Riemannian Geometry and Molecular Similarity II: K\"ahler Quantization

TL;DR

This paper introduces a novel molecular shape descriptor based on Riemannian geometry and Kähler quantization, offering an alternative to existing methods with promising results in drug discovery applications.

Contribution

It presents a new shape descriptor derived from Riemannian geometry and Kähler quantization, improving molecular similarity analysis.

Findings

Method handles different conformers effectively

Compared favorably to existing shape similarity methods

Demonstrated utility on PDE5 inhibitors

Abstract

Shape-similarity between molecules is a tool used by chemists for virtual screening, with the goal of reducing the cost and duration of drug discovery campaigns. This paper reports an entirely novel shape descriptor as an alternative to the previously described RGMolSA descriptors \cite{cole2022riemannian}, derived from the theory of Riemannian geometry and K\"ahler quantization (KQMolSA). The treatment of a molecule as a series of intersecting spheres allows us to obtain the explicit \textit{Riemannian metric} which captures the geometry of the surface, which can in turn be used to calculate a Hermitian matrix $\mathbb{M}$ as a directly comparable surface representation. The potential utility of this method is demonstrated using a series of PDE5 inhibitors considered to have similar shape. The method shows promise in its capability to handle different conformers, and compares well to existing shape similarity methods. The code and data used to produce the results are available at: \url{https://github.com/RPirie96/KQMolSA}.