Modeling T Cell Fate.

Many of the pathways that underlie the diversification of naive T cells into effector and memory subsets, and the maintenance of these populations, remain controversial. In recent years a variety of experimental tools have been developed that allow us to follow the fates of cells and their descendants. In this review we describe how mathematical models provide a natural language for describing the growth, loss, and differentiation of cell populations. By encoding mechanistic descriptions of cell behavior, models can help us interpret these new datasets and reveal the rules underpinning T cell fate decisions, both at steady state and during immune responses.

Replicative history marks transcriptional and functional disparity in the CD8+ T cell memory pool.

Clonal expansion is a core aspect of T cell immunity. However, little is known with respect to the relationship between replicative history and the formation of distinct CD8+ memory T cell subgroups. To address this issue, we developed a genetic-tracing approach, termed the DivisionRecorder, that reports the extent of past proliferation of cell pools in vivo. Using this system to genetically 'record' the replicative history of different CD8+ T cell populations throughout a pathogen-specific immune response, we demonstrate that the central memory T (TCM) cell pool is marked by a higher number of prior divisions than the effector memory T cell pool, owing to the combination of strong proliferative activity during the acute immune response and selective proliferative activity after pathogen clearance. Furthermore, by combining DivisionRecorder analysis with single-cell transcriptomics and functional experiments, we show that replicative history identifies distinct cell pools within the TCM compartment. Specifically, we demonstrate that lowly divided TCM cells display enriched expression of stem-cell-associated genes, exist in a relatively quiescent state, and are superior in eliciting a proliferative recall response upon activation. These data provide the first evidence that a stem-cell-like memory T cell pool that reconstitutes the CD8+ T cell effector pool upon reinfection is marked by prior quiescence.

The Branching Point in Erythro-Myeloid Differentiation.

Development of mature blood cell progenies from hematopoietic stem cells involves the transition through lineage-restricted progenitors. The first branching point along this developmental process is thought to separate the erythro-myeloid and lymphoid lineage fate by yielding two intermediate progenitors, the common myeloid and the common lymphoid progenitors (CMPs and CLPs). Here, we use single-cell lineage tracing to demonstrate that so-called CMPs are highly heterogeneous with respect to cellular output, with most individual CMPs yielding either only erythrocytes or only myeloid cells after transplantation. Furthermore, based on the labeling of earlier progenitors, we show that the divergence between the myeloid and erythroid lineage develops within multipotent progenitors (MPP). These data provide evidence for a model of hematopoietic branching in which multiple distinct lineage commitments occur in parallel within the MPP pool.

Better safe than sorry: Naive T-cell dynamics in healthy ageing.

It is well-known that the functioning of the immune system gradually deteriorates with age, and we are increasingly confronted with its consequences as the life expectancy of the human population increases. Changes in the T-cell pool are among the most prominent features of the changing immune system during healthy ageing, and changes in the naive T-cell pool in particular are generally held responsible for its gradual deterioration. These changes in the naive T-cell pool are thought to be due to involution of the thymus. It is commonly believed that the gradual loss of thymic output induces compensatory mechanisms to maintain the number of naive T cells at a relatively constant level, and induces a loss of diversity in the T-cell repertoire. Here we review the studies that support or challenge this widely-held view of immune ageing and discuss the implications for vaccination strategies.

Age-Dependent Normalization Functions for T Lymphocytes in Healthy Individuals.

Lymphocyte numbers naturally change through age. Normalization functions to account for this are sparse and mostly disregard measurements from children in which these changes are most prominent. In this study, we analyze cross-sectional numbers of mainly T lymphocytes (CD3+, CD3+CD4+, and CD3+CD8+) and their subpopulations (naive and memory) from 673 healthy Dutch individuals ranging from infancy to adulthood (0-62 y). We fitted the data by a delayed exponential function and estimated parameters for each lymphocyte subset. Our modeling approach follows general laboratory measurement procedures in which absolute cell counts of T lymphocyte subsets are calculated from observed percentages within a reference population that is truly counted (typically the total lymphocyte count). Consequently, we obtain one set of parameter estimates per T cell subset representing both the trajectories of their counts and percentages. We allow for an initial time delay of half a year before the total lymphocyte counts per microliter of blood start to change exponentially, and we find that T lymphocyte trajectories tend to increase during the first half a year of life. Thus, our study provides functions describing the general trajectories of T lymphocyte counts and percentages of the Dutch population. These functions provide important references to study T lymphocyte dynamics in disease, and they allow one to quantify losses and gains in longitudinal data, such as the CD4+ T cell decline in HIV-infected children and/or the rate of T cell recovery after the onset of treatment.

Hematopoiesis in numbers.

Hematopoiesis is a dynamic process in which stem and progenitor cells give rise to the ~1013 blood and immune cells distributed throughout the human body. We argue that a quantitative description of hematopoiesis can help consolidate existing data, identify knowledge gaps, and generate new hypotheses. Here, we review known numbers in murine and, where possible, human hematopoiesis, and consolidate murine numbers into a set of reference values. We present estimates of cell numbers, division and differentiation rates, cell size, and macromolecular composition for each hematopoietic cell type. We also propose guidelines to improve the reporting of measurements and highlight areas in which quantitative data are lacking. Overall, we show how quantitative approaches can be used to understand key properties of hematopoiesis.

Turnover of Murine Cytomegalovirus-Expanded CD8+ T Cells Is Similar to That of Memory Phenotype T Cells and Independent of the Magnitude of the Response.

The potential of memory T cells to provide protection against reinfection is beyond question. Yet, it remains debated whether long-term T cell memory is due to long-lived memory cells. There is ample evidence that blood-derived memory phenotype CD8+ T cells maintain themselves through cell division, rather than through longevity of individual cells. It has recently been proposed, however, that there may be heterogeneity in the lifespans of memory T cells, depending on factors such as exposure to cognate Ag. CMV infection induces not only conventional, contracting T cell responses, but also inflationary CD8+ T cell responses, which are maintained at unusually high numbers, and are even thought to continue to expand over time. It has been proposed that such inflating T cell responses result from the accumulation of relatively long-lived CMV-specific memory CD8+ T cells. Using in vivo deuterium labeling and mathematical modeling, we found that the average production rates and expected lifespans of mouse CMV-specific CD8+ T cells are very similar to those of bulk memory-phenotype CD8+ T cells. Even CMV-specific inflationary CD8+ T cell responses that differ 3-fold in size were found to turn over at similar rates.

TCRß rearrangements without a D segment are common, abundant, and public.

T cells play an important role in adaptive immunity. An enormous clonal diversity of T cells with a different specificity, encoded by the T cell receptor (TCR), protect the body against infection. Most TCRß chains are generated from a V, D, and J segment during recombination in the thymus. Although complete absence of the D segment is not easily detectable from sequencing data, we find convincing evidence for a substantial proportion of TCRß rearrangements lacking a D segment. Additionally, sequences without a D segment are more likely to be abundant within individuals and/or shared between individuals. Our analysis indicates that such sequences are preferentially generated during fetal development and persist within the elderly. Summarizing, TCRß rearrangements without a D segment are not uncommon, and tend to allow for TCRß chains with a high abundance in the naive repertoire.

Quantification of T-cell dynamics during latent cytomegalovirus infection in humans.

Cytomegalovirus (CMV) infection has a major impact on the T-cell pool, which is thought to be associated with ageing of the immune system. The effect on the T-cell pool has been interpreted as an effect of CMV on non-CMV specific T-cells. However, it remains unclear whether the effect of CMV could simply be explained by the presence of large, immunodominant, CMV-specific memory CD8+ T-cell populations. These have been suggested to establish through gradual accumulation of long-lived cells. However, little is known about their maintenance. We investigated the effect of CMV infection on T-cell dynamics in healthy older adults, and aimed to unravel the mechanisms of maintenance of large numbers of CMV-specific CD8+ T-cells. We studied the expression of senescence, proliferation, and apoptosis markers and quantified the in vivo dynamics of CMV-specific and other memory T-cell populations using in vivo deuterium labelling. Increased expression of late-stage differentiation markers by CD8+ T-cells of CMV+ versus CMV- individuals was not solely explained by the presence of large, immunodominant CMV-specific CD8+ T-cell populations. The lifespans of circulating CMV-specific CD8+ T-cells did not differ significantly from those of bulk memory CD8+ T-cells, and the lifespans of bulk memory CD8+ T-cells did not differ significantly between CMV- and CMV+ individuals. Memory CD4+ T-cells of CMV+ individuals showed increased expression of late-stage differentiation markers and decreased Ki-67 expression. Overall, the expression of senescence markers on T-cell populations correlated positively with their expected in vivo lifespan. Together, this work suggests that i) large, immunodominant CMV-specific CD8+ T-cell populations do not explain the phenotypical differences between CMV+ and CMV- individuals, ii) CMV infection hardly affects the dynamics of the T-cell pool, and iii) large numbers of CMV-specific CD8+ T-cells are not due to longer lifespans of these cells.

What explains the poor contraction of the viral load during paediatric HIV infection?

An acute HIV infection in young children differs markedly from that in adults: Children have higher viral loads (VL), and a poor contraction to a setpoint VL that is not much lower than the peak VL. As a result, children progress faster towards AIDS in the absence of treatment. We used a classical ordinary differential equation model for viral infection dynamics to study why children have a lower viral contraction ratio than adults. We performed parameter sweeps to identify factors explaining the observed difference between children and adults. We grouped parameters associated with the host, the infection, or the immune response. Based on paediatric data available from datasets within the EPIICAL project (https://www.epiical.org/), we refuted that viral replication rates differ between young children and adults, and therefore these cannot be responsible for the low VL contraction ratios seen in children. The major differences in lowering VL contraction ratio resulted from sweeping the parameters linked to the immune response. Thus, we postulate that an "ineffective" (late and/or weak) immune response is the most parsimonious explanation for the higher setpoint VL in young children, and hence the reason for their fast disease progression.

The limitations, dangers, and benefits of simple methods for testing identifiability.

In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading) have commented on our paper in which we proposed a simple scaling method to test structural identifiability. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries. We agree with the limitations raised by these authors but, also, we emphasize that the method is still valuable for its applicability to a wide variety of models, its simplicity, and even as a tool to introduce the problem of identifiability to investigators with little training in mathematics.

Current best estimates for the average lifespans of mouse and human leukocytes: reviewing two decades of deuterium-labeling experiments.

Deuterium is a non-toxic, stable isotope that can safely be administered to humans and mice to study their cellular turnover rates in vivo. It is incorporated into newly synthesized DNA strands during cell division, without interference with the kinetics of cells, and the accumulation and loss of deuterium in the DNA of sorted (sub-)populations of leukocytes can be used to estimate their cellular production rates and lifespans. In the past two decades, this powerful technology has been used to estimate the turnover rates of various types of leukocytes. Although it is the most reliable technique currently available to study leukocyte turnover, there are remarkable differences between the cellular turnover rates estimated by some of these studies. We have recently established that part of this variation is due to (a) difficulties in estimating deuterium availability in some deuterium-labeling studies, and (b) assumptions made by the mathematical models employed to fit the data. Being aware of these two problems, we here aim to approach a consensus on the life expectancies of different types of T cells, B cells, monocytes, and neutrophils in mice and men. We address remaining outstanding problems whenever appropriate and discuss for which immune subpopulations we currently have too little information to draw firm conclusions about their turnover.

Local actin dynamics couple speed and persistence in a cellular Potts model of cell migration.

Cell migration is astoundingly diverse. Molecular signatures, cell-cell interactions, and environmental structures each play their part in shaping cell motion, yielding numerous morphologies and migration modes. Nevertheless, in recent years, a simple unifying law was found to describe cell migration across many different cell types and contexts: faster cells turn less frequently. This universal coupling between speed and persistence (UCSP) was explained by retrograde actin flow from front to back, but it remains unclear how this mechanism generalizes to cells with complex shapes and cells migrating in structured environments, which may not have a well-defined front-to-back orientation. Here, we present an in-depth characterization of an existing cellular Potts model, in which cells polarize dynamically from a combination of local actin dynamics (stimulating protrusions) and global membrane tension along the perimeter (inhibiting protrusions). We first show that the UCSP emerges spontaneously in this model through a cross talk of intracellular mechanisms, cell shape, and environmental constraints, resembling the dynamic nature of cell migration in vivo. Importantly, we find that local protrusion dynamics suffice to reproduce the UCSP-even in cases in which no clear global, front-to-back polarity exists. We then harness the spatial nature of the cellular Potts model to show how cell shape dynamics limit both the speed and persistence a cell can reach and how a rigid environment such as the skin can restrict cell motility even further. Our results broaden the range of potential mechanisms underlying the speed-persistence coupling that has emerged as a fundamental property of migrating cells.

Maintenance of peripheral naive T cells is sustained by thymus output in mice but not humans.

Parallels between T cell kinetics in mice and men have fueled the idea that a young mouse is a good model system for a young human, and an old mouse, for an elderly human. By combining in vivo kinetic labeling using deuterated water, thymectomy experiments, analysis of T cell receptor excision circles and CD31 expression, and mathematical modeling, we have quantified the contribution of thymus output and peripheral naive T cell division to the maintenance of T cells in mice and men. Aging affected naive T cell maintenance fundamentally differently in mice and men. Whereas the naive T cell pool in mice was almost exclusively sustained by thymus output throughout their lifetime, the maintenance of the adult human naive T cell pool occurred almost exclusively through peripheral T cell division. These findings put constraints on the extrapolation of insights into T cell dynamics from mouse to man and vice versa.

Testing structural identifiability by a simple scaling method.

Successful mathematical modeling of biological processes relies on the expertise of the modeler to capture the essential mechanisms in the process at hand and on the ability to extract useful information from empirical data. A model is said to be structurally unidentifiable, if different quantitative sets of parameters provide the same observable outcome. This is typical (but not exclusive) of partially observed problems in which only a few variables can be experimentally measured. Most of the available methods to test the structural identifiability of a model are either too complex mathematically for the general practitioner to be applied, or require involved calculations or numerical computation for complex non-linear models. In this work, we present a new analytical method to test structural identifiability of models based on ordinary differential equations, based on the invariance of the equations under the scaling transformation of its parameters. The method is based on rigorous mathematical results but it is easy and quick to apply, even to test the identifiability of sophisticated highly non-linear models. We illustrate our method by example and compare its performance with other existing methods in the literature.

Local Attachment Explains Small World-like Properties of Fibroblastic Reticular Cell Networks in Lymph Nodes.

Fibroblastic reticular cells (FRCs) form a cellular network that serves as the structural backbone of lymph nodes and facilitates lymphocyte migration. In mice, this FRC network has been found to have small-world properties. Using a model based on geographical preferential attachment, we simulated the formation of a variety of cellular networks and show that similar small-world properties robustly emerge under such natural conditions. By estimating the parameters of this model, we generated FRC network representations with realistic topological properties. We found that the topological properties change markedly when the network is expanded from a thin slice to a three-dimensional cube. Typical small-world properties were found to persist as network size was increased. The simulated networks were very similar to two-dimensional and three-dimensional lattice networks. According to the used metrics, these lattice networks also have small-world properties, indicating that lattice likeness is sufficient to become classified as a small-world network. Our results explain why FRC networks have small-world properties and provide a framework for simulating realistic FRC networks.

Characterization of the ferret TRB locus guided by V, D, J, and C gene expression analysis.

The domestic ferret, Mustela putorius furo, is an important mammalian animal model to study human respiratory infection. However, insufficient genomic annotation hampers detailed studies of ferret T cell responses. In this study, we analyzed the published T cell receptor beta (TRB) locus and performed high-throughput sequencing (HTS) of peripheral blood of four healthy adult ferrets to identify expressed V, D, J, and C genes. The HTS data is used as a guide to manually curate the expressed V, D, J, and C genes. The ferret locus appears to be most similar to that of the dog. Like other mammalian TRB loci, the ferret TRB locus contains a library of variable genes located upstream of two D-J-C gene clusters, followed by a (in the ferret non-functional) V gene with an inverted transcriptional orientation. All TRB genes (expressed or not) reported here have been approved by the IMGT/WHO-IUIS nomenclature committee.

Toxin production spontaneously becomes regulated by local cell density in evolving bacterial populations.

The production of anticompetitor toxins is widespread among bacteria. Because production of such toxins is costly, it is typically regulated. In particular, many toxins are produced only when the local cell density is high. It is unclear which selection pressures shaped the evolution of density-dependent regulation of toxin production. Here, we study the evolution of toxin production, resistance and the response to a cell-density cue in a model of an evolving bacterial population with spatial structure. We present results for two growth regimes: (i) an undisturbed, fixed habitat in which only small fluctuations of cell density occur, and (ii) a serial-transfer regime with large fluctuations in cell density. We find that density-dependent toxin production can evolve under both regimes. However, the selection pressures driving the evolution of regulation differ. In the fixed habitat, regulation evolves because it allows cells to produce toxin only when opportunities for reproduction are highly limited (because of a high local cell density), and the effective fitness costs of toxin production are hence low. Under serial transfers, regulation evolves because it allows cells to switch from a fast-growing non-toxic phenotype when colonising a new habitat, to a slower-growing competitive toxic phenotype when the cell density increases. Colonies of such regulating cells rapidly expand into unoccupied space because their edges consist of fast-growing, non-toxin-producing cells, but are also combative because cells at the interfaces with competing colonies do produce toxin. Because under the two growth regimes different types of regulation evolve, our results underscore the importance of growth conditions in the evolution of social behaviour in bacteria.