A novel, customizable and optimizable parameter method using spherical harmonics for molecular shape similarity comparisons

A novel molecular shape similarity comparison method, namely SHeMS, derived from spherical harmonic (SH) expansion, is presented in this study. Through weight optimization using genetic algorithms for a customized reference set, the optimal combination of weights for the translationally and rotationally invariant (TRI) SH shape descriptor, which can specifically and effectively distinguish overall and detailed shape features according to the molecular surface, is obtained for each molecule. This method features two key aspects: firstly, the SH expansion coefficients from different bands are weighted to calculate similarity, leading to a distinct contribution of overall and detailed features to the final score, and thus can be better tailored for each specific system under consideration. Secondly, the reference set for optimization can be totally configured by the user, which produces great flexibility, allowing system-specific and customized comparisons. The directory of useful decoys (DUD) database was adopted to validate and test our method, and principal component analysis (PCA) reveals that SH descriptors for shape comparison preserve sufficient information to separate actives from decoys. The results of virtual screening indicate that the proposed method based on optimal SH descriptor weight combinations represents a great improvement in performance over original SH (OSH) and ultra-fast shape recognition (USR) methods, and is comparable to many other popular methods. Through combining efficient shape similarity comparison with SH expansion method, and other aspects such as chemical and pharmacophore features, SHeMS can play a significant role in this field and can be applied practically to virtual screening by means of similarity comparison with 3D shapes of known active compounds or the binding pockets of target proteins.