Axioms of mathe- matical immunology

Abstract

Current wisdom describes the immune system as a defense against microbial pathogens. It is claimed that the virgin immune system has a capacity to produce antibodies against the entire antigenic universe. We assume, by contrast, that the responding capacity of the immune system is limited. Thus it cannot stand in readiness to deal with a practi- cally endless diversity and abundance 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 twofold: (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 of 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-peptide complexes. At the highest level of complementarity a local free energy minimum is achieved, thus a homeostatic system is created. Homeostatic interactions happen at intermediate afinity and are reversible. Alteration in the presented peptides typically decreases complementarity. That pushes the system away from the free energy minimum, which activates T cells. Complementarity is restored when cytotoxic T cells destroy altered (mutated/infected) 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 in uence of the normal intestinal micro o- ra, self-proteins and alimentary antigens must go through a hypermutation process to be able to produce specific antibodies. It has a certain probability that hypermutation will successfully change the genome in some clones to switch from low afinity IgM antibody production to high afinity IgG production. Interactions (typically antibody antigen reac- tions) in an immune response happen at high afinity and are irreversible. High afinity clones will be selected, stimulated and enriched by the invading microbes. A complete account of the course of an infectious disease must also include a descrip- tion of the ecology of the immune response. It is therefore suggested 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 reper- toire, in accordance with the Baldwin effect in the evolution of instinct (see Appendix 6).