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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]

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]

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]

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]

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]