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Markovian chemicals "in silico" design (MARCH-INSIDE), a promising approach for computer-aided molecular design I: discovery of anticancer compounds

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Abstract

A simple stochastic approach, designed to model the movement of electrons throughout chemical bonds, is introduced. This model makes use of a Markov matrix to codify useful structural information in QSAR. The self-return probabilities of this matrix throughout time (SRπ k ) are then used as molecular descriptors. Firstly, a calculation of SRπ k is made for a large series of anticancer and non-anticancer chemicals. Then, k-Means Cluster Analysis allows us to split the data series into clusters and ensure a representative design of training and predicting series. Next, we develop a classification function through Linear Discriminant Analysis (LDA). This QSAR discriminates between anticancer compounds and non-active compounds with a correct global classification of 90.5% in the training series. The model also correctly classified 86.07% of the compounds in the predicting series. This classification function is then used to perform a virtual screening of a combinatorial library of coumarins. In this connection, the biological assay of some furocoumarins, selected by virtual screening using the present model, gives good results. In particular, a tetracyclic derivative of 5-methoxypsoralen (5-MOP) has an IC50 against HL-60 tumoral line around 6 to 10 times lower than those for 8-MOP and 5-MOP (reference drugs), respectively. Finally, application of Iso-contribution Zone Analysis (IZA) provides structural interpretation of the biological activity predicted with this QSAR.

Figure IZA of compound 1

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References

  1. Markov AA (1906) Bull Soc Phys Math Kasan 15:155–156

    Google Scholar 

  2. Bharucha-Reid AT (1960) Elements of theory of markov process on the application. McGraw-Hill Series in Probability and Statistics. McGraw-Hill, New York, pp 167–434

  3. Freund JA, Poschel T (eds) (2000) Stochastic processes in physics, chemistry, and biology. In: Lecture Notes in Physics. Springer, Berlin Heidelberg New York

  4. Graepel T, Obermayer K (1998) Neural Comput 11:39–55

    Google Scholar 

  5. Geng J, Xu D, Gong J, Li W (1998) Int J Epidemiol 27:320–322

    CAS  PubMed  Google Scholar 

  6. Yakovlev A, Boucher K, DiSario J (1999) Math Biosci 1:45–60

    Article  Google Scholar 

  7. Vorodovsky M, Koonin EV, Rudd KE (1994) Trends Biochem Sci 19:309–313

    PubMed  Google Scholar 

  8. Vorodovsky M, MacIninch JD, Koonin EV, Rudd KE, Médigue C, Danchin A (1995) Nucleic Acid Res 23:3554–3562

    PubMed  Google Scholar 

  9. Chou KC (1997) Biopolymers 42:837–853

    CAS  PubMed  Google Scholar 

  10. Yuan Z (1999) FEBS Lett 451:23–26

    CAS  PubMed  Google Scholar 

  11. Hua S, Sun Z (2001) Bioinformatics 17:721–728

    CAS  PubMed  Google Scholar 

  12. Hubbard TJ, Park J (1995) Proteins Struct Funct Genet 23:398–402

    CAS  PubMed  Google Scholar 

  13. Krogh A, Brown M, Mian IS, Sjeander K, Haussler D (1994) J Mol Biol 235:1501–1531

    CAS  PubMed  Google Scholar 

  14. Di Francesco V, Munson PJ, Garnier J (1999) Bioinformatics 15:131–140

    PubMed  Google Scholar 

  15. James AJ (1995) Solving the many electron problem with quantum Monte-Carlo methods. Imperial College of Science, Technology and Medicine, London, pp 12–202

  16. Landau LD, Lifshitz EM (1963) Mecánica Quántica no-Relativista. In: Curso de Física Teórica, vol 3. Reverté, Barcelona, pp 1–49

  17. Dreizler RM, Gross EKU (1990) Density functional theory: an approach to the quantum many-body problem. Springer, Berlin Heidelberg New York, pp 1–30

    Google Scholar 

  18. Estrada E, Uriarte E (2001) Curr Med Chem 8:1573–1588

    CAS  PubMed  Google Scholar 

  19. Kubinyi H (1999) J Recept Signal Transduct Res 19:15–39

    CAS  PubMed  Google Scholar 

  20. Kier LB, Hall LH (1999) Topological indices and related descriptors in QSAR and QSPR. Gordon and Breach, Amsterdam, pp 455–489

  21. Devillers J, Balaban AT (2000) Topological indices and related descriptors in QSAR and drug design. Amsterdam, pp 3–41

  22. Hall LH, Kier LB (1977) Tetrahedron 33:1953–1957

    CAS  Google Scholar 

  23. Bonchev D (1983) Information theoretic indices for characterization of chemical structure. RSP-Wiley, Chichester, UK, pp 4–20

  24. Trinjastic N (1992) Chemical graph theory. CRC Press, Boca Raton, Fla., pp 1–30

  25. Bonchev D, Rouvray DH (1991) Chemical graph theory. Gordon and Breach, New York, pp 6–23

  26. Dewar MJ (1991) MOTEC 91, modern technique in computational chemistry. Leiden, pp 6–15

  27. Ögnetir C, Csizmadia IG (1991) Computational advances in organic chemistry: molecular structure and reactivity. Kluwer, Dordrecht

    Google Scholar 

  28. Kikuchi O (1987) Quant Struct–Act Relat 6:179–184

    Google Scholar 

  29. Gajewski JJ, Gilbert KE, Mckelvey J (1990) Advances in molecular modeling. JAI Press, Greenwich, pp 65–68

  30. Estrada E (1997) J Chem Inf Comput Sci 37:320–328

    CAS  Google Scholar 

  31. Estrada E (1996) J Chem Inf Comput Sci 36:844–849

    CAS  Google Scholar 

  32. Stewart JJ (1989) J Comput Chem 10:209–221

    CAS  Google Scholar 

  33. Dewar MJ, Zoebish EG, Healy EF, Stewart JJ (1985) J Am Chem Soc 107:3902–3909

    CAS  Google Scholar 

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

  35. Denny WA (1992) The role of medicinal chemistry in the discovery of DNA-active anticancer drugs: from random searching, through lead development, to the novo design. In: Waring MJ, Ponder BAJ (eds) The search for anticancer drugs. Kluwer, Dordrecht, chapter 2

  36. Lunney EA (1998) Med Chem Res 8:352–361

    CAS  Google Scholar 

  37. Walters WP, Stahl MT, Murcko MA (1998) Drug Discovery Today 3:160–178

    Article  CAS  Google Scholar 

  38. Kubinyi H (1999) J Recept Signal Transduct Res 19:15–39

    CAS  PubMed  Google Scholar 

  39. Lien EJ, Lien LL (1998) Chin Phar J 50:249–256

    CAS  Google Scholar 

  40. Lunney EA (1998) Med Chem Res 8:352–361

    CAS  Google Scholar 

  41. Walters WP, Stahl MT, Murcko MA (1998) Drug Discovery Today 3:160–178

    Article  CAS  Google Scholar 

  42. Drie JHV, Lajines MS (1998) Drug Discovery Today 3:274–283

    Article  Google Scholar 

  43. Ferrante K, Winograd B, Canetta R (1999) Cancer Chemother Pharmacol 43:S61-S83

    CAS  PubMed  Google Scholar 

  44. Menta E, Palumbo M (1998) Expert Opin Ther Pat 8:1627–1672

    CAS  Google Scholar 

  45. Estrada E, Gutiérrez Y, González DH (2000) J Chem Inf Comput Sci 40:1386–1399

    CAS  PubMed  Google Scholar 

  46. Estrada E, Gonzalez DH (2003) J Chem Inf Comput Sci 43:75–84

    CAS  PubMed  Google Scholar 

  47. Randič M (1991) J Math Chem 7:155–168

    Google Scholar 

  48. Padron JA, Carrasco R, Pellón RF (2002) J Pharm Pharmaceut Sci 5:267–274

    Google Scholar 

  49. González DH, Olazábal E, Castañedo N, Hernádez SI, Morales A, Serrano HS, González J, Ramos de Armas R (2002) J Mol Mod 8:237–245

    Article  Google Scholar 

  50. González DH, Hernádez SI, Uriarte E, Santana L (2003) Comput Chem (in press, corrected proofs published online)

  51. González DH, De Armas RR, Uriarte E (2002) Online J Bioinformatics 1:83–95

    Google Scholar 

  52. Cabrera MA, González DH, Teruel C, Pla-Delfina JM, Bermejo del Val M (2002) Eur J Pharm Biopharm 53:317–325

    PubMed  Google Scholar 

  53. Randič M (1991) Chemom Intell Lab Sist 10:213–227

    Article  Google Scholar 

  54. Hall LH, Mohney B, Kier LB (1991) Quant Struct–Act Relat 10:43–51

    Google Scholar 

  55. Gálvez J, García R, Salabert MT, Soler R (1994) J Chem Inf Comput Sci 34:520–525

    Google Scholar 

  56. Gnedenko B (1978) The theory of probability. Mir, Moscow, pp 107–112

  57. Pauling L (1939) The nature of the chemical bond. Cornell University Press, Ithaca, N.Y., pp 2–60

  58. Grimmett GR, Stirzaker DR (1992) Probability and random processes. Clarendon Press, Oxford, pp 194–264

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

  60. Estrada E, Molina E (2001) J Chem Inf Comput Sci 41:791-797

    CAS  PubMed  Google Scholar 

  61. Hernández I, González H (2002) MARCH-INSIDE version 1.0 (Markovian chemicals "in silico" design). Chemicals Bio-actives Center, Central University of Las Villas, Cuba. This is a preliminary experimental version future professional version shall be available to the public. For any information about it, send an e-mail to the corresponding author humbertogd@cbq.uclv.edu.cu

  62. Rogers KS, Camnarata A (1969) J Med Chem 12:692–693

    CAS  PubMed  Google Scholar 

  63. Jiang Y, Tang A, Hoffman R (1984) Theor Chim Acta 66:183–192

    CAS  Google Scholar 

  64. Burdett JK, Lee S (1985) J Am Chem Soc 107:3063–3082

    CAS  Google Scholar 

  65. Burdett JK, Lee S (1985) J Am Chem Soc 107:3050–3063

    CAS  Google Scholar 

  66. Lee S (1991) Acc Chem Res 24:249–254

    CAS  Google Scholar 

  67. Markovick S, Gutman I (1991) J Mol Struct (THEOCHEM) 81:81–87

    Google Scholar 

  68. Gutman I, Rosenfield VR (1996) Theor Chim Acta 93:191–197

    CAS  Google Scholar 

  69. Gutman I (1992) Theor Chim Acta 83:313–318

    CAS  Google Scholar 

  70. Karwowski J, Bielinska-Waz D, Jurkowski J (1996) Int Quantum Chem 60:185–193

    CAS  Google Scholar 

  71. Estrada E, Peña A, García-Domenech R (1998) J Comp Aided Mol Design 12:583–595

    CAS  Google Scholar 

  72. STATISTICA for Windows (2001) release 6.0. Statsoft Inc

  73. van Waterbeemd H (1995) Discriminant analysis for activity prediction. In: Manhnhold R, Krogsgaard-Larsen P, Timmerman H (eds) Method and principles in medicinal chemistry, vol 2. Chemometric methods in molecular design, van Waterbeemd H (ed). VCH, Weinhiem, pp 265–282

  74. Julián-Ortiz JV, Gálvez J, Mullños-Collado C, García-Domenech R, Gimeno-Cardona C (1999) J Med Chem 42:3308–3314

    PubMed  Google Scholar 

  75. Kowalski RB, Wold S (1982) Pattern recognition in chemistry. In: Krishnaiah PR, Kanal LN (eds) Handbook of statistics. North-Holland, Amsterdam, pp 673–697

  76. Mc Farland JW, Cooper CB, Newcomb DM (1991) J Med Chem 34:1908–1911

    PubMed  Google Scholar 

  77. Negwer M (1987) Organic chemical drugs and their synonyms. Akademie-Verlag, Berlin

  78. Mc Farland JW, Gans DJ (1995) Cluster significance analysis. In: Manhnhold R, Krogsgaard-Larsen P, Timmerman H (eds) Method and principles in medicinal chemistry, vol 2. Chemometric methods in molecular design, van Waterbeemd H (ed). VCH, Weinhiem, pp 295–307

  79. Johnson RA, Wichern DW (1988) Applied multivariate statistical analysis. Prentice-Hall, N.J.

  80. Via DL, Gia O, Magno MS, Da Settimo A, Primofiore G, Da Settimo F, Simorini F, Marini AM (2002) Eur J Med Chem 37:475–486

    PubMed  Google Scholar 

  81. Galvez J, Garcia-Domenech R, Gomez-Lechon MJ, astell JV (1996) Bioorg Med Chem Lett 6:2301–2306

    CAS  Google Scholar 

  82. Via DL, Gia O, Viola G, Bertoloni G, Santana L, Uriarte E (1998) Il Farmaco 53:638–644

    Article  PubMed  Google Scholar 

  83. Gia O, Anselmo A, Conconi MT, Antonello C, Uriarte E, Caffieri S (1996) J Med Chem 39:4489–4496

    CAS  PubMed  Google Scholar 

  84. Via DL, Gia O, Magno MS, Santana L, Teijeira M, Uriarte E (1999) J Med Chem 42:4405–4413

    Article  PubMed  Google Scholar 

  85. Fejzo J, Lepre ChA, Peng WJ, Bemis WG, Ajay MAM, Moore MJ (1999) Chem Biol 6:755–769

    CAS  PubMed  Google Scholar 

  86. Gramatica P, Corradi M, Consonni V (2000) Chemosphere 41:763–777

    CAS  PubMed  Google Scholar 

  87. Estrada E, Uriarte E, Montero A, Teijeira M, Santana L, De Clercq E (2000) J Med Chem 43:163–166

    Article  Google Scholar 

  88. Frank IE, Todeschini R (1994) The data analysis handbook. Elsevier, Amsterdam

  89. Gia O, Uriarte E, Zagotto G, Baccichetti F, Antonello C, Marciani-Magno S (1992) J Photochem Photobiol B: Biol 14:95–104

    Google Scholar 

  90. Gia O, Via LD, Marciani S, Angelini G, Margonelli A, Rodighiero P (2000) Photochem Photobiol B 56:132–138

    CAS  Google Scholar 

  91. Rodighiero P, Pastorini G, Via LD, Gia O, Marciani S (1998) Il Farmaco 53:313–319

    CAS  PubMed  Google Scholar 

  92. Hermann T, Westhof E (2000) Combinatorial Chem High Throughput Screening 3:219–234

    CAS  Google Scholar 

  93. Gozalbes R, Gálvez J, García-Domenech R, Derouin F (1999) SAR QSAR Environ Res 10:47–60

    CAS  PubMed  Google Scholar 

  94. Foye WO, Lemke TL, Williams DA (1995) Principles of medicinal chemistry. Williams and Wilkins, Baltimore, Md., pp 896–900

  95. Arabzadeh A, Bathaiee SZ, Farsam H, Amanlou M, Saboury AA, Shockravi A, Moosavi-Movahedi AA (2002) Int J Pharmaceutics 237:47–45

    CAS  Google Scholar 

  96. Spicer JA, Swarna GA, Graene JF, Denny FW (2002) Bioorg Med Chem 10:19–29

    CAS  PubMed  Google Scholar 

  97. Dollery C, Boobis A, Rawlins M, Thomas S, Wilkins M (1999) Therapeitic drugs. Churchill Livingston, Edimburgh, pp 102–108

  98. Scott BR, Pathak MA, Mohn GR (1976) Mutat Res 39:29–74

    CAS  PubMed  Google Scholar 

  99. Bridges BA, Mottershead RP (1977) Mutat Res 44:305–312

    CAS  PubMed  Google Scholar 

  100. Ekins S, Boulanger B, Swaan WP, Hucpey AZ (2002) J Comput Aided Mol Des 16:381-401

    CAS  PubMed  Google Scholar 

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Acknowledgements

We would like to offer our sincere thanks to the two unknown referees and the editor for their critical opinions about the manuscript, which have significantly contributed to improving its presentation and quality. González DH would like to express his thanks to Dr. Jose Luis Garcia and the Cuban Ministry of Higher Education for partial financial support and help. The same author acknowledges Dr. Kier L. B. (USA) for his kind revision of other work related to our Markovian model, and who suggested several useful ideas to us. We are also indebted to Dr. Estrada (England) for former tutorship (1994–2000) and training in computational chemistry. We are also grateful for a series of lectures given in Cuba by Dr. Gutman I., which introduced us to the study of the theory of information, and to some extent random process in chemistry. Last but not least, we would like to thank Prof. Nicolais Guevara (Mexico), Prof. Israel Queiroz (Cuba) and Dr. Jorge Galvez (Valencia, Spain) for their useful help, and the Xunta the Galicia for providing us with a grant (PR405A2001/65-0).

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Authors and Affiliations

  1. Chemical Bioactives Center, Central University of Las Villas, 54830, Santa Clara, Villa Clara, Cuba

    Humberto Gonzáles-Díaz, Ivan Hernádez, Mayrelis Chaviano, Santiago Seijo, Juan A. Castillo, Lázaro Morales, Delali Akpaloo, Enrique Molina, Maikel Cruz, Luis A. Torres & Miguel A. Cabrera

  2. Department of Pharmaceutical Sciences, University of Padua, Via Marzolo 5, 35131, Padua, Italy

    Ornella Gia

  3. Department of Organic Chemistry, Faculty of Pharmacy, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Humberto Gonzáles-Díaz, Eugenio Uriarte & Lourdes Santana

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

    Ronal Ramos

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

    Luis A. Torres

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  1. Humberto Gonzáles-Díaz
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Correspondence to Humberto Gonzáles-Díaz.

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Gonzáles-Díaz, H., Gia, O., Uriarte, E. et al. Markovian chemicals "in silico" design (MARCH-INSIDE), a promising approach for computer-aided molecular design I: discovery of anticancer compounds. J Mol Model 9, 395–407 (2003). https://doi.org/10.1007/s00894-003-0148-7

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