Skip to main content
Springer Nature Link
Log in

Bond-based global and local (bond, group and bond-type) quadratic indices and their applications to computer-aided molecular design. 1. QSPR studies of diverse sets of organic chemicals

  • Original paper
  • Published:
Journal of Computer-Aided Molecular Design Aims and scope Submit manuscript

Abstract

The concept of atom-based quadratic indices is extended to a series of molecular descriptors (MDs) (both total and local) based on adjacency between edges. The kth edge-adjacency matrix (E k) denotes the matrix of bond-based quadratic indices (non-stochastic) with respect to the 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-based quadratic indices are calculated using ES k as operators of quadratic transformations. The study of six representative physicochemical properties of octane isomers was used to compare the ability of both series of MDs to produce significant quantitative structure–property relationship (QSPR) models. Moreover, the general performance of the new MDs in this QSPR study has been evaluated with respect to other 2D/3D well-known sets of indices and the obtained results shown a quite satisfactory behavior of the present method. The novel bond-level MDs were also used for the description and prediction of the boiling point of 28 alkyl-alcohols and to the modeling of the specific rate constant (log k) of 34 derivatives of 2-furylethylenes. These models were statistically significant and showed very good stability to data variation in leave-one-out (LOO) cross-validation experiment. 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) expose a good behavior of our method in this QSPR studies. The approach described in this report appears to be a very promising structural invariant, useful for QSPR/QSAR studies, similarity/diversity analysis, and computer-aided “rational” molecular (drug) design.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Todeschini R, Consonni V (2000) Handbook of molecular descriptors. Wiley-VCH, Germany

    Google Scholar 

  2. Consonni V, Todeschini R, Pavan M (2002) J Chem Inf Comput Sci 42:682

    Article  CAS  Google Scholar 

  3. Seybold PG, May M, Bagal UA (1987) J Chem Educ 64:575

    Article  CAS  Google Scholar 

  4. Estrada E, Molina E (2001) J Mol Graph Model 20:54

    Article  CAS  Google Scholar 

  5. Kier LB, Hall LH (1999) Molecular structure description. The Electrotopological state. Academic Press, New York

    Google Scholar 

  6. Estrada E (1995) J Chem Inf Comput Sci 35:31

    Article  CAS  Google Scholar 

  7. Estrada E, Ramirez A (1996) J Chem Inf Comput Sci 36:837

    Article  CAS  Google Scholar 

  8. Estrada E (1996) J Chem Inf Comput Sci 36:844

    Article  CAS  Google Scholar 

  9. Marković S, Gutman I (1991) J Mol Struct (Theochem) 235:81

    Article  Google Scholar 

  10. Estrada E, Guevara N, Gutman I (1998) J Chem Inf Comput Sci 38:428

    Article  CAS  Google Scholar 

  11. Estrada E (1999) J Chem Inf Comput Sci 39:1042

    Article  CAS  Google Scholar 

  12. Karelson M (2000) Molecular descriptors in QSAR/QSPR. John Wiley & Sons, New York

    Google Scholar 

  13. Marrero-Ponce Y (2003) Molecules 8:687

    Google Scholar 

  14. Marrero-Ponce Y (2004) Bioorg Med Chem 12:6351

    Article  CAS  Google Scholar 

  15. Marrero-Ponce Y, Huesca-Guillen A, Ibarra-Velarde F (2005) J Mol Struct (Theochem) 717:67

    Article  CAS  Google Scholar 

  16. Marrero-Ponce Y, Iyarreta-Veitia M, Montero-Torres A, Romero-Zaldivar C, Brandt CA, Avila PE, Kirchgatter K, Machado Y (2005) J Chem Inf Model 45:1082

    Article  CAS  Google Scholar 

  17. Marrero-Ponce Y, Castillo-Garit JA, Olazabal E, Serrano HS, Morales A, Castañedo N, Ibarra-Velarde F, Huesca-Guillen A, Jorge E, del Valle A, Torrens F, Castro EA (2004) . J Comput Aided Mol Des 18:615

    Article  CAS  Google Scholar 

  18. Marrero-Ponce Y, Medina-Marrero R, Torrens F, Martinez Y, Romero-Zaldivar V, Castro EA (2005) Bioorg Med Chem 13:2881

    Article  CAS  Google Scholar 

  19. Montero-Torres A, García-Sánchez RN, Marrero-Ponce Y, Machado-Tugores Y, Nogal-Ruiz JJ, Martínez-Fernández AR, Arán VJ, Ochoa C, Meneses-Marcel A, Torrens F (2006) Eur J Med Chem 41:483–493

    Article  CAS  Google Scholar 

  20. Meneses-Marcel A, Marrero-Ponce Y, Machado-Tugores Y, Montero-Torres A, Montero Pereira D, Escario JA, Nogal-Ruiz JJ, Ochoa C, Arán VJ, Martínez-Fernández AR, García Sánchez RN (2005) Bioorg Med Chem Lett 17:3838

    Article  CAS  Google Scholar 

  21. Montero-Torres A, Celeste Vega M, Marrero-Ponce Y, Rolón M, Gómez-Barrio A, Escario JA, Arán VJ, Martínez-Fernández AR, Meneses-Marcel A (2005) Bioorg Med Chem 13:6264–6275

    Article  CAS  Google Scholar 

  22. Marrero-Ponce Y, Díaz HG, Romero V, Torrens F, Castro EA (2004) Bioorg Med Chem 12:5331

    Article  CAS  Google Scholar 

  23. Castillo-Garit JA, Marrero-Ponce Y, Torrens F (2006) Bioorg Med Chem 14:2398–2408

    Article  CAS  Google Scholar 

  24. Marrero-Ponce Y, Cabrera MA, Romero V, Ofori E, Montero LA (2003) Int J Mol Sci 4:512

    Google Scholar 

  25. Marrero-Ponce Y, Cabrera MA, Romero V, González DH, Torrens F (2004) J Pharm Pharmaceut Sci 7:186

    Google Scholar 

  26. Marrero-Ponce Y, Cabrera MA, Romero-Zaldivar V, Bermejo M, Siverio D, Torrens F (2005) Internet Electron J Mol Des 4:124

    Google Scholar 

  27. Marrero-Ponce Y, Nodarse D, González HD, Ramos de Armas R, Romero-Zaldivar V, Torrens F, Castro E (2004) Int J Mol Sci 5:276

    Google Scholar 

  28. Marrero-Ponce Y, Medina R, Castro EA, de Armas R, González H, Romero V, Torrens F (2004) Molecules 9:1124

    Google Scholar 

  29. Rouvray DH (1976) Chemical applications of graph theory. Academic Press, London

    Google Scholar 

  30. Trinajstić N (1983) Chemical graph theory. CRC Press, Boca Raton FL

    Google Scholar 

  31. Edwards CH, Penney DE (1988) Elementary linear algebra. sPrentice-Hall, Englewood Cliffs, New Jersey, USA

    Google Scholar 

  32. Gonzalez-Diaz H, Tenorio E, Castanedo N, Santana L, Uriarte E (2005) Bioorg Med Chem 13:1523

    Article  CAS  Google Scholar 

  33. Diaz HG, Bastida I, Castanedo N, Nasco O, Olazabal E, Morales A, Serrano HS, de Armas RR (2004) Bull Math Biol 66:1285

    Article  CAS  Google Scholar 

  34. Gonzales-Diaz H, Gia O, Uriarte E, Hernadez I, Ramos R, Chaviano M, Seijo S, Castillo JA, Morales L, Santana L, Akpaloo D, Molina E, Cruz M, Torres LA, Cabrera MA (2003) J Mol Model 9:395

    Article  CAS  Google Scholar 

  35. Marrero-Ponce Y, Torrens F (2006) Int J Mol Sci Accepted for publication

  36. Marrero-Ponce Y, Medina-Marrero R, Martinez Y, Torrens F, Romero-Zaldivar V, Castro EA (2006) J Mol Mod 12:255

    Article  CAS  Google Scholar 

  37. Vilar S, Estrada E, Uriarte E, Santana L, Gutierrez Y (2005) J Chem Inf Model 45:502

    Article  CAS  Google Scholar 

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

    Google Scholar 

  39. Wang R, Gao Y, Lai L (2000) Perspect Drug Discov Des 19:47

    Article  CAS  Google Scholar 

  40. Ertl P, Rohde B, Selzer P (2000) J Med Chem 43:3714

    Article  CAS  Google Scholar 

  41. Ghose AK, Crippen GM (1987) J Chem Inf Comput Sci 27:21

    Article  CAS  Google Scholar 

  42. Millar KJ (1990) J Am Chem Soc 112:8533

    Article  Google Scholar 

  43. Gasteiger J, Marsilli MA (1978) Tetrahedron Lett 34:3181

    Article  Google Scholar 

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

    Google Scholar 

  45. Browder A (1996) Mathematical analysis. An introduction. Springer-Verlag, New York Inc

    Google Scholar 

  46. Axler S (1996) Linear algebra done right. Springer-Verlag, New York

    Google Scholar 

  47. Walker PD, Mezey PG (1993) J Am Chem Soc 115:12423

    Article  CAS  Google Scholar 

  48. Klein DJ (2003) Internet Electron J Mol Des 2:814

    CAS  Google Scholar 

  49. Diudea MV, Minailiuc OM, Katona G (1997) Rev Roum Chim 42:239

    CAS  Google Scholar 

  50. Randić M, Guo X, Oxley T, Krishnapriyan H, Naylor L (1994) . J Chem Inf Comput Sci 34:361

    Article  Google Scholar 

  51. Randić M (1993) Croat Chim Acta 66:289

    Google Scholar 

  52. Randić M (1991) J Mol Struct (Theochem) 233:45

    Article  Google Scholar 

  53. Randić M, Trinajstić N (1993) J Mol Struct (Theochem) 284:209

    Article  Google Scholar 

  54. Randić M, Trinajstić N (1993) . J Mol Struct (Theochem) 300:551

    Google Scholar 

  55. Estrada E, Rodríguez L (1999) J Chem Inf Comput Sci 39:1037

    Article  CAS  Google Scholar 

  56. Diudea MV (1996) J Chem Inf Comput Sci 36:535

    Article  CAS  Google Scholar 

  57. Randić M (1991) J Math Chem 7:155

    Article  Google Scholar 

  58. Needham DE, Wei I.-C, Seybold PG (1988) J Am Chem Soc 110:4186

    Article  CAS  Google Scholar 

  59. Balaz S, Sturdik E, Rosenberg M, Augustin J, Skara B (1988) J Theor Biol 131:115

    CAS  Google Scholar 

  60. Dore JC, Viel C (1975) Farmaco 30:81

    CAS  Google Scholar 

  61. Sturdik E, Drobnica L, Balaz S (1985) Coll Czch Chem Comm 50:470

    Article  Google Scholar 

  62. Blondeau JM,Castañedo N, Gonzalez O, Medina R, Silveira E (1999) Antimicrob Agents Chemother 11:1663

    Google Scholar 

  63. Marrero-Ponce Y, Romero V (2002) TOMOCOMD-CARDD software. TOMOCOMD (TOpological MOlecular COMputer Design) for Windows, version 1.0 is a preliminary experimental version; in future a professional version can be obtained upon request to Y. Marrero: yovanimp@qf.uclv.edu.cu or ymarrero77@yahoo.es Central University of Las Villas, Santa Clara, Villa Clara

  64. Senese CL, Hopfinger AJ (2003) J Chem Inf Comput Sci 43:1297

    Article  CAS  Google Scholar 

  65. Goldberg DE (1989) Genetic algorithms. Addison Wesley, Reading, MA

    Google Scholar 

  66. Willet P (1995) Trends Biotechnol 13:516–521

    Article  Google Scholar 

  67. So SS, Karplus M (1996) J Med Chem 39:1521

    Article  CAS  Google Scholar 

  68. So SS, Karplus M (1997) J Med Chem 40:4347

    Article  CAS  Google Scholar 

  69. Rogers D, Hopfinger AJ (1994) J Chem Inf Comput Sci 34:854

    Article  CAS  Google Scholar 

  70. Hopfinger AJ, Wang S, Tokarski JS, Jin B, Albuquerque M, Madhav PJ, Duraiswami C (1997) J Am Chem Soc 119:10509

    Article  CAS  Google Scholar 

  71. Senese CL, Hopfinger AJ (2003) J Chem Inf Comput Sci 43:2180

    Article  CAS  Google Scholar 

  72. De Oliveira DB, Gaudio AC (2000) Quant Struct-Act Relat 19:599

    Article  Google Scholar 

  73. Wold S, Erikson L (1995) In: van de Waterbeemd H (ed) Chemometric methods in molecular design. VCH Publishers, New York, p 309

    Google Scholar 

  74. Marrero-Ponce Y, Castillo-Garit JA, Torrens F, Romero-Zaldivar V, Castro E (2004) Molecules 9:1100

    Article  Google Scholar 

Download references

Acknowledgments

No person is an island; much is owed to many.

H. P. Schultz

Y. M-P thanks the program “Estades Temporals per a Investigadors Convidats” for a fellowship to work at Valencia University (2006–2007). The authors acknowledges financial support from the Spanish MEC DGI (Proyect No. CTQ2004-07768-C02-01/BQU) and Generalitat Valenciana (DGEUI INFO1-051 and INFRA03-047, and OCYT GRUPOS03-173). Comments of both reviewers contributed to a significant improvement of this material. Last, but not least, we are also indebted to the journal Editor Prof. Dr. Federico Gago for his kind attention.

Author information

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, Villa Clara, 54830, Cuba

    Yovani Marrero-Ponce

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

    Yovani Marrero-Ponce & Francisco Torrens

  3. Laboratorio de Electrónica Molecular, Departamento de Química, Modulo II, grano de Oro, Facultad Experimental de Ciencias, La Universidad del Zulia (LUZ), Maracaibo, Venezuela

    Ysaias J. Alvarado

  4. Mediscovery, Inc. Suite 1050, 601 Carlson Parkway, Minnetonka, MN, 55305, USA

    Richard Rotondo

Authors
  1. Yovani Marrero-Ponce
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Francisco Torrens
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Ysaias J. Alvarado
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Richard Rotondo
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Yovani Marrero-Ponce.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marrero-Ponce, Y., Torrens, F., Alvarado, Y.J. et al. Bond-based global and local (bond, group and bond-type) quadratic indices and their applications to computer-aided molecular design. 1. QSPR studies of diverse sets of organic chemicals. J Comput Aided Mol Des 20, 685–701 (2006). https://doi.org/10.1007/s10822-006-9089-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10822-006-9089-4

Keywords