Citation: Dong CHEN, Ming-Zheng ZHANG, Hai-Biao CHEN, Zuo-Wei XIE, Guo-Wei WEI, Feng PAN. Persistent Homology for the Quantitative Analysis of the Structure and Stability of Carboranes[J]. Chinese Journal of Structural Chemistry, ;2020, 39(6): 999-1008. doi: 10.14102/j.cnki.0254-5861.2011-2889 shu

Persistent Homology for the Quantitative Analysis of the Structure and Stability of Carboranes

Dong CHEN ^a ,
Ming-Zheng ZHANG ^a ,
Hai-Biao CHEN ^a ,
Zuo-Wei XIE ^b ,
Guo-Wei WEI ^{c, d, e,,} ,
Feng PAN ^a,,

a.
School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen 518055, China
b.
Department of Chemistry and State Key Laboratory of Synthetic Chemistry, The Chinese University of HongKong, Shatin, New Territories, Hong Kong, China
c.
Department of Mathematics, Michigan State University, MI 48824 USA
d.
Department of Electrical and Computer Engineering, Michigan State University, MI 48824, USA
e.
Department of Biochemistry and Molecular Biology, Michigan State University, MI 48824, USA

Corresponding author: Guo-Wei WEI, weig@msu.edu Feng PAN, panfeng@pkusz.edu.cn
Received Date: 25 May 2020
Accepted Date: 5 June 2020

Fund Project: the National Key R & D Program of China 2016YFB0700600Soft Science Research Project of Guangdong Province 2017B030301013Shenzhen Science and Technology Research Grant ZDSYS201707281026184

Figures(5)

Persistent homology is a powerful and novel tool for quantifying the inherent topological features of structure. In this work, we used the persistent homology for the first time to study the closo-carboranes C₂B_n-2H_n (n = 5~20) and their parent structures closo-boranes dianions B_nH_n^2- (n = 5~20), where multiple elements are present. All these structures are first investigated with the standard Vitoris-Rips complex. We interpret all barcodes representation and associate them with structural details. By means of average bar length, a linear regression model was established to construct the relationship between persistent homology features and molecular stability, which was expressed by the relative energies. For closo-boranes dianions, we only use B atom set since B and H atoms are in pairs. The average lengths of β₀, β₁ and β₂ bars are used as the features for linear regression, and excellent correlation coefficient (0.977) between the values predicted by persistent homology and those by quantum calculations was achieved. For closo-carboranes, C–B atom set (ignore the differences in the atoms), B atom set and C atom set were considered to get the persistent homology features (since there were only two C atoms in C₂B_n-2H_n, only β₀ bars were considered), and seven average bar lengths were calculated, respectively. Pearson coefficient of 0.937 was obtained. We found that the stability of carboranes showed a high linear correlation with the characteristics generated from topological bars in H₀, H₁ and H₂. The results show that the topological information generated by persistent homology can be extended and applied to multi-element systems.
- topology,
- persistent homology,
- carboranes,
- filtration,
- stability,
- relative energy
1. [1]
  Edelsbrunner, H.; Letscher, D.; Zomorodian, A. Topological persistence and simplification. FOCS 2000, 28, 454–463.
2. [2]
  Zomorodian, A.; Carlsson, G. Computing persistent homology. Discrete Comput. Geom. 2005, 33, 249–274. doi: 10.1007/s00454-004-1146-y
3. [3]
  Edelsbrunner, H.; Mucke, E. P. Three-dimensional alpha shapes. ACM Trans. Graph. 1994, 13, 43–72. doi: 10.1145/174462.156635
4. [4]
  Edelsbrunner, H.; Harer, J. Computational topology: an introduction; American Mathematical Soc. 2010, 1-241.
5. [5]
  Dey, T. K.; Li, K.; Sun, J.; Cohen-Steiner, D. Computing geometry-aware handle and tunnel loops in 3D models. ACM Trans. Graph. 2008, 27, 1–9.
6. [6]
  Dey, T. K.; Wang, Y. Reeb graphs: approximation and persistence. Discrete Comput. Geom. 2013, 49, 46–73. doi: 10.1007/s00454-012-9463-z
7. [7]
  Mischaikow, K.; Nanda, V. Morse theory for filtrations and efficient computation of persistent homology. Discrete Comput. Geom. 2013, 50, 330–353. doi: 10.1007/s00454-013-9529-6
8. [8]
  Ghrist, R. Barcodes: the persistent topology of data. Bull. Amer. Math. Soc. 2008, 45, 61–75.
9. [9]
  Carlsson, G.; Ishkhanov, T.; De Silva, V.; Zomorodian, A. On the local behavior of spaces of natural images. Int. J. Comput. Vis. 2008, 76, 1–12. doi: 10.1007/s11263-007-0056-x
10. [10]
  Pachauri, D.; Hinrichs, C.; Chung, M. K.; Johnson, S. C.; Singh, V. Topology-based kernels with application to inference problems in Alzheimer's disease. IEEE Trans Med Imaging. 2011, 30, 1760–1770. doi: 10.1109/TMI.2011.2147327
11. [11]
  Singh, G.; Memoli, F.; Ishkhanov, T.; Sapiro, G.; Carlsson, G.; Ringach, D. L. Topological analysis of population activity in visual cortex. J VISION. 2008, 8, 11–11.
12. [12]
  De Silva, V.; Ghrist, R.; Muhammad, A. Blind swarms for coverage in 2-D. Robotics: Science and Systems 2005, 335–342.
13. [13]
  Lee, H.; Kang, H.; Chung, M. K.; Kim, B. N.; Lee, D. S. Persistent brain network homology from the perspective of dendrogram. IEEE Trans. Med. Imaging. 2012, 31, 2267–2277. doi: 10.1109/TMI.2012.2219590
14. [14]
  Horak, D.; Maleti´c, S.; Rajkovi´c, M. Persistent homology of complex networks. J. Stat. Mech. Theory Exp. 2009, 2009, P03034.
15. [15]
  Carlsson, G. Topology and data. Bull New Ser. Am. Math Soc. 2009, 46, 255–308. doi: 10.1090/S0273-0979-09-01249-X
16. [16]
  Feng, X.; Tong, Y. Choking loops on surfaces. IEEE Trans. Med. Imaging. 2013, 19, 1298–1306.
17. [17]
  Kasson, P. M.; Zomorodian, A.; Park, S.; Singhal, N.; Guibas, L. J.; Pande, V. S. Persistent voids: a new structural metric for membrane fusion. Bioinformatics 2007, 23, 1753–1759. doi: 10.1093/bioinformatics/btm250
18. [18]
  Gameiro, M.; Hiraoka, Y.; Izumi, S.; Kramar, M.; Mischaikow, K.; Nanda, V. A topological measurement of protein compressibility. Jpn. J. Ind. Appl. Math. 2015, 32, 1–17. doi: 10.1007/s13160-014-0153-5
19. [19]
  Dabaghian, Y.; M´emoli, F.; Frank, L.; Carlsson, G. A topological paradigm for hippocampal spatial map formation using persistent homology. PLoS Comput. Biol. 2012, 8, 1–14.
20. [20]
  Yao, Y.; Sun, J.; Huang, X.; Bowman, G. R.; Singh, G.; Lesnick, M.; Guibas, L. J.; Pande, V. S.; Carlsson, G. Topological methods for exploring low-density states in biomolecular folding pathways. J. Chem. Phys. 2009, 130, 144115. doi: 10.1063/1.3103496
21. [21]
  Xia, K.; Feng, X.; Tong, Y.; Wei, G. W. Persistent homology for the quantitative prediction of fullerene stability. J. Comput. Chem. 2015, 36, 408–422. doi: 10.1002/jcc.23816
22. [22]
  Schleyer, P. V. R.; Najafian, K. Stability and three-dimensional aromaticity of closomonocarbaborane anions, CB_n-1H_n^-, and closo-dicarboranes, C₂B _n-2H_n. Inorg. Chem. 1998, 37, 3454–3470. doi: 10.1021/ic980110v
23. [23]
  Williams, R. E. Early carboranes and their structural legacy. Adv. Organomet. Chem. 1994, 36, 1–55.
24. [24]
  Mingos, D. M. P.; Wales, D. J. Introduction to cluster chemistry. Prentice Hall. 1990, 1–318.
25. [25]
  Zhang, J.; Xie, Z. Synthesis, structure, and reactivity of 13- and 14-vertex carboranes. Acc. Chem. Res. 2014, 47, 1623–1633.
26. [26]
  Qiu, Z.; Ren, S.; Xie, Z. Transition metal-carboryne complexes: synthesis, bonding, and reactivity. Acc. Chem. Res. 2011, 44, 299–309.
27. [27]
  Zhang, J.; Lin, Z.; Xie, Z. DFT studies on structures, stabilities, and electron affinities of closo-supercarboranes C₂B_n-₂H_n (n = 13~20). Organometallics 2015, 34, 5576–5588.
28. [28]
  Diaz, M.; Jaballas, J.; Tran, D.; Lee, H.; Arias, J.; Onak, T. Interaction of trimethylamine and closo-1, 6-C₂B₇H₉. Evidence for an "open" cage C₂B₇H₉/amine adduct. Inorg. Chem. 1996, 35, 4536–4540.
29. [29]
  Buhl, M.; Gauss, J.; Hofmann, M.; Schleyer, P. V. R. Decisive electron correlation effects on computed boron-11 and carbon-13 NMR chemical shifts. Application of the GIAO-MP2 method to boranes and carbaboranes. J. Am. Chem. Soc. 1993, 115, 12385–12390.
30. [30]
  McKee, M. L. Theoretical study of the reaction of acetylene with B₄H₈. A proposed mechanism of carborane formation. J. Am. Chem. Soc. 1996, 118, 421–428.
31. [31]
  Munch, E. Applications of Persistent Homology to Time Varying Systems. USA, Duke University 2013, 1–112.
32. [32]
  Fornberg, B. A Practical Guide to Pseudospectral Methods. Cambridge University Press 1996, 1–231.
33. [33]
  Xia, K.; Opron, K.; Wei, G. W. Multiscale multiphysics and multidomain models-flexibility and rigidity. J. Chem. Phys. 2013, 139, 194109.
34. [34]
  Xia, K.; Wei, G. W. Stochastic model for protein flexibility analysis. Phys. Rev. E 2013, 88, 062709.
35. [35]
  Xia, K.; Wei, G. W. Molecular nonlinear dynamics and protein thermal uncertainty quantification. J. Nonlinear. Sci. 2014, 24, 013103.
36. [36]
  Pedregosa, F.; Gaël, V.; Alexandre, G.; Vincent, M.; Bertrand, T.; Olivier, G.; Mathieu, B.; Peter, P.; Ron, W.; Vincent, D.; Jacob, T. V.; Alexandre, P.; David, C.; Matthieu, B.; Matthieu, P.; Édouard, D. Scikit-learn: machine learning in python. J. Mach. Learn Res. 2011, 12, 2825–2830.
37. [37]
  Buitinck, L.; Louppe, G.; Blondel, M.; Pedregosa, F.; Mueller, A.; Grisel, O.; Niculae, V.; Prettenhofer, P.; Gramfort, A.; Grobler, J.; Layton, R.; VanderPlas, J.; Joly, A.; Holt, B.; Varoquaux, G. API design for machine learning software: experiences from the scikit-learn project. ECML PKDD Workshop: Languages for Data Mining and Machine Learning 2013, 108–122.
38. [38]
  Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; Li, X.; Caricato, M.; Marenich, A. V.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V.; Izmaylov, A. F.; Sonnenberg, J. L.; Williams-Young, D.; Ding, F.; Lipparini, F.; Egidi, F.; Goings, J.; Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.; Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; Montgomery, J. A. Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J. J.; Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Keith, T. A.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Farkas, O.; Foresman, J. B.; Gaussian 16, Wallingford CT, Gaussian Inc. 2016.
39. [39]
  Becke, A. The quantum theory of atoms in molecules: from solid state to DNA and drug design. John Wiley & Sons. 2007, 1–567.
40. [40]
  Momma, K.; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 2011, 44, 1272–1276.
41. [41]
  Roy, D. K.; Mondal, B.; Shankhari, P.; Anju, R.; Geetharani, K.; Mobin, S. M.; Ghosh, S. Supraicosahedral polyhedra in metallaboranes: synthesis and structural characterization of 12-, 15-, and 16-vertex rhodaboranes. Inorg. Chem. 2013, 52, 6705–6712.
42. [42]
  Kang, S. O.; Furst, G. T.; Sneddon, L. G. Reactions of nitriles with polyhedral borane anions. Reductive cyclocondensation and carbon insertion reactions: syntheses of hypho-5-CH₃-5, 11, 7, 14-CNS₂B₇H₉ and nido-6-CH₃-5, 6, 9-C₃B₇H₁₀. Inorg. Chem. 1989, 28, 2339–2347.
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