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Blood First Edition Paper, prepublished online July 6, 2012; DOI 10.1182/blood-2012-04-424655
The race for the prize: T cell trafficking strategies for optimal surveillance
Short title: Optimal T cell trafficking strategies
Minyi Lee , Judith N. Mandl , Ronald N. Germain , Andrew J. Yates
1
2
2
1,3,*
1 Department of Systems & Computational Biology, Albert Einstein College of Medicine,
1300 Morris Park Avenue, Bronx, NY 10461, USA
Lymphocyte Biology Section, Laboratory of Systems Biology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, MD 20892 USA
Department of Microbiology & Immunology, Albert Einstein College of Medicine, 1300
Morris Park Avenue, Bronx, NY 10461, USA
2
3
* Corresponding author
[email protected]; phone 718 678 1198; fax 718 678 1018
1
Copyright © 2012 American Society of Hematology
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Abstract
The initiation of T cell responses requires rare precursors to locate a draining lymph
node (dLN) and encounter dendritic cells (DC) presenting peptide-major histocompatibility complexes (pMHC). To locate this needle in the haystack rapidly, T cells face an
optimization problem – what is the most efficient trafficking strategy for surveillance
and recirculation through blood? Two extremes are scanning low numbers of DC per
node with frequent recirculation, or meticulous surveillance with infrequent recirculation. Naive T cells also require stimulation by self-pMHC. To enable efficient location of
both foreign and self, has evolution settled on an optimum time for T cells to spend surveying each lymph node? Using a data-driven mathematical model, we show the most
efficient strategy for detecting antigen in a dLN depends on its abundance. Detection of
low-density antigen is optimized with systemically slow transit. In contrast, at high densities or if dLN egress is restricted, rapid transit through other nodes is optimal. We argue that blood-lymph recirculation dynamics facilitate a trade-off, and are consistent
with dominant roles for the very early detection of rare foreign antigens in a dLN, and
the efficient accumulation of signals from systemically-distributed self antigens.
2
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Introduction
Naive T cells have the task of surveying both for foreign antigens and for weak interactions with self, which are required for optimal function (1–3). Recognition of both takes
place in lymph nodes, exquisitely constructed environments that facilitate the encounter
of T and B lymphocytes with antigens. In mice, the naive CD4 and CD4 T cell pools each
comprise roughly 5 × 10 cells, but the diversity of TCR sequences is such that a remarkably small proportion are capable of recognizing a given antigen with sufficient affinity
to reach an activation threshold. Estimates of the typical antigen-specific pool size in
mice are in the range 10-1200 cells (4–9). A high degree of polyclonality ensures both
broad coverage and fine specificity of the TCR repertoire, but will come at the price of
increasing the time required for the relevant cells in the total repertoire to locate a given
peptide-MHC complex.
7
In their search for TCR stimulation, naive T cells circulate continuously through the
spleen, lymph nodes, lymphatic vessels and blood (10). At steady state, naive T cells enter lymph nodes from the blood at random through the high endothelial venules (HEV),
taking a few minutes to cross into the lymph node cortex (11, 12). There they encounter
and survey DC presenting peptide-MHC ligands. While in the cortical region T cells acquire competence to egress, at most 4 hours (13) but possibly as little as 20 minutes (14)
after crossing the HEV. T cells exit from the lymph node through lymphatic sinuses and
return to the blood, first through lymphatics, and finally through the thoracic duct.
Smith and Ford (11) studied lymphocyte recirculation in rats and found that intravenously injected cells returned to the thoracic duct 4-16 hours later. They estimated that
at steady state approximately 1-3% of the transferred cells were in blood, and blood residence times were exponentially distributed with mean 25 minutes. Thus the majority of
a naive T cell’s time is spent in lymphoid organs.
The benefit of this skewed allocation of attention between blood and lymph appears obvious; time spent in blood is wasted as far as identifying antigen is concerned. However,
recirculation via the blood is essential to allow rare T cells to encounter rare antigens,
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such as those appearing in a single lymph node draining a site of infection. To search for
pMHC ligands, a circulating T cell might then in principle take strategies ranging from
making small numbers of DC encounters in each transit of a lymph node, with frequent
recirculation, to more numerous DC encounters per transit but sampling fewer nodes in
a given time interval. Here we explore how these strategies influence the efficiency with
which a population of relevant T cells locates a specific antigen, and identify the constraints that may have shaped the optimal surveillance strategy for a naive T cell.
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Methods
Modeling lymph node transit and recirculation
Following systemic blocking of entry to HEVs, naive CD4 and CD8 T cells egress from
inguinal, brachial and mesenteric lymph nodes in mice with exponentially distributed
transit times with mean 12 hours for CD4 T cells and 21 hours for CD8 T cells (15).
These estimates are comparable to those of 7-12 hours obtained from lymphocyte recirculation experiments in rats (11, 16). While in lymph nodes, in the absence of foreign antigen, T cells make sequential contacts with dendritic cells with mean duration of approximately 3-4 minutes (15, 17). For CD4 T cells the durations of these contacts with
DC are influenced by processes that involve recognition of self pMHC class II ligands, as
mean contact times are approximately 50% shorter when the DC lack such ligands (15).
The mechanisms underlying a cell’s decision to egress from a lymph node are complex
(18, 19), but these observations suggest a remarkably simple explanatory model; in the
absence of inflammation, T cells typically make several hundred encounters with DC
while transiting a lymph node, and leave via efferent lymphatics with a constant probability following each encounter (15).
Mathematical models have been used to describe lymphocyte recirculation (16), using
data from experiments in rats (11) and sheep (20). Together these suggest that different
lymphoid organs exhibit different efficiencies of lymphocyte recruitment, perhaps in
part due to differences in local rates of blood flow. There is also a distribution of lymph
node sizes within an individual, and any variation in the density of lymphatic sinuses in
the cortical region may mean that the probability of egress per unit time (and hence
transit time) could vary from node to node. Thus following each transit through blood,
naive T cells may enter different lymph nodes with different probabilities, and potentially take different times to transit the node that they enter. However, for our purposes the
important features of T cell trafficking are the following: (i) naive T cells move continuously between blood and the lymphoid compartment, entering lymph nodes at random; (ii) the typical time spent between lymph nodes, in blood, TB , is approximately 30
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minutes; (iii) in the absence of infection there is a mean time TL taken for transit
through each lymph node; and (iv) the appearance of foreign antigen in a node may
eventually result in (possibly transient) restriction of egress from that node. In the Supplemental Information we show that our results hold when we relax the third assumption and allow heterogeneity in mean transit times through lymph nodes.
We encapsulate these observations and assumptions in a mathematical model, illustrated in Fig. 1 and described below. The model follows a population of antigen-specific
T cells circulating between blood and lymph. To model the search for antigen, we assume that in one lymph node, every encounter between one of the specific T cells and a
DC results in recognition of the cognate foreign pMHC with probability f . We refer to f
as the antigen density. Assuming random encounters between T cells and DC, f can be
interpreted either as the proportion of DC that present cognate pMHC at an adequate
level to trigger an activation response by that T cell, or the proportion of MHC molecules
in the lymph node as a whole that bear the relevant pathogen-derived peptides. More
generally, if τ is the mean time between encounters with DC, f is interpreted as the
probability per time interval τ that a T cell accumulates multiple signals from pMHC
above some threshold required for activation. This more general measure allows for
non-random sampling of DC by T cells – activated DC may attract T cells in their vicinity to increase their rate of contacts (21, 22). We return to this issue below.
Given specific antigen in one lymph node, the model yields the cumulative probability
P(t) of recognition of that antigen within a time t . This is the probability that at least
one specific T cell has been triggered by interacting with cognate pMHC within a time
interval t . Note that we are concerned with the time until the first cognate recognition
event, and not the time until such events as the onset of clonal expansion, recruitment of
all antigen-specific cells into a response, or migration to infection sites. In what follows
we model naive T cell circulation in mice, assuming N =30 lymph nodes (23) and antigen-specific populations of 10 and 100 T cells.
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Mathematical formulation
At a time t after antigen appears in one lymph node at density f, a given specific T cell is
any of the following locations; the blood with probability B(t) , the antigen-bearing
(draining) node with probability Y (t) , and one of the N −1 other lymph nodes with
probability Xi (t). Each contact with a DC has mean duration τ , and the mean times
spent in each lymph node and blood are TL and TB respectively. The cumulative probability that this particular T cell has encountered antigen by a time t is denoted p(t) ; successful encounters occur with probability f per T-DC encounter in the draining lymph
node, and so with rate f / τ per cell per unit time. The ‘leakiness’ parameter λ is 1 for
normal egress from the antigen-bearing node, and 0 for blocked egress. The initial conditions p(0), B(0), Xi (0), Y (0) reflect the T cell being randomly located in the system at
time t = 0 , with λ = 1 initially (no restriction of egress). If there are s antigen-specific
cells in the body, the probability that at least one of them has encountered antigen by
time t is P(t) = 1− (1− p(t)) . This is the quantity presented in Figs. 2-4. The equations
representing the model are as follows:
s
dB / dt = −
B(t) N −1 Xi (t) λ
+∑
+ Y (t)
TL
TB
i=1 TL
B(t) Xi (t)
−
, i = 1…(N −1)
TL
NTB
f
B(t) λ
− Y (t) − Y (t)
dY / dt =
τ
NTB TL
dXi / dt =
dp / dt =
p(0) = 0,
f
τ
Y (t)
B(0) =
Xi (0) = Y (0) =
1
1+ (TL / TB )
1
N(1+ (TB / TL ))
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Results
Antigen density and precursor frequency influence the optimum lymph node transit
time
We begin by calculating the probability that, following the appearance of antigen in a
lymph node, at least one antigen-specific T cell has arrived in that node and detected antigen within 12 hours. We do this for different LN transit times, antigen densities, and
specific population sizes (Fig. 2). Initially we assume that egress from the draining node
is not restricted ( λ = 1), recruitment to this node is not increased, and that T cells within
the node do not preferentially home to antigen-bearing DC. This calculation then provides a lower bound on the predicted efficiency of detection.
With a population of 10 specific cells and 30 LN, there is a substantial probability (≈
70%) that any given node will not contain an antigen-specific cell. In this scenario, when
antigen is rare in the target node, slow transit maximizes the rate of detection (Fig 2A,
lower curves) but as antigen density increases, more rapid transit becomes optimal (Fig.
2A, upper curves). The probability of detection by 12h saturates with increasing transit
times. In this regime, the majority of cells have surveyed only one lymph node by 12h. In
this case detection occurs within 12h only if specific cells are already resident in the target node.
At this low precursor frequency (1 in 5 × 10 ), the influence of antigen density on the optimal strategy is the result of the two-step process of locating antigen. Cells must first
enter the correct lymph node; this is facilitated by rapid transit and frequent recirculation. Once in the correct node, their probability of detecting antigen is increased with
slower transit. When antigen is rare, the importance of thorough scanning dominates
and longer transit times are the best strategy (Fig. 2B). In contrast, when antigen is abundant the rate-limiting step becomes locating the correct lymph node, so rapid transit
is optimal (Fig. 2C).
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We see a trade-off in Figs. 2A and 2D. The probability of early detection drops sharply
for all antigen densities when transit times are very short compared to the mean time
transiting between lymph nodes. In this regime an increasingly large proportion of specific cells are expected to be in the blood at any time. So the effective precursor frequency falls, reducing the net surveillance rate; thus very rapid transit through lymph nodes
(TL ≪ TB) is not optimal at any density of antigen.
When populations of specific cells are larger than the number of lymph nodes – in the
example that follows, 100 cells (a precursor frequency of 1 in 5 × 10 ) distributed across
30 nodes – the probability of the target node being initially devoid of specific cells is
much lower (≈3%). Here the situation is different (Fig. 2, D-F). Recirculation has the
effect of resampling for the possibility of a specific cell arriving in the correct node.
However, because it is likely a node already contains a specific cell, the benefit of rapid
transit (frequent resampling) is lost and detection efficiency becomes weakly dependent
on transit time (Fig. 2D). As before, detection efficiency declines at low transit times due
to the increasing proportion of specific cells resident in the blood. This insensitivity to
transit time becomes more pronounced as antigen densities increase (Figs. 2E and 2F),
as resampling from the circulation becomes even less important for efficient detection.
5
In summary, when precursor frequencies are low ( < 1 specific T cell per node on average), rapid transit is optimal for the detection of abundant antigen in one node. Slower
transit is optimal for rarer antigen. If the mean number of specific cells per node is
greater than one, a wide range of transit times suffices for all antigen densities. This
condition may be important with respect to the activation of central memory cells
present at larger precursor frequencies than naive T cells.
Restriction of egress favours rapid transit of non-target nodes
Activated antigen-bearing DC usually migrate from the site of infection to a draining
lymph node. For some (but not all) infections, inflammatory signals then begin to restrict egress of lymphocytes from that node (24– 26) and enrich the node for antigen9
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specific cells (27). If we alter the model to include restriction of egress by setting the parameter λ = 0 , shorter lymph node transit times in the other nodes increase the rate of
recruitment of specific T cells to the draining node, and so increase rates of detection for
all frequencies of specific antigen and for all precursor frequencies (Fig. 3, both panels;
we use specific population sizes of 100 cells, and results for 10 cells are qualitatively
similar). Retention of T cells in the target lymph node removes the cost of frequent recirculation, and the best transit strategy then is to move through other nodes as rapidly
as possible (Fig 3A, green curve). Blocking of egress in a target node may be transient
(24), perhaps to allow the continued recruitment of antigen specific cells into a node of
finite capacity. By this time antigen will have accumulated in the target lymph node, and
rapid transit gives efficient detection of abundant antigen at all precursor frequencies
(Figs. 2C and 2F). Thus the optimal strategy when egress from a dLN is only transiently
restricted is still to transit nodes rapidly.
Antigen density is effectively increased by DC activation
Miller et al. (17) estimated that following an infection, an activated DC in a dLN encounters 80 new T cells per minute and is in contact with approximately 250 T cells at any
time. From this they calculated that with 100 antigen-bearing DC in a node, and a CD4 T
cell precursor frequency of 1 in 10 , this rate of turnover provides a 95% chance of at
least one encounter between a specific T cell and an antigen-bearing DC within approximately 6h.
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This calculation makes the implicit assumption that T cells compete for residence or
contact sites on DC, for which there is evidence (28, 29), and it does not consider the
timescale of recruitment of specific cells to the relevant LN. However we can use it to
show how the activation status of antigen-bearing DC might influence the estimation of
the antigen density f . Under steady-state conditions in the absence of infection, a
lymph node may contain of the order 106 CD4 T cells and approximately (5 − 40) × 104
DC. So under normal conditions there will be approximately 10 naive CD4 T cells in contact with each resting DC at any time, and with a mean contact time of 3 minutes each
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DC makes new encounters with approximately 3 T cells per minute. This together with
the calculation by Miller et al. suggests that DC activation may boost the rate at which a
DC encounters T cells as much as 30-fold, perhaps due to increased T cell densities in
the draining LN and/or preferential homing to activated DC (22).
Directed motion of a T cell towards relevant DC clearly will increase its probability of
encountering antigen per unit time and so increase the effective density of antigen. To
illustrate, assume a LN contains 1 specific T cell on average, corresponding to a precursor frequency of approximately 10− . We predict that to achieve a 95% probability of detection by 6h requires antigen to be present at density f ≈ 0.02, or roughly 1 in 50. Miller
et al. estimate that this detection efficiency can be achieved with only 100 antigenbearing DC in a node, which yields a naive estimate of antigen density of between 1 in
40,000 and 1 in 500. Thus, unsurprisingly, increased recruitment of T cells to activated
DC will boost the effective antigen density above the simple estimate of the proportion
of DC in the node presenting relevant antigens, and increase the detection efficiency following recruitment of specific cells to the draining lymph node.
6
Surveillance for self antigens
In the first section we modeled the search by a population of antigen-specific T cells for
antigen immediately following its appearance in one lymph node, without restricted
egress. This model can equally well be used to describe a single cell’s search for selfantigens in the absence of infection.
The nature of naive T cells’ requirement for interactions with self-pMHC is unclear, and
the signals may operate at several levels. Very low-level stimulation could be obtainable
from a broad spectrum of ligands and frequent ‘tonic’ signaling from these contacts may
contribute to the maintenance of TCR responsiveness (30). Signals from self-pMHC
may also be required for homeostasis. Some studies suggest that the absence of MHC
impairs survival, with mature CD4 and CD8 T cells declining with half lives of a few
weeks (3, 31–33). These observations support the idea that cells can survive on signals
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derived from infrequent encounters, or sequences of encounters, with self-pMHC. Thus,
under non-lymphopenic conditions in which other survival factors such as cytokines
may be limiting it may be that only rare encounters with a subset of self-pMHC occur
that promote survival or (even more rarely, in mice) induce division.
Whatever the frequency of relevant ligands, if we assume they are distributed at random
among all nodes, a cell’s rate of encounter with them can be modeled by grouping all N
lymph nodes into effectively a single lymphoid compartment. Modifying the model appropriately, we see in Fig. 4 that longer lymph node transit times always favour the accumulation of contacts with relevant self-pMHC, irrespective of their abundance. The
model predicts that meticulous scanning of each lymph node facilitates the acquisition
of signals from self, simply because this strategy minimizes the proportion of time spent
in blood; if relevant self antigens are distributed at random, recirculation between nodes
confers no benefit, on average. Diminishing returns are obtained from slower transit as
the proportion of time spent surveying for antigen in lymph nodes, TL / (TL +TB ) , approaches one; notably, the transit times of 12h or more that are observed in mice are
close to this saturating regime of maximum efficiency of detection (Fig. 4B). We also
note that slow transit may maximize the rate of tolerance induction in the periphery, by
minimizing the time taken for a naive T cell to encounter rare high-affinity self-peptide
ligands that were not encountered in the thymus.
Fig. 4A shows that the timescale for detection of antigens at frequencies of 1 in 105 or
less is of the order months to years. Homeostatic turnover of naive T cells is almost undetectable in healthy mice and may be as slow as once every several months to years in
adult humans (34–36). Together these observations are consistent with a model of homeostasis in which, under normal conditions, division of naive T cells is induced by encounters of sufficient duration and affinity with rare self-pMHC ligands. These may be
rare in absolute terms, or effectively at very low frequency due to competition within T
cell clones.
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Discussion
To identify optimal strategies in biology risks conjuring just-so stories using convenient
assumptions, perhaps missing other constraints that are the true determinants of behaviour. However, establishing that trade-offs exist at all in a naive T cell’s surveillance
strategy requires only a few biologically grounded assumptions. Our understanding of
the trafficking patterns of naive T cells and their clear purpose – to search for ligands,
both self and foreign – quite straightforwardly reveals conflicting demands.
We have shown rates of transit through lymph nodes influences how well T cells satisfy
these demands. The strategies vary slightly with precursor frequency, but the consistent
findings are that slow transit optimizes the very early detection of rare foreign antigen,
when the density of antigen in the lymph node draining an infection site is low and
egress is yet to be restricted; and is also optimal for the acquisition of signals from self
pMHC (for function, survival, division, or for the induction of peripheral tolerance). In
contrast, faster transit improves response times when antigen is abundant or when
egress from an antigen-bearing lymph node is restricted. We argue here that LN transit
times reflect a strategy that is the result of a compromise between these conflicting demands.
Adaptive behaviour. Within the ‘Goldilocks’ region described by our analysis, the
immune system may adaptively switch between different modes of behaviour that facilitate the search for self or foreign antigens when appropriate. For example, inflammatory
signals that increase the probability per blood transit that a cell enters an antigenbearing node (37) will effectively reduce the number of nodes to be searched (N), Similarly, as discussed above, preferential homing of T cells to activated DC within a lymph
node (22) boosts the effective antigen density. Both of these adaptive changes facilitate
the recruitment of naive precursors, which for many responses may be complete (9, 38).
The ability of the immune system to modulate the surveillance process in these ways
suggests that transit rates may be optimized most strongly for the detection of rare or
self antigens in the absence of inflammation, consistent with the transit times observed
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experimentally, and that other mechanisms specific to the draining LN come into play to
progressively increase the rate of recruitment the dLN and homing to Ag-bearing DC.
External constraints. We have assumed that any optimization has occurred against a
background of (i) a constant mean transit time through blood, and (ii) a constant mean
time for a T cell to survey a DC. The first assumption seems reasonable since this is determined, at least in part, by external factors such as lymphatic and blood pressure, and
the distances cells must travel in the vasculature between exit from the thoracic duct
and reaching a HEV. The second assumption is reasonable since the efficiency of detection depends on the machinery of TCR-pMHC recognition, which is presumably tuned
to give a balance between sensitivity and specificity within as short a time as possible.
Body mass may also influence the optimal strategy. Humans have many more lymph
nodes compared to the 30 we assume for mice, and the increased mean distance from
thoracic duct to HEVs means recirculation times may be longer. The typical size of antigen-specific naive T cell populations may also be larger in humans. T cell repertoire diversity has proved difficult to measure, in part due to potential cross-reactivity of different TCRs for the same pMHC ligands; but in humans number of different TCRβ chains
in the naive T cell pool is estimated to be approximately 106 (39, 40), generating approximately 2.5 ×107 distinct TCRαβ sequences (39). Assuming a naive T cell compartment
size of 1011, this suggests naive T clone sizes may be of the order 103 − 104 cells in humans. These mouse-human differences will likely alter the optimal transit time, although the direction of the effect is unclear – for given LN and blood transit times, increasing the number of lymph nodes reduces the efficiency of recognition, but larger
clone sizes will increase it.
Stochasticity in LN transit. In our analysis the existence of a trade-off determining
an optimal mean transit time is independent of whether transit is of a fixed duration or
is a random variable. Nevertheless, it can be shown that for a search process through
patches (lymph nodes) with unknown and possibly time-varying probabilities of detecting a target (antigen) at each timestep, a fixed transit time through each patch is the op14
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timal strategy for rapid detection (41), an assumption made in a recently study of LN
transit (42). However, the duration of a given naive T cell’s transit through lymph node
from blood is very likely a sum of random variables corresponding to crossing HEV, migrating throughout paracortical regions surveying DC, and egressing via cortical sinusoid structures (12). Our observation that transit time is approximately exponentially distributed suggests that one of these processes accounts for the majority of transit time,
likely the movement within the paracortex; superimposed on this is a constant probability per unit time of initiating egress, which then occurs relatively rapidly. DC are broadly
distributed throughout the paracortex, and to a good approximation T cells perform
random walks among them (43), guided by the fibroblastic reticular network (44). Rapid detection of antigen is likely facilitated by each T cell performing independent random sampling of DC; thus the spatial distribution of DC within the paracortex may dictate that random walks with stochastic egress are optimal for surveillance, rather than
(for example) directed transit between entry and exit sites.
Lymphocyte ecology. The study of the population dynamics of lymphocytes might be
described as lymphocyte ecology. Optimizing the rate of accumulation of signals from
self-antigens (rather than optimizing the time to encounter an antigen for the first time,
for the initiation of an immune response) has some analogies to the use of foraging
theory to determine how predators maximize their rate of encounter with resources as
they move between spatial patches. Here predators, resources and patches are the obvious analogs of naive T cells, their required self-pMHC ligands and lymph nodes. Iwasa
et al. (45) show that the best strategy depends on the variance of the distribution of resources between patches. If resources are distributed randomly (with Poisson statistics),
maximal uptake comes from a fixed time spent in each patch. Very high variance in resources, corresponding to ligands that are relatively abundant in some nodes and scarce
in others, leads to an optimal strategy in which a predator leaves a patch if the interval
between successive detection of resources (here, ligands) exceeds a certain threshold.
This suggests a more sophisticated model of transit in which a naive T cell’s number of
encounters with DC in lymph node may depend on the availability of patchilydistributed pMHC ligands. We find some experimental support for this (15). In inguinal
and brachial lymph nodes in mice, polyclonal naive CD4 T cells make approximately
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110-180 contacts with DC during transits of duration 9-12 hours. In the absence of
MHCII, naive CD4 T cells make many more DC contacts (200-300) of shorter duration,
but egress more rapidly, within 7-8 hours. Conversely, recirculation is slower under
lymphopenic conditions when competition for ligands is presumably reduced (16, 46).
Our model assumes that cells are memoryless over timescales of hours, and that the
quality of stimulation received has no effect on transit times. However, these data suggest T cells sense their recent history of stimulation, and may make the decision to
egress informed by their perceived measure of the local abundance of ligands.
Naive T cell homeostasis and ligand availability. We suggest that any pMHC
ligands required for naive T cell survival or division under non-lymphopenic conditions
may be rare and randomly distributed, perhaps with an affinity for the TCR that are
above certain thresholds. We were motivated here in part by the ecological principle of
competitive exclusion (47). This suggests that stable co-existence of multiple species
(TCR specificities) reliant on resources (self-pMHC) requires a diversity of resources or
ecological niches comparable to the diversity of species. This avoids the eventual outgrowth of the strongest competitor for a common resource. The idea of the diversity of
self-antigens reflecting the diversity of the TCR repertoire has also been raised in the
context of self-tolerance (48) and may underlie the relation between abundance and
survival of naive CD4 T cell clones (49).
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Acknowledgments
All computation was performed in Mathematica (Wolfram Research, Inc., Champaign,
Illinois). We thank Johannes Textor, Rob de Boer, Andras Fiser, Charles Sinclair and
Benedict Seddon for comments and discussions. This study was supported by the NIH,
R01 AI093870-01 to AJY.
Author Contributions
This study arose from discussions between JNM and AJY regarding lymphocyte trafficking and surveillance. AJY formulated the question and the model. ML performed the
analyses of the model supervised by AJY, JNM and RNG provided experimental data,
and AJY wrote the manuscript with input and discussion from all co-authors.
Conflict of Interest Disclosures
The authors declare no conflicts of interest.
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Figure 1: A model of naive T cell trafficking and surveillance. A naive T cell enters one of
N lymph nodes at random, from the blood. It transits the node making contacts of duration τ with DC (shown in blue), surveying for antigen; it egresses with a constant probability per DC encounter, returning to blood after a mean transit time TL . (If q is the
probability of egress per DC encounter, TL = τ / q .) It then spends an average time TB in
the blood before re-entering a lymph node, again at random. In one node (orange), antigen is present on a proportion f of DC (purple) and contact between a T cell and antigen-bearing DC results in detection. The rate of egress from this node may also be reduced in an infection scenario.
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Figure 2: Conservative estimates of the efficiency of detection depend on antigen abundance, precursor numbers and lymph node transit time. We consider detection without
blocking of egress from a draining LN (dLN). When precursors are rare (upper panels,
A-C), slow LN transit favours the detection of rare antigen in the dLN (A, lower curves,
and B) but increasingly rapid transit is optimal for Ag at higher densities (A, lower
curves, and C). At higher precursor frequencies, when every node is likely to contain at
least one specific cell at steady state, slower transit is optimal at all antigen densities (DF).
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Figure 3: Restricting egress from an infected lymph node. The rate-limiting step is recruitment into the correct lymph node; thus rapid transit (A, left-most region; B, upper
curves) yields more efficient detection.
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Figure 4: Slow transit facilitates the detection of rare self antigens. The self-pMHC ligands required for survival by a given clone are assumed to be distributed at random
across all lymph nodes. A: Cumulative probability of a single cell encountering a selfantigen present a frequency of 1 in 10 , for different transit times. B: The probability of
detection by 180 days as function of self-antigen density. In both panels predictions
quickly saturate for transit times longer than 12 hours (not shown).
5
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Prepublished online July 6, 2012;
doi:10.1182/blood-2012-04-424655
The race for the prize: T cell trafficking strategies for optimal surveillance
Minyi Lee, Judith N. Mandl, Ronald N. Germain and Andrew J. Yates
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