Mathematical modeling reveals the biological program regulating lymphopenia-induced proliferation

Quantifying cellular dynamics in mice using a novel fluorescent division reporter system

The dynamics of cell populations are frequently studied in vivo using pulse-chase DNA labeling techniques. When combined with mathematical models, the kinetic of label uptake and loss within a population of interest then allows one to estimate rates of cell production and turnover through death or onward differentiation. Here we explore an alternative method of quantifying cellular dynamics, using a cell fate-mapping mouse model in which dividing cells can be induced to constitutively express a fluorescent protein, using a Ki67 reporter construct. We use a pulse-chase approach with this reporter mouse system to measure the lifespans and division rates of naive CD4 and CD8 T cells using a variety of modeling approaches, and show that they are all consistent with estimates derived from other published methods. However we propose that to obtain unbiased parameter estimates and full measures of their uncertainty one should simultaneously model the timecourses of the frequencies of labeled cells within both the population of interest and its precursor. We conclude that Ki67 reporter mice provide a promising system for modeling cellular dynamics.

What's self got to do with it: Sources of heterogeneity among naive T cells

There is a long-standing assumption that naive CD4⁺ and CD8⁺ T cells are largely homogeneous populations despite the extraordinary diversity of their T cell receptors (TCR). The self-immunopeptidome plays a key role in the selection of the naive T cell repertoire in the thymus, and self-peptides are also an important driver of differences between individual naive T cells with regard to their subsequent functional contributions to an immune response. Accumulating evidence suggests that as early as the β-selection stage of T cell development, when only one of the recombined chains of the mature TCR is expressed, signaling thresholds may be established for positive selection of immature thymocytes. Stochastic encounters subsequently made with self-ligands during positive selection in the thymus imprint functional biases that a T cell will carry with it throughout its lifetime, although ongoing interactions with self in the periphery ensure a level of plasticity in the gene expression wiring of naive T cells. Identifying the sources of heterogeneity in the naive T cell population and which functional attributes of T cells can be modulated through post-thymic interventions versus those that are fixed during T cell development, could enable us to better select or generate T cells with particular traits to improve the efficacy of T cell therapies.

Effect of cellular aging on memory T-cell homeostasis

The fact that T-cell numbers remain relatively stable throughout life, and that T-cell proliferation rates increase during lymphopenia, has led to the consensus that T-cell numbers are regulated in a density-dependent manner. Competition for resources among memory T cells has been proposed to underlie this ‘homeostatic’ regulation. We first review how two classic models of resource competition affect the T-cell receptor (TCR) diversity of the memory T-cell pool. First, ‘global’ competition for cytokines leads to a skewed repertoire that tends to be dominated by the very first immune response. Second, additional ‘cognate’ competition for specific antigens results in a very diverse and stable memory T-cell pool, allowing every antigen to be remembered, which we therefore define as the ‘gold-standard’. Because there is limited evidence that memory T cells of the same specificity compete more strongly with each other than with memory T cells of different specificities, i.e., for ‘cognate’ competition, we investigate whether cellular aging could account for a similar level of TCR diversity. We define cellular aging as a declining cellular fitness due to reduced proliferation. We find that the gradual erosion of previous T-cell memories due to cellular aging allows for better establishment of novel memories and for a much higher level of TCR diversity compared to global competition. A small continual source (either from stem-cell-like memory T-cells or from naive T-cells due to repeated antigen exposure) improves the diversity of the memory T-cell pool, but remarkably, only in the cellular aging model. We further show that the presence of a source keeps the inflation of chronic memory responses in check by maintaining the immune memories to non-chronic antigens. We conclude that cellular aging along with a small source provides a novel and immunologically realistic mechanism to achieve and maintain the ‘gold-standard’ level of TCR diversity in the memory T-cell pool.

Towards a unified model of naive T cell dynamics across the lifespan

Naive CD4 and CD8 T cells are cornerstones of adaptive immunity, but the dynamics of their establishment early in life and how their kinetics change as they mature following release from the thymus are poorly understood. Further, due to the diverse signals implicated in naive T cell survival, it has been a long-held and conceptually attractive view that they are sustained by active homeostatic control as thymic activity wanes. Here we use multiple modelling and experimental approaches to identify a unified model of naive CD4 and CD8 T cell population dynamics in mice, across their lifespan. We infer that both subsets divide rarely, and progressively increase their survival capacity with cell age. Strikingly, this simple model is able to describe naive CD4 T cell dynamics throughout life. In contrast, we find that newly generated naive CD8 T cells are lost more rapidly during the first 3-4 weeks of life, likely due to increased recruitment into memory. We find no evidence for elevated division rates in neonates, or for feedback regulation of naive T cell numbers at any age. We show how confronting mathematical models with diverse datasets can reveal a quantitative and remarkably simple picture of naive T cell dynamics in mice from birth into old age.

T-cell dysregulation in COVID-19

T-cells play key roles in immunity to COVID-19 as well as the development of severe disease. T-cell immunity to COVID-19 is mediated through differentiated CD4⁺ T-cells and cytotoxic CD8⁺ T-cells, although their differentiation is often atypical and ambiguous in COVID-19 and single cell dynamics of key genes need to be characterized. Notably, T-cells are dysregulated in severe COVID-19 patients, although their molecular features are still yet to be fully revealed. Importantly, it is not clear which T-cell activities are beneficial and protective and which ones can contribute to the development of severe COVID-19. In this article, we examine the latest evidence and discuss the key features of T-cell responses in COVID-19, showing how T-cells are dysregulated in severe COVID-19 patients. Particularly, we highlight the impairment of FOXP3 induction in CD4⁺ T-cells and how the impaired FOXP3 expression can lead to the differentiation of abnormally activated (hyperactivated) T-cells and the dysregulated T-cell responses in severe patients. Furthermore, we characterise the feature of hyperactivated T-cells, showing their potential contribution to T-cell dysregulation and immune-mediated tissue destruction (immunopathology) in COVID-19.

Narcissistic T cells: reactivity to self makes a difference

It has been appreciated for more than three decades that the interactions between the T-cell antigen receptor and self-antigens are the major determinants of the cell fates of developing thymocytes and the establishment of central tolerance. However, recent evidence shows that the level of self-reactivity substantially contributes to fate choices of positively selected mature T cells in homeostasis, as well as during immune responses. This implies that individual clones of peripheral T cells are predisposed to specific functional properties based on the self-reactivity of their antigen receptors. Overall, the relative difference in the self-reactivity among peripheral T cells is an important factor contributing to the diversity of T-cell responses to foreign antigens.

The natural history of naive T cells from birth to maturity

Generating and maintaining a diverse repertoire of naive T cells is essential for protection against pathogens, and developing a mechanistic and quantitative description of the processes involved lies at the heart of our understanding of vertebrate immunity. Here, we review the biology of naive T cells from birth to maturity and outline how the integration of mathematical models and experiments has helped us to develop a full picture of their life histories.

Age is not just a number: Naive T cells increase their ability to persist in the circulation over time

The processes regulating peripheral naive T-cell numbers and clonal diversity remain poorly understood. Conceptually, homeostatic mechanisms must fall into the broad categories of neutral (simple random birth–death models), competition (regulation of cell numbers through quorum-sensing, perhaps via limiting shared resources), adaptation (involving cell-intrinsic changes in homeostatic fitness, defined as net growth rate over time), or selection (involving the loss or outgrowth of cell populations deriving from intercellular variation in fitness). There may also be stably maintained heterogeneity within the naive T-cell pool. To distinguish between these mechanisms, we confront very general models of these processes with an array of experimental data, both new and published. While reduced competition for homeostatic stimuli may impact cell survival or proliferation in neonates or under moderate to severe lymphopenia, we show that the only mechanism capable of explaining multiple, independent experimental studies of naive CD4⁺ and CD8⁺ T-cell homeostasis in mice from young adulthood into old age is one of adaptation, in which cells act independently and accrue a survival or proliferative advantage continuously with their post-thymic age. However, aged naive T cells may also be functionally impaired, and so the accumulation of older cells via ‘conditioning through experience’ may contribute to reduced immune responsiveness in the elderly.

The body maintains large populations of naive T cells, a type of white blood cell that is able to respond specifically to pathogens. This arsenal is essential for our capacity to fight novel infections throughout our lifespan, and their numbers remain quite stable despite a gradual decline in the production of new naive T cells as we age. However, the mechanisms that underlie this stability are not well understood. In this study, we address this problem by testing a variety of potential mechanisms, each framed as a mathematical model, against multiple datasets obtained from experiments performed in mice. Our analysis supports a mechanism by which naïve T cells gradually increase their ability to survive the longer they reside in the circulation. Paradoxically, however, naïve T cells may also lose their ability to respond effectively to infections as they age. Together, these processes may drive the accumulation of older, functionally impaired T cells, potentially at the expense of younger and more immunologically potent cells, as we age.

Predicting CD4 T-Cell Reconstitution Following Pediatric Hematopoietic Stem Cell Transplantation

Hematopoietic stem cell transplantation (HSCT) is an increasingly common treatment for children with a range of hematological disorders. Conditioning with cytotoxic chemotherapy and total body irradiation leaves patients severely immunocompromised. T‐cell reconstitution can take several years due to delayed restoration of thymic output. Understanding T‐cell reconstitution in children is complicated by normal immune system maturation, heterogeneous diagnoses, and sparse uneven sampling due to the long time spans involved. We describe here a mechanistic mathematical model for CD4 T‐cell immune reconstitution following pediatric transplantation. Including relevant biology and using mixed‐effects modeling allowed the factors affecting reconstitution to be identified. Bayesian predictions for the long‐term reconstitution trajectories of individual children were then obtained using early post‐transplant data. The model was developed using data from 288 children; its predictive ability validated on data from a further 75 children, with long‐term reconstitution predicted accurately in 81% of the patients.

Memory CD4 T cell subsets are kinetically heterogeneous and replenished from naive T cells at high levels

Characterising the longevity of immunological memory requires establishing the rules underlying the renewal and death of peripheral T cells. However, we lack knowledge of the population structure and how self-renewal and de novo influx contribute to the maintenance of memory compartments. Here, we characterise the kinetics and structure of murine CD4 T cell memory subsets by measuring the rates of influx of new cells and using detailed timecourses of DNA labelling that also distinguish the behaviour of recently divided and quiescent cells. We find that both effector and central memory CD4 T cells comprise subpopulations with highly divergent rates of turnover, and show that inflows of new cells sourced from the naive pool strongly impact estimates of memory cell lifetimes and division rates. We also demonstrate that the maintenance of CD4 T cell memory subsets in healthy mice is unexpectedly and strikingly reliant on this replenishment.

Temporal fate mapping reveals age-linked heterogeneity in naive T lymphocytes in mice

Understanding how our T-cell compartments are maintained requires knowledge of their population dynamics, which are typically quantified over days to weeks using the administration of labels incorporated into the DNA of dividing cells. These studies present snapshots of homeostatic dynamics and have suggested that lymphocyte populations are heterogeneous with respect to rates of division and/or death, although resolving the details of such heterogeneity is problematic. Here we present a method of studying the population dynamics of T cells in mice over timescales of months to years that reveals heterogeneity in rates of division and death with respect to the age of the host at the time of thymic export. We use the transplant conditioning drug busulfan to ablate hematopoetic stem cells in young mice but leave the peripheral lymphocyte compartments intact. Following their reconstitution with congenically labeled (donor) bone marrow, we followed the dilution of peripheral host T cells by donor-derived lymphocytes for a year after treatment. Describing these kinetics with mathematical models, we estimate rates of thymic production, division and death of naive CD4 and CD8 T cells. Population-averaged estimates of mean lifetimes are consistent with earlier studies, but we find the strongest support for a model in which both naive T-cell pools contain kinetically distinct subpopulations of older host-derived cells with self-renewing capacity that are resistant to displacement by naive donor lymphocytes. We speculate that these incumbent cells are conditioned or selected for increased fitness through homeostatic expansion into the lymphopenic neonatal environment.

Parameters identification for a model of T cell homeostasis

In this study, we consider a model of T cell homeostasis based on the Smith-Martin model. This nonlinear model is structured by age and CD44 expression. First, we establish the mathematical well-posedness of the model system. Next, we prove the theoretical identifiability regarding the up-regulation of CD44, the proliferation time phase and the rate of entry into division, by using the experimental data. Finally, we compare two versions of the Smith-Martin model and we identify which model fits the experimental data best.

Zap70 is essential for long-term survival of naive CD8 T cells

Survival of naive T cells requires engagement of TCR with self-peptide major histocompatibility Ags. The signaling pathways required to transmit this survival signal are poorly understood. In this study, we asked whether the tyrosine kinase Zap70 is required to transmit survival signals in naive CD8 T cells. In the absence of Zap70 expression, thymic development is completely blocked. Using a tetracycline-inducible Zap70 transgene (TetZap70), thymic development of Zap70-deficient TCR transgenic F5 mice was restored. Feeding mice doxycycline to induce Zap70 expression resulted in repopulation of the peripheral naive compartment. Zap70 transgene expression was then ablated by withdrawal of doxycycline. Survival of Zap70-deficient naive CD8 T cells depended on host environment. In hosts with a replete T cell compartment, naive T cells died rapidly in the absence of Zap70 expression. In lymphopenic hosts, Zap70-deficient T cells survived far longer, in an IL-7-dependent manner, but failed to undergo lymphopenia-induced proliferation. Analyzing mixed bone marrow chimeras revealed that intact Zap70-dependent signaling was important for integration of recent thymic emigrants into the mature naive compartment. Finally, we asked whether adaptor function conferred by Zap70 tyrosines 315 and 319 was necessary for transmission of homeostatic TCR signals. This was done by analyzing F5 mice expressing mutant Zap70 in which these residues had been mutated to alanines (Zap70(YYAA)). Inducible Zap70 expression rescued thymic development in F5 TetZap70 Zap70(YYAA) mice. However, in the absence of wild-type Zap70 expression, the Zap70(YYAA) mutant failed to transmit either survival or proliferative homeostatic signals.

Parameter identification for model of T cell proliferation in lymphopenia conditions

The number of T Lymphocytes (T cells) in the body is under homeostatic control. At equilibrium, the majority of naive T cells are non-dividing and express low levels of the surface protein CD44. In conditions of T cell deficiency (lymphopenia), naive T cells enter into a proliferative phase, undergoing cell division accompanied by a subtle change in their surface expression of CD44. In this study, we use a mathematical modelling approach to analyse the proliferative response of transgenic T cells in lymphopenic conditions. Our nonlinear model is composed of ordinary differential equations and partial differential equations structured by age (maturity of cell) and CD44 expression. To better understand the evolution of CD44 expression on the surface of T cells during cell division, we present a numerical analysis to solve a parameter identification problem. Finally, we show the parameters and the simulations that we obtain from the model and compare them to experimental data.

A mechanistic model for naive CD4 T cell homeostasis in healthy adults and children

The size and composition of the T lymphocyte compartment is subject to strict homeostatic regulation and is remarkably stable throughout life in spite of variable dynamics in cell production and death during T cell development and immune responses. Homeostasis is achieved by careful orchestration of lymphocyte survival and cell division. New T cells are generated from the thymus and the number of peripheral T cells is regulated by controlling survival and proliferation. How these processes combine is however very complex. Thymic output increases in the first year of life and then decreases but is crucial for establishing repertoire diversity. Proliferation of new naive T cells plays a crucial role for maintaining numbers but at a potential cost to TCR repertoire diversity. A mechanistic two-compartment model of T cell homeostasis is described here that includes specific terms for thymic output, cell proliferation, and cell death of both resting and dividing cells. The model successfully predicts the homeostatic set point for T cells in adults and identifies variables that determine the total number of T cells. It also accurately predicts T cell numbers in children in early life despite rapid changes in thymic output and growth over this period.

Quantifying T lymphocyte turnover

Peripheral T cell populations are maintained by production of naive T cells in the thymus, clonal expansion of activated cells, cellular self-renewal (or homeostatic proliferation), and density dependent cell life spans. A variety of experimental techniques have been employed to quantify the relative contributions of these processes. In modern studies lymphocytes are typically labeled with 5-bromo-2'-deoxyuridine (BrdU), deuterium, or the fluorescent dye carboxy-fluorescein diacetate succinimidyl ester (CFSE), their division history has been studied by monitoring telomere shortening and the dilution of T cell receptor excision circles (TRECs) or the dye CFSE, and clonal expansion has been documented by recording changes in the population densities of antigen specific cells. Proper interpretation of such data in terms of the underlying rates of T cell production, division, and death has proven to be notoriously difficult and involves mathematical modeling. We review the various models that have been developed for each of these techniques, discuss which models seem most appropriate for what type of data, reveal open problems that require better models, and pinpoint how the assumptions underlying a mathematical model may influence the interpretation of data. Elaborating various successful cases where modeling has delivered new insights in T cell population dynamics, this review provides quantitative estimates of several processes involved in the maintenance of naive and memory, CD4(+) and CD8(+) T cell pools in mice and men.

Clonally diverse T cell homeostasis is maintained by a common program of cell-cycle control

Lymphopenia induces T cells to undergo cell divisions as part of a homeostatic response mechanism. The clonal response to lymphopenia is extremely diverse, and it is unknown whether this heterogeneity represents distinct mechanisms of cell-cycle control or whether a common mechanism can account for the diversity. We addressed this question by combining in vivo and mathematical modeling of lymphopenia-induced proliferation (LIP) of two distinct T cell clonotypes. OT-I T cells undergo rapid LIP accompanied by differentiation that superficially resembles Ag-induced proliferation, whereas F5 T cells divide slowly and remain naive. Both F5 and OT-I LIP responses were most accurately described by a single stochastic division model where the rate of cell division was exponentially decreased with increasing cell numbers. The model successfully identified key biological parameters of the response and accurately predicted the homeostatic set point of each clone. Significantly, the model was successful in predicting interclonal competition between OT-I and F5 T cells, consistent with competition for the same resource(s) required for homeostatic proliferation. Our results show that diverse and heterogeneous clonal T cell responses can be accounted for by a single common model of homeostasis.

A mechanistic model for bromodeoxyuridine dilution naturally explains labelling data of self-renewing T cell populations

Bromodeoxyuridine (BrdU) is widely used in immunology to detect cell division, and several mathematical models have been proposed to estimate proliferation and death rates of lymphocytes from BrdU labelling and de-labelling curves. One problem in interpreting BrdU data is explaining the de-labelling curves. Because shortly after label withdrawal, BrdU+ cells are expected to divide into BrdU+ daughter cells, one would expect a flat down-slope. As for many cell types, the fraction of BrdU+ cells decreases during de-labelling, previous mathematical models had to make debatable assumptions to be able to account for the data. We develop a mechanistic model tracking the number of divisions that each cell has undergone in the presence and absence of BrdU, and allow cells to accumulate and dilute their BrdU content. From the same mechanistic model, one can naturally derive expressions for the mean BrdU content (MBC) of all cells, or the MBC of the BrdU+ subset, which is related to the mean fluorescence intensity of BrdU that can be measured in experiments. The model is extended to include subpopulations with different rates of division and death (i.e. kinetic heterogeneity). We fit the extended model to previously published BrdU data from memory T lymphocytes in simian immunodeficiency virus-infected and uninfected macaques, and find that the model describes the data with at least the same quality as previous models. Because the same model predicts a modest decline in the MBC of BrdU+ cells, which is consistent with experimental observations, BrdU dilution seems a natural explanation for the observed down-slopes in self-renewing populations.

IL-7 determines the homeostatic fitness of T cells by distinct mechanisms at different signalling thresholds in vivo

The cytokine interleukin (IL)-7 is essential for Treg-cell homeostasis. It remains unclear, however, whether IL-7 regulates the homeostatic fitness of T cells quantitatively and, if so, by what mechanisms. We addressed this question by analysing T cells exposed to different levels of IL-7 signalling in vivo. Using TCR transgenic mice that conditionally express IL-7Rα, we show that T-cell longevity in the absence of survival cues is not a cell-intrinsic property but rather a dynamic process of which IL-7 signalling is a key regulator. Naïve T cells deficient in IL-7Rα expression underwent rapid cell death within hours of in vitro culture. In contrast, the same T cells from lymphopenic hosts, in which IL-7 is non-limiting, were able to survive in culture independently of growth factors for many days. Surprisingly, different levels of IL-7 signalling in vivo evoked distinct molecular mechanisms to regulate homeostatic fitness. When IL-7 was non-limiting, increased survival was associated with up-regulation of anti-apoptotic Bcl2 family members. In contrast, in T-cell replete conditions i.e. when IL-7 is limiting, we found evidence that IL-7 regulated T-cell fitness by distinct non-transcriptional mechanisms. Together, these data demonstrate a quantitative aspect to IL-7 signalling dependent on distinct molecular mechanisms.

Regulation of T cell-dendritic cell interactions by IL-7 governs T-cell activation and homeostasis

Interleukin-7 (IL-7) plays a central role in the homeostasis of the T-cell compartment by regulating T-cell survival and proliferation. Whether IL-7 can influence T-cell receptor (TCR) signaling in T cells remains controversial. Here, using IL-7-deficient hosts and TCR-transgenic T cells that conditionally express IL-7R, we examined antigen-specific T-cell responses in vitro and in vivo to viral infection and lymphopenia to determine whether IL-7 signaling influences TCR-triggered cell division events. In vitro, we could find no evidence that IL-7 signaling could costimulate T-cell activation over a broad range of conditions, suggesting that IL-7 does not directly tune TCR signaling. In vivo, however, we found an acute requirement for IL-7 signaling for efficiently triggering T-cell responses to influenza A virus challenge. Furthermore, we found that IL-7 was required for the enhanced homeostatic TCR signaling that drives lymphopenia-induced proliferation by a mechanism involving efficient contacts of T cells with dendritic cells. Consistent with this, saturating antigen-presenting capacity in vivo overcame the triggering defect in response to cognate peptide. Thus, we demonstrate a novel role for IL-7 in regulating T cell-dendritic cell interactions that is essential for both T-cell homeostasis and activation in vivo.

Lymphocyte kinetics in health and disease

Quantitative understanding of immunology requires the development of experimental and mathematical techniques for estimation of rates of division and death of lymphocytes under different conditions. Here, we review the advantages and limitations of several labelling methods that are currently used to quantify turnover of lymphocytes in vivo. In addition to highlighting insights into lymphocyte kinetics which have recently been gained thanks to the development of novel techniques, we discuss important directions for future experimental and theoretical work in the field of lymphocyte turnover.

Quantifying the development of the peripheral naive CD4+ T-cell pool in humans

What are the rules that govern a naive T cell's prospects for survival or division after export from the thymus into the periphery? To help address these questions, we combine data from existing studies with robust mathematical models to estimate the absolute contributions of thymopoiesis, peripheral division, and loss or differentiation to the human naive CD4+ T-cell pool between the ages of 0 and 20 years. Despite their decline in frequency in the blood, total body numbers of naive CD4+ T cells increase throughout childhood and early adulthood. Our analysis shows that postthymic proliferation contributes more than double the number of cells entering the pool each day from the thymus. This ratio is preserved with age; as the thymus involutes, the average time between naive T-cell divisions in the periphery lengthens. We also show that the expected residence time of naive T cells increases with time. The naive CD4+ T-cell population thus becomes progressively less dynamic with age. Together with other studies, our results suggest a complex picture of naive T-cell homeostasis in which population size, time since export from the thymus, or time since the last division can influence a cell's prospects for survival or further divisions.