Modeling positive and negative selection and differentiation processes in the thymus

T cells begin their development as precursor cells in the bone marrow. These cells migrate to the thymus, where they further divide, differentiate, and mature into functional T cells. Most thymocytes (95-99%) die in the course of this process, and only relatively few exit the thymus as mature cells. Here we develop a differential equation model of cell proliferation, differentiation and death in the thymus that can account for both the total number of thymus cells and the fractions of various types of immature and mature thymocytes. Our model suggests that positive and negative selection may have more complex effects than simply deleting some cells and allowing others to survive.