Automata network theories in immunology: their utility and their underdetermination

Small networks of threshold automata are used to model complex interactions between populations of regulatory cells (helpers and suppressors, antigen specific and anti-idiotypic) which participate in the immune response. The models, being discrete and semiquantitative, are well adapted to the situation of incomplete information often encountered in vivo. However, the dynamics of many different network structures usually end up in the same attractor set. Thus, many different theories are equivalent in their explicative power for the same facts. This property, known as underdetermination of the theories by the facts, is given a quantitative estimate. It appears that such an underdetermination, as a kind of irreducible complexity, can be expected in many in vivo biological processes, even when the number of interacting and functionally coupled elements is relatively small.