Discrete Event Modeling of CD4+ Memory T Cell Generation

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.

Investigating mathematical models of immuno-interactions with early-stage cancer under an agent-based modelling perspective

Many advances in research regarding immuno-interactions with cancer were developed with the help of ordinary differential equation (ODE) models. These models, however, are not effectively capable of representing problems involving individual localisation, memory and emerging properties, which are common characteristics of cells and molecules of the immune system. Agent-based modelling and simulation is an alternative paradigm to ODE models that overcomes these limitations. In this paper we investigate the potential contribution of agent-based modelling and simulation when compared to ODE modelling and simulation. We seek answers to the following questions: Is it possible to obtain an equivalent agent-based model from the ODE formulation? Do the outcomes differ? Are there any benefits of using one method compared to the other? To answer these questions, we have considered three case studies using established mathematical models of immune interactions with early-stage cancer. These case studies were re-conceptualised under an agent-based perspective and the simulation results were then compared with those from the ODE models. Our results show that it is possible to obtain equivalent agent-based models (i.e. implementing the same mechanisms); the simulation output of both types of models however might differ depending on the attributes of the system to be modelled. In some cases, additional insight from using agent-based modelling was obtained. Overall, we can confirm that agent-based modelling is a useful addition to the tool set of immunologists, as it has extra features that allow for simulations with characteristics that are closer to the biological phenomena.

Modeling using discrete event simulation: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-4

Discrete event simulation (DES) is a form of computer-based modeling that provides an intuitive and flexible approach to representing complex systems. It has been used in a wide range of health care applications. Most early applications involved analyses of systems with constrained resources, where the general aim was to improve the organization of delivered services. More recently, DES has increasingly been applied to evaluate specific technologies in the context of health technology assessment. The aim of this article is to provide consensus-based guidelines on the application of DES in a health care setting, covering the range of issues to which DES can be applied. The article works through the different stages of the modeling process: structural development, parameter estimation, model implementation, model analysis, and representation and reporting. For each stage, a brief description is provided, followed by consideration of issues that are of particular relevance to the application of DES in a health care setting. Each section contains a number of best practice recommendations that were iterated among the authors, as well as the wider modeling task force.

Modeling using discrete event simulation: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force--4

Discrete event simulation (DES) is a form of computer-based modeling that provides an intuitive and flexible approach to representing complex systems. It has been used in a wide range of health care applications. Most early applications involved analyses of systems with constrained resources, where the general aim was to improve the organization of delivered services. More recently, DES has increasingly been applied to evaluate specific technologies in the context of health technology assessment. The aim of this article was to provide consensus-based guidelines on the application of DES in a health care setting, covering the range of issues to which DES can be applied. The article works through the different stages of the modeling process: structural development, parameter estimation, model implementation, model analysis, and representation and reporting. For each stage, a brief description is provided, followed by consideration of issues that are of particular relevance to the application of DES in a health care setting. Each section contains a number of best practice recommendations that were iterated among the authors, as well as among the wider modeling task force.

Modelling experimental uveitis: barrier effects in autoimmune disease

OBJECTIVE AND DESIGN

A mathematical analysis of leukocytes accumulating in experimental autoimmune uveitis (EAU), using ordinary differential equations (ODEs) and incorporating a barrier to cell traffic.

MATERIALS AND SUBJECTS

Data from an analysis of the kinetics of cell accumulation within the eye during EAU.

METHODS

We applied a well-established mathematical approach that uses ODEs to describe the behaviour of cells on both sides of the blood-retinal barrier and compared data from the mathematical model with experimental data from animals with EAU.

RESULTS

The presence of the barrier is critical to the ability of the model to qualitatively reproduce the experimental data. However, barrier breakdown is not sufficient to produce a surge of cells into the eye, which depends also on asymmetry in the rates at which cells can penetrate the barrier. Antigen-presenting cell (APC) generation also plays a critical role and we can derive from the model the ratio for APC production under inflammatory conditions relative to production in the resting state, which has a value that agrees closely with that found by experiment.

CONCLUSIONS

Asymmetric trafficking and the dynamics of APC production play an important role in the dynamics of cell accumulation in EAU.

In vitro derivation of interferon-γ producing, IL-4 and IL-7 responsive memory-like CD4(+) T cells

CD4(+) memory is critical for successful protection against pathogenic challenge. As such, understanding the heterogeneity of cells that arise and survive after initial stimulation of naïve CD4(+) T cells will aid in the design of more successful vaccines. In previous studies, in vivo experimental systems have been extensively used to generate functional memory responses by lymphocytes. Here, we have attempted to develop an in vitro experimental system to generate memory CD4(+) T lymphocytes. CD4(+) T cells stimulated through the antigen receptor complex were examined for their memory-like characteristics after 3 weeks of cell culture. A subset of surviving cells expressed high levels of CD44 and low levels of CD45RB (CD44(hi)CD45(lo)), a phenotype that is similar to bonafide memory CD4(+) T cells. In vitro generated memory-like CD4(+) T cells secreted higher levels of IFN-γ, with rapid kinetics, upon re-stimulation than their naïve counterparts. In addition, these memory-like CD4(+) T cells did not produce either IL-2 or IL-4 but readily proliferated when cultured in the presence of IL-7 and IL-4. These observations suggest that CD4(+) cells surviving the expansion phase of immune response produce a Th1-signature cytokine and retain responsiveness to IL-4, a Th-2 cytokine, as well as to a well described survival factor, interleukin-7.

An age-dependent branching process model for the analysis of CFSE-labeling experiments

BACKGROUND

Over the past decade, flow cytometric CFSE-labeling experiments have gained considerable popularity among experimentalists, especially immunologists and hematologists, for studying the processes of cell proliferation and cell death. Several mathematical models have been presented in the literature to describe cell kinetics during these experiments.

RESULTS

We propose a multi-type age-dependent branching process to model the temporal development of populations of cells subject to division and death during CFSE-labeling experiments. We discuss practical implementation of the proposed model; we investigate a competing risk version of the process; and we identify the classes of cellular dependencies that may influence the expectation of the process and those that do not. An application is presented where we study the proliferation of human CD8+ T lymphocytes using our model and a competing risk branching process.

CONCLUSIONS

The proposed model offers a widely applicable approach to the analysis of CFSE-labeling experiments. The model fitted very well our experimental data. It provided reasonable estimates of cell kinetics parameters as well as meaningful insights into the processes of cell division and cell death. In contrast, the competing risk branching process could not describe the kinetics of CD8+ T cells. This suggested that the decision of cell division or cell death may be made early in the cell cycle if not in preceding generations. Also, we show that analyses based on the proposed model are robust with respect to cross-sectional dependencies and to dependencies between fates of linearly filiated cells.

REVIEWERS

This article was reviewed by Marek Kimmel, Wai-Yuan Tan and Peter Olofsson.

Discriminating between different pathways of memory CD8+ T cell differentiation

Despite the rapid accumulation of quantitative data on the dynamics of CD8(+) T cell responses following acute viral or bacterial infections of mice, the pathways of differentiation of naive CD8(+) T cells into memory during an immune response remain controversial. Currently, three models have been proposed. In the "stem cell-associated differentiation" model, following activation, naive T cells differentiate into stem cell-like memory cells, which then convert into terminally differentiated short-lived effector cells. In the "linear differentiation" model, following activation, naive T cells first differentiate into effectors, and after Ag clearance, effectors convert into memory cells. Finally, in the "progressive differentiation" model, naive T cells differentiate into memory or effector cells depending on the amount of specific stimulation received, with weaker stimulation resulting in formation of memory cells. This study investigates whether the mathematical models formulated from these hypotheses are consistent with the data on the dynamics of the CD8(+) T cell response to lymphocytic choriomeningitis virus during acute infection of mice. Findings indicate that two models, the stem cell-associated differentiation model and the progressive differentiation model, in which differentiation of cells is strongly linked to the number of cell divisions, fail to describe the data at biologically reasonable parameter values. This work suggests additional experimental tests that may allow for further discrimination between different models of CD8(+) T cell differentiation in acute infections.

Costs versus benefits: best possible and best practical treatment regimens for HIV

Current HIV therapy, although highly effective, may cause very serious side effects, making adherence to the prescribed regimen difficult. Mathematical modeling may be used to evaluate alternative treatment regimens by weighing the positive results of treatment, such as higher levels of helper T cells, against the negative consequences, such as side effects and the possibility of resistance mutations. Although estimating the weights assigned to these factors is difficult, current clinical practice offers insight by defining situations in which therapy is considered "worthwhile". We therefore use clinical practice, along with the probability that a drug-resistant mutation is present at the start of therapy, to suggest methods of rationally estimating these weights. In our underlying model, we use ordinary differential equations to describe the time course of in-host HIV infection, and include populations of both activated CD4(+) T cells and CD8(+) T cells. We then determine the best possible treatment regimen, assuming that the effectiveness of the drug can be continually adjusted, and the best practical treatment regimen, evaluating all patterns of a block of days "on" therapy followed by a block of days "off" therapy. We find that when the tolerance for drug-resistant mutations is low, high drug concentrations which maintain low infected cell populations are optimal. In contrast, if the tolerance for drug-resistant mutations is fairly high, the optimal treatment involves periods of reduced drug exposure which consequently boost the immune response through increased antigen exposure. We elucidate the dependence of the optimal treatment regimen on the pharmacokinetic parameters of specific antiviral agents.

Distinct mechanisms control human naive and antigen-experienced CD8+ T lymphocyte proliferation

Human Ag-specific CD8(+) T lymphocytes are heterogeneous and include functionally distinct populations. In this study, we report that at least two distinct mechanisms control the expansion of circulating naive, memory, and effector CD8(+) T lymphocytes when exposed to mitogen or Ag stimulation. The first one leads to apoptosis and occurs shortly after in vitro stimulation. Susceptibility to cell death is prominent among primed T cell subsets, and it is inversely correlated with the size of the ex vivo Bcl-2(high) population within these subsets. Importantly, the Bcl-2(high) phenotype is associated to the proportion of responsive CD8(+) T cells, independently of their differentiation stage. The second one depends on the expression of newly synthesized cyclin-dependent kinase inhibitor p16(INK4a) that occurs in a significant fraction of T cells that had been actively cycling, leading to their cell cycle arrest upon stimulation. Strikingly, accumulation of p16(INK4a) protein preferentially occurs in naive as opposed to primed derived T lymphocytes and is not related to apoptosis. Significant levels of p16 are readily detectable in a small number of ex vivo CD8(+) T cells. Our observations reveal that activation-induced p16 expression represents an alternative process to apoptosis, limiting the proliferation potential of activated naive derived T lymphocytes.

The role of models in understanding CD8+ T-cell memory

Immunological memory - the ability to 'remember' previously encountered pathogens and respond faster on re-exposure - is a central feature of the immune response of vertebrates. We outline how mathematical models have contributed to our understanding of CD8(+) T-cell memory. Together with experimental data, models have helped to quantitatively describe and to further our understanding of both the generation of memory after infection with a pathogen and the maintenance of this memory throughout the life of an individual.