Rethinking "shape space": evidence from simulated docking suggests that steric shape complementarity is not limiting...

The concept of "shape space" is based on the assumption that the relevant properties of individual molecules can be adequately specified by a finite list of N parameters; and that cij, the affinity between molecules i and j, can be specified by an equation of the form: cij = f(xi, xj), where xi and xj are N-dimensional vectors representing the absolute positions of molecules i and j in an objective, referential "shape space", and f is an appropriate function. We have performed simulated docking of the combining sites of immunoglobulin molecules, based on their crystallographic structures. The results suggest that shape complementarity cannot account for the specificity of idiotypic interactions, since in the simulations each pair of docked proteins had a buried surface area as great as that occurring in known complexes. It therefore seems likely that the atomic interactions accounting for the specificity of immunoglobulin recognition are highly relational. This casts doubt on the basic assumptions underlying the shape-space concept, at least in the simple form hitherto used in theoretical modelling of the immune system. In order to be realistic, the dimensionality N would have to be high (more than 20), and the function f would be irregular and discontinuous. Alternatively, if the equation cij = f(xi, xj) is interpreted as a purely formal construction in an abstract "inversion space", its validity is entirely relative to the empirical affinity matrix on which the construction is based. We conclude that at present there is no sure way of adequately characterizing the internal structure of idiotypic affinity matrices; and that models of the immune system should therefore aim at being generic and robust with respect to the structure of the idiotypic affinity matrices of unselected immunoglobulins.