Search

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 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]

Replication-competent viruses have the potential to overcome the delivery barrier in tumors that has plagued traditional gene-therapy approaches to cancer treatment. However, recent clinical data suggests that a cytokine-based immune response against the virus-infected tumor cells may severely limit the efficacy of the replication-competent approach. This paper generalizes our earlier spatial model to incorporate an immune response against the infected tumor cells. An approximate but accurate condition is derived for the virus—if uniformly injected throughout the tumor—to eradicate the tumor in the presence of the immune response. To validate the model using clinical data describing the temporal interaction of tumor necrosis factor and free virus in the plasma, we needed the immune response to be time-delayed and experience either saturated stimulation or second-order clearance. The resulting estimates of some unknown parameters provide some implications for the delivery of treatment. [Copyright &y& Elsevier]

Type 1 diabetes (T1D) is often triggered by a viral infection, but the T1D prevalence is rising among populations that have a lower exposure to viral infection. In an animal model of T1D, the NOD mouse, viral infection at different ages may either accelerate or delay disease depending on the age of infection and the type of virus. Viral infection may affect the progression of T1D via multiple mechanisms: triggering inflammation, bystander activation of self-reactive T-cells, inducing a competitive immune response, or inducing a regulatory immune response. In this paper, we create mathematical models of the interaction of viral infection with T1D progression, incorporating each of these four mechanisms. Our goal is to understand how each viral mechanism interacts with the age of infection. The model predicts that each viral mechanism has a unique pattern of interaction with disease progression. Viral inflammation always accelerates disease, but the effect decreases with age of infection. Bystander activation has little effect at younger ages and actually decreases incidence at later ages while accelerating disease in mice that do get the disease. A competitive immune response to infection can decrease incidence at young ages and increase it at older ages, with the effect decreasing over time. Finally, an induced Treg response decreases incidence at any age of infection, but the effect decreases with age. Some of these patterns resemble those seen experimentally. [ABSTRACT FROM AUTHOR]

Airway exposure levels of lipopolysaccharide (LPS) are known to determine type I versus type II helper T cell induced experimental asthma. While low doses of LPS derive Th2 inflammatory responses, high (and/or intermediate) LPS levels induce Th1- or Th17-dominant responses. The present paper develops a mathematical model of the phenotypic switches among three Th phenotypes (Th1, Th2, and Th17) in response to various LPS levels. In the present work, we simplify the complex network of the interactions between cells and regulatory molecules. The model describes the nonlinear cross-talks between the IL-4/Th2 activities and a key regulatory molecule, transforming growth factor β (TGF- β), in response to high, intermediate, and low levels of LPS. The model characterizes development of three phenotypes (Th1, Th2, and Th17) and predicts the onset of a new phenotype, Th17, under the tight control of TGF- β. Analysis of the model illustrates the mono-, bi-, and oneway-switches in the key regulatory parameter sets in the absence or presence of time delays. The model also predicts coexistence of those phenotypes and Th1- or Th2-dominant immune responses in a spatial domain under various biochemical and bio-mechanical conditions in the microenvironment. [ABSTRACT FROM AUTHOR]

Collective cell migration is a fundamental process that takes place during several biological phenomena such as embryogenesis, immunity response, and tumorogenesis, but the mechanisms that regulate it are still unclear. Similarly to collective animal behavior, cells receive feedbacks in space and time, which control the direction of the migration and the synergy between the cells of the population, respectively. While in single cell migration intra-synchronization (i.e. the synchronization between the protrusion-contraction movement of the cell and the adhesion forces exerted by the cell to move forward) is a sufficient condition for an efficient migration, in collective cell migration the cells must communicate and coordinate their movement between each other in order to be as efficient as possible (i.e. inter-synchronization). Here, we propose a 2D mechanical model of a cell population, which is described as a continuum with embedded discrete cells with or without motility phenotype. The decomposition of the deformation gradient is employed to reproduce the cyclic active strains of each single cell (i.e. protrusion and contraction). We explore different modes of collective migration to investigate the mechanical interplay between intra- and inter-synchronization. The main objective of the paper is to evaluate the efficiency of the cell population in terms of covered distance and how the stress distribution inside the cohort and the single cells may in turn provide insights regarding such efficiency. [ABSTRACT FROM AUTHOR]

The human immune response to bacterial pathogens is a remarkably complex process, involving many different cell types, chemical signals, and extensive lines of communication. Mathematical models of this system have become increasingly high-dimensional and complicated, as researchers seek to capture many of the major dynamics. In this paper, we argue that, in some important instances, preference should be given to low-dimensional models of immune response, as opposed to their high-dimensional counterparts. One such model is analyzed and shown to reflect many of the key phenomenological properties of the immune response in humans. Notably, this model includes a single parameter that, when combined with a single set of reference parameter values, may be used to quantify the overall immunocompetence of individual hosts. [ABSTRACT FROM AUTHOR]

This paper analyzes the biochemical equilibria between bivalent receptors, homo-bifunctional ligands, monovalent inhibitors, and their complexes. Such reaction schemes arise in the immune response, where immunoglobulins (bivalent receptors) bind to pathogens or allergens. The equilibria may be described by an infinite system of algebraic equations, which accounts for complexes of arbitrary size n ( n being the number of receptors present in the complex). The system can be reduced to just 3 algebraic equations for the concentrations of free (unbound) receptor, free ligand and free inhibitor. Concentrations of all other complexes can be written explicitly in terms of these variables. We analyze how concentrations of key (experimentally-measurable) quantities vary with system parameters. Such measured quantities can furnish important information about dissociation constants in the system, which are difficult to obtain by other means. We provide analytical expressions and suggest specific experiments that could be used to determine the dissociation constants. [ABSTRACT FROM AUTHOR]

In this paper, we show how a game theoretic analysis can provide a model to explain the interdependence of host produced APOBEC3G levels and virus encoded Vif levels. We then use the relationship between these two opposing proteins in order to predict the success of two different HIV-1 viral variants, R5 and X4. From our analysis, we show that when APOBEC3G strongly favors mutation from an R5 strain to an X4 strain, it can be optimal for HIV-1 to suppress transmission of the X4 variant, despite the loss of X4 fitness potential. This is particularly true when the X4 strain significantly interferes with the host adaptive immune response, when Vif production is limited, or when host APOBEC3G targets the X4 strain more severely than the R5 strain. Using the proposed game theoretic analysis, we show that transmitting only R5 viruses has two advantages so far as HIV-1 is concerned. First, it allows for an increased R5 viral load due to immune interference caused by the X4 strain, and second, it forces the host to down-regulate APOBEC3G production, which is automatically favorable to the virus. APOBEC3G down-regulation, which is predicted in our model for a wide range of parameter values, may offer an explanation for the observed low level of APOBEC3G transcription and translation in hosts infected with HIV-1. [ABSTRACT FROM AUTHOR]

lthough imatinib is an effective treatment for chronic myelogenous leukemia (CML), and nearly all patients treated with imatinib attain some form of remission, imatinib does not completely eliminate leukemia. Moreover, if the imatinib treatment is stopped, most patients eventually relapse (Cortes et al. in Clin. Cancer Res. 11:3425-3432, ). In Kim et al. (PLoS Comput. Biol. 4(6):e1000095, ), the authors presented a mathematical model for the dynamics of CML under imatinib treatment that incorporates the anti-leukemia immune response. We use the mathematical model in Kim et al. (PLoS Comput. Biol. 4(6):e1000095, ) to study and numerically simulate strategic treatment interruptions as a potential therapeutic strategy for CML patients. We present the results of numerous simulated treatment programs in which imatinib treatment is temporarily stopped to stimulate and leverage the anti-leukemia immune response to combat CML. The simulations presented in this paper imply that treatment programs that involve strategic treatment interruptions may prevent leukemia from relapsing and may prevent remission for significantly longer than continuous imatinib treatment. Moreover, in many cases, strategic treatment interruptions may completely eliminate leukemic cells from the body. Thus, strategic treatment interruptions may be a feasible clinical approach to enhancing the effects of imatinib treatment for CML. We study the effects of both the timing and the duration of the treatment interruption on the results of the treatment. We also present a sensitivity analysis of the results to the parameters in the mathematical model. [ABSTRACT FROM AUTHOR]

We present a theoretical study of superficial bladder cancer growth and its treatment via pulsed immunotherapy with Bacillus Calmette-Guérin (BCG), an attenuated strain of Mycobacterium bovis. BCG pulsed immunotherapy is a clinically established procedure for the treatment of superficial bladder cancer. In this paper, periodic BCG instillations are modeled using impulsive differential equations, which are studied using a combination of analytical and numerical techniques. In this way, we determine critical threshold values of the BCG instillation dose and rate of pulsing for successful treatment. We also identify treatment regimes in which tumor destruction occurs, but undesirable side effects are maintained at low levels by the immune system. [ABSTRACT FROM AUTHOR]

Immunotherapy with Bacillus Calmette-Guérin (BCG)-an attenuated strain of Mycobacterium bovis (M. bovis) used for anti tuberculosis immunization-is a clinically established procedure for the treatment of superficial bladder cancer. However, the mode of action has not yet been fully elucidated, despite much extensive biological experience. The purpose of this paper is to develop a first mathematical model that describes tumor-immune interactions in the bladder as a result of BCG therapy. A mathematical analysis of the ODE model identifies multiple equilibrium points, their stability properties, and bifurcation points. Intriguing regimes of bistability are identified in which treatment has potential to result in a tumor-free equilibrium or a full-blown tumor depending only on initial conditions. Attention is given to estimating parameters and validating the model using published data taken from in vitro, mouse and human studies. The model makes clear that intensity of immunotherapy must be kept in limited bounds. While small treatment levels may fail to clear the tumor, a treatment that is too large can lead to an over-stimulated immune system having dangerous side effects for the patient. [ABSTRACT FROM AUTHOR]

In this paper, we use both mathematical modeling and simulation to explore homeostasis of peripheral immune system effector cells, particularly alveolar macrophages. Our interest is in the distributed control mechanisms that allow such a population to maintain itself. We introduce a multi-purpose simulator designed to study individual cell responses to local molecular signals and their effects on population dynamics. We use the simulator to develop a model of growth factor regulation of macrophage proliferation and survival. We examine the effects of this form of regulation in the context of two competing hypotheses regarding the source of new alveolar macrophages. In one model, local cells divide to replenish the population; in the other, only cells migrating from circulation divide. We find that either scenario is plausible, although the influx-driven system is inherently more stable. The proliferation-driven system requires lower cell death and efflux rates than the influx-driven system. [Copyright &y& Elsevier]

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]

Here, we discuss how the tendency of a liver infection to chronify can be seen as an evolutionary advantage for infected individuals. For this purpose, we present a set of reaction–diffusion equations as a mathematical model of viral liver infections, which allows chronic and acute courses of the liver infection. We introduce a cumulative wealth function, and finally, we show that an immune response favoring the chronification is evolutionary advantageous at the same time. [ABSTRACT FROM AUTHOR]

We develop an age-structured ODE model to investigate the role of intermittent preventive treatment (IPT) in averting malaria-induced mortality in children, and its related cost in promoting the spread of antimalarial drug resistance. IPT, a malaria control strategy in which a full curative dose of an antimalarial medication is administered to vulnerable asymptomatic individuals at specified intervals, has been shown to reduce malaria transmission and deaths in children and pregnant women. However, it can also promote drug resistance spread. Our mathematical model is used to explore IPT effects on drug resistance and deaths averted in holoendemic malaria regions. The model includes drug-sensitive and drug-resistant strains as well as human hosts and mosquitoes. The basic reproduction, and invasion reproduction numbers for both strains are derived. Numerical simulations show the individual and combined effects of IPT and treatment of symptomatic infections on the prevalence of both strains and the number of lives saved. Our results suggest that while IPT can indeed save lives, particularly in high transmission regions, certain combinations of drugs used for IPT and to treat symptomatic infection may result in more deaths when resistant parasite strains are circulating. Moreover, the half-lives of the treatment and IPT drugs used play an important role in the extent to which IPT may influence spread of the resistant strain. A sensitivity analysis indicates the model outcomes are most sensitive to the reduction factor of transmission for the resistant strain, rate of immunity loss, and the natural clearance rate of sensitive infections. [ABSTRACT FROM AUTHOR]

Immune interventions consisting in repeated injections are broadly used as they are thought to improve the quantity and the quality of the immune response. However, they also raise several questions that remain unanswered, in particular the number of injections to make or the delay to respect between different injections to achieve this goal. Practical and financial considerations add constraints to these questions, especially in the framework of human studies. We specifically focus here on the use of interleukin-7 (IL-7) injections in HIV-infected patients under antiretroviral treatment, but still unable to restore normal levels of CD4+ T lymphocytes. Clinical trials have already shown that repeated cycles of injections of IL-7 could help maintaining CD4+ T lymphocytes levels over the limit of 500 cells/μL, by affecting proliferation and survival of CD4+ T cells. We then aim at answering the question: how to maintain a patients level of CD4+ T lymphocytes by using a minimum number of injections (i.e., optimizing the strategy of injections)? Based on mechanistic models that were previously developed for the dynamics of CD4+ T lymphocytes in this context, we model the process by a piecewise deterministic Markov model. We then address the question by using some recently established theory on impulse control problem in order to develop a numerical tool determining the optimal strategy. Results are obtained on a reduced model, as a proof of concept: the method allows to define an optimal strategy for a given patient. This method could be applied to optimize injections schedules in clinical trials. [ABSTRACT FROM AUTHOR]

The human body’s immune response to bacterial challenge, even when successful in controlling the infection, can result in negative consequences for the host, including reduced functionality of associated tissues. We present and analyze a low-dimensional mathematical model of this immune response to pathogen invasion, incorporating the coordinated actions of active immune cells, and both pro- and anti-inflammatory cytokines. The model simulates both the positive (pathogen reduction) and negative (local tissue dysfunction) effects of the immune response and includes the important role of immunologic memory in the process of a return to stasis. This differential equation-based model is sufficiently general to be applicable to a wide range of human tissues and organs. [ABSTRACT FROM AUTHOR]

We describe here a simple model for the interaction between leukemic cells and the autologous immune response in chronic phase chronic myelogenous leukemia (CML). This model is a simplified version of the model we proposed in Clapp et al. (Cancer Res 75:4053-4062, 2015). Our simplification is based on the observation that certain key characteristics of the dynamics of CML can be captured with a three-compartment model: two for the leukemic cells (stem cells and mature cells) and one for the immune response. We characterize the existence of steady states and their stability for generic forms of immunosuppressive effects of leukemic cells. We provide a complete co-dimension one bifurcation analysis. Our results show how clinical response to tyrosine kinase inhibitors treatment is compatible with the existence of a stable low disease, treatment-free steady state. [ABSTRACT FROM AUTHOR]

Does target cell depletion, innate immunity, or adaptive immunity play the dominant role in controlling primary acute viral infections? Why do some individuals have higher peak virus titers than others? Answering these questions is a basic problem in immunology and can be particularly difficult in humans due to limited data, heterogeneity in responses in different individuals, and limited ability for experimental manipulation. We address these questions for infections following vaccination with the live attenuated yellow fever virus (YFV-17D) by analyzing viral load data from 80 volunteers. Using a mixed effects modeling approach, we find that target cell depletion models do not fit the data as well as innate or adaptive immunity models. Examination of the fits of the innate and adaptive immunity models to the data allows us to select a minimal model that gives improved fits by widely used model selection criteria (AICc and BIC) and explains why it is hard to distinguish between the innate and adaptive immunity models. We then ask why some individuals have over 1000-fold higher virus titers than others and find that most of the variation arises from differences in the initial/maximum growth rate of the virus in different individuals. [ABSTRACT FROM AUTHOR]

Collective cell migration and proliferation are integral to tissue repair, embryonic development, the immune response and cancer. Central to collective cell migration and proliferation are interactions among neighbouring cells, such as volume exclusion, contact inhibition and adhesion. These individual-level processes can have important effects on population-level outcomes, such as growth rate and equilibrium density. We develop an individual-based model of cell migration and proliferation that includes these interactions. This is an extension of a previous model with neighbour-dependent directional bias to incorporate neighbour-dependent proliferation and death. A deterministic approximation to this individual-based model is derived using a spatial moment dynamics approach, which retains information about the spatial structure of the cell population. We show that the individual-based model and spatial moment model match well across a range of parameter values. The spatial moment model allows insight into the two-way interaction between spatial structure and population dynamics that cannot be captured by traditional mean-field models. [ABSTRACT FROM AUTHOR]

We present a spatiotemporal mathematical model of chlamydial infection, host immune response, and movement of infectious particles. The resulting partial differential equations model both the dynamics of the infection and changes in infection profile observed spatially along the length of the host genital tract. This model advances previous Chlamydia modelling by incorporating spatial change. Numerical solutions and model analysis are carried out, and we present a hypothesis regarding the potential for treatment and prevention of infection by increasing chlamydial particle motility. [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]

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]

Cytotoxic T lymphocytes (CTLs) play an important role in the immune response to HIV during the acute stage of infection, but the effect of CTLs on HIV intrahost genetic diversity is poorly understood. We introduce a model of CTL attack during the acute stage. Assuming this model, we develop a method to sample HIV intrahost genealogies. Using our sampling approach, we characterize the evolutionary forces that shape HIV genealogies. In particular, we show that early mutation events can have significant impact on HIV genealogies and that certain types of CTL attack are best at controlling HIV genetic diversity. Our sampler represents a first step toward using HIV genetic data to infer properties of CTL attack. [ABSTRACT FROM AUTHOR]

Recent advances in virology, gene therapy, and molecular and cell biology have provided insight into the mechanisms through which viruses can boost the anti-tumor immune response, or can infect and directly kill tumor cells. A recent experimental report (Bridle et al. in Molec. Ther. 18(8):1430-1439, ) showed that a sequential treatment approach that involves two viruses that carry the same tumor antigen leads to an improved anti-tumor response compared to the effect of each virus alone. In this article, we derive a mathematical model to investigate the anti-tumor effect of two viruses, and their interactions with the immune cells. We discuss the conditions necessary for permanent tumor elimination and, in this context, we stress the importance of investigating the long-term effect of non-linear interactions. In particular, we discuss multi-stability and multi-instability, two complex phenomena that can cause abrupt transitions between different states in biological and physical systems. In the context of cancer immunotherapies, the transitions between a tumor-free and a tumor-present state have so far been associated with the multi-stability phenomenon. Here, we show that multi-instability can also cause the system to switch from one state to the other. In addition, we show that the multi-stability is driven by the immune response, while the multi-instability is driven by the presence of the virus. [ABSTRACT FROM AUTHOR]

Human T-lymphotropic virus type I (HTLV-I) is a persistent human retrovirus characterized by life-long infection and risk of developing HAM/TSP, a progressive neurological and inflammatory disease, and adult T-cell leukemia (ATL). Chronically infected individuals often harbor high proviral loads despite maintaining a persistently activated immune response. Based on a new hypothesis for the persistence of HTLV-I infection, a three-dimensional compartmental model is constructed that describes the dynamic interactions among latently infected target cells, target-cell activation, and immune responses to HTLV-I, with an emphasis on understanding the role of Tax expression in the persistence of HTLV-I. [ABSTRACT FROM AUTHOR]

The minimum duration of treatment periods and the optimal multidrug therapy for human immunodeficiency virus (HIV) type 1 infection are considered. We formulate an optimal tracking problem, attempting to drive the states of the model to a 'healthy' steady state in which the viral load is low and the immune response is strong. We study an optimal time frame as well as HIV therapeutic strategies by analyzing the free terminal time optimal tracking control problem. The minimum duration of treatment periods and the optimal multidrug therapy are found by solving the corresponding optimality systems with the additional transversality condition for the terminal time. We demonstrate by numerical simulations that the optimal dynamic multidrug therapy can lead to the long-term control of HIV by the strong immune response after discontinuation of therapy. [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]

Foot-and-mouth disease virus (FMDV) causes an economically important disease of cloven-hoofed livestock; of interest here is the difference in lytic behaviour that is observed in bovine epithelium. On the skin around the feet and tongue, the virus rapidly replicates, killing cells, and resulting in growing lesions, before eventually being cleared by the immune response. In contrast, there is usually minimal lysis in the soft palate, but virus may persist in tissue long after the animal has recovered from the disease. Persistence of virus has important implications for disease control, while identifying the determinant of lysis in epithelium is potentially important for the development of prophylactics. To help identify which of the differences between oral and pharyngeal epithelium are responsible for such dramatically divergent FMDV dynamics, a simple model has been developed, in which virus concentration is made explicit to allow the lytic behaviour of cells to be fully considered. Results suggest that localised structuring of what are fundamentally similar cells can induce a bifurcation in the behaviour of the system, explicitly whether infection can be sustained or results in mutual extinction, although parameter estimates indicate that more complex factors may be involved in maintaining viral persistence, or that there are as yet unquantified differences between the intrinsic properties of cells in these regions. [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]

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]

We use a mathematical model to determine the factors affecting the delayed or rare coreceptor switch in HIV-1 subtype C infected individuals. The model takes into account the two main target cells for the CXCR4-tropic and CCR5-tropic virus and includes the the lytic and non-lytic immune responses. Computer-based simulations and a sensitivity analysis of the model predict that a persistent immune response suppresses the CXCR4-tropic virus to low levels and hence preventing a phenotypic switch. However, not only should the immune response be persistent, but it should have an efficient lytic immune response rather that an efficient non-lytic response. In addition, we also find that the availability of macrophage cells and enhanced viral kinetics are also crucial for the dominance of the R5 strain. We suggest that an altered host environment probably as a result of immune activation may explain the difference in coreceptor switching kinetics between HIV-1 subtype B and subtype C individuals. [ABSTRACT FROM AUTHOR]

The decision of the immune system to trigger immune responses that are, respectively, induced by Th1 or Th2 effectors is a critical one, because it profoundly influences disease outcome. We have recently constructed a mathematical model of Th1–Th2-pathogen interactions that shows that the major decisional events can often be successfully determined by the intrinsic behaviour of the T helper system itself. For certain dangerous types of pathogens, however, which replicate rapidly or have developed strategies to evade the immune response, additional stimuli may be necessary.As a possible mechanism for the decision-making process innate immune recognition has been proposed. Here we present an enlarged version of our model, which incorporates signals created from the innate immune system after pathogen recognition. The model analysis suggests that there is fault-tolerance of the T helper system to incorrect Th1 signals. In the presence of incorrect Th1 stimuli an initial Th1 response is shifted to the correct Th2-dominated response owing to the intrinsic T helper dynamics. By contrast, according to our model there is no fault-tolerance for incorrect Th2 signals. In fact, if timing is unimportant then Th2 signals are superfluous since the intrinsic T helper dynamics provide an automatic switch to Th2 if Th1 effectors fail to control the pathogen. Th2 signals may, however, be required to accelerate the onset of the Th2 response.Additionally, we discuss the role of feedback where successful pathogen destruction leads to up-regulation of activation of the effective T helper type. As one possibility we examine the role of CpG motifs as indicators for successful pathogen destruction. Differences between instructive and feedback mechanisms are highlighted. [Copyright &y& Elsevier]