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.