Axioms of mathematical immunology

Current wisdom describes the immune system as a defense against microbial p athogens. It is claimed that the virgin immune system has a capacity to pro duce antibodies against the entire antigenic universe. We assume, by contra st, that the responding capacity of the immune system is limited. Thus it c annot stand in readiness to deal with a practically endless diversity and a bundance of microbes. Axioms and theorems are suggested for a mathematician audience delineating how the immune system could use its limited resources economically. It is suggested that the task of the immune system is twofol d: (i) It sustains homeostasis to preserve the genome by constant surveillance of the intracellular antigenic milieu. This is achieved by standardization of the T cell repertoire through a positive selection. The driving force o f positive selection is immune cell survival. T cells must constantly seek contact with complementary MHC structures to survive. Such contact is based on molecular complementarity between immune cell receptors and MHC/self-pe ptide complexes. At the highest level of complementarity a local free energ y minimum is achieved, thus a homeostatic system is created. Homeostatic in teractions happen at intermediate affinity and are reversible. Alteration i n the presented peptides typically decreases complementarity. That pushes t he system away from the free energy minimum, which activates T cells. Compl ementarity is restored when cytotoxic T cells destroy altered (mutated/infe cted) host cells. (ii) B cells carry out an immune response to foreign proteins what requires a change in the genome. B cells raised under the antigenic influence of th e normal intestinal microflora, self-proteins and alimentary antigens must go through a hypermutation process to be able to produce specific antibodie s. It has a certain probability that hypermutation will successfully change the genome in some clones to switch from low affinity IgM antibody product ion to high affinity IgG production. Interactions (typically antibody antig en reactions) in an immune response happen at high affinity and are irrever sible. High affinity clones will be selected, stimulated and enriched by th e invading microbes. A complete account of the course of an infectious disease must also include a description of the ecology of the immune response. It is therefore sugge sted that during prolonged interaction between host and infectious organism , carried on across many generations, the adaptive antibody population may facilitate the evolution of the natural antibody repertoire, in accordance with the Baldwin effect in the evolution of instinct (see Appendix 6).