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Derivatives in discrete mathematics: a novel graph-theoretical invariant for generating new 2/3D molecular descriptors. I. Theory and QSPR application
- 作者:Yovani Marrero-Ponce (1) (2)
Oscar Martínez Santiago (1) (3) Yoan Martínez López (1) (4) Stephen J. Barigye (1) Francisco Torrens (2)
- 关键词:Discrete mathematics ; Chemical graph theory ; Molecular graph ; Sub ; graph ; Incidence matrix ; Frequency matrix ; Derivative of molecular graph ; Invariant ; QSPR study ; Physicochemical property ; Derivatives of 2 ; furylethylene
- 刊名:Journal of Computer-Aided Molecular Design
- 出版年:2012
- 出版时间:November 2012
- 年:2012
- 卷:26
- 期:11
- 页码:1229-1246
- 全文大小:557KB
- 参考文献:1. Todeschini R, Consonni V (2000) Handbook of molecular descriptors. Wiley-VCH, Germany CrossRef
2. Todeschini R, Consonni V, Pavan M (2002) 2.1 ed., Milano Chemometric and QSAR Research Group, Milano, Italy 3. Katritzky AR, Perumal S, Petrukhin R, Kleinpeter E (2001) J Chem Inf Comput Sci 41:569 CrossRef 4. 2.13 ed. 7204 Mullen, Shawnee, KS 66216, USA 5. Gugisch R, Kerber A, Laue R, Meringer M, Weidinger J University of Bayreuth, D-95440 Bayreuth, Germany 6. Topological Indices and Related Descriptors in QSAR and QSPR; Devillers, J. B., A. T, Ed.; Gordon and Breach Amsterdam, The Netherlands, 1999 7. Todeschini R, Consonni V (2010) MATCH Commun. Math. Comput. Chem 64:359 8. Devillers J (2000) Curr Opin Drug Discovery Dev. 3 9. Karelson M (2000) Molecular descriptors in QSAR/QSPR. Wiley, New York 10. Estrada E, Uriarte E (2001) Curr Med Chem 8:1573 CrossRef 11. Estrada E, Rodríguez L (1997) Comm Math Chem (MATCH) 35:157 12. Randi? M (1991) J Math Chem 7:155 CrossRef 13. Randi? M, Trinajsti? NJ (1993) Mol Struct (Theochem) 300:551 14. Kier LB, Hall LH (1999) Molecular structure description. The electrotopological state. Academic Press, New York 15. Rouvray DH (1976) Chemical applications of graph theory. Academic Press, London 16. Kier LB, Hall LH (1986) Molecular connectivity in structure—activity analysis. Research Studies Press, Letchworth 17. Ivanciuc O, Gasteiger J (2003) Ed. Wiley-VCH, Weinheim, p 103 18. Balaban AT (1997) From chemical graphs to three-dimensional geometry. Plenum Press, New York 19. Estrada E (2001) Chem Phys Lett 336:248 CrossRef 20. Estrada E, Rodríguez L, Gutierrez A (1997) Commun Math Chem (MATCH) 35:145 21. Aires-de-Sousa J, Gasteiger J (2002) J Mol Graph Model 20:373 CrossRef 22. Golbraikh A, Bonchev D, Tropsha A (2001) J Chem Inf Comput Sci 41:147 CrossRef 23. Marrero-Ponce Y, Castillo-Garit JA, Castro EA, Torrens F, Rotondo RJ (2008) Math. Chem. doi:10.1007/s10910-008-9386-3 24. Gorbátov VA (1988) Fundamentos de la Matematica discreta, Mir, Moscow, URSS 25. Daudel R, Lefebre R, Moser C (1984) Quantum chemistry: methods and applications. Wiley, New York 26. Marrero-Ponce Y (2002) version 1.0 ed., Unit of computer-aided molecular “Biosilico-Discovery and Bioinformatic Research (CAMD-BIR Unit): Santa Clara, Villa Clara 27. Estrada E, Molina E (2001) J Mol Graph Model 20:54 CrossRef 28. Estrada E, Molina E (2001) J Chem Inf Comput Sci 41:791 CrossRef 29. Dore JC, Viel C (1975) Farmaco 30:81 30. Martínez Santiago O, Martínez-López Y, Marrero-Ponce Y (2010) version 1.0 ed., Unit of computer-aided molecular “Biosilico-discovery and bioinformatic research (CAMD-BIR Unit), Santa Clara, Villa Clara, Cuba 31. Todeschini R, Consonni V, Mauri A, Pavan M (2005) 1.0 ed., Talete, Milano 32. Goldberg DE (1989) Genetic algorithms. Addison Wesley, Reading 33. Rogers D, Hopfinger AJJ (1994) Chem Inf Comput Sci 34:854 CrossRef 34. So SS, Karplus M (1996) J Med Chem 39:1521 CrossRef 35. Stankevich V, Skvortsova MI, Zefirov NSJ (1995) Mol Struct (THEOCHEM) 342:173 CrossRef 36. Galvez JJ (1998) Mol Struct (THEOCHEM) 429:255 CrossRef 37. Kier LB, Hall LHJ (2000) Chem Inf Comput Sci 40:792 CrossRef 38. Kier LB, Hall LH (2001) J Mol Graph Model 20:76 CrossRef 39. Randic M, Hansen PJ, Jurs PCJ (1988) Chem Inf Comput Sci 28:60 CrossRef 40. Estrada EJ (2002) Phys Chem A 106:9085 CrossRef
- 作者单位:Yovani Marrero-Ponce (1) (2)
Oscar Martínez Santiago (1) (3) Yoan Martínez López (1) (4) Stephen J. Barigye (1) Francisco Torrens (2)
1. Unit of Computer-Aided Molecular “Biosilico-Discovery and Bioinformatic Research (CAMD-BIR Unit), Faculty of Chemistry-Pharmacy, Central University of Las Villas, 54830, Santa Clara, Villa Clara, Cuba 2. Institut Universitari de Ciència Molecular, Universitat de València, Edifici d’Instituts de Paterna, P.O. Box 22085, 46071, València, Spain 3. Department of Chemical Science, Faculty of Chemistry-Pharmacy, Central University of Las Villas, 54830, Santa Clara, Villa Clara, Cuba 4. Department of Computer Sciences, Faculty of Informatics, Camaguey University, 74650, 70100, Camagüey City, Camagüey, Cuba
- ISSN:1573-4951
文摘
In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ( $ \partial $ ) of a molecular graph (MG) with respect to a given event (E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph’s theory’s traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub-graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns (n) and rows (m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Δ i , can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j′s atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ i for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating among different atoms, an atomic weighting scheme (atom-type labels) is used in the formation of the matrix Q or in LOVIs state. The obtained indices were utilized to describe the partition coefficient (Log P) and the reactivity index (Log K) of the 34 derivatives of 2-furylethylenes. In all the cases, our MDs showed better statistical results than those previously obtained using some of the most used families of MDs in chemometric practice. Therefore, it has been demonstrated to that the proposed MDs are useful in molecular design and permit obtaining easier and robust mathematical models than the majority of those reported in the literature. All this range of mentioned possibilities open “the doors-to the creation of a new family of MDs, using the graph derivative, and avail a new tool for QSAR/QSPR and molecular diversity/similarity studies.
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