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Highlights • This is the first mathematical model of RA which quantitatively describes the progression of the disease. • The model explains the roles of macrophages, inflammatory fibroblasts, and T cells in the degradation of cartilage in a joint. • Example is given how to achieve the same efficacy in stabilization of the cartilage while decreasing negative side-effects. Abstract Rheumatoid arthritis (RA) is a common autoimmune disease that mainly affects the joints. It is characterized by synovial inflammation, which may result in cartilage and bone destruction. The present paper develops a mathematical model of chronic RA. The model is represented by a system of partial differential equations (PDEs) in the synovial fluid, the synovial membrane, and the cartilage. The model characterizes the progression of the disease in terms of the degradation of the cartilage. More precisely, we assume a simplified geometry in which the synovial membrane and the cartilage are planar layers adjacent to each other. We then quantify the state of the disease by how much the cartilage layer has decreased, or, equivalently, how much the synovial layer has increased. The model is used to evaluate treatments of RA by currently used drugs, as well as by experimental drugs. [ABSTRACT FROM AUTHOR]

Type 1 diabetes is a T cell-mediated organ-specific autoimmune disease. Antigen-specific immune intervention allows the selective targeting of autoreactive T cell, while leaving the remainder of the immune system intact. However, immune intervention for type 1 diabetes has not yielded perfect results clinically. In our paper published previously, we asked whether pancreatic duodenal home box 1 (PDX1) is a target of anti-islet autoimmunity in type 1 diabetes. In this experiment, we assessed the therapeutic effect of oral administration of PDX1 on diabetes development of 4-week-old non-obese diabetic (NOD) mice. The results indicate that PDX1 immunization is an effective intervention strategy for delaying the onset of diabetes in NOD mice in association with: 1) reduced insulitis; 2) suppression of destructive autoreactive T cells; 3) augmentation of regulatory T cells; 4) a shift in cytokine production. The present observations suggest that immunization with PDX1 modulates immune cell responses in NOD mice, raising the possibility that it is beneficial in ameliorating autoimmune destruction of beta-cells and delaying type 1 diabetes development clinically. [ABSTRACT FROM AUTHOR]

Abstract: Some self-reactive immature T cells escape negative selection in the thymus and may cause autoimmune diseases later. In the periphery, if T cells are stimulated insufficiently by peptide-major histocompatibility complex, they become inactive and their production of cytokines changes, a phenomenon called “T cell anergy”. In this paper, we explore the hypothesis that T cell anergy may function to reduce the risk of autoimmunity. The underlying logic is as follows: Since those self-reactive T cells that receive strong stimuli from self-antigens are eliminated in the thymus, T cells that receive strong stimuli in the periphery are likely to be non-self-reactive. As a consequence, when a T cell receives a weak stimulus, the likelihood that the cell is self-reactive is higher than in the case that it receives a strong stimulus. Therefore, inactivation of the T cell may reduce the danger of autoimmunity. We consider the formalism in which each T cell chooses its response depending on the strength of stimuli in order to reduce the risk of autoimmune diseases while maintaining its ability to attack non-self-antigens effectively. The optimal T cell responses to a weak and a strong stimulus are obtained both when the cells respond in a deterministic manner and when they respond in a probabilistic manner. We conclude that T cell anergy is the optimal response when a T cell meets with antigen-presenting cells many times in its lifetime, and when the product of the autoimmunity risk and the number of self-reactive T cells has an intermediate value. [Copyright &y& Elsevier]

Abstract: The adaptive immune system of a vertebrate may attack its own body, causing autoimmune diseases. Regulatory T cells suppress the activity of the autoreactive effector T cells, but they also interrupt normal immune reactions against foreign antigens. In this paper, we discuss the optimal number of regulatory T cells that should be produced. We make the assumptions that some self-reactive immature T cells may fail to interact with their target antigens during the limited training period and later become effector T cells causing autoimmunity, and that regulatory T cells exist that recognize self-antigens. When a regulatory T cell is stimulated by its target self-antigen on an antigen-presenting cell (APC), it stays there and suppresses the activation of other naive T cells on the same APC. Analysis of the benefit and the harm of having regulatory T cells suggests that the optimal number of regulatory T cells depends on the number of self-antigens, the severity of the autoimmunity, the abundance of pathogenic foreign antigens, and the spatial distribution of self-antigens in the body. For multiple types of self-antigen, we discuss the optimal number of regulatory T cells when the self-antigens are localized in different parts of the body and when they are co-localized. We also examine the separate regulation of the abundances of regulatory T cells for different self-antigens, comparing it with the situation in which they are constrained to be equal. [Copyright &y& Elsevier]

Abstract: Cytotoxic T lymphocytes (CTLs) play a dominant role in the pathogenesis of autoimmune diabetes, commonly denoted Type 1 Diabetes (T1D). These CTLs (notably T cells) recognize and kill insulin-secreting pancreatic cells, reducing their number by . The resulting reduction of insulin secretion causes the defective regulation of glucose metabolism, leading to the characteristic symptoms of diabetes. Recognition of cells as targets by CTLs depends on the interactions between MHC-peptide complexes on the surface of cells and receptors (TCRs) on T cells. Those CTLs with high affinity TCRs (also called high avidity T cells) cause most of the harm, while those with low affinity TCRs (also called low avidity T cells) play a more mysterious role. Recent experimental evidence suggests that low avidity T cells accumulate as memory T cells during the disease and may be protective in NOD mice (a strain prone to developing T1D), delaying disease progression. It has been hypothesized that such low avidity T cells afford disease protection either by crowding the islets of Langerhans, where cells reside, or by killing antigen presenting cells (APCs). In this paper, we explore the hypothesized mechanisms for this protective effect in the context of a series of models for (1) the interactions of low and high avidity T cells, (2) the effect of APCs and (3) the feedback from cell killing to autoantigen-induced T cell proliferation. We analyze properties of these models, noting consistency of predictions with observed behaviour. We then use the models to examine the influence of various treatment strategies on the progression of the disease. The model reveals that progressive accumulation of memory low avidity autoreactive T cells during disease progression makes treatments aimed at expanding these protective T cell types more effective close to, or at the onset of clinical disease. It also provides evidence for the hypothesis that low avidity T cells kill APCs (rather than the alternate hypothesis that they crowd the islets). [Copyright &y& Elsevier]