Rob J. de Boer

Dynamics of HIV infection of CD4 T cells

We examine a model for the interaction of HIV with CD4+ T cells that considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. Using this model we show that many of the puzzling quantitative features of HIV infection can be explained simply. We also consider effects of AZT on viral growth and T-cell population dynamics. The model exhibits two steady states, an uninfected state in which no virus is present and an endemically infected state, in which virus and infected T cells are present. We show that if N, the number of infectious virions produced per actively infected T cell, is less a critical value, Ncrit, then the uninfected state is the only steady state in the nonnegative orthant, and this state is stable. For N > Ncrit, the uninfected state is unstable, and the endemically infected state can be either stable, or unstable and surrounded by a stable limit cycle. Using numerical bifurcation techniques we map out the parameter regimes of these various behaviors. oscillatory behavior seems to lie outside the region of biologically realistic parameter values. When the endemically infected state is stable, it is characterized by a reduced number of T cells compared with the uninfected state. Thus T-cell depletion occurs through the establishment of a new steady state. The dynamics of the establishment of this new steady state are examined both numerically and via the quasi-steady-state approximation. We develop approximations for the dynamics at early times in which the free virus rapidly binds to T cells, during an intermediate time scale in which the virus grows exponentially, and a third time scale on which viral growth slows and the endemically infected steady state is approached. Using the quasi-steady-state approximation the model can be simplified to two ordinary differential equations the summarize much of the dynamical behavior. We compute the level of T cells in the endemically infected state and show how that level varies with the parameters in the model. The model predicts that different viral strains, characterized by generating differing numbers of infective virions within infected T cells, can cause different amounts of T-cell depletion and generate depletion at different rates. Two versions of the model are studied. In one the source of T cells from precursors is constant, whereas in the other the source of T cells decreases with viral load, mimicking the infection and killing of T-cell precursors.(ABSTRACT TRUNCATED AT 400 WORDS)

In vivo labeling with 2H2O reveals a human neutrophil lifespan of 5.4 days

Neutrophils are essential effector cells of the innate immune response and are indispensable for host defense. Apart from their antimicrobial functions, neutrophils inform and shape subsequent immunity. This immune modulatory functionality might however be considered limited because of their generally accepted short lifespan (< 1 day). In contrast to the previously reported short lifespans acquired by ex vivo labeling or manipulation, we show that in vivo labeling in humans with the use of (2)H(2)O under homeostatic conditions showed an average circulatory neutrophil lifespan of 5.4 days. This lifespan is at least 10 times longer than previously reported and might lead to reappraisal of novel neutrophil functions in health and disease.

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.

MHC polymorphism under host-pathogen coevolution

The genes encoding major histocompatibility (MHC) molecules are among the most polymorphic genes known for vertebrates. Since MHC molecules play an important role in the induction of immune responses, the evolution of MHC polymorphism is often explained in terms of increased protection of hosts against pathogens. Two selective pressures that are thought to be involved are (1) selection favoring MHC heterozygous hosts, and (2) selection for rare MHC alleles by host-pathogen coevolution. We have developed a computer simulation of coevolving hosts and pathogens to study the relative impact of these two mechanisms on the evolution of MHC polymorphism. We found that heterozygote advantage per se is insufficient to explain the high degree of polymorphism at the MHC, even in very large host populations. Host-pathogen coevolution, on the other hand, can easily account for realistic polymorphisms of more than 50 alleles per MHC locus. Since evolving pathogens mainly evade presentation by the most common MHC alleles in the host population, they provide a selective pressure for a large variety of rare MHC alleles. Provided that the host population is sufficiently large, a large set of MHC alleles can persist over many host generations under host-pathogen coevolution, despite the fact that allele frequencies continuously change.

Heterogeneous Differentiation Patterns of Individual CD8+ T Cells

Dynamic Protection During an immune response, CD8+ T cells are recruited to provide protection. Most cells differentiate into short-lived effectors that help to clear the pathogen, whereas others form long-lived memory cells to protect against reinfection. Gerlach et al. (p. 635, published online 14 March) and Buchholz et al. (p. 630, published online 14 March) used in vivo fate mapping of mouse T cells with a defined specificity during a bacterial infection to show that the dynamics of the single-cell response are not uniform. The response of a particular T cell population is the average of a small number of clones that expand greatly (“large clones”) and many clones that only proliferate at low amounts (“small clones”). The memory pool arises largely from small clones whereas effectors are primarily made up of large clones. The single-cell dynamics as cytotoxic T cells respond to a bacterial infection are analyzed in mice. Upon infection, antigen-specific CD8+ T lymphocyte responses display a highly reproducible pattern of expansion and contraction that is thought to reflect a uniform behavior of individual cells. We tracked the progeny of individual mouse CD8+ T cells by in vivo lineage tracing and demonstrated that, even for T cells bearing identical T cell receptors, both clonal expansion and differentiation patterns are heterogeneous. As a consequence, individual naïve T lymphocytes contributed differentially to short- and long-term protection, as revealed by participation of their progeny during primary versus recall infections. The discordance in fate of individual naïve T cells argues against asymmetric division as a singular driver of CD8+ T cell heterogeneity and demonstrates that reproducibility of CD8+ T cell responses is achieved through population averaging.

Different Dynamics of CD4+ and CD8+ T Cell Responses During and After Acute Lymphocytic Choriomeningitis Virus Infection

We fit a mathematical model to data characterizing the primary cellular immune response to lymphocytic choriomeningitis virus. The data enumerate the specific CD8+ T cell response to six MHC class I-restricted epitopes and the specific CD4+ T cell responses to two MHC class II-restricted epitopes. The peak of the response occurs around day 8 for CD8+ T cells and around day 9 for CD4+ T cells. By fitting a model to the data, we characterize the kinetic differences between CD4+ and CD8+ T cell responses and among the immunodominant and subdominant responses to the various epitopes. CD8+ T cell responses have faster kinetics in almost every aspect of the response. For CD8+ and CD4+ T cells, the doubling time during the initial expansion phase is 8 and 11 h, respectively. The half-life during the contraction phase following the peak of the response is 41 h and 3 days, respectively. CD4+ responses are even slower because their contraction phase appears to be biphasic, approaching a 35-day half-life 8 days after the peak of the response. The half-life during the memory phase is 500 days for the CD4+ T cell responses and appears to be lifelong for the six CD8+ T cell responses. Comparing the responses between the various epitopes, we find that immunodominant responses have an earlier and/or larger recruitment of precursors cells before the expansion phase and/or have a faster proliferation rate during the expansion phase.

Diverse and heritable lineage imprinting of early haematopoietic progenitors

Haematopoietic stem cells (HSCs) and their subsequent progenitors produce blood cells, but the precise nature and kinetics of this production is a contentious issue. In one model, lymphoid and myeloid production branch after the lymphoid-primed multipotent progenitor (LMPP), with both branches subsequently producing dendritic cells. However, this model is based mainly on in vitro clonal assays and population-based tracking in vivo, which could miss in vivo single-cell complexity. Here we avoid these issues by using a new quantitative version of ‘cellular barcoding’ to trace the in vivo fate of hundreds of LMPPs and HSCs at the single-cell level. These data demonstrate that LMPPs are highly heterogeneous in the cell types that they produce, separating into combinations of lymphoid-, myeloid- and dendritic-cell-biased producers. Conversely, although we observe a known lineage bias of some HSCs, most cellular output is derived from a small number of HSCs that each generates all cell types. Crucially, in vivo analysis of the output of sibling cells derived from single LMPPs shows that they often share a similar fate, suggesting that the fate of these progenitors was imprinted. Furthermore, as this imprinting is also observed for dendritic-cell-biased LMPPs, dendritic cells may be considered a distinct lineage on the basis of separate ancestry. These data suggest a ‘graded commitment’ model of haematopoiesis, in which heritable and diverse lineage imprinting occurs earlier than previously thought.

Recruitment Times, Proliferation, and Apoptosis Rates during the CD8+ T-Cell Response to Lymphocytic Choriomeningitis Virus

ABSTRACT The specific CD8+ T-cell response during acute lymphocytic choriomeningitis virus (LCMV) infection of mice is characterized by a rapid proliferation phase, followed by a rapid death phase and long-term memory. In BALB/c mice the immunodominant and subdominant CD8+ responses are directed against the NP118 and GP283 epitopes. These responses differ mainly in the magnitude of the epitope-specific CD8+ T-cell expansion. Using mathematical models together with a nonlinear parameter estimation procedure, we estimate the parameters describing the rates of change during the three phases and thereby establish the differences between the responses to the two epitopes. We find that CD8+ cell proliferation begins 1 to 2 days after infection and occurs at an average rate of 3 day−1, reaching the maximum population size between days 5 and 6 after immunization. The 10-fold difference in expansion to the NP118 and GP283 epitopes can be accounted for in our model by a 3.5-fold difference in the antigen concentration of these epitopes at which T-cell stimulation is half-maximal. As a consequence of this 3.5-fold difference in the epitope concentration needed for T-cell stimulation, the rates of activation and proliferation of T cells specific for the two epitopes differ during the response and in combination can account for the large difference in the magnitude of the response. After the peak, during the death phase, the population declines at a rate of 0.5 day−1, i.e., cells have an average life time of 2 days. The model accounts for a memory cell population of 5% of the peak population size by a reversal to memory of 1 to 2% of the activated cells per day during the death phase.

Thymic output: a bad TREC record

TREC assays are used to detect recent thymic emigrants and quantitate thymic output. However, the longevity of naive T cells combined with T cell division suggest TREC data should be interpreted with caution.

Implications of spatial heterogeneity for the paradox of enrichment

We analyze a simple model to show that spatial heterogeneity of zooplankton can explain discrepancies between the behavior of classical predator-prey models and the patterns observed in natural planktonic systems. We use a Lotka-Volterra type model of Daphnia and algae. Daphnia occupies only part of a total volume whereas the algae grow in the entire volume and diffuse between the two compartments. This simple spatial structure suffices to explain the observations that (1) natural Daphnia-algae systems tend to be relatively stable up to high nutrient values, and that (2) in the presence of Daphnia edible algae do increase with enrichment. Additionally, the model trivially explains confusing observations of oscillating Daphnia densities in the presence of a practically constant density of edible algae. The model is supported by the results of a laboratory experiment with a cascade of zooplankton-phytoplankton containers, devised originally to test ratio- dependent foraging. We derive minimalizations of our model, which no longer explicitly account for the spatial structure, but still preserve the essential behavior of the full model.