Evaluating 3D Shape-Similarity Using the Kähler Potential

The principle that molecules with similar shapes are likely to share similar biological activity has recently been increasingly used to screen large databases in drug discovery. Mathematical approximations to molecular shape are less expensive to compute than quantum-mechanical models, while still allowing for consideration of the different conformers a molecule can adopt. These methods also enable scaffold hopping, which can aid rescue of drug candidates found to have issues such as poor solubility or toxicity. 
This poster, presented at the YMF2021 conference, outlines a new approach to represent shape by approximating the molecular surface using the quantised Kähler potential (a concept taken from differential geometry). The surface is treated as topologically equivalent to a sphere embedded in complex projective space, with the Kähler potential is then calculated as a Taylor series. This represents a molecule using a Hermitian Matrix, whose dimensions depend on the number of terms included in the Taylor expansion of the function. The distance between two matrices then allows us to determine their similarity. We present our results from initial development of the method, as well as some of the challenges faced, and an outline of our proposed benchmark study to compare our new method to existing open-source software.