A shape space approach to the dynamics of the immune system

A simple mathematical model of Jerne's immune network is proposed where interactions among idiotypes are set according to their location in a shape space. Although the number of interacting idiotypes is potentially infinite, the simplicity of the model makes it possible to compute the attractors of the dynamics, to define the regions in the four parameters space related to the dynamical behavior and to predict the scaling law giving the number of different antigens that can be presented to the network without triggering dangerous instabilities. It is shown that only a low connectivity regime is safe for the immune network.