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Algorithmic challenges in structure-based drug design and NMR structural biology

  • Research Article
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Frontiers of Electrical and Electronic Engineering

Abstract

The three-dimensional structure of a biomolecule rather than its one-dimensional sequence determines its biological function. At present, the most accurate structures are derived from experimental data measured mainly by two techniques: X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy. Because neither X-ray crystallography nor NMR spectroscopy could directly measure the positions of atoms in a biomolecule, algorithms must be designed to compute atom coordinates from the data. One salient feature of most NMR structure computation algorithms is their reliance on stochastic search to find the lowest energy conformations that satisfy the experimentally-derived geometric restraints. However, neither the correctness of the stochastic search has been established nor the errors in the output structures could be quantified. Though there exist exact algorithms to compute structures from angular restraints, similar algorithms that use distance restraints remain to be developed.

An important application of structures is rational drug design where protein-ligand docking plays a critical role. In fact, various docking programs that place a compound into the binding site of a target protein have been used routinely by medicinal chemists for both lead identification and optimization. Unfortunately, despite ongoing methodological advances and some success stories, the performance of current docking algorithms is still data-dependent. These algorithms formulate the docking problem as a match of two sets of feature points. Both the selection of feature points and the search for the best poses with the minimum scores are accomplished through some stochastic search methods. Both the uncertainty in the scoring function and the limited sampling space attained by the stochastic search contribute to their failures. Recently, we have developed two novel docking algorithms: a data-driven docking algorithm and a general docking algorithm that does not rely on experimental data. Our algorithms search the pose space exhaustively with the pose space itself being limited to a set of hierarchical manifolds that represent, respectively, surfaces, curves and points with unique geometric and energetic properties. These algorithms promise to be especially valuable for the docking of fragments and small compounds as well as for virtual screening.

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References

  1. Cavanaugh J, Fairbrother W J, Palmer A G III, Skelton N J. Protein NMR Spectroscopy: Principles and Practice. San Diego, CA: Academic Press, 1995

    Google Scholar 

  2. Brünger A T. X-PLOR: A System for X-ray Crystallography and NMR. New Haven, CT: Yale University Press, 1993

    Google Scholar 

  3. Schwieters C D, Kuszewski J J, Clore G M. Using Xplor-NIH for NMR molecular structure determination. Progress in Nuclear Magnetic Resonance Spectroscopy, 2006, 48(1): 47–62

    Article  Google Scholar 

  4. Güntert P. Automated NMR structure calculation with CYANA. Methods in Molecular Biology, 2004, 278: 353–378

    Google Scholar 

  5. Rieping W, Habeck M, Nilges M. Inferential structure determination. Science, 2005, 309(5732): 303–306

    Article  Google Scholar 

  6. Crippen G M, Havel T F. Distance Geometry and Molecular Conformations. New York, NY: John Wiley and Sons, Inc., 1988

    Google Scholar 

  7. Wang L, Kurochkin A V, Zuiderweg E R P. An iterative fitting procedure for the determination of longitudinal NMR cross-correlation rates. Journal of Magnetic Resonance, 2000, 144(1): 175–185

    Article  Google Scholar 

  8. Güntert P, Mumenthaler C, Wüthrich K. Torsion angle dynamics for NMR structure calculation with the new program DYANA. Journal of Molecular Biology, 1997, 273(1): 283–298

    Article  Google Scholar 

  9. Saxe J B. Embeddability of weighted graphs in k-space is strongly NP-hard. In: Proceedings of the 17th Allerton Conference on Communications, Control, and Computing. 1979, 480–489

  10. Berger B, Kleinberg J, Leighton F T. Reconstructing a three-dimensional model with arbitrary errors. Journal of the ACM, 1999, 46(2): 212–235

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang L, Mettu R, Donald B R. A polynomial-time algorithm for de novo protein backbone structure determination from nuclear magnetic resonance data. Journal of Computational Biology, 2006, 13(7): 1276–1288

    Article  MathSciNet  Google Scholar 

  12. Rieping W, Habeck M, Nilges M. Inferential structure determination. Supporting Online Material. Science, 2005, http://www.sciencemag.org/cgi/content/full/309/5732/303/DC1

  13. Habeck M, Nilges M, Rieping W. Bayesian inference applied to macromolecular structure determination. Physical Review E, 2005, 72: 031912

    Article  Google Scholar 

  14. Swendsen R H, Wang J S. Replica Monte Carlo simulation of spin-glasses. Physical Review Letters, 1986, 57(21): 2607–2609

    Article  MathSciNet  Google Scholar 

  15. Landau L D, Lifshitz E M. Statistical Physics, Volume 5. Oxford: Pergamon Press, 1980

    Google Scholar 

  16. Feller W. An Introduction to Probability Theory and Its Applications, Volume II. New York, NY: John Wiley and Sons, Inc., 1970

    Google Scholar 

  17. Dyer M, Sinclair A, Vigoda E, Weitz D. Mixing in time and space for lattice spin systems: A combinatorial view. Random Structures and Algorithms, 2004, 24(4): 461–479

    Article  MathSciNet  MATH  Google Scholar 

  18. Wang L, Mettu R, Donald B R. An algebraic geometry approach to backbone structure determination from NMR data. In: Proceedings of IEEE Computer Society Bioinformatics Conference. 2005, 235–246

  19. Wang L, Donald B R. Analysis of a systematic search-based algorithm for determining protein backbone structure from a minimal number of residual dipolar couplings. In: Proceedings of IEEE Computer Society Bioinformatics Conference. 2004, 319–330

  20. Wang L, Donald B R. Exact solutions for internuclear vectors and backbone dihedral angles from NH residual dipolar couplings in two media, and their application in a systematic search algorithm for determining protein backbone structure. Journal of Biomolecular NMR, 2004, 29(3): 223–242

    Article  Google Scholar 

  21. Wang L, Donald B R. An efficient and accurate algorithm for assigning nuclear Overhauser effect restraints using a rotamer library ensemble and residual dipolar couplings. In: Proceedings of IEEE Computer Society Bioinformatics Conference. 2005, 189–202

  22. Wang L, Donald B R. A data-driven, systematic search algorithm for structure determination of denatured or disordered proteins. In: Proceedings of IEEE Computer Society Bioinformatics Conference. 2006, 67–78

  23. Hu W, Wang L. Residual dipolar couplings: Measurements and applications to biomolecular studies. Annual Reports on NMR Spectroscopy, 2006, 58: 231–303

    Article  Google Scholar 

  24. Wang L, Mettu R, Lilien R, Donald B R. An exact algorithm for determining protein backbone structure from NH residual dipolar couplings. In: Proceedings of IEEE Computer Society Bioinformatics Conference. 2003, 611–612

  25. Kuntz I D, Blaney J M, Oatley S J, Langridge R L, Ferrin T E. A geometric approach to macromolecule-ligand interactions. Journal of Molecular Biology, 1982, 161(2): 269–288

    Article  Google Scholar 

  26. Abagyan R, Totrov M, Kuznetzov D. A new method for protein modeling and design: Applications to docking and structure prediction from the distorted native conformation. Journal of Computational Chemistry, 1994, 15(5): 488–506

    Article  Google Scholar 

  27. Morris G M, Goodsell D S, Halliday R S, Huey R, Hart W E, Belew R K, Olson A J. Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function. Journal of Computational Chemistry, 1998, 19(14): 1639–1662

    Article  Google Scholar 

  28. Claußen H, Buning C, Rarey M, Lengauer T. FlexE: Efficient molecular docking considering protein structure variations. Journal of molecular biology, 2001, 308(2): 377–395

    Article  Google Scholar 

  29. Jones G, Willett P, Glen R C, Leach A R, Taylor R. Development and validation of a genetic algorithm for flexible docking. Journal of Molecular Biology, 1997, 267(3): 727–748

    Article  Google Scholar 

  30. McMartin C, Bohacek R S. QXP: Powerful, rapid computer algorithms for structure-based drug design. Journal of Computer-Aided Molecular Design, 1997, 11(4): 333–344

    Article  Google Scholar 

  31. Jain A N. Surflex: Fully automatic flexible molecular docking using a molecular similarity-based search engine. Journal of Medicinal Chemistry, 2003, 46(4): 499–511

    Article  Google Scholar 

  32. McGann M R, Almond H R, Nicholls A, Grant J A, Brown F K. Gaussian docking functions. Biopolymers, 2003, 68(1): 76–90

    Article  Google Scholar 

  33. Taylor R D, Jewsbury P J, Essex J W. A review of proteinsmall molecule docking methods. Journal of Computer-Aided Molecular Design, 2002, 16(3): 151–166

    Article  Google Scholar 

  34. Friesner R A, Banks J L, Murphy R B, Halgren T A, Klicic J J, Mainz D T, Repasky M P, Knoll E H, Shelley M, Perry J K, Shaw D E, Francis P, Shenkin P S. Glide: A new approach for rapid, accurate docking and scoring. 1. Method and assessment of docking accuracy. Journal of Medicinal Chemistry, 2004, 47(7): 1739–1749

    Article  Google Scholar 

  35. Pei J, Wang Q, Liu Z, Li Q, Yang K L, Lai L. PSI-DOCK: Towards highly efficient and accurate flexible ligand docking. Proteins: Structure, Function, and Bioinformatics, 2006, 62(4): 934–946

    Article  Google Scholar 

  36. Venkatachalam C M, Jiang X, Oldfield T, Waldman M. LigandFit: A novel method for the shape-directed rapid docking of ligands to protein active sites. Journal of Molecular Graphics & Modelling, 2003, 21(4): 289–307

    Article  Google Scholar 

  37. Baxter C A, Murray C W, Clark D E, Westhead D R, Eldridge M D. Flexible docking using Tabu search and an empirical estimate of binding affinity. Proteins: Structure, Function, and Genetics, 1998, 33(3): 367–382

    Article  Google Scholar 

  38. Chen H M, Liu B F, Huang H L, Hwang S F, Ho S Y. SODOCK: Swarm optimization for highly flexible proteinligand docking. Journal of Computational Chemistry, 2007, 28(2): 612–623

    Article  Google Scholar 

  39. Korb O, Stützle T, Exner T E. Empirical scoring functions for advanced protein-ligand docking with PLANTS. Journal of Chemical Information and Modeling, 2009, 49(1): 84–96

    Article  Google Scholar 

  40. Totrov M, Abagyan R. Flexible ligand docking to multiple receptor conformations: A practical alternative. Current Opinion in Structural Biology, 2008, 18(2): 178–184

    Article  Google Scholar 

  41. Leach A R, Shoichet B K, Peishoff C E. Prediction of proteinligand interactions. Docking and scoring: Successes and gaps. Journal of Medicinal Chemistry, 2006, 49(20): 5851–5855

    Google Scholar 

  42. Warren G L, Andrews C W, Capelli A M, Clarke B, LaLonde J, Lambert M H, Lindvall M, Nevins N, Semus S F, Senger S, Tedesco G, Wall I D, Woolven J M, Peishoff C E, Head M S. A critical assessment of docking programs and scoring functions. Journal of Medicinal Chemistry, 2006, 49(20): 5912–5931

    Article  Google Scholar 

  43. Moitessier N, Englebienne P, Lee D, Lawandi J, Corbeil C R. Towards the development of universal, fast and highly accurate docking/scoring methods: A long way to go. British Journal of Pharmacology, 2008, 153(S1): S7–S26

    Article  Google Scholar 

  44. Erickson J A, Jalaie M, Robertson D H, Lewis R A, Vieth M. Lessons in molecular recognition: The effects of ligand and protein flexibility on molecular docking accuracy. Journal of Medicinal Chemistry, 2004, 47(1): 45–55

    Article  Google Scholar 

  45. Cornell W D, Cieplak P, Bayly C I, Gould I R, Merz Jr K M, Ferguson D M, Spellmeyer D C, Fox T, Caldwell J W, Kollman P A. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. Journal of the American Chemical Society, 1995, 117(19): 5179–5197

    Article  Google Scholar 

  46. Jorgensen W L, Tirado-Rives J. The OPLS potential funtions for proteins. Energy minimizations for crystals of cyclic peptides and crambin. Journal of the American Chemical Society, 1988, 110(6): 1657–1666

    Google Scholar 

  47. Jorgensen W L, Maxwell D S, Tirado-Rives J. Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids. Journal of the American Chemical Society, 1996, 118(45): 11225–11236

    Article  Google Scholar 

  48. Brooks B R, Bruccoleri R E, Olafson B D, States D J, Swaminathan S, Karplus M. CHARMM: A program for macromolecular energy, minimization, and dynamics calculations. Journal of Computational Chemistry, 1983, 4(2): 187–217

    Article  Google Scholar 

  49. MacKerell A D, Bashford D, Bellott M, Dunbrack R L, Evanseck J D, Field M J, Fischer S, Gao J, Guo H, Ha S, Joseph-McCarthy D, Kuchnir L, Kuczera K, Lau F T K, Mattos C, Michnick S, Ngo T, Nguyen D T, Prodhom B, Reiher W E, Roux B, Schlenkrich M, Smith J C, Stote R, Straub J, Watanabe M, Wiorkiewicz-Kuczera J, Yin D, Karplus M. All-atom empirical potential for molecular modeling and dynamics studies of proteins. Journal of Physical Chemistry B, 1998, 102(18): 3586–3616

    Article  Google Scholar 

  50. Halgren T A. Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94. Journal of Computational Chemistry, 1996, 17(5–6): 490–519

    Article  Google Scholar 

  51. Landau L D, Lifshitz E M. Quantum Physics, Volume 3. Oxford: Pergamon Press, 1980

    Google Scholar 

  52. Kohn W. Electronic structure of matter-wave functions and density functionals. Reviews of Modern Physics, 1999, 71(5): 1253–1266

    Article  Google Scholar 

  53. Kohn W, Meir Y, Makarov D E. van der Waals energies in density functional theory. Physical Review Letters, 1998, 80(19): 4153–4156

    Article  Google Scholar 

  54. Huang K. Statistical Mechanics. New York, NY: John Wiley and Sons, Inc., 1987

    MATH  Google Scholar 

  55. Baxter R J. Exactly Solved Models in Statistical Mechanics. London: Academic Press, 1982

    MATH  Google Scholar 

  56. Lebowitz J. Statistical mechanics: A selective review of two central issues. Reviews of Modern Physics, 1999, 71(2): 346–357

    Article  Google Scholar 

  57. Istrail S. Statistical mechanics, three-dimensionality and NPcompleteness: I. Universality of intractability of the partition functions of the Ising model across non-planar lattices. In: Proceedings of the 32nd ACM Symposium on the Theory of Computing (STOC00). 2000, 87–96

  58. Graves A P, Shivakumar D M, Boyce S E, Jacobson M P, Case D A, Shoichet B K. Rescoring docking hit lists for model cavity sites: Predictions and experimental testing. Journal of Molecular Biology, 2008, 377(3): 914–934

    Article  Google Scholar 

  59. Böhm H J. The computer program LUDI: A new method for the de novo design of enzyme inhibitors. Journal of Computer-Aided Molecular Design, 1992, 6(1): 61–78

    Article  Google Scholar 

  60. Böhm H J. LUDI: Rule-based automatic design of new substituents for enzyme inhibitor leads. Journal of Computer-Aided Molecular Design, 1992, 6(6): 593–606

    Article  Google Scholar 

  61. Rarey M, Kramer B, Lengauer T, Klebe G. A fast flexible docking method using an incremental construction algorithm. Journal of Molecular Biology, 1996, 261(3): 470–489

    Article  Google Scholar 

  62. Krammer A, Kirchhoff P D, Jiang X, Venkatachalam C M, Waldman M. LigScore: A novel scoring function for predicting binding affinities. Journal of Molecular Graphics & Modelling, 2005, 23(5): 395–407

    Article  Google Scholar 

  63. Eldridge M D, Murray C W, Auton T R, Paolini G V, Mee R P. Empirical scoring functions: I. The development of a fast empirical scoring function to estimate the binding affinity of ligands in receptor complexes. Journal of Computer-Aided Molecular Design, 1997, 11(5): 425–445

    Article  Google Scholar 

  64. Murray C W, Auton T R, Eldridge M D. Empirical scoring functions. II. The testing of an empirical scoring function for the prediction of ligand-receptor binding affinities and the use of Bayesian regression to improve the quality of the model. Journal of Computer-Aided Molecular Design, 1998, 12(5): 503–519

    Article  Google Scholar 

  65. Wang R, Liu L, Lai L, Tang Y. A new empirical method for estimating the binding affinity of a protein-ligand complex. Journal of Molecular Modeling, 1998, 4(12): 379–394

    Article  Google Scholar 

  66. Wang R, Lai L, Wang S. Further development and validation of empirical scoring functions for structure-based binding affinity prediction. Journal of Computer-Aided Molecular Design, 2002, 16(1): 11–26

    Article  Google Scholar 

  67. Halgren T A, Murphy R B, Friesner R A, Beard H S, Frye L L, Pollard W T, Banks J L. Glide: A new approach for rapid, accurate docking and scoring. 2. Enrichment factors in database screening. Journal of Medicinal Chemistry, 2004, 47(7): 1750–1759

    Article  Google Scholar 

  68. Gohlke H, Hendlich M, Klebe G. Knowledge-based scoring function to predict protein-ligand interactions. Journal of Molecular Biology, 2000, 295(2): 337–356

    Article  Google Scholar 

  69. Velec H F G, Gohlke H, Klebe G. DrugScore(CSD)-knowledge-based scoring function derived from small molecule crystal data with superior recognition rate of nearnative ligand poses and better affinity prediction. Journal of Medicinal Chemistry, 2005, 48(20): 6296–6303

    Article  Google Scholar 

  70. DeWitte R S, Shakhnovich E I. SMoG: de novo design method based on simple, fast, and accurate free energy estimate. 1. Methodology and supporting evidence. Journal of the American Chemical Society, 1996, 118(47): 11733–11744

    Article  Google Scholar 

  71. Muegge I. PMF scoring revisited. Journal of Medicinal Chemistry, 2006, 49(20): 5895–5902

    Article  Google Scholar 

  72. Lovell S C, Word J M, Richardson J S, Richardson D C. The penultimate rotamer library. Proteins: Structure, Function, and Genetics, 2000, 40(3): 389–408

    Article  Google Scholar 

  73. Jones G, Willett P, Glen R C. Molecular recognition of receptor sites using a genetic algorithm with a description of desolvation. Journal of Molecular Biology, 1995, 245(1): 43–53

    Article  Google Scholar 

  74. Dorigo M, Stützle T. Ant Colony Optimization. Cambridge, MA: MIT Press, 2004

    Book  MATH  Google Scholar 

  75. Leach A R, Kuntz I D. Conformational analysis of flexible ligands in macromolecular receptor sites. Journal of Computational Chemistry, 1992, 13(6): 730–748

    Article  Google Scholar 

  76. Ulrich E L, Akutsu H, Doreleijers J F, Harano Y, Ioannidis Y E, Lin J, Livny M, Mading S, Maziuk D, Miller Z, Nakatani E, Schulte C F, Tolmie D E, Kent Wenger R, Yao H, Markley J L. BioMagResBank. Nucleic Acids Research, 2008, 36(suppl 1): D402–D408

    Google Scholar 

  77. Debye P, Hückel E. The theory of electrolytes. I. Lowering of freezing point and related phenomena. Physikalische Zeitschrift, 1923, 24: 185–206

    Google Scholar 

  78. Nicholls A, Honig B. A rapid finite difference algorithm, utilizing successive over-relaxation to solve the Poisson-Boltzmann equation. Journal of Computational Chemistry, 1991, 12(4): 435–445

    Article  Google Scholar 

  79. Holst M, Saied F. Multigrid solution of the Poisson-Boltzmann equation. Journal of Computational Chemistry, 1993, 14(1): 105–113

    Article  Google Scholar 

  80. Kirkwood J G, Poirier J C. The statistical mechanical basis of the Debye-Hüchel theory of strong electrolytes. Journal of Physical Chemistry, 1954, 58(8): 591–596

    Article  Google Scholar 

  81. Chern S S, Chen W, Lam K L. Lectures on Differential Geometry. Singapore: World Scientific Publishing Co., 1999

    MATH  Google Scholar 

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Authors and Affiliations

  1. College of Computer Science and Technology, The Joint Center for Systems Biology of Jilin University and the University of Georgia, Jilin University, Changchun, 130012, China

    Lincong Wang, Shuxue Zou & Yao Wang

  2. Key Laboratory of Symbol Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun, 130012, China

    Lincong Wang & Shuxue Zou

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  1. Lincong Wang
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  2. Shuxue Zou
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  3. Yao Wang
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Correspondence to Lincong Wang.

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Lincong WANG received his Ph.D. degree in biochemistry from Michigan State University in 1998 and then did a postdoctoral research with Prof. Erik Zuiderweg in the Biophysical Research Division, the University of Michigan. During that period of time, his research focused on the quantification of biochemical functions of proteins using various biochemical and biophysical techniques. After switched to computer science in 2001, he first joined Prof. Bruce Donald’s laboratory in Dartmouth Computer Science Department and did research on the design, analysis and implementation of algorithms for NMR structure computation using high-throughput experimental data. After spent a few years in the structure research group of the Medicinal Chemistry Department of Boehringer Ingelheim Pharma KG, he came to the College of Computer Science and Technology of Jilin University in 2010. His current research is in the broad area of computer-aided drug design with an emphasis in the design, analysis and implementation of algorithms for protein-protein docking, the analysis of protein-ligand interactions and target identification.

Shuxue ZOU received her M.Sc. and Ph.D. degrees in the College of Computer Science and Technology, Jilin University, China, in 2002 and 2009, respectively. She is currently a lecture in the college. Her research interests are computational intelligence, pattern recognition, protein structure prediction, and computer-aided drug design.

Yao WANG received her B.Sc. and M.Sc. degrees in electronic engineering from Jilin University, China, in 2004 and 2007, respectively, M.Sc. degree in computer science from Uppsala University, Sweden, in 2007, and completed Ph.D. degree in bioinformatics at Jilin University in 2011. Her research interests include cancer genomic data analysis and DNA-protein interaction.

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Wang, L., Zou, S. & Wang, Y. Algorithmic challenges in structure-based drug design and NMR structural biology. Front. Electr. Electron. Eng. 7, 69–84 (2012). https://doi.org/10.1007/s11460-012-0193-z

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