Stochastic Effects in Autoimmune Dynamics

Abstract

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”. In this paper we propose and analyse a stochastic model of immune response to a viral infection and subsequent autoimmunity, with account for the populations of T cells with different activation thresholds, regulatory T cells, and cytokines. We show analytically and numerically how stochasticity can result in sustained oscillations around deterministically stable steady states, and we also investigate stochastic dynamics in the regime of bi-stability. These results provide a possible explanation for experimentally observed variations in the progression of autoimmune disease. Computations of the variance of stochastic fluctuations provide practically important insights into how the size of these fluctuations depends on various biological parameters, and this also gives a headway for comparison with experimental data on variation in the observed numbers of T cells and organ cells affected by infection.

Effects of Viral and Cytokine Delays on Dynamics of Autoimmunity

“…Including these immune mediators explicitly in the model can provide further significant insights into the dynamics of immune response, as has been recently demonstrated on the example of a detailed model of immune response to hepatitis B [72]. Another biologically relevant and mathematically challenging problem is the investigation of the interplay between stochasticity, which is known to be an intrinsic feature of immune response [49,73], and effects of time delays associated with various aspects of immune dynamics.…”

“…A particularly important practical insight provided by this model is the observation that it is not only the system parameters, but also the initial level of infection and the initial state of the immune system, that determine whether the host will just successfully clear the infection, or will proceed to develop autoimmunity. Approaching the same problem from another perspective, Fatehi et al [49] have investigated the role of stochasticity in driving the dynamics of immune response and determining which of the immune states is more likely to be attained. The authors have also determined an experimentally important characterisation of autoimmune state, as provided by the dependence of variance in cell populations on various system parameters.…”

Bifurcations and Multistability in a Model of Cytokine-Mediated Autoimmunity

“…Therefore, in this model we assume that T nor and T aut produce IL-2 at rates σ 1 and σ 2 . On the other hand, whilst regulatory T cells do not produce IL-2, similar to other T cells they need this cytokine for their activation and proliferation [94,95]. Thus, we assume that IL-2 promotes proliferation of T reg , T nor and T aut at rates ρ 1 , ρ 2 and ρ 3 , respectively.…”

Quantifying the Role of Stochasticity in the Development of Autoimmune Disease

“…Blyuss and Nicholson [34,35] used a TAT-based model to investigate autoimmunity arising through a mechanism of molecular mimicry from immune response to a viral infection. To capture a dynamical regime where autoimmunity arises as a by-product of viral infection but after that initial infection has already been cleared by the immune system, Fatehi et al [36][37][38][39][40] developed this model further by including cytokines mediating T cell proliferation, as well as time delays associated with various aspects of the immune response.…”

“…Due to an intrinsically complex multi-factor nature of immune response [41], several mathematical models have investigated stochastic aspects of immune dynamics. They have included, among others, analyses of T cell homeostasis [42] and repertoire [43,44]; the dynamics of T cell activation thresholds [45,46]; T-cell proliferation and activation, including the role of cytokines [47][48][49]; self-tolerance based on regulatory T cells [23]; cytokine-mediated pathogen-induced autoimmunity [36]; T cell recruitment in response to a viral infection [50]; as well as an investigation of how a variable affinity between T cell receptors and MHC-peptide complexes may affect possible outcomes during T cell selection [51]. These models have focused primarily on investigating such aspects of stochastic dynamics as the probability distribution of T cell activation thresholds, or simulations of immune dynamics that are valid for relatively small numbers of cell populations (thus going beyond the mean-field models).…”