Towards a logical analysis of the immune response.

We present a new way to conceive, formalize and analyse models of the immune network. The models proposed are minimal ones, based essentially on the well-established negative feedback loop between helper and suppressor T cells. The occurrence of T-T interactions in both helper and suppressor circuits. These T-T interactions are represented here by autocatalytic feedback loops on TH and TS. The fact that immature B cells are sensitive to negative signaling, as was originally suggested by Lederberg (1959). There is a functional inactivation of immature B cells encountering antigen or anti-idiotypic antibody. This prevents further differentiation to a stage where the B cells become fully responsive. We describe the role of a logical method in the generation and analysis of the models, and the complementarity between this logical method and the more classical description by continuous differential equations. Logical analysis and numerical simulations of the differential equations show that the emerging model accounts for, the occurrence of multiple steady states (a virgin state, a memory state and a non-responsive state) in the absence of antigen, the kinetics of primary and secondary responses, high dose paralysis, low dose of paralysis. Its fit with real situations is surprisingly good for a model of this simplicity. Nevertheless, we give it as an example of what can now be done in the field rather than as a stable model.