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Classifying Calpain Inhibitors for the Treatment of Cataracts: A Self Organising Map (SOM) ANN/KM Approach in Drug Discovery

  • I. L. HudsonEmail author
  • S. Y. Leemaqz
  • A. T. Neffe
  • A. D. Abell
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 628)

Abstract

Calpain inhibitors are possible therapeutic agents in the treatment of cataracts. These covalent inhibitors contain an electrophilic anchor (“warhead”), an aldehyde that reacts with the active site cysteine. Whilst high throughput docking of such ligands into high resolution protein structures (e.g. calpain) is a standard computational approach in drug discovery, there is no docking program that consistently achieves low rates of both false positives (FPs) and negatives (FNs) for ligands that react covalently (via irreversible interactions) with the target protein. Schroedinger’s GLIDE score, widely used to screen ligand libraries, is known to give high false classification, however a two-level Self Organizing Map (SOM) artificial neural network (ANN) algorithm, with KM clustering proved that the addition of two structural components of the calpain molecule, number hydrogen bonds and warhead distance, combined with GLIDE score (or its partial energy subcomponents) provide a superior predictor set for classification of true molecular binding strength (IC50). SOM ANN/KM significantly reduced the number of FNs by 64 % and FPs by 26 %, compared to the glide score alone. FPs were shown to be mostly esters and amides plus alcohols and non-classical, and FNs mainly aldehydes and ketones, masked aldehydes and ketones and Michael.

Keywords

Virtual Screening Good Binder Calpain Inhibitor Best Match Unit Michael Acceptor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    V.G. Maltarollo, et al., Applications of Artificial Neural Networks in Chemical Problems, Artificial Neural NetworksArchitectures and Applications (InTech, 2013)Google Scholar
  2. 2.
    V.G. Maltarollo et al., Applying machine learning techniques for ADME-Tox prediction: a review. Exp. Opin. Drug Metab. Toxicol. 11, 259–271 (2015)CrossRefGoogle Scholar
  3. 3.
    F. Marini et al., Artificial neural networks in chemometrics: History, examples and perspectives. Microchem. J. 88, 178–185 (2008)CrossRefGoogle Scholar
  4. 4.
    L. Wang, et al., Self-organizing map clustering analysis for molecular data, ed. by J. Wang, et al., in Advances in Neural Networks, ISNN 2006, vol. 3971 (Springer, Berlin, 2006), pp. 1250–1255Google Scholar
  5. 5.
    J.C. Gertrudes et al., Machine learning techniques and drug design. Curr. Med. Chem. 19, 4289–4297 (2012)CrossRefGoogle Scholar
  6. 6.
    R.G. Brereton, Self organising maps for visualising and modelling. Chem. Cent. J. 6(Suppl 2), S1 (2012)CrossRefGoogle Scholar
  7. 7.
    Y.D. Xiao, et al., Supervised self-organizing maps in drug discovery. 1. Robust behavior with overdetermined data sets. J. Chem. Inf. Model 45, 1749–1758 (2005)Google Scholar
  8. 8.
    Y.D. Xiao, et al., Supervised self-organizing maps in drug discovery. 2. Improvements in descriptor selection and model validation. J. Chem. Inf. Model 46, 137–144 (2006)Google Scholar
  9. 9.
    F. Marini et al., Class-modeling using Kohonen artificial neural networks. Anal. Chim. Acta 544, 306–314 (2005)CrossRefGoogle Scholar
  10. 10.
    M. Stahl et al., Mapping of protein surface cavities and prediction of enzyme class by a self-organizing neural network. Protein Eng. 13, 83–88 (2000)CrossRefGoogle Scholar
  11. 11.
    A.T. Neffe, A.D. Abell, Developments in the design and synthesis of calpain inhibitors. Curr. Opin. Drug Discov. Dev. 8, 684–700 (2005)Google Scholar
  12. 12.
    A.D. Abell et al., Molecular modeling, synthesis, and biological evaluation of macrocyclic calpain inhibitors. Angew. Chem. Int. Ed. Engl. 48, 1455–1458 (2009)CrossRefGoogle Scholar
  13. 13.
    A.D. Abell et al., Investigation into the P3 binding domain of m-calpain using photoswitchable diazo- and triazene-dipeptide aldehydes: new anticataract agents. J. Med. Chem. 50, 2916–2920 (2007)CrossRefGoogle Scholar
  14. 14.
    M.A. Jones et al., Synthesis, biological evaluation and molecular modelling of N-heterocyclic dipeptide aldehydes as selective calpain inhibitors. Bioorg. Med. Chem. 16, 6911–6923 (2008)CrossRefGoogle Scholar
  15. 15.
    S.A. Jones et al., The preparation of macrocyclic calpain inhibitors by ring closing metathesis and cross metathesis. Aust. J. Chem. 67, 1257–1263 (2014)Google Scholar
  16. 16.
    S.A. Jones et al., A template-based approach to inhibitors of calpain 2, 20S proteasome, and HIV-1 protease. ChemMedChem 8, 1918–1921 (2013)CrossRefGoogle Scholar
  17. 17.
    J.D. Morton et al., A macrocyclic calpain inhibitor slows the development of inherited cortical cataracts in a sheep model. Invest. Ophthalmol. Vis. Sci. 54, 389–395 (2013)CrossRefGoogle Scholar
  18. 18.
    A.D. Pehere et al., Synthesis and extended activity of triazole-containing macrocyclic protease inhibitors. Chemistry 19, 7975–7981 (2013)CrossRefGoogle Scholar
  19. 19.
    M. Pietsch et al., Calpains: attractive targets for the development of synthetic inhibitors. Curr. Top. Med. Chem. 10, 270–293 (2010)CrossRefGoogle Scholar
  20. 20.
    B.G. Stuart et al., Molecular modeling: a search for a calpain inhibitor as a new treatment for cataractogenesis. J. Med. Chem. 54, 7503–7522 (2011)CrossRefGoogle Scholar
  21. 21.
    K.C.H. Chua et al., Macrocyclic Protease Inhibitors with reduced peptide character. Angew. Chem. Int. Ed. 53, 7828–7831 (2014)CrossRefGoogle Scholar
  22. 22.
    J.P. Hughes et al., Principles of early drug discovery. Br. J. Pharmacol. 162, 1239–1249 (2011)CrossRefGoogle Scholar
  23. 23.
    A.D. Bochevarov et al., Jaguar: a high-performance quantum chemistry software program with strengths in life and materials sciences. Int. J. Quantum Chem. 113, 2110–2142 (2013)CrossRefGoogle Scholar
  24. 24.
    E. Kellenberger et al., Comparative evaluation of eight docking tools for docking and virtual screening accuracy. Proteins 57, 225–242 (2004)CrossRefGoogle Scholar
  25. 25.
    R. Sink et al., False positives in the early stages of drug discovery. Curr. Med. Chem. 17, 4231–4255 (2010)CrossRefGoogle Scholar
  26. 26.
    R. Macarron, Critical review of the role of HTS in drug discovery. Drug Discov. Today 11, 277–279 (2006)CrossRefGoogle Scholar
  27. 27.
    E. Yuriev, P.A. Ramsland, Latest developments in molecular docking: 2010–2011 in review. J. Mol. Recognit. 26, 215–239 (2013)CrossRefGoogle Scholar
  28. 28.
    K. Zhu et al., Docking covalent inhibitors: a parameter free approach to pose prediction and scoring. J. Chem. Inf. Model. 54, 1932–1940 (2014)CrossRefGoogle Scholar
  29. 29.
    S. Kawatkar et al., Virtual fragment screening: an exploration of various docking and scoring protocols for fragments using Glide. J. Comput. Aided Mol. Des. 23, 527–539 (2009)CrossRefGoogle Scholar
  30. 30.
    T.A. Halgren et al., Glide: a new approach for rapid, accurate docking and scoring. 2. Enrichment factors in database screening. J. Med. Chem. 47, 1750–1759 (2004)CrossRefGoogle Scholar
  31. 31.
    A.R. Leach et al., Prediction of protein-ligand interactions. Docking and scoring: successes and gaps. J. Med. Chem. 49, 5851–5855 (2006)CrossRefGoogle Scholar
  32. 32.
    T. Schulz-Gasch, M. Stahl, Scoring functions for protein-ligand interactions: a critical perspective. Drug Discov. Today Technol. 1, 231–239 (2004)CrossRefGoogle Scholar
  33. 33.
    P. Ferrara et al., Assessing scoring functions for protein-ligand interactions. J. Med. Chem. 47, 3032–3047 (2004)CrossRefGoogle Scholar
  34. 34.
    G.D. Geromichalos, Importance of molecular computer modeling in anticancer drug development. J. Buon. 12(Suppl 1), S101–118 (2007)Google Scholar
  35. 35.
    A.J. Knox, et al., Considerations in compound database preparation—“hidden” impact on virtual screening results. J. Chem. Inf. Model. 45, 1908–1919 (2005)Google Scholar
  36. 36.
    N. Moitessier et al., Towards the development of universal, fast and highly accurate docking/scoring methods: a long way to go. Br. J. Pharmacol. 153(Suppl 1), S7–26 (2008)Google Scholar
  37. 37.
    T. Tuccinardi, Docking-based virtual screening: recent developments. Comb. Chem. High Throughput Screen. 12, 303–314 (2009)CrossRefGoogle Scholar
  38. 38.
    R. Mah et al., Drug discovery considerations in the development of covalent inhibitors. Bioorg. Med. Chem. Lett. 24, 33–39 (2014)CrossRefGoogle Scholar
  39. 39.
    S.J. Macalino, et al., Role of computer-aided drug design in modern drug discovery. Arch. Pharm. Res. (2015)Google Scholar
  40. 40.
    T. Kohonen, Essentials of the self-organizing map. Neural Netw. 37, 52–65 (2013)CrossRefGoogle Scholar
  41. 41.
    J. Vesanto, E. Alhoniemi, Clustering of the self-organizing map. IEEE Trans. Neural Netw. 11, 586–600 (2000)CrossRefGoogle Scholar
  42. 42.
    R. Rojas, Neural Networks: A Systematic Introduction (Springer, New York, Inc., 1996)Google Scholar
  43. 43.
    G. Schneider, Analysis of chemical space, in Madame Curie Bioscience Database [Internet] (Landes Bioscience, 2000). http://www.ncbi.nlm.nih.gov/books/NBK6062/
  44. 44.
    J. Sadowski, H. Kubinyi, A scoring scheme for discriminating between drugs and nondrugs. J. Med. Chem. 41, 3325–3329 (1998)CrossRefGoogle Scholar
  45. 45.
    V.N. Viswanadhan, et al., Atomic physicochemical parameters for three dimensional structure directed quantitative structure-activity relationships. 4. Additional parameters for hydrophobic and dispersive interactions and their application for an automated superposition of certain naturally occurring nucleoside antibiotics. J. Chem. Inf. Comput. Sci. 29, 163–172 (1989)Google Scholar
  46. 46.
    M. Otto, Chemometrics: Statistics and Computer Application in Analytical Chemistry Weinheim (Wiley-VCH, New York, 1999)Google Scholar
  47. 47.
    D.W. Wichern, R.A. Johnson, Applied Multivariate Statistical Analysis (Prentice Hall, Upper Saddle River, 2007)Google Scholar
  48. 48.
    J.C. Fort, SOM’s mathematics. Neural Netw. 19, 812–816 (2006)CrossRefzbMATHGoogle Scholar
  49. 49.
    J. Vesanto, SOM-based data visualization methods. Intell. Data Anal. 3, 111–126 (1999)CrossRefzbMATHGoogle Scholar
  50. 50.
    J. Himberg, et al., The Self-organizing map as a tool in knowledge engineering, in Pattern Recognition in Soft Computing Paradigm, ed. (World Scientific Publishing Co., Inc., 2001), pp. 38–65Google Scholar
  51. 51.
    MATLAB:2015, version R2015a (The MathWorks Inc., Natick, 2015)Google Scholar
  52. 52.
    J. Vesanto, et al., Self-organizing map in Matlab: the SOM Toolbox, in Matlab DSP Conference, 1999, pp. 35–40Google Scholar
  53. 53.
    R. Wehrens, L.M.C. Buydens, Self- and Super-organizing maps in R: The kohonen package. J. Stat. Softw. 21, 19 (2007)Google Scholar
  54. 54.
    T. Vatanen et al., Self-organization and missing values in SOM and GTM. Neurocomputing 147, 60–70 (2015)CrossRefGoogle Scholar
  55. 55.
    B. Everitt et al., Cluster Analysis (Wiley, New York, 2011)CrossRefzbMATHGoogle Scholar
  56. 56.
    I.L. Hudson, et al., SOM clustering and modelling of Australian railway drivers’ sleep, wake, duty profiles, in 28th International Workshop on Statistical Modelling, Palermo, Italy, 2013, pp. 177–182Google Scholar
  57. 57.
    I.L. Hudson, J.A. Sleep, Comparison of self-organising maps, mixture, K-means and hybrid approaches to risk classification of passive railway crossings, in 23rd International Workshop on Statistical Modelling (IWSM), Utrecht, The Netherlands, 2008, pp. 396–401Google Scholar
  58. 58.
    F. Lopez-Vallejo et al., Integrating virtual screening and combinatorial chemistry for accelerated drug discovery. Comb. Chem. High Throughput Screen. 14, 475–487 (2011)CrossRefGoogle Scholar
  59. 59.
    S.Y. Huang, X. Zou, Advances and challenges in protein-ligand docking. Int. J. Mol. Sci. 11, 3016–3034 (2010)CrossRefGoogle Scholar
  60. 60.
    X. Li et al., Evaluation of the performance of four molecular docking programs on a diverse set of protein-ligand complexes. J. Comput. Chem. 31, 2109–2125 (2010)CrossRefGoogle Scholar
  61. 61.
    C. Bissantz et al., Protein-based virtual screening of chemical databases. 1. Evaluation of different docking/scoring combinations. J. Med. Chem. 43, 4759–4767 (2000)CrossRefGoogle Scholar
  62. 62.
    D.B. Kitchen et al., Docking and scoring in virtual screening for drug discovery: methods and applications. Nat. Rev. Drug Discov. 3, 935–949 (2004)CrossRefGoogle Scholar
  63. 63.
    W. Xu et al., Comparing sixteen scoring functions for predicting biological activities of ligands for protein targets. J. Mol. Graph. Model. 57, 76–88 (2015)CrossRefGoogle Scholar
  64. 64.
    Swiss Institute of Bioinformatics, Click2Drug: Directory of Computer-Aided Drug Design Tools (2013)Google Scholar
  65. 65.
    I.D. Kuntz et al., A geometric approach to macromolecule-ligand interactions. J. Mol. Biol. 161, 269–288 (1982)CrossRefGoogle Scholar
  66. 66.
    C.A. Baxter et al., Flexible docking using Tabu search and an empirical estimate of binding affinity. Proteins 33, 367–382 (1998)CrossRefGoogle Scholar
  67. 67.
    J.S. Dixon, Evaluation of the CASP2 docking section. Proteins 1(Suppl), 198–204 (1997)CrossRefGoogle Scholar
  68. 68.
    D.K. Jones-Hertzog, W.L. Jorgensen, Binding affinities for sulfonamide inhibitors with human thrombin using Monte Carlo simulations with a linear response method. J. Med. Chem. 40, 1539–1549 (1997)CrossRefGoogle Scholar
  69. 69.
    H. Li et al., GAsDock: a new approach for rapid flexible docking based on an improved multi-population genetic algorithm. Bioorg. Med. Chem. Lett. 14, 4671–4676 (2004)CrossRefGoogle Scholar
  70. 70.
    M.D. Miller et al., FLOG: a system to select ‘quasi-flexible’ ligands complementary to a receptor of known three-dimensional structure. J. Comput. Aided Mol. Des. 8, 153–174 (1994)CrossRefGoogle Scholar
  71. 71.
    G.M. Morris et al., Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function. J. Comput. Chem. 19, 1639–1662 (1998)CrossRefGoogle Scholar
  72. 72.
    E. Perola et al., Successful virtual screening of a chemical database for farnesyltransferase inhibitor leads. J. Med. Chem. 43, 401–408 (2000)CrossRefGoogle Scholar
  73. 73.
    M. Rarey et al., A fast flexible docking method using an incremental construction algorithm. J. Mol. Biol. 261, 470–489 (1996)CrossRefGoogle Scholar
  74. 74.
    C.M. Venkatachalam et al., LigandFit: a novel method for the shape-directed rapid docking of ligands to protein active sites. J. Mol. Graph. Model. 21, 289–307 (2003)CrossRefGoogle Scholar
  75. 75.
    W. Welch et al., Hammerhead: fast, fully automated docking of flexible ligands to protein binding sites. Chem. Biol. 3, 449–462 (1996)CrossRefGoogle Scholar
  76. 76.
    P.A. Buckley et al., Protein-protein recognition, hydride transfer and proton pumping in the transhydrogenase complex. Structure 8, 809–815 (2000)CrossRefGoogle Scholar
  77. 77.
    B.K. Shoichet et al., Lead discovery using molecular docking. Curr. Opin. Chem. Biol. 6, 439–446 (2002)CrossRefGoogle Scholar
  78. 78.
    H.-J. Böhm, M. Stahl, The use of scoring functions in drug discovery applications, in Reviews in Computational Chemistry, ed (Wiley, Inc., New York, 2003), pp. 41–87Google Scholar
  79. 79.
    H. Gohlke, G. Klebe, Approaches to the description and prediction of the binding affinity of small-molecule ligands to macromolecular receptors. Angew. Chem. Int. Ed. Engl. 41, 2644–2676 (2002)CrossRefGoogle Scholar
  80. 80.
    H. Li et al., An effective docking strategy for virtual screening based on multi-objective optimization algorithm. BMC Bioinformatics 10, 58 (2009)CrossRefGoogle Scholar
  81. 81.
    P.S. Charifson et al., Consensus scoring: A method for obtaining improved hit rates from docking databases of three-dimensional structures into proteins. J. Med. Chem. 42, 5100–5109 (1999)CrossRefGoogle Scholar
  82. 82.
    R.D. Clark et al., Consensus scoring for ligand/protein interactions. J. Mol. Graph. Model. 20, 281–295 (2002)CrossRefGoogle Scholar
  83. 83.
    I.J. Enyedy, W.J. Egan, Can we use docking and scoring for hit-to-lead optimization? J. Comput. Aided Mol. Des. 22, 161–168 (2008)Google Scholar
  84. 84.
    T. Oprea, G. Marshall, Receptor-based prediction of binding affinities. Persp. Drug Discov. Des. 911, 35–61 (1998)Google Scholar
  85. 85.
    S. Betzi, et al., GFscore: a general nonlinear consensus scoring function for high-throughput docking. J. Chem. Inf. Model 46, 1704–1712 (2006)Google Scholar
  86. 86.
    M. Feher, Consensus scoring for protein-ligand interactions. Drug Discov. Today 11, 421–428 (2006)CrossRefGoogle Scholar
  87. 87.
    E. Perola, Minimizing false positives in kinase virtual screens. Proteins 64, 422–435 (2006)CrossRefGoogle Scholar
  88. 88.
    T.V. Pyrkov et al., Complementarity of hydrophobic properties in ATP-protein binding: a new criterion to rank docking solutions. Proteins 66, 388–398 (2007)CrossRefGoogle Scholar
  89. 89.
    V. Katritch, et al., Discovery of small molecule inhibitors of ubiquitin-like poxvirus proteinase I7L using homology modeling and covalent docking approaches. J. Comput. Aided Mol. Des. 21, 549–558 (2007)Google Scholar
  90. 90.
    G. Bianco, et al., Covalent docking using autodock: two-point attractor and flexible side chain methods. Protein Sci. (2015)Google Scholar
  91. 91.
    H.M. Kumalo et al., Theory and applications of covalent docking in drug discovery: merits and pitfalls. Molecules 20, 1984–2000 (2015)CrossRefGoogle Scholar
  92. 92.
    X. Fradera et al., Unsupervised guided docking of covalently bound ligands. J. Comput. Aided Mol. Des. 18, 635–650 (2004)CrossRefGoogle Scholar
  93. 93.
    L. Wang et al., Accurate and reliable prediction of relative ligand binding potency in prospective drug discovery by way of a modern free-energy calculation protocol and force field. J. Am. Chem. Soc. 137, 2695–2703 (2015)CrossRefGoogle Scholar
  94. 94.
    G.A. Ross, et al., One size does not fit all: the limits of structure-based models in drug discovery. J. Chem. Theory Comput. 9, 4266–4274 (2013)Google Scholar
  95. 95.
    E. Yuriev, et al., Challenges and advances in computational docking: 2009 in review. J. Mol. Recognit. 24, 149–164 (2011)Google Scholar
  96. 96.
    I.O. Donkor, Calpain inhibitors: a survey of compounds reported in the patent and scientific literature. Expert Opin. Ther. Pat. 21, 601–636 (2011)CrossRefGoogle Scholar
  97. 97.
    E. Perola et al., A detailed comparison of current docking and scoring methods on systems of pharmaceutical relevance. Proteins 56, 235–249 (2004)CrossRefGoogle Scholar
  98. 98.
    R.A. Friesner et al., Glide: a new approach for rapid, accurate docking and scoring. 1. Method and assessment of docking accuracy. J. Med. Chem. 47, 1739–1749 (2004)CrossRefGoogle Scholar
  99. 99.
    T. Schulz-Gasch, M. Stahl, Binding site characteristics in structure-based virtual screening: evaluation of current docking tools. J. Mol. Model. 9, 47–57 (2003)Google Scholar
  100. 100.
    A. Taube, Sensitivity, specificity and predictive values: a graphical approach. Stat. Med. 5, 585–591 (1986)Google Scholar
  101. 101.
    A. Agresti, Categorical data analysis, 2nd edn. (Wiley, Hoboken, 2002)CrossRefzbMATHGoogle Scholar
  102. 102.
    N. Mantel, W. Haenszel, Statistical aspects of the analysis of data from retrospective studies of disease. J. Natl. Cancer Inst. 22, 719–748 (1959)Google Scholar
  103. 103.
    T. Fawcett, An introduction to ROC analysis. Pattern Recogn. Lett. 27, 861–874 (2006)CrossRefGoogle Scholar
  104. 104.
    N.A. Obuchowski et al., ROC curves in clinical chemistry: uses, misuses, and possible solutions. Clin. Chem. 50, 1118–1125 (2004)CrossRefGoogle Scholar
  105. 105.
    W.J. Youden, Index for rating diagnostic tests. Cancer 3, 32–35 (1950)CrossRefGoogle Scholar
  106. 106.
    D. Hand, R. Till, A simple generalisation of the area under the ROC curve for multiple class classification problems. Mach. Learn. 45, 171–186 (2001)Google Scholar
  107. 107.
    X. Robin et al., pROC: an open-source package for R and S + to analyze and compare ROC curves. BMC Bioinformatics 12, 77 (2011)CrossRefGoogle Scholar
  108. 108.
    D. Bohning et al., Revisiting Youden’s index as a useful measure of the misclassification error in meta-analysis of diagnostic studies. Stat. Methods Med. Res. 17, 543–554 (2008)MathSciNetCrossRefGoogle Scholar
  109. 109.
    N. Novoselova et al., HUM calculator and HUM package for R: easy-to-use software tools for multicategory receiver operating characteristic analysis. Bioinformatics 30, 1635–1636 (2014)CrossRefGoogle Scholar
  110. 110.
    Z. Cai et al., Classification of lung cancer using ensemble-based feature selection and machine learning methods. Mol. BioSyst. 11, 791–800 (2015)CrossRefGoogle Scholar
  111. 111.
    J. Hu, et al., Comparison of three-dimensional ROC surfaces for clustered and correlated markers, with a proteomics application. Stat. Neerlandica, Wiley Online Library (2015)Google Scholar
  112. 112.
    B. Carstensen, et al. (2015). Epi: A Package for Statistical Analysis in Epidemiology. R package version 1.1.71. http://CRAN.R-project.org/package=Epi
  113. 113.
    W. Venables, B. Ripley. (2015). nnet: Feed-forward neural networks and multinomial log-linear models. R package version 7.3-11. http://CRAN.R-project.org/package=nnet
  114. 114.
    R Core Team. (2015). R: A language and environment for statistical computing. R Foundation for Statistical Computing. http://www.R-project.org/
  115. 115.
    C.N. Cavasotto, A.J. Orry, Ligand docking and structure-based virtual screening in drug discovery. Curr. Top. Med. Chem. 7, 1006–1014 (2007)CrossRefGoogle Scholar
  116. 116.
    C. McInnes, Virtual screening strategies in drug discovery. Curr. Opin. Chem. Biol. 11, 494–502 (2007)CrossRefGoogle Scholar
  117. 117.
    K.L. Mengersen, et al., Mixtures: Estimation and Applications, vol. 896 (Wiley, New York, 2011)Google Scholar
  118. 118.
    I.L. Hudson, et al., EMMIX skew classification of molecular ligand binding potency of calpain inhibitors. Mol. Inf. (in prep)Google Scholar
  119. 119.
    S. Lee, et al., Visualizing improved prognosis in psychiatric treatment via mixtures, SOMs and Chernoff faces, in Australian Statistical Conference, Adelaide, Australia, 2012, p. 131Google Scholar
  120. 120.
    I.L. Hudson, et al., Druggability in drug discovery: Self organising maps with a mixture discriminant approach, presented at the Austraian Statistical Conference, Adelaide, South Australia, 2012, p. 108Google Scholar
  121. 121.
    S.X. Lee, G.J. McLachlan, Model-based clustering and classification with non-normal mixture distributions. Stat. Methods Appl. 22, 427–454 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  122. 122.
    S.X. Lee, G.J. McLachlan, On mixtures of skew-normal and skew t-distributions. Adv. Data Anal. Classif. 7, 241–266 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  123. 123.
    S.X. Lee, G.J. McLachlan, EMMIX-uskew: An R package for fitting mixtures of multivariate skew t-distributions via the EM algorithm. J. Stat. Softw. 55, 1–22 (2013)Google Scholar
  124. 124.
    S. Lee, G.J. McLachlan, Finite mixtures of multivariate skew t-distributions: some recent and new results. Stat. Comput. 24, 181–202 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  125. 125.
    N. London et al., Covalent docking of large libraries for the discovery of chemical probes. Nat. Chem. Biol. 10, 1066–1072 (2014)CrossRefGoogle Scholar
  126. 126.
    X. Ouyang et al., CovalentDock: automated covalent docking with parameterized covalent linkage energy estimation and molecular geometry constraints. J. Comput. Chem. 34, 326–336 (2013)CrossRefGoogle Scholar
  127. 127.
    J. Polanski et al., Priveleged structures-dream or reality: preferential organization of azanaphthalene scaffold. Curr. Med. Chem. 19(13), 1921–1945 (2012)CrossRefGoogle Scholar
  128. 128.
    S.W. Kim, Bayesian and non-Bayesian mixture paradigms for clustering multivariate data: time series synchrony tests. PhD, University of South Australia, Adelaide, Australia (2011)Google Scholar
  129. 129.
    S. Zafar, et al., Linking ordinal log-linear models with correspondence analysis: an application to estimating drug-likeness in the drug discovery process, ed. by J. Piantadosi, R.S. Anderssen, J. Boland, MODSIM2013, in 20th International Congress on Modelling and Simulation (Modelling and Simulation Society of Australia and NZ, 2013), pp. 1945–1951. ISBN: 978-0-9872143-3-1. http://www.mssanz.org.au./modsim2013/I1/zafar.pdfGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • I. L. Hudson
    • 1
    Email author
  • S. Y. Leemaqz
    • 2
  • A. T. Neffe
    • 3
  • A. D. Abell
    • 4
  1. 1.School of Mathematical and Physical SciencesThe University of NewcastleNSWAustralia
  2. 2.Robinson Research InstituteThe University of AdelaideAdelaideAustralia
  3. 3.Institute of Biomaterial ScienceHelmholtz-Zentrum GeesthachtTeltowGermany
  4. 4.School of Physics and ChemistryThe University of AdelaideAdelaideAustralia

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