ABSTRACT
This chapter presents the idea of peptide spaces, which molecular biologist choose to rename "affinity landscapes," to reflect our interest in the binding of antigens by antibodies. The actual structure of fitness landscapes in protein space for specific catalytic or ligand-binding functions is unknown, but increasingly opens to direct investigation by genetic engineering and site-directed mutagenesis studies. The chapter discusses the NK class of mathematical models, and discusses enough of its properties to motivate the modeling steps employed subsequently. The general interest in the family of landscapes lies in understanding the implications of the richness of epistasis on the expected structure of fitness landscapes. The NK models have the important property that, as the parameter K increases, the "ruggedness" of the NK landscape varies from a single-peaked "Fujiyama" landscape to a multi-peaked "badlands" landscape. The chapter examines the biological facts regarding the maturation of the immune response.
