A Fuzzy Continuous Petri Net Model for Helper T cell Differentiation

Helper T(Th) cells regulate immune response by producing various kinds of cytokines in response to antigen stimulation. The regulatory functions of Th cells are promoted by their differentiation into two distinct subsets, Th1 and Th2 cells. Th1 cells are involved in inducing cellular immune response by activating cytotoxic T cells. Th2 cells trigger B cells to produce antibodies, protective proteins used by the immune system to identify and neutralize foreign substances. Because cellular and humoral immune responses have quite different roles in protecting the host from foreign substances, Th cell differentiation is a crucial event in the immune response. The destiny of a naive Th cell is mainly controlled by cytokines such as IL-4, IL-12, and IFN-${\gamma}$. To understand the mechanism of Th cell differentiation, many mathematical models have been proposed. One of the most difficult problems in mathematical modeling is to find appropriate kinetic parameters needed to complete a model. However, it is relatively easy to get qualitative or linguistic knowledge of a model dynamics. To incorporate such knowledge into a model, we propose a novel approach, fuzzy continuous Petri nets extending traditional continuous Petri net by adding new types of places and transitions called fuzzy places and fuzzy transitions. This extension makes it possible to perform fuzzy inference with fuzzy places and fuzzy transitions acting as kinetic parameters and fuzzy inference systems between input and output places, respectively.