Can you hear the shape of a drug? applying Riemannian geometry for shape-based virtual screening

Abstract

The use of virtual screening in drug discovery to minimise human effort and required resources has gained popularity in recent years. In the absence of structural information, methods based on the similar property principle, which states that two molecules that are similar are also likely to have similar biological activity, can be used to rank large libraries using known binders as templates. An emerging approach to quantify similarity is the use of molecular shape described by using mathematical approximations to the volume, distribution of interatomic distances, or the surface of the molecule. The use of surface-based methods offers a promising intermediate between the accuracy of volume-based methods and the speed of atomic distance-based methods, but it is yet to be widely adopted in the context of drug discovery. This thesis aims to address this with the application of Riemannian geometry to produce two novel descriptors of molecular surface shape. Both use the Riemannian metric associated with the surface, which is a matrix of functions that captures the geometric properties of the molecule. However, two metrics cannot be easily compared. Riemannian Geometry for Molecular Surface Approximation (RGMolSA) gives a 9-element vector by using the metric to approximate the spectrum of the Laplacian. Kähler Quantization for Molecular Surface Approximation (KQMolSA) applies the theory of Kähler geometry to transform the metric into a Hermitian matrix descriptor of shape. Both descriptors are alignment-free and are fast to compute. An initial investigation using a series of PDE5 inhibitors of known shape is reported. Both methods outperform existing open-source descriptors, with RGMolSA slightly outperforming KQMolSA. A full retrospective benchmarking study, focusing primarily on the Directory of Useful Decoys - Enhanced (DUD-E) data set, was also completed. The performance of both methods across the full data set compared favourably with the existing work in the field. Improvements could be made in the ability to place true actives early in the ranked list in both cases, but both methods gave overall promising performance after the first round of development.