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

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Abstract

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.

Schematic diagram of spherical harmonic (SH) based weighted similarity calculation. First, molecular surfaces are projected to groups of SH producing a series of projection coefficients which are used to calculate SH descriptors. Then, a genetic algorithm based searching process will be carried out, producing a group of optimal weights which can best separate actives from negatives. Finally, combining the SH descriptor and corresponding weights, a similarity score was calculated and used to rank the candidate molecules

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Acknowledgments

This work was supported by the Special Fund for Major State Basic Research Project (grant 2009CB918501), the National Natural Science Foundation of China (grants 20803022), the Shanghai Committee of Science and Technology (grants 09dZ1975700 and 10431902600), the 863 Hi-Tech Program of China (grant 2007AA02Z304), and the Major National Scientific and Technological Project of China (grant 2009ZX09501-001). H.L. is also sponsored by Shanghai Rising-Star Program (grant 10QA1401800) and the Fundamental Research Funds for the Central Universities. The program and test sets of SHeMS are available from H.L. upon request.

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Authors and Affiliations

  1. School of Information Science and Engineering, East China University of Science and Technology, Shanghai, 200237, China

    Chaoqian Cai, Jiayu Gong & Daqi Gao

  2. State Key Laboratory of Bioreactor Engineering,Shanghai Key Laboratory of Chemical Biology, School of Pharmacy, East China University of Science and Technology, Shanghai, 200237, China

    Xiaofeng Liu, Hualiang Jiang & Honglin Li

Authors
  1. Chaoqian Cai
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  2. Jiayu Gong
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  3. Xiaofeng Liu
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  4. Hualiang Jiang
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  5. Daqi Gao
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  6. Honglin Li
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Corresponding authors

Correspondence to Daqi Gao or Honglin Li.

Additional information

Author contributions

C.C. designed and validated the Cyndi method, and also contributed to analysis and data interpretation and co-drafted the manuscript with J.G. and X.L. J.G. contributed to the design of method. X.L. contributed to method validation. H.L. conceived the idea of the SHeMS and provided direction for its development and revised the subsequent drafts of this manuscript with D.G., and H.J. All authors read and approved the final manuscript.

Electronic supplementary material

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Supplementary material

Supplementary file 1 – ESM_1.pdf

This file contains the ZINC codes of molecules passed pre-process and used for weights optimization. (PDF 183 kb)

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Cai, C., Gong, J., Liu, X. et al. A novel, customizable and optimizable parameter method using spherical harmonics for molecular shape similarity comparisons. J Mol Model 18, 1597–1610 (2012). https://doi.org/10.1007/s00894-011-1173-6

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