From quantum similarity measures to quantum analogy functors: tools for QShAR, quantitative shape-activity relations

Abstract

An analogy can be regarded as a relation between two families of similarities, and the mathematical tool of functor has been proposed for certain chemical applications where not just one type of similarity, but entire families of similarities, hence, analogies, are playing important roles. Some of the relevant background important in molecular applications, especially, in studies of chemical and biochemical activity problems are discussed, where several factors of various levels of similarities are determining the overall chemical processes. Such analogies are highly relevant in the interpretation of complex biochemical actions, as well as in pharmaceutical drug design. The Quantum Similarity Measures and alternative measures based on quantum chemistry are combined into a Quantum Analogy Functor model, with special emphasis on the 3D molecular shapes represented by the electron density clouds, and the associated Quantitative Shape-Activity Relations, QShAR. Some aspects of the Quantum Analogy Functor approach, with focus on Molecular Shapes and QShAR are discussed in this contribution.