ABSTRACT
In this chapter, the authors aim to apply Darwin's idea of natural selection to the maturation of the immune response. They introduce recent results concerning the character of adaptive walks via fitter mutants to local optima, where such walks occur in rugged fitness landscapes with many peaks, ridges, and valleys. The authors review some of the major facts concerning clonal selection and the maturation of the immune response, and introduce a simple model of the maturation process. They introduce the concept of an affinity landscape. The authors develop a theoretical framework in which to study the character of adaptive walks that lead to B cells which secrete antibodies of high affinity for the immunizing epitope. They also introduce a new model, somewhat analogous to models of spin glasses, to study the statistical character of adaptive walks on rugged landscapes. The authors discuss injunctions to experimentalists and theoreticians for steps to improve the initial crude model.
