Untreated human immunodeficiency virus (HIV)
infection in humans is typically characterised by
persistent high virus load, failure of the immune
response to clear the virus, and fatal disease outcome. Natural
hosts of closely related simian immunodeficiency viruses
(SIVs)—e.g., sooty mangabeys [1,2]—maintain comparably
high persistent virus levels and yet remain healthy.
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 Daphia and algae. Daphnia occupies only a part of total volumes 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.
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 models that are most commonly used are in fact mathematically identical and differ only in their interpretation of the estimated parameters. By extending these previous models, we here propose a more mechanistic 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 mechanistic 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.
Purpose of review The mechanisms by which infection with CCR5 tropic HIV causes the depletion of naive CD4+ and CD8+ T cells are poorly understood. As HIV infection affects the thymus, one hypothesis is 'reduced thymic output'. As HIV infection is associated with hyperactivation, another hypothesis is 'depletion by activation'. The best technique that is currently available for measuring thymic output in humans is to quantify TCR excision circles (TRECs) in peripheral T cells. Unfortunately, TREC data are very difficult to interpret. Recent findings The depletion of memory CD4+ T cells can be accounted for by the massive infection of these cells in the gut and mucosal tissues. The major controversy therefore remains to explain the depletion of naive T cells. SIV infection of thymectomized and euthymic Rhesus macaques revealed important new insights into the effects of thymectomy and SIV infection on naive T cell depletion. Summary Changes in the TREC content, i.e. the average number of TRECs per cell, are confounded by changes in division rates. By also expressing TREC measurements in terms of total TREC numbers, one obtains a much more reliable indication of thymic production. The relatively rapid changes in TREC contents observed in subsets of HIV patients are best explained by changes in T cell division rates. Infection of the thymus is expected to play a role in the long-term depletion of naive T cells, but direct evidence remains scarce. Routinely measuring TREC totals, in addition to the TREC content and naive T cell counts, would help to finally sort this out.
Summary Helper T ( T h)‐cell differentiation is a key event in the development of the adaptive immune response. By the production of a range of cytokines, T h cells determine the type of immune response that is raised against an invading pathogen. Th cells can adopt many different phenotypes, and T h‐cell phenotype decision‐making is crucial in mounting effective host responses. This review discusses the different T h‐cell phenotypes that have been identified and how T h cells adopt a particular phenotype. The regulation of T h‐cell phenotypes has been studied extensively using mathematical models, which have explored the role of regulatory mechanisms such as autocrine cytokine signalling and cross‐inhibition between self‐activating transcription factors. At the single cell level, T h responses tend to be heterogeneous, but corrections can be made soon after T ‐cell activation. Although pathogens and the innate immune system provide signals that direct the induction of T h‐cell phenotypes, these instructive mechanisms could be easily subverted by pathogens. We discuss that a model of success‐driven feedback would select the most appropriate phenotype for clearing a pathogen. Given the heterogeneity in the induction phase of the T h response, such a success‐driven feedback loop would allow the selection of effective T h‐cell phenotypes while terminating incorrect responses.