CAPACITY OF A MODEL IMMUNE NETWORK

G\'erard Weisbuch and Mihaela Oprea, Santa Fe NM87501, USA .

The evaluation of the capacity of a neural net is a rather classical problem, and the purpose of this paper is to compute the capacity of a model immune network in the same spirit. Antigen presentation results in a local modification of the clone populations that form the attractors of the dynamics. In other words, the new attractor reached after antigen presentation only differs from the previous attractor in a localized patch of clones that are connected to the clones that recognize the antigen.The network is then both sensitive to new antigens, and robust enough to maintain memories of previously presented antigens. The independence property cannot be kept indefinitely when successive antigens are added to the network: since the network is finite in size, the local perturbations induced by the presented antigens have a finite probability of interaction which increases when new antigens are presented. We derive in the paper the scaling laws: The maximum number of independant clones scales as the square root of the number of clones for the simplest memory algorithm. The scaling coefficient increases up to one for more thrifty algorithms.

Bull. Math. Biol 56, 899-921, (1994).