Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening

Abstract

This work introduces a number of algebraic topology approaches, including multi-component persistent homology, multi-level persistent homology, and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. In contrast to the conventional persistent homology, multi-component persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for protein-ligand binding analysis and virtual screening of small molecules. Extensive numerical experiments involving 4,414 protein-ligand complexes from the PDBBind database and 128,374 ligand-target and decoy-target pairs in the DUD database are performed to test respectively the scoring power and the discriminatory power of the proposed topological learning strategies. It is demonstrated that the present topological learning outperforms other existing methods in protein-ligand binding affinity prediction and ligand-decoy discrimination.

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References 126

1. 1.

   Krizhevsky A, Sutskever I, Hinton GE. Imagenet classification with deep convolutional neural networks In: Advances in neural information processing systems; 2012 p. 1097–1105.

   Not in our library

2. 2.

   Simonyan K, Zisserman A. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:14091556. 2014;.

   Not in our library

3. 3.
   Deep learning · 2015

   No notice
4. 4.

   Hinton G, Deng L, Yu D, Dahl GE, Mohamed Ar, Jaitly N, et al Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups. IEEE Signal Processing Magazine. 2012;29(6):82–97. doi: 10.1109/MSP.2012.2205597

   Not in our library

5. 5.

   Schmidhuber J. Deep learning in neural networks: An overview. Neural Networks. 2015;61:85–117. doi: 10.1016/j.neunet.2014.09.003

   Not in our library10.1016/j.neunet.2014.09.003

6. 6.

   Ngiam J, Khosla A, Kim M, Nam J, Lee H, Ng AY. Multimodal deep learning. In: Proceedings of the 28th international conference on machine learning (ICML-11); 2011. p. 689–696.

   Not in our library

7. 7.

   Hughes TB, Miller GP, Swamidass SJ. Modeling epoxidation of drug-like molecules with a deep machine learning network. ACS Central Science. 2015;1(4):168–180. doi: 10.1021/acscentsci.5b00131

   Not in our library10.1021/acscentsci.5b00131

8. 8.

   Unterthiner T, Mayr A, Klambauer G, Hochreiter S. Toxicity prediction using deep learning. arXiv preprint arXiv:150301445. 2015;.

   Not in our library

9. 9.

   Lusci A, Pollastri G, Baldi P. Deep architectures and deep learning in chemoinformatics: the prediction of aqueous solubility for drug-like molecules. Journal of chemical information and modeling. 2013;53(7):1563–1575. doi: 10.1021/ci400187y

   Not in our library10.1021/ci400187y

10. 10.

    Wallach I, Dzamba M, Heifets A. AtomNet: A Deep Convolutional Neural Network for Bioactivity Prediction in Structure-based Drug Discovery. arXiv preprint arXiv:151002855. 2015;.

    Not in our library

11. 11.

    Dahl GE, Jaitly N, Salakhutdinov R. Multi-task neural networks for QSAR predictions. arXiv preprint arXiv:14061231. 2014;.

    Not in our library

12. 12.

    Ramsundar B, Kearnes S, Riley P, Webster D, Konerding D, Pande V. Massively multitask networks for drug discovery. arXiv preprint arXiv:150202072. 2015;.

    Not in our library

13. 13.

    Wu Z, Ramsundar B, Feinberg EN, Gomes J, Geniesse C, Pappu AS, et al. MoleculeNet: A Benchmark for Molecular Machine Learning. arXiv preprint arXiv:170300564. 2017;.

    Not in our library10.1039/c7sc02664a

14. 14.

    Cang Z, Wei GW. Analysis and prediction of protein folding energy changes upon mutation by element specific persistent homology. Bioinformatics. 2017;33,3549–3557.

    Not in our library10.1093/bioinformatics/btx460

15. 15.

    Bates PW, Wei GW, Zhao S. Minimal molecular surfaces and their applications. Journal of Computational Chemistry. 2008;29(3):380–391. doi: 10.1002/jcc.20796

    Not in our library10.1002/jcc.20796

16. 16.

    Bates PW, Chen Z, Sun YH, Wei GW, Zhao S. Geometric and potential driving formation and evolution of biomolecular surfaces. J Math Biol. 2009;59:193–231. doi: 10.1007/s00285-008-0226-7

    Not in our library10.1007/s00285-008-0226-7

17. 17.

    Zheng Q, Yang SY, Wei GW. Molecular surface generation using PDE transform. International Journal for Numerical Methods in Biomedical Engineering. 2012;28:291–316.

    Not in our library10.1002/cnm.1469

18. 18.

    Chen Z, Baker NA, Wei GW. Differential geometry based solvation models I: Eulerian formulation. J Comput Phys. 2010;229:8231–8258. doi: 10.1016/j.jcp.2010.06.036

    Not in our library10.1016/j.jcp.2010.06.036

19. 19.

    Chen Z, Baker NA, Wei GW. Differential geometry based solvation models II: Lagrangian formulation. J Math Biol. 2011;63:1139–1200. doi: 10.1007/s00285-011-0402-z

    Not in our library10.1007/s00285-011-0402-z

20. 20.

    Chen Z, Zhao S, Chun J, Thomas DG, Baker NA, Bates PB, et al Variational approach for nonpolar solvation analysis. Journal of Chemical Physics. 2012;137(084101).

    Not in our library10.1063/1.4745084

21. 21.

    Nguyen DD, Wei GW. The impact of surface area, volume, curvature and Lennard-Jones potential to solvation modeling. Journal of Computational Chemistry. 2017;38:24–36. doi: 10.1002/jcc.24512

    Not in our library10.1002/jcc.24512

22. 22.

    Feng X, Xia K, Tong Y, Wei GW. Geometric modeling of subcellular structures, organelles and large multiprotein complexes. International Journal for Numerical Methods in Biomedical Engineering. 2012;28:1198–1223. doi: 10.1002/cnm.2532

    Not in our library10.1002/cnm.2532

23. 23.

    Feng X, Xia KL, Tong YY, Wei GW. Multiscale geometric modeling of macromolecules II: Lagrangian representation. Journal of Computational Chemistry. 2013;34:2100–2120. doi: 10.1002/jcc.23364

    Not in our library10.1002/jcc.23364

24. 24.

    Xia KL, Feng X, Tong YY, Wei GW. Multiscale geometric modeling of macromolecules I: Cartesian representation. Journal of Computational Physics. 2014;275:912–936. doi: 10.1016/j.jcp.2013.09.034

    Not in our library10.1016/j.jcp.2013.09.034

25. 25.

    Kandathil SM, Fletcher TL, Yuan Y, Knowles J, Popelier PL. Accuracy and tractability of a Kriging model of intramolecular polarizable multipolar electrostatics and its application to histidine. Journal of computational chemistry. 2013;34(21):1850–1861. doi: 10.1002/jcc.23333

    Not in our library10.1002/jcc.23333

26. 26.

    Xia KL, Wei GW. Persistent homology analysis of protein structure, flexibility and folding. International Journal for Numerical Methods in Biomedical Engineering. 2014;30:814–844. doi: 10.1002/cnm.2655

    Not in our library10.1002/cnm.2655

27. 27.

    Cang Z, Wei GW. Integration of element specific persistent homology and machine learning for protein-ligand binding affinity prediction. International Journal for Numerical Methods in Biomedical Engineering. 2017; p. e2914–n/a. doi: 10.1002/cnm.2914

    Not in our library10.1002/cnm.2914

28. 28.

    Schlick T, Olson WK. Trefoil knotting revealed by molecular dynamics simulations of supercoiled DNA. Science. 1992;257(5073):1110–1115. doi: 10.1126/science.257.5073.1110

    Not in our library10.1126/science.257.5073.1110

29. 29.

    Zomorodian A, Carlsson G. Computing persistent homology. Discrete Comput Geom. 2005;33:249–274. doi: 10.1007/s00454-004-1146-y

    Not in our library

30. 30.

    Sumners DW. Knot theory and DNA. In: Proceedings of Symposia in Applied Mathematics. vol. 45; 1992. p. 39–72.

    Not in our library

31. 31.

    Darcy IK, Vazquez M. Determining the topology of stable protein-DNA complexes. Biochemical Society Transactions. 2013;41:601–605. doi: 10.1042/BST20130004

    Not in our library10.1042/bst20130004

32. 32.

    Heitsch C, Poznanovic S. Combinatorial insights into RNA secondary structure, in Jonoska N. and Saito M., editors. Discrete and Topological Models in Molecular Biology. 2014;Chapter 7:145–166.

    Not in our library

33. 33.

    Demerdash ONA, Daily MD, Mitchell JC. Structure-Based Predictive Models for Allosteric Hot Spots. PLOS Computational Biology. 2009;5:e1000531 doi: 10.1371/journal.pcbi.1000531

    Not in our library10.1371/journal.pcbi.1000531

34. 34.

    DasGupta B, Liang J. Models and Algorithms for Biomolecules and Molecular Networks. John Wiley & Sons; 2016.

    Not in our library

35. 35.

    Shi X, Koehl P. Geometry and topology for modeling biomolecular surfaces. Far East J Applied Math. 2011;50:1–34.

    Not in our library

36. 36.

    Edelsbrunner H, Letscher D, Zomorodian A. Topological persistence and simplification. Discrete Comput Geom. 2002;28:511–533. doi: 10.1007/s00454-002-2885-2

    Not in our library

37. 37.

    Bendich P, Harer J. Persistent Intersection Homology. Foundations of Computational Mathematics (FOCM). 2011;11(3):305–336. doi: 10.1007/s10208-010-9081-1

    Not in our library

38. 38.

    Cohen-Steiner D, Edelsbrunner H, Harer J. Stability of Persistence Diagrams. Discrete & Computational Geometry. 2007;37(1):103–120. doi: 10.1007/s00454-006-1276-5

    Not in our library

39. 39.

    Cohen-Steiner D, Edelsbrunner H, Harer J. Extending Persistence Using Poincaré and Lefschetz Duality. Foundations of Computational Mathematics. 2009;9(1):79–103. doi: 10.1007/s10208-008-9038-9

    Not in our library

40. 40.

    Cohen-Steiner D, Edelsbrunner H, Harer J, Morozov D. Persistent Homology for Kernels, Images, and Cokernels. In: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 09; 2009. p. 1011–1020.

    Not in our library

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