Understanding the roles of activation threshold and infections in the dynamics of autoimmune disease

A biological and a mathematical model of SLE treated by mesenchymal stem cells covering all the stages of the disease

In this study, we proposed a biological model explaining the progress of autoimmune activation along different stages of systemic lupus erythematosus (SLE). For any upcoming stage of SLE, any new component is introduced, when it is added to the model. Particularly, the interaction of mesenchymal stem cells, with the components of the model, is specified in a way that both the inflammatory and anti-inflammatory functions of these cells would be covered. The biological model is then recapitulated to a model with less complexity that explains the main features of the problem. Later, a 7th-order mathematical model for SLE is proposed, based on this simplified model. Finally, the range of validity of the proposed mathematical model was assessed. For this purpose, we simulated the model and analyzed the simulation results in case of some known behaviors of the disease, such as tolerance breach, the appearance of systemic inflammation, development of clinical signs, and occurrence of flares and improvements. The model was able to reproduce these events, qualitatively.

Autoimmune diseases initiated by pathogen infection: Mathematical modeling

Many incurable diseases in humans are related to autoimmunity and are initially induced by a viral infection. Presumably, the virus has antigens with epitopes similar to those found in components of the host's body, thus allowing it to evade immune surveillance. Viral infection activates the immune system, which results in viral clearance. After infection, the enhanced immune system may begin to attack the host's cells, tissues, and organs. In this study, we developed a simple mathematical model in which we identify the conditions needed to trigger an autoimmune response. This model considers the dynamics of T helper (Th) cells, viruses, self-antigens, and memory T cells. Viral infection results in a temporal increase in viral abundance, which is suppressed by an increase in the number of Th cells. For the virus to be eliminated from the body, the level of Th cells must be maintained above a certain threshold to prevent viral replication, even in the absence of virus in the body. This role is realized by memory T cells produced during temporal viral infections. Thus, we investigated the conditions needed for the immune response to be enhanced after viral infection and concluded that cross-immunity must be weak for negative selection and T-cell activation but strong for antigen-suppressing reactions. We also discuss alternative models of cross-immunity and possible extensions of the model.

Quantifying the Role of Stochasticity in the Development of Autoimmune Disease

In this paper, we propose and analyse a mathematical model for the onset and development of autoimmune disease, with particular attention to stochastic effects in the dynamics. Stability analysis yields parameter regions associated with normal cell homeostasis, or sustained periodic oscillations. Variance of these oscillations and the effects of stochastic amplification are also explored. Theoretical results are complemented by experiments, in which experimental autoimmune uveoretinitis (EAU) was induced in B10.RIII and C57BL/6 mice. For both cases, we discuss peculiarities of disease development, the levels of variation in T cell populations in a population of genetically identical organisms, as well as a comparison with model outputs.

Stochastic dynamics in a time-delayed model for autoimmunity

In this paper we study interactions between stochasticity and time delays in the dynamics of immune response to viral infections, with particular interest in the onset and development of autoimmune response. Starting with a deterministic time-delayed model of immune response to infection, which includes cytokines and T cells with different activation thresholds, we derive an exact delayed chemical master equation for the probability density. We use system size expansion and linear noise approximation to explore how variance and coherence of stochastic oscillations depend on parameters, and to show that stochastic oscillations become more regular when regulatory T cells become more effective at clearing autoreactive T cells. Reformulating the model as an Itô stochastic delay differential equation, we perform numerical simulations to illustrate the dynamics of the model and associated probability distributions in different parameter regimes. The results suggest that even in cases where the deterministic model has stable steady states, in individual stochastic realisations, the model can exhibit sustained stochastic oscillations, whose variance increases as one gets closer to the deterministic stability boundary. Furthermore, in the regime of bi-stability, whereas deterministically the system would approach one of the steady states (or periodic solutions) depending on the initial conditions, due to the presence of stochasticity, it is now possible for the system to reach both of those dynamical states with certain probability. Biological significance of this result lies in highlighting the fact that since normally in a laboratory or clinical setting one would observe a single individual realisation of the course of the disease, even for all parameters characterising the immune system and the strength of infection being the same, there is a proportion of cases where a spontaneous recovery can be observed, and similarly, where a disease can develop in a situation that otherwise would result in a normal disease clearance.

Mathematical model of immune response to hepatitis B

A new detailed mathematical model for dynamics of immune response to hepatitis B is proposed, which takes into account contributions from innate and adaptive immune responses, as well as cytokines. Stability analysis of different steady states is performed to identify parameter regions 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.

Stochastic Effects in Autoimmune Dynamics

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.

The Role of Aggregates of Therapeutic Protein Products in Immunogenicity: An Evaluation by Mathematical Modeling

Therapeutic protein products (TPP) have been widely used to treat a variety of human diseases, including cancer, hemophilia, and autoimmune diseases. However, TPP can induce unwanted immune responses that can impact both drug efficacy and patient safety. The presence of aggregates is of particular concern as they have been implicated in inducing both T cell-independent and T cell-dependent immune responses. We used mathematical modeling to evaluate several mechanisms through which aggregates of TPP could contribute to the development of immunogenicity. Modeling interactions between aggregates and B cell receptors demonstrated that aggregates are unlikely to induce T cell-independent immune responses by cross-linking B cell receptors because the amount of signal transducing complex that can form under physiologically relevant conditions is limited. We systematically evaluate the role of aggregates in inducing T cell-dependent immune responses using a recently developed multiscale mechanistic mathematical model. Our analysis indicates that aggregates could contribute to T cell-dependent immune response by inducing high affinity epitopes which may not be present in the nonaggregated TPP and/or by enhancing danger signals to break tolerance. In summary, our computational analysis is suggestive of novel insights into the mechanisms underlying aggregate-induced immunogenicity, which could be used to develop mitigation strategies.