Modeling T Cell Antigen Discrimination
Based on Feedback Control of Digital ERK
Gre ´goire Altan-Bonnet, Ronald N. Germain*
Lymphocyte Biology Section, Laboratory of Immunology, National Institute of Allergy and Infectious Disease, National Institutes of Health, Bethesda, Maryland, United States
T-lymphocyte activation displays a remarkable combination of speed, sensitivity, and discrimination in response to
peptide–major histocompatibility complex (pMHC) ligand engagement of clonally distributed antigen receptors (T cell
receptors or TCRs). Even a few foreign pMHCs on the surface of an antigen-presenting cell trigger effective signaling
within seconds, whereas 13105–13106self-pMHC ligands that may differ from the foreign stimulus by only a single
amino acid fail to elicit this response. No existing model accounts for this nearly absolute distinction between closely
related TCR ligands while also preserving the other canonical features of T-cell responses. Here we document the
unexpected highly amplified and digital nature of extracellular signal-regulated kinase (ERK) activation in T cells.
Based on this observation and evidence that competing positive- and negative-feedback loops contribute to TCR
ligand discrimination, we constructed a new mathematical model of proximal TCR-dependent signaling. The model
made clear that competition between a digital positive feedback based on ERK activity and an analog negative
feedback involving SH2 domain-containing tyrosine phosphatase (SHP-1) was critical for defining a sharp ligand-
discrimination threshold while preserving a rapid and sensitive response. Several nontrivial predictions of this model,
including the notion that this threshold is highly sensitive to small changes in SHP-1 expression levels during cellular
differentiation, were confirmed by experiment. These results combining computation and experiment reveal that
ligand discrimination by T cells is controlled by the dynamics of competing feedback loops that regulate a high-gain
digital amplifier, which is itself modulated during differentiation by alterations in the intracellular concentrations of
key enzymes. The organization of the signaling network that we model here may be a prototypic solution to the
problem of achieving ligand selectivity, low noise, and high sensitivity in biological responses.
Citation: Altan-Bonnet G, Germain RN (2005) Modeling T cell antigen discrimination based on feedback control of digital ERK responses. PLoS Biol 3(11): e356.
The functions of the adaptive immune system are regulated
by intracellular signals arising from the interaction of
clonally distributed, somatically generated receptors on T
or B lymphocytes with antigens derived from invading
infectious organisms [1,2]. The antigen receptors (T cell
receptors or TCRs) on most conventional CD4þand CD8þT
lymphocytes recognize short peptides extracted from patho-
gen proteins and displayed on cell surfaces in association with
integral membrane proteins encoded by the major histo-
compatibility complex (peptide–MHC molecule ligands or
pMHCs) . Because the cellular machinery that creates
pMHCs does not distinguish in most cases between pathogen
proteins and host proteins, the surface of a cell that is being
scanned by TCRs is typically a mosaic of self- and foreign-
pMHC ligands . This imposes a critical task on the T-cell
recognition and intracellular signaling machinery, which is to
avoid triggering functional responses to the highly abundant
self-pMHCs while fostering rapid, highly sensitive, and
specific responses to low densities of non-self-pMHCs on
the same membrane. One major factor contributing to this
discrimination by mature T cells is the elimination during
thymic development of many immature cells possessing TCRs
that are highly reactive with self-pMHCs [5,6]. However, this
cellular selection itself depends on the capacity of the TCR to
make fine distinctions between closely related pMHC
structures when transducing signals that regulate cell survival
and differentiation—distinctions that also must be made by
mature, post-thymic T cells.
Two models have been put forward to account for the
exquisite discrimination capacity of T cells. The first model is
based on the idea that agonist pMHCs capable of functional
T-cell activation induce a specific conformational change in
the TCR complex [7–9]. The second model suggests that the
signaling machinery of the T cell employs kinetic
thresholding based on the lifetime of pMHC–TCR complexes
to discriminate agonist pMHCs from non-agonist pMHCs
[10–12]. Two experimental observations cannot be explained
Received March 16, 2005; Accepted August 22, 2005; Published October 25, 2005
Copyright: ? 2005 Altan-Bonnet and Germain. This is an open-access article
distributed under the terms of the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided
the original author and source are credited.
Abbreviations: APC, antigen-presenting cell; CV, coefficient of variation; ERK,
extracellular signal-regulated kinase; IFNc, interferon gamma; MAPK, mitogen-
activated protein kinase; MSCV, mouse stem-cell virus; pMHC, peptide–major
histocompatibility complex molecule; ppERK, doubly phosphorylated, kinase-active
ERK; SHP-1, SH2 domain-containing tyrosine phosphatase; TAP, transporter
associated with antigen processing; TCR, T cell receptor
Academic Editor: Philippa Marrack, National Jewish Medical and Research Center/
Howard Hughes Medical Institute, United States of America
*To whom correspondence should be addressed. E-mail: firstname.lastname@example.org
PLoS Biology | www.plosbiology.orgNovember 2005 | Volume 3 | Issue 11 | e3561925
Open access, freely available online P PL Lo oS S BIOLOGY
by the former model. First, among all the X-ray crystallo-
graphic structures of TCRs in complex with different pMHC
ligands [13,14], none have displayed a change in conforma-
tion that is specific for an agonist pMHC in comparison to a
non-agonist pMHC. Some investigators have proposed that a
conformational change takes place in the signaling CD3 or f
chains associated with the ab ligand-binding subunits of the
TCR [7–9,15,16], but the structures of these subunits in
combination with the TCR remain to be solved, and
convincing evidence for this hypothesis has yet to be
reported. Second, and more significantly, the potency of
pMHCs in activation of T cells endowed with a particular
TCR is modulated during intrathymic differentiation .
Developing T cells (thymocytes) signal and respond function-
ally to self-pMHCs that are non-agonists for T cells in the
periphery [18,19]. Hence, T cells with a given TCR can
respond differently to the same set of pMHCs. This
observation challenges explanations of ligand discrimination
in T-cell activation on the basis of pMHC-specific conforma-
tional changes in TCRs, because responses to a given ligand
differ in immature and mature cells despite the identity of
the antigen-receptor structure.
In the second model, the signaling machinery of the T cell
employs kinetic thresholding based on the lifetime of pMHC–
TCR complexes to discriminate agonist pMHCs from non-
agonist pMHCs [20,21]. The kinetic-proofreading concept, as
first detailed for T cells by McKeithan  and then
elaborated in several later variants of this original model
[11,22,23], postulates that small differences in the longevity of
pMHC–TCR associations are amplified into large differences
in downstream signaling output by a signal-transduction
pathway with many steps, each of which requires continued
ligand–receptor interaction to occur. Indeed, the only
biophysical parameter reported in multiple studies to
correlate with the quality of T-cell activation is the lifetime
of the pMHC–TCR complex. Measurements based on surface
plasmon resonance with soluble TCR and pMHC suggest that
the dissociation rate, rather than the association rate, of the
complex is most sensitive to pMHC structure and relates best
with biological potency of the ligand . In one study, Kersh
et al.  reported that a single amino acid substitution
converted an agonist pMHC into a weak-agonist pMHC with
a 2 3 104-fold reduction in biological potency, while only
decreasing 5-fold the lifetime of the corresponding pMHC–
TCR complex (from 10.8 to 2.3 s at room temperature). Thus,
modest biophysical differences in the pMHC–TCR interac-
tion appear to result in exquisite functional pMHC discrim-
ination by T cells.
T cells not only show this capacity to distinguish among
closely related ligand structures, but also have a response to
antigen that is fast, extremely sensitive, and frequently digital
in nature. A single pMHC is sufficient to trigger a calcium
response  or cytotoxic activity  in primed T cells.
Measurements of the early phosphorylation of the TCRf
chains  and of the calcium response of T cells [23,28]
demonstrated that T-cell signaling occurs on a very short
timescale (within as few as 15 s) after antigen-presenting cell
(APC)–T-cell contact. Functional activation of T cells, after
hours of contact with APC, is typically characterized at the
individual cell level by an all-or-none response, whether
measured as cytokine gene activation  or proliferation.
These considerations make the classical kinetic-proofreading
schemes for TCR signaling unsatisfactory because these
models provide adequate ligand discrimination only at the
expense of sensitivity or speed of response [12,30] and fail to
account for a T cell’s digital response to receptor engagement
 (see Protocol S1 for a quantitative analysis of the
limitations of classical kinetic-proofreading schemes in
replicating the known features of TCR signaling).
The primary aim of the present study was to develop a
detailed, quantitative model of early TCR signaling that
accounts for these conjoint characteristics of a T cell’s
response to antigen. The model incorporates direct measure-
ments of key concentrations of signaling molecules and of
pMHC–TCR ligand interactions. Experiments conducted
simultaneously with the model building revealed that T cells
exhibit an unexpected property in their TCR-dependent
signaling, namely a digital extracellular signal-regulated
kinase (ERK) response that involves an extremely high level
of input amplification. By constructing our model around a
kinetic-proofreading scheme modified through the inclusion
of two competing feedback pathways previously proposed to
sharpen the discrimination threshold between closely related
TCR ligands , we show how spurious activation of this
explosive ERK amplifier by abundant non-agonist ligands can
be prevented, while retaining sensitivity to low numbers of
agonist ligands. The validity of our model was examined
directly by cell-based experiments testing three predictions:
the rapid increase of the signaling response time when the
number of ligands is decreased, the hierarchy of antagonism
in T-cell signaling, and the tunability of ligand discrimination
during T-cell clonal expansion. The biological responses all
fit well with the predictions of the model, providing strong
support for the conclusion that this differential feedback
scheme represents the core network of reactions that guide
T-cell signaling responses to ligands and accounts for the
characteristics of this key immune event.
Highly Amplified, Digital ERK Responses Induced by
To develop and test a predictive model of T-cell activation,
we needed quantitative measurements of the early signaling
events associated with TCR engagement by pMHC. In
addition, because functional data on T-cell activation show
a sharp distinction between agonist ligands (that elicit T-cell
responses even at low densities) and structurally related non-
agonist ligands (that do not elicit such responses even at high
densities), we specifically sought to identify a feature of the
proximal T-cell signaling pathway that reflects this ability to
discriminate, in a nearly absolute manner, between agonist
and non-agonist pMHCs. We focused initially on the cascade
activating the ERKs. These enzymes are members of the
mitogen-activated protein kinase (MAPK) family [20,31] and
are particularly attractive candidates for participating in such
digital discrimination because prior studies have emphasized
the importance of this pathway in both regulation of TCR
signaling  and in functional responses , while other
work with Xenopus oocytes has shown that the organization of
this enzyme cascade can produce an ultrasensitive response
associated with cell-fate decisions [33,34].
As a model system, we chose to examine the ERK-
phosphorylation response of OT-1 CD8þT cells upon
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Modeling T Cell Ligand Discrimination
activation with peptide-pulsed APCs. The transporter asso-
ciated with antigen processing (TAP)–deficient lymphoma
RMA-S was used as the APC because this cell line does not
efficiently load self-peptides into newly synthesized major
histocompatibility complex class I molecules, but does
effectively present exogenously added peptide via those class
I molecules that reach the cell surface . Thus, peptide-
pulsed RMA-S cells present a homogeneous pMHC-ligand
display spanning several decades in number without an
appreciable pool of co-expressed self-ligands . Although
there is evidence that self-recognition can synergize with
contemporaneous agonist recognition in the activation of at
least some CD4þT cells , a previous study failed to
demonstrate a substantial role for self-ligands in the
activation of OT-1 T cells using RMA-S APC , and we
have confirmed the latter findings (unpublished data). The
absence of such self-pMHCs on RMA-S APC and the evidence
against such ligands contributing to T-cell activation in this T
cell–APC combination allowed us to simplify both our model
of TCR signaling and the corresponding experimental
studies. In addition, a monoclonal antibody (25D1.16) to an
agonist pMHC ligand for the OT-1 T cells (SIINFEKL-Kb) was
available , permitting direct quantitation of the absolute
number of agonist ligands generated at each concentration of
pulsing peptide (Figure S1).
Using RMA-S APCs with calibrated numbers of ligands to
activate T cells, the ERK-phosphorylation response was
measured by intracellular staining combined with flow
cytometry. We found that the dual phosphorylation of ERK
necessary for the activity of this kinase can be detected in an
individual T cell when as few as ten agonist SIINFEKL-Kb
ligands are presented on average by the APCs, with 10% of T
cells showing a robust response after 3 min of T cell–APC
contact (Figure 1A). These studies also revealed a previously
unappreciated aspect of the T-cell ERK-signaling response:
after 3 min of contact with APCs, the pattern of staining is
strictly bimodal, i.e., the ERK response of T cells is essentially
digital. Control experiments confirmed that the intracellular
staining protocol we used was capable of detecting doubly
phosphorylated, kinase-active ERK (ppERK) levels within T
cells that were lower or higher than the fixed level seen
among the responding cells in Figure 1A (Figure S2),
indicating that the quantitatively constant nature of this
signaling response is an inherent property of the T cells and
not an artifact of the measurement technique. This bimodal
distribution could be fitted as a sum of two discrete log-
normal distributions, indicating that the individual cell
ppERK response is switch-like with a nearly infinite Hill
coefficient (Figure 1B). We also measured the number of ERK
molecules phosphorylated during T-cell activation, using
purified phosphorylated ERK for calibration. This analysis
showed that the digital response of a T cell is macroscopic
with the phosphorylation of 100,000 ERK proteins (Figures S2
and S3), revealing that the ERK pathway in T cells acts as a
high-gain digital amplifier.
In contrast to the single-cell results, the dose-response
curve for ERK activation of a population of OT-1 T cells can
be fitted with a Hill coefficient of 1.9 6 0.1 (n¼3) and an EC50
¼ 24 6 4 (n ¼ 3) SIINFEKL-Kbper RMA-S (Figure 1C). The
apparent discrepancy between the infinite Hill coefficient
determined at the individual cell level and the shallower dose
response measured at the population level can be understood
by taking into account the distribution of ligand densities on
APCs and variations in responsiveness among individual T
cells (‘‘biological noise’’) (Figures 1D and S1; Protocol S2).
Based on these data, the average threshold for the digital
ppERK response in OT-1 T cells is 24 SIINFEKL-Kbpresented
per RMA-S. Because the surface area of naı ¨ve OT-1 T cells is
three times less than the surface of the RMA-S used as APCs
in our experiments, the absolute threshold to trigger the
phosphorylation of 100,000 ERK molecules within 3 min of T
cell–APC contact may be as few as eight SIINFEKL-Kbligands.
This ERK-phosphorylation response of OT-1 T cells is also
specific. When non-agonist peptide variants (such as EIIN-
FEKL or SIIRFEKL), as defined by functional response
measurements, are presented on the surface of the APC, no
phosphorylation of ERK above the background could be
detected, even with 1 3 105pMHCs per APC (Figure 1E).
Moreover, ERK phosphorylation in T cells after 3 min of
activation also correlated with the functional specificity of
activation when assayed by CD69 upregulation, interferon
gamma (IFNc) expression, or cytotoxicity (Figure S4). Because
the only known differences between SIINFEKL-Kb(agonist)
and the non-stimulatory EIINFEKL-Kbor SIIRFEKL-Kb
ligands for the OT-1 TCR are the lifetimes of the pMHC–
TCR interactions (31.5, 10.7, or 6.3 s, respectively, at room
temperature ), our data indicate that modest differences
in ligand–receptor interaction are translated into robust
discrimination by the digital ppERK response of a T cell’s
Model of the Early Events in T-Cell Activation
The large and rapid signal amplification associated with
ERK phosphorylation in T cells, coupled with a capacity of
these cells to discriminate over four orders of magnitude of
ligand density between two pMHCs that differ in TCR-
binding lifetime by less than 5-fold, raises major questions
about how this can be accommodated by traditional kinetic-
proofreading schemes. Superficially, it would seem that the
system should be extremely sensitive to noise, with even very
poor ligands for the TCR eventually ‘‘sneaking through’’ 
and causing the digital ERK response to be activated. To deal
with this problem, some form of filtration or noise
suppression is needed, which in signal processing would
typically be mediated by a negative-feedback system .
Recently, the SH2 domain-containing tyrosine phosphatase
(SHP-1) has been shown to play such a role in TCR signaling
[27,42], and some models of TCR discrimination have
incorporated this feedback to limit responses to high levels
of weakly binding ligands [23,43]. However, such negative
feedback alone would also act to diminish the sensitivity of
the system to otherwise agonist (stimulatory) ligands. The
discovery of a positive-feedback loop involving ERK-1 that
protects TCRs from the inhibitory effects of SHP-1 
provides a possible solution to this dilemma involving
sensitivity. However, because no explicit model has yet tested
whether the combination of these two divergent feedback
pathways with a proofreading-based scheme would quantita-
tively account for the key characteristics of TCR signaling, we
set out to construct such a model and test its predictive
In Figure 2A, we present a simplified block diagram
summarizing the key kinetic components of our model.
Interaction of a pMHC with a TCR yields successive steps of
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Modeling T Cell Ligand Discrimination
Figure 1. Quantitation of Speed, Sensitivity, and Specificity of the Digital ppERK Response in Naı ¨ve T Cells
(A) Distribution of ERK phosphorylation (measured by flow cytometry) among individual naı ¨ve OT-1 T cells after 3 min of activation by RMA-S APCs at
different levels of presentation of the agonist pMHC SIINFEKL-Kb.
(B) Fit of the distribution of ppERK responses among OT-1 T cells activated with an average of 130 SIINFEKL-Kbligands on the surface of each RMA-S
APC. The fit (a sum of two log-normal distributions) is statistically adequate (v2¼ 1.72 for 128 points, and three fitting parameters).
(C) Theoretical effect of biological variation (‘‘noise’’) in ligand presentation by APCs and the responsiveness of individual T cells on the steepness of the
dose response of a population of T cells. The ppERK response of an individual T cell is essentially digital (infinite Hill coefficient), but the low observed
Hill coefficient (1.9) for the dose response of real T cells at a population level can be explained by taking into account the noise in ligand presentation
(CV ¼ 50%) and the possible noise in the activation threshold of the T cells (CV ¼ 75%).
(D) Experimental ppERK dose response of naı ¨ve OT-1 T cells activated for 3 min with peptide-pulsed RMA-S cells, plotted as the percentage of
responding cells. The Hill coefficient measured for this dose response is 1.9 6 0.1 (n¼3). The threshold for activation (midpoint) is 24 6 4 SIINFEKL-Kb
on each RMA-S APC. Because the T cell’s surface area is three times less than that of an RMA-S cell, as few as eight SIINFEKL-Kbligands may be sufficient
to trigger a full ppERK response if a full surface sweep of the RMA-S membrane by the T cell is not accomplished before signaling takes place.
(E) Dose response for ERK phosphorylation among naı ¨ve OT-1 T cells, after 3 min of activation by RMA-S APC pulsed with SIINFEKL peptide variants. The
peptide SIINFEKL is a known agonist for OT-1 T cells, whereas EIINFEKL and SIIRFEKL are non-agonists. The percentage of responding cells is plotted as a
function of the number of peptide-Kbligands presented on the surface of each RMA-S APC.
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Modeling T Cell Ligand Discrimination
phosphorylation of the TCR complex (e.g., of the associated
CD3/f chains via activation of the Src family kinase Lck).
Dissociation of the pMHC–TCR complex is assumed to
permit the rapid dephosphorylation of TCR-complex com-
ponents by a highly abundant active phosphatase (e.g., CD45
), which is not explicitly simulated here. Kinetic proof-
reading of pMHC–TCR interactions is based on the assump-
tion that phosphorylation requires pMHC–TCR contact and
that dephosphorylation rapidly reverses these events upon
ligand dissociation owing to the action of abundant phos-
phatases. The phosphorylated TCR complexes can activate
two divergent pathways. Beginning shortly after TCR engage-
ment occurs, the phosphatase SHP-1 is tyrosine phosphory-
lated by active Lck . The resulting pSHP-1 binds stably to
Lck-containing TCR complexes via interaction with the
kinase’s SH2 domain. This docked SHP-1 becomes enzymati-
cally activated upon further tyrosine phosphorylation in the
TCR complex, leading to dephosphorylation of the Lck, CD3/
f, and associated ZAP-70 kinase components of the signaling
complex [27,42]. This mechanism of action permits pSHP-1 to
act as a spreading negative feedback by decorating unengaged
Lck-containing TCR complexes and quickly deactivating the
receptor when ligand engagement initiates phosphorylation
events within that complex .
At slightly later times after TCR engagement, TCR
complexes can proceed to full phosphorylation and trigger
a kinase cascade activating ERK. Active ERK, in turn, acts as a
positive feedback by serine phosphorylation of the Lck in
TCR complexes, a biochemical modification that prevents the
kinase from binding to pSHP-1 . Hence, our model
network for TCR signaling can be summarized as a kinetic
proofreading of the pMHC–TCR interactions, triggering the
MAPK cascade as a high-gain digital amplifier, with a rapid-
onset analog SHP-1-mediated negative feedback and a slower
digital ERK-1-dependent positive feedback modulating the
triggering threshold. The evidence for signal spreading that
we have reported previously , in concert with the digital
nature of the ERK response, enables this counter-intuitive
arrangement of an early arising negative feedback and
delayed positive feedback to support effective signaling.
For the purpose of comparing computer simulations with
experiments, we implemented explicit chemical reactions
using parameters derived as much as possible from direct
measurements rather than fitting, although the latter was
necessary for many of the enzymatic rates that have not been
measured in a cellular context (Figures 2B, S3, and S5;
Protocol S3). The only quantitative parameter distinguishing
different pMHC ligands in our model is the lifetime of their
interaction with TCR. The expression levels of signaling
molecules were determined by quantitative immunoblotting
or flow cytometry and their concentration calculated based
on the measured cytoplasmic volume of naı ¨ve T cells (15 fl)
(Figures 2C and S5). These measurements underscore the fact
that T cells contain large concentrations of signaling
molecules (.3 lMol), which is consistent with the high speed
of response and also limits the impact of stochastic behavior
on the chemical reactions. We therefore assumed that
diffusion kinetics were not limiting and used a stirred-cell
model in our simulations.
The macroscopic clustering and spatial reorganization of
proteins in the immunological synapse is not required for the
early rapid signals we are assessing here [20,47], and hence,
the correlation of the formation of this organized multi-
protein structure with effective T-cell activation  is not
inconsistent with our assumption. JDesigner software  was
used to define the biochemical network for TCR signaling
(see Figure S6 and Protocol S4 for a complete description of
the model and Protocol S3 for a complete description of the
kinetic parameters used in our experiments and their origin).
The computer modeling of this network involved solving a set
of deterministic differential equations with a Rosenbrock
formula of order 2, implemented using Matlab (see Protocol
Solving our computer model for different quantities and
qualities of ligands (i.e., different lifetimes of the pMHC–TCR
complex) shows how the competition between positive and
negative feedbacks defines a digital threshold of T-cell
activation in terms of the dynamics of this ligand–receptor
interaction. Figure 2D presents the simulated ppERK
response after 3 min of exposure to different numbers of
ligands of different receptor-binding lifetimes. This response
is nearly digital with a sharp threshold at a pMHC–TCR
lifetime of 3 s, comparable to the experimentally reported
threshold in pMHC–TCR complex lifetime for agonist
activity, extrapolated to 37 8C (see Protocol S3). Hence our
model shows almost absolute discrimination with respect to
the quality of pMHC–TCR ligand interaction, while also
showing both fast kinetics and sensitivity to a few agonist
Testing Three Predictions of the Differential Feedback
Model of T-Cell Signaling Control
Lengthening of the ppERK response time at low ligand
densities. In our model, the MAPK cascade of concatenated
kinase phosphorylations amplifies sparse input signals (the
output of the kinetic proofreading of pMHC–TCR inter-
action) to yield a robust ppERK response (Figures S7 and S8):
indeed ten ligands were shown to drive the phosphorylation
of 100,000 ERK molecules in T cells (see Figure 1A). One
hallmark of such a kinase cascade is the digital response of
ERK phosphorylation (i.e., large Hill coefficient at the cellular
level [see Figure S8C]), which we have confirmed experimen-
tally (see Figure 1B). A key predicted feature of such a
response scheme is the nonlinear lengthening of the response
time at low ligand densities (see Figure S8B and S8D).
To examine whether this behavior seen in the simulations
(Figure 3A) was characteristic of the biological system, we
systematically measured the kinetics of ERK phosphorylation
in T cells exposed to different numbers of agonist ligands
(Figure 3B). In qualitative agreement with the model (see
Figure 3A; Protocol S5), the time delay before the digital ERK
response increased dramatically as the number of ligands was
decreased towards threshold levels (Figure 3C). There was also
a second, less-pronounced, slowing-down of the kinetics of
ERK phosphorylation at high levels of presentation, an effect
that the model indicates arises from a rapid and massive
activation of the negative feedback that limits the efficiency
of triggering of the MAPK cascade at high (.13104) agonist
display. In the case of non-agonist ligands, a similar temporal
imbalance in favor of negative feedback, even at modest
ligand levels, abrogates the activation of the MAPK cascade
and allows the suppressive regime to dominate at all pMHC
densities, preventing effective responses. Although the
simulation results and experimental data fit well qualitatively,
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Modeling T Cell Ligand Discrimination
Figure 2. Computer Model of the Early Events of T-Cell Activation
(A) Sketch of model. Differential positive-/negative-feedback loops are added to a kinetic-proofreading scheme of pMHC–TCR interaction. At early
times, phosphorylated TCR complexes activate SHP-1 (a tyrosine phosphatase), which provides a negative-feedback effect by dephosphorylating
components within the TCR complex. Upon TCR engagement by an agonist-quality ligand, but with a time delay, the MAPK (ERK) cascade is activated
and provides a positive-feedback effect by protecting the TCR complex from binding and dephosphorylation by SHP-1.
(B) Explicit model of core module of the early events of TCR signaling (see Figure S6 for an expanded view of the model).
(C) Table of the number and corresponding cytoplasmic concentrations of the signaling components involved in the model. An asterisk indicates
molecules whose number and concentration are estimated.
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Modeling T Cell Ligand Discrimination
there was a systematic discrepancy of 13 s in response time
that could not be resolved by parameter adjustment without
losing other predictions of our simulation. More detailed
modeling (in particular by taking into account membrane
protein pre-clustering) or more accurate measurements of
the relevant kinetic and expression parameters at physiologic
temperature may help eliminate this modest kinetic discrep-
Hierarchy of antagonism in T-cell signaling. Our computer
simulation also enabled us to probe the role of SHP-1
negative feedback in setting the threshold of ligand discrim-
ination. Given the ‘‘explosive’’ responsiveness of the MAPK
cascade, T cells must activate a negative feedback that is
tuned to the strength and quantity of ligands, to blunt
spurious activation with large quantities of low-affinity
ligands while allowing sensitive responses towards small
Figure 3. Experimental Test of Two Predictions of the Computer Simulation of the Early Events in TCR Signaling
(A–C) Characteristic response time for ERK phosphorylation. The characteristic time of the ERK-phosphorylation response was derived by computer
simulations of TCR signaling for increasing numbers of agonist ligands (whose lifetime of interaction with the TCR is set at 18 s) (A). This timescale
diverges in a nonlinear fashion when the number of agonist ligands is decreased. We then systematically measured the kinetics of the ppERK response
of naı ¨ve OT-1 T cells upon activation with RMA-S APCs presenting different numbers of SIINFEKL-Kb(B) and derived the characteristic time of response
using a generic sigmoidal fit. The divergence of this timescale as the number of agonist ligands is decreased (C) is characteristic of kinase cascades
acting as digital filters (A).
(D–F) Comparison of antagonism in T-cell activation in computer simulations and experiments.
(D) Computer simulation of antagonism. We simulated the ppERK response of T cells upon activation with increasing numbers of agonist ligands
(whose interaction with the TCR has a lifetime of 18 s) in the presence of 30,000 non-agonist ligands (the two putative antagonist ligands being tested
have TCR-interaction lifetimes of 1.7 s [weak antagonist] and 3 s [strong antagonist], respectively). The presence of a large number of sub-threshold
ligands inhibits the agonist-induced ppERK response of T cells. The inhibition is calculated as the ratio of the ppERK response in T cells activated with
agonist and antagonist together as compared to the ppERK response seen using the agonist alone. This hierarchy of antagonism in early T-cell
responses is consistent with the graded activation of SHP-1-mediated negative feedback associated with signaling by sub-threshold ligands.
(E) Experimental test of antagonism. Naı ¨ve OT-1 T cells were activated with RMA-S APCs pulsed with an increasing amount of agonist SIINFEKL peptide
and an excess of EIINFEKL or SIIRFEKL peptides.
(F) Experimental ppERK response of OT-1 T cells upon activation with RMA-S APCs presenting 25 agonist SIINFEKL-Kbligands with or without 30,000
antagonists (SIIRFEKL-Kb[weak antagonist] or EIINFEKL-Kb[strong antagonist]).
(D) Output of the computer simulation. After 3 min of simulated time, the TCR signaling machinery produces a sensitive and specific ppERK response.
There is also a sharp transition in the ppERK response depending on the quality of the pMHC ligands (as measured by the lifetime, s, of their interaction
with TCR). Four categories of ligands can be defined from the simulation. For pMHCs whose t is above 15 s, a complete ppERK response is obtained with
as few as ten ligands; these are the strong agonists. For pMHCs whose s is between 3 and 15 s, a ppERK response is obtained when sufficient numbers
of ligands are present; these are the weak agonists. pMHCs whose s is below 3 s fail to trigger a ppERK response; these are non-agonists. Finally,
because different combinations of feedback control are triggered by each category of ligands, ligands whose s is below 1 s do not trigger negative
feedback efficiently. These may constitute the majority of self-ligands, preventing self-recognition from depressing responses to full agonists .
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Modeling T Cell Ligand Discrimination
quantities of more strongly binding complexes. Negative
feedback mediated by SHP-1 has previously been shown to be
responsible for TCR antagonism , a phenomenon in
which simultaneous exposure of a T cell to a large quantity of
sub-threshold ligands and a small, otherwise stimulatory,
number of agonist ligands results in blunting of the expected
response [49,50]. The present quantitative model predicts
that TCR antagonism has a counter-intuitive characteristic:
the more closely the lifetime of a TCR–non-agonist complex
approaches the threshold needed for full signaling, the more
strongly this ligand will antagonize T-cell activation by
agonists. That is, better binders will actually be better
inhibitors until a bifurcation point is reached and they
become overtly stimulatory ligands themselves.
This hierarchy of antagonism can be seen in the results of
Dittel et al. , who reported greater TCRf phosphorylation
by more potent antagonists. This effect is shown in Figure 3D,
in which we present a computer simulation of the ppERK
response of our TCR signaling model for increasing numbers
of agonist pMHCs (whose TCR-binding lifetime is 18 s) in
conjunction with 3 3 104antagonist pMHCs (whose TCR-
binding lifetimes are either 3 s or 1.7 s). We examined this
prediction experimentally by measuring the OT-1 ERK
response to RMA-S cells bearing an increasing amount of
agonist SIINFEKL-Kbwith or without a large number (3 3
104) of non-agonist ligands on the same cell membrane
(Figure 3E and 3F). EIINFEKL-Kbantagonized more effec-
tively than SIIRFEKL-Kb, consistent with the fact that the
former ligand forms a longer-lived complex with OT-1 TCR
than does the latter (10.7 s versus 6.3 s at room temperature
), in accord with the expectations of the model. The slight
decrease in the ppERK level among cells responding in the
presence of antagonist is also seen with cells stimulated with
very low densities of agonist alone and appears to arise from
the 3-min assay point capturing these cells prior to their
achieving maximum ppERK levels. This slower rise to the
maximum at low effective ligand densities is predicted by our
model (see Figure 3A).
Flexibility in ligand discrimination for T cells undergoing
differentiation. A third general prediction of our computer
model is that the precise positioning of the kinetic threshold
between agonist and non-agonist ligands for a particular TCR
is set by the dynamics of the competition between positive-
and negative-feedback loops, which in turn is highly sensitive
to modest changes in the intracellular concentration of key
components such as SHP-1. Thus, we predicted that T cells
could alter their discrimination threshold by small changes in
the concentration of these molecules during differentiation.
Consistent with this expectation, analysis of the TCR
signaling response of activated OT-1 T cells revealed that
these cells transiently demonstrated ERK responses to
EIINFEKL-Kb5 or 6 d after the initial activation, whereas
naı ¨ve OT-1 f(OT-1)naı ¨veg and activated OT-1 T cells rested for
11 d f(OT-1)day 11g were strictly unresponsive towards this
ligand (Figures S9 and S10). An assessment of protein
concentrations in these cells revealed a substantial (.10-
fold) decrease in the concentration of SHP-1 relative to other
measured key signaling molecules in (OT-1)day-5 T cells as
compared to (OT-1)naiveor (OT-1)day-11T cells (see Figure S9).
The model suggested that the acquisition of responsiveness to
a ligand showing poor TCR-binding characteristics, as we saw
for (OT-1)day-5T cells, could be accounted for by this relative
diminution in SHP-1 levels. Simulations also predicted that
the selective decrease in SHP-1 should yield a peculiar dose
response to the low-affinity ligand, with a measurable ppERK
response at moderate ligand concentrations, followed by a
rapid loss of this signaling response as ligand density
increases. This is because the decreased SHP-1 levels slow
down the functioning of the negative-feedback pathway in
response to moderate levels of weak ligand, allowing
activation of ERK; at high levels of presentation, the pace
of the SHP-1-mediated negative feedback is accelerated and
overrides the delayed activation of ERK. The same change in
SHP-1 level was predicted to have no detectable effect on the
dose response to a strong agonist.
To test these predictions experimentally, agonist-activated
OT-1 T cells were infected with a retrovirus encoding EGFP
only or encoding both SHP-1 and EGFP as a bicistronic
mRNA. Five days after activation, the control infected OT-1 T
cells showed the expected selective decrease in SHP-1
concentration, though the decrease was of smaller magnitude
than typically seen with uninfected cells and the correspond-
ing gain in reactivity to weak ligands was less pronounced.
Infection with the SHP-1-encoding virus restored the SHP-1
concentration to a level similar to that found in naı ¨ve cells
(Figure 4A). As the model predicted (Figure 4B), (OT-1)day-5T
cells infected with EGFP-expressing retrovirus responded to
EIINFEKL-Kb, but only at intermediate ligand densities, while
cells infected with SHP-1/IRES/EGFP-expressing mouse stem-
cell virus (MSCV) selectively lost the EIINFEKL-Kbresponse
without any associated loss of sensitivity to activation by the
full agonist SIINFEKL-Kb(Figure 4C). These data demon-
strate that ligand discrimination is not ‘‘hard-wired’’ into the
affinity or structural match between a particular TCR and its
ligand, but is modulated by differentiation-related changes in
the stoichiometry of components of the signaling network
downstream of the receptor.
An extensive literature on the intracellular signals trig-
gered by pMHC-ligand engagement of the TCR suggests that
the response is rapid, sensitive, and highly discriminatory. In
this study, we have documented another key feature, namely
the digital, highly amplified ERK response that occurs at short
timescales (,3 min) but correlates with functional responses
at .1 h post-TCR engagement. This finding raised a
fundamental issue: how can T cells trigger such an ‘‘ex-
plosive’’ response while maintaining the specificity of ligand
discrimination? In an attempt to construct a model that
accounted simultaneously for all four key characteristics of
TCR signaling in response to ligand engagement, we
combined two recently reported opposing feedback modules
[20,27] with a core scheme based on kinetic proofreading
[10,11,30,43]. Using realistic kinetic parameter sets for
computer simulation of the signaling cascade downstream
of TCR engagement, our model yielded an output that had
the striking characteristic of a sharp transition in ligand
agonist functionality at TCR-binding lifetimes corresponding
to those measured in several different T-cell systems . We
showed that this transition is also consistent with the very
large (13 .104) shift in potency of pMHC ligands that differ
by only a few fold in their binding lifetimes. Our modeling
suggests that the sharp threshold for pMHC-receptor life-
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Modeling T Cell Ligand Discrimination
times yielding agonist responses originates from the distinct
kinetic characteristics of the phosphatase-mediated negative
feedback that suppresses signaling by weak ligands and the
ERK-mediated positive feedback that is induced effectively
only by more avid ligands of the TCR.
We built upon the observations of Stefanova et al.  in
constructing a model in which SHP-1 mediated inhibition
begins to function quickly upon TCR engagement, but scales
in an analog way with input. In contrast, the ERK response
was modeled as delayed but (as newly documented here)
digital in nature. This combination allows TCR activity
induced by a large number of weak ligands to be constantly
repressed by a proportional negative feedback that has
enough time to quench upstream signals before they reach
the limit necessary to trigger the ERK response. Both
modeling and experiment confirm that the ERK response is
increasingly delayed in onset as the duration of pMHC–TCR
binding decreases. In contrast, more strongly binding ligands,
though also inducing an initial SHP-1 inhibitory response,
override the limited nature of this negative feedback early
after ligand engagement by quickly triggering the highly
amplified ERK digital response. The magnitude of this ERK
activation then prevents inhibition of those TCR not yet
inactivated by the gradually rising pSHP-1 levels, permitting
effective downstream signaling through diverse pathways that
impinge on genes involved in T-cell differentiation. The
latter expectation of a transient recruitment of pSHP-1 to
agonist-engaged TCRs and the generation of an abortive
proximal tyrosine-phosphorylation response in T cells
exposed to an agonist when the ERK cascade is inhibited
have both been observed in biochemical studies . Overall,
these observations provide new insight into how control
circuits can be organized to suppress noise generated by large
numbers of ligands while promoting highly sensitive re-
sponses to a few optimal stimuli in the same cellular context.
Our simulations enabled us to make several predictions
that were verified by experiment. Most relevant to our
understanding of how T cells set the threshold for discrim-
inating between foreign and self-ligands to promote effective
responses without fostering autoimmunity, we predicted that
modest changes in intracellular enzyme levels would ‘‘tune’’
this agonist threshold during differentiation [51–53]. This
prediction was confirmed in studies showing that the
decreased amount of SHP-1 in T cells a few days after
activation of naı ¨ve T cells accounts for a gain in response to a
pMHC ligand that is incapable of stimulating naı ¨ve or resting
primed cells expressing the same TCR. This sensitivity of the
Figure 4. Experimental Verification of the Predicted Role of Small SHP-1
Concentration Changes in Altering Ligand Discrimination by OT-1 T Cells
(A) Concentrations of signaling molecules in OT-1 T cells 5 d after
activation and infection with MSCV retrovirus in vitro (day 5). These
concentrations are normalized using the corresponding concentrations
in the unstimulated naı ¨ve state (day 0).
(B) Computer simulation of the responsiveness of T cells at day 5 after
activation with the SHP-1 level set to that seen in the naı ¨ve state. The
agonist pMHC is set to bind TCR with a characteristic time of 18 s and the
non-agonist pMHC is set to bind TCR with a characteristic time of 3 s.
(C) Elimination of the response of day-5 activated cells to EIINFEKL/Kbby
expression of additional SHP-1. OT-1 T cells were infected with MSCV
retrovirus expressing EGFP (control) or SHP-1/IRES/EGFP, and the ppERK
response of infected OT-1 T cells to peptide-pulsed RMA-S was tested on
day 5 after initial activation.
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Modeling T Cell Ligand Discrimination
response-threshold position to modest alterations in the
intracellular concentrations of key components of the
network, particularly SHP-1, was a somewhat surprising
result. Stochastic noise in the production and degradation
of signaling components might be expected to produce
fluctuations of a similar magnitude in key molecules  and
hence to jeopardize accurate self-/non-self-discrimination by
T cells in the periphery after the threshold is set during
positive and negative selective events in the thymus.
One possible explanation for how this is avoided is that
naı ¨ve T cells may have a very stable metabolism that enables
them to preserve the phenotype selected for in the thymus
prior to overt activation by foreign ligand. Alternatively,
others have proposed that T cells can respond to tonic
exposure to self-ligands by abrogating self-responsiveness
while maintaining reactivity to pathogen-derived ligand [51–
53,55]. Perhaps this ‘‘self-tuning’’ involves dynamic adjust-
ment of the competition between positive and negative
feedbacks. A third possibility is that such fluctuations do
result in an occasional T cell producing potential activation
signals upon self-recognition; however, in the non-inflamed
state, this would lead to tolerance through deletion or anergy
. The danger would be if this occurred during an
inflammatory response, but indeed it is just such situations
that may be inciting events for autoimmunity .
In this same regard, the acquisition among activated T cells
of overt signaling responses to variant pMHC ligands that do
not evoke such responses among naı ¨ve or resting primed T
cells with the same TCR is an intriguing finding whose
physiological relevance is only evident in one circumstance.
Hogquist et al. originally identified EIINFEKL as a peptide
driving positive selection of OT-1 T cells under organ-culture
conditions in which the usual display of self-peptides is
limited . EIINFEKL was also the strongest antagonist of
OT-1 T-cell activation by SIINFEKL presented in the context
of H-2Kb. Hence, EIINFEKL-Kbwas a ligand known to
induce some positive signaling in the OT-1 thymocytes and
antagonistic negative signaling in peripheral OT-1 lympho-
cytes. Our model and experiments enable us to hypothesize
how this divergent signaling capacity of EIINFEKL-Kbmay
correlate with up/down expression of components of the TCR
signaling machinery and, specifically, SHP-1 . Thus,
actively keeping SHP-1 levels low during early T-cell differ-
entiation could allow self-ligands to have weak-agonist
function and drive the positive selection of the T-cell
repertoire, while increased SHP-1 levels would eliminate this
response capacity among the mature T cells that populate the
periphery . The ‘‘bell-shaped’’ dose response induced by
EIINFEKL-Kbusing (OT-1)day-5T cells has been observed in
other biological systems [58,59]: our model suggests that such
a nonmonotonic dose response is in fact a reflection of the
activation of excess negative feedback at a high dose of weak
Why more mature T cells that have been recently activated
should alter SHP-1 levels so as to regain sensitivity to
stimulation by weak ligands is not yet clear, but one
possibility is that activated cells use this reprogramming of
the signaling threshold to take advantage of abundant self-
ligands to promote further differentiation once their initial
activation has been ‘‘validated’’ by foreign-agonist recogni-
tion. Our biological studies and simulations were both
conducted in the absence of such potentially active self-
pMHCs. However, a very recent study indicates that this
synergy can occur in a narrow time window after previous
agonist-mediated T-cell activation , consistent with the
gain in sensitivity to fast off-rate pMHCs that has been shown
here to be due to decreased SHP-1 levels in this time frame.
What are some of the potential limitations of the current
model? While it has proved very successful in simulating
aspects of T-cell biology that can be verified experimentally
and even has correctly predicted some behaviors not
previously recognized, we do not know the extent to which
the simplifications we have introduced to keep the model
tractable have compromised its ability to reflect T-cell
physiology. First, this model lacks spatial constraints and
treats the T cell as a well-stirred vessel for the first 3 min of
TCR signaling. We believe this is justified, based on our
quantitative analysis of naı ¨ve T cells and their contents, which
reemphasized the small cytoplasmic volume of these cells and
the resulting high concentrations of signaling components.
For this reason, most enzymatic reactions involved in T-cell
signaling are not diffusion-limited. Moreover, the spatial
reorganization of membrane signaling proteins during T-cell
activation that results in a mature immunological synapse
 takes place over a substantially longer timescale than the
one considered in our model , and initial signaling occurs
prior to the large-scale protein clustering involved in the
formation of this synaptic structure. This does not mean that
local inhomogeneities in protein distribution in the mem-
brane (e.g., ‘‘rafts’’), or involving scaffolded protein com-
plexes in the cytoplasm, do not influence signaling behavior.
More elaborate modeling tools that preserve spatial
information (; M. Meier-Schellersheim et al., unpublished
data) will be needed to expand analyses of T-cell signaling.
This may be particularly relevant in understanding how self-
ligands can synergize with agonist pMHCs in promoting T-
cell activation  and in better modeling the role of signal
spreading among engaged and nonengaged TCR in the action
of pSHP-1 and ppERK. Second, we have omitted explicit
specification of a number of molecules that are well
documented in the literature to affect T-cell signaling
responses, such as CD45, Csk, and several adapter proteins
[63,64]. However, the influence of these components on
signaling was implicitly incorporated in some of the kinetic
parameters (e.g., tonic dephosphorylation), and we feel this is
justified by the absence of evidence that any of these
components has first-order sensitivity to the quality of the
pMHC–TCR ligand interaction. Third, we have introduced
modifications to the kinetic parameters of pMHC–TCR
interaction measured at room temperature to match the
model’s output to biological experiments conducted at 37 8C.
Whether our approximations in this regard are accurate are
not yet clear, because evidence for both linear and nonlinear
effects of temperature on pMHC interactions with TCRs have
been reported [9,39,65]. Finally, we have considered here only
the signaling involved under conditions in which the CD8
coreceptor plays a key role in the response. This is not an
absolute necessity for all TCR-mediated activation, but it is a
common feature of many physiological T-cell responses
including that of the OT-1 cells we used for the biological
component of the present study.
Although the primary aim of this work has been to better
understand how TCR signaling is regulated and contributes
to the proper performance of T cells in the immune system,
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Modeling T Cell Ligand Discrimination
the results we have obtained showing how simple feedback
loops operate to suppress biological noise, amplify responses,
and allow flexibility of function are likely to be relevant to
many other biological systems. The roles of negative and
positive feedback are well documented in gene regulatory
networks  and, in particular, in developmental systems,
where they can impose irreversible state changes on the
system, providing unidirectionality to differentiation events
. It remains to be seen whether the specific features of the
opposing feedback pathways modeled here, (rapidly initiating
analog negative feedback versus delayed, digital positive
feedback) are critical in other biological systems. More
generally, the value we document here for quantitative
modeling rather than just qualitative cartoon depiction of
signaling circuits, and the importance of documenting
physiologically relevant signaling dynamics in simulation
outputs, indicate that methods and tools for constructing
models, conducting simulations, and measuring values will be
increasingly critical aspects of experimental biology.
Materials and Methods
Computer modeling of the early events in T-cell activation. The
network of the biochemical reactions taking place upon pMHC
interaction with a TCR was created using JDesigner (http://www.cds.
caltech.edu/;hsauro/JDesigner.htm) and converted into a Matlab file.
The resulting set of deterministic differential equations was solved
with a Rosenbrock formula of order 2 implemented. Complete
descriptions of the models (for the simple kinetic-proofreading
schemes and for the full TCR signaling cascade) are available in
Protocol S1 and Figure S6.
Cells, peptides, proteins, and antibodies. Splenocytes and lympho-
cytes were isolated from H-2bOT-1 TCR transgenic mice (Tacline
175, Taconic ) on a Rag-2?/?background  and used directly as
responding naı ¨ve OT-1 T cells. RMA-S TAP-deficient T cell
lymphoma cells  were used as APCs. The agonist ovalbumin
peptide SIINFEKL and its variants SAINFEKL, EIINFEKL, SIIRFEKL
(all .95% pure) were obtained through the National Institute of
Allergy and Infectious Disease Research Technologies Branch. E10
antibody against ppERK was purchased from Cell Signaling Tech-
nology (Beverly, Massachusetts, United States); MR9–4(PE) against
Vb5.2, 53–6.7(PE) against CD8a, H1-2F3(PE) against CD69, and
XMG1.2(APC) against IFNc were from BD Biosciences Pharmingen
(San Diego, California, United States); K-23 against ERK1, C-19
against SHP-1, and C-14 against ERK2 were from Santa Cruz
Biotechnology (Santa Cruz, California, United States); 3A5 against
Lck, purified MEK, purified ppERK, and purified ZAP70 proteins
were from Upstate Technologies (http://www.upstate.com). SHP-1 was
purified from the lysates of Escherichia coli cells transformed with a
SHP-1-GST-encoding plasmid (a gift from D. Nandan, University of
British Columbia, Vancouver, Canada) and calibrated against pure
GST. The 25D1.16 monoclonal antibody specific for SIINFEKL-Kb
 was used as a hybridoma supernatant.
Quantitation of peptide presentation. RMA-S cells were pulsed
with serial dilutions of stimulating peptides for 1–2 h at 37 8C in
serum-supplemented RPMI-1640 medium. Cells were washed and
then stained with phycoerythrin-coupled anti-H-2KbAF6–88.5 anti-
body, whose fluorescence was calibrated with Quantibrite beads (BD
Biosciences Pharmingen) and anti-IgG beads (Bangs Laboratories,
http://www.bangslabs.com). We also used the combination of anti-
SIINFEKL-Kb25D1.16 antibody and phycoerythrin-conjugated anti-
mouse antibodies (Jackson Immunoresearch, West Grove, PA),
calibrated with the anti-H-2Kbstaining at high levels of presentation,
to achieve better resolution at low concentration of pulsing peptides.
Flow-cytometric measurement of intracellular signaling responses.
T cells (5 3 105) were mixed with peptide-pulsed RMA-S (2 3 106),
spun at 370 g for 5 s, and placed at 37 8C for various amount of time.
T cell–APC conjugates were then separated with ice-cold PBS/2.5 mM
EDTA, and fixed with 4% paraformaldehyde for 30 min on ice. Cells
were then permeabilized with 90% methanol for 30 min on ice,
washed twice with PBS/4% fetal bovine serum (FACS buffer),
incubated with 1 lg/ml E10 in FACS buffer, and finally stained with
1 lg/ml of phycoerythrin-labeled anti-mouse immunoglobulin.
Staining was immediately measured by flow cytometry (FACSCalibur,
BD Biosciences Pharmingen), after gating for small cells based on
forward scatter. Calculation of the percentage of ppERKþcells was
performed with FlowJo (Treestar, http://www.treestar.com).
Determination of the characteristic ppERK response time. We
defined the characteristic ppERK response time of a T cell as the time
yielding 50% of the maximal response for a given level of
presentation of SIINFEKL-Kb.
Flow-cytometric analysis of functional T-cell activation. T cells (53
105) were mixed with peptide-pulsed RMA-S (23106), spun at 10,000
rpm for 5 s in an Eppendorf microfuge (Hamburg, Germany), and
placed at 37 8C for 3 h. T cell–APC complexes were then dissociated
with ice-cold PBS/2.5 mM EDTA, and stained for CD69, then analyzed
by FACS. The fraction of live APC was also determined to yield a
measure of thecytotoxic activityof the T cells. ForIFNc expression,T-
cell activation was performed as before, with the addition of 2 lm
monensin. Cells were fixed, permeabilized with FACS buffer contain-
ing 0.1% saponin, stained for IFNc, and analyzed by flow cytometry.
Quantitative measurements of intracellular protein levels. Intra-
cellular protein levels were assessed by the lysis of 100,000 naı ¨ve OT-1
T cells in 1% NP-40 (Pierce Biotechnology, Rockford, Illinois, United
States) with complete protease inhibitor (Boehringer Ingelheim,
Ingelheim, Germany). The proteins in these lysates were separated by
SDS-PAGE using an 8%–16% gel in parallel with serial dilutions of
protein standards for immunoblotting calibration and then trans-
ferred to nitrocellulose membranes. After development of the blot
with the relevant antibodies, a Kodak Image Station 440 was used to
quantitate the bands and yield the protein content per cell. To
quantitate the expression of receptors on the surface of T cells, we
used standard beads (Quantibrite, BD Biosciences Pharmingen) to
calibrate the antibody staining of Vb5.2 and CD8a.
Fit of the distribution of ppERK. The pattern of ppERK in T cells
as measured by flow cytometry was fitted with the sum of two log-
normal distributions, representing nonactivated and fully activated T
cells. Free parameters were the modes of staining of ppERK?cells and
ppERKþcells, and the percentage of ppERKþcells. Coefficients of
variation (CVs) were set at 55%, corresponding to the measured CV
for the distribution of ERKs in naı ¨ve T cells.
Overexpression of SHP-1 by retroviral infection of activated OT-1
T cells. To examine the effect of altering SHP-1 levels on signaling in
response to various pMHC ligands of the TCR, we used the retroviral
vector MSCV expressing either SHP-1/IRES/EGFP or just EGFP .
Ecotropic Phoenix packaging cells (a kind gift of G. Nolan, Stanford
University, Palo Alto, California, United States) were transfected with
DNA corresponding to these two viral constructs, and supernatants
were collected for spin-infection of OT-1 T cells undergoing
proliferation after activation with OVA-pulsed splenocytes from B6
mice, followed by culture in 7.5% T-STIM (BD Biosciences
Pharmingen) . The ppERK response of infected cells to peptide-
pulsed RMA-S was measured after gating on EGFPþcells. Estimate of
intracellular levels of expression of signaling components was
performed by immunoblotting using lysates corresponding to
100,000 T cells. Correction for the low percentage of infection
(typically 15%) was made to estimate the overexpression of SHP-1 in
MSCV(SHP-1/IRES/EGFP)–infected T cells compared to
MSCV(EGFP)–infected T cells.
Figure S1. Calibration of the Presentation of SIINFEKL-Kbon the
Surface of RMA-S APC
(A) Distribution of presentation of SIINFEKL-Kbon the surface of
RMA-S APCs, measured by staining with 25D1.16 antibody, for
different concentrations of the agonist peptide SIINFEKL.
(B) Quantitation of agonist pMHC presentation on the surface of
RMA-S APCs. Calibration of the fluorescence staining (mean
fluorescence intensity) by the 25D1.16 antibody was performed with
Quantibrite beads (BD Biosciences Pharmingen).
(C) Fit of the distribution of 25D1.16 antibody fluorescence staining
on the surface of RMA-S APC pulsed with 10 nM SIINFEKL peptide.
The distribution is log normal with CV¼51% (v2¼3.2 for 100 points,
and three fitting parameters).
(D) CV of the distributions presented in (A) for different concen-
trations of SIINFEKL.
Found at DOI: 10.1371/journal.pbio.0030356.sg001 (213 KB PDF).
Figure S2. Estimate of the Absolute Number of ERK Molecules
Involved in the pMHC Response of Naı ¨ve OT-1 T Cells
To estimate the intrinsic ERK phosphorylation in OT-1 T cells
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Modeling T Cell Ligand Discrimination
independently of pMHC stimulation and the maximal possible
response, we compared the FACS staining with E10 anti-ppERK or
anti-mouse IgG1 isotype control for OT-1 cells alone, OT-1 cells
activated with unpulsed RMA-S, OT-1 cells activated with SIINFEKL-
pulsed RMA-S cells, and phorbol myristic acetate–activated OT-1
cells (as a control for maximal response). Typically, the full ppERK
response of naı ¨ve T cells to APC stimulation involves 50% of the total
pool of ERK. The ppERK response that is independent of pMHC
stimulation is negligible within our experimental resolution.
Found at DOI: 10.1371/journal.pbio.0030356.sg002 (221 KB PDF).
Figure S3. Quantitation of Surface and Cytoplasmic Signaling
(1A and 1B) The numbers of TCR and CD8 molecules on OT-1 T cells
were determined using calibrated flow-cytometric measurements.
(2A and 2B) The number of intracellular signaling proteins per cell
was determined by immunoblotting using purified proteins as
calibration standards. An example of the method as applied to
ERK2 is presented.
Found at DOI: 10.1371/journal.pbio.0030356.sg003 (405 KB PDF).
Figure S4. Comparison of ERK Phosphorylation, IFNc Production,
and the Cytotoxic Activity of Rested OT-1 T Cells Following
Activation by Peptide-Pulsed RMA-S APCs
(A) ERK phosphorylation, (B) IFNc production, and (C) cytotoxic
activity. Biological responses of OT-1 T cells were measured as
described in Materials and Methods for various concentrations of
SIINFEKL, EIINFEKL, and SIIRFEKL peptides used to pulse RMA-S
APCs. For these experiments, we used OT-1 T cells that had been
previously activated 8 d prior to the assay, expanded in medium
supplemented with 7.5% T-stim and 10% FCS, and rested for 2 d
Found at DOI: 10.1371/journal.pbio.0030356.sg004 (165 KB PDF).
Figure S5. Measurement of the Cytoplasmic Volume of Naı ¨ve OT-1 T
Confocal microscopy was used to determine the cytoplasmic volume
of naı ¨ve OT-1 T cells. The diameter of naı ¨ve T cells is 5.6 6 0.5 lm (n
¼10)—hence a cellular volume of 90 fl. After measuring the volume of
the nucleus, the cytoplasmic volume of T cells can be estimated to be
15 6 3 fl. The cytoplasmic concentrations of ZAP70, MEK1, and
ERK2 are 120 lm, 20 lm, and 10 lm, respectively.
Found at DOI: 10.1371/journal.pbio.0030356.sg005 (1.4 MB PDF).
Figure S6. Explicit Description of the Computer Model of the early
TCR Signaling Events
Our model was designed using JDesigner software. To view the model
itself, download the software from http://www.cds.caltech.edu/
;hsauro/JDesigner.htm. Then download the model and open it using
the JDesigner program. Boxes represent molecules or molecular
complexes. Arrows represent chemical reactions (either reversible or
irreversible). Boxes labeled ‘‘Node’’ represent active intermediates in
enzymatic reactions. Dashed boxes are alias nodes (used when the
same molecular species appears at many places in the model). It
should be noted that two parameters must be specified before
running any simulation: first, the number (i.e., concentration) of
pMHC, and second, the lifetime of the pMHC–TCR complex.
(A and B) Complete model for TCR signaling, yielding fast and
sensitive ligand discrimination.
(C–K) Separate modules of the biochemical network.
Found at DOI: 10.1371/journal.pbio.0030356.sg006 (13 MB PDF).
Figure S7. Three Outputs of the Computer Simulation of the Early
Events in Naı ¨ve T-Cell Activation
Four different pMHC ligands are tested in these simulations, with
TCR-binding lifetimes of 0.3 s (representing a self-ligand involved in
thymic selection of mature T cells), 3 s (antagonist), 7 s (weak agonist),
and 18 s (strong agonist). These simulations were performed with 13
104pMHC being presented to a naı ¨ve T cell on each APC.
(A) Kinetics of phosphorylation of the adapter.
(B) Kinetics of loading of pSHP-1 onto Lck in TCR complexes. SHP-1-
decorated TCR complexes cannot drive downstream signaling. Note
the transient decoration of TCR by SHP-1 for strong-agonist and
weak-agonist ligands: these ligands trigger a ppERK response, which
protects TCR-bound Lck from further SHP-1 binding. This transient
binding of pSHP-1 to components of the TCR complex has been
observed in 5C.C7 T cells activated using agonist ligand 
(C) Kinetics of ppERK response. Only weak- and strong-agonist
pMHC can trigger a ppERK response. These simulations fit well with
the experimental results presented in Figure 3B.
Found at DOI: 10.1371/journal.pbio.0030356.sg007 (72 KB PDF).
Figure S8. Computer Simulation of the MAPK Module
(A) Molecular scheme to simulate the MAPK cascade .
(B) Computer simulation of the kinetics of ppERK response in the
MAPK module for different numbers of Ras–GTP ligands.
(C) Dose-response curve for the phosphorylation of ERK as a function
of the number of Ras–GTP ligands. This curve could be fitted with a
Hill coefficient of 13 and an EC50of 5.3. In our model, the MAPK
module acts as digital filter with a low threshold.
(D) Characteristic time of ERK phosphorylation in our computer
simulation as a function of input Ras–GTP. Note the divergence of
time to ppERK generation when Ras–GTP decreases towards the
absolute threshold of response.
Found at DOI: 10.1371/journal.pbio.0030356.sg008 (220 KB PDF).
Figure S9. Modulation of Peptide-KbResponsiveness of OT-1 T Cells
at Three Stages of Differentiation
(A) Comparison of the ppERK response of OT-1 T cells to TCR
restimulation at different times after activation, proliferation, and
differentiation in vitro. The response was measured after 3 min of
contact with RMA-S APCs pulsed with agonist (SIINFEKL) or non-
agonist (EIINFEKL) peptides. The response to the agonist is
essentially the same at the three stages of differentiation. Non-
agonist EIINFEKL peptide does trigger a ppERK response in day-5 T
cells, but only for intermediate levels of presentation.
(B) Measurement of the concentrations of different signaling
molecules in OT-1 T cells 5 d after activation in vitro (day 5), or 11
d after activation in vitro (day 11). These concentrations were
measured by flow cytometry after intracellular staining and are
presented after normalization by the corresponding concentrations
in the unstimulated naı ¨ve state (day 0). Note that SHP-1 is
significantly reduced in day-5 cells.
Found at DOI: 10.1371/journal.pbio.0030356.sg009 (301 KB PDF).
Figure S10. Functional Response of OT-1 T Cells (6 d after Initial
Activation in vitro)
Examples of the gain of functional responses (CD69 upregulation [A]
and cytotoxicity [B]) to a narrow presentation range of EIINFEKL-Kb
that parallel with the ppERK responses shown in Figure S9. This
experiment is representative of seven experiments. In three other
experiments, no acquisition of EIINFEKL-Kbresponsiveness was
observed on the particular day that was studied after activation.
Neither was SHP-1 decreased relative to other signaling components
in these particular experiments. This appears to reflect the narrow
time window within which the discordance in signaling molecule
concentrations occurs in these cultures, and which can vary by a day,
or more in individual experiments, such that the phenomenon can be
missed when only a single day post-activation is analyzed.
Found at DOI: 10.1371/journal.pbio.0030356.sg010 (202 KB PDF).
Protocol S1. Comparison of Kinetic Proofreading Schemes of TCR
Protocol S1 presents quantitative arguments to show that classical
kinetic-proofreading schemes fail to reconcile the conjoint require-
ments of speed, sensitivity, and specificity in T-cell activation.
Found at DOI: 10.1371/journal.pbio.0030356.sd001 (198 KB PDF).
Protocol S2. Computation of the ppERK Response of T Cells at the
Population Level Based on the ppERK Response at the Individual Cell
Protocol S2 presents a quantitative derivation of the ppERK dose
response of T cells to presented ligands. The noise in the number of
presented ligands and the all-or-none ppERK response of T cells are
convolved to yield the final dose response of T cells. This derivation
reconciles the all-or-none response of T cells as measured at the
individual cell level, with the broad dose response measured at the
Found at DOI: 10.1371/journal.pbio.0030356.sd002 (41 KB DOC).
Protocol S3. Biochemical Kinetic Parameters Used in the Computer
Model of TCR Signaling in Naı ¨ve OT-1 T Cells
Protocol S3 reports all the biochemical kinetic parameters derived
from biophysical and enzymological measurements drawn from the
PLoS Biology | www.plosbiology.org November 2005 | Volume 3 | Issue 11 | e3561936
Modeling T Cell Ligand Discrimination
literature. These are the parameters that we used to model the early
events in TCR signaling.
Found at DOI: 10.1371/journal.pbio.0030356.sd003 (83 KB DOC).
Protocol S4. Computer Model of the Early TCR Signaling Events
See Figure S6 for viewing instructions.
Found at DOI: 10.1371/journal.pbio.0030356.sd004 (257 KB XML).
Protocol S5. Reduction of the Divergence in Response Times of T
Cells at Low Ligand Presentation by the Biological Variation
(‘‘Noise’’) in Ligand Presentation
To match computer simulation to experiment, the theoretical output
for the time required to generate a ppERK response in T cells was
convolved taking into account the log-normal distribution of ligand
presentation on individual APCs.
Found at DOI: 10.1371/journal.pbio.0030356.sd005 (28 KB DOC).
This research was supported by the Intramural Research Program of
the National Institutes of Health, National Institute of Allergy and
Infectious Disease. GAB wishes to acknowledge helpful discussions
with and/or technical help from Irena Stefanova ´, Nihal Altan-Bonnet,
Je ´ro ˆme Delon, David Margulies, and Martin Meier-Schellersheim.
Special thanks go to Ravi Rao and Herbert Sauro for updating
JDesigner to produce the final versions of the network figures that
appear in this paper and in the supplementary figures. GAB was
supported by the Helen Hay Whitney foundation.
Competing interests. The authors have declared that no competing
Author contributions. GAB and RNG conceived and designed the
experiments. GAB performed the experiments. GAB and RNG
analyzed the data and wrote the paper.
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