Advertisement

Journal of Mathematical Chemistry

, Volume 53, Issue 9, pp 2028–2064 | Cite as

Novel global and local 3D atom-based linear descriptors of the Minkowski distance matrix: theory, diversity–variability analysis and QSPR applications

  • Néstor Cubillán
  • Yovani Marrero-Ponce
  • Harold Ariza-Rico
  • Stephen J. Barigye
  • César R. García-Jacas
  • José R. Valdes-Martini
  • Ysaías J. Alvarado
Original Paper

Abstract

A new family of alignment-free 3D descriptors based on TOMOCOMD-CARDD framework has been designed, namely 3D-linear indices. In this report, we have proposed the use of a generalized form of the geometric pairwise atom-atom distance matrix as structural information matrix. This matrix, denominated as non-stochastic, uses as matrix form of linear maps as well as their algebraic transformations: stochastic, double stochastic and mutual probabilities matrices. The methodology for 3D-QSAR studies is based on the combined use of global and local approaches. Principal component analysis reveals that the novel indices are capable of capturing structural information not codified by the indices implemented in the DRAGON’s software. Moreover, Shannon’s entropy based variability analysis comparing the 3D-linear indices with some relevant descriptors suggests that the former encode similar-to-better amount of structural information than these descriptors. Finally, a search for the best regressions for congeneric databases in QSPR modeling was performed. The overall results demonstrates satisfactory behavior.

Keywords

TOMOCOMD-CARDD 3D-linear index Variability analysis  QSPR study 

Notes

Acknowledgments

Cubillán, N. thanks Consejo de Desarrollo Científico y Humanístico (CONDES-LUZ, Grant CC-0593-10), Fondo Nacional de Ciencia, Tecnología e Innovación (FONACIT, Grant G-2005000403), Misión Ciencia (Grant 2007000881) and Instituto Zuliano de Investigaciones Tecnológicas (INZIT, Project LOCTI) for partial financial support of this work. Marrero-Ponce, Yovani thanks the program ‘Estades Temporals per an Investigadors Convidats’ for a fellowship to work at Valencia University. The authors acknowledge also the partial financial support from Spanish Ministry of Science and Innovation (MICINN, Project Reference: SAF2009-10399). Last, but not least, the authors want to express their acknowledgements to Prof. Jorge Galvez (VU) and Prof. Ramón García-Domenech (VU) for their help and useful comments about these new MDs.

Supplementary material

10910_2015_533_MOESM1_ESM.doc (4.7 mb)
Supplementary Information: The Table S1 shows the values of the atomic weights used for molecular vectors. Table S2 reports the factor loadings (varimax normalized rotation) for the 0D--3D DRAGON MDs as well as the total and local (atom type) 3D-Linear indices for 41 heterogeneous chemicals. And, Table S3 shows the chemical structure and numbering of atoms in 2-furylethylene database. (DOC 4791KB)

References

  1. 1.
    D.E. Clark, S.D. Pickett, Drug Discov. Today 5, 49 (2000)CrossRefGoogle Scholar
  2. 2.
    B.L. Claus, D.J. Underwood, Drug Discov. Today 7, 957 (2002)CrossRefGoogle Scholar
  3. 3.
    So Jonsdottir, F.S. Jorgensen, S. Brunak, Bioinformatics 21, 2145 (2005)CrossRefGoogle Scholar
  4. 4.
    R. Perkins, H. Fang, W. Tong, W.J. Welsh, Environ. Toxicol. Chem. 22, 1666 (2003)CrossRefGoogle Scholar
  5. 5.
    C. Hansch, P.P. Maloney, T. Fujita, R.M. Muir, Nature 194, 178 (1962)CrossRefGoogle Scholar
  6. 6.
    H. Kubinyi, Drug Discov. Today 2, 457 (1997)CrossRefGoogle Scholar
  7. 7.
    J.J. Sutherland, L.A. O’Brien, D.F. Weaver, J. Med. Chem. 47, 5541 (2004)CrossRefGoogle Scholar
  8. 8.
    A.R. Katritzky, M. Kuanar, S. Slavov, C.D. Hall, M. Karelson, I. Kahn, D.A. Dobchev, Chem. Rev. (Washington, DC, United States) 110, 5714 (2010)CrossRefGoogle Scholar
  9. 9.
    J.A. Castillo-Garit, Y. Marrero-Ponce, F. Torrens, R. Rotondo, J. Mol. Graph. Model. 26, 32 (2007)CrossRefGoogle Scholar
  10. 10.
    A. Golbraikh, A. Tropsha, J. Chem. Inf. Comput. Sci. 43, 144 (2003)CrossRefGoogle Scholar
  11. 11.
    A.R. Katritzky, E.V. Gordeeva, J. Chem. Inf. Comput. Sci. 33, 835 (1993)CrossRefGoogle Scholar
  12. 12.
    Y. Marrero-Ponce, E. Martínez-Albelo, G. Casañola-Martín, J. Castillo-Garit, Y. Echeverría-Díaz, V. Zaldivar, J. Tygat, J. Rodríguez Borges, R. García-Domenech, F. Torrens, F. Pérez-Giménez, Mol Divers 14, 731 (2010)CrossRefGoogle Scholar
  13. 13.
    W. Tong, D.R. Lowis, R. Perkins, Y. Chen, W.J. Welsh, D.W. Goddette, T.W. Heritage, D.M. Sheehan, J. Chem. Inf. Comput. Sci. 38, 669 (1998)CrossRefGoogle Scholar
  14. 14.
    M. Atabati, K. Zarei, A. Borhani, Fluid Phase Equilib. 293, 219 (2010)CrossRefGoogle Scholar
  15. 15.
    M. Devereux, P.L.A. Popelier, I.M. McLay, J. Chem. Inf. Model. 49, 1497 (2009)CrossRefGoogle Scholar
  16. 16.
    M. Hechinger, K. Leonhard, W. Marquardt, J. Chem. Inf. Model. 52, 1984–1993 (2012)CrossRefGoogle Scholar
  17. 17.
    A. Klamt, F. Eckert, M. Hornig, M.E. Beck, T. Bürger, J. Comput. Chem. 23, 275 (2002)CrossRefGoogle Scholar
  18. 18.
    K. Masuch, A. Fatemi, H. Murrenhoff, K. Leonhard, Lubr. Sci. 23, 249 (2011)CrossRefGoogle Scholar
  19. 19.
    G. Occhipinti, H.-R. Bjørsvik, V.R. Jensen, J. Am. Chem. Soc. 128, 6952 (2006)CrossRefGoogle Scholar
  20. 20.
    J.J. Panek, A. Jezierska, M. Vracko, J. Chem. Inf. Model. 45, 264 (2005)CrossRefGoogle Scholar
  21. 21.
    O.M. Rivera-Borroto, Y. Marrero-Ponce, J.M. García-de la Vega, RdC Grau-Ábalo, J. Chem. Inf. Model. 51, 3036 (2011)CrossRefGoogle Scholar
  22. 22.
    S.-S. Yang, W.-C. Lu, T.-H. Gu, L.-M. Yan, G.-Z. Li, QSAR Comb. Sci. 28, 175 (2009)CrossRefGoogle Scholar
  23. 23.
    K. Kim, G. Greco, E. Novellino, Perspect. Drug Discovery Des. 12–14, 257 (1998)CrossRefGoogle Scholar
  24. 24.
    M. Pastor, G. Cruciani, I. McLay, P. Pickett, S. Clementi, J. Med. Chem. 43, 3233 (2000)CrossRefGoogle Scholar
  25. 25.
    A.N. Jain, K. Koile, D. Chapman, J. Med. Chem. 37, 2315 (1994)CrossRefGoogle Scholar
  26. 26.
    D.E. Walters, 3D QSAR in Drug Design (Springer, Netherlands, 1998)Google Scholar
  27. 27.
    M.F. Parretti, R.T. Kroemer, J.H. Rothman, G.W. R, J. Comput. Chem. 18, 1344 (1997)CrossRefGoogle Scholar
  28. 28.
    S.-S. So, M. Karplus, J. Med. Chem. 40, 4347 (1997)CrossRefGoogle Scholar
  29. 29.
    Y. Tominaga, I. Fujiwara, J. Chem. Inf. Comput. Sci. 37, 1158 (1997)CrossRefGoogle Scholar
  30. 30.
    C.T. Klein, D. Kaiser, G. Ecker, J. Chem. Inf. Comput. Sci. 44, 200 (2004)CrossRefGoogle Scholar
  31. 31.
    R. Todeschini, M. Lasagni, E. Marengo, J. Chemometrics 8, 263 (1994)CrossRefGoogle Scholar
  32. 32.
    G. Bravi, E. Gancia, P. Mascagni, M. Pegna, R. Todeschini, A.J. Zaliani, J. Comput. Aided Mol. Des. 11, 79 (1997)CrossRefGoogle Scholar
  33. 33.
    M. Wagener, J. Sadowski, J. Gasteiger, J. Am. Chem. Soc. 117, 7769 (1995)CrossRefGoogle Scholar
  34. 34.
    R. Bursi, D. Dao, T. van Wijk, M. de Gooyer, M. Kellenbach, P. Verwer, J. Chem. Inf. Comput. Sci. 39, 861 (1999)CrossRefGoogle Scholar
  35. 35.
    D.B. Turner, P. Willett, Eur. J. Med. Chem. 35, 367–375 (2000)CrossRefGoogle Scholar
  36. 36.
    D.B. Turner, P. Willett, A.M. Ferguson, T.W. Heritage, J. Comput. Aided Mol. Des. 13, 271 (1999)CrossRefGoogle Scholar
  37. 37.
    S.A. Wildman, G.M. Crippen, J. Mol. Graphics Modell. 21, 161 (2002)CrossRefGoogle Scholar
  38. 38.
    G. Gasteiger, J. Sadowski, J. Schuur, P. Selzer, L. Steinhauer, V. Steinhauer, J. Chem. Inf. Comput. Sci. 36, 1030 (1996)CrossRefGoogle Scholar
  39. 39.
    B.D. Silverman, D. Platt, M. Pitman, I. Rigoutsos, Perspect. Drug Discov. Des. 12–14, 183 (1998)CrossRefGoogle Scholar
  40. 40.
    R. Todeschini, V. Consonni, Molecular Descriptors for Chemoinformatics, vol. 1. Alphabetical Listing, vol 2. Appendices, References (Wiley-VCH, Weinheim, 2009), p. 2125Google Scholar
  41. 41.
    A.T. Balaban, From Chemical Topology to Three-Dimensional Geometry (Plenum Press, New York, 1997), p. 420Google Scholar
  42. 42.
    B. Bogdanov, S. Nikolic, N. Trinajstic, J. Math. Chem. 3, 299 (1989)CrossRefGoogle Scholar
  43. 43.
    B. Bogdanov, S. Nikolic, N. Trinajstic, J. Math. Chem. 5, 305 (1990)CrossRefGoogle Scholar
  44. 44.
    O. Mekenyan, D. Peitchev, D. Bonchev, N. Trinajstic, I.P. Bangov, Arzneim. Forsch. 36, 176 (1986)Google Scholar
  45. 45.
    M. Randić, New J. Chem. 19, 781 (1995)Google Scholar
  46. 46.
    M. Randić, J. Chem. Inf. Comput. Sci. 35, 373 (1995)CrossRefGoogle Scholar
  47. 47.
    M. Randić, New J. Chem. 20, 1001 (1996)Google Scholar
  48. 48.
    M. Randić, M. Razinger, J. Chem. Inf. Comput. Sci. 35, 594 (1995)CrossRefGoogle Scholar
  49. 49.
    J. Aires-de-Sousa, J. Gasteiger, I. Gutman, D. Vidovic, J. Chem. Inf. Comput. Sci. 44, 831 (2004)CrossRefGoogle Scholar
  50. 50.
    R. Benigni, M. Cotta-Ramusino, G. Gallo, F. Giorgi, A. Guliani, M.R. Vari, J. Med. Chem. 43, 3699 (2000)CrossRefGoogle Scholar
  51. 51.
    A. Golbraikh, D. Bonchev, A. Tropsha, J. Chem. Inf. Comput. Sci. 41, 147 (2001)CrossRefGoogle Scholar
  52. 52.
    J.V. Julian-Ortiz, C.G. Alapont, I. Rıos-Santamarina, R. Garcıa-Domenech, J. Galvez, J. Mol. Graphics Model. 16, 14 (1998)CrossRefGoogle Scholar
  53. 53.
    Y. Marrero-Ponce, J. Castillo-Garit, E. Castro, F. Torrens, R. Rotondo, J. Math. Chem. 44, 755 (2008)CrossRefGoogle Scholar
  54. 54.
    H.B. Schulz, E.B. Schulz, T.P. Schulz, J. Chem. Inf. Comput. Sci. 35, 864 (1995)CrossRefGoogle Scholar
  55. 55.
    Y. Marrero Ponce, J. Chem. Inf. Comput. Sci. 44, 2010 (2004)CrossRefGoogle Scholar
  56. 56.
    Y. Marrero-Ponce, J. Castillo-Garit, F. Torrens, V. Romero Zaldivar, E. Castro, Molecules 9, 1100 (2004)CrossRefGoogle Scholar
  57. 57.
    Y. Marrero-Ponce, J. Chem. Inf. Comput. Sci. 44, 2010 (2004)CrossRefGoogle Scholar
  58. 58.
    Y. Marrero-Ponce, J.A. Castillo-Garit, E. Olazabal, H.S. Serrano, A. Morales, N. Castañedo, F. Ibarra-Velarde, A. Huesca-Guillen, A.M. Sánchez, F. Torrens, E.A. Castro, Bioorg. Med. Chem. 13, 1005 (2005)CrossRefGoogle Scholar
  59. 59.
    G.M. Casañola-Martín, M.T.H. Khan, Y. Marrero-Ponce, A. Ather, M.N. Sultankhodzhaev, F. Torrens, Bioorg. Med. Chem. Lett. 16, 324 (2006)CrossRefGoogle Scholar
  60. 60.
    G.M. Casañola-Martín, Y. Marrero-Ponce, M.T.H. Khan, A. Ather, S. Sultan, F. Torrens, R. Rotondo, Bioorg. Med. Chem. 15, 1483 (2007)CrossRefGoogle Scholar
  61. 61.
    J.A. Castillo-Garit, M.C. Vega, M. Rolon, Y. Marrero-Ponce, V.V. Kouznetsov, D.F.A. Torres, A. Gómez-Barrio, A.A. Bello, A. Montero, F. Torrens, F. Pérez-Giménez, Eur. J. Pharm. Sci. 39, 30 (2010)CrossRefGoogle Scholar
  62. 62.
    Y. Marrero-Ponce, Y. Machado-Tugores, D.M. Pereira, J.A. Escario, A.G. Barrio, J.J. Nogal-Ruiz, C. Ochoa, V.J. Aran, A.R. Martinez-Fernandez, R.N. Garcia Sanchez, Curr. Drug Discov. Technol. 2, 245 (2005)CrossRefGoogle Scholar
  63. 63.
    Y. Marrero-Ponce, A. Meneses-Marcel, O.M. Rivera-Borroto, R. Garcia-Domenech, J.V. De Julian-Ortiz, A. Montero, J.A. Escario, A.G. Barrio, D.M. Pereira, J.J. Nogal, R. Grau, F. Torrens, C. Vogel, V.J. Aran, J. Comput. Aided Mol. Des. 22, 523 (2008)CrossRefGoogle Scholar
  64. 64.
    Y. Marrero-Ponce, A. Montero-Torres, C. RomeroZaldivar, M. IyarretaVeitıa, M. MayonPerez, R. GarcıaSanchez, Bioorg. Med. Chem. 13, 1293 (2005)CrossRefGoogle Scholar
  65. 65.
    J.A. Castillo-Garit, Y. Marrero-Ponce, F. Torrens, R. García-Domenech, V. Romero-Zaldivar, J. Comput. Chem. 29, 2500 (2008)CrossRefGoogle Scholar
  66. 66.
    J.W. Godden, J. Bajorath, J. Chem. Inf. Comput. Sci. 42, 87 (2001)CrossRefGoogle Scholar
  67. 67.
    J.W. Godden, F.L. Stahura, J. Bajorath, J. Chem. Inf. Comput. Sci. 40, 796 (2000)CrossRefGoogle Scholar
  68. 68.
    Y. Marrero Ponce, J.A. Castillo Garit, D. Nodarse, Bioorg. Med. Chem. 13, 3397 (2005)CrossRefGoogle Scholar
  69. 69.
    B. Vargas-Quesada, F.M. Anegón, Visualizing the Structure of Science (Springer, New York, 2007)Google Scholar
  70. 70.
    S. Nikolic, N. Trinajstic, Z. Mihalic, S. Carter, Chem. Phys. Lett. 179, 21 (1991)CrossRefGoogle Scholar
  71. 71.
    J.A. Castillo-Garit, O. Martinez-Santiago, Y. Marrero-Ponce, G.M. Casañola-Martín, F. Torrens, Chem. Phys. Lett. 464, 107 (2008)CrossRefGoogle Scholar
  72. 72.
    Y. Marrero Ponce, A. Montero-Torres, C. Romero Zaldivar, M. Iyarreta Veitía, M. Mayón Peréz, R.N. García Sánchez, Bioorg. Med. Chem. 13, 1293 (2005)CrossRefGoogle Scholar
  73. 73.
    Y. Marrero-Ponce, A. Huesca-Guillén, F. Ibarra-Velarde, J. Mol. Struct. (Thoechem) 717, 67 (2005)CrossRefGoogle Scholar
  74. 74.
    Y. Marrero-Ponce, R. Medina-Marrero, F. Torrens, Y. Martinez, V. Romero-Zaldivar, E.A. Castro, Bioorg. Med. Chem. 13, 2881 (2005)CrossRefGoogle Scholar
  75. 75.
    A. Montero-Torres, R.N. García-Sánchez, Y. Marrero-Ponce, Y. Machado-Tugores, J.J. Nogal-Ruiz, A.R. Martínez-Fernández, V.J. Arán, C. Ochoa, A. Meneses-Marcel, F. Torrens, Eur. J. Med. Chem. 41, 483 (2006)CrossRefGoogle Scholar
  76. 76.
    A. Montero-Torres, M.C. Vega, Y. Marrero-Ponce, M. Rolón, A. Gómez-Barrio, J.A. Escario, V.J. Arán, A.R. Martínez-Fernández, A. Meneses-Marcel, Bioorg. Med. Chem. 13, 6264 (2005)CrossRefGoogle Scholar
  77. 77.
    S.I. Sandler, An Introduction to Applied Statistical Thermodynamics (Wiley, New Jersey, USA, 2010)Google Scholar
  78. 78.
    G.A.F. Seber, A Matrix Handbook for Statisticians (Wiley-Interscience, New Jersey, USA, 2008)Google Scholar
  79. 79.
    D. Serre, Matrices: Theory and Applications (Springer, New York, 2002)Google Scholar
  80. 80.
    R. Sinkhorn, Ann. Math. Stat. 35, 876 (1964)CrossRefGoogle Scholar
  81. 81.
    R. Sinkhorn, P. Knopp, Pac. J. Math. 21, 343 (1967)CrossRefGoogle Scholar
  82. 82.
    C.R. Johnson, R.D. Masson, M.W. Trosset, Linear Algebra Appl. 397, 253 (2005)CrossRefGoogle Scholar
  83. 83.
    S.J. Axler, Linear Algebra Done Right (Springer, New York, 1997)CrossRefGoogle Scholar
  84. 84.
    A. Browder, Mathematical Analysis: An Introduction (Springer, New York, 1996)CrossRefGoogle Scholar
  85. 85.
    C.H. Edwards, D.E. Penney, Elementary Linear Algebra (Prentice Hall, Englewoods Cliffs, 1988)Google Scholar
  86. 86.
    R. Todeschini, V. Consonni, M. Pavan, Dragon Software (Talete, Italy, 2002)Google Scholar
  87. 87.
    A. Basilevsky, Statistical Factor Analysis Rel Method: Theory and Applications (Wiley, New York, USA, 1994)CrossRefGoogle Scholar
  88. 88.
    E. Estrada, J. Chem. Inf. Comput. Sci. 39, 1042 (1999)CrossRefGoogle Scholar
  89. 89.
    I.E. Frank, J.H. Friedman, Technometrics 35, 109 (1993)CrossRefGoogle Scholar
  90. 90.
    R. Franke, Theoretical Drug Design Methods (Elsevier Science Amsterdam, The Netherlands, 1984)Google Scholar
  91. 91.
    E.R. Malinowski, Factor Analysis in Chemistry (Wiley Interscience, Hoboken, USA, 1991)Google Scholar
  92. 92.
    Statsoft, STATISTICA, (Statsoft, Tulsa, 2001)Google Scholar
  93. 93.
    B.A. Bunin, Chemoinformatics: Theory, Practice & Products (Springer, Dordrecht, 2007), p. 295Google Scholar
  94. 94.
    C.E. Shannon, Bell Syst. Tech. J. 27, 379 (1948)CrossRefGoogle Scholar
  95. 95.
    R.P. Urias, S. Barigye, Y. Marrero-Ponce, C. García-Jacas, J. Valdes-Martiní, F. Perez-Gimenez, Mol. Divers 19, 305 (2015)CrossRefGoogle Scholar
  96. 96.
    H. Hong, Q. Xie, W. Ge, F. Qian, H. Fang, L. Shi, Z. Su, R. Perkins, W. Tong, J. Chem. Inf. Model. 48, 1337 (2008)CrossRefGoogle Scholar
  97. 97.
    Y. Marrero-Ponce, Molecules 8, 687 (2003)CrossRefGoogle Scholar
  98. 98.
    Y. Marrero-Ponce, R. Marrero, E. Castro, R. Ramos de Armas, H.G. Díaz, V. Zaldivar, F. Torrens, Molecules 9, 1124 (2004)CrossRefGoogle Scholar
  99. 99.
    C.W. Yap, J. Comput. Chem. 32, 1466 (2011)CrossRefGoogle Scholar
  100. 100.
    E. Estrada, J. Chem. Inf. Comput. Sci. 36, 844 (1996)CrossRefGoogle Scholar
  101. 101.
    E. Estrada, SAR QSAR Environ. Res. 11, 55 (2000)CrossRefGoogle Scholar
  102. 102.
    E. Estrada, E. Molina, J. Mol. Graph. Model. 20, 54 (2001)CrossRefGoogle Scholar
  103. 103.
    H. Georg, BlueDesc-Molecular Descriptor Calculator (University of Tübingen, Tübingen, Germany, 2008)Google Scholar
  104. 104.
    L. H. Hall, L. B. Kier, Molconn-Z 4.00 (Hall Associates Consulting, Quincy, 2002)Google Scholar
  105. 105.
    J. Liu, J. Feng, A. Brooks, S. Young, PowerMV: A Software Environment for Statistical Analysis, Molecular Viewing, Descriptor Generation, and Similarity Search (National Institute of Statistical Sciences, North Carolina, USA, 2005)Google Scholar
  106. 106.
    R. Guha, The CDK Descriptor Calculator (NIH Chemical Genomics Center, Indiana, USA, 1991)Google Scholar
  107. 107.
    M. Randic, N. Trinajstic, J. Mol. Struct. (Thoechem) 284, 209 (1993)CrossRefGoogle Scholar
  108. 108.
    M. Randic, N. Trinajstic, J. Mol. Struct. 300, 551 (1993)CrossRefGoogle Scholar
  109. 109.
    V. Consonni, R. Todeschini, M. Pavan, P. Gramatica, J. Chem. Inf. Comput. Sci. 42, 693 (2002)CrossRefGoogle Scholar
  110. 110.
    M.V. Diudea, J. Chem. Inf. Comput. Sci. 36, 535 (1996)CrossRefGoogle Scholar
  111. 111.
    M.V. Diudea, O.M. Minailiuc, G. Katona, Revue roumaine de chimie 42, 239 (1997)Google Scholar
  112. 112.
    E. Estrada, L. Rodríguez, J. Chem. Inf. Comput. Sci. 39, 1037 (1999)CrossRefGoogle Scholar
  113. 113.
    M. Randic, J. Mol. Struct. (Thoechem) 233, 45 (1991)CrossRefGoogle Scholar
  114. 114.
    M. Randic, Croat. Chem. Acta 66, 289 (1993)Google Scholar
  115. 115.
    M. Randic, X. Guo, T. Oxley, H. Krishnapriyan, L. Naylor, J. Chem. Inf. Comput. Sci. 34, 361 (1994)CrossRefGoogle Scholar
  116. 116.
    S. Markovic, I. Gutman, J. Mol. Struct. (Thoechem) 235, 81 (1991)CrossRefGoogle Scholar
  117. 117.
    L.B. Kier, L.H. Hall, Molecular Structure Description: The Electrotopological State (Academic Press, San Diego, 1999)Google Scholar
  118. 118.
    E. Estrada, E. Molina, J. Chem. Inf. Comput. Sci. 41, 791 (2001)CrossRefGoogle Scholar
  119. 119.
    Š. Baláž, E. Šturdík, M. Rosenberg, J. Augustín, B. Škára, J. Theor. Biol. 131, 115 (1988)CrossRefGoogle Scholar
  120. 120.
    J. Stewart, J. Mol. Model. 13, 1173 (2007)CrossRefGoogle Scholar
  121. 121.
    D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley Pub. Co., Reading, 1989)Google Scholar
  122. 122.
    A.J. Hopfinger, S. Wang, J.S. Tokarski, B. Jin, M. Albuquerque, P.J. Madhav, C. Duraiswami, J. Am. Chem. Soc. 119, 10509 (1997)CrossRefGoogle Scholar
  123. 123.
    D. Rogers, A.J. Hopfinger, J. Chem. Inf. Comput. Sci. 34, 854 (1994)CrossRefGoogle Scholar
  124. 124.
    S.-S. So, M. Karplus, J. Med. Chem. 39, 1521 (1996)CrossRefGoogle Scholar
  125. 125.
    P. Willett, Trends Biotechnol. 13, 516 (1995)CrossRefGoogle Scholar
  126. 126.
    R. Todeschini, V. Consonni, A. Mauri, M. Pavan, R. Leardi, Data Handling in Science and Technology (Elsevier, Amsterdam, 2003)Google Scholar
  127. 127.
    J. Devillers, A.T. Balaban, Topological Indices and Related Descriptors in QSAR and QSPR (Gordon and Breach, Amsterdam, The Netherland, 1999)Google Scholar
  128. 128.
    V. Consonni, R. Todeschini, M. Pavan, J. Chem. Inf. Comput. Sci. 42, 682 (2002)CrossRefGoogle Scholar
  129. 129.
    A. Golbraikh, A. Tropsha, J. Mol. Graph. Model. 20, 269 (2002)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Néstor Cubillán
    • 1
    • 2
  • Yovani Marrero-Ponce
    • 3
    • 4
  • Harold Ariza-Rico
    • 1
  • Stephen J. Barigye
    • 5
  • César R. García-Jacas
    • 6
  • José R. Valdes-Martini
    • 7
  • Ysaías J. Alvarado
    • 8
  1. 1.Laboratorio de Electrónica Molecular, Departamento de Química, Facultad Experimental de CienciasUniversidad del ZuliaMaracaiboBolivarian Republic of Venezuela
  2. 2.Departamento de Física, Facultad Experimental de Ciencias, Centro de Modelado CientíficoUniversidad del ZuliaMaracaiboBolivarian Republic of Venezuela
  3. 3.Computer-Aided Molecular “Biosilico” Discovery and Bioinformatic Research International Network (CAMD-BIR IN)Cartagena de IndiasColombia
  4. 4.Grupo de Investigación en Estudios Químicos y Biológicos, Facultad de Ciencias BásicasUniversidad Tecnológica de Bolívar (UTB)Cartagena de IndiasColombia
  5. 5.Departamento de QuímicaUniversidade Federal de LavrasLavrasBrazil
  6. 6.Departamento de BioinformáticaUniversidad de las Ciencias InformáticasHavanaCuba
  7. 7.Laboratorio de Inteligencia Artificial, Facultad de Matemática, Física y Computación, Centro de Estudios de Informática (CEI)Universidad Central “Marta Abreu” de Las VillasSanta ClaraCuba
  8. 8.Laboratorio de Caracterización Molecular y Biomolecular, Departamento de Investigación en Tecnología de los Materiales y el Ambiente (DITeMA)Instituto Venezolano de Investigaciones Científicas (IVIC)MaracaiboBolivarian Republic of Venezuela

Personalised recommendations