The model is used to infer a set of criteria that determines susceptibility to T1D in high risk (HR) subjects. interactions of these components during T1D progression, a mathematical model of T-cell dynamics is usually developed as a predictor of -cell loss, with the underlying hypothesis that avidity of Teffs and Tregs, i.e., the binding affinity of T-cell receptors to peptide-major histocompatibility complexes on host cells, is usually continuum. The model is FTY720 (S)-Phosphate used to infer a set of criteria that determines susceptibility to T1D in high risk (HR) subjects. Our findings show that diabetes onset is usually guided by the absence of Treg-to-Teff dominance at specific high avidities rather than over the whole range of avidity, and that the lack of overall dominance of Teffs-to-Tregs over time is the underlying cause of the honeymoon period, the remission phase observed in some T1D patients. The model also suggests that competition between Teffs and Tregs is more effective than Teff-induction into iTregs in suppressing Teffs, and that a prolonged full width at half maximum of IL-2 release is usually a necessary condition for curbing disease onset. Finally, the model provides a rationale for observing rapid and slow progressors of T1D based on modest heterogeneity in the kinetic parameters. methods to study this disease very compelling. These approaches have been previously applied to increase our understanding of immunological responses and self-tolerance in other contexts (Borghans and De Boer, 1995; Borghans et al., 1998; Kim et al., 2007; Nevo et al., 2004). Mathematical models, mostly comprised of ordinary differential equations, were developed to achieve this goal. In T1D, comparable approaches have been applied to investigate the role of macrophages in disease onset (Mare et al., 2006; Mare et al., 2008), as well as the role T-cell avidity and killing efficacy in the formation of autoimmune response(s), T-cell cycles and autoantibody release in high risk (HR) subjects (Jaberi-Douraki et al., 2014a; Jaberi-Douraki et al., 2014b; Jaberi-Douraki et al., 2014; Khadra et al., 2009; Khadra et al., 2011). These studies were later extended (Jaberi-Douraki et al., 2014b) to determine how T-cell-dependent autoimmune destruction of cells compares to -cell apoptosis induced by ER-stress caused by an increase in metabolic demand on surviving cells. The study revealed that targeting this pathway for therapeutic purposes, by enhancing the unfolded protein response (UPR) in cells to increase insulin secretion and inhibit ER-stress (Marchetti et al., 2007), may not be successful due to the dominance of autoimmune destruction. The avidity in these models was quantified using the effective dissociation of pMHCs from TCRs (Mammen et al., 1998) and was assumed to be discrete by considering competing clones of T cells. Here we assume more complex processing for the binding avidities, activation and proliferation of T cells in order to relate regulatory T-cell distributions to that of Teff cell populations. This is achieved by developing a continuum avidity model of integro-differential equations that describes the dynamics of Teffs, Tregs, FTY720 (S)-Phosphate cells, IL-2 and autoantigen processing. The model provides important insights about the interactions of these components in health and disease. MATHEMATICAL MODEL In our previous work, we have developed a series of mathematical models comprised of system of ordinary differential equations to study the role of avidity and killing efficacy of Teffs in forming autoimmune responses in T1D. These predictive models provided important insights into the implication of both T-cell FTY720 (S)-Phosphate cycles on autoantibody release and non-recursive endoplasmic reticulum (ER) stress in exacerbating autoimmune destruction of cells (Jaberi-Douraki et al., 2014a; Jaberi-Douraki et al., 2014b; Khadra et al., 2009; Khadra et al., 2011). In these models, T-cell avidity was assumed to be discrete with finite Sema3d number (at most three) of competing clones of T cells. Here, we extend these studies by assuming that ER-stress is usually recursive, by taking into account the continuum nature of T-cell avidity and by developing an integro-differential equation model to analyze the effect of immunomodulation, exerted by Tregs on Teffs in the presence of the autocrine/paracrine factor of IL-2, on -cell survival. The model excludes the unconfirmed role of plasma cells in the destruction of cells, and only focuses on the dynamics of T cells to provide predictive criteria for susceptibility to T1D and to answer important basic questions about the disease. Model description Based on the scheme of Physique 1, our model is composed of the.