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Methods for Macromolecular Modeling (M3): Assessment of Progress and Future Perspectives

  • Hin Hark Gan
  • Tamar Schlick
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 24)

Abstract

The workshop on Methods for Macromolecular Modeling (M3), held at New York University on 12–14 October 2000, provided the 187 participants from Europe, Asia, the Americas, and the Middle East1, a forum for reviewing progress in the field, discussing promising developments for the future, and voicing concerns about multidisciplinary efforts. Inspired by these issues, we review progress in several key areas, discuss challenging problems in structural biology, and address scientific and cultural issues of mathematics/biology interface research. Specifically, we mention opportunities in structural genomics and more broadly structural biology (protein folding, protein folding disorders and disease, and energetic/conformational pathways in proteins); we also highlight emerging mathematical methods, unified molecular force fields, biomolecular dynamics simulations, and free energy computations. Finally, we discuss three obstacles to interdisciplinary research: quantitative problem formulations, formulation of benchmarks, and understanding the biological significance of research topics.

Keywords

Force Field Multigrid Method Chromatin Fiber Fold Type Free Energy Simulation 
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.

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References

  1. 1.
    F. Jacob, Of flies, mice, and men, Harvard University Press, 1998, p. 127.Google Scholar
  2. 2.
    T. Schlick, Computational molecular biophysics today: A confluence of methodological advances and complex biomolecular applications, J. Comp. Phys., 151, 1–9, May 1999. Special Volume on Computational Biophysics.CrossRefGoogle Scholar
  3. 3.
    S. Tsoka and C. A. Ouzounis, Recent developments and future directions in computational genomics, FEBS Letters 480, 42–48 (2000).PubMedCrossRefGoogle Scholar
  4. 4.
    M. Kanehisa, Post-genomics informatics, Oxford, New York, 2000.Google Scholar
  5. 5.
    J. A. Graves, Background and overview of comparative genomics. ILAR J. 39, 48–65 (1998).PubMedGoogle Scholar
  6. 6.
    M. L. Yaspo, Taking a functional genomics approach in molecular medicine. Trends Mol Med. 7, 494–501 (2001).PubMedCrossRefGoogle Scholar
  7. 7.
    D. Sankoff, and J. H. Nadeau, eds., Comparative genomics. Dordrecht: Kluwer Academic Publishers, 2000.Google Scholar
  8. 8.
    O. G. Vukmirovic and S. M. Tilghman, Exploring genome space, Nature 405, 820–822 (2000).PubMedCrossRefGoogle Scholar
  9. 9.
    D. Endy and R. Brent, Modelling cellular behaviour, Nature (Nature Insight), 409, 391–395 (2001).Google Scholar
  10. 10.
    S. K. Burley, An Overview of Structural Genomics, Nature Struct. Biol. 7 Suppl., 932–934 (2000).PubMedCrossRefGoogle Scholar
  11. 11.
    R. Sánchez, U. Pieper, F. Melo, N. Eswar, M. A. Martí-Renom, M. S. Mad-husudhan, N. Mirković, and A. Šali, Protein structure modeling for structural genomics. Nature Struct. Biol. 7 Suppl., 986–990 (2000).PubMedCrossRefGoogle Scholar
  12. A. Kolinski and J. Skolnick, Lattice models of protein folding, dynamics, and thermodynamics. Landes, Austin, Texas, 1996.Google Scholar
  13. 13.
    J. Clarke and C. M. Dobson, Folding and binding: Emerging themes in protein folding and assembly. Curr. Opin. Struct. Biol, 11, 67–59 (2001).CrossRefGoogle Scholar
  14. 14.
    K. W. Plaxco, K. T. Simons, and D. Baker, Contact order, transition state placement and the refolding rates of single domain proteins. J. Mol. Biol., 277, 985–994 (1998).PubMedCrossRefGoogle Scholar
  15. 15.
    R. B. Laughlin, D. Pines, J. Schmalian, B. P. Stojković, and P. Wolynes. The middle way. Proc. Natl. Acad. Sci. (USA), 97, 32–37 (2000).CrossRefGoogle Scholar
  16. 16.
    C. M. Dobson and M. Karplus, The fundamentals of protein folding: bringing together theory and experiment. Curr. Opin. Struct. Biol 9, 92–101 (1999).PubMedCrossRefGoogle Scholar
  17. 17.
    K. A. Dill and H. S. Chan, From Levinthal to pathways to funnels. Nature Struct. Biol. 4, 10–19 (1997).PubMedCrossRefGoogle Scholar
  18. 18.
    J. E. Shea and C. L. Brooks III, From folding theories to folding proteins: a review and assessment of simulation studies of protein folding and unfolding. Annu. Rev. Phys. Chem. 52, 499–535 (2001).PubMedCrossRefGoogle Scholar
  19. 19.
    A. Liwo, C. Czaplewski, J. Pillardy, and H. A. Scheraga, Cumulant-based expressions for the multibody terms for the correlation between local and electrostatic interactions in the united-residue force field. J. Chem. Phys. 115, 2323–2347 (2001).CrossRefGoogle Scholar
  20. 20.
    B. Honig, Protein folding: from the Levinthal paradox to structure prediction. J. Mol Biol., 293, 283–293 (1999).PubMedCrossRefGoogle Scholar
  21. 21.
    E. Alm and D. Baker, Matching theory and experiment in protein folding. Curr. Opin. Struct Biol., 9, 189–196 (1999).PubMedCrossRefGoogle Scholar
  22. 22.
    D. Baker, A surprising simplicity to protein folding. Nature, 405, 39–42 (2000).PubMedCrossRefGoogle Scholar
  23. 23.
    A. Fersht, Structure and mechanism in proteins science. Freeman, New York, 2000.Google Scholar
  24. 24.
    Liwo A, Kazmierkiewicz R, Czaplewski C, Groth M, Oldziej S, Wawak RJ, Rackovsky S, Pincus MR, Scheraga HA. United-residue force field for off-lattice protein-structure simulations: III. Origin of backbone hydrogen-bonding coop-erativity in united-residue potentials. J Comput Chem 1998;19:259–276.CrossRefGoogle Scholar
  25. 25.
    K.T. Simons, R. Bonneau, I. Ruczinski, and Baker, D. Ab initio Protein Structure Prediction of CASP III Targets Using ROSETTA. Proteins 37 S3, 171–176 (1999).CrossRefGoogle Scholar
  26. 26.
    J. Skolnick, A. Kolinski, and A. Ortiz, MONSSTER: a method for folding globular proteins with a small number of distance restraints. J. Mol Biol. 265, 217–241.Google Scholar
  27. 27.
    J. Lee, A. Liwo, and H. A. Scheraga, Energy-based de novo protein folding by conformational space annealing and an off-lattice united-residue force field: application to the 10–55 fragment of staphylococcal protein A and to apo calbindin D9K. Proc. Natl Acad. Sci. USA. 96, 2025–2030 (1999).PubMedCrossRefGoogle Scholar
  28. 28.
    H. H. Gan, A. Tropsha, and T. Schlick, Lattice protein folding with two and four-body statistical potentials. Proteins: Struct. Fund. Genet., 43, 161–174 (2001).CrossRefGoogle Scholar
  29. 29.
    S. W. Lockless and R. Ranganathan, Evolutionarily conserved pathways of energetic connectivity in protein families. Science, 286, 295–299 (1999).PubMedCrossRefGoogle Scholar
  30. 30.
    M. Doi and S. Edwards, The theory polymer dynamics. Oxford University Press, Oxford, 1986; P. J. de Gennes, Scaling concepts in polymer physics. Cornell University Press, Ithaca, New York, 1979.Google Scholar
  31. 31.
    S. B. Prusiner, Shattuck lecture — Neurodegenerative diseases and prions. New Eng. J. Med. 344, 1516–1526 (2001).PubMedCrossRefGoogle Scholar
  32. 32.
    C. M. Dobson, Protein misfolding, evolution and disease. Trends Biochem. Sci. 24(9), 329–367 (2001).CrossRefGoogle Scholar
  33. 33.
    I. V. Baskakov, G. Legname, S. B. Prusiner, and F. E. Cohen, Folding of prion to its native α-helical conformation is under kinetic control. J. Biol. Chem., April 16. 2001.Google Scholar
  34. 34.
    J. H. Viles, D. Donne, G. Kroon, S. B. Prusiner, F. E. Cohen, H. J. Dyson, and P. E. Wright, Local structural plasticity of the prion protein. Analysis of NMR relaxation dynamics. Biochemistry 40, 2743–2753 (2001).PubMedCrossRefGoogle Scholar
  35. 35.
    P. M. Harrison, H. S. Chan, S. B. Prusiner, and F. E. Cohen. Conformational propagation with prion-like characteristics in a simple model of protein folding. Protein Sci., 10, 819–835 (2001).PubMedCrossRefGoogle Scholar
  36. 36.
    A. Slepoy, R. R. Singh, F. Pazmandi, R. V. Kulkarni, and D. L. Cox, Statistical mechanics of prion diseases. Phys. Rev. Lett. 87, 058101 (2001).PubMedCrossRefGoogle Scholar
  37. 37.
    L. Duan and P. Kollman, Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. Science, 282, 740–744.Google Scholar
  38. 38.
    Protein Structure Prediction Center, http://predictioncenter.llnl.gov/.Google Scholar
  39. 39.
    A. Kolinski, M. R. Betancourt, D. Kihara, P. Rotkiewicz, and J. Skolnick, Generalized comparative modeling (GENECOMP): A combination of sequence comparison, threading, and lattice modeling for protein structure prediction and refinement. Proteins 44, 133–149 (2001).PubMedCrossRefGoogle Scholar
  40. 40.
    K. F. Lau and K. A. Dill, A lattice statistical mechanics model of the conformational and sequence spaces of proteins. Macromolecules 22, 2986–3997 (1989).CrossRefGoogle Scholar
  41. 41.
    M. Levitt and A. Warshel, Computer simulation of protein folding. Nature 253, 694–698 (1975).PubMedCrossRefGoogle Scholar
  42. 42.
    A. Liwo, S. Oldziej, M. R. Pincus, R. J. Wawak, S. Rackovsky, and H. A. Scheraga, A united-residue force-field for off-lattice protein-structure simulations. I. Functional forms and parameters of long-ramge side-chain interaction potentials from protein crystal data. J. Comput. Chem. 18, 849–872 (1997).CrossRefGoogle Scholar
  43. 43.
    A. Sali, E. Shakhnovich, and M. Karplus, How does a protein fold? Nature 369, 248–251 (1994).PubMedCrossRefGoogle Scholar
  44. 44.
    D. L. Beveridge and K. J. McConnell, Nucleic acids: theory and computer simulation, Y2K. Curr. Opin. Struct. Biol. 10, 182–196 (2000).PubMedCrossRefGoogle Scholar
  45. 45.
    W. Wang, O. Donini, C. M. Reyes, and P. A. Kollman, Biomolecular simulations: recent developments in force fields, simulations of enzyme catalysis, protein-ligand, protein-protein, and protein-nucleic acid noncovalent interactions. Annu. Rev. Biophys. Biomol. Struct. 30, 211–243 (2001).PubMedCrossRefGoogle Scholar
  46. 46.
    J. Huang, T. Schlick, and A. Vologodskii, Dynamics of site juxtaposition in supercoiled DNA. Proc. Natl. Acad. Sci. USA 98, 968–973 (2001).PubMedCrossRefGoogle Scholar
  47. 47.
    H. Jian, T. Schlick, and A. Vologodskii, Internal motion of supercoiled DNA: Brownian dynamics simulations of site juxtaposition. J. Mol. Biol. 284, 287–296 (1998).PubMedCrossRefGoogle Scholar
  48. 48.
    D. A. Beard and T. Schlick, Modeling salt-mediated electrostatics of macro-molecules: The discrete surface charge optimization algorithm and its application to the nucleosome. Biopolymers 58, 106–115 (2001).PubMedCrossRefGoogle Scholar
  49. 49.
    D. A. Beard and T. Schlick, Computational modeling predicts the structure and dynamics of chromatin fiber. Structure 9, 105–114 (2001).PubMedCrossRefGoogle Scholar
  50. 50.
    M. Feig, P. Rotkiewcz, A. Kolinski, J. Skolnick, and C. L. Brooks III, Accurate reconstruction of all-atom protein representations from side-chain-based low-resolution models. Proteins 41, 86–97 (2000).PubMedCrossRefGoogle Scholar
  51. 51.
    J. Aishima, R. Gitti, J. E. Noah, H. H. Gan, T. Schlick, and C. Wolberger, Crystal structure of MATalpha2 homeodomain-DNA complex contains a Hoogsteen base pair, submitted to Nature Struct. Biol, 2001.Google Scholar
  52. 52.
    T. Schlick, D. A. Beard. J. Huang, D. A. Strahs, and X. Qian, Computational challenges in simulating large DNA over long times. Computing in Science and Engineering, 38–51, Nov./Dec. 1999.Google Scholar
  53. 53.
    X. Qian and D. Strahs and T. Schlick Dynamic simulations of 13 TATA variants refine kinetic hypotheses of sequence/activity relationships. J. Mol. Biol. 308, 681–703 (2001).PubMedCrossRefGoogle Scholar
  54. 54.
    T. Schlick, Time-trimming tricks for dynamics simulations: splitting force updates to reduce computational work. Structure 9, R45–R53 (2001).PubMedCrossRefGoogle Scholar
  55. 55.
    D. Beard and T. Schlick, Modeling salt-mediated electrostatics of macromolecules: The Algorithm DiSCO (Discrete Charge Surface Charge Optimization) and its application to the nucleosome. Biopolymers 58, 106–115 (2001).PubMedCrossRefGoogle Scholar
  56. 56.
    J. Huang and T. Schlick and A. Vologodskii, Dynamics of site juxtaposition in supercoiled DNA. Proc. Natl. Acad. Sci USA 98, 968–973 (2001).PubMedCrossRefGoogle Scholar
  57. 57.
    D. Bai and A. Brandt, Multiscale computation of polymer models. In Multiscale Computational Methods in Chemistry and Physics, Eds. Brandt, A., Bernholc J. and Binder, K. NATO Science Series: Series III Computer and Systems Sciences, 2001.Google Scholar
  58. 58.
    T. Schlick and A. Brandt, A multigrid tutorial with applications to molecular dynamics, IEEE Comput. Sci. Engineer. 3, 78–83, Fall 1996.CrossRefGoogle Scholar
  59. 59.
    U. Trottenberg, C. Oosterlee, and A. Schüller, Multigrid. Academic Press, New York, 2001.Google Scholar
  60. 60.
    C. Sagui and T. Darden, Multigrid methods for classical molecular dynamics simulations. Preprint, 2000.Google Scholar
  61. 61.
    J. Lee, A. Liwo, D. R. Ripoll, J. Pillardy, J. A. Saunders, K. D. Gibson, and H. A. Scheraga, Hierarchical energy-based approach to protein-structure prediction: blind-test evaluation with CASP3 targets. Intl. J. Quantum Chem. 77, 90–117 (2000).CrossRefGoogle Scholar
  62. 62.
    J. A. McCammon, B. R. Gelin, and M. Karplus, Dynamics of folded proteins. Nature 267, 585–590 (1977).PubMedCrossRefGoogle Scholar
  63. 63.
    W. F. van Gunsteren and H. J. C. Berendsen, Algorithms for macromolecular dynamics and constraint dynamics. Mol. Phys. 34, 1311–1327 (1977).CrossRefGoogle Scholar
  64. 64.
    M. Levitt, Computer simulation of DNA double-helix dynamics. Cold Spring Harbor Symp. Quant. Biol. 47, 251–275 (1983).CrossRefGoogle Scholar
  65. 65.
    G. L. Seibel, U. C. Singh, and P. A. Kollman, A molecular dynamics simulation of double-helical B-DNA including counterions and water. Proc. Natl. Acad. Sci. USA 82, 6537–6540 (1985).PubMedCrossRefGoogle Scholar
  66. 66.
    M. Prabhakaran, S. C. Harvey, B. Mao, and J. A. McCammon, Molecular dynamics of phenylalanine transfer RNA. J. Biomol. Struct. Dynam. 1, 357–369 (1983).CrossRefGoogle Scholar
  67. 67.
    B. J. Alder and T. E. Wainwright, Studies in molecular dynamics. I. General method. J. Chem. Phys. 31, 459–466 (1959).CrossRefGoogle Scholar
  68. 68.
    A. Rahman and F. H. Stillinger, Molecular dynamics study of liquid water. J. Chem. Phys. 55, 3336–3359 (1971).CrossRefGoogle Scholar
  69. 69.
    W. B. Streett, D. J. Tildesley, and G. Saville, Multiple time step methods in molecular dynamics. Mol. Phys. 35, 639–648 (1978).CrossRefGoogle Scholar
  70. 70.
    H. Grubmüller, H. Heller, A. Windemuth, and K. Schulten, Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Mol. Sim. 6, 121–142 (1991).CrossRefGoogle Scholar
  71. 71.
    J. J. Biesiadecki and R. D. Skeel, Dangers of multiple-time-step methods. J. Comput. Phys. 109, 318–328 (1993).CrossRefGoogle Scholar
  72. 72.
    M. E. Tuckerman, B. J. Berne, and G. J. Martyna, Reversible multiple time scale molecular dynamics. J. Chem. Phys. 97, 1990–2001 (1992).CrossRefGoogle Scholar
  73. 73.
    B. Leimkuhler and S. Reich, Symplectic integration of constrained Hamiltonian systems. Math. Comput. 63, 589–605 (1994).CrossRefGoogle Scholar
  74. 74.
    R. D. Skeel, G. Zhang, and T. Schlick, A family of symplectic integrators: Stability, accuracy, and molecular dynamics applications. SIAM J. Sci. Comput. 18(1), 202–222, January 1997.CrossRefGoogle Scholar
  75. 75.
    B. J. Leimkuhler, S. Reich, and R. D. Skeel, Integration methods for molecular dynamics. In J. P. Mesirov, K. Schulten, and D. W. Sumners, editors, Mathematical Approaches to Biomolecular Structure and Dynamics, volume 82 of IMA Volumes in Mathematics and Its Applications, pages 161–186, New York, NY, 1996. Springer-Verlag.Google Scholar
  76. 76.
    E. Barth and T. Schlick, Overcoming stability limitations in biomolecular dynamics: I. Combining force splitting via extrapolation with Langevin dynamics in LN. J. Chem. Phys. 109, 1617–1632 (1998).CrossRefGoogle Scholar
  77. 77.
    B. Garcia-Archilla, J.M. Sanz-Serna, and R.D. Skeel, Long-time-step methods for oscillatory differential equations. SIAM J. Sci. Comput. 20, 930–963 (1998).CrossRefGoogle Scholar
  78. 78.
    J. A. Izaguirre, S. Reich, and R. D. Skeel, Longer time steps for molecular dynamics. J. Chem. Phys. 110, 9853–9864 (1999).CrossRefGoogle Scholar
  79. 79.
    J. M. Sanz-Serna and M. P. Calvo, Numerical Hamiltonian Problems. Chapman & Hall, London, England, 1994.Google Scholar
  80. 80.
    H. C. Andersen, Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys. 72, 2384–2393 (1980).CrossRefGoogle Scholar
  81. 81.
    S. Nosé, A molecular dynamics method for simulations in the canonical ensemble. Mol. Phys. 52, 255–268 (1984).CrossRefGoogle Scholar
  82. 82.
    S. Nosé, Constant temperature molecular dynamics methods. Prog. Theor. Phys. Suppl. 103, 1–46 (1991).CrossRefGoogle Scholar
  83. 83.
    G. J. Martyna, M. E. Tuckerman, D. J. Tobias, and M. L. Klein. Explicit reversible integrators for extended systems dynamics. Mol. Phys. 87, 1117–1157 (1996).CrossRefGoogle Scholar
  84. 84.
    T. Schlick, Time-trimming tricks for dynamic simulations: Splitting force updates to reduce computational work. Structure 9, R45–R53 (2001).PubMedCrossRefGoogle Scholar
  85. 85.
    P. Batcho, D. A. Case, and T. Schlick, Optimized particle-mesh Ewald/ multiple-timestep integration for molecular dynamics simulations. J. Chem. Phys. 115, 4003–4018 (2001).Google Scholar
  86. 86.
    R. Zhou, E. Harder, H. Xu, and B.J. Berne, Efficient multiple time step method for use with Ewald and particle mesh Ewald for large biomolecular systems. J. Chem. Phys. 115, 2348–2358 (2001).CrossRefGoogle Scholar
  87. 87.
    E. Barth and T. Schlick, Extrapolation versus impulse in multiple-timestepping schemes: II. Linear analysis and applications to Newtonian and Langevin dynamics. J. Chem. Phys. 109, 1632–1642 (1998).Google Scholar
  88. 88.
    E. Paci and M. Karplus, Unfolding proteins by external forces and temperature: The importance of topology and energetics. Proc. Natl. Acad. Sci. USA 97, 6521–6526 (2000).PubMedCrossRefGoogle Scholar
  89. 89.
    R. Elber, J. Melier, and R. Ölender, Stochastic path approach to compute atomically detailed trajectories: Application to the folding of C peptide. J. Phys. Chem. B 103, 899–911 (1999).CrossRefGoogle Scholar
  90. 90.
    G. Zou, R. D. Skeel, and S. Subramanian, Biased Brownian dynamics for rate constant calculation. Biophys. J. 79, 638–645 (2000).PubMedCrossRefGoogle Scholar
  91. 91.
    S. Duane, A. D. Kennedy, B. J. Pendleton, and D. Roweth. Hybrid Monte Carlo, Phys. Lett. B 195, 216–222 (1987).CrossRefGoogle Scholar
  92. 92.
    A. Brass, B. J. Pendleton, Y. Chen, and B. Robson, Hybrid Monte Carlo simulations theory and initial comparison with molecular dynamics. Biopolymers 33, 1307–1315 (1993).CrossRefGoogle Scholar
  93. 93.
    A. Brass, B. J. Pendleton, Y. Chen, and B. Robson, Hybrid Monte Carlo simulations theory and initial comparison with molecular dynamics. Biopolymers 33, 1307–1315 (1993).CrossRefGoogle Scholar
  94. 94.
    B. J. Berne and J. E. Straub, Novel methods of sampling phase space in the simulation of biological systems. Curr. Opin. Struct. Biol. 7, 181–189 (1997).PubMedCrossRefGoogle Scholar
  95. 95.
    A. Fischer, F. Cordes, and C. Süchtte, Hybrid Monte Carlo with adaptive temperature in mixed-canonical ensemble: Efficient conformational analysis of RNA. J. Comput. Chem. 19, 1689–1697 (1998).CrossRefGoogle Scholar
  96. 96.
    H. Senderowitz and W. C. Still, MC(JBW): Simple but smart Monte Carlo algorithm for free energy simulations of multiconformational molecules. J. Comput Chem. 19, 1736–1745 (1998).CrossRefGoogle Scholar
  97. 97.
    L. J. LaBerge and J. C. Tully, A rigorous procedure for combining molecular dynamics and Monte Carlo simulation algorithms. Chem. Phys. 260, 183–191 (2000).CrossRefGoogle Scholar
  98. 98.
    P. A. Kollman, I. Massova, C. Reyes, B. Kuhn, S. Huo, L. Chong, M. Lee, T. Lee, Y. Duan, W. Wang, O. Donini, P. Cieplak, J. Srinivasan, D. A. Case, and T. E. Cheatham, 3rd., Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models. Chem. Res. 33, 889–897 (2000).CrossRefGoogle Scholar
  99. 99.
    M. A. Eriksson, J. Pitera, P. A. Kollman, Prediction of the binding free energies of new TIBO-like HIV-1 reverse transcriptase inhibitors using a combination of PROFEC, PB/SA, CMC/MD, and free energy calculations. J. Med. Chem. 42, 868–881 (1999).PubMedCrossRefGoogle Scholar
  100. 100.
    G. Hummer and A. Szabo, Free energy reconstruction from nonequilibrium single-molecule pulling experiments. Proc. Natl. Acad. Sci. USA, 98, 3658–3661 (2000).CrossRefGoogle Scholar
  101. 101.
    A. R. Leach, Macromolecular modeling: principles and applications. Addison Wesley Longman, 1996.Google Scholar
  102. 102.
    H. Hu, R. H. Yun, and J. Hermans, Reversibility of free energy simulations: slow growth may have a unique advantage. (With a not on use of Ewald summation.), Mol. Sim., In Press.Google Scholar
  103. 103.
    B. Isralewitz, M. Gao, and K. Schulten, Steered molecular dynamics and mechanical functions of proteins. Curr. Opin. Struct. Biol. 11, 224–30 (2001).PubMedCrossRefGoogle Scholar
  104. 104.
    B. A. Berg and T. Neuhaus, Multicanonical ensemble: A new approach to simulate first-order phase transitions. Phys. Rev. Lett., 68, 9–12 (1992).CrossRefGoogle Scholar
  105. 105.
    A. Pollack, Scientists at work: Leroy Hood; A biotech superstar looks at the bigger picture. The New York Times, April 17, 2001.Google Scholar
  106. 106.
    C. L. Brooks III, M. Karplus, B. M. Pettitt, Proteins. A theoretical perspectives of dynamics, structure and thermodynamics. Adv. Chem. Phys. 71 (1988).Google Scholar
  107. 107.
    D. Poland and H. A. Scheraga, Theory of helix-coil transitions in biopolymers. Academic, New York, 1970.Google Scholar
  108. 108.
    C. Sagui and T. A. Darden, Molecular dynamics simulations of biomolecules: long-range electrostatic effects. Annu. Rev. Biophys. Biomol. Struct. 28, 155–179 (1999).PubMedCrossRefGoogle Scholar
  109. 109.
    T. Schlick and W. Olson, Supercoiled DNA energetics and dynamics by computer simulation. J. Mol. Biol. 223, 1089–1119 (1992).PubMedCrossRefGoogle Scholar
  110. 110.
    R. Samudrala and M. Levitt, Decoys ‘R’ Us: A database of incorrect conformations to improve protein structure prediction. Protein Sci. 9, 1399–1401 (2000).PubMedCrossRefGoogle Scholar
  111. 111.
    M. Vásquez, G. Némethy, and H. A. Scheraga, Conformational energy calculations on polypeptides and proteins. Chem. Rev. 94, 2183–2239 (1994).CrossRefGoogle Scholar
  112. 112.
    A. Abbott, Computer modellers seek out ‘Ten Most Wanted’ proteins. Nature 409, 4 (2001).PubMedCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Hin Hark Gan
    • 1
  • Tamar Schlick
    • 1
  1. 1.Department of Chemistry and Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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