Mathematical modeling of a network theory of self-regulation in the immune system

Some features of a network theory of the regulation of the immune system are described briefly, and a mathematical model of the interactions that are important in the four stable states of the theory is presented. The network idea is that variable regions of antibodies themselves can act as antigens (specific stimulants) of the immune system, and that the anti-variable region response is important in the regulation of the system. The mathematical model consists of a pair of differential equations, describing the concentrations of cells that are specific for the antigen ("positive" cells) and cells that have receptors specific for the receptors on the positive cells ("negative" cells). The equations have four stable states, corresponding to the virgin state, the suppressed (unresponsive) state, the immune state and the anti-immune state for the antigen. The model illustrates the necessity of a switch from IgM to IgG in making all four states properly stable.