Statistical physics of immune networks

Several discrete models of immune networks have been developed in the last few years to describe the dynamics of the various aspects of immune response. The populations of the various types of cells involved in immune response are represented in these theries by “automata” and the population dynamics of these cells are formulated in terms of discrete maps in discrete time, in contrast to the classical approaches where differential equations describe the time evolution of the populations, which are taken to be real variables. We summarize here the main results of these investigations and present a critical analysis of the successes and limitations of this discrete approach by comparing with the results of corresponding continuum models. Recently, interclonal interactions have been taken into account by implementing Jerne's idea of a “functional network” using a “shape space” approach. We report some of the progress made recently in this area of interdisciplinary research and also outline a simple theory of T-cell anergy.