Conformational Dynamics Simulations of Proteins

Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 4)


Molecular dynamics (MD) simulations of proteins provide descriptions of atomic motions, which allow to relate observable properties of proteins to microscopic processes. Unfortunately, such MD simulations require an enormous amount of computer time and, therefore, are limited to time scales of nanoseconds. We describe first a fast multiple time step structure adapted multipole method (FAMUSAMM) to speed up the evaluation of the computationally most demanding Coulomb interactions in solvated protein models, secondly an application of this method aiming at a microscopic understanding of single molecule atomic force microscopy experiments, and, thirdly, a new method to predict slow conformational motions at microsecond time scales.


Hierarchy Level Force Profile Rupture Force Fast Multipole Method Water Bridge 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Levitt and Shneior Lifson. Refinement of protein conformation using a macromolecular energy minimization procedure. J. Mol. Biol, 46: 269–279, 1969.CrossRefGoogle Scholar
  2. 2.
    J. A. McCammon, B. R. Gelin, and M. Karplus. Dynamics of folded proteins. Nature (London), 267: 585–590, 1977.CrossRefGoogle Scholar
  3. 3.
    W. F. van Gunsteren and H. J. C. Berendsen. Algorithms for macromolecular dynamics and constraint dynamics. Mol. Phys., 34(5): 1311–1327, 1977.CrossRefGoogle Scholar
  4. 4.
    Olle Edholm, Oliver Berger, and Fritz Jähnig. Structure and fluctuations of bacteriorhodopsin in the purple membrane. J. Mol. Biol, 250: 94–111, 1995.CrossRefGoogle Scholar
  5. 5.
    M. Levitt and R. Sharon. Accurate simulation of protein dynamics in solution. Proc. Natl. Acad. Sci. USA, 85: 7557–7561, 1988.CrossRefGoogle Scholar
  6. 6.
    Walter Nadler, Axel T. Brünger, Klaus Schulten, and Martin Karplus. Molecular and stochastic dynamics of proteins. Proc. Natl. Acad. Sci. USA, 84: 7933–7937, Nov. 1987.CrossRefGoogle Scholar
  7. 7.
    H. Kovacs, A.E. Mark, J. Johansson, and W.F. van Gunsteren. The effect of environment on the stability of an integral membrane helix: Molecular dynamics simulations of surfactant protein C in chloroform, methanol and water. J. Mol. Biol, 247: 808–822, 1995.Google Scholar
  8. 8.
    G.H. Peters, D.M.F van Aalten, O. Edholm, S. Toxvaerd, and R. Bywater. Dynamics of proteins in different solvent systems: Analysis of essential motion in lipases. Biophys. J., 71: 2245–2255, 1996.CrossRefGoogle Scholar
  9. 9.
    M. C. Nuss, W. Zinth, W. Kaiser, E. Kölling, and D. Oesterhelt. Femtosecond spectroscopy of the first events of the photochemical cycle in bacteriorhodopsin. Chem. Phys. Lett, 117(1): 1–7, 1985.CrossRefGoogle Scholar
  10. 10.
    Feng Zhou, Andreas Windemuth, and Klaus Schulten. Molecular-dynamis study of the proton pump cycle of bacteriorhodopsin. Biochem., 32(9): 2291–2306, 1993.CrossRefGoogle Scholar
  11. 11.
    B. Leimkuhler and R. D. Skeel. J. Comp. Phys., 112: 117, 1994.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    B.J. Leimkuhler, S. Reich, and R. D. Skeel. Integration methods for molecular dynamics. In Mathematical approaches to biomolecular structure and dynamics, Seiten 161–185, New York, 1996. Springer.Google Scholar
  13. 13.
    R. D. Skeel, G. H. Zhang, and T. Schlick. A family of symplectic integrators: Stability, accuracy, and molecular dynamics applications. SIAM J. Scient. COMP., 18: 203–222, 1997.MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    A. Ahmad and L. Cohen. A numerical integration scheme for the iV-body gravitational problem. J. Comp. Phys., 12: 389–402, 1973.zbMATHCrossRefGoogle Scholar
  15. 15.
    W. B. Streett, D. J. Tildesley, and G. Saville. Multiple time step methods in molecular dynamics. Mol. Phys., 35: 639–648, 1978.CrossRefGoogle Scholar
  16. 16.
    R. C. Y. Chin, G. W. Hedstrom, and F. A. Howes. Considerations on Solving Problems with Multiple Scales. Academic Press, Orlando, Florida, 1985.Google Scholar
  17. 17.
    Andreas Windemuth. Dynamiksimulation von Makromolekülen. Diplomarbeit, Technical University of Munich, Physics Department, T 30, James-Franck-Street, 8046 Garching, August 1988.Google Scholar
  18. 18.
    Mark E. Tuckerman, Glenn J. Martyna, and Bruce J. Berne. Molecular dynamics algorithm for condensed systems with multiple time scales. J. Chem. Phys., 93(2): 1287–1291, Jul. 1990.CrossRefGoogle Scholar
  19. 19.
    Helmut Grubmüller, Helmut Heller, Andreas Windemuth, and Klaus Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Mol. Sim., 6: 121–142, 1991.CrossRefGoogle Scholar
  20. 20.
    Mark E. Tuckerman and Bruce J. Berne. Molecular dynamics algorithm for multiple time scales: Systems with disparate masses. J. Chem. Phys., 94(2): 1465–1469, January 1991.CrossRefGoogle Scholar
  21. 21.
    Mark E. Tuckerman, Bruce J. Berne, and Glenn J. Martyna. Molecular dynamics algorithm for multiple time scales: Systems with long range forces. J. Chem. Phys., 94(10): 6811–6815, May 1991.CrossRefGoogle Scholar
  22. 22.
    Robert D. Skeel, Jeffrey J. Biesiadecki, and Daniel Okunbor. Symplectic integration for macromolecular dynamics. In Proceedings of the International Conference Computation of Differential Equations and Dynamical Systems. World Scientific Publishing Co., 1992. in press.Google Scholar
  23. 23.
    Robert D. Skeel and Jeffrey J. Biesiadecki. Symplectic integration with variable stepsize. Ann. Num. Math., 1: 191–198, 1994.MathSciNetzbMATHGoogle Scholar
  24. 24.
    Helmut Grubmüller. Molekulardynamik von Proteinen auf langen Zeitskalen. Doktorarbeit, Technische Universität München, Germany, Jan. 1994.Google Scholar
  25. 25.
    D. Okunbor and R. D. Skeel. Explicit canonical methods for Hamiltonian systems. Working document, Numerical Computing Group, University of Illinois at Urbana-Champaign, 1991.Google Scholar
  26. 26.
    Andreas Windemuth. Advanced Algorithms for Molecular Dynamics Simulation: The Program PMD. ACS Books, 1995.Google Scholar
  27. 27.
    D. D. Humphreys, R. A. Friesner, and B. J. Berne. Simulated annealing of a protein in a continuum solvent by multiple-time-step molecular dynamics. J. Phys. Chem., 99: 10674–10685, 1995.CrossRefGoogle Scholar
  28. 28.
    P. Procacci, T. Darden, and M. Marchi. A very fast molecular dynamics method to simulate biomolecular systems with realistic electrostatic interactions. J. Phys. Chem., 100: 10464–10468, 1996.CrossRefGoogle Scholar
  29. 29.
    S. J. Stuart, R. Zhou, and B. J. Berne. Molecular dynamics with multiple time scales: The selection of efficient reference system propagators. J. Chem. Phys., 105: 1426–1436, 1996.CrossRefGoogle Scholar
  30. 30.
    R. Zhou and B. J. Berne. A new molecular dynamics method combining the reference system propagator algorithm with a fast multipole method for simulating proteins and other complex systems. J. Phys. Chem., 103: 9444–9459, 1995.CrossRefGoogle Scholar
  31. 31.
    T. Schlick, E. Bartha, and M. Mandziuk. Biomolecular dynamics at long timesteps: Bridging the timescale gap between simulation and experimentation. Ann. Rev. Biophys. Biom. Structure, 26: 181–222, 1997.CrossRefGoogle Scholar
  32. 32.
    Andrew. W. Appel. An efficient program for many-body simulation. SIAM J. Sci. Stat. Comput., 6(1): 85–103, January 1985.MathSciNetCrossRefGoogle Scholar
  33. 33.
    Josh Barnes and Piet Hut. A hierarchical o(n log n) force-calculation algorithm. Nature (London), 324: 446–449, December 1986.CrossRefGoogle Scholar
  34. 34.
    L. Greengard and V. Rokhlin. On the evaluation of electrostatic interactions in molecular modeling. Chem. Scr., 29A: 139–144, 1989.Google Scholar
  35. 35.
    James F. Leathrum and John A. Board. The parallel fast multipole algorithm in three dimensions. Technical report, Dept. of Electrical Engineering, Duke University, Durham, 1992.Google Scholar
  36. 36.
    C. Niedermeier and P. Tavan. A structure adapted multipole method for electrostatic interactions in protein dynamics. J. Chem. Phys., 101: 734–748, 1994.CrossRefGoogle Scholar
  37. 37.
    Christoph Niedermeier. Modellierung elektrostatischer Wechselwirkungen in Proteinen: Eine strukturadaptierte Multipolmethode. Doktorarbeit, Ludwig-Maximilians-Universität, München, Germany, 1995.Google Scholar
  38. 38.
    C. Niedermeier and P. Tavan. Fast version of the structure adapted multipole method — efficient calculation of electrostatic forces in protein dynamics. Mol. Sim., 17: 57–66, 1996.CrossRefGoogle Scholar
  39. 39.
    B. A. Luty, I. G. Tironi, and W. F. van Gunsteren. Lattice-sum methods for calculating electrostatic interactions in molecular simulations. J. Chem. Phys., 103: 3014–3021, 1995.CrossRefGoogle Scholar
  40. 40.
    U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen. The smooth particle mesh ewald method. J. Chem. Phys., 103: 8577, 1995.CrossRefGoogle Scholar
  41. 41.
    Brock A. Luty, Ilario G. Tironi, and Wilfried F. van Gunsteren. Lattice-sum methods for calculating electrostatic interactions in molecular simulations. J. Chem. Phys., 103: 3014–3021, 1995.CrossRefGoogle Scholar
  42. 42.
    Brock A. Luty and Wilfried F. van Gunsteren. Calculating electrostatic interactions using the particleparticle particlemesh method with nonperiodic long-range interactions. J. Phys. Chem., 100: 2581–2587, 1996.CrossRefGoogle Scholar
  43. 43.
    Bernhard R. Brooks, Robert E. Bruccoleri, Barry D. Olafson, David J. States, S. Swaminathan, and Martin Karplus. CHARMM: A program for macromolecular energy, minimization, and dynamics calculations. J. Comp. Chem., 4(2): 187–217, 1983.CrossRefGoogle Scholar
  44. 44.
    Charles L. Brooks III, B. Montgomery Pettitt, and Martin Karplus. Structural and energetic effects of truncating long ranged interactions in ionic and polar fluids. J. Chem. Phys., 83(11): 5897–5908, December 1985.CrossRefGoogle Scholar
  45. 45.
    Richard J. Loncharich and Bernard R. Brooks. The effects of truncating longrange forces on protein dynamics. Proteins, 6: 32–45, 1989.CrossRefGoogle Scholar
  46. 46.
    M. Eichinger, H. Grubmüller, H. Heller, and P. Tavan. FAMUSAMM: An algorithm for rapid evaluation of electrostatic interaction in molecular dynamics simulations. J. Comp. Chem., 18: 1729–1749, 1997.CrossRefGoogle Scholar
  47. 47.
    M. Eichinger. Paralleler schneller Multipolalgorithmus mit Mehrschrittverfahren für Molekulardynamiksimulationen. Diplomarbeit, Ludwig-Maximilians-Universität, München, Germany, 1995.Google Scholar
  48. 48.
    M. Eichinger, H. Grubmüller, and H. Heller. User Manual for EGO-V1II, Release 2.0. Theoretische Biophysik, Institut für Medizinische Optik, Ludwig-Maximilians-Universität, Theresienstr. 37, D-80333 München, Germany, 1995. Electronic access:
  49. 49.
    Helmut Grubmüller, Berthold Heymann, and Paul Tavan. Ligand binding: Molecular mechanics calculation of the streptavidin-biotin rupture force. Science, 271(5251): 997–999, 1996.CrossRefGoogle Scholar
  50. 50.
    E.-L. Florin, V. T. Moy, and H. E. Gaub. Adhesion forces between individual ligand-receptor pairs. Science, 264: 415–417, Apr. 15 1994.CrossRefGoogle Scholar
  51. 51.
    N. M. Green. Avidin. Adv. Protein Chem., 29: 85, 1975.CrossRefGoogle Scholar
  52. 52.
    S. Miyamoto and P. A. Kollman. Absolute and relative binding free energy calculations of the interaction of biotin and its analogs with streptavidin using molecular dynamics/free energy perturbation approaches. Proteins, 16: 226–245, 1993.CrossRefGoogle Scholar
  53. 53.
    S. Izrailev, S. Stepaniants, M. Baisera, Y. Oono, and K. Schulten. Molecular dynamics study of unbinding of the avidin-biotin complex. Biophys. J., 72: 1568–1581, 1997.CrossRefGoogle Scholar
  54. 54.
    Evan Evans and Ken Ritchie. Dynamic strength of molecular adhesion bonds. Biophys. J., 72: 1541, 1997.CrossRefGoogle Scholar
  55. 55.
    J. S. Griffith. Nature (London), 215: 1043–1044, 1967.CrossRefGoogle Scholar
  56. 56.
    S. B. Prusiner. Science, 252: 1515–1522, 1991.CrossRefGoogle Scholar
  57. 57.
    Hans Frauenfelder, Sthephen G. Sligar, and Peter G. Wolynes. The energy landscape and motions of proteins. Science, 254: 1598–1603, 1991.CrossRefGoogle Scholar
  58. 58.
    R. H. Austin, K. W. Beeson, L. Eisenstein, H. Frauenfelder, and L.C. Gunsalus. Dynamics of ligand binding to myoglobin. Biochem., 14(24): 5355–5373, 1975.CrossRefGoogle Scholar
  59. 59.
    Helmut Grubmüller. Predicting slow structural transitions in macromolecular systems: conformational flooding. Phys. Rev. E, 52: 2893, 1995.CrossRefGoogle Scholar
  60. 60.
    T. Huber, A. E. Torda, and W. F. van Gunsteren. Local elevation: A method for improving the searching properties of molecular dynamics simulation. J. of Computer-Aided Molecular Design, 8: 695–708, 1994.CrossRefGoogle Scholar
  61. 61.
    J. C. Gower. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53: 325, 1966.MathSciNetzbMATHGoogle Scholar
  62. 62.
    A. Amadei, A. B. M. Linssen, and H. J. C. Berendsen. Essential dynamics of proteins. Proteins, 17: 412–425, 1993.CrossRefGoogle Scholar
  63. 63.
    Steven Hayward, Akio Kitao, and Nobuhiro Gō. Harmonic and anharmonic aspects in the dynamics of BPTI: A normal mode analysis and principal component analysis. Physica Scripta, 3: 936–943, 1994.Google Scholar
  64. 64.
    H. Grubmüller, N. Ehrenhofer, and P. Tavan. Conformational dynamics of proteins: Beyond the nanosecond time scale. In M. Peyard, editor, Proceedings of the Workshop ‘Nonlinear Excitations in Biomolecules’, May 30-June 4, 1994, Les H ouches (France), Seiten 231–240. Centre de Physique des Houches (France), Springer-Verlag, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  1. 1.Institut für Medizinische Optik, Theoretische BiophysikLudwig-Maximilians-Universität MünchenMünchenGermany

Personalised recommendations