Tcell phenotypes in multiple infections

In response to an antigen, the body proliferates T-cells (Graham 2002). In a very broad brush, the proliferated cells are called T-helper cells and come in two forms (Mosmann and Sad 1996, Fishman and Perelson 1999): T-helper type 1 (Th1) cells that generally work best against intracellular parasites or pathogens and T-helper type 2 (Th2) cells that generally work best against extracelluar parasites or pathogens (Graham 2001). However, this simple description is not uniformly accepted (for a discussion of whether this is a reliable paradigm or dangerous dogma, see Romagnani (1996) and Allen and Maizels (1997)). It is agreed, however, that the two kinds of helper cells have some unique biochemical signals: interferon gamma (IFN-g) is uniquely associated with Th1 cells and interleukin4 (IL-4) is uniquely associated with Th2 cells. Consequently, the ratio, with [x] denoting the concentration of x, t — [IFN-g] (5 43)

is a measure of the fraction of T-helper type 1 cells in response to an antigen.

Graham (2001) asks the following question: suppose that there are a wide variety of pathogens or parasites that might attack an organism, and that the ith disease evokes an optimal T-helper response t,-, understood to be the fraction of Th1 cells. What will happen when the organism is simultaneously attacked by n different pathogens or parasites? This question is particularly interesting because of the generally held view of the emergent properties of the immune system. To begin, we will follow Graham's model, and then extend it. Suppose that the probability of surviving attack by the ith parasite or pathogen when the Th1 response is t is

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