Bifurcations and multistability in a model of cytokine-mediated autoimmunity

This paper investigates the dynamics of immune response and autoimmunity with particular emphasis on the role of regulatory T cells (Tregs), T cells with different activation thresholds, and cytokines in mediating T cell activity. Analysis of the steady states yields parameter regions corresponding to regimes of normal clearance of viral infection, chronic infection, or autoimmune behavior, and the boundaries of stability and bifurcations of relevant steady states are found in terms of system parameters. Numerical simulations are performed to illustrate different dynamical scenarios, and to identify basins of attraction of different steady states and periodic solutions, highlighting the important role played by the initial conditions in determining the outcome of immune interactions

Mathematical modelling of cytokine-mediated immune response and autoimmunity

One of the major outstanding challenges in immunology is the development of a comprehensive, quantitative and accurate approach to understanding the causes and dynamics of immune responses. The immune system normally protects the body against infections, but at the same time it is possible that it can fail to distinguish the host’s own cells from the cells affected by the infection, which can lead to autoimmune disease. The question of what releases the auto-pathogenic potential of T lymphocytes is at the heart of understanding autoimmune disease. Among various possible causes of autoimmune disease, an important role is played by infections that can result in a breakdown of immune tolerance, primarily through the mechanism of molecular mimicry, where the introduction of pathogenic peptides that structurally resemble self-peptides, derived from infection, may induce T lymphocytes to proliferate and leave them with the ability to respond to self, as well as foreign antigens. Deterministic and stochastic models have been extensively used in the past to study the dynamics of immune responses and analyse a possible onset of autoimmunity. The main focus of this thesis is the development and analysis of mathematical models of immune response to infection, as well as the onset and progress of autoimmunity. Particular emphasis is made on developing new mathematical approaches for elucidating the roles played by various cytokines in the immune dynamics. In the first part of the thesis I develop a mathematical model for dynamics of immune response to hepatitis B. This model explicitly includes contributions from innate and adaptive immune responses, as well as from cytokines. Analysis of the model identifies parameter regimes where the model exhibits clearance of infection, maintenance of a chronic infection, or periodic oscillations. Effects of nucleoside analogues and interferon treatments are analysed, and the critical drug efficiency is determined. The second part of the thesis investigates the dynamics of immune response to a general viral infection and a possible onset of autoimmunity, which account for regulatory T cells, T cells with different activation thresholds, and cytokines. Feasibility and stability analyses of different steady states yield boundaries of stability and bifurcations in terms of system parameters. This model exhibits bi-stability and shows different regimes of normal clearance of viral infection, chronic infection, or autoimmune behaviour. Therefore, it can provide significant new insights into autoimmune dynamics. To investigate the role of stochasticity in immune dynamics, I developed a stochastic version of the model, and the major result is that adding stochasticity can lead to the emergence of sustained oscillations around deterministically stable steady states, thus providing a possible explanation for experimentally observed variations in the progression of autoimmune disease. I also have investigated stochastic dynamics in the regime of bi-stability and computed the magnitude of these fluctuations. I have also analysed the effects of different time delays, as well as the inhibiting effect of regulatory T cells on secretion of interleukin-2 on autoimmune dynamics. To this end, I have performed a systematic analysis of stability of all steady states of the corresponding model both analytically, and numerically. The identification of basins of attraction of different steady states and periodic solutions indicates that time delays can change the shape of these basins of attraction, and the new results show better qualitative agreement with the experimental observations. My thesis culminates with the last part, where I explore stochastic effects in a time-delayed model for autoimmunity. The major achievement in this part of the thesis is the development of a new methodology for deriving an Itô stochastic delay differential equation (SDDE) from delay discrete stochastic models, as well as showing the equivalency of previously proposed methods. Using this equivalence, I derived a simpler SDDE model to perform numerical simulations. I have used a linear noise approximation (LNA) to determine the magnitude of stochastic fluctuations around deterministic steady states, and to obtain insights into how the coherence of stochastic oscillations around deterministically stable steady states depends on system parameters

Mathematical models of cellular decisions: investigating immune response and apoptosis

The main objective of this thesis is to develop and analyze mathematical models of cellular decisions. This work focuses on understanding the mechanisms involved in specific cellular processes such as immune response in the vascular system, and those involved in apoptosis, or programmed cellular death. A series of simple ordinary differential equation (ODE) models are constructed describing the macrophage response to hemoglobin:haptoglobin (Hb:Hp) complexes that may be present in vascular inflammation. The models proposed a positive feedback loop between the CD163 macrophage receptor and anti-inflammatory cytokine interleukin-10 (IL-10) and bifurcation analysis predicted the existence of a cellular phenotypic switch which was experimentally verified. Moreover, these models are extended to include the intracellular mediator heme oxygenase-1 (HO-1). Analysis of the proposed models find a positive feedback mechanism between IL-10 and HO-1. This model also predicts cellular response of heme and IL-10 stimuli. For the apoptotic (cell suicide) system, a modularized model is constructed encompassing the extrinsic and intrinsic signaling pathways. Model reduction is performed by abstracting the dynamics of complexes (oligomers) at a steady-state. This simplified model is analyzed, revealing different kinetic properties between type I and type II cells, and reduced models verify results. The second model of apoptosis proposes a novel mechanism of apoptosis activation through receptor-ligand clustering, yielding robust bistability and hysteresis. Using techniques from algebraic geometry, a model selection criterion is provided between the proposed and existing model as experimental data becomes available to verify the mechanism. The models developed throughout this thesis reveal important and relevant mechanisms specific to cellular response; specifically, interactions necessary for an organism to maintain homeostasis are identified. This work enables a deeper understanding of the biological interactions and dynamics of vascular inflammation and apoptosis. The results of these models provide predictions which may motivate further experimental work and theoretical study

Modular analysis of signal transduction networks

Modularity, signaling networks, sytems biologyMagdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2007von Julio Sáez RodríguezZsfassung in dt. Sprach

Mathematical Modelling of Inter- and Intracellular Signal Transduction: The Regulatory Role of Multisite Interactions

Signalling processes regulate various aspects of living cells via modulation of protein activity. The interactions between the signalling proteins can occur at single or multiple sites. Although single site protein interactions are relatively easy to understand, these rarely occur in living systems. It is therefore important to investigate multisite interactions. Despite the recent progress in experimental studies, the underlying molecular mechanisms and molecular functions of the multisite interactions are still not clear and therefore require systems approaches for deeper understanding, for example to understand how the system will react to perturbation of one of its components. The examples of the molecular functions that are studied in this thesis are: kinetics of multisite calcium binding to proteins such as calmodulin (CaM), multisite phosphorylation of interferon regulatory factor 5 (IRF-5) and signal transducers and activators of transcription (STATs). We also study the role of STATs in the overall immune response and in T cell phenotype switching as well as multisite phosphorylation of high osmolarity glycerol factor 1 (Hog1) in mitogen activated protein kinase (MAPK) cascade during the adaptation of Candida glabrata to osmotic stress. In this thesis, these examples are studied using the systems approach in the context of human diseases: cancer, candidiasis, immunity-related pathologies such as rheumatoid arthritis, inflammatory bowel disease and systemic lupus erythematosus. We discuss potential therapeutic implications of the proposed models in these diseases. The predictions of the models developed in this thesis are supported by the experimental data and propose possible mechanisms of the multisite interactions involved in the cellular regulation

Mathematical Modelling of Bacterial Quorum Sensing: A Review

Bacterial quorum sensing (QS) refers to the process of cell-to-cell bacterial communication enabled through the production and sensing of the local concentration of small molecules called autoinducers to regulate the production of gene products (e.g. enzymes or virulence factors). Through autoinducers, bacteria interact with individuals of the same species, other bacterial species, and with their host. Among QS-regulated processes mediated through autoinducers are aggregation, biofilm formation, bioluminescence, and sporulation. Autoinducers are therefore “master” regulators of bacterial lifestyles. For over 10�years, mathematical modelling of QS has sought, in parallel to experimental discoveries, to elucidate the mechanisms regulating this process. In this review, we present the progress in mathematical modelling of QS, highlighting the various theoretical approaches that have been used and discussing some of the insights that have emerged. Modelling of QS has benefited almost from the onset of the involvement of experimentalists, with many of the papers which we review, published in non-mathematical journals. This review therefore attempts to give a broad overview of the topic to the mathematical biology community, as well as the current modelling efforts and future challenges. � 2016, Society for Mathematical Biology