From Shape Similarity to Shape Complementarity: Toward a Docking Theory

Formal relations between similarity and docking are analyzed, and a general docking theory is proposed for colored mixtures of multivariate distributions. X and Y being two colored mixtures with given marginal distributions, their shape complementarity coefficient is defined as the lower bound of the variance of (X−Y)′· (X-Y), taken over the set of joint distributions of X and Y. The docking is performed via minimization of the shape complementarity coefficient for all translations and rotations of the mixtures. The properties of the docking criterion are derived, and are shown to satisfy the practical requirements encountered in molecular shape analysis.