Inverse analysis of empirical matrices of idiotypic network interactions

The concept of shape space proposed by Perelson and Oster (1979, J. Theor. Biol. 81, 645-670) has been a useful tool for the theoretical immunologists, who have invoked it to model idiotypic binding, which plays a significant role in mathematical models of immune networks. The actual construction of such a space from its definition requires specialized experimental information, which is not completely available. In this article, we discuss, with illustrative examples, how graphical representations similar to the idea of shape space can be derived by analyzing real affinity matrices, and the relative merits of such representations to approximations that might be obtained by the approach of Perelson and Oster. We also give directions for future research with a view toward applications.