Adaptive learning properties (of clonal selection and affinity maturation) in the immune network model are investigated in this paper under a nonlinear data structural representation of the involved molecules. Weighted trees are constructed to model the multiple paratopes/epitopes on the antibodies/antigens. Parallel computing experiments are carried out for the canonical coding of these trees and the corresponding multiple matching interactions. Our experiments on real data have shown significant results on the cognitive properties of the immune network. These and other computational results are presented along with a discussion of future applications.