©1995 by The American Society for Biochemistry and Molecular Biology, Inc.
Kinetics of Tyrosine Phosphorylation When IgE Dimers Bind to FC Receptors on Rat Basophilic Leukemia Cells (*)

(Received for publication, February 21, 1995; and in revised form, May 9, 1995)

Carla Wofsy (1) Ute M. Kent (2) Su-Yau Mao (2) Henry Metzger (2) Byron Goldstein (3)(§)

From the  (1)Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, (2)NIAMS, National Institutes of Health, Bethesda, Maryland 20892, and the (3)Theoretical Biology and Biophysics Group, Theoretical Division, T-10, MS K710, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
APPENDIX
FOOTNOTES
REFERENCES

ABSTRACT

Previously, we demonstrated that aggregates of the high affinity receptor for IgE (FcRI), formed by the binding of chemically cross-linked oligomers of IgE, continue to signal early and late cellular responses long after the formation of new aggregates is blocked. In the present work, we explore quantitatively the relationship between aggregation of the receptors and one of the earliest biochemical changes this initiates. We compare the time course of aggregate formation, inferred from studies of the binding of dimers of IgE, and the time course of phosphorylation of tyrosines on receptor subunits when the receptors are aggregated. A simple model does not fit the data. It appears that aggregates formed late in the response are less effective signaling units than those formed initially. We propose new explanations for the persistence of the response and the unusual kinetics.


INTRODUCTION

Several types of receptors central to the functioning of the immune system stimulate cellular responses when they are aggregated by ligand, directly or indirectly. Among the earliest observable responses to such aggregation is enhanced phosphorylation of tyrosines on one or more of the subunits of the receptor and on a variety of other proteins. In this respect, these receptors resemble many receptor kinases(1) ; however, unlike the latter, the multi-subunit immune response receptors (2) have no known intrinsic kinase domains. Instead, there is increasing evidence that their action is mediated by constitutively bound and newly recruited kinases(3, 4) .

In basophils and mast cells, aggregation of the high affinity receptor for IgE (FcRI) stimulates morphological, secretory, and biosynthetic changes in the cells(5, 6) . As with other multi-subunit immune response receptors, increased phosphorylation of tyrosine residues on subunits of the receptor (beta and in this instance) and on several other cellular proteins is among the earliest molecularly defined consequences of the aggregation of FcRI(7, 8, 9) . Recent studies of the kinase activity induced by FcRI aggregation on rat basophilic leukemia (RBL) (^1)cells indicate that the kinases Lyn and Syk are among those whose activity is observable following aggregation of FcRI(10, 11, 12) . A fraction of FcRI on RBL cells is associated with Lyn prior to activation, and additional Lyn is associated with the receptor after activation(13, 14, 15) . Syk appears not to be pre-associated with the receptor, but there is evidence that it associates with both the beta and the subunits, primarily , following activation(13, 14) .

The relation between the degree of receptor aggregation and subsequent cellular events is often complex. For example, receptor aggregation is not always stimulatory but, depending on the concentration of ligand and receptor, can turn on or turn off cellular responses(16) . It is therefore important to understand the quantitative relationships between the aggregation of such receptors and the early biochemical signals they generate. To pursue these quantitative relationships, we chose an experimental system that is particularly tractable, both theoretically and experimentally. We used chemically cross-linked dimers of IgE to aggregate FcRI on RBL cells. The only receptor aggregates that form in this case consist of two FcRI, bound to the distinct IgE molecules in single IgE dimers. Because the dissociation of IgE from FcRI is slow(17) , receptor aggregates are long-lived. Excess monomeric IgE can be used to stop the formation of new aggregates without breaking up existing ones.

Previously, we used such a protocol and found that receptors aggregated by oligomers continue to signal both early and late events for protracted periods(18) . The early signal we monitored was phosphorylation of tyrosines on the receptor itself and on other proteins. Those studies also suggested that the stable aggregates undergo a dynamic process of phosphorylation and dephosphorylation. The goal of the present study was 2-fold. First, we wanted to determine the time course of receptor aggregation and compare it with the time course of phosphorylation of tyrosines on the receptor. Second, we wanted to see whether carefully quantitated results from similar experiments could be accounted for by a simple model in which the extent of phosphorylation was related to the extent of aggregation by a series of internally consistent rate constants. Aggregation of receptors is not readily assessed directly and must be inferred from binding studies. The use of dimeric rather than trimeric aggregates makes such inferences much more reliable, and so we principally used this type of oligomer for the present studies.


MATERIALS AND METHODS

Reagents

We used anti-DNP monoclonal mouse IgE from the hybridoma Hi-DNP e26.82(19) , rat IgE of unknown specificity from the immunocytoma IR162 (20) purified according to Holowka and Metzger(21) , rabbit IgG specific for the F(ab`)(2) of IgE (22) , mouse anti-phosphotyrosine antibody PY20 conjugated with horseradish peroxidase (ICN), ECL chemiluminescence reagents and hyperfilm-ECL (Amersham Corp.), and 12 and 14% SDS-polyacrylamide gels (1.5 mm) (Novex). All other reagents were of the highest purity available.

Cells

RBL 2H3 cells were cultured as previously described(23) . For phosphorylation assays, the cells were detached with 0.05% trypsin, 0.02% EDTA in Hanks' buffered salt solution (Cellgrow) and assayed in suspension.

Preparation and Purification of Oligomers

IgE oligomers were prepared essentially as previously described(24) . Rat IgE or mouse anti-DNP IgE in 200 mM Tris-HCl, pH 8.6, was concentrated to approximately 50 mg/ml in a centricon concentrator. A 16-fold molar excess of dimethylsuberimidate (prepared fresh as a 20 mg/ml stock solution in the above buffer) was added to the antibody solution, mixed, and incubated at 30 °C for 2 h with periodic mixing. The reaction was quenched by addition of 0.2 ml of 200 mM glycine. Monomeric, dimeric, or trimeric IgE was separated by gel filtration chromatography on a Superose 6 column (Pharmacia Biotech Inc.). A maximum sample volume of 200 µl was injected onto the column equilibrated with borate-buffered saline, and the species were resolved at a flow rate of 0.5 ml/min. Monomeric IgE was eluted at approximately 28 min, dimeric IgE at 24 min, and trimeric IgE at 22 min. The peak fractions were pooled and if necessary, concentrated. Some preparations of IgE were iodinated with chloramine T (25) . Following iodination, monomeric or dimeric IgE was concentrated and repurified by Superose 6 chromatography as described above.

Activation of Cells

Cells from 3-day cultures were detached with trypsin. The cells were washed once with medium and twice with warm assay buffer containing 1 mM CaCl(2), 0.4 mM MgCl(2), and 0.1% bovine serum albumin. For tyrosine phosphorylation assays, the cells were suspended in the above buffer at 5 10^6 cells/ml and stimulated with 0.3 µg/ml dimeric IgE at 37 °C with periodic mixing. After 2 min of dimer stimulation, some cell samples were removed and added to purified monomeric IgE at a final concentration of 10 µg/ml. Control samples received either 10 µg/ml monomeric IgE alone or 10 µg/ml monomer together with 0.3 µg/ml dimeric IgE at the beginning of the experiment. At the indicated times, samples for cell extracts or for immunoprecipitation were removed. For some experiments, cells were also incubated with 0.6 or 1.2 µg/ml dimeric IgE.

Sample Preparation and Sample Analysis

For cell extracts, 80 µl of 2 cell suspension was added to 80 µl or 2 SDS-sample buffer (50 mM Tris-HCl, pH 6.8, glycerol, 4% SDS, 1 mM Na(3)VO(4)) vortexed and boiled immediately for 5 min. Proteins from cell extracts were resolved on 12% SDS-Tris-glycine gels. Each lane contained 40 µl or 1 10^5 cell equivalents. For immunoprecipitation, 1 ml (5 10^6 cells) was removed. The cells were pelleted for 3 s at 16,000 g in an Eppendorf microcentrifuge, the supernatant was removed, and the cell pellet was solubilized immediately with 100 µl of ice-cold 10 mM CHAPS in borate-buffered saline, 30 mM sodium pyrophosphate, 1 mM Na(3)VO(4), 5 mM EDTA, 10 µg/ml aprotinin, 10 µg/ml leupeptin, 10 µg/ml pepstatin on ice for 30 min. The samples were then diluted to 500 µl with ice-cold borate-buffered saline containing 1 mM Na(3)VO(4), mixed, and centrifuged to remove insoluble material at 16,000 g for 15 min at 4 °C in an Eppendorf microcentrifuge. Solubilized IgE receptors were immunoprecipitated with 4 µg/ml F(ab`)(2) specific rabbit anti-mouse IgE. After 1.5 h, 50 µl of a 50% protein A-Sepharose (Pharmacia) suspension was added and incubated at 4 °C for an additional 1.5 h. The protein A-Sepharose pellet was washed twice with 2 mM CHAPS containing the above inhibitors. Each protein A pellet received 25 µl of 2 SDS-sample buffer, 1 mM Na(3)VO(4) and was boiled for 5 min. The denatured proteins were expelled by puncturing the bottom of the microfuge tube with a 30-gauge needle and centrifuging the solution into a new tube. The entire sample was resolved on a 14% SDS-Tris-glycine polyacrylamide gel. To compare all samples from different gels with each other, each gel also contained one sample from the same time point, usually obtained from the 8-min dimer-stimulated sample. Duplicates of each time point were loaded and analyzed. Proteins were transblotted to 0.2-µm nitrocellulose membranes (Schleicher and Schuell) and probed for tyrosine-phosphorylated proteins with the anti-phosphotyrosine antibody PY20 as previously described(26) . The intensities of the protein bands were quantified by densitometric scanning (Imagequant, Molecular Dynamics). The values for each sample were normalized to the average intensity obtained from all gels for the 8-min time point standard.

Binding Studies

Some binding studies were carried out with I-labeled dimers to assess the amount of dimeric IgE bound to the receptors under the above conditions of stimulation. Cells were detached, washed, resuspended, and stimulated exactly as described for the tyrosine phosphorylation assays above except that I-labeled dimeric IgE was used. At the indicated time points, 100 µl of cell suspension (5 10^5 cells) were removed and centrifuged through a cushion of phthalate oil to separate cell bound from free IgE(27) . Bound I-IgE was determined by counting triplicate cell pellets in a counter (Minaxi gamma 5000, Packard Instrument Co.). For some binding studies, cells were trypsinized and suspended at 5 10^6 cells/ml in complete medium. The cells were then incubated at room temperature while shaking with 2 µg/ml monomeric I-IgE or 4 µg/ml dimeric I-IgE. At the indicated times, triplicate 100-µl samples were removed and centrifuged through a cushion of phthalate oil as above. For preparing cells partially saturated with IgE, the cells were first incubated with 2 µg/ml unlabeled rat IgE for 75 min. Approximately 70% of the receptors were occupied under these conditions. The cells were pelleted, washed, and resuspended at 5 10^6 cells/ml, followed by addition of labeled monomers or dimers as for non-saturated cells. Total cellular receptor numbers were obtained by incubating non-saturated cells with 5 µg/ml I-labeled monomeric IgE for 1 h at room temperature.


RESULTS

Binding Characteristics of IgE Dimers

To relate quantitatively signal transduction to aggregation of receptors, we first had to relate the binding of IgE dimers to dimerization of receptors. As already noted, the latter cannot be assessed directly. Because the preparation of chemically cross-linked oligomers of IgE can lead to partial inactivation of the antibody(28) , we first needed to determine the fraction of dimers capable of binding to FcRI (P(1)) and the fraction of bindable dimers that could bind bivalently and therefore aggregate the receptors (P(2)). It is known that each FcRI has only a single binding site for IgE and, likewise, that each IgE binds to only a single receptor(29, 30) . Therefore, once we determined P(1) and P(2), we could estimate single site binding and dissociation rate constants (Fig. 1) from kinetic binding studies and thereby estimate the time course of dimer-induced aggregation of the receptors.


Figure 1: Binding to and aggregation of IgE FcRI by bifunctional dimers of IgE. The forward and reverse rate constants are k and k for the binding (or dissociation) of one IgE in a dimer to (from) a single FcRI and k and k for the binding (or dissociation) of the second IgE in a monovalently bound dimer to (from) a second receptor.



The model used to analyze the binding data is presented in detail under ``Appendix.'' Least squares fits of the model to binding data from a variety of experiments, described below, yielded estimates of the parameters.

Bindable Dimer Fraction (P)

To determine P(1), the fraction of dimers capable of binding to FcRI, we added I-IgE dimers to an excess of receptors (0.33 nMI-IgE in dimer form to approximately 2.5 nM FcRI). 1, 1.5, and 2 h after the addition, the cells were centrifuged, and the fraction of the radioactivity remaining in the supernatant was measured. We determined the bindable dimer fraction from the relation between the inverse of the fraction of dimer bound, 1/b, and the inverse of the incubation time, 1/t (, ``Appendix''). The 1/b intercept, which is the limit of 1/b as time tends to infinity, is 1/P(1). With the preparation of dimers used here, the best fit of the data (measurements from triplicate samples at each of the three time points) is obtained with P(1) = 0.54.

Fraction of Bindable Dimers Capable of Binding Doubly (P)

The simplest explanation of why IgE in the chemically cross-linked dimers may fail to bind to FcRI is that the chemical cross-linking occurs in or around the binding site for the receptor. If so, then there are two extreme cases that are useful to consider to estimate the fraction of IgE dimers that can bind bivalently on intact cells. One possibility is that the IgEs in a dimer are tethered randomly, so that the binding sites on the distinct IgE molecules are inactivated independently. As described under ``Appendix,'' we show that in this case, with P(1) = 0.54, P(2) would equal 0.19. However, the partial saturation experiments described below provided evidence against random inactivation. Instead, they support the other extreme, that at the high concentrations used for preparing the oligomers(24) , the IgEs are sufficiently aligned in solution so that chemical cross-linking tends either to inactivate the receptor binding sites of both IgEs in a dimer (e.g. when the covalent cross-link forms between juxtaposed FcRI binding regions) or neither (e.g. when they are cross-linked through lysines occurring outside both binding regions). In the case of perfect alignment, P(2) = 1.

Results of Monomer Quench Experiments

Fig. 2shows the best simultaneous fit of the model to the data from three experiments. In each, cells were exposed to 1.5 nMI-IgE as dimers alone or in the presence of a 33-fold molar excess of unlabeled monomer added either simultaneously or 2 min after the addition of the dimers. The fit of the model to the data is very sensitive to the value used for the forward rate constant k but less so to other parameters. In particular, the fraction of bindable dimer that can bind doubly (P(2)) and the forward rate constant for receptor dimerization (k) can vary over a wide range and give essentially equally good fits. In all fits, we used the value P(1) = 0.54 (above) and the previously determined value of the IgE dissociation rate constant (k = 1 10 s) (17, 31, 32, 33) for the dissociation reactions (i.e. monomer dissociation and the first and second steps in dimer dissociation).


Figure 2: The kinetics of binding of I-IgE dimer (1.6 nM) to FcRI (2.5 nM (a), 3.2 nM (b), and 2.7 nM (c)) in the presence and absence of unlabeled IgE monomer (53 nM) for each of the three replicate experiments. black square shows the data for dimer binding when no monomer was present; bullet shows when monomer was added after 2 min; and demonstrates when monomer was added initially, along with dimer. The theoretical curves (solidlines) plot the best simultaneous fit of the binding model (``Appendix'') to the nine data sets (three experiments, each with three conditions). The parameter values are: P(1) = 0.54, P(2) = 1, k = 0.8 10^5M s, k = 1.4 10^5M s, k = k = k = 1 10 s. Essentially the same fit is obtained for any k value within 3 orders of magnitude of the diffusion limit.



One observation that will be important in the interpretation of data on phosphorylation of protein tyrosines from analogous experiments is that monomer, at the concentration used, terminates new dimer binding within minutes (Fig. 2, lowercurves).

Forward Rate Constant for Dimer Binding (k)

Using the two extreme values of the parameter P(2), we obtained essentially equally close fits of the model to the monomer quench data. However, different values of P(2) had to be paired with different values of the forward rate constant to obtain the closest fits. If P(2) = 1, the best fit is achieved with k = 0.8 10^5M s (shown in Fig. 2); if P(2) = 0.19, the best estimate for k is 1.4 10^5M s (fit not shown). The difference comes from the fact that to account for the observed rate of binding, the forward rate constant must be larger if only one IgE in a dimer can bind than if both can. For both pairs of P(2), k values, the forward rate constant for monomer binding that gave the best fit of the model to the data was 1.4 10^5M s. This value is consistent with the previously determined range of 1-2 10^5M s(17, 32, 33) .

Partial Saturation Experiments

To determine the values of the two parameters related to dimer-induced aggregation of FcRI, P(2) and k, we performed experiments under conditions where the concentration of vacant receptors was sharply reduced. Fig. 3shows the binding of dimers to RBL cells, all of whose receptors were initially vacant (uppercurves), or to cells 70-80% of whose FcRI became occupied during a preincubation with unlabeled monomeric IgE (lowercurves). The dimers were added at a concentration (21 nM IgE) that was eight times the total receptor concentration (approximately 2.5 nM) in the samples.


Figure 3: Binding kinetics of dimers when receptors are limiting. In two separate experiments (a, b), RBL cells, all of whose FcRI (3-4 nM) were initially unoccupied (uppercurves) or 70-80% of whose FcRI were occupied by unlabeled monomeric IgE (lowercurves), were incubated with I-IgE dimer (21 nM) for the indicated times. The best simultaneous fit of the binding model to the data (average cpm from triplicate samples at each time point) was obtained with P(2) = 1, k equal to the diffusion limit (``Appendix''), and corrections of 15% (a) and 1% (b) in the number of receptors per cell determined experimentally. The P(2) and k values giving the best fits were the same, with or without a correction in the number of receptors per cell. Other parameters were as previously determined (Fig. 2). The results of two analogous experiments on Chinese hamster ovary cells transfected with FcRI are consistent with the same parameter set (data not shown).



The value of P(2) that gave the best fit of the model to the data is P(2) = 1, corresponding to the case where either both or neither of the IgEs in a dimer can bind to FcRI. Under the alternative assumption of independent inactivation of IgEs in a dimer, so that P(2) = 0.19, the predictions made by the model deviate markedly from the data both qualitatively and quantitatively.

Forward Rate Constant for Dimer-induced Receptor Aggregation (k)

The best fits of the model to the data from the partial saturation experiments are achieved with an aggregation rate constant that would cause the second IgE in a singly bound dimer to bind to a second FcRI in fractions of a second, even on cells with 90% of receptors already occupied. However, acceptable fits of the model to the data are obtained with the forward rate constant for aggregation (k) ranging over several orders of magnitude. In terms of the mean time for a monovalently bound IgE dimer to bind to a second FcRI on an RBL cell with most receptors vacant, the data were consistent with times ranging from 0 (instantaneous binding) to 10 min. Under ``Appendix,'' we show that the diffusion limit of the rate of aggregation on an RBL cell with a total of 3 10^5 FcRI is roughly 65-330 s. This corresponds to a mean time of 0.003-0.01 s for a monovalently bound dimer to become bound bivalently.

Phosphorylation of Protein Tyrosines

Fig. 4illustrates typical results from an experiment in which we followed phosphorylation of the receptor upon addition of dimers whose ability to dimerize receptors had been rigorously assessed. The phosphorylation reached a steady state level in approximately 20 min in the samples to which no monomer had been added. In those samples to which a 33-fold excess of monomers was added at 2 min, a steady state level was achieved much more rapidly and was substantially lower than that achieved in the samples containing the dimer alone. We next compared these time courses of phosphorylation with the time courses for the rate of formation of aggregates and the concentration of aggregates.


Figure 4: Time course of tyrosine phosphorylation of the and beta subunits of FcRI and two other cellular proteins, p72 and p30, in RBL cells stimulated with IgE dimer (1.6 nM), in the absence of IgE monomer, and with monomer (53 nM) added after 2 min. The results shown are from densitometric scans of autophotographs of the gels on which the samples were analyzed. The intensity values are averages from duplicate samples in representative single experiments. The cellular protein p38 had a time course of tyrosine phosphorylation similar to those of p72 and p30 (not shown).



In Fig. 5we present the result of calculations of how the rate of formation of aggregates (dimers) of FcRI is expected to vary with time under the conditions used for the experiments shown in Fig. 4. It is apparent that dimer-induced phosphorylation of protein tyrosines does not follow the time course of the rate of aggregation of receptors. In contrast with the time course of phosphorylation observed experimentally when monomeric IgE blocked further binding of dimers (Fig. 4), the predicted rate of formation of aggregated receptors decreases rapidly to zero under the same conditions (Fig. 5). Even in the absence of monomer, phosphorylation of protein tyrosines continued to increase and then remained elevated well after the predicted rate of aggregation had peaked and begun to decrease.


Figure 5: Predicted variation of the rate of dimerization of receptors with time, plotted with k 1000-fold lower than the diffusion limit. The other parameters are as in Fig. 2. The difference between the observed phosphorylation levels and the predicted aggregation rate becomes even more pronounced if the forward rate constant is closer to the diffusion limit. The model presented under ``Appendix'' was used to calculated the rate of dimerization.



How the concentration of receptor aggregates changes in time can be seen from Fig. 2where, for the range of binding parameters identified in the binding experiments, plots of the predicted concentration of receptors that are aggregated are indistinguishable from the plotted binding curves. The kinetics of phosphorylation of protein tyrosines on beta and (Fig. 4) paralleled more closely the time course for the total number of aggregated receptors than the predicted time course of the rate of formation of aggregates (Fig. 5). In particular, phosphorylation levels were maintained for at least an hour after the addition of monomeric IgE had blocked further binding and aggregation of FcRI (compare the lowercurves in Fig. 2and Fig. 4).

However, there were also significant differences between the patterns of aggregation of FcRI (Fig. 2) and phosphorylation of tyrosine residues on the subunits of the receptor (Fig. 4). First, when IgE dimer bound in the absence of IgE monomer, the level of phosphorylation of tyrosines on the and beta subunits of the receptor stopped rising after 10-20 min, although receptor dimerization continued to increase for over an hour. Second, the levels of dimer-induced phosphotyrosine in the presence and absence of IgE monomer were much closer to each other than were the predicted concentrations of receptors in dimers in the corresponding samples. For example, in the first panel of Fig. 4, the ratio of the apparent steady state levels of phosphotyrosine associated with the chain when dimer bound in the absence of monomer and when monomer was added after 2 min was approximately 4. The ratio of the concentrations of receptors in dimers, under the same two experimental conditions, estimated from I-IgE binding data for cells with approximately 3 10^5 receptors, was 7 at the end of an hour and was still increasing (Fig. 2a).

To compare in a more rigorous way the relationship between aggregation and phosphorylation, we extended the binding model to include dimer-induced phosphorylation of tyrosines. The model, illustrated in Fig. 6and detailed under ``Appendix,'' allows for both reversible and irreversible dephosphorylation.


Figure 6: Extension of the binding model (Fig. 1) to include dimer-induced tyrosine phosphorylation (rate ), reversible dephosphorylation (rate µ(1)), and irreversible dephosphorylation (rate µ(2)).



Fig. 7shows the best fit of the model to the data for tyrosine phosphorylation of the subunit, obtained under the two conditions where monomer was added to block further dimer binding and receptor aggregation (lowercurves). The uppercurve shows the prediction of the model for the case when IgE dimer binds in the absence of monomer. The theoretical curve was generated using the phosphorylation and dephosphorylation rates that provided the best fit of the model to the experiments in which monomer was added. That fit was obtained by assuming that irreversible dephosphorylation was negligible on the time scale of the experiments (µ(2) = 0) and that phosphorylation was rapid ( geq 10 min). The fit was not sensitive to the reversible dephosphorylation rate µ(1). In generating the theoretical curves in Fig. 7, we used the value µ(1) = 1 s. Values in the range 1 min to 1 s are consistent with the time course of dephosphorylation in our earlier experiments in which EDTA was added to inhibit kinase activity(18) .


Figure 7: Time course of tyrosine phosphorylation of the subunit of FcRI. The twolowercurves represent the best fit of the model (Fig. 5) to the data from experiments with excess monomer added after 2 min (bullet) or along with dimer (). The binding parameters used are as previously determined (Fig. 2, 3). The data do not determine the phosphorylation rate or the reversible dephosphorylation rate µ(1). Values used in the fit were = 10 s and µ(1) = 1 s, consistent with the observation that phosphorylation increases rapidly after cell activation and dephosphorylation is rapid after kinase removal(18) . The irreversible dephosphorylation rate determined from the fit is µ(2) = 0 s. The uppercurve shows the result of using these parameters in the model to predict tyrosine phosphorylation of when dimer binds in the absence of monomer. The corresponding data are indicated by black square.



We also fit the model to the data obtained in the absence of monomer and used the resulting parameters to predict phosphotyrosine levels in the experiments where monomer was added (results not shown). The irreversible dephosphorylation rate needed to fit data from experiments where dimer bound in the absence of monomer predicted rapid dephosphorylation under the other two conditions. As it stands, the model cannot give an adequate simultaneous fit of both types of data, i.e. dimer-induced phosphotyrosine levels observed in the presence and absence of monomer. In particular, it cannot account for the ``squeezing'' together of the tyrosine phosphorylation curves obtained with and without the addition of excess IgE monomer.

A possible explanation for the leveling off of phosphorylation while aggregation continues to increase is that the kinases responsible for phosphorylation are in limited supply so that the phosphorylation reaction saturates. The model can be modified to allow for this possibility by replacing the constant phosphorylation rate (per aggregated receptor) by a rate that depends on the concentration of one or more kinases and adding equations to keep track of the changing kinase concentration(s). However, Fig. 8shows that when the concentration of IgE dimers was increased, the height of the plateau increased, demonstrating that the phosphorylation reaction had not been saturated.


Figure 8: Time course of phosphorylation of tyrosines on the subunit of FcRI, following stimulation of RBL cells by IgE dimer at 3 nM (bullet) and 6 nM (black square) concentrations. Data are from duplicate samples in one of two experiments. The solidcurves show the corresponding predictions of the model. The irreversible dephosphorylation rate used, µ(2) = 2.6 10 s, was determined from the best simultaneous fit of the model to six data sets (two experiments, three dimer concentrations each; data at 1.6 nM not shown). The other parameters were as previously estimated (Fig. 7).



The fundamental quantities calculated from the model are fractions of FcRI in the distinct states illustrated in Fig. 5. Therefore, we could calculate the fraction of receptor subunits that were phosphorylated over time in the various experiments. In the experiments where dimer bound in the absence of monomer, separate fits of phosphotyrosine levels measured on the and beta subunits of FcRI indicated that phosphorylation of tyrosines peaked when about 8-9% of the receptors were phosphorylated.


DISCUSSION

Previously, we showed that stable aggregates of Fc receptors continue to signal RBL cell responses without the formation of new aggregates(18) . The use of chemically cross-linked oligomers of IgE to induce receptor aggregation made the observation possible, since aggregation could be stopped (with monomeric IgE) without breaking up previously formed aggregates. This class of ligands has the further advantage that, since few states form, one can characterize the binding in detail and draw inferences about the time course of receptor aggregation. In this study, we used the simplest IgE oligomer, a dimer. We found that the response (phosphorylation) leveled off while the number of aggregates was still rising steeply. By comparing the observed time courses with predictions of a simple model, we could eliminate a number of possible explanations for the data. The surprising conclusion we are left with is that although the aggregates that form initially are effective and persistent signaling units, aggregates that form later are relatively ineffective.

We first determined the kinetics with which dimers bound to the cells in the presence and absence of monomeric IgE. Analyzing the data within the framework of a model for the binding of IgE dimers to RBL cells, we determined binding and aggregation parameters and used them to predict the time course of the formation of dimerized FcRI. The model ( Fig. 1and ``Appendix'') is straightforward and gave close fits to the data (Fig. 2, 3). The results also indicate clearly that the concentration of IgE monomer used to block the binding of IgE dimers was effective.

To investigate the relationship between the aggregation of FcRI and the phosphorylation of tyrosines on the and beta subunits of the receptor, we compared the predicted time course of receptor aggregation with the time course of phosphorylation of FcRI (Fig. 4). The comparison showed that the kinetics of phosphorylation does not correspond with the rate of formation of the aggregates (Fig. 5); in particular, once formed, the stable aggregates show persistent activity. Initially, the time course of phosphorylation parallels quite closely the time course of the number of receptors in aggregates, but the comparison reveals a difference at later times (compare Fig. 2and Fig. 4). What was striking was that phosphorylation reached a plateau while aggregate formation continued. The shape of the phosphorylation curve when no monomeric IgE was present was similar to the shape of the phosphorylation curve when monomer was added after 2 min and the formation of new aggregates was blocked.

To make quantitative comparisons between the predicted kinetics of aggregation and the experimentally determined kinetics of phosphorylation and to estimate the fraction of aggregated receptors that are phosphorylated, a mathematical description of the time course of phosphorylation is an essential tool. We therefore introduced a phenomenological model that allows for tyrosine phosphorylation and both reversible and irreversible (on the time scale of the experiments) dephosphorylation (Fig. 6). The role of this minimal model is to help identify the types of interactions of receptors, kinases, and phosphatases that are consistent with the data and those that can be rejected.

The model depicted in Fig. 5is inconsistent with the experimental results, in that it cannot account simultaneously for apparent steady state levels of phosphotyrosine observed both in the absence and presence of new aggregate formation (i.e. in experiments with and without the addition of monomeric IgE). Parameters that account for the early plateau in levels of phosphotyrosine in the absence of monomer predict a rapid decay of phosphotyrosine after monomer is added, but no such decay is observed. Parameters consistent with the continued elevation of levels of phosphotyrosine after monomer is added predict that in the absence of monomer, phosphorylation of tyrosines should reach higher levels than those observed and should continue to rise over the hour period of our experiments. Again, this contrasts with our observations (Fig. 7).

In rejecting the phenomenological model, we reject a wide array of potential phosphorylation/dephosphorylation schemes. The model has a constant rate of phosphorylation of non-phosphorylated receptor dimers and a constant rate of dephosphorylation of phosphorylated receptor dimers. A constant rate of phosphorylation is consistent with a pool of specific kinases that is not substantially depleted, either because the pool is large or because kinases remain active and interact with multiple receptor aggregates. Also consistent with the constant phosphorylation rate is a model where some or all of the receptors are stably associated with kinases that trans-phosphorylate adjacent receptors when dimers form(34) . Even if only a small fraction of FcRI is associated with kinase, phosphorylation of receptor tyrosines should increase in proportion with the formation of additional aggregates. Constant recruitment of additional kinases to complexes of aggregated receptors and associated kinases is also consistent with the model and therefore cannot fully explain the data. A constant rate of dephosphorylation is consistent with an undepleted pool of phosphatases. If we invoke the activation or recruitment of phosphatases to explain why phosphorylation remains constant in the absence of monomer, despite continued aggregation, we would then predict the decay of phosphorylation in the presence of monomer, contrary to observation.

Simple alternatives to the model do not correct the problems with fitting the data. In particular, we have shown that phosphorylation of tyrosines on the subunits of FcRI does not appear to saturate under the conditions of our experiments (Fig. 8).

One possibility we have not ruled out is that because of the dynamics of recruitment of kinases, aggregates that form ``late'' in the response are essentially left out of the response. This could occur, for example, if kinases that were pre-associated with receptors were capable of dissociating and binding to newly created phosphotyrosines on other proteins. Since Lyn kinase is only weakly associated with unaggregated receptors but is recruited to phosphorylated tyrosines on aggregated FcRI(15) , the creation of new high affinity binding sites that could compete for Lyn might reduce the number of pre-associated Lyn-receptor complexes available late in the response. If this were so, phosphorylation of beta and would level off while aggregates continued to accumulate because such newly formed aggregates, lacking associated kinase, would be ineffective.

Additional evidence that aggregates formed late in a response are less effective than aggregates formed initially comes from degranulation studies. We have observed that when RBL cell degranulation is induced by either dimeric (^2)or trimeric (18) oligomers of IgE, the kinetics of the response (secretion of hexosaminidase) is similar whether or not high concentrations of monomeric IgE are added shortly (2-3 min) after oligomer addition. For at least the first 30 min, the curves increase and tend to parallel each other. The addition of monomer reduces release but not to the extent that it reduces binding. That is, the additional aggregates that form late after the addition of oligomer appear to contribute less to the secretory response than those formed earlier.

In closing, we wish to extend our previous discussion (18) concerning how our results on persistent activity after cessation of aggregate formation can be reconciled with the apparently conflicting results of experiments in which aggregation of FcRI was induced by highly multivalent antigens. In the latter studies, the cellular response (secretion) halted abruptly after the addition of competing monovalent hapten, even though receptor aggregation, as judged by persistence of cell-bound antigen, was not fully reversed(35, 36, 37, 38) . The degree of persistence of bound antigen depended on the time between the addition of antigen and the addition of hapten. The longer the delay, the greater the fraction of antigen that became resistant to dissociation(37) .

The molecular basis for the dissociation-resistant state is not known. The resistant state is not due to an induced change in the affinity of IgE for an antigenic site since the aggregation of IgE-FcRI does not alter the affinity of IgE for monovalent ligand(39) . The aggregation of three or more Fc receptors does lead to the immobilization of FcRI (40) and, at supraoptimal antigen concentrations, to interaction of the receptor with the detergent-resistant cell skeleton (41, 42, 43, 44, 45) . An immobilized IgE cannot diffuse away from an antigen when it dissociates. If the antigen is bound to two or more immobile IgEs, its motion is also restricted when one of the bound IgEs dissociates. Consequently, immobilization of the receptors may enhance the interaction of their bound IgE with the antigen, thus reducing the hapten's ability to break up aggregates effectively.

That the dissociation-resistant aggregates no longer signal suggests that the receptors in such aggregates have been specifically desensitized(46, 47, 48) . In turn, this has been interpreted to indicate that signal transduction is short lived; that to maintain signaling, new aggregates must constantly be made, and that cellular responses are proportional to the rate of formation of aggregates rather than to the number of such clustered receptors. This interpretation is not consistent with our result or previous results (49) on persistent signaling by dimers and trimers of IgE.

One way to reconcile the results in the two systems is to postulate that the rate of desensitization differs markedly from one system to the other(18) . However, there is an interpretation of the experiments with multivalent antigen that is consistent with the oligomer results and that does not depend on postulating differences between the systems. The new interpretation we propose is that desensitization is a slow process, that desensitized receptors become immobile, and that because of the rebinding effects discussed above, only a small number of desensitized, immobilized receptors is needed to keep some of the bound antigen on the cell surface after hapten addition. Since only desensitized receptors remain aggregated, signal transduction ceases. In the oligomer experiments, signaling persists because both active and inactive receptors remain aggregated.


APPENDIX

Kinetic Model for Binding of Monomers and Dimers

The total concentrations (in nM) of FcRI, monomeric IgE, and IgE in dimers are denoted R, M, and C, respectively. The concentration of unoccupied FcRI is denoted R; the concentration of unbound monomeric IgE is denoted M. C(0), C(1), and C(2) refer to the concentrations of IgE in unbound dimers that are totally inactive, monofunctional, or bifunctional, respectively. For concentrations of bound ligands, we use the notation Y(1) for bifunctional dimers bound monovalently, Y(2) for bifunctional dimers bound bivalently, Y(3) for bound monofunctional dimers, and Y(4) for bound monomeric IgE. The fraction of dimers capable of binding (mono- or bivalently) is P(1), and the fraction of bindable dimers that are bifunctional is P(2). Then the fraction of dimers that can bind bivalently is P(1)P(2). The conservation laws for receptors and ligands are as follows.

The single site forward and reverse rate constants for binding of IgE in solution to an unoccupied FcRI are k and k for monomeric IgE and k and k for a functional IgE in a dimer; k and k are the corresponding rate constants for aggregation, i.e. for a bifunctional dimer to bind to (or dissociate from) a second FcRI. The concentrations of bound ligand satisfy the following differential equations.

We have modeled the binding of IgE to its receptor as a simple bimolecular reaction. There is evidence that the binding reaction is more complicated than this, with a conformational change occurring after the bound complex is formed(50) . For the limited range of binding experiments we analyze however, the simple model suffices.

Inverse Relation for Fraction of Dimers That Are Bindable (P)

In experiments where receptors are in excess, the fraction of dimer that is bound, b, satisfies a differential equation of the form db/dt = (P(1) - b), where is a constant that depends on the forward rate constant and the number of receptors per cell. The solution yields the following inverse relation,

where P(1) is the inverse of the 1/b intercept, i.e.P(1) is the limit of the bound dimer fraction as t or, equivalently, as 1/t 0.

Fraction of Bifunctional Dimer in the Case of Random Mixing

If IgE molecules come together randomly in the chemical cross-linking reaction and if the loss of IgE's capacity to bind to receptors is caused primarily because the cross-linking reagent reacts with lysines in or near the binding site for the receptor, then P(2), the fraction of bindable dimers capable of binding to FcRI bivalently, is given by .

is obtained by equating two expressions for the fraction q of non-binding IgE in dimers. The expressions for q come from the following two relations. First, with random mixing, the fraction of non-binding dimers 1 - P(1) = q^2. Second, the fraction of doubly binding dimers P(1)P = (1 - q). Substituting P = 0.54 into , we find P = 0.19.

Diffusion-limited Rate of Aggregation

The diffusion limit of the forward rate constant for aggregation (dimerization) of FcRI, k, calculated under the assumption that both the vacant and occupied receptors diffuse in the plasma membrane with the same two-dimensional diffusion coefficient D(51) , has the form (modified from (52) )

where A, the fraction of the cell surface occupied by FcRI, is assumed to be small. Measurements by both post-field relaxation (51) and fluorescence photobleaching recovery(40, 53, 54) give values for the lateral diffusion coefficient for mobile FcRI on RBL cells of approximately 3 10 cm^2 s at ambient temperatures (19-24 °C). Because k depends on A logarithmically, it is relatively insensitive to the exact value of A. Thus if A varies 100-fold, e.g. between 0.002 and 0.20, then with D = 3 10 cm^2 s, k varies only 5-fold, from 1.3 to 6.6 10 cm^2 s.

The actual rate at which a singly bound dimer encounters a free receptor depends not only on the forward rate constant k but also on the concentration of vacant receptors, R. If most receptors are unoccupied, i.e.R approx R, the product kR is the encounter rate, and 1/kR is the mean encounter time. For an RBL cell with 300,000 receptors/cell and a surface area of roughly 600 square microns (6 10 cm^2/cell), kR is in the range 65-330 encounters per second. Then, the diffusion limit of the mean time for a singly bound dimer, capable of binding doubly, to bind to a second FcRI is on the order of 0.01 seconds. Because of its convoluted structure, the RBL cell surface area is the least reliable parameter in this estimate. We have taken it to be approximately twice that of a 5-µm sphere, but it is possible that it is larger than this, which would increase the estimate of the diffusion limit of the mean cross-linking time.

Kinetic Model for Tyrosine Phosphorylation and Dephosphorylation

Fig. 6summarizes the simplest extension of the binding model (see above) that includes dimer-induced phosphorylation of tyrosines on the subunits of the receptors and both reversible and irreversible dephosphorylation. We have shown previously that the phosphorylation of tyrosines induced by the oligomers is a dynamic process that involves a rapid cycling between phosphorylated and dephosphorylated states(18) . A slow, irreversible decrease in phosphorylation is also evident in some experiments (e.g.Fig. 4, the non-receptor proteins). By irreversible dephosphorylation, we mean the conversion of a tyrosine on a receptor in an aggregate from a site that is readily phosphorylated to one that cannot be phosphorylated. This could arise, for example, if an active kinase, associated with a receptor in an aggregate, were inactivated, preventing rephosphorylation of tyrosines in the aggregate.

Therefore, there are two additional states to follow: aggregated receptors phosphorylated on one or more tyrosine residues (concentration Y(5)) and aggregated receptors that are irreversibly dephosphorylated (concentration Y(6)). No account is taken either of the sites of phosphorylation or of the extent to which the pairs of receptors are phosphorylated. Y(2) is now interpreted as the concentration of bivalently bound dimers associated with unphosphorylated receptors capable of becoming phosphorylated. The rate of tyrosines on aggregated receptors becoming phosphorylated is , and the rates of reversible and irreversible dephosphorylation are µ(1) and µ(2), respectively. In the equations that follow, phosphorylation and dephosphorylation are not limited by the supply of kinases and phosphatases. for Y(2) becomes

The equations for Y(5) and Y(6) are as follows.

Equations 6, 8, and 9 remain the same. The conservation laws become

Phosphotyrosine (measured as densitometric intensity) is then taken to be a linear function of Y(5), the fraction of receptors that are phosphorylated on tyrosines. The slope and intercept differ from experiment to experiment.


FOOTNOTES

*
This work was supported in part by National Institutes of Health Grant GM35556 and National Science Foundation Grant DMS9101969 and was performed in part under the auspices of the National Institutes of Health and the United States Department of Energy. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore by hereby marked ``advertisement'' in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

§
To whom correspondence should be addressed. Tel.: 505-667-6538; Fax: 505-665-3493.

(^1)
The abbreviations used are: RBL, rat basophilic leukemia; DNP, 2,4-dinitrophenyl; CHAPS, 3-[(3-cholamidopropyl)dimethylammonio]-1-propanesulfonate.

(^2)
C. Wofsy, U. M. Kent, S.-Y. Mao, H. Metzger, and B. Goldstein, unpublished observations.


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