Changing the way of viewing QSAR methods: the application of hyperbolic projection in medicinal chemistry

Abstract

Lligand-based methods used in medicinal chemistry permit mathematical relationships to be established between molecular structure and the prediction of a property or biological activity (QSPR/QSAR) in the design of drugs with specific characteristics. The resulting models are usually defined by a large number of variables, which complicates their graphical representation in Euclidean space. The use of hyperbolic geometry in the definition of space has been found to enable the representation of multidimensional points on a bidimensional space by changing the metric definition (in this case, using Poincaré’s disk model). The projection of multidimensional points is performed by optimising genetic algorithms to find the coordinates which maintain intramolecular similarity. This methodology has been applied with other dimensional reduction techniques to identify the most appropriate variables to be used in the prediction of the subcellular localization of photosensitizers.

Keywords: Hyperbolic geometry, Poincaré’s disk model, multidimensional spaces, QSPR, QSAR, photodynamic therapy.