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Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules

Molecular Diversity volume 14, pages 731–753 (2010)Cite this article

Abstract

Novel bond-level molecular descriptors are proposed, based on linear maps similar to the ones defined in algebra theory. The kth edge-adjacency matrix (E k) denotes the matrix of bond linear indices (non-stochastic) with regard to canonical basis set. The kth stochastic edge-adjacency matrix, ES k, is here proposed as a new molecular representation easily calculated from E k. Then, the kth stochastic bond linear indices are calculated using ES k as operators of linear transformations. In both cases, the bond-type formalism is developed. The kth non-stochastic and stochastic total linear indices are calculated by adding the kth non-stochastic and stochastic bond linear indices, respectively, of all bonds in molecule. First, the new bond-based molecular descriptors (MDs) are tested for suitability, for the QSPRs, by analyzing regressions of novel indices for selected physicochemical properties of octane isomers (first round). General performance of the new descriptors in this QSPR studies is evaluated with regard to the well-known sets of 2D/3D MDs. From the analysis, we can conclude that the non-stochastic and stochastic bond-based linear indices have an overall good modeling capability proving their usefulness in QSPR studies. Later, the novel bond-level MDs are also used for the description and prediction of the boiling point of 28 alkyl-alcohols (second round), and to the modeling of the specific rate constant (log k), partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (third round). The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) exposes a good behavior of our method in this QSPR studies. Finally, the approach described in this study appears to be a very promising structural invariant, useful not only for QSPR studies but also for similarity/diversity analysis and drug discovery protocols.

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References

  1. Todeschini R, Consonni V, Mannhold R (2000) Methods and principles in medicinal chemistry. In: Kubinyi H, Timmerman H (Series eds) Handbook of molecular descriptors. Wiley-VCH, Weinheim

  2. Ivanciuc O (2003) Graph theory in chemistry. In: Gasteiger J (ed) Handbook of chemoinformatics. Wiley-VCH, Weinheim, pp 103–138

    Chapter  Google Scholar 

  3. Estrada E, Uriarte E (2001) Recent advances on the role of topological indices in drug discovery research. Curr Med Chem 8: 1573–1588. doi:10.2174/0929867013371923

    PubMed  CAS  Google Scholar 

  4. Devillers J, Balaban AT (1999) Topological indices and related descriptors in QSAR and QSPR. Gordon and Breach, Amsterdam, Netherlands

  5. Torrens F (2003) Structural, chemical topological, electrotopological and electronic structure hypotheses. Comb Chem High Throughput Screen 6: 801–809

    PubMed  CAS  Google Scholar 

  6. Randić M (1997) On characterization of chemical structure. J Chem Inf Comput Sci 37: 672–687. doi:10.1021/ci960174t

    Google Scholar 

  7. Estrada E (2001) Generalization of topological indices. Chem Phys Lett 336: 248–252. doi:10.1016/S0009-2614(01)00127-0

    Article  CAS  Google Scholar 

  8. Estrada E (1995) Edge adjacency relationships and a novel topological index related to molecular volume. J Chem Inf Comput Sci 35: 31–33. doi:10.1021/ci00023a004

    CAS  Google Scholar 

  9. Estrada E, Ramírez A (1996) Edge adjacency relationships and molecular topographic descriptors: definition and QSAR applications. J Chem Inf Comput Sci 36: 837–843. doi:10.1021/ci950186z

    CAS  Google Scholar 

  10. Estrada E (1996) Spectral moments of the edge adjacency matrix in molecular graphs. 1. Definition and applications to the prediction of physical properties of alkanes. J Chem Inf Comput Sci 36: 844–849. doi:10.1021/ci950187r

    CAS  Google Scholar 

  11. Marković S, Gutman I (1991) Dependence of spectral moments of benzenoid hydrocarbons on molecular structure. J Mol Struct (Theochem) 235: 81–87. doi:10.1016/0166-1280(91)85087-N

    Article  Google Scholar 

  12. Estrada E, Guevara N, Gutman I (1998) Extension of edge connectivity index. Relationships to line graph indices and QSPR applications. J Chem Inf Comput Sci 38: 428–431. doi:10.1021/ci970091s

    CAS  Google Scholar 

  13. Estrada E, Rodríguez L (1999) Edge-connectivity indices in QSPR/QSAR studies. 2. Accounting for long-range bond contributions. J Chem Inf Comput Sci 39: 1037–1041. doi:10.1021/ci990031h

    CAS  Google Scholar 

  14. Estrada E, Molina E (2001) Novel local (fragment-based) topological molecular descriptors for QSPR/QSAR and molecular design. J Mol Graphics Mod 20: 54–64. doi:10.1016/S1093-3263(01)00100-0

    Article  CAS  Google Scholar 

  15. Kier LB, Hall LH (1999) Molecular structure description: the electrotopological state. Academic Press, New York

    Google Scholar 

  16. Marrero-Ponce Y (2004) Linear indices of the “molecular pseudograph’s atom adjacency matrix”: definition, significance-interpretation, and application to QSAR analysis of flavone derivatives as HIV-1 integrase inhibitors. J Chem Inf Comput Sci 44: 2010–2026. doi:10.1021/ci049950k

    PubMed  CAS  Google Scholar 

  17. Marrero-Ponce Y, Castillo-Garit JA, Torrens F, Romero-Zaldivar V, Castro E (2004) Atom, atom-type, and total linear indices of the molecular pseudographs atom adjacency matrix: application to QSPR/QSAR studies of organic compounds. Molecules 9: 1100–1123. doi:10.3390/91201100

    Article  Google Scholar 

  18. Marrero-Ponce Y, Montero-Torres A, Romero-Zaldivar C, Iyarreta-Veitía I, Mayón-Peréz M, García-Sánchez R (2005) Non-stochastic and stochastic linear indices of the “molecular pseudograph’s atom adjacency matrix”: application to in silico studies for the rational discovery of new antimalarial compounds. Bioorg Med Chem 13: 1293–1304. doi:10.1016/j.bmc.2004.11.008

    Article  PubMed  CAS  Google Scholar 

  19. Marrero-Ponce Y, Medina-Marrero R, Martinez Y, Torrens F, Romero-Zaldivar V, Castro E A (2006) Non-stochastic and stochastic linear indices of the molecular pseudograph’s atom-adjacency matrix: a novel approach for computational in silico screening and “Rational” selection of new lead antibacterial agents. J Mol Mod 12: 255–271. doi:10.1007/s00894-005-0024-8

    Article  CAS  Google Scholar 

  20. Marrero-Ponce Y, Castillo-Garit JA, Olazabal E, Serrano HS, Morales A, Castañedo N, Ibarra-Velarde F, Huesca-Guillen A, Jorge E, Sánchez AM, Torrens F, Castro EA (2005) Atom, atom-type and total molecular linear indices as a promising approach for bioorganic and medicinal chemistry: theoretical and experimental assessment of a novel method for virtual screening and rational design of new lead anthelmintic. Bioorg Med Chem 13: 1005–1020. doi:10.1016/j.bmc.2004.11.040

    Article  PubMed  CAS  Google Scholar 

  21. Marrero-Ponce Y, Castillo-Garit JA (2005) 3D-chiral atom, atom-type, and total non-stochastic and stochastic molecular linear indices and their applications to central chirality codification. J Comput-Aided Mol Des 19: 369–383. doi:10.1007/s10822-005-7575-8

    Article  PubMed  CAS  Google Scholar 

  22. Marrero-Ponce Y, Castillo-Garit JA, Nodarse D (2005) Linear indices of the macromolecular graph’s nucleotides adjacency matrix as a promising approach for bioinformatics studies. Part 1: prediction of paromomycin’s affinity constant with HIV-1 Ψ-RNA packaging region. Bioorg Med Chem 13: 3397–3404. doi:10.1016/j.bmc.2005.03.010

    Article  PubMed  CAS  Google Scholar 

  23. Marrero-Ponce Y, Medina-Marrero R, Castillo-Garit JA, Romero-Zaldivar V, Torrens F, Castro EA (2005) Protein linear indices of the macromolecular pseudograph alpha-carbon atom adjacency matrix in bioinformatics. Part 1: prediction of protein stability effects of a complete set of alanine substitutions in arc repressor. Bioorg Med Chem 13: 3003–3015. doi:10.1016/j.bmc.2005.01.062

    Article  PubMed  CAS  Google Scholar 

  24. Talete, 2005 Talete srl, DRAGON for Windows (software for molecular descriptor calculations). Version 5.3—2005. Available at http://www.talete.mi.it.

  25. Trinajstić N (1992) Chemical graph theory. CRC Press, Boca Raton

    Google Scholar 

  26. Edwards CH, Penney DE (1988) Elementary linear algebra. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  27. Marrero-Ponce Y (2003) Total and local quadratic indices of the molecular pseudograph’s atom adjacency matrix: applications to the prediction of physical properties of organic compounds. Molecules 8: 687–726. doi:10.3390/80900687

    Article  Google Scholar 

  28. Marrero-Ponce Y, Iyarreta-Veitía M, Montero-Torres A, Romero-Zaldivar C, Brandt CA, Ávila PE, Kirchgatter K, Machado Y (2005) Ligand-based virtual screening and in silico design of new antimalarial compounds using nonstochastic and stochastic total and atom-type quadratic maps. J Chem Inf Comput Sci 45: 1082–1100. doi:10.1021/ci050085t

    CAS  Google Scholar 

  29. Marrero-Ponce Y (2004) Total and local (atom and atom type) molecular quadratic indices: significance interpretation, comparison to other molecular descriptors, and QSPR/QSAR applications. Bioorg Med Chem 12: 6351–6369. doi:10.1016/j.bmc.2004.09.034

    Article  CAS  Google Scholar 

  30. Marrero-Ponce Y, Cabrera MA, Romero V, Ofori E, Montero LA (2003) Total and local quadratic indices of the “molecular pseudograph’s atom adjacency matrix”: application to prediction of caco-2 permeability of drugs. Int J Mol Sci 4: 512–536. doi:10.3390/i4080512

    Article  Google Scholar 

  31. Marrero-Ponce Y, Cabrera MA, Romero V, González DH, Torrens F (2004) A new topological descriptors based model for predicting intestinal epithelial transport of drugs in caco-2 cell culture. J Pharm Pharm Sci 7: 186–199

    PubMed  Google Scholar 

  32. Marrero-Ponce Y, Cabrera MA, Romero-Zaldivar V, Bermejo M, Siverio D, Torrens F (2005) Prediction of intestinal epithelial transport of drug in (caco-2) cell culture from molecular structure using in silico approaches during early drug discovery. Internet Electron J Mol Des 4: 124–150

    Google Scholar 

  33. Marrero-Ponce Y, Castillo-Garit JA, Olazabal E, Serrano HS, Castañedo N, Ibarra-Velarde F, Huesca-Guillen A, Valle AD, Torrens F, Castro E (2004) TOMOCOMD-CARDD, a novel approach for computer-aided rational drug design: I. Theoretical and experimental assessment of a promising method for computational screening and in silico design of new anthelmintic compounds. J Comput-Aided Mol Des 18: 615–633. doi:10.1007/s10822-004-5171-y

    Article  PubMed  CAS  Google Scholar 

  34. Marrero-Ponce Y, Huesca-Guillen A, Ibarra-Velarde F (2005) Quadratic indices of the molecular pseudograph’s atom adjacency matrix and their stochastic forms: a novel approach for virtual screening and in silico discovery of new lead paramphistomicide drugs-like compounds. J Mol Struct (Theochem) 717: 67–79. doi:10.1016/j.theochem.2004.11.027

    Article  CAS  Google Scholar 

  35. Marrero-Ponce Y, Medina-Marrero R, Torrens F, Martinez Y, Romero-Zaldivar V, Castro EA (2005) Atom, atom-type, and total nonstochastic and stochastic quadratic fingerprints: a promising approach for modeling of antibacterial activity. Bioorg Med Chem 13: 2881–2899. doi:10.1016/j.bmc.2005.02.015

    Article  PubMed  CAS  Google Scholar 

  36. Estrada E, Vilar S, Uriarte E, Gutierrez Y (2002) In silico studies toward the discovery of new anti-HIV nucleoside compounds with the use of TOPS-MODE and 2D/3D connectivity indices. 1. Pyrimidyl derivatives. J Chem Inf Comput Sci 42: 1194–1203. doi:10.1021/ci0255331

    PubMed  CAS  Google Scholar 

  37. Estrada E, Uriarte E, Montero A, Teijeira M, Santana L, De Clercq E (2000) A novel approach for the virtual screening and rational design of anticancer compounds. J Med Chem 43: 1975–1985. doi:10.1021/jm991172d

    Article  PubMed  CAS  Google Scholar 

  38. Estrada E, Peña A, García-Domenech RJ (1998) Designing sedative/hypnotic compounds from a novel substructural graph-theoretical approach. J Comput-Aided Mol Des 12: 583–595. doi:10.1023/A:1008048003720

    Article  PubMed  CAS  Google Scholar 

  39. Potapov VM (1978) Stereochemistry. Mir, Moscow

  40. Wang R, Gao Y, Lai L (2000) Calculating partition coefficient by atom-additive method. Perspect Drug Discov Des 19: 47–66. doi:10.1023/A:1008763405023

    Article  CAS  Google Scholar 

  41. Ertl P, Rohde B, Selzer P (2000) Fast calculation of molecular polar surface area as a sum of fragment-based contribution and its application to the prediction of drug transport properties. J Med Chem 43: 3714–3717. doi:10.1021/jm000942e

    Article  PubMed  CAS  Google Scholar 

  42. Ghose AK, Crippen GM (1987) Atomic physicochemical parameters for three-dimensional-structure-directed quantitative structure-activity relationships. 2. Modeling dispersive and hydrophobic interactions. J Chem Inf Comput Sci 27: 21–35. doi:10.1021/ci00053a005

    PubMed  CAS  Google Scholar 

  43. Miller KJ (1990) Additivity methods in molecular polarizability. J Am Chem Soc 112: 8533–8542. doi:10.1021/ja00179a044

    Article  CAS  Google Scholar 

  44. Gasteiger J, Marsilli MA (1978) A new model for calculating atomic charges in molecules. Tetrahedron Lett 34: 3181–3184

    Article  Google Scholar 

  45. Pauling L (1939) The nature of chemical bond. Cornell University Press, Ithaca, New York

    Google Scholar 

  46. Browder A (1996) Mathematical analysis: an introduction. Springer, New York

    Google Scholar 

  47. Axler S (1996) Linear algebra done right. Springer, New York

    Google Scholar 

  48. Daudel R, Lefebre R, Moser C (1984) Quantum chemistry: methods and applications. Wiley, New York

    Google Scholar 

  49. Klein DJ (2003) Graph theoretically formulated electronic-structure theory. Internet Electron J Mol Des 2: 814–834

    CAS  Google Scholar 

  50. Randić M, Trinajstić N (1993) Viewpoint 4-comparative structure-property studies: the connectivity basis. J Mol Struct (Theochem) 284: 209–221. doi:10.1016/0166-1280(93)87005-X

    Article  Google Scholar 

  51. Randić M, Trinajstić N (1993) In search for graph invariants of chemical interest. J Mol Struct (Theochem) 300: 551–572

    Google Scholar 

  52. Estrada E, Rodríguez L (1999) Edge-connectivity indices in QSPR/QSAR studies. 1. Comparison to other topological indices in QSPR studies. J Chem Inf Comput Sci 39: 1037–1041. doi:10.1021/ci990030p

    CAS  Google Scholar 

  53. Consonni V, Todeschini R, Pavan M (2002) Structure/response correlations and similarity/diversity analysis by GETAWAY descriptors. 1. Theory of the novel 3D molecular descriptors. J Chem Inf Comput Sci 42: 682–692. doi:10.1021/ci015504a

    PubMed  CAS  Google Scholar 

  54. Randić M (1991) Correlation of enthalpy of octanes with orthogonal connectivity indices. J Mol Struct (Theochem) 233: 45–59. doi:10.1016/0166-1280(91)85053-A

    Article  Google Scholar 

  55. Randić M (1993) Comparative regression analysis. Regressions based on a single descriptor. Croat Chim Acta 66: 289–312

    Google Scholar 

  56. Randić M, Guo X, Oxley T, Krishnapriyan H, Naylor L (1994) Wiener matrix invariants. J Chem Inf Comput Sci 34: 361–367. doi:10.1021/ci00018a022

    Google Scholar 

  57. Diudea M V (1996) Walk numbers: Wiener-type numbers of higher rank. J Chem Inf Comput Sci 36: 535–540. doi:10.1021/ci950134+

    Google Scholar 

  58. Diudea MV, Minailiuc O M, Katona G (1997) Molecular topology. 26. SP indices: novel connectivity descriptors. Rev Roum Chim 42: 239–249

    CAS  Google Scholar 

  59. Randić M (1991) Generalized molecular descriptors. J Math Chem 7: 155–168. doi:10.1007/BF01200821

    Article  Google Scholar 

  60. Needham DE, Wei IC, Seybold PG (1988) Molecular modeling of the physical properties of alkanes. J Am Chem Soc 110: 4186–4194. doi:10.1021/ja00221a015

    Article  CAS  Google Scholar 

  61. Marrero-Ponce Y, Romero V (2002) TOMOCOMD (TOpological MOlecular COMputer Design) for Windows, 1.0. Central University of Las Villas, Santa Clara

  62. Goldberg DE (1989) Genetic algorithms. Addison-Wesley, Reading

    Google Scholar 

  63. Willet P (1995) Genetic algorithms in molecular recognition and design. Trends Biotechnol 13: 516–521. doi:10.1016/S0167-7799(00)89015-0

    Article  Google Scholar 

  64. So SS, Karplus M (1996) Evolutionary optimization in quantitative structure–activity relationship: an application of genetic neural networks. J Med Chem 39: 1521–1530. doi:10.1021/jm9507035

    Article  PubMed  CAS  Google Scholar 

  65. So SS, Karplus M (1997) Three-dimensional quantitative structure–activity relationships from molecular similarity matrices and genetic neural networks. 1. Method and validations. J Med Chem 40: 4347–4359. doi:10.1021/jm970487v

    Article  PubMed  CAS  Google Scholar 

  66. Rogers D, Hopfinger AJ (1994) Application of genetic function approximation to quantitative structure-activity relationships and quantitative structure–property relationships. J Chem Inf Comput Sci 34: 854–866. doi:10.1021/ci00020a020

    CAS  Google Scholar 

  67. Hopfinger AJ, Wang S, Tokarski JS, Jin B, Albuquerque M, Madhav PJ (1997) Construction of 3D-QSAR models using the 4D-QSAR analysis formalism. J Am Chem Soc 119: 10509–10524. doi:10.1021/ja9718937

    Article  CAS  Google Scholar 

  68. Senese CL, Hopfinger AJ (2003) Receptor-independent 4D-QSAR analysis of a set of norstatine derived inhibitors of HIV-1 protease. J Chem Inf Comput Sci 43: 1297–1307. doi:10.1021/ci0340456

    PubMed  CAS  Google Scholar 

  69. Liu J, Pan D, Tseng Y, Hopfinger AJ (2003) 4D-QSAR analysis of a series of antifungal p450 inhibitors and 3D-pharmacophore comparisons as a function of alignment. J Chem Inf Comput Sci 43: 2170–2179. doi:10.1021/ci034142z

    PubMed  CAS  Google Scholar 

  70. Senese CL, Hopfinger AJ (2003) A simple clustering technique to improve QSAR model selection and predictivity: application to a receptor independent 4D-QSAR analysis of cyclic urea derived inhibitors of HIV-1 protease. J Chem Inf Comput Sci 43: 2180–2193. doi:10.1021/ci034168q

    PubMed  CAS  Google Scholar 

  71. DeOliveira DB, Gaudio AC (2000) BuildQSAR: a new computer program for QSAR studies. Quant Struct-Act Relat 19: 599–601. doi:10.1002/1521-3838(200012)19:6<599::AID-QSAR599>3.0.CO;2-B

    Article  CAS  Google Scholar 

  72. Wold S, Erikson L (1995) Statistical validation of QSAR results. Validation tools. In: van de Waterbeemd H (ed) Chemometric methods in molecular design. VCH, New York

    Google Scholar 

  73. Balaz S, Sturdik E, Rosenberg M, Augustin J, Skara B (1988) Kinetics of drug activities as influenced by their physico-chemical properties: antibacterial effects of alkylating 2-furylethylenes. J Theor Biol 131: 115–134. doi:10.1016/S0022-5193(88)80125-5

    Article  PubMed  CAS  Google Scholar 

  74. Dore JC, Viel C (1975) Antitumoral chemoterapy. X. Cytotoxic and antitumoral activity of β-nitrostyrenes and nitrovinyl derivatives. Farmaco Sci 30: 81–109

    PubMed  CAS  Google Scholar 

  75. Sturdik E, Drobnica L, Balaz S (1985) Reaction of 2-furylethylenes with thiols in vivo. Coll Czch Chem Comm 50: 470–480

    Article  Google Scholar 

  76. Blondeau J, Castañedo N, Gonzalez O, Medina R, Silveira E (1999) In vitro evaluation of G-1: a novel antimicrobial compound. Int J Antimicrob Agents Chemother 11: 163–166. doi:10.1016/S0924-8579(98)00086-7

    Article  CAS  Google Scholar 

  77. Estrada E, Molina E (2001) 3D connectivity indices in QSPR/QSAR studies. J Chem Inf Comput Sci 41: 791–797. doi:10.1021/ci000156i

    PubMed  CAS  Google Scholar 

  78. Marrero-Ponce Y, Torrens F, Alvarado YJ, Rotondo R (2006) Bond-based global and local (bond and bond-type) quadratic indices and their applications to computer-aided molecular design. 1. QSPR studies of octane isomers. J Comput-Aided Mol Des 20: 685–701. doi:10.1007/s10822-006-9089-4

    Article  PubMed  CAS  Google Scholar 

  79. Casañola-Martín G, Marrero-Ponce Y, HassanKhan MT, Ather A, Sultan S, Torrens F, Rotondo R (2007) TOMOCOMD-CARDD descriptors-based virtual screening of tyrosinase inhibitors: Evaluation of different classification model combinations using bond-based linear indices. Bioorg Med Chem 15: 1483–1503. doi:10.1016/j.bmc.2006.10.067

    Article  PubMed  CAS  Google Scholar 

  80. Marrero-Ponce Y, Meneses-Marcel A, Rivera-Borroto O, García-Domenech R, Julián-Ortiz V, Montero A, Escario JA, Gómez-Barrio A, Montero-Pereira D, Nogal JJ, Grau G, Torrens F, Vogel C, Arán VJ (2008) Bond-based linear indices in QSAR: computational discovery of novel anti-trichomonal compounds. J Comput- Aided Mol Des 22: 523–540. doi:10.1007/s10822-008-9171-1

    Article  PubMed  CAS  Google Scholar 

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Authors and Affiliations

  1. Unit of Computer-Aided Molecular “Biosilico” Discovery and Bioinformatic Research (CAMD-BIR Unit), Faculty of Chemistry-Pharmacy, Central University of Las Villas, Santa Clara, 54830, Villa Clara, Cuba

    Yovani Marrero-Ponce, Eugenio R. Martínez-Albelo, Gerardo M. Casañola-Martín, Juan A. Castillo-Garit, Yunaimy Echevería-Díaz & Vicente Romero Zaldivar

  2. Institut Universitari de Ciència Molecular, Universitat de València, Edifici d’Instituts de Paterna, P. O. Box 22085, 46071, Valencia, Spain

    Yovani Marrero-Ponce, Juan A. Castillo-Garit & Francisco Torrens

  3. Unidad de Investigación de Diseño de Fármacos y Conectividad Molecular, Departamento de Química Física, Facultad de Farmacia, Universitat de València, Valencia, Spain

    Yovani Marrero-Ponce, Ramón García-Domenech & Facundo Pérez-Giménez

  4. Department of Chemistry, Faculty of Chemistry-Pharmacy, Central University of Las Villas, Santa Clara, 54830, Villa Clara, Cuba

    Eugenio R. Martínez-Albelo

  5. Applied Chemistry Research Center, Central University of Las Villas, Santa Clara, 54830, Villa Clara, Cuba

    Juan A. Castillo-Garit

  6. Laboratory of Toxicology, University of Leuven (KULeuven), Campus Gasthuisberg, O&N2, Herestraat 49, P. O. Box 922, 3000, Leuven, Belgium

    Jan Tygat

  7. Associação para o desenvolvimento da Faculdade de Ciências do Porto, Rua do Campo Alegre, 687, 4169-007, Porto, Portugal

    José E. Rodriguez Borges

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  1. Yovani Marrero-Ponce
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Correspondence to Yovani Marrero-Ponce.

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Dedicated to Professor Ernesto Estrada for his many contributions to the graph-theoretical chemistry and specifically by the relevant extension of well-known atom-based mathematical invariants to bond-level relationship.

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Marrero-Ponce, Y., Martínez-Albelo, E.R., Casañola-Martín, G.M. et al. Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules. Mol Divers 14, 731–753 (2010). https://doi.org/10.1007/s11030-009-9201-5

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Keywords

  • TOMOCOMD-CARDD software
  • Edge-adjacency matrix
  • Stochastic linear map
  • Non-stochastic and stochastic bond-based linear index
  • QSPR study
  • Physicochemical property
  • Antibacterial activity
  • Octane isomers
  • 2-Furylethylene derivative