Alignment-Free Molecular Shape Comparison Using Spectral Geometry. The Framework.

A framework is presented for the calculation of novel alignment-free descriptors of molecular shape. The methods are based on the technique of spectral geometry which has been developed in the field of computer vision where it has shown impressive performance for the comparison of deformable objects such as people and animals. Spectral geometry techniques encode shape by capturing the curvature of the surface of an object into a compact, information-rich representation that is alignment-free while also being invariant to isometric deformations, that is, changes that do not distort distances over the surface. Here, we adapt the technique to the new domain of molecular shape representation. We describe a series of parametrization steps aimed at optimizing the method for this new domain. Our focus here is on demonstrating that the basic approach is able to capture a molecular shape into a compact and information-rich descriptor. We demonstrate improved performance in virtual screening over a more established alignment-free method and impressive performance compared to a more accurate, but much more computationally demanding, alignment-based approach.