Some remarks on the stability of the idiotypic network
Abstract
The regulation of the immune response is a complex phenomenon whose details are not yet well known. Recently, Jerne has described the immune system as a complex idiotypic network. He has proposed that the interactions between elements involved in the latter are responsible for the main regulatory patterns of the immune system. Some experimental results are in favour of this hypothesis. A few theoretical models have been developed to described more precisely the nature of the interactions between the lymphocytes and the antibodies inside the network as well as their implications. In such a model, the time evolution of the concentration of those elements is described by kinetic equations whose integration over time can reproduce roughly the dynamic behaviour of the immune system. Those theoretical models should at least account for phenomena such as a memory or tolerance, which implies the maintenance of a stationary state. This latter statement can be directly related to the mathematical concept of stability. We illustrate this point on various models. More precisely, we show how each mode of the immune response may be interpreted as a transition from one steady state to another one, following antigenic or any other stimulation.
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