Immunological self-tolerance: Lessons from mathematical modeling

Carneiro, Jorge; Paixão, Tiago; Milutinović, Dejan; Sousa, João de; León, Kalet; Gardner, Rui; Faro, José

doi:10.1016/j.cam.2004.10.025

Cited by 54 publications

(49 citation statements)

References 57 publications

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“…A bistable dynamical system provides a natural deterministic representation for dependence on initial conditions. Bistability is a recurring theme among previous mathematical models of autoimmunity (Borghans et al 1998;León et al 2000;Chan et al 2004;Burroughs et al 2006;Carneiro et al 2005;Iwami et al 2007). We expect that a sigmoidal antigen uptake function (similar to the functional form used by Iwami et al 2007, to model the immune response), rather than the linear or Michaelis-Menten functions we explored here, might yield bistability in our deterministic model.…”

Section: Dependence On Initial Conditionsmentioning

confidence: 92%

“…In two further papers, Carneiro et al extend investigations along similar lines as León et al In Carneiro et al (2005), the authors present two models of self-tolerance: one based on the tunable activation threshold hypothesis, and one based on suppression by regulatory T cells. The latter, which the authors conclude is better able to explain the experimental results of Sakaguchi et al, is relevant to our current topic.…”

Section: Previous Workmentioning

confidence: 92%

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Self-tolerance and Autoimmunity in a Regulatory T Cell Model

Alexander

Wahl

2010

Bull. Math. Biol.

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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(0) for each system. When R(0)<1, only the trivial equilibrium exists and is stable; when R(0)>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).

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Section: Dependence On Initial Conditionsmentioning

confidence: 92%

Section: Previous Workmentioning

confidence: 92%

Self-tolerance and Autoimmunity in a Regulatory T Cell Model

Alexander

Wahl

2010

Bull. Math. Biol.

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“…Would a consideration of the dynamics of allele product concentration change this conclusion? From equation 1 and through the same analysis described 28 we can derive the probability density function (PDF) for the allele product concentration x in a population of cells, denoted r(x i ). This is given by the following expression:…”

Section: Resultsmentioning

confidence: 99%

Quantitative insights into stochastic monoallelic expression of cytokine genes

et al. 2007

Self Cite

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Gene expression from both parental alleles is beneficial by masking the effects of deleterious recessive mutations and by reducing the noise in gene expression in diploid organisms. However, a class of genes are expressed preferentially or strictly from a single allele. The selective advantage of avoiding biallelic expression is clear for allelic-excluded antigen receptor and odorant receptor genes, genes undergoing X-chromosome inactivation in females and parental genomic imprinted genes. In contrast, there is no clear biological rationale for the predominant and stochastic monoallelic expression of cytokine genes in the immune system, and the underlying mechanism is elusive and controversial. A clarification of the mechanism of predominant monoallelic expression would be instrumental in better understanding its eventual biological functional. This prompted the development of a quantitative framework that could describe the dynamics of the pattern of allele expression of the IL-10 gene, from which general quantitative insights could be gained. We report that the experimental observations on these patterns of allelic expression cannot be easily reconciled with a simple model of stochastic transcriptional activation, in which the two alleles are, at any time, equally competent for transcription. Instead, these observations call into action a general model of eukaryotic transcriptional regulation according to which the locus competence for transcription is dynamic, involving multiple, cooperative and stochastic modification steps. In this model, the probability that an allele becomes transcriptionally active is a function of the number of chromatin modifications that it accumulated. On the basis of the properties of this model, we argue that predominant monoallelic expression might have had no adaptive role, and may have evolved under indirect selection for low frequency of expressing cells.

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“…Similar models were later studied by Borghans et al [17,18] who demonstrated possible onset of autoimmune state, defined as stable above-threshold oscillations in the number of autoreactive cells, as a result of interactions between regulatory and autoreactive T cells. León et al [19][20][21] and Carneiro et al [22] have studied interactions between different T cells, with an emphasis on the suppressing role of regulatory T cells in the dynamics of immune response and control of autoimmunity. Alexander and Wahl [23] have also looked into the role of regulatory T cells, in particular focusing on their interactions with professional APCs and effector cells for the purpose of controlling immune response.…”

Section: Introductionmentioning

confidence: 99%

Effects of Viral and Cytokine Delays on Dynamics of Autoimmunity

Chenar¹,

Kyrychko²,

Blyuss³

2018

Mathematics

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Abstract:A major contribution to the onset and development of autoimmune disease is known to come from infections. An important practical problem is identifying the precise mechanism by which the breakdown of immune tolerance as a result of immune response to infection leads to autoimmunity. In this paper, we develop a mathematical model of immune response to a viral infection, which includes T cells with different activation thresholds, regulatory T cells (Tregs), and a cytokine mediating immune dynamics. Particular emphasis is made on the role of time delays associated with the processes of infection and mounting the immune response. Stability analysis of various steady states of the model allows us to identify parameter regions associated with different types of immune behaviour, such as, normal clearance of infection, chronic infection, and autoimmune dynamics. Numerical simulations are used to illustrate different dynamical regimes, and to identify basins of attraction of different dynamical states. An important result of the analysis is that not only the parameters of the system, but also the initial level of infection and the initial state of the immune system determine the progress and outcome of the dynamics.

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Immunological self-tolerance: Lessons from mathematical modeling

Cited by 54 publications

References 57 publications

Self-tolerance and Autoimmunity in a Regulatory T Cell Model

Self-tolerance and Autoimmunity in a Regulatory T Cell Model

Quantitative insights into stochastic monoallelic expression of cytokine genes

Effects of Viral and Cytokine Delays on Dynamics of Autoimmunity

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