Modeling Cyclic Waves of Circulating T Cells in Autoimmune Diabetes

Type 1 diabetes (T1D) is an autoimmune disease in which immune cells, notably T-lymphocytes target and kill the insulin-secreting pancreatic beta cells. Elevated blood sugar levels and full blown diabetes result once a large enough fraction of these beta cells have been destroyed. Recent investigation of T1D in animals, the non-obese diabetic (NOD) mice, has revealed large cyclic fluctuations in the levels of T cells circulating in the blood, weeks before the onset of diabetes [23], but the mechanism for these oscillations is unclear. We here describe a mathematical model for the immune response that suggests a possible explanation for the cyclic pattern of behaviour. We show that cycles similar to those observed experimentally can occur when activation of T cells is an increasing function of self-antigen level, whereas the production of memory cells declines with that level. Our model extends previous theoretical work on T cell dynamics in T1D [14], and leads to interesting nonlinear dynamics, including Hopf and homoclinic bifurcations in biologically reasonable regimes of parameters. The model leads to the following explanation for cycles: High rates of beta cell death, and corresponding elevation of self-antigen, shut off memory cell production, leading to a gap in the population of activated T cells. Once peptide has been cleared by nonspecific mechanisms, the memory pool is renewed, and the cyclic behaviour results.