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(Received for publication, February 21, 1995; and in revised form, May 9, 1995) From the
Previously, we demonstrated that aggregates of the high affinity
receptor for IgE (Fc
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 (Fc 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 Fc 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.
Figure 1:
Binding to and aggregation of IgE
Fc
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.
Figure 2:
The kinetics of binding of
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).
Figure 3:
Binding kinetics of dimers when receptors
are limiting. In two separate experiments (a, b), RBL
cells, all of whose Fc
The value of P
Figure 4:
Time
course of tyrosine phosphorylation of the
In Fig. 5we present the result
of calculations of how the rate of formation of aggregates (dimers) of
Fc
Figure 5:
Predicted variation of the rate of
dimerization of receptors with time, plotted with k
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 However, there were also significant differences
between the patterns of aggregation of Fc 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
Fig. 7shows the best fit of the model to
the data for tyrosine phosphorylation of the
Figure 7:
Time course of tyrosine phosphorylation of
the
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
Figure 8:
Time
course of phosphorylation of tyrosines on the
The fundamental quantities calculated from the model are
fractions of Fc Previously, we showed that stable aggregates of Fc 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 Fc To investigate the relationship between
the aggregation of Fc 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
Fc 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 Fc 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 Fc 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 ( 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 Fc 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-Fc 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.
The single site forward and reverse rate constants for binding
of IgE in solution to an unoccupied Fc
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.
where P
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
where A, the fraction of the cell surface occupied by
Fc The actual rate at which a singly bound dimer encounters a free
receptor depends not only on the forward rate constant k
Therefore, there are two additional states to follow: aggregated
receptors phosphorylated on one or more tyrosine residues
(concentration Y
The equations for Y
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
Volume 270,
Number 35,
Issue of September 01, pp. 20264-20272, 1995
©1995 by The American Society for Biochemistry and Molecular Biology, Inc.
Receptors on
Rat Basophilic Leukemia Cells (*)
RI), 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.
RI)
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 (
and in this instance) and on
several other cellular proteins is among the earliest molecularly
defined consequences of the aggregation of
Fc
RI(7, 8, 9) . Recent studies of the
kinase activity induced by Fc
RI aggregation on rat basophilic
leukemia (RBL) (
)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
Fc
RI 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
and the subunits, primarily
,
following activation(13, 14) .
RI on RBL cells. The only receptor
aggregates that form in this case consist of two Fc
RI, bound to
the distinct IgE molecules in single IgE dimers. Because the
dissociation of IgE from Fc
RI 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.
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`)
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, 0.4 mM MgCl, and 0.1% bovine
serum albumin. For tyrosine phosphorylation assays, the cells were
suspended in the above buffer at 5 10
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
VO
) 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
cell
equivalents. For immunoprecipitation, 1 ml (5 10
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
VO, 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 NaVO, 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`)
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
VO 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
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
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
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.
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
) and the
fraction of bindable dimers that could bind bivalently and therefore
aggregate the receptors (P). 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
and P, 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.
RI 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 Fc
RI and k
and k
for the binding (or dissociation) of the
second IgE in a monovalently bound dimer to (from) a second
receptor.
Bindable Dimer Fraction (P
To determine P)
, the fraction of dimers capable of binding to
FcRI, we added
I-IgE dimers to an excess of
receptors (0.33 nM
I-IgE in dimer form to
approximately 2.5 nM Fc
RI). 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
. 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 = 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 Fc)
RI 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
= 0.54, P 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
= 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
) 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
= 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).
I-IgE dimer (1.6 nM) to Fc
RI (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.
shows the data for dimer binding when no monomer was present; 
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
= 0.54, P =
1, k = 0.8
10
M s
,
k
= 1.4
10
M 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.
Forward Rate Constant for Dimer Binding
(k
Using the two extreme values of the
parameter P)
, we obtained essentially equally close
fits of the model to the monomer quench data. However, different values
of P had to be paired with different values of the
forward rate constant to obtain the closest fits. If P = 1, the best fit is achieved with k = 0.8
10
M s
(shown in Fig. 2); if P
= 0.19, the best estimate for k is 1.4
10
M 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
, k values, the
forward rate constant for monomer binding that gave the best fit of the
model to the data was 1.4
10
M s
. This value is
consistent with the previously determined range of 1-2
10
M s
(17, 32, 33) .
Partial Saturation Experiments
To
determine the values of the two parameters related to dimer-induced
aggregation of FcRI, P
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 Fc
RI 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.
RI (3-4 nM) were initially
unoccupied (uppercurves) or 70-80% of whose
Fc
RI 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
= 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
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 Fc
RI
are consistent with the same parameter set (data not
shown).
that gave the best fit of the model to the data
is P = 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
= 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 Fc)
RI 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 Fc
RI 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
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.
and
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).
RI 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.
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.
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 Fc
RI
(compare the lowercurves in Fig. 2and Fig. 4).
RI (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
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
receptors,
was 7 at the end of an hour and was still increasing (Fig. 2a).
), reversible dephosphorylation (rate µ
), and
irreversible dephosphorylation (rate
µ).
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
= 0) and that phosphorylation was
rapid (
10 min). The fit was not sensitive
to the reversible dephosphorylation rate µ
. In
generating the theoretical curves in Fig. 7, we used the value
µ = 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) .
subunit of Fc
RI. The twolowercurves represent the best fit of the model (Fig. 5) to the data from experiments with excess monomer added
after 2 min (
) 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
. Values used in the fit were
= 10 s
and µ
= 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
= 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
.
(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.
subunit of
Fc
RI, following stimulation of RBL cells by IgE dimer at 3 nM (
) and 6 nM () 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 = 2.6 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).
RI 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
subunits of FcRI indicated that phosphorylation of tyrosines
peaked when about 8-9% of the receptors were phosphorylated.
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.
RI. 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.
RI and the phosphorylation of tyrosines on
the
and
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.
RI 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.
RI
does not appear to saturate under the conditions of our experiments (Fig. 8).
RI(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
and would level off while aggregates continued to
accumulate because such newly formed aggregates, lacking associated
kinase, would be ineffective.
)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.RI
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) .
RI 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 Fc
RI (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.
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 Fc
RI is denoted R; the concentration of
unbound monomeric IgE is denoted M. C
, C, and C 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 for
bifunctional dimers bound monovalently, Y for
bifunctional dimers bound bivalently, Y for bound
monofunctional dimers, and Y for bound monomeric
IgE. The fraction of dimers capable of binding (mono- or bivalently) is P, and the fraction of bindable dimers that are
bifunctional is P. Then the fraction of dimers
that can bind bivalently is PP. The conservation laws for
receptors and ligands are as follows.
RI 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 Fc
RI.
The concentrations of bound ligand satisfy the following differential
equations.
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
- 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,
is the inverse of the 1/b intercept, i.e.P 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, the fraction of bindable dimers
capable of binding to FcRI bivalently, is given by .
= q. Second, the fraction of doubly
binding dimers PP = (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) )
RI, 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 Fc
RI on RBL cells of
approximately 3
10
cm
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
s, k
varies only 5-fold, from 1.3 to 6.6
10
cm
s.
but also on the concentration of vacant
receptors, R. If most receptors are unoccupied, i.e.R
R, the product k
R
is the
encounter rate, and 1/k
R
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
/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 Fc
RI 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. ) and aggregated receptors that
are irreversibly dephosphorylated (concentration Y). No account is taken either of the sites of
phosphorylation or of the extent to which the pairs of receptors are
phosphorylated. Y 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
and µ, respectively. In the equations
that follow, phosphorylation and dephosphorylation are not limited by
the supply of kinases and phosphatases. for Y becomes
and Y are as follows.
, the fraction
of receptors that are phosphorylated on tyrosines. The slope and
intercept differ from experiment to experiment.
))
©1995 by The American Society for Biochemistry and Molecular Biology, Inc.
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