The JI
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     
 

The Journal of Immunology, 2008, 180, 1414 -1422
Copyright © 2008 by The American Association of Immunologists, Inc.
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow Request Permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Yates, A.
Right arrow Articles by Seddon, B.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Yates, A.
Right arrow Articles by Seddon, B.

Mathematical Modeling Reveals the Biological Program Regulating Lymphopenia-Induced Proliferation1

Andrew Yates{dagger}, Manoj Saini*, Anne Mathiot* and Benedict Seddon2,*

* Division of Immune Cell Biology, National Institute for Medical Research, London, United Kingdom; and {dagger} Department of Biology, Emory University, Atlanta, GA 30322


   Abstract
Top
 Abstract
Introduction
 Materials and Methods
 Results
 Discussion
 Disclosures
 References
 
Recognition of peptide-MHC by the TCR induces T lymphocytes to undergo cell division. Although recognition of foreign peptide induces a program of cellular division and differentiation by responding T cells, stimulation by self-peptide MHC complexes in lymphopenic conditions induces a slower burst of divisions that may or may not be accompanied by effector differentiation. Although both responses are triggered by signals from the TCR, it is not known whether they represent distinct programs of cell cycle control. In this study, we use a mathematical modeling approach to analyze the proliferative response of TCR transgenic F5 T cells to lymphopenia. We tested two fundamentally different models of cell division: one in which T cells are triggered into an "autopilot" deterministic burst of divisions, a model successfully used elsewhere to describe T cell responses to cognate Ag, and a second contrasting model in which cells undergo independent single stochastic divisions. Whereas the autopilot model provided a very poor description of the F5 T cell responses to lymphopenia, the model of single stochastic divisions fitted the experimental data remarkably closely. Furthermore, this model proved robust because specific predictions of cellular behavior made by this model concerning the onset, rate, and nature of division were successfully validated experimentally. Our results suggest cell division induced by lymphopenia involves a process of single stochastic divisions, which is best suited to a homeostatic rather than differentiation role.


   Introduction
Top
 Abstract
 Introduction
Materials and Methods
 Results
 Discussion
 Disclosures
 References
 
The peripheral T cell compartment is maintained in a remarkably stable state of homeostasis despite its heterogenous composition and the constant influx of cells into the different pools (1). This stability is achieved by close regulation of cell survival and proliferation of the constituent subsets. For naive CD4 and CD8 T cells, these homeostatic survival and proliferative mechanisms are regulated by cytokines and TCR signals. In contrast, memory cell homeostasis appears to depend only on cytokines including IL-7 and IL-15. During Ag responses, specific T cells are released from normal homeostatic control and proliferation and survival is governed by the presence of specific Ag. Upon resolution of a response and clearance of Ag, specific T cells return to normal homeostatic control.

Recognition of self-peptide MHC complexes by naive T cells delivers signals that are important for T cell survival (2, 3, 4, 5, 6, 7, 8), and in conditions of lymphopenia, these same signals can induce T cells to undergo so-called homeostatic or lymphopenia-induced proliferation (LIP)3 (4, 9, 10, 11). Although induction of proliferation in lymphopenia is critically dependent on TCR signals, and therefore could rely on similar proliferative mechanisms that govern responses to Ag, the precise relation between these two responses remains unclear. Studies using different CD8+ TCR transgenic models have revealed a complex picture in which a broad range of proliferative responses to lymphopenia can be observed. Some TCR transgenic T cells proliferate slowly (12) or not at all (6), whereas others undergo extensive cell division accompanied by development of effector function (13, 14). LIP may also have a strong stochastic (random) component because even within an apparently homogeneous monoclonal population, some cells divide extensively, whereas in the same environment and time frame others will not divide at all. In the instances where lymphopenia induces the most rapid division, the similarity with true Ag-driven proliferation is quite considerable both in terms of dependency on CD4 T cell help (15) and at a genetic level where they share similar profiles of gene expression (16). However, in other regards, such as the lower rate of division and its dependence on IL-7 (17), lymphopenia-induced proliferation is distinct from that induced by Ag.

Despite the extensive molecular and cellular characterization, it remains unclear whether proliferation induced by lymphopenia follows a pattern similar to that induced by Ag, differing from it only quantitatively, or whether induction and/or maintenance of cell division in these two types of proliferation are regulated in fundamentally distinct ways. To gain a better understanding of how LIP is regulated, we took a different approach, constructing mathematical models to describe the proliferative process quantitatively and thus provide new insights into the control required to achieve the complex responses observed. Previous studies have successfully used mathematical modeling to better understand T cell proliferation to Ag (18, 19, 20, 21), in which cells divide in a "programmed" manner, largely independent of the requirement for continued antigenic stimulation (22, 23). This program can be represented mathematically as a rapid and deterministic or autopilot series of divisions that follow a relatively slow and stochastic (probabilistic) entry into the first division, the mean time to which can be affected by costimulation and cytokines. This model can accurately describe the processes involved in T cell activation and provide quantitative insights into how costimulation shapes the proliferative response.

In the present study, we show that F5 TCR transgenic T cells undergo a distinct and defined program of cell division in response to lymphopenia. Proliferation is slower than compared with Ag-induced proliferation and cells fail to up-regulate activation markers or develop effector function, a response profile found to be in common with a large proportion of the CD8 T cell repertoire in polyclonal mice. Significantly, we show that homeostatic proliferation of F5 T cells is best described by a remarkably simple model of infrequent, stochastic single divisions and does not fit a model of an autopilot burst of proliferation. Our data suggest that Ag- and lymphopenia-induced proliferation may represent fundamentally distinct programs of cell division.


   Materials and Methods
Top
 Abstract
 Introduction
 Materials and Methods
Results
 Discussion
 Disclosures
 References
 
Mice

C57Bl6/J wild-type (WT), Ly5.1 C57Bl/6J, RAG-1-deficient (Rag1–/–) mice, Il7–/– (The Jackson Laboratory), F5 Rag1–/– mice, and breeding combinations thereof were bred in a conventional colony free of pathogens at the National Institute for Medical Research (London, U.K.). All lines used were of H-2b haplotype. Animal experiments were done according to institutional guidelines and Home Office regulations.

Flow cytometry

Flow cytometry was conducted using 2–5 x 106 lymph node or spleen cells. Cell concentrations were determined using a Scharf Instruments Casy Counter. Cells were incubated with saturating concentrations of Abs in 100 µl of PBS-BSA (0.1%)-azide (1 mM) for 1 h at 4°C followed by three washes in PBS-BSA-azide. Monoclonal Ab used in this study were as follows: allophycocyanin-TCR (H57–597) (BD Pharmingen), allophycocyanin-CD44 (Leinco Technologies), bio-CD44 (BD Pharmingen), and PerCP- and PE-CD8 (BD Pharmingen). Biotinylated mAb staining was detected using PerCP steptavidin (BD Pharmingen) and PE-TR steptavidin (Caltag Laboratories). Four- and five-color cytometric staining was analyzed on a FACSCalibur and LSR Instruments (BD Biosciences), respectively, and data analysis was performed using FlowJo V8.1 software (TreeStar).

Labeling and adoptive transfer of T cells

Lymphocytes were teased from lymph nodes and spleen of donor mice and single cell suspensions were prepared. Cells were labeled with 2 µM CFSE (Molecular Probes) in Dulbecco’s PBS (Invitrogen Life Technologies) for 10 min at 37°C and washed twice. Cells were transferred into various recipient mice via tail vein injections. Mice further challenged with influenza virus (A/NT/60-68) were injected i.v. with 107 hemagglutinating units of virus.

Cellular expansion of CFSE-labeled cells was calculated by determining the frequency (Fi) of recovered donor cells that had undergone i divisions, {Sigma}Fi = 1. Adjusted frequencies, or precursor frequencies, fi were calculated by dividing Fi by 2i to remove the effects of expansion ({Sigma}fi ≤ 1). The fold expansion was then given by the quantity 1/{Sigma}fi. Mean divisions were calculated as {Sigma}i fi/{Sigma}fi.

In vivo killing assay

Splenocytes from Ly5.1 C57BL/6J were incubated with either 10–6 M, 10–7 M, 10–8 M, 10–9 M, or no Ag as control for 2 h at 37°C, then labeled with 4 µM, 1 µM, 250 nM, 62 nM, and 16 nM CFSE, respectively, for 10 min at 37°C and washed twice. Four x 106 of each population of cells were mixed and injected into Rag1–/– recipients. Rag1–/– and F5 Rag1–/– recipients received targets alone as controls. Twenty-four hours later, recipients were killed and splenocytes isolated. Target cells were stained with Ly5.1 and analyzed by FACS. Percent killing was determined by comparison of target populations remaining in experimental hosts with control hosts that received targets alone and normalized to the unpulsed control population.

Mathematical modeling of homeostatic proliferation

Gett-Hodgkin (GH) (programmed divisions) model. In this model, used successfully to describe programmed T cell responses to Ag stimulation (18), the first division for each cell takes a time t drawn from a distribution with probability density {phi}(t), and subsequent divisions for each cell are deterministic, each division taking a time {Delta}. We assumed no cell death over the course of the experiments. We attempted to fit the data using three left-bounded unimodal distributions {phi}(t)-gamma, lognormal, and Weibull. Whatever the specific form of {phi}(t), if cells are exposed to a stimulus at a time T after transfer, this model predicts that the precursor frequency of cells that have divided i times (that is, the frequency of cells in generation i after adjustment for their expansion) at time t after transfer is (18):

Formula

Stochastic single divisions model. To describe cells undergoing single divisions randomly, we used a version of the Smith-Martin (SM) model of the cell cycle (24) in which cells spend exponentially distributed times in a resting "A phase" with rate constant {lambda} (such that the average waiting time for a cell in A phase is 1/{lambda}). In this model, all cells have an equal probability of committing to division in any time interval. After committing to division, cells transit deterministically through a "B phase" of duration {Delta} before undergoing mitosis and returning to A phase. Let the expected numbers of cells in generation i (that is, cells that have divided i times since transfer) in the A and B phases at time t after transfer be xiA(t) and xiB(t), respectively. Assuming N cells survive the transfer and are capable of dividing in the recipient, these quantities can be calculated using the following system of equations:

Formula
where xiB(s, t) is the population density of cells at time t that have already divided i times and have been in B phase for a time s, 0 ≤ s ≤ {Delta}. The solution is subject to the boundary conditions xiB(t, 0) = {lambda}xiA(t), i = 0... n, x0A(t = T) = N, xiA(T) = 0, i = 1... n, and xiB(s, 0), i + 1... n, for all s. The subscripts i = 0... n refer to division or generation number, n is the maximum number of divisions that can be resolved (typically 8–9 with CFSE labeling), and we assumed no division was possible during an initial lag period of duration T after transfer. With CFSE information alone only the sum of the populations in the A and B phases are observable; that is, the number of cells in CFSE peak corresponding to cells divided i times is

Formula
These quantities are proportional to the initial undivided cell number, N, or the number of transferred cells that survive the transfer and participate in the homeostatic expansion. This number is unknown and may vary from animal to animal. The assumption of no cell death allowed us to remove this dependence on N and work instead with the precursor frequencies of cells in each generation predicted at time t,

Formula
We also fitted a modified SM model with an additional parameter µ that allowed a progressive reduction in the division rate with time to mimic competition for homeostatic resources as the population expands. We assumed an exponential decline, such that {lambda}(t) = {lambda}0 exp(–µt).

Estimation of parameters. Best-fit values of the parameters (that is, for the GH model, the parameters describing {phi}(t) together with the lag time T and the division time {Delta}; for the simple SM model, {lambda}, {Delta}, and T; and for the modified SM model; {lambda}0, µ, {Delta}, and T) were found using a custom-written Mathematica script. The model equations were solved numerically to generate the predicted precursor frequencies pi(t); independent components of the frequency data pi(t) and their observed counterparts fi(t) were arcsin-square root transformed to normalize their distributions across animals at each division at each time point; the weighted sum of squared residuals between the pi(t) and the fi(t) was then minimized with respect to the parameters using a Nelder-Mead optimization algorithm. By fitting the model to 500 datasets generated by resampling with replacement, we obtained empirical (bootstrap) distributions of the parameter estimates and 95% confidence intervals were obtained using the percentile method (25). The Mathematica script is available on request from the authors.

Comparing models. The improvement in fit obtained by adding a parameter to the SM model was assessed with an F-test. If SSR denotes the sum of the squares of the weighted residuals, each term in which is assumed be the square of a normally distributed variable with unit variance, then the quantity (SSR1 – SSR2)/(SSR2/(m – q)) is F-distributed on (1, m – q) degrees of freedom, where SSR1 is the original model, SSR2 is the extended model with extra parameter µ (SSR2 < SSR1), m is the number of independent frequency measurements used in the fits (m = 186), and q = 4 is the number of parameters in the larger model. Measures of relative support for the GH and SM models were obtained with the Akaike information criterion (AIC), using the definition AIC = m log (SSR/m) + 2(K + 1) where K is the number of parameters in the model (26).


   Results
Top
 Abstract
 Introduction
 Materials and Methods
 Results
Discussion
 Disclosures
 References
 
Lymphopenia and Ag induce distinct programs of cell division and differentiation in F5 T cells

A mouse model extensively used in our laboratory for studying the processes that govern homeostatic survival and proliferative responses is the F5 TCR transgenic mouse strain that expresses a class I restricted TCR specific for a peptide of influenza nucleoprotein (27). F5 T cells make relatively weak proliferative responses under conditions of T cell deficiency (12) as compared with other TCR transgenic strains (14). However, to directly compare the proliferative response of F5 T cells in lymphopenia with that induced by Ag, we transferred F5 T cells labeled with the cell dye CFSE into Rag1–/– T cell-deficient hosts either in the presence or absence of influenza (Flu) virus. At various days post transfer, cells were recovered from host mice and analyzed by FACS. In the absence of Flu virus, T cells underwent a sustained but slow process of cell division. In hosts additionally challenged with flu virus, F5 T cells underwent a rapid and robust proliferation with most cells losing CFSE dye by day 7 (Fig. 1A). In fact, in lymphopenic hosts it took approximately 2 wk for F5 T cells to proliferate to a similar degree as observed in only 3 days in the presence of Ag (Fig. 1B). Furthermore, F5 T cells failed to up-regulate activation markers such as CD44 compared with the same cells challenged with Flu virus (Fig. 1B) and failed to elicit any effector function when challenged with Ag pulse targets in vivo (Fig. 1C).


Figure 1
View larger version (28K):
[in this window]
[in a new window]

  		FIGURE 1. F5 T cells maintain their naive state following lymphopenia induce proliferation. CD8+ T cells from F5 Rag1–/– mice were labeled with CFSE and transferred i.v. to Rag1–/– recipients (2 x 106/mouse) with or without influenza virus. At days 3, 7, and 14, splenocytes were recovered from recipient mice and analyzed by FACS for expression of CD8, TCR, CD44, and CFSE labeling. A, Histograms show CFSE labeling of CD8+ TCRhigh cells 3 and 7 days post transfer, either in the absence (top) or presence (bottom) of challenge with influenza virus. B, Dot plots show CD44 expression vs CFSE labeling of F5 T cells either 3 days after transfer and influenza challenge, or 14 days post transfer in the absence of influenza challenge. C, 1.5 x 107 F5 T cells were transferred to Rag1–/– hosts or 2 x 106 F5 T cells were transferred to Rag1–/– hosts and challenged with flu. Eleven days later, killing capacity of F5 T cells in these mice was determined by injecting hosts with a mixture of target splenocyte populations pulsed with varying concentrations of NP68 peptide. Dot plots show the frequency of F5 T cells in the lymph nodes of recipient mice. The graph shows the percentage killing of targets by F5 T cells undergo homeostatic ({circ}) or Ag-induced (•) proliferation. D, CD8 T cells were purified from WT mice, labeled with CFSE and transferred to Rag1–/– hosts. At days 6 and 13, lymph node cells from recipients were stained for CD8, CD44, TCR and analyzed by FACS. Dot plots show CFSE vs CD44 expression by CD8+TCRhigh cells. Percentages indicate frequency of CD44high and CD44low cells. Histograms show CFSE labeling of CD44high and CD44low populations from the dot plots. Numbers on CFSE histograms indicate mean division within the precursor population. Percentage of input indicates the proportion of the precursor population that gave rise to the corresponding CD44high and CD44low populations on the dot plots as determined by current frequency and CFSE labeling.

 
Because of the wide variation in lymphopenic proliferative responses reported in different TCR transgenic systems, we more closely examined homeostatic proliferation of WT CD8+ T cells to collectively quantify the variety of responses made within a polyclonal repertoire. Purified CD8+ T cells from WT mice were labeled with CFSE and transferred into Rag1–/– hosts. At 6 and 13 days post transfer, cells were recovered and the lymphopenia-induced proliferation assessed by FACS. By day 13, it appeared the majority of cells recovered were CFSE negative and CD44high (Fig. 1D) as described previously (9, 13, 28). However, a significant proportion of T cells were still labeled with varying levels of CFSE and remained CD44low. Examination of responses at day 6 allowed more detailed quantitative analysis because all cells were still CFSE positive. More than 40% of T cells had up-regulated CD44 at this stage and had undergone more divisions than the CD44low population. However, using the CFSE profile to calculate the precursor frequency (see Materials and Methods) revealed that the CD44high population arose from only 17% of the precursor population. The remaining 83% of the precursor pool remained CD44low and divided more slowly or not at all. In fact, 37% of the injected T cells were still undivided by day 6. Therefore, it appears that the abundance of the CD44high population at day 13 reflects the extensive proliferation of a small proportion of the starting population rather than a majority response by the entire initial cohort. These data suggest that the ability of T cells to undergo extensive proliferation and phenotypic conversion is a feature of a relatively small proportion of the normal WT repertoire. Rather, the majority of CD8 T cells divided slowly, or not at all, without up-regulating activation markers. Therefore, the slow division rate of F5 TCR transgenic T cells in Rag1–/– hosts closely resembles the slow dividing population of WT CD8 T cells, further highlighting the suitability of F5 T cells for the present analysis.

Quantifying the F5 T cell response to lymphopenia

F5 T cells proliferate in response to lymphopenia in a manner quite distinct from that induced by cognate Ag (Fig. 1A). Previous studies have demonstrated that T cell stimulation with cognate Ag results in the induction of a predetermined program of cell division with distinct characteristics, such as time to first division and subsequent interdivisional durations. To gain an insight into the cell cycle regulation controlling homeostatic cell division and how it compares to that described following T cell activation, we aimed to use models to describe the cell division processes quantitatively. To do this, we required a precise experimental description of lymphopenia-induced proliferation by F5 T cells to underpin any modeling. Therefore, we first attempted to measure the F5 T cell response to lymphopenia in detail.

F5 T cells were labeled with CFSE and transferred into T cell-deficient Rag1–/– hosts. At various time points, cohorts of mice were taken and the proliferative and expansive behavior of the F5 T cells determined by cellular enumeration in lymph nodes and spleen and analysis of CFSE labeling by FACS. Over the duration of the experiments, F5 T cells were seen to undergo steady progressive divisions (Fig. 2A). Calculating the mean number of divisions undergone revealed a brief lag followed by a near linear increase in mean division with time corresponding to roughly exponential growth (Fig. 2B), confirmed by measurement of absolute cell numbers (Fig. 2C). The F5 T cell precursor number, calculated by removing the effects of expansion predicted by the cells’ CFSE profile from the cell recovery, did not decline during the course of the experiment, suggesting that there was negligible cell death of F5 T cells in the lymphopenic hosts (Fig. 2C).


Figure 2
View larger version (21K):
[in this window]
[in a new window]

  		FIGURE 2. Kinetics of F5 T cells homeostatic proliferation. CD8+ T cells from F5 Rag1–/– mice were labeled with CFSE and transferred to Rag1–/– hosts (106/mouse). At different time points, lymph nodes were recovered from recipient mice and analyzed by FACS for expression of CD8, TCR, and CFSE labeling. A, Histograms show CFSE labeling of CD8+TCRhigh cell at the days indicated. B, The line graphs show the mean divisions by CD8+TCRhigh cells in lymph node at different days post transfer (left) and the population expansion predicted by the profile of cell divisions revealed by the CFSE (right). C, In a similar experiment described in A, cell recoveries and CFSE labeling of F5 T cells transferred to Rag1–/– hosts (n = 5) was determined at different times post transfer. The graph shows total cell recoveries (•) and cell recoveries of the precursor population that excludes the expansive effects of cell division ({circ}). D, CD8+ T cells from F5 Rag1–/– mice were labeled with CFSE and transferred to Rag1–/– hosts at a range of doses. The graph shows the mean divisions of CFSE-labeled F5 T cells at day 14 after transfer of the cell doses indicated. E, CFSE-labeled F5 T cells (2 x 106/mouse) were transferred to either Il7+/+ Rag1–/– or Il7+/–Rag1–/– recipients. Two, 7, and 13 days later, lymph node cells were harvested from groups of mice and analyzed by FACS for expression of CD8, TCR, and CFSE labeling. The graph shows mean division of F5 T cells with time in Il7+/+ Rag1–/– (filled squares) or Il7+/–Rag1–/– (half filled squares) hosts. Data are representative of at least three experiments.

 
We next assessed the sensitivity of the homeostatic proliferative response to host environment. First, we compared the proliferative response when different numbers of F5 T cells were transferred to Rag1–/– recipients. Hosts were injected with cell doses between 5 x 105 and 1.5 x 107 CFSE-labeled F5 T cells and cell division assessed 14 days post transfer. F5 T cell proliferation as measured by mean division number was inversely proportional to inoculum size and the response was indeed exquisitely sensitive to initial cell dose, with reproducible differences observed between as little as 2-fold variations in initial cell dose (Fig. 2D). Since IL-7 is critically required for homeostatic cell division, we asked whether varying IL-7 availability would have a quantitative effect on F5 T cell proliferation. We tested this by transferring CFSE-labeled F5 T cells into control Rag1–/– hosts or into Rag1–/– Il7+/– hosts that have only one functional Il7 allele. F5 T cells in Il7+/– hosts proliferated more slowly than in controls as measured by mean division number versus time (Fig. 2E), further illustrating that homeostatic proliferation was very sensitive to the availability of resources in the host.

Modeling the homeostatic proliferation of F5 T cells

To test different hypotheses for the regulation of LIP, we fitted a series of mathematical models of cell division to these time series data. For each model, we searched for values of the model parameters that gave predicted patterns of cell division over time that best fitted our experimental time course data. In all cases we assumed that cell death among the cohort of cells that survived the transfer was negligible. This seemed reasonable on biological grounds as the lymphopenic host is likely to present an abundance of T cell survival signals or resources, but this assumption was also validated by the observation that the precursor number calculated from cells recovered from spleen and lymph nodes was approximately constant during the first 14 days after transfer (Fig. 2C).

We attempted to describe the data with two classes of stochastic model. The formulation of the models and the fitting procedure are described in detail in Materials and Methods. The first class of model assumed that the mode of proliferation observed was analogous to the programmed proliferation of Ag-stimulated T cells observed in vitro, a model first studied quantitatively by Gett and Hodgkin (18) and extended in further studies (19, 21). We refer to it here as the GH model. To apply this model in the context of lymphopenia-induced proliferation in vivo we assume cells receive a proliferative stimulus from their environment soon after transfer to the lymphopenic host. For each cell, the time between receipt of this stimulus and first mitosis is assumed to be a random variable drawn from a left-bounded unimodal distribution. We used log-normal, gamma, and Weibull distributions as candidates. Cells that have divided once then embark on a program of divisions each of duration {Delta} before returning to a quiescent state (Fig. 3A).


Figure 3
View larger version (28K):
[in this window]
[in a new window]

  		FIGURE 3. Models of lymphopenia-induced proliferation of T cells. A model of asynchronous "programmed" T cell proliferation based on the GH model (18 ) (upper panel). Cells transferred to the lymphopenic host take a time to their first mitosis drawn from a probability distribution (shown schematically) and subsequently divide deterministically. Our model includes the additional assumption that division is not possible during a time interval T immediately following transfer. Two cells are illustrated here: cell 1 undergoes its first division at time t1, cell 2 at a later time t2. Both continue to divide with each subsequent division taking a fixed time {Delta}. An alternative model of homeostatic proliferation, based on the stochastic SM model (24 ) (lower panel). T cells in a lymphopenic environment receive signals that induce cell division. However, not all cells divide at once. As in the model above, entry into division (here denoted B phase) is a process of chance, and in this model within a given time interval all cells have an equal probability of receiving the necessary signals to stimulate division. However, cells that receive the necessary stimulus only divide once (taking a time {Delta}) before returning to the resting state (A phase). In this figure, we illustrate a single cell dividing, but recruitment into B phase is continuous and at any given moment, many cells may progress through a single division. The process is memoryless in the sense that cells that have divided have the same chance as other resting T cells of receiving further division signals.

 
The free parameters in this model were the mean and variance specifying the probability distribution of times to first division, the division time {Delta}, and a delay before any cell could divide at all (T). The Weibull distribution provided the best fit of the three candidates ({Delta}AIC values; log-normal-Weibull = 75; gamma-Weibull = 35). The best fit parameters were as follows: distribution shape parameter = 2.26, scale parameter = 8.27 (mean time to first mitosis = 7.33 days, SD = 3.43 days), division time {Delta} = 2.88 days, lag time T = 0. On comparing the time course of cell division predicted by this GH model to the response observed experimentally, the model appeared to provide a very poor description of the data (Fig. 4A), both in terms of the kinetics of mean division for the whole population and the predicted profiles of cell divisions at the various time points.


Figure 4
View larger version (34K):
[in this window]
[in a new window]

  		FIGURE 4. Models of lymphopenia-induced proliferation. The upper graphs show the mean and variance of division number in each animal (solid triangles); these quantities averaged over independent experiments at each time point (gray lines); and the best-fit model predictions of the mean and variance of division number (black lines). Histograms indicating the proportion of F5 T cells that have undergone different numbers of divisions at the days indicated. Gray bars show the observed experimental profiles, each bar corresponding to one CFSE peak and with height equal to the proportion of cells observed in each division (averaged over several independent experiments and not adjusted for expansion). Black bars indicate the corresponding model predictions using the best-fit parameters. In A, we show the best fit from a programmed divisions model, a variant of the GH model in which times to first division are Weibull-distributed and subsequent divisions are deterministic, each with duration {Delta}. B and C, Variants of the SM model. In B, we assumed constant mean rate of entry into division ({lambda}). An extended SM model (C) assumed an exponential decline in {lambda} with time as the cells divide to fill the host, and provided a significantly better fit.

 
The second class of model assumed that cells circulate and compete for homeostatic division signals such that a given cell has a constant probability of entering the cell cycle in any short time interval and dividing once. We used a version of the canonical SM model of the cell cycle (24), illustrated schematically in Fig. 3B, in which cells spend exponentially distributed times in a quiescent A phase (corresponding approximately to the G0/G1 states of the cell cycle) and then progress through a B phase (S, G2, and M) before dividing and returning to the A phase. The B phase was taken to be of fixed duration. The rate of transition from A to B phase, i.e., the rate at which T cells are triggered into cell division, is represented by the term {lambda}, and duration of the B phase by {Delta}. The rate {lambda} is defined such that the probability of any given cell entering B phase in a short time interval {delta}t is simply {lambda}{delta}t. We also estimated a lag time T after transfer during which no entry into B phase is possible.

The assumption of a constant mean rate of entry into division ({lambda}) after the lag time T gave a reasonable fit to the data (Fig. 4B). This model predicts a linear increase in the mean and variance of division number with time after a brief transient. The best-fit parameter estimates with 95% confidence intervals were {lambda} = 0.210 day–1 (0.157, 0.266), {Delta} = 6.65 h (3.29, 18.8), and T = 2.03 days (0.172, 2.72). Therefore we estimate the mean duration of the A phase, {lambda}–1, to be around 4.8 days, and the average time between divisions for each cell ({lambda}–1 + {Delta}) as just over 5 days. The trend in the mean division number averaged over all animals at each time point (Fig. 4) suggested a progressive slowing of the division rate with time. To investigate this possibility we extended the model to allow a time-dependent change in division rate, defined by an additional parameter µ such that {lambda} = {lambda}0 exp(–µt). This improved the fit significantly (partial F-test, p < 10–4; {Delta}AIC = 14; Fig. 4C). Best-fit parameter estimates were {lambda}0 = 0.455 day–1 (0.228, 3.58), µ = 0.115 day–1 (0.020, 0.683), {Delta} = 6.19 h (2.26, 15.1), and T = 2.44 days (1.99, 2.90). The slowing of the division rate means that at day 3 the mean interdivision time was 3.4 days, increasing to 11.3 days at day 14.

Both the simple and modified SM model provided a significantly better fit to the data than the best fitting "programmed divisions" GH model ({Delta}AIC values; GH – basic SM model = 214; GH – modified SM model = 227). Despite the poor fit of the GH model, however, we clearly cannot rule out this model with other distributions for the times to first division. In particular the assumption that all cells receive their first division stimulus at the same time, as is likely in in vitro Ag-driven proliferation assays, may be questioned in vivo. Nevertheless we note that the gradient of the curve of mean division number with time is the inverse of the average time between divisions, which is roughly 5 days for the linear fit predicted by the simple SM model (the quantity {lambda}–1 + {Delta}) and between 3 and 11 days for the extended SM model with slowing division. Irrespective of the precise form of the distribution of times to first division, the GH model predicts that a plot of mean division number versus time tends to a straight line with slope 1/{Delta} after all cells have entered the proliferative program and are dividing asynchronously but uniformly with constant division time {Delta}. Crucially, the slope we observe indicates an interdivision >10-fold slower than that observed in Ag-driven T cell responses (18) and such slow proliferation is unprecedented in programmed responses. In summary, the SM model is a good description of the data, with even the more parsimonious three-parameter version describing proliferation better than the GH autopilot model.

Testing the biological predictions of the mathematical model in vivo

Although the SM-based model of stochastic cell divisions appears to provide the best description of the observed response by F5 T cells to lymphopenia, this observation neither proves the model is correct nor indeed excludes the possibility that other models might equally well or better describe the data. The model did, however, make several specific predictions about the nature of the F5 T cell response to lymphopenia. Therefore, we sought to further validate the model by directly testing its predictions experimentally.

A key biological prediction of the model was that TCR stimulation by self-peptide MHC should induce independent, single stochastic cell divisions. That being the case, ongoing homeostatic cell division should rely on constant signals from the lymphopenic environment to maintain continued cell division. Reversal of lymphopenia should, therefore, bring about a cessation of cell division, which would not be the case if the divisions were programmed or on autopilot. To test this directly, we injected groups of Rag1–/– mice with CFSE-labeled F5 T cells. Three days later, when cell division of F5 T cells had already started and was at its highest rate, we injected cohorts of mice with very high doses of WT T cells (108/mouse) to quickly reverse the lymphopenia. Strikingly, such treatment abruptly halted the observed cell division of F5 T cells in these hosts, whereas the same cells in untreated Rag1–/– hosts continued to divide (Fig. 5A). Although F5 T cells had divided when examined 2 days later in treated hosts, they had undergone fewer divisions than F5 T cells from untreated control hosts and there was no further cell division detected in the treated hosts up to 17 days later. Only 27% of cells in treated hosts underwent any cell division, compared with 83% in controls. Were a deterministic program of division at work, then cells triggered into division before treatment would be expected to complete their program of divisions. Rather, in treated mice, the vast majority of the dividing population (80%) underwent only a single division.


Figure 5
View larger version (25K):
[in this window]
[in a new window]

  		FIGURE 5. Validation of predictions made by the mathematical model. A, F5 T cells were labeled with CFSE and injected (106/mouse) into Rag1–/– hosts. At day 3, one group of mice was injected with 108 WT T cells. Mice were bled at days 3, 5, 6, and 11 and expression of CD8 and CFSE labeling analyzed by FACS. The graph shows the mean divisions of F5 T cells in the two different groups at the days indicated. B, Rag1 –/– hosts were injected with 106 F5 T cells. Two weeks later, CFSE-labeled F5 T cells (106/mouse) were injected into the pretreated hosts or empty Rag1–/– mice as control. Groups of these mice were taken at different times and the mean division of CFSE-labeled F5 T cells determined. The graph shows the mean divisions with time of CFSE-labeled F5 T cells in empty Rag1–/– controls (•) and in Rag1–/– mice pretreated with unlabeled F5 T cells (^). Data are representative of three independent experiments. C, F5 T cells were injected (2 x 106/mouse) into either Rag1–/– or C57BL/6 Ly5.1 WT hosts. At days 1, 2, and 3 post transfer, cells were recovered and labeled for CD8, TCR, Ly5.2, and CD5. Histograms are of FSc (top row) and CD5 (bottom row) for CD8+ Ly5.2+ TCRhigh gated F5 T cells from either Rag1–/– hosts (solid lines), WT hosts (broken line) or from F5 control mice (gray filled). Data are representative of two independent experiments with 4 mice per group.

 
Although the simple SM model described the data well (Fig. 4B), introducing a time-dependent reduction in division rate resulted in a significantly better fit (Fig. 4C). The slowing in division rate indicated by this analysis was also supported by our observation that F5 T cell homeostatic division is very sensitive to cell numbers in the host environment (Fig. 2D). It seems reasonable that the rate of cell division should slow as the T cells expand in number, either due to the effects of competition or adaptation to the host. This slowing was not always evident in longer time courses because at later time points many cells had become CFSE negative, and mean cell divisions could not be accurately determined. To overcome this limitation and examine the cell kinetics of expansion over longer time periods, we measured the division rate by injecting hosts first with unlabeled F5 T cells and then transferring CFSE-labeled F5 sensor cells 2 wk later and measuring their cell division over time compared with the same cells in untreated Rag1–/– hosts. As the data show, F5 T cells injected into the pretreated hosts proliferated at a significantly reduced rate compared with cells transferred to empty hosts (Fig. 5B). The division rate also further reduced with time in both hosts.

Finally, another prediction of the model was that there is a lag phase of ~2 days before cells started to respond to lymphopenia. To investigate whether there was evidence of such a delay in responsiveness of F5 T cells to the lymphopenic environment, we assessed cell size and CD5 expression by F5 T cells following transfer to lymphopenic hosts. Previous studies have shown that environmental signals in lymphopenia have trophic affects on T cells (29), resulting in increases in cell size, while the level of CD5 expression by peripheral T cells has been shown to be positively regulated by contact with self-peptide-MHC complexes (5, 30). Upon transfer to Rag1–/– hosts, F5 T cells did indeed increase their cell size and up-regulated CD5 expression compared with the same cells transferred to C57Bl6 controls, indicative of enhanced contact with self-peptide-MHC that is required to induce LIP (Fig. 5C). However, these changes in F5 T cell phenotype were not evident until 2 days post transfer and not maximal until day 3. By 24 h post transfer, the phenotype of F5 T cells in lymphopenic Rag1–/– hosts was almost indistinguishable from the same cells in replete C57BL/6 controls.


   Discussion
Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
Disclosures
 References
 
Cell division induced in T cells by cognate Ag or by lymphopenia both depend on TCR signaling but result in distinct patterns of proliferation and, for many cells, differences in development of effector function. Previous studies have successfully used mathematical modeling to describe T responses to cognate Ag and greatly facilitated our understanding of the proliferative control involved. Here, we used a mathematical modeling approach to better understand the program of cell division that is induced in lymphopenia. In contrast to the autopilot program of deterministic cell divisions induced following stimulation by cognate Ag, we found that a model in which T cells underwent independent single stochastic divisions better described the F5 T cell response to lymphopenia.

Variants of the SM stochastic single divisions model have been used by other authors to describe turnover of both T (31, 32) and B (33) cells and implicitly held it to be a good description of their data but did not formally compare alternative proliferation mechanisms. Our successful application of the SM-based model of single stochastic divisions (Fig. 3), however, still does not prove it is correct or exclude other possible models. What did provide strong support for the SM model was the predictions it made that were successfully validated experimentally and that some of these predictions were incompatible with an autopilot model. Reversing the lymphopenia at the peak of the proliferative response had a profound inhibitory affect on the response, consistent with the SM model in which cells underwent independent single stochastic divisions and that additional divisions required further stimulus from the lymphopenia. Were cells stimulated into a deterministic program of divisions, they would have already received their proliferative stimulus and would have continued upon the deterministic program of division that could not be reversed by later removal of the inducing stimulus, i.e., by reversing lymphopenia. In contrast, this is certainly the case for activation of CD8+ T cells by cognate Ag that requires as little as 4 h stimulation to evoke a full proliferative response (34).

Another prediction made by the SM model that we tested was that the division rate slowed with time. Both models were compatible with a strictly linear increase in mean division that was close to what was observed experimentally. However, the fit of the SM model was improved by introducing a time dependent reduction in rate of entry of cells into division. Closer experimental scrutiny revealed that lymphopenia-induced proliferation of F5 T cells did indeed slow with time (Fig. 5). The magnitude of the F5 T cell response to lymphopenia was exquisitely sensitive to the lymphopenic environment, such that altered levels of IL-7 or even increasing T cell competition by varying T cell numbers was sufficient to have appreciable impact on proliferation. Therefore, it seems that the strength of the environmental signals that induce T cell proliferation in lymphopenia are subject to dynamic change as a consequence of T cell expansion, resulting in increasing cellular competition for key resources such as IL-7 and self-peptide MHC. Requiring T cells to re-audition after single divisions for further lymphopenia-induced divisions, as described in the model, also explains how the proliferation can be so finely tuned to relatively subtle changes in the competitive environment. The SM model also predicted that F5 T cells required an initial 24–48 h period of exposure to lymphopenic environment before undergoing LIP responses, a prediction also validated experimentally by the kinetics of phenotypic changes observed in F5 T cells. Such a delay may allow for transient, localized fluctuations in microenvironment that might otherwise stimulate LIP but not in fact necessitate a homeostatic response.

Although the GH model describes Ag-induced proliferation well, our study required an entirely distinct model of proliferation to describe lymphopenia-induced proliferation and yet both responses are triggered through TCR stimulation. This raises the question of how it is possible for signals from the same receptor to elicit such distinct programs of cell division? One factor might by that the TCR signals required for induction of lymphopenia-induced proliferation depend on self-peptide MHC recognition which are likely to be low avidity interactions compared with cognate Ag. However, even low affinity TCR ligands can induce autopilot proliferation, just requiring a longer duration of stimulus (34). Another possibility may be the differential requirements for IL-7 and IL-2 for lymphopenia vs Ag-induced proliferation. T cell responses to cognate Ag have no apparent requirement for IL-7, either in vivo (17) or in vitro (B. Seddon, unpublished data). Indeed, IL-7R expression is largely lost following activation (17, 35). A key step in the Ag-induced program of proliferation is the induction of IL-2 and its receptor, following TCR stimulation. This autocrine axis plays an important role in promoting cell division and survival following T cell activation. In contrast, lymphopenia-induced proliferation is highly dependent on IL-7 (17, 36, 37). Like IL-2, IL-7 is also an important T cell survival factor (17, 38) and has also been described to affect cell cycle by its effects on expression of negative regulators such as p27kip (39) and FOXO proteins (40). Both IL-2 and IL-7 are members of the common {gamma}-chain ({gamma}c) family of cytokines, and consequently, use similar signaling pathways to mediate their biological properties, such as Stat5 (41) and PI3K (42). Therefore, IL-2 and IL-7 may play parallel biochemical roles in supporting survival and proliferation of T cells during Ag and lymphopenia-induced proliferation, respectively, even if their administration is different. Also, it is interesting to note that activated T cells do not express IL-7R, while cells undergoing lymphopenia-induced proliferation do not express IL-2R.

Crucial differences in the biology of IL-2 and IL-7 may ultimately account for the fundamentally different programs of cell division they support. Following T cell activation, induction of IL-2 and IL-2R forms part of an autocrine loop that plays a key role in the burst of proliferation T cells undergo following antigenic stimulation, and it is therefore possible that it is the maintenance of just such a loop that underlies the deterministic program of divisions that is characteristic of Ag-induced responses. In contrast, enhanced self-peptide MHC recognition and increased bioavailability of IL-7 in lymphopenia are the key events that trigger some T cells into cell division. However, since IL-7 is made by stromal cells within the lymphoid compartment (43) and not by T cells and all T cells express IL-7R, dividing T cells are therefore in equal competition with nondividing T cells for continued stimulation from IL-7 to support continued division. Since T cells cannot make IL-7, there is no autocrine loop that might permit a deterministic burst of cell division. Demanding that T cells repeatedly audition for further lymphopenia-induced cell division permits the homeostatic responses to be highly reactive to the current size of the T cell compartment. In conclusion, the SM model of cell division not only provides a remarkably accurate description of lymphopenia-induced proliferation by F5 T cells but also has many of the features required for dynamic homeostatic regulation of T cell numbers.


   Acknowledgment
 
We thank Roslyn Kemp for critical reading of the manuscript.


   Disclosures
Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Disclosures
References
 
The authors have no financial conflict of interest.


   Footnotes
 
The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

1 This work was supported by the Medical Research Council (U.K.) and the National Institutes of Health. Back

2 Address correspondence and reprint requests to Dr. B. Seddon, Division of Immune Cell Biology, National Institute for Medical Research, The Ridgeway, London NW7 1AA, U.K. E-mail address: bseddon{at}nimr.mrc.ac.uk Back

3 Abbreviations used in this paper: LIP, lymphopenia-induced proliferation; flu, influenza; SM, Smith-Martin; GH, Gett-Hodgkin; WT, wild type. Back

Received for publication July 26, 2007. Accepted for publication November 20, 2007.


   References
Top
 Abstract
 Introduction
 Materials and Methods
 Results
 Discussion
 Disclosures
 References
 

  1. Freitas, A. A., B. Rocha. 2000. Population biology of lymphocytes: the flight for survival. Annu. Rev. Immunol. 18: 83-111. [Medline]
  2. Brocker, T.. 1997. Survival of mature CD4 T lymphocytes is dependent on major histocompatibility complex class II-expressing dendritic cells. J. Exp. Med. 186: 1223-1232. [Abstract/Free Full Text]
  3. Kirberg, J., A. Berns, H. von Boehmer. 1997. Peripheral T cell survival requires continual ligation of the T cell receptor to major histocompatibility complex-encoded molecules. J. Exp. Med. 186: 1269-1275. [Abstract/Free Full Text]
  4. Rooke, R., C. Waltzinger, C. Benoist, D. Mathis. 1997. Targeted complementation of MHC class II deficiency by intrathymic delivery of recombinant adenoviruses. Immunity 7: 123-134. [Medline]
  5. Seddon, B., R. Zamoyska. 2002. TCR signals mediated by Src family kinases are essential for the survival of naive T cells. J. Immunol. 169: 2997-3005. [Abstract/Free Full Text]
  6. Tanchot, C., F. A. Lemonnier, B. Perarnau, A. A. Freitas, B. Rocha. 1997. Differential requirements for survival and proliferation of CD8 naive or memory T cells. Science 276: 2057-2062. [Abstract/Free Full Text]
  7. Viret, C., F. S. Wong, C. A. Janeway, Jr. 1999. Designing and maintaining the mature TCR repertoire: the continuum of self-peptide:self-MHC complex recognition. Immunity 10: 559-568. [Medline]
  8. Witherden, D., N. van Oers, C. Waltzinger, A. Weiss, C. Benoist, D. Mathis. 2000. Tetracycline-controllable selection of CD4+ T cells: half-life and survival signals in the absence of major histocompatibility complex class II molecules. J. Exp. Med. 191: 355-364. [Abstract/Free Full Text]
  9. Ernst, B., D. S. Lee, J. M. Chang, J. Sprent, C. D. Surh. 1999. The peptide ligands mediating positive selection in the thymus control T cell survival and homeostatic proliferation in the periphery. Immunity 11: 173-181. [Medline]
  10. Goldrath, A. W., M. J. Bevan. 1999. Low-affinity ligands for the TCR drive proliferation of mature CD8+ T cells in lymphopenic hosts. Immunity 11: 183-190. [Medline]
  11. Kieper, W. C., S. C. Jameson. 1999. Homeostatic expansion and phenotypic conversion of naive T cells in response to self peptide/MHC ligands. Proc. Natl. Acad. Sci. USA 96: 13306-13311. [Abstract/Free Full Text]
  12. Ferreira, C., T. Barthlott, S. Garcia, R. Zamoyska, B. Stockinger. 2000. Differential maintenance of naive and CD8 T cells in normal and T cell receptor transgenic mice. J. Immunol. 165: 3689-3694. [Abstract/Free Full Text]
  13. Cho, B. K., V. P. Rao, Q. Ge, H. N. Eisen, J. Chen. 2000. Homeostasis-stimulated proliferation drives naive T cells to differentiate directly into memory T cells. J. Exp. Med. 192: 549-556. [Abstract/Free Full Text]
  14. Ge, Q., V. P. Rao, B. K. Cho, H. N. Eisen, J. Chen. 2001. Dependence of lymphopenia-induced T cell proliferation on the abundance of peptide/ MHC epitopes and strength of their interaction with T cell receptors. Proc. Natl. Acad. Sci. USA 98: 1728-1733. [Abstract/Free Full Text]
  15. Hamilton, S. E., M. C. Wolkers, S. P. Schoenberger, S. C. Jameson. 2006. The generation of protective memory-like CD8+ T cells during homeostatic proliferation requires CD4+ T cells. Nat. Immunol. 7: 475-481. [Medline]
  16. Goldrath, A. W., C. J. Luckey, R. Park, C. Benoist, D. Mathis. 2004. The molecular program induced in T cells undergoing homeostatic proliferation. Proc. Natl. Acad. Sci. USA 101: 16885-16890. [Abstract/Free Full Text]
  17. Schluns, K. S., W. C. Kieper, S. C. Jameson, L. Lefrancois. 2000. Interleukin-7 mediates the homeostasis of naive and memory CD8 T cells in vivo. Nat. Immunol. 1: 426-432. [Medline]
  18. Gett, A. V., P. D. Hodgkin. 2000. A cellular calculus for signal integration by T cells. Nat. Immunol. 1: 239-244. [Medline]
  19. Deenick, E. K., A. V. Gett, P. D. Hodgkin. 2003. Stochastic model of T cell proliferation: a calculus revealing IL-2 regulation of precursor frequencies, cell cycle time, and survival. J. Immunol. 170: 4963-4972. [Abstract/Free Full Text]
  20. Antia, R., C. T. Bergstrom, S. S. Pilyugin, S. M. Kaech, R. Ahmed. 2003. Models of CD8+ responses: 1. what is the antigen-independent proliferation program. J. Theor. Biol. 221: 585-598. [Medline]
  21. De Boer, R. J., V. V. Ganusov, D. Milutinovic, P. D. Hodgkin, A. S. Perelson. 2006. Estimating lymphocyte division and death Rates from CFSE data. Bull. Math. Biol. 68: 1011-1031. [Medline]
  22. Kaech, S. M., R. Ahmed. 2001. Memory CD8+ T cell differentiation: initial antigen encounter triggers a developmental program in naive cells. Nat. Immunol. 2: 415-422. [Medline]
  23. van Stipdonk, M. J., E. E. Lemmens, S. P. Schoenberger. 2001. Naive CTLs require a single brief period of antigenic stimulation for clonal expansion and differentiation. Nat. Immunol. 2: 423-429. [Medline]
  24. Smith, J. A., L. Martin. 1973. Do cells cycle?. Proc. Natl. Acad. Sci. USA 70: 1263-1267. [Abstract/Free Full Text]
  25. Davison, A. C., D. V. Hinkley. 1997. Bootstrap Methods and Their Applications Cambridge University Press, Cambridge, U.K.
  26. Burnham, K. P., D. R. Anderson. 2002. Model Selection and Multimodel Inference Springer, New York.
  27. Mamalaki, C., J. Elliott, T. Norton, N. Yannoutsos, A. R. Townsend, P. Chandler, E. Simpson, D. Kioussis. 1993. Positive and negative selection in transgenic mice expressing a T-cell receptor specific for influenza nucleoprotein and endogenous superantigen. Dev. Immunol. 3: 159-174. [Medline]
  28. Oehen, S., K. Brduscha-Riem. 1999. Naive cytotoxic T lymphocytes spontaneously acquire effector function in lymphocytopenic recipients: a pitfall for T cell memory studies?. Eur. J. Immunol. 29: 608-614. [Medline]
  29. Tanchot, C., A. Le Campion, B. Martin, S. Leaument, N. Dautigny, B. Lucas. 2002. Conversion of naive T cells to a memory-like phenotype in lymphopenic hosts is not related to a homeostatic mechanism that fills the peripheral naive T cell pool. J. Immunol. 168: 5042-5046. [Abstract/Free Full Text]
  30. Smith, K., B. Seddon, M. A. Purbhoo, R. Zamoyska, A. G. Fisher, M. Merkenschlager. 2001. Sensory adaptation in naive peripheral CD4 T cells. J. Exp. Med. 194: 1253-1261. [Abstract/Free Full Text]
  31. Ganusov, V. V., S. S. Pilyugin, R. J. de Boer, K. Murali-Krishna, R. Ahmed, R. Antia. 2005. Quantifying cell turnover using CFSE data. J. Immunol. Methods 298: 183-200. [Medline]
  32. Pilyugin, S. S., V. V. Ganusov, K. Murali-Krishna, R. Ahmed, R. Antia. 2003. The rescaling method for quantifying the turnover of cell populations. J. Theor. Biol. 225: 275-283. [Medline]
  33. Asquith, B., C. Debacq, A. Florins, N. Gillet, T. Sanchez-Alcaraz, A. Mosley, L. Willems. 2006. Quantifying lymphocyte kinetics in vivo using carboxyfluorescein diacetate succinimidyl ester (CFSE). Proc. Biol. Sci. 273: 1165-1171. [Abstract/Free Full Text]
  34. Auphan-Anezin, N., G. Verdeil, A. M. Schmitt-Verhulst. 2003. Distinct thresholds for CD8 T cell activation lead to functional heterogeneity: CD8 T cell priming can occur independently of cell division. J. Immunol. 170: 2442-2448. [Abstract/Free Full Text]
  35. Buentke, E., A. Mathiot, M. Tolaini, J. Di Santo, R. Zamoyska, B. Seddon. 2006. Do CD8 effector cells need IL-7R expression to become resting memory cells?. Blood 108: 1949-1956. [Abstract/Free Full Text]
  36. Seddon, B., R. Zamoyska. 2002. TCR and IL-7 receptor signals can operate independently or synergize to promote lymphopenia-induced expansion of naive T cells. J. Immunol. 169: 3752-3759. [Abstract/Free Full Text]
  37. Tan, J. T., E. Dudl, E. LeRoy, R. Murray, J. Sprent, K. I. Weinburg, C. D. Surh. 2001. IL-7 is critical for homeostatic proliferation and survival of naive T cells. Proc. Nat. Acad Sci. USA 98: 8732-8737. [Abstract/Free Full Text]
  38. Maraskovsky, E., M. Teepe, P. J. Morrissey, S. Braddy, R. E. Miller, D. H. Lynch, J. J. Peschon. 1996. Impaired survival and proliferation in IL-7 receptor-deficient peripheral T cells. J. Immunol. 157: 5315-5323. [Abstract]
  39. Li, W. Q., Q. Jiang, E. Aleem, P. Kaldis, A. R. Khaled, S. K. Durum. 2006. IL-7 promotes T cell proliferation through destabilization of p27Kip1. J. Exp. Med. 203: 573-582. [Abstract/Free Full Text]
  40. Riou, C., B. Yassine-Diab, J. Van grevenynghe, R. Somogyi, L. D. Greller, D. Gagnon, S. Gimmig, P. Wilkinson, Y. Shi, M. J. Cameron, et al 2007. Convergence of TCR and cytokine signaling leads to FOXO3a phosphorylation and drives the survival of CD4+ central memory T cells. J. Exp. Med. 204: 79-91. [Abstract/Free Full Text]
  41. Lin, J. X., W. J. Leonard. 2000. The role of Stat5a and Stat5b in signaling by IL-2 family cytokines. Oncogene 19: 2566-2576. [Medline]
  42. Rathmell, J. C., E. A. Farkash, W. Gao, C. B. Thompson. 2001. IL-7 enhances the survival and maintains the size of naive T cells. J. Immunol. 167: 6869-6876. [Abstract/Free Full Text]
  43. Mazzucchelli, R., S. K. Durum. 2007. Interleukin-7 receptor expression: intelligent design. Nat. Rev. Immunol. 7: 144-154. [Medline]



This article has been cited by other articles:


Home page
 BloodHome page
M. Saini, C. Pearson, and B. Seddon
Regulation of T cell-dendritic cell interactions by IL-7 governs T-cell activation and homeostasis
Blood, June 4, 2009; 113(23): 5793 - 5800.
[Abstract] [Full Text] [PDF]

Home page
 BloodHome page
I. Bains, R. Antia, R. Callard, and A. J. Yates
Quantifying the development of the peripheral naive CD4+ T-cell pool in humans
Blood, May 28, 2009; 113(22): 5480 - 5487.
[Abstract] [Full Text] [PDF]

This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow Request Permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Yates, A.
Right arrow Articles by Seddon, B.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Yates, A.
Right arrow Articles by Seddon, B.

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS