented in Table I, the rate constants for monovalent binding and dissociation, k+1 and k−1(=k−2), are similar for DCT, DNP-BSA, and DNP-BGG. Parameters derived from the model indicate that DNP-BSA and DNP-BGG binding kinetics are limited by hapten exposure as reflected by the equilibrium constant λ. Specifically, λ values for DNP-BSA and DNP-BGG are ∼0.16 and ∼0.59, respectively, and corresponding values for Dav (average number of exposed hapten per Ag before encounter with IgE; Eq. 13) are ∼0.28 and ∼0.74, respectively. Thus, the observation that DNP-BGG binds and cross-links faster than DNP-BSA is consistent with its larger value for λ and therefore for Dav.

FIGURE 4.

Comparison of the kinetics of DNP-BSA binding (upper trace) with the kinetics of DNP-BGG binding (lower trace; offset) to cell-bound FITC-anti-DNP-IgE and their fits with slow hapten exposure model (Eqs. 5–22FD5FD6FD7FD8FD9FD10FD11FD12AFD13FD14FD15FD16FD17FD18FD19FD20FD21FD22A; solid lines). The cells were saturated with FITC-anti-DNP-IgE (∼0.5 nM bulk IgE) and maintained in suspension at 15°C. Amounts equal to 1.1 nM DNP-BSA (DNP:BSA = 15) and 0.66 nM DNP-BGG (DNP:BGG = 25) were added to two identical aliquots of cells, as indicated by the arrows, so that the final DNP concentrations in both samples was 16.5 nM. The parameters derived from DNP-BSA binding are k+1 = 7.82 × 106 M−1 · s−1, k−1 = k−2 = 1.4 × 10−2 s−1, k+2[R]total = 1.3 × 10−1 s−1, λ+ = 1.7 × 10−4 s−1, λ = 5.4 × 10−4 s−1. The parameters derived from DNP-BGG binding are k+1 = 8.1 × 106 M−1 · s−1, k−1 = k−2 = 6.3 × 10−3 s−1, k+2[R]total = 1.8 × 10−1 s−1, λ+ = 1.1 × 10−3 s−1, λ = 1.9 × 10−3 s−1.

FIGURE 4.

Comparison of the kinetics of DNP-BSA binding (upper trace) with the kinetics of DNP-BGG binding (lower trace; offset) to cell-bound FITC-anti-DNP-IgE and their fits with slow hapten exposure model (Eqs. 5–22FD5FD6FD7FD8FD9FD10FD11FD12AFD13FD14FD15FD16FD17FD18FD19FD20FD21FD22A; solid lines). The cells were saturated with FITC-anti-DNP-IgE (∼0.5 nM bulk IgE) and maintained in suspension at 15°C. Amounts equal to 1.1 nM DNP-BSA (DNP:BSA = 15) and 0.66 nM DNP-BGG (DNP:BGG = 25) were added to two identical aliquots of cells, as indicated by the arrows, so that the final DNP concentrations in both samples was 16.5 nM. The parameters derived from DNP-BSA binding are k+1 = 7.82 × 106 M−1 · s−1, k−1 = k−2 = 1.4 × 10−2 s−1, k+2[R]total = 1.3 × 10−1 s−1, λ+ = 1.7 × 10−4 s−1, λ = 5.4 × 10−4 s−1. The parameters derived from DNP-BGG binding are k+1 = 8.1 × 106 M−1 · s−1, k−1 = k−2 = 6.3 × 10−3 s−1, k+2[R]total = 1.8 × 10−1 s−1, λ+ = 1.1 × 10−3 s−1, λ = 1.9 × 10−3 s−1.

Close modal

Because FITC fluorescence quenching caused by DNP-BSA binding is proportional to the Fab site occupation, this method cannot directly distinguish between that caused by monovalent binding and that caused by cross-linking to additional IgE-FcεRI. To dissect the contribution of these two processes, we fluorescently labeled DNP-BSA with Cy3 and monitored the binding of DNP-BSA to cell-bound IgE with flow cytometry. Monovalent binding of Cy3-DNP-BSA to cell-bound IgE causes cell-associated Cy3 fluorescence, and subsequent cross-linking steps cause no additional fluorescence. Therefore, the rate of increase of cell-associated Cy3 fluorescence reflects the rate of the monovalent binding of DNP-BSA to cell-bound IgE. A control experiment conducted with excess DCT showed that nonspecific binding of Cy3-DNP-BSA is negligible (data not shown). Fluorescence-quenching curves confirmed that Cy3-DNP-BSA binds to FITC-IgE on cells with kinetics identical to DNP-BSA (Fig. 1 and data not shown).

Figure 5 compares the time courses from these two fluorescence methods. The increase in cell-associated Cy3 fluorescence caused by binding of DNP-BSA is substantially faster (t1/2 ≤ 15 s) than the FITC fluorescence quenching caused by the binding and cross-linking of the same concentrations of DNP-BSA (t1/2 ≃ 150 s). These results indicate that the cross-linking of DNP-BSA occurs significantly slower than the initial association of DNP-BSA with the cells. Furthermore, it appears that the fraction of FITC fluorescence quenching caused by monovalent binding is smaller than that caused by subsequent cross-linking events. We estimate that <20% of fluorescence quenching after 50 s is due to monovalent binding under these conditions.4 That the fluorescence quenching curve after 50 s reflects primarily cross-linking is valuable for comparison to the time course of the cellular response, as is described below. Implications of this numerical estimate for our minimal model are considered in the Discussion.

FIGURE 5.

Comparison of the kinetics of association of Cy3-DNP-BSA to cell-bound IgE monitored by flow cytometry (B) with the kinetics of DNP-BSA-induced FITC fluorescence quenching on FITC-IgE-saturated cells (A). Cells (1 × 106 cells/ml) saturated with unlabeled IgE (B) or FITC-IgE (A) were suspended at 15°C, at t = 0, 2.2 nM of Cy3-DNP-BSA (B) or unlabeled DNP-BSA (A) was added to the cells. For B, data points are from three separate experiments (□, ○, Δ).

FIGURE 5.

Comparison of the kinetics of association of Cy3-DNP-BSA to cell-bound IgE monitored by flow cytometry (B) with the kinetics of DNP-BSA-induced FITC fluorescence quenching on FITC-IgE-saturated cells (A). Cells (1 × 106 cells/ml) saturated with unlabeled IgE (B) or FITC-IgE (A) were suspended at 15°C, at t = 0, 2.2 nM of Cy3-DNP-BSA (B) or unlabeled DNP-BSA (A) was added to the cells. For B, data points are from three separate experiments (□, ○, Δ).

Close modal

We further evaluated fluorescence quenching caused by monovalent binding vs cross-linking by comparing DNP-BSA-dependent quenching for FITC-IgE in solution with that for cell-bound FITC-IgE. Cross-linking on the cell surface is expected to be accelerated by the high local IgE concentrations. Therefore, if fluorescence quenching on cell surface is mostly due to cross-linking, one would expect that fluorescence quenching for DNP-BSA binding to IgE in solution would approach a plateau more slowly than that for DNP-BSA binding to IgE on the cell surface. The data shown in Figure 6 are consistent with this prediction. For FITC-IgE in solution (upper trace), there is a small, fast phase of fluorescence quenching just after the addition of DNP-BSA, presumably due to the monovalent binding of the preexisting exposed DNP groups to FITC-IgE. Thirty minutes after its addition to IgE in solution, 5.5 nM DNP-BSA has quenched less than half of the maximum quenching (∼25%) that occurs with excess (55 nM) DNP-BSA, suggesting that equilibrium is approached at the lower concentration with a significant fraction of IgE sites unoccupied. In contrast, DNP-BSA binding to IgE on cells (lower trace) causes rapid quenching in the first 100 s, and this levels off to the same maximal quenching (35%) observed with higher concentrations of Ag within 30 min, indicating that occupancy of the IgE combining sites is nearly complete by this time.

FIGURE 6.

DNP-BSA binds more slowly to IgE in solution than to IgE-FcεRI on cell surface. The same concentration of DNP-BSA (5.5 nM, DNP:BSA = 15) was added to soluble FITC-IgE (1.5 nM; upper curve) and FITC-IgE-saturated RBL cells (1 × 106 cells/ml, 0.5 nM bulk; lower curve) at the arrows. The light dashed line represents saturation fluorescence quenching for IgE in solution, determined by the fluorescence quenching of soluble FITC-IgE (1.5 nM) by 55 nM DNP-BSA at steady state. Saturation fluorescence quenching for FITC-IgE in solution (∼25%) is somewhat smaller than that for FITC-IgE on cell surface (∼35%), as expected from previous results with monovalent ligands (13).

FIGURE 6.

DNP-BSA binds more slowly to IgE in solution than to IgE-FcεRI on cell surface. The same concentration of DNP-BSA (5.5 nM, DNP:BSA = 15) was added to soluble FITC-IgE (1.5 nM; upper curve) and FITC-IgE-saturated RBL cells (1 × 106 cells/ml, 0.5 nM bulk; lower curve) at the arrows. The light dashed line represents saturation fluorescence quenching for IgE in solution, determined by the fluorescence quenching of soluble FITC-IgE (1.5 nM) by 55 nM DNP-BSA at steady state. Saturation fluorescence quenching for FITC-IgE in solution (∼25%) is somewhat smaller than that for FITC-IgE on cell surface (∼35%), as expected from previous results with monovalent ligands (13).

Close modal

Results from Figures 5 and 6 are consistent with the conclusion that facilitated cross-linking of IgE on the cell surface serves to stabilize the exposure of DNP groups on DNP-BSA. Furthermore, these results indicate that the time course of DNP-BSA-dependent FITC fluorescence quenching on the cell surface is dominated by cross-linking after a short period of time (∼1 min for these Ag concentrations), such that this quenching curve can serve as a cross-linking curve at the later time points. We emphasize that FITC fluorescence quenching is parallel to Ag cross-linking only at the low concentrations of DNP-BSA that are suboptimal to optimal for cell activation. As the concentration of Ag increases, the concentration of immediately exposed DNP groups will increase, such that the fraction of the fluorescence quenching due to monovalent binding will also increase. This prediction is consistent with our flow cytometric measurements, which showed that the maximal cell-associated Cy3 fluorescence increases as the concentration of Cy3-DNP-BSA increases (data not shown).

A major motivation for our binding studies is to understand the relationship between Ag-induced receptor aggregation and consequent signal transduction. For this purpose we examined tyrosine phosphorylation of FcεRI, which is the earliest known cytoplasmic signaling event. We matched experimental conditions to compare directly the kinetics of DNP-BSA-stimulated tyrosine phosphorylation with the kinetics of DNP-BSA-induced IgE-FcεRI cross-linking as indicated by the DNP-BSA-induced fluorescein fluorescence quenching. We previously showed that cross-linking-dependent tyrosine phosphorylation of FcεRI occurs to a similar extent, albeit more slowly, at lower temperatures (4°C) as it does at 37°C (24). Figure 7,A shows a representative western blot of time-dependent tyrosine phosphorylation of FcεRI stimulated by 3 nM DNP-BSA at 15°C. The probing Ab (4G10) detects phosphorylated β subunit more strongly than phosphorylated γ subunit (see Fig. 8,a), and, therefore, phosphorylation of β was monitored for comparison to the binding kinetics. Densitometric measurements of β tyrosine phosphorylation stimulated by 3 nM DNP-BSA at 15°C in three independent experiments are plotted in Figure 7,B, together with fluorescence quenching occurring under the same conditions. These phosphorylation and binding curves show a strong correlation. Similar experiments were conducted with 1.1 nM DNP-BSA at 15°C (Fig. 7 C). At this lower concentration, both fluorescence quenching and tyrosine phosphorylation are slower (t1/2 ≃ 230 s for binding by 1.1 nM DNP-BSA vs t1/2 ≃ 120 s for binding by 3.0 nM DNP-BSA), but the correlation between these two processes remains similar for both concentrations of DNP-BSA. For both, the curves overlap at all but the earliest phosphorylation time points when monovalent binding dominates. Thus, these results at 15°C show parallel time courses for IgE-FcεRI aggregation caused by DNP-BSA and consequent cytoplasmic signaling.

FIGURE 7.

Time courses for DNP-BSA-induced FITC fluorescence quenching and DNP-BSA-stimulated FcεRI tyrosine phosphorylation in suspended RBL-2H3 cells at 15°C. A, Representative western blot for immunoprecipitated FcεRI from cells stimulated by 3.0 nM DNP-BSA for indicated times and probed with an anti-phosphotyrosine Ab (4G10). The time courses of binding of 3.0 nM (B) or 1.1 nM (C) DNP-BSA to FITC-IgE-FcεRI are compared with the time courses for β tyrosine phosphorylation stimulated with the same respective DNP-BSA concentrations. Data from three separate phosphorylation experiments (as represented for 3.0 nM DNP-BSA in A) quantified by densitometry are combined for each concentration in B and C.

FIGURE 7.

Time courses for DNP-BSA-induced FITC fluorescence quenching and DNP-BSA-stimulated FcεRI tyrosine phosphorylation in suspended RBL-2H3 cells at 15°C. A, Representative western blot for immunoprecipitated FcεRI from cells stimulated by 3.0 nM DNP-BSA for indicated times and probed with an anti-phosphotyrosine Ab (4G10). The time courses of binding of 3.0 nM (B) or 1.1 nM (C) DNP-BSA to FITC-IgE-FcεRI are compared with the time courses for β tyrosine phosphorylation stimulated with the same respective DNP-BSA concentrations. Data from three separate phosphorylation experiments (as represented for 3.0 nM DNP-BSA in A) quantified by densitometry are combined for each concentration in B and C.

Close modal
FIGURE 8.

Time courses for DNP-BSA-induced FITC fluorescence quenching and DNP-BSA-stimulated FcεRI tyrosine phosphorylation in suspended RBL-2H3 cells at 35°C. A, Representative western blot of immunoprecipitated FcεRI from cells stimulated by 1.1 nM DNP-BSA for times indicated and probed with an anti-phosphotyrosine Ab (4G10). The dark bands above the 30-kDa standard is FcεRI β, and the lower bands are FcεRI γ. B, The time course of binding of 1.1 nM DNP-BSA to FITC-IgE-FcεRI is compared with the time course for β tyrosine phosphorylation stimulated under the same conditions.

FIGURE 8.

Time courses for DNP-BSA-induced FITC fluorescence quenching and DNP-BSA-stimulated FcεRI tyrosine phosphorylation in suspended RBL-2H3 cells at 35°C. A, Representative western blot of immunoprecipitated FcεRI from cells stimulated by 1.1 nM DNP-BSA for times indicated and probed with an anti-phosphotyrosine Ab (4G10). The dark bands above the 30-kDa standard is FcεRI β, and the lower bands are FcεRI γ. B, The time course of binding of 1.1 nM DNP-BSA to FITC-IgE-FcεRI is compared with the time course for β tyrosine phosphorylation stimulated under the same conditions.

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Because most tyrosine phosphorylation experiments documented in the literature are performed at higher, more physiologic temperatures, we also compared binding and phosphorylation at 35°C. We find that tyrosine phosphorylation of FcεRI stimulated by 1.1 nM DNP-BSA at this higher temperature (Fig. 8,A) is somewhat stronger than that observed at 15°C, and the phosphorylation level peaks at about 5 min and then declines. This time course is similar to that observed by others at 35°C (25), and it is very different from what we observed at 15°C where tyrosine phosphorylation is sustained for at least 20 min (Fig. 7). The time courses for fluorescence quenching and β tyrosine phosphorylation caused by 1.1 nM DNP-BSA at 35°C are directly compared in Figure 8,B. The kinetics of the cross-linking of 1.1 nM DNP-BSA at 35°C are not very different from those of 3 nM DNP-BSA at 15°C, while the corresponding kinetics of β tyrosine phosphorylation are dramatically different (Figs. 7 and 8).

These studies represent part of our continuing effort to determine the features of IgE-FcεRI cross-linking that are critical for initiating the signaling cascade in RBL-2H3 cells. Multivalent ligands such as DNP-BSA are commonly used as potent stimuli. However, they have complicated structures, and, unlike the simpler bivalent ligands, examination of their binding to cell-associated Igs has been very limited (26, 27). The present study analyzed the kinetics of DNP-BSA binding with plausible mathematical models. The data indicate that the time course of FITC quenching after the first minute of binding is dominated by cross-linking events in the Ag concentration range examined. Thus, we could compare the kinetics of DNP-BSA-mediated receptor cross-linking to the kinetics of DNP-BSA-stimulated phosphorylation of receptor tyrosines. This comparison at 15°C shows that these two processes occurs at the same rate, indicating that cross-linking is likely to be the rate-limiting step and providing strong evidence for a direct relationship between FcεRI aggregation and the earliest known signaling events.

Time-dependent binding of DNP-BSA to FITC-IgE revealed that binding of multivalent Ag DNP-BSA to cell-bound anti-DNP-IgE is surprisingly slow compared with the binding of an equimolar concentration of monovalent ligand DCT (Fig. 1). Neither monovalent nor bivalent ligand models can account for the data, and models that invoke Ag heterogeneity with respect to absolute DNP exposure are also inadequate. For example, a model in which a small subpopulation of the total Ag concentration has all DNP groups available for binding while the DNP groups on most Ags are irreversibly buried could not account for the capacity of 0.2 nM DNP-BSA (3 nM DNP) to fully occupy the FITC-IgE combining sites (1 nM) as we have observed (unpublished results). As shown in Figure 5, comparison of combining site occupancy monitored by fluorescence quenching and flow cytometric measurement of DNP-BSA association with cells reveals that a large fraction of the DNP-BSA-induced fluorescence quenching occurs more slowly than DNP-BSA association with cells and must therefore be due to cross-linking events. Consistent with this, we observed that DNP-BSA-induced fluorescence quenching is significantly slower for IgE in solution than for IgE-FcεRI on the cell surface where cross-linking is facilitated by the local high concentration of IgE (Fig. 6). The observations that DNP-BSA stimulates robust cellular responses (28) and also causes immobilization of most of the IgE-FcεRI (5, 29) further indicate that most IgE-FcεRI can be cross-linked into aggregates by this Ag.

To account for both the initially low effective valency of DNP-BSA and the efficient cross-linking of DNP-BSA to IgE-FcεRI on the cell surface, we developed a transient hapten exposure model (Fig. 3,A). In this model most of the n DNP groups are generally unavailable for binding to IgE, but each has a finite probability of transient exposure, and binding to IgE stabilizes the exposed state. For a first approximation, we truncated the model at n = 2 DNP groups that can be exposed. This truncated model effectively describes the association and dissociation of DNP-BSA on the cell surface (Fig. 3), and the dissociation rate constants derived from the dissociation data are consistent with those derived from the association data (Table I). Furthermore, we find that association and dissociation data can be fit simultaneously with this model (our unpublished results). Also, several sets of association or dissociation data obtained at different concentrations of DNP-BSA can be fit simultaneously as effectively as they are fit individually, and similar rate constants are obtained (our unpublished results). The estimated k+1 and k−1 = k−2 for DNP-BSA derived from this model are comparable to those obtained for DCT (Table I), consistent with our interpretation that the slow association of DNP-BSA to IgE is not because the DNP group has a slower binding rate constant or lower intrinsic affinity when conjugated to BSA, but, rather, that the availability of DNP groups is limited.

This model quantitatively accounts for the faster binding of DNP-BGG than DNP-BSA at equimolar DNP, and it predicts that, on average, the availability of DNP groups on DNP-BGG is somewhat greater, but still significantly restricted. The small differences observed may be related to the secondary structures of these two different proteins (30, 31), or, more likely, to more subtle structural features near the surfaces of these proteins where the lysine-conjugated DNP groups are expected to be located (32). The faster binding by DNP-BGG compared with DNP-BSA indicates that diffusion of these Ags is not likely to play a major role in their binding to the cell surface, as D20,w for BSA and γ-globulin are 5.9 × 10−7 cm2/s and 3.8 × 10−7 cm2/s, respectively (33, 34). The restricted availability of DNP groups on both BSA and BGG to Ab binding is likely to be a general property of DNP-conjugated proteins, although chemically unrelated haptens conjugated to proteins will not necessarily share this property.

As described in Materials and Methods, the transient hapten exposure model includes several simplifying assumptions. Our assumption that IgE can be considered in terms of two equivalent Fab binding sites is supported by our observation that the binding of DNP-BSA to these Fab fragments is slow and quite similar to DNP-BSA binding to intact IgE in solution (our unpublished results). This similar binding behavior indicates it is unlikely that limited accessibility or intramolecular cross-linking of IgE binding sites by DNP-BSA contributes substantially to the overall binding.

With our initial approximation that a maximum of two DNP groups become exposed (n = 2; Fig. 3,A), each cross-linking event must be preceded by a monovalent binding event. This would predict that cross-linking can cause no more than 50% of FITC fluorescence quenching. However, we calculate from the data of Figure 5 that more than half of the DNP-BSA-induced quenching on cell surface is due to cross-linking. The fact that DNP-BSA stimulates much more robust cellular responses than does bivalent ligand (DCT)2-cys also makes it appear unlikely that DNP-BSA only forms IgE-FcεRI dimers (3). Therefore, a more realistic description of the binding of DNP-BSA to cell-bound FITC-IgE requires that the model be expanded to n > 2. Because the Figure 5 analysis estimates that monovalent binding contributes about 30% to the FITC quenching, the model with n = 2 is probably not too far off. Expansion of the model should not change the estimated value of the dissociation rate constant k−1 (k−2) as it is determined by the single exponential of the dissociation data. Trends in the estimated values of the other parameters due to expanding the model further can be predicted from changes occurring with expanding the model from n = 1 to n = 2. We predict that expanding the model from n = 2 to n = 3 will decrease somewhat the estimated values of λ, k+1, and k+2. However, consistency with the DCT results suggest that more accurate values for n > 2 will not be very different. The lumped parameter, nk3+1λ/(1+λ), corresponds to the initial rate for binding of DNP-BSA to IgE, and an algorithm fitting the initial slope of the binding data will yield an accurate value for this parameter. Table I shows that, as the DNP-BSA concentration decreases, the values for this parameter (n = 2) fluctuate about a constant of ∼2 × 106 M−1 · s−1, while the values of k+1 decrease and the values for λ increase. Thus, it will be possible to determine an accurate value for this lumped parameter as well as for k+1 and λ for the correct choice of n.

Whereas the values for λ listed in Table I are likely to be close to accurate, the absolute values of λ+ and λ are much less well defined. The absolute values we have extracted for λ+ and λ are probably too small because the characteristic times associated with these values are on the order of 103 to 104 s whereas the fluorescence quenching we observe occurs on the time scale of 0 to 103 s. Better estimates of the absolute values of λ+ and λ will require more experiments and development of better fitting procedures. For present purposes, the ratio λ = λ+ provides the most useful parameter, the equilibrium constant for the exposure of DNP groups.

We observe a direct correlation between the time course for receptor cross-linking and receptor tyrosine phosphorylation at 15°C (Fig. 7, B and C). This correlation does not appear at 35°C where there is a biphasic tyrosine phosphorylation response (Fig. 8). A similar biphasic time course for receptor tyrosine phosphorylation at similar Ag concentrations and physiologic temperatures was observed by Pribluda and Metzger (25), who also showed that the onset of tyrosine phosphorylation after addition of Ag was the same for β and γ subunits. In their experiments, addition of excess hapten quickly reversed the receptor phosphorylation, suggesting this is regulated by a dynamic interplay of kinases and phosphatases (25, 35). The observation that the phosphatase inhibitor phenylarsine oxide inhibited the time-dependent decrease in phosphorylation (25) supports this model. Our results at 35°C that tyrosine phosphorylation declines as cross-linking continues to increase are also consistent with the involvement of regulatory phosphatases; at 15°C these regulatory processes appear to be suppressed. Thus, this lower temperature provides a simpler situation for examining the relationship between receptor aggregation and receptor tyrosine phosphorylation.

Wofsy et al. (36) compared at 37°C the time course for binding of covalently linked dimers of IgE with the time course for the resulting phosphorylation of tyrosines on FcεRI. They found that phosphorylation reached a plateau much more rapidly than dimer binding and cross-linking. They proposed that the leveling off of phosphorylation while receptor aggregation continued to increase occurred because receptor aggregates competed for limited amounts of the initiating kinase, presumably Lyn. They further suggested that, as receptors were aggregated, new high affinity sites (phosphotyrosines on receptors) that bind the initiating kinase were created and these sites also entered the competition for Lyn. Competition experiments subsequently demonstrated that the initiating kinase can rapidly redistribute in response to the formation and dissociation of receptor aggregates (37). Interpreting our DNP-BSA binding and receptor phosphorylation data in terms of this model suggests that redistribution of Lyn is slowed and the effects of competition for Lyn is diminished at the lower temperature of 15°C.

In summary, our observations that DNP-BSA binds substantially more slowly to cell-bound IgE than does equimolar DCT reveal that the average effective number of DNP groups per BSA is less than one. After eliminating simpler models, we found that this slow binding of DNP-BSA to cell-bound IgE is consistent with a transient hapten exposure model in which most DNP groups are unavailable for binding to FITC-IgE, but they have a finite probability of exposure. At the DNP-BSA concentrations that are suboptimal to optimal for cell activation, DNP-BSA-induced FITC fluorescence quenching curves can serve as indicators for the time course of IgE-FcεRI cross-linking on the cell surface. We observe that the kinetics of DNP-BSA-induced FITC fluorescence quenching correlates with the kinetics of DNP-BSA-stimulated FcεRI-β tyrosine phosphorylation at 15°C. This observation demonstrates a direct relationship between the kinetics of receptor aggregation and this early signaling event. Based on this correlation and our ability to fit DNP-BSA binding data with the transient hapten exposure model, we are now in position to predict the rate of DNP-BSA-mediated cross-linking of IgE-FcεRI over a wide range of Ag concentrations for comparison to the time courses of FcεRI tyrosine phosphorylation. In particular, ability to predict the kinetics of cross-link formation at 37°C should permit a greater understanding of the temporal relationships between cross-linking, receptor phosphorylation, and the activation of signaling and regulatory pathways that result from these earliest events.

1

This work was supported by National Institutes of Health Research Grants GM35556 and AI22449, by National Science Foundation Grant GER-9023463, and by the United States Department of Energy.

3

Abbreviations used in this paper: (DCT)2-cys, N,N′-bis(ε-N-(2, 4-DNP)aminocaproyl-l-tyrosine)-cystine; BSS, buffered saline solution; BGG, bovine γ-globulin.

4

Figure 5,B shows that Cy3-DNP-BSA binding to IgE-sensitized cells causes ∼60% of the maximal fluorescence increase at 50 s. Figure 5 A shows that DNP-BSA binding to cell-bound FITC-IgE causes ∼20% of the maximal fluorescence quenching at 50 s. If we assume that the fluorescence quenching before 50 s is all due to monovalent binding of DNP-BSA, then the maximal percentage of the total fluorescence quenching that is due to monovalent binding can be estimated as: (20%/60%) × 100% = 33%. We further calculate that total fluorescence quenching by monovalent binding that occurs after t = 50 s is 33% − 20% = 13%. Fluorescence quenching after t = 50 s accounts for 100% − 20% = 80% of the total fluorescence quenching. Therefore, the fraction of this fluorescence quenching after t = 50 s that is due to monovalent binding is calculated as 13%/80% = 16%.

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