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The cellular adaptive immune response to influenza has been analyzed through several recent mathematical models. In particular, Zarnitsyna et al. (Front Immunol 7:1–9, 2016) show how central memory CD8+ T cells reach a plateau after repeated infections, and analyze their role in the immune response to further challenges. In this paper, we further investigate the theoretical features of that model by extracting from the infection dynamics a discrete map that describes the build-up of memory cells. Furthermore, we show how the model by Zarnitsyna et al. (Front Immunol 7:1–9, 2016) can be viewed as a fast-scale approximation of a model allowing for recruitment of target epithelial cells. Finally, we analyze which components of the model are essential to understand the progressive build-up of immune memory. This is performed through the analysis of simplified versions of the model that include some components only of immune response. The analysis performed may also provide a theoretical framework for understanding the conditions under which two-dose vaccination strategies can be helpful. [ABSTRACT FROM AUTHOR]

The human adaptive immune response is known to weaken in advanced age, resulting in increased severity of pathogen-born illness, poor vaccine efficacy, and a higher prevalence of cancer in the elderly. Age-related erosion of the T cell compartment has been implicated as a likely cause, but the underlying mechanisms driving this immunosenescence have not been quantitatively modeled and systematically analyzed. T cell receptor diversity, or the extent of pathogen-derived antigen responsiveness of the T cell pool, is known to diminish with age, but inherent experimental difficulties preclude accurate analysis on the full organismal level. In this paper, we formulate a mechanistic mathematical model of T cell population dynamics on the immunoclonal subpopulation level, which provides quantitative estimates of diversity. We define different estimates for diversity that depend on the individual number of cells in a specific immunoclone. We show that diversity decreases with age primarily due to diminished thymic output of new T cells and the resulting overall loss of small immunoclones. [ABSTRACT FROM AUTHOR]

Exosomes are nanovesicles shed by cells as a means of communication with other cells. Exosomes contain mRNAs, microRNAs (miRs) and functional proteins. In the present paper, we develop a mathematical model of tumor-immune interaction by means of exosomes shed by pancreatic cancer cells and dendritic cells. Cancer cells’ exosomes contain miRs that promote their proliferation and that inhibit immune response by dendritic cells, and by CD4+ and CD8+ T cells. Dendritic cells release exosomes with proteins that induce apoptosis of cancer cells and that block regulatory T cells. Simulations of the model show how the size of the pancreatic cancer can be determined by measurement of specific miRs (miR-21 and miR-203 in the case of pancreatic cancer), suggesting these miRs as biomarkers for cancer. [ABSTRACT FROM AUTHOR]

Caspase-1-mediated pyroptosis is the predominance for driving CD4+ T cells death. Dying infected CD4+ T cells can release inflammatory signals which attract more uninfected CD4+ T cells to die. This paper is devoted to developing a diffusive mathematical model which can make useful contributions to understanding caspase-1-mediated pyroptosis by inflammatory cytokines IL-1β released from infected cells in the within-host environment. The well-posedness of solutions, basic reproduction number, threshold dynamics are investigated for spatially heterogeneous infection. Travelling wave solutions for spatially homogeneous infection are studied. Numerical computations reveal that the spatially heterogeneous infection can make R0>1, that is, it can induce the persistence of virus compared to the spatially homogeneous infection. We also find that the random movements of virus have no effect on basic reproduction number for the spatially homogeneous model, while it may result in less infection risk for the spatially heterogeneous model, under some suitable parameters. Further, the death of infected CD4+ cells which are caused by pyroptosis can make R0<1, that is, it can induce the extinction of virus, regardless of whether or not the parameters are spatially dependent. [ABSTRACT FROM AUTHOR]

The currently accepted paradigm for the primary T cell response is that effector T cells commit to autonomous developmental programs. This concept is based on several experiments that have demonstrated that the dynamics of a T cell response is largely determined shortly after antigen exposure and that T cell dynamics do not depend on the level and duration of antigen stimulation. Another experimental study has also shown that T cell responses are robust to variations in antigen-specific precursor frequency. Various mathematical models have corroborated the first result that programmed T cell responses are insensitive to the level of antigen stimulation. However, this paper proposes that programmed responses do not entirely explain the robustness of T cell dynamics to variations in precursor frequency. This work studies the hypothesis that the dynamics of a T cell response may also be governed by a feedback loop involving adaptive regulatory cells rather than by intrinsic developmental programs. We formulate two mathematical models based on T cell developmental programs. In one model, effector cells undergo a fixed number of divisions before dying. In the second model, effector cells live for a fixed time during which they may divide. The study of these models suggests that developmental programs are not sufficiently robust as they produce an immune response that directly scales with precursor frequencies. Consequently, we derive a third model based on the principle that adaptive regulatory T cells develop in the course of an immune response and suppress effector cells. Our simulations show that this feedback mechanism responds robustly over a range of at least four orders of magnitude of precursor frequencies. We conclude that the proliferation program paradigm does not entirely capture the observed robustness of T cell responses to variations in precursor frequency. We propose an alternative mechanism by which the primary T cell response is governed by an emergent group dynamic and not by individual T cell programs. [ABSTRACT FROM AUTHOR]

It is widely accepted that the primary immune system contains a subpopulation of cells, known as regulatory T cells whose function is to regulate the immune response. There is conflicting biological evidence regarding the ability of regulatory cells to lose their regulatory capabilities and turn into immune promoting cells. In this paper, we develop mathematical models to investigate the effects of regulatory T cell switching on the immune response. Depending on environmental conditions, regulatory T cells may transition, becoming effector T cells that are immunostimulatory rather than immunoregulatory. We consider this mechanism both in the context of a simple, ordinary differential equation (ODE) model and in the context of a more biologically detailed, delay differential equation (DDE) model of the primary immune response. It is shown that models that incorporate such a mechanism express the usual characteristics of an immune response (expansion, contraction, and memory phases), while being more robust with respect to T cell precursor frequencies. We characterize the affects of regulatory T cell switching on the peak magnitude of the immune response and identify a biologically testable range for the switching parameter. We conclude that regulatory T cell switching may play a key role in controlling immune contraction. [ABSTRACT FROM AUTHOR]

Gut mucosal homeostasis depends on complex interactions among the microbiota, the intestinal epithelium, and the gut associated immune system. A breakdown in some of these interactions may precipitate inflammation. Inflammatory bowel diseases, Crohn’s disease, and ulcerative colitis are chronic inflammatory disorders of the gastrointestinal tract. The initial stages of disease are marked by an abnormally high level of pro-inflammatory helper T cells, Th1. In later stages, Th2 helper cells may dominate while the Th1 response may dampen. The interaction among the T cells includes the regulatory T cells (Treg). The present paper develops a mathematical model by a system of differential equations with terms nonlocal in the space spanned by the concentrations of cytokines that represents the interaction among T cells through a cytokine signaling network. The model demonstrates how the abnormal levels of T cells observed in inflammatory bowel diseases can arise from abnormal regulation of Th1 and Th2 cells by Treg cells. [ABSTRACT FROM AUTHOR]

While antiretroviral drugs can drive HIV to undetectably low levels in the blood, eradication is hindered by the persistence of long-lived, latently infected memory CD4 T cells. Immune activation therapy aims to eliminate this latent reservoir by reactivating these memory cells, exposing them to removal by the immune system and the cytotoxic effects of active infection. In this paper, we develop a mathematical model that investigates the use of immune activation strategies while limiting virus and latent class rebound. Our model considers infection of two memory classes, central and transitional CD4 T cells and the role that general immune activation therapy has on their elimination. Further, we incorporate ways to control viral rebound by blocking activated cell proliferation through anti proliferation therapy. Using the model, we provide insight into the control of latent infection and subsequently into the long term control of HIV infection. [ABSTRACT FROM AUTHOR]

Systems of differentiating cells are often regarded by experimental biologists as unidirectional processes, in which cells spend a fixed time at each successive developmental stage. However, mathematical modeling has in several cases revealed that differentiating cell systems are more complex than previously believed. For example, non-linear transitions, feedback effects, and even apparent reversals have been suggested by our studies on models for the development of lymphocytes and their receptor repertoires, and are reviewed in this paper. These studies have shown that cell population growth in developing lymphocyte subsets is usually nonlinear, as it depends on the density of cells in each compartment. Additionally, T cell development has been shown to be subject to feedback regulation by mature T cell subsets, and B cell development has been shown to include a phenotypic reflux from an advanced to an earlier developmental stage. The challenges we face in our efforts to understand how the repertoires of these cells are generated and regulated are also discussed here. [ABSTRACT FROM AUTHOR]

Mathematical modeling provides a rigorous way to quantify immunological processes and discriminate between alternative mechanisms driving specific biological phenomena. It is typical that mathematical models of immunological phenomena are developed by modelers to explain specific sets of experimental data after the data have been collected by experimental collaborators. Whether the available data are sufficient to accurately estimate model parameters or to discriminate between alternative models is not typically investigated. While previously collected data may be sufficient to guide development of alternative models and help estimating model parameters, such data often do not allow to discriminate between alternative models. As a case study, we develop a series of power analyses to determine optimal sample sizes that allow for accurate estimation of model parameters and for discrimination between alternative models describing clustering of CD8 T cells around Plasmodium liver stages. In our typical experiments, mice are infected intravenously with Plasmodium sporozoites that invade hepatocytes (liver cells), and then activated CD8 T cells are transferred into the infected mice. The number of T cells found in the vicinity of individual infected hepatocytes at different times after T cell transfer is counted using intravital microscopy. We previously developed a series of mathematical models aimed to explain highly variable number of T cells per parasite; one of such models, the density-dependent recruitment (DDR) model, fitted the data from preliminary experiments better than the alternative models, such as the density-independent exit (DIE) model. Here, we show that the ability to discriminate between these alternative models depends on the number of parasites imaged in the analysis; analysis of about n = 50 parasites at 2, 4, and 8 h after T cell transfer will allow for over 95% probability to select the correct model. The type of data collected also has an impact; following T cell clustering around individual parasites over time (called as longitudinal (LT) data) allows for a more precise and less biased estimates of the parameters of the DDR model than that generated from a more traditional way of imaging individual parasites in different liver areas/mice (cross-sectional (CS) data). However, LT imaging comes at a cost of a need to keep the mice alive under the microscope for hours which may be ethically unacceptable. We finally show that the number of time points at which the measurements are taken also impacts the precision of estimation of DDR model parameters; in particular, measuring T cell clustering at one time point does not allow accurately estimating all parameters of the DDR model. Using our case study, we propose a general framework on how mathematical modeling can be used to guide experimental designs and power analyses of complex biological processes. [ABSTRACT FROM AUTHOR]

Lck (lymphocyte-specific protein tyrosine kinase) is an enzyme which plays a number of important roles in the function of immune cells. It belongs to the Src family of kinases which are known to undergo autophosphorylation. It turns out that this leads to a remarkable variety of dynamical behaviour which can occur during their activation. We prove that in the presence of autophosphorylation one phenomenon, bistability, already occurs in a mathematical model for a protein with a single phosphorylation site. We further show that a certain model of Lck exhibits oscillations. Finally, we discuss the relations of these results to models in the literature which involve Lck and describe specific biological processes, such as the early stages of T cell activation and the stimulation of T cell responses resulting from the suppression of PD-1 signalling which is important in immune checkpoint therapy for cancer. [ABSTRACT FROM AUTHOR]

The clonal expansion of T cells during an infection is tightly regulated to ensure an appropriate immune response against invading pathogens. Although experiments have mapped the trajectory from expansion to contraction, the interplay between mechanisms that control this response is not fully understood. Based on experimental data, we propose a model in which the dynamics of CD4+ T cell expansion is controlled through the interactions between T cells and antigen-presenting cells, where T cell stimulation is proportional to antigen availability, and antigen availability is regulated through downregulation of antigen by T cells. This antigen-dependent-feedback mechanism operates alongside an intrinsic reduction in cell proliferation rate that may also be responsible for slowing expansion. Our model can successfully predict T cell recruitment rates into division, expansion, and clonal burst size per cell when initial precursors are varied or when T cells are introduced late into an ongoing immune response. Importantly, the findings demonstrate that a feedback mechanism between T cells and antigen-presenting cells, along with a reduction in cell proliferation rate, can explain the ability of the immune system to adapt its response to variations in initial conditions or changes that occur later in the response, ensuring a robust yet controlled line of defence against pathogens. [ABSTRACT FROM AUTHOR]

A major question in immunology is what role antigen load plays in determining the size of the CD8 immune response. Is the amount of antigen important during recruitment, proliferation, and/or memory formation? Animal studies have shown that antigen is only strictly required early during activation of T cells, but the importance of antigen at later timepoints is unclear. Using data from 24 volunteers infected with the yellow fever vaccine virus (YFV), we analyzed the dependence of T cell proliferation upon viral load. We found that volunteers with high viral load initially have greater T cell responses, but by 28 days post-vaccination those with lower viral load are able to 'catch-up.' Using differential equation modeling we show that this pattern is consistent with viral load only affecting recruitment (i.e., programmed proliferation) as opposed to affecting recruitment and proliferation (i.e., antigen-dependent proliferation). A quantitative understanding of the dependence of T cell dynamics on antigen load will be of use to modelers studying not only vaccination, but also cancer immunology and autoimmune disorders. [ABSTRACT FROM AUTHOR]

A growing body of experimental evidence indicates that immune cells move in an unrestricted search pattern if they are in the pre-activated state, whilst they tend to stay within a more restricted area upon activation induced by the presence of tumour antigens. This change in movement is not often considered in the existing mathematical models of the interactions between immune cells and cancer cells. With the aim to fill such a gap in the existing literature, in this work we present a spatially structured individual-based model of tumour-immune competition that takes explicitly into account the difference in movement between inactive and activated immune cells. In our model, a Lévy walk is used to capture the movement of inactive immune cells, whereas Brownian motion is used to describe the movement of antigen-activated immune cells. The effects of activation of immune cells, the proliferation of cancer cells and the immune destruction of cancer cells are also modelled. We illustrate the ability of our model to reproduce qualitatively the spatial trajectories of immune cells observed in experimental data of single-cell tracking. Computational simulations of our model further clarify the conditions for the onset of a successful immune action against cancer cells and may suggest possible targets to improve the efficacy of cancer immunotherapy. Overall, our theoretical work highlights the importance of taking into account spatial interactions when modelling the immune response to cancer cells. [ABSTRACT FROM AUTHOR]

We modify the classical virus dynamics model by incorporating an immune response with fixed or fluctuating vaccination frequencies and dosages to obtain a system of impulsive differential equations for the virus dynamics of both the wild-type and mutant strains. This model framework permits us to obtain precise conditions for the virus elimination, which are much more feasible compared with existing results, which require frequent vaccine administration with large dosage. We also consider the corresponding impulsive optimal control problem to describe when and how much of the vaccine should be administered in order to maximize levels of healthy CD4 T cells and immune response cells. A gradient-based optimization method is applied to obtain the optimal schedule numerically. For a case study when the CTL vaccine is administered in a period of one year, our numerical studies support the optimal vaccination schedule consisting of vaccine administration three times, with the first dosage strong (to boost the immune system), followed by a second dosage shortly after (to strengthen the immune response) and then the third and final dosage long after (to ensure the immune system can handle viruses rebound). [ABSTRACT FROM AUTHOR]

Immunity to diseases is conferred by pathogen-specific memory cells that prevent disease reoccurrences. A broad repertoire of memory T-cells must be developed and maintained to effectively protect against viral invasions; yet, the total number of memory T-cells is constrained between infections. Thus, creating memory to new infections can require attrition of some existing memory cells. Furthermore, some viruses induce memory T-cell death early in an infection, after which surviving cells proliferate to refill the memory compartment. We develop mathematical models of cellular attrition and proliferation in order to examine how new viral infections impact existing immunity. With these probabilistic models, we qualitatively and quantitatively predict how the composition and diversity of the memory repertoire changes as a result of viral infections. In addition, we calculate how often immunity to prior diseases is lost due to new infections. Comparing our results across multiple general infection types allows us to draw conclusions about, which types of viral effects most drastically alter existing immunity. We find that early memory attrition does not permanently alter the repertoire composition, while infections that spark substantial new memory generation drastically shift the repertoire and hasten the decline of existing immunity. [ABSTRACT FROM AUTHOR]

Cytotoxic T lymphocytes (CTLs) are immune system cells that are thought to play an important role in controlling HIV infection. We develop a stochastic ODE model of HIV-CTL interaction that extends current deterministic ODE models. Based on this stochastic model, we consider the effect of CTL attack on intrahost HIV lineages assuming that CTLs attack several epitopes with equal strength. In this setting, we introduce a limiting version of our stochastic ODE under which we show that the coalescence of HIV lineages can be described through Poisson-Dirichlet distributions. Through numerical experiments, we show that our results under the limiting stochastic ODE accurately reflect HIV lineages under CTL attack when the HIV population size is on the low end of its hypothesized range. Current techniques of HIV lineage construction depend on the Kingman coalescent. Our results give an explicit connection between CTL attack and HIV lineages. [ABSTRACT FROM AUTHOR]

TGF- β is an immunoregulatory protein that contributes to inadequate antitumor immune responses in cancer patients. Recent experimental data suggests that TGF- β inhibition alone, provides few clinical benefits, yet it can significantly amplify the anti-tumor immune response when combined with a tumor vaccine. We develop a mathematical model in order to gain insight into the cooperative interaction between anti-TGF- β and vaccine treatments. The mathematical model follows the dynamics of the tumor size, TGF- β concentration, activated cytotoxic effector cells, and regulatory T cells. Using numerical simulations and stability analysis, we study the following scenarios: a control case of no treatment, anti-TGF- β treatment, vaccine treatment, and combined anti-TGF- β vaccine treatments. We show that our model is capable of capturing the observed experimental results, and hence can be potentially used in designing future experiments involving this approach to immunotherapy. [ABSTRACT FROM AUTHOR]

Stable periodic oscillations have been shown to exist in mathematical models for the CTL response to HTLV-I infection. These periodic oscillations can be the result of mitosis of infected target CD4 cells, of a general form of response function, or of time delays in the CTL response. In this study, we show through a simple mathematical model that time delays in the CTL response process to HTLV-I infection can lead to the coexistence of multiple stable periodic solutions, which differ in amplitude and period, with their own basins of attraction. Our results imply that the dynamic interactions between the CTL immune response and HTLV-I infection are very complex, and that multi-stability in CTL response dynamics can exist in the form of coexisting stable oscillations instead of stable equilibria. Biologically, our findings imply that different routes or initial dosages of the viral infection may lead to quantitatively and qualitatively different outcomes. [ABSTRACT FROM AUTHOR]

Immunodominance refers to the phenomenon in which simultaneous T cell responses against multiple target epitopes organize themselves into distinct and reproducible hierarchies. In many cases, eliminating the response to the most dominant epitope allows responses to subdominant epitopes to expand more fully. The mechanism that drives immunodominance is still not well understood, although various hypotheses have been proposed. One of the more prevalent views is that immunodominance is driven by passive T cell competition for space on antigen presenting cells (APCs) or for access to specific MHC:epitope complexes on the surface of APCs. However, several experimental studies suggest that passive competition alone may not fully explain the robustness of immunodominance under physiological conditions or varying proportions of antigen-specific precursor T cells and APCs. These studies propose that a mechanism of active suppression among T cells gives rise to immunodominance. In this work, we present the novel hypothesis that mutual suppression of simultaneous T cell responses results from the appearance of adaptive regulatory T cells (iTregs) during the course of the overall T cell expansion. We extend the mathematical model of T cell expansion proposed in Kim et al. (Bull. Math. Biol. , doi:) to consider multiple, concurrent T cell responses. The model is formulated as a system of independent feedback loops, in which antigen-specific T cell population produces a nonspecific feedback response. Our simulations show that the fastest response to expand gives rise to a de novo generated population of iTregs that induces a premature contraction in slower or weaker T cell responses, leading to a hierarchical expansion as observed in immunodominance. Furthermore, in some cases, removing the dominant T cell response allows previously subdominant responses to develop more fully. [ABSTRACT FROM AUTHOR]

The class of immunosuppressive lymphocytes known as regulatory T cells (Tregs) has been identified as a key component in preventing autoimmune diseases. Although Tregs have been incorporated previously in mathematical models of autoimmunity, we take a novel approach which emphasizes the importance of professional antigen presenting cells (pAPCs). We examine three possible mechanisms of Treg action (each in isolation) through ordinary differential equation (ODE) models. The immune response against a particular autoantigen is suppressed both by Tregs specific for that antigen and by Tregs of arbitrary specificities, through their action on either maturing or already mature pAPCs or on autoreactive effector T cells. In this deterministic approach, we find that qualitative long-term behaviour is predicted by the basic reproductive ratio R for each system. When R<1, only the trivial equilibrium exists and is stable; when R>1, this equilibrium loses its stability and a stable non-trivial equilibrium appears. We interpret the absence of self-damaging populations at the trivial equilibrium to imply a state of self-tolerance, and their presence at the non-trivial equilibrium to imply a state of chronic autoimmunity. Irrespective of mechanism, our model predicts that Tregs specific for the autoantigen in question play no role in the system's qualitative long-term behaviour, but have quantitative effects that could potentially reduce an autoimmune response to sub-clinical levels. Our results also suggest an important role for Tregs of arbitrary specificities in modulating the qualitative outcome. A stochastic treatment of the same model demonstrates that the probability of developing a chronic autoimmune response increases with the initial exposure to self antigen or autoreactive effector T cells. The three different mechanisms we consider, while leading to a number of similar predictions, also exhibit key differences in both transient dynamics (ODE approach) and the probability of chronic autoimmunity (stochastic approach). [ABSTRACT FROM AUTHOR]

We briefly review spatially homogeneous mechanistic mathematical models describing the interactions between a malignant tumor and the immune system. We begin with the simplest (single equation) models for tumor growth and proceed to consider greater immunological detail (and correspondingly more equations) in steps. This approach allows us to clarify the necessity for expanding the complexity of models in order to capture the biological mechanisms we wish to understand. We conclude by discussing some unsolved problems in the mathematical modeling of cancer-immune system interactions. [ABSTRACT FROM AUTHOR]

A mathematical model of the host’s immune response to HIV infection is proposed. The model represents the dynamics of 13 subsets of T cells (HIV-specific and nonspecific, healthy and infected, T4 and T8 cells), infected macrophages, neutralizing antibodies, and virus. The results of simulation are in agreement with published data regarding T4 cell concentration and viral load, and exhibit the typical features of HIV infection, i.e. double viral peaks in the acute stage, sero conversion, inverted T cell ratio, establishment of set points, steady state, and decline into AIDS. This result is achieved by taking into account thymic aging, viral and infected cell stimulation of specific immune cells, background nonspecific antigens, infected cell proliferation, viral production by infected macrophages and T cells, tropism, viral, and immune adaptation. Starting from this paradigm, changes in the parameter values simulate observed differences in individual outcomes, and predict different scenarios, which can suggest new directions in therapy. In particular, large parameter changes highlight the potentially critical role of both very vigorous and extremely damped specific immune response, and of the elimination of virus release by macrophages. Finally, the time courses of virus, antibody and T cells production and removal are systematically investigated, and a comparison of T4 and T8 cell dynamics in a healthy and in a HIV infected host is offered. [ABSTRACT FROM AUTHOR]

The fluorescent dye carboxyfluorescein diacetate succinimidyl ester (CFSE) classifies proliferating cell populations into groups according to the number of divisions each cell has undergone (i.e., its division class). The pulse labeling of cells with radioactive thymidine provides a means to determine the distribution of times of entry into the first cell division. We derive in analytic form the number of cells in each division class as a function of time based on the distribution of times to the first division. Choosing the distribution of time to the first division to fit thymidine labeling data for T cells stimulated in vitro under different concentrations of IL-2, we fit CFSE data to determine the dependence of T cell kinetic parameters on the concentration of IL-2. As the concentration of IL-2 increases, the average cell cycle time is shortened, the death rate of cells is decreased, and a higher fraction of cells is recruited into division. We also find that if the average cell cycle time increases with division class then the qualify of our fit to the data improves. [ABSTRACT FROM AUTHOR]

The division tracking dye, carboxyfluorescin diacetate succinimidyl ester (CFSE) is currently the most informative labeling technique for characterizing the division history of cells in the immune system. Gett and Hodgkin [Nat. Immunol. 1:239-244, 2000] have pioneered the quantitative analysis of CFSE data. We confirm and extend their data analysis approach using simple mathematical models. We employ the extended Gett and Hodgkin [Nat. Immunol. 1:239-244, 2000] method to estimate the time to first division, the fraction of cells recruited into division, the cell cycle time, and the average death rate from CFSE data on T cells stimulated under different concentrations of IL-2. The same data is also fitted with a simple mathematical model that we derived by reformulating the numerical model of Deenick et al. [J. Immunol. 170:4963-4972, 2003]. By a non-linear fitting procedure we estimate parameter values and confidence intervals to identify the parameters that are influenced by the IL-2 concentration. We obtain a significantly better fit to the data when we assume that the T cell death rate depends on the number of divisions cells have completed. We provide an outlook on future work that involves extending the Deenick et al. [J. Immunol. 170:4963-4972, 2003] model into the classical Smith-Martin model, and into a model with arbitrary probability distributions for death and division through subsequent divisions. [ABSTRACT FROM AUTHOR]

Abstract: Human T-cell Lymphotropic Virus Type I (HTLV-I) primarily infects CD4+ helper T cells. HTLV-I infection is clinically linked to the development of Adult T-cell Leukemia/Lymphoma and of HTLV-I Associated Myelopathy/Tropical Spastic Paraparesis, among other illnesses. HTLV-I transmission can be either horizontal through cell-to-cell contact, or vertical through mitotic division of infected CD4+ T cells. It has been observed that HTLV-I infection has a high proviral load but a low rate of proviral genetic variation. This suggests that vertical transmission through mitotic division of infected cells may play an important role. We consider and analyze a mathematical model for HTLV-I infection of CD4+ T cells that incorporates both horizontal and vertical transmission. Among interesting dynamical behaviors of the model is a backward bifurcation which raises many new challenges to effective infection control. [Copyright &y& Elsevier]

The kinetics of the cytotoxic T lymphocyte (CTL) response against intracellular pathogens has been found to have many stereotypical features that appear to be programmed early in the infection. We explain these findings here in terms of CTL response kinetics that minimize the probability that a pathological symptom will occur in association with the infection and its eradication. We assume that both the infection and the CTLs contribute to this pathology. We find that contraction kinetics is influenced by the relative pathogenicities of infection and CTLs, as well as on the virulence of the infection and the efficiency of the CTLs, but not by the magnitude of expansion or the dose and duration of infection. Our analysis explains the finding that the duration of the CTL expansion is highly stereotypical, with the maximum expansion of the CTL response dependent on the dose of the infection. Finally, we show that the stereotypical nature of CTL kinetics relies upon stringent regulation of the rates at which CTLs proliferate and die. [Copyright &y& Elsevier]

We present an immunological model that considers the dynamics of CD4+ T cells interacting with free virions, reverse transcriptase inhibiting drugs and protease inhibiting drugs. We divide the T cells into multiple classes and use impulsive differential equations to describe the drug activity. As expected, we find that insufficient dosing of either drug corresponds to high viral load and a large population of infectious T cells. The model further predicts that, in the absence of physiological limits on tolerable drug concentrations, sufficiently frequent dosing with the reverse transcriptase inhibitor alone could theoretically maintain the CD4+ T cell count arbitrarily close to the T cell count in the uninfected immune system. However, for frequent dosing of the protease inhibitor alone, the limiting T cell populations may not be enough to maintain the immune system. Furthermore, frequent dosing of both drugs has the same net effect on the T cell population as frequent dosing of the reverse transcriptase inhibitor only. Thus, the two drug classes can have fundamentally different effects on the long-term dynamics and the reverse transcriptase inhibitor, in particular, plays a crucial role in maintaining the immune system. We also provide estimates for the dosing intervals of each drug that could theoretically sustain the T cell population at a desired level. [Copyright &y& Elsevier]

An overwhelming virus infection that spreads within a few days throughout the host can cause deletion of the specific cytotoxic T lymphocytes (CTL). This phenomenon is known as ‘clonal exhaustion’. Current explanations for this phenomenon are ‘clonal’, and consider either the terminal differentiation of the virus-specific CTL to an effector phenotype, or the lack of help and antigen presentation for a specific CTL clone. The virus remains controlled by some other form of immunity in the exhausted state. Candidates are innate immunity (especially NK cells and macrophages) and a T helper type 2 based immune response. Surprisingly, the role of this other form of immunity in causing exhaustion has been ignored so far. Developing a mathematical model, we here investigate the possibility that this inter-clonal immunity is responsible for exhaustion by down regulating the CTL response. The model is based on previously published exhaustion data for Lymphocytic choriomeningitis virus as an in vivo model. We demonstrate that several complicated experiments on clonal exhaustion are consistent with inter-clonal regulation. By interpreting the available data with a mathematical model, we compare this novel mechanism with the mechanisms suggested previously. [Copyright &y& Elsevier]