Estimating average cellular turnover from 5-bromo-2'-deoxyuridine (BrdU) measurements

Fate Mapping Quantifies the Dynamics of B Cell Development and Activation throughout Life

Follicular mature (FM) and germinal center (GC) B cells underpin humoral immunity, but the dynamics of their generation and maintenance are not clearly defined. Here, we exploited a fate-mapping system in mice that tracks B cells as they develop into peripheral subsets, together with a cell division fate reporter mouse and mathematical models. We find that FM cells are kinetically homogeneous, recirculate freely, are continually replenished from transitional populations, and self-renew rarely. In contrast, GC B cell lineages persist for weeks with rapid turnover and site-specific dynamics. Those in the spleen derive from transitional cells and are kinetically homogeneous, while those in lymph nodes derive from FM B cells and comprise both transient and persistent clones. These differences likely derive from the nature of antigen exposure at the different sites. Our integrative approach also reveals how the host environment drives cell-extrinsic, age- related changes in B cell homeostasis.

Verheijen and Rane et al. combine fate mapping and mathematical models to quantify the development and dynamics of follicular mature B cells and germinal center B cells in spleen and lymph nodes, and show how these processes vary across the mouse lifespan.

Modeling the immune response to HIV infection

The interplay between immune response and HIV is intensely studied via mathematical modeling, with significant insights but few direct answers. In this short review, we highlight advances and knowledge gaps across different aspects of immunity. In particular, we identify the innate immune response and its role in priming the adaptive response as ripe for modeling. The latter have been the focus of most modeling studies, but we also synthesize key outstanding questions regarding effector mechanisms of cellular immunity and development of broadly neutralizing antibodies. Thus far, most modeling studies aimed to infer general immune mechanisms; we foresee that significant progress will be made next by detailed quantitative fitting of models to data, and prediction of immune responses.

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.

Modeling T cell responses to antigenic challenge

T cell responses are a crucial part of the adaptive immune system in the fight against infections. This article discusses the use of mathematical models for understanding the dynamics of cytotoxic T lymphocyte (CTL) responses against viral infections. Complementing experimental research, mathematical models have been very useful for exploring new hypotheses, interpreting experimental data, and for defining what needs to be measured to improve understanding. This review will start with minimally parameterized models of CTL responses, which have generated some valuable insights into basic dynamics and correlates of control. Subsequently, more biological complexity is incorporated into this modeling framework, examining different mechanisms of CTL expansion, different effector activities, and the influence of T cell help. Models and results are discussed in the context of data from specific infections.

Quantifying the length and variance of the eukaryotic cell cycle phases by a stochastic model and dual nucleoside pulse labelling

A fundamental property of cell populations is their growth rate as well as the time needed for cell division and its variance. The eukaryotic cell cycle progresses in an ordered sequence through the phases and and is regulated by environmental cues and by intracellular checkpoints. Reflecting this regulatory complexity, the length of each phase varies considerably in different kinds of cells but also among genetically and morphologically indistinguishable cells. This article addresses the question of how to describe and quantify the mean and variance of the cell cycle phase lengths. A phase-resolved cell cycle model is introduced assuming that phase completion times are distributed as delayed exponential functions, capturing the observations that each realization of a cycle phase is variable in length and requires a minimal time. In this model, the total cell cycle length is distributed as a delayed hypoexponential function that closely reproduces empirical distributions. Analytic solutions are derived for the proportions of cells in each cycle phase in a population growing under balanced growth and under specific non-stationary conditions. These solutions are then adapted to describe conventional cell cycle kinetic assays based on pulse labelling with nucleoside analogs. The model fits well to data obtained with two distinct proliferating cell lines labelled with a single bromodeoxiuridine pulse. However, whereas mean lengths are precisely estimated for all phases, the respective variances remain uncertain. To overcome this limitation, a redesigned experimental protocol is derived and validated in silico. The novelty is the timing of two consecutive pulses with distinct nucleosides that enables accurate and precise estimation of both the mean and the variance of the length of all phases. The proposed methodology to quantify the phase length distributions gives results potentially equivalent to those obtained with modern phase-specific biosensor-based fluorescent imaging.

Among the important characteristics of dividing cell populations is the time necessary for cells to complete each of the cell cycle phases, that is, to increase the cell's mass, to duplicate and repair its genome, to properly segregate its chromosomes, and to make decisions whether to continue dividing or enter a quiescent state. The cycle phase times also determine the maximal rate at which a dividing cell population can grow in size. Cell cycle phase completion times largely differ between cell types, cellular environments as well as metabolic stages, and can thus be considered as part of the phenotype of a given cell. Our article advances the methods to quantitatively characterize this phenotype. We introduce a novel phase-resolved cell cycle progression model and use it to estimate the mean and variance of the cycle phase completion times based on nucleoside analog pulse labelling experiments. This classic workhorse of cell cycle kinetic studies is revamped by our approach to potentially rival in accuracy and precision with modern phase-specific biosensor-based fluorescent imaging, while superseding the latter in its application scope.

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.

Accelerated in vivo proliferation of memory phenotype CD4+ T-cells in human HIV-1 infection irrespective of viral chemokine co-receptor tropism

CD4⁺ T-cell loss is the hallmark of HIV-1 infection. CD4 counts fall more rapidly in advanced disease when CCR5-tropic viral strains tend to be replaced by X4-tropic viruses. We hypothesized: (i) that the early dominance of CCR5-tropic viruses results from faster turnover rates of CCR5⁺ cells, and (ii) that X4-tropic strains exert greater pathogenicity by preferentially increasing turnover rates within the CXCR4⁺ compartment. To test these hypotheses we measured in vivo turnover rates of CD4⁺ T-cell subpopulations sorted by chemokine receptor expression, using in vivo deuterium-glucose labeling. Deuterium enrichment was modeled to derive in vivo proliferation (p) and disappearance (d*) rates which were related to viral tropism data. 13 healthy controls and 13 treatment-naive HIV-1-infected subjects (CD4 143–569 cells/ul) participated. CCR5-expression defined a CD4⁺ subpopulation of predominantly CD45R0⁺ memory cells with accelerated in vivo proliferation (p = 2.50 vs 1.60%/d, CCR5⁺ vs CCR5⁻; healthy controls; P<0.01). Conversely, CXCR4 expression defined CD4⁺ T-cells (predominantly CD45RA⁺ naive cells) with low turnover rates. The dominant effect of HIV infection was accelerated turnover of CCR5⁺CD45R0⁺CD4⁺ memory T-cells (p = 5.16 vs 2.50%/d, HIV vs controls; P<0.05), naïve cells being relatively unaffected. Similar patterns were observed whether the dominant circulating HIV-1 strain was R5-tropic (n = 9) or X4-tropic (n = 4). Although numbers were small, X4-tropic viruses did not appear to specifically drive turnover of CXCR4-expressing cells (p = 0.54 vs 0.72 vs 0.44%/d in control, R5-tropic, and X4-tropic groups respectively). Our data are most consistent with models in which CD4⁺ T-cell loss is primarily driven by non-specific immune activation.

Loss of CD4⁺ T-cells is the cardinal feature of HIV/AIDS, resulting in pathological susceptibility to opportunistic infections. Mechanisms underlying CD4-depletion remain unclear, although the role of chronic immune activation is now well-recognized. Selectivity of the virus for its co-receptor target (either chemokine-receptor CCR5 or CXCR4) is also pivotal. We explored the relationship between these two factors by directly measuring in vivo proliferation rates of CD4⁺ T-cell subpopulations according to their expression of chemokine-receptors and the tropism of circulating virus in clinically-well people with HIV infection, and healthy human controls. We used stable isotope labeling with deuterium-labeled glucose to quantify proliferation and disappearance rate constants of CD4⁺ T-cells sorted by CCR5, CXCR4 and CD45R0/RA expression. We found that CCR5-expression defines a high turnover subpopulation which is therefore likely to be preferentially infected and produce more (CCR5-tropic) virus. CXCR4-tropic viruses induced a similar pattern of proliferation as R5-tropic strains, with no apparent selectivity for viral strains to induce proliferation in their targeted subpopulations. This study is significant in providing directly-measured in vivo human data supporting postulates generated in ex vivo human studies and SIV models suggesting that non-specific factors, such as immune activation, rather than cell-specific cytotoxicity, are dominant drivers for HIV pathogenesis.

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.

Modelling deuterium labelling of lymphocytes with temporal and/or kinetic heterogeneity

To study the kinetics of lymphocytes, models have divided the cell population into subpopulations with different turnover rates. These have been called 'kinetic heterogeneity models' so as to distinguish them from 'temporal heterogeneity models', in which a cell population may have different turnover rates at different times, e.g. when resting versus when activated. We model labelling curves for temporally heterogeneous populations, and predict that they exhibit equal biphasic up- and downslopes. We show when cells divide only once upon activation, these slopes are dominated by the slowest exponent, yielding underestimates of the average turnover rate. When cells undergo more than one division, the labelling curves allow fitting of the two exponential slopes in the temporal heterogeneity model. The same data can also be described with a two-compartment kinetic heterogeneity model. In both instances, the average turnover rate is correctly estimated. Because both models assume a different cell biology but describe the data equally well, the parameters of either model have no simple biological interpretation, as each parameter could reflect a combination of parameters of another biological process. Thus, even if there are sufficient data to reliably estimate all exponentials, one can only accurately estimate an average turnover rate. We illustrate these issues by re-fitting labelling data from healthy and HIV-infected individuals.

Explicit kinetic heterogeneity: mathematical models for interpretation of deuterium labeling of heterogeneous cell populations

Estimation of division and death rates of lymphocytes in different conditions is vital for quantitative understanding of the immune system. Deuterium, in the form of deuterated glucose or heavy water, can be used to measure rates of proliferation and death of lymphocytes in vivo. Inferring these rates from labeling and delabeling curves has been subject to considerable debate with different groups suggesting different mathematical models for that purpose. We show that the three most common models, which are based on quite different biological assumptions, actually predict mathematically identical labeling curves with one parameter for the exponential up and down slope, and one parameter defining the maximum labeling level. By extending these previous models, we here propose a novel approach for the analysis of data from deuterium labeling experiments. We construct a model of “kinetic heterogeneity” in which the total cell population consists of many sub-populations with different rates of cell turnover. In this model, for a given distribution of the rates of turnover, the predicted fraction of labeled DNA accumulated and lost can be calculated. Our model reproduces several previously made experimental observations, such as a negative correlation between the length of the labeling period and the rate at which labeled DNA is lost after label cessation. We demonstrate the reliability of the new explicit kinetic heterogeneity model by applying it to artificially generated datasets, and illustrate its usefulness by fitting experimental data. In contrast to previous models, the explicit kinetic heterogeneity model 1) provides a novel way of interpreting labeling data; 2) allows for a non-exponential loss of labeled cells during delabeling, and 3) can be used to describe data with variable labeling length.

Understanding of cellular processes is impossible without quantitative estimates of how quickly cells in an organism divide and die. The most widely used approach to measure rates of cell turnover in humans is by labeling dividing cells with deuterium given in the form of deuterated glucose or heavy water. Surprisingly, quantitative estimates of the rates of cell turnover obtained from accumulation and decay of the labeled nucleotides in the cell population varied between different studies. We demonstrate that these differences were not likely to arise because of different mathematical models used in data fitting, since the previously used models have an identical mathematical structure. We extend these previous models to allow for cell populations with different rates of turnover and show how such a new explicit kinetic heterogeneity model can be applied to simulated and experimental data. The new model opens a new way of interpreting data from deuterium labeling experiments and will likely lead to new insights into how infections and/or treatments affect cell turnover in humans.

Estimating dormant and active hematopoietic stem cell kinetics through extensive modeling of bromodeoxyuridine label-retaining cell dynamics

Bone marrow hematopoietic stem cells (HSCs) are responsible for both lifelong daily maintenance of all blood cells and for repair after cell loss. Until recently the cellular mechanisms by which HSCs accomplish these two very different tasks remained an open question. Biological evidence has now been found for the existence of two related mouse HSC populations. First, a dormant HSC (d-HSC) population which harbors the highest self-renewal potential of all blood cells but is only induced into active self-renewal in response to hematopoietic stress. And second, an active HSC (a-HSC) subset that by and large produces the progenitors and mature cells required for maintenance of day-to-day hematopoiesis. Here we present computational analyses further supporting the d-HSC concept through extensive modeling of experimental DNA label-retaining cell (LRC) data. Our conclusion that the presence of a slowly dividing subpopulation of HSCs is the most likely explanation (amongst the various possible causes including stochastic cellular variation) of the observed long term Bromodeoxyuridine (BrdU) retention, is confirmed by the deterministic and stochastic models presented here. Moreover, modeling both HSC BrdU uptake and dilution in three stages and careful treatment of the BrdU detection sensitivity permitted improved estimates of HSC turnover rates. This analysis predicts that d-HSCs cycle about once every 149-193 days and a-HSCs about once every 28-36 days. We further predict that, using LRC assays, a 75%-92.5% purification of d-HSCs can be achieved after 59-130 days of chase. Interestingly, the d-HSC proportion is now estimated to be around 30-45% of total HSCs - more than twice that of our previous estimate.

Type I IFN regulate DC turnover in vivo

DC are the most potent antigen-presenting cells that recognise signs of infection and serve as the main activators of naïve T cells. We have previously shown that type I IFN (IFN-I) are produced by DC and can act in an autocrine manner to activate DC. In the present study, we have investigated the role of IFN-I in regulating the turnover and lifespan of DC. We found that DC, especially the CD8alpha(+) subset, from type I IFN receptor knock out (IFNAR KO) mice, display a reduced turnover rate when compared with DC from WT mice, as revealed by BrdU labelling kinetics. In vitro, IFNAR KO BM precursor cells cultured in the presence of GM-CSF generated CD11c(+) DC less efficiently than WT BM, and the IFNAR KO DC that arose displayed reduced migratory ability. Interestingly, splenic DC from IFNAR KO mice exhibited a higher survival rate in short-term culture compared with control DC. Exposure to IFN-I in vivo markedly increased the turnover rate of splenic DC, particularly CD8alpha(+) DC, which was preceded by a transient induction of apoptosis. In accordance with this, IFN-I stimulated the apoptosis of splenic DC in vitro. Overall, our data indicate that IFN-I are important regulators of DC turnover in vivo and suggest that these cytokines may exert this function through the modulation of multiple processes involving DC apoptosis, proliferation and migration.

Towards estimating the true duration of dendritic cell interactions with T cells

To initiate an adaptive immune response, T cells need to interact with dendritic cells (DCs), and the duration of these interactions plays an important role. In vitro and in vivo experiments have generally tried to estimate the required period of opportunity for T cell stimulation rather than the duration of individual T cell-DC interactions. Since the application of multi-photon microscopy (MPM) to living lymphoid tissues, the interactions between immune cells, as well as the duration thereof, can directly be observed in vivo. Indeed, long-lasting interactions between T cells and DCs were shown to be important for the onset of immune responses. However, because MPM imaging is typically restricted to experiments lasting 1 h, and because T cell-DC conjugates frequently move into and out of the imaged volume, it is difficult to estimate the true duration of interactions from MPM contact data. Here, we present a method to properly make such an estimate of (the average of) the distribution of contact durations. We validate the method by applying it to spatially explicit computer simulations where the true distribution of contact duration is known. Finally, we apply our analysis to a large experimental data set of T-DC contacts, and predict an average contact time of about three hours. However, we identify a mismatch between the experimental data and the model predictions, and investigate possible causes of the mismatch, including minor tissue drift during imaging experiments. We discuss in detail how future experiments can be optimized such that MPM contact data will be minimally affected by these factors.

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.

Modeling the adaptive immune system: predictions and simulations

MOTIVATION

Immunological bioinformatics methods are applicable to a broad range of scientific areas. The specifics of how and where they might be implemented have recently been reviewed in the literature. However, the background and concerns for selecting between the different available methods have so far not been adequately covered.

SUMMARY

Before using predictions systems, it is necessary to not only understand how the methods are constructed but also their strength and limitations. The prediction systems in humoral epitope discovery are still in their infancy, but have reached a reasonable level of predictive strength. In cellular immunology, MHC class I binding predictions are now very strong and cover most of the known HLA specificities. These systems work well for epitope discovery, and predictions of the MHC class I pathway have been further improved by integration with state-of-the-art prediction tools for proteasomal cleavage and TAP binding. By comparison, class II MHC binding predictions have not developed to a comparable accuracy level, but new tools have emerged that deliver significantly improved predictions not only in terms of accuracy, but also in MHC specificity coverage. Simulation systems and mathematical modeling are also now beginning to reach a level where these methods will be able to answer more complex immunological questions.

Dynamics of T- and B-lymphocyte turnover in a natural host of simian immunodeficiency virus

Increased lymphocyte turnover is a hallmark of pathogenic lentiviral infection. To investigate perturbations in lymphocyte dynamics in natural hosts with nonpathogenic simian immunodeficiency virus (SIV) infection, the nucleoside analog bromodeoxyuridine (BrdU) was administered to six naturally SIV-infected and five SIV-negative sooty mangabeys. As a measure of lymphocyte turnover, we estimated the mean death rate by fitting a mathematical model to the fraction of BrdU-labeled cells during a 2-week labeling and a median 10-week delabeling period. Despite significantly lower total T- and B-lymphocyte counts in SIV-infected sooty mangabeys than in SIV-negative mangabeys, the turnover rate of B lymphocytes and CD4(+) and CD8(+) T lymphocytes was not increased in the SIV-infected animals. A small, rapidly proliferating CD45RA(+) memory subset and a large, slower-proliferating CD45RA(-) central memory subset of CD4(+) T lymphocytes identified in the peripheral blood of sooty mangabeys also did not show evidence of increased turnover in the context of SIV infection. Independently of SIV infection, the turnover of CD4(+) T lymphocytes in sooty mangabeys was significantly higher (P < 0.01) than that of CD8(+) T lymphocytes, a finding hitherto not reported in rhesus macaques or humans. The absence of aberrant T-lymphocyte turnover along with an inherently high rate of CD4(+) T-lymphocyte turnover may help to preserve the pool of central memory CD4(+) T lymphocytes in viremic SIV-infected sooty mangabeys and protect against progression to AIDS.

Quantification of T-cell dynamics: from telomeres to DNA labeling

Immunology has traditionally been a qualitative science describing the cellular and molecular components of the immune system and their functions. Only quite recently have new experimental techniques paved the way for a more quantitative approach of immunology. Lymphocyte telomere lengths have been measured to get insights into the proliferation rate of different lymphocyte subsets, T-cell receptor excision circles have been used to quantify the daily output of new T cells from the thymus, and bromodeoxyuridine and stable isotope labeling have been applied to measure proliferation and death rates of naive and memory lymphocytes. A common problem of the above techniques is the translation of the resulting data into relevant parameters, such as the typical division and death rate of the different lymphocyte populations. Theoretical immunology has contributed significantly to the interpretation of such quantitative experimental data, thereby resolving diverse controversies and, most importantly, has suggested novel experiments, allowing for more conclusive and quantitative interpretations. In this article, we review a variety of different models that have been used to interpret data on lymphocyte kinetics in healthy human subjects and discuss their contributions and limitations.

Modelling the human immune system by combining bioinformatics and systems biology approaches

Over the past decade a number of bioinformatics tools have been developed that use genomic sequences as input to predict to which parts of a microbe the immune system will react, the so-called epitopes. Many predicted epitopes have later been verified experimentally, demonstrating the usefulness of such predictions. At the same time, simulation models have been developed that describe the dynamics of different immune cell populations and their interactions with microbes. These models have been used to explain experimental findings where timing is of importance, such as the time between administration of a vaccine and infection with the microbe that the vaccine is intended to protect against. In this paper, we outline a framework for integration of these two approaches. As an example, we develop a model in which HIV dynamics are correlated with genomics data. For the first time, the fitness of wild type and mutated virus are assessed by means of a sequence-dependent scoring matrix, derived from a BLOSUM matrix, that links protein sequences to growth rates of the virus in the mathematical model. A combined bioinformatics and systems biology approach can lead to a better understanding of immune system-related diseases where both timing and genomic information are of importance.

Quantifying lymphocyte kinetics in vivo using carboxyfluorescein diacetate succinimidyl ester (CFSE)

The cytoplasmic dye carboxyfluorescein diacetate succinimidyl ester (CFSE) is used to quantify cell kinetics. It is particularly important in studies of lymphocyte homeostasis where its labelling of cells irrespective of their stage in the cell cycle makes it preferable to deuterated glucose and BrdU, which only label dividing cells and thus produce unrepresentative results. In the past, experiments have been limited by the need to obtain a clear separation of CFSE peaks forcing scientists to adopt a strategy of in vitro labelling of cells followed by their injection into the host. Here we develop a framework for analysis of in vivo CFSE labelling data. This enables us to estimate the rate of proliferation and death of lymphocytes in situ, and thus represents a considerable advance over current procedures. We illustrate this approach using in vivo CFSE labelling of B lymphocytes in sheep.

Ecological and evolutionary principles in immunology

Experimental immunology has given rise to detailed insights into how immune cells react to infectious agents and fight pathogens. At the same time, however, the interplay between infectious agents and immune responses can be viewed as an ecological system in vivo. This is characterized by complex interactions between species of immune cells and populations of pathogens. This review discusses how an understanding of the immune system can be aided by the application of ecological and evolutionary principles: competition, predation, and the evolution of viruses in vivo. These concepts can shed light onto important immunological concepts such as the correlates of efficient virus control, immunodominance, the relationship between viral evolution and the development of pathology, as well as the ability of the immune system to control immunosuppressive infections.

Reduced mitotic activity at the periphery of human embryonic stem cell colonies cultured in vitro with mitotically-inactivated murine embryonic fibroblast feeder cells

This study attempted to investigate whether different levels of mitotic activity exist within different physical regions of a human embryonic stem (hES) cell colony. Incorporation of 5-bromo-2-deoxyuridine (BrdU) within newly-synthesized DNA, followed by immunocytochemical staining was used as a means of detecting mitotically-active cells within hES colonies. The results showed rather surprisingly that the highest levels of mitotic activity are primarily concentrated within the central regions of hES colonies, whereas the peripheral regions exhibited reduced levels of cellular proliferation. Two hypothetical mechanisms are therefore proposed for hES colony growth and expansion. Firstly, it is envisaged that the less mitotically-active hES cells at the periphery of the colony are continually migrating outwards, thereby providing space for newly-divided daughter cells within the more mitotically-active central region of the hES colony. Secondly, it is proposed that the newly-divided hES cells within the central region of the colony somehow migrate to the outer periphery. This could possibly explain why the periphery of hES colonies are less mitotically-active, since there would obviously be an extended time-lag before newly-divided daughter cells are ready again for the next cell division. Further investigations need to be carried out to characterize the atypical mechanisms by which hES colonies grow and expand in size.

An introduction to lymphocyte and viral dynamics: the power and limitations of mathematical analysis

Mathematics is a useful tool in the analysis and understanding of population dynamic aspects of the immune response. However, the power of mathematical modelling in immunology is frequently limited by the shortage of experimental data. Here, we review the contribution of mathematics to two areas of immunology. We highlight the problem caused by lack of knowledge of the system, which can greatly restrict the use of mathematics and lead to errors caused by model-specific results.