Skip to main content
SpringerLink
Log in

Replica Exchange Molecular Dynamics Method for Protein Folding Simulation

  • Protocol
Protein Folding Protocols

Part of the book series: Methods in Molecular Biology™ ((MIMB,volume 350))

Abstract

Understanding protein folding is one of the most challenging problems remaining in molecular biology. In this chapter, a highly parallel replica exchange molecular dynamics (REMD) method and its application to protein folding are described. The REMD method couples molecular dynamics trajectories with a temperature exchange Monte Carlo process for efficient sampling of the conformational space. A series of replicas are run in parallel at temperatures ranging from the desired temperature to a high temperature at which the replica can easily surmount the energy barriers. From time to time the configurations of neighboring replicas are exchanged and this exchange is accepted or rejected based on a Metropolis acceptance criterion that guarantees the detailed balance. Two example protein systems, one α-helix and one β-hairpin, are used as case studies to demonstrate the power of the algorithm. Up to 64 replicas of solvated protein systems are simulated in parallel over a wide range of temperatures. The simulation results show that the combined trajectories in temperature and configurational space allow a replica to overcome free energy barriers present at low temperatures. These large-scale simulations also reveal detailed results on folding mechanisms, intermediate state structures, thermodynamic properties, and the temperature dependences for both protein systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Brooks, C. L., Onuchic, J. N., and Wales, D. J. (2001) Taking a walk on a landscape. Science 293, 612–613.

    Article  CAS  PubMed  Google Scholar 

  2. Dobson, C. M., Sali, A., and Karplus, M. (1998) Protein folding: a perspective from theory and experiment. Angrew Chem. Int. Edit. Engl. 37, 868–893.

    Article  Google Scholar 

  3. Brooks, C. L., Gruebele, M., Onuchic, J. N., and Wolynes, P. G. (1998) Chemical physics of protein folding. Proc. Natl. Acad. Sci. USA 95, 11,037–11,038.

    Article  CAS  PubMed  Google Scholar 

  4. Zhou, Y. and Karplus, M. (1999) Interpreting the folding kinetics of helical proteins. Nature 401, 400–403.

    CAS  PubMed  Google Scholar 

  5. Zhou, R., Huang, X., Margulius, C. J., and Berne, B. J. (2004) Hydrophobic collapse in multidomain protein folding. Science 305, 1605–1609.

    Article  CAS  PubMed  Google Scholar 

  6. Daggett, V. and Levitt, M. (1993) Realistic simulations of native-protein dynamics in solution and beyond. Annu. Rev. Biophys. Biomol. Struct. 22, 353–380.

    Article  CAS  PubMed  Google Scholar 

  7. Duan, Y. and Kollman, P. A. (1998) Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. Science 282, 740–744.

    Article  CAS  PubMed  Google Scholar 

  8. Frantz, D. D., Freeman, D. L., and Doll, J. D. (1990) Reducing quasi-ergodic behavior in Monte Carlo simulations by J-Walking. Applications to atomic clusters. J. Chem. Phys. 93, 2769–2784.

    Article  CAS  Google Scholar 

  9. Freeman, D. L., Frantz, D. D., and Doll, J. D. (1992) Extending j walking to quantum systems: applications to atomic clusters. J. Chem. Phys. 97, 5713.

    Article  Google Scholar 

  10. Zhou, R. and Berne, B. J. (1997) Smart walking: a new method for boltzmann sampling of protein confromations. J. Chem. Phys. 107, 9185–9196.

    Article  CAS  Google Scholar 

  11. Andricioaei, I. and Straub, J. E. (1997) On Monte Carlo and molecular dynamics methods inspired by Tsallis statistics: methodology, optimization, and application to atomic clusters. J. Chem. Phys. 107, 9117–9124.

    Article  CAS  Google Scholar 

  12. Berg, B. A. and Neuhaus, T. (1991) Multicanonical algorithms for first order phase transitions. Phys. Lett. B. 267, 249–253.

    Article  Google Scholar 

  13. Hukushima, K. and Nemoto, K. (1996) Exchange monte carlo method and application to spin glass simulations. J. Phys. Soc. Japan 65, 1604–1608.

    Article  CAS  Google Scholar 

  14. Marinari, E., Parisi, G., and Ruiz-Lorenzo, J. J. (1998) Numerical simulations of spin glass systems. In: Spin Glass and Random Fields, (Young, A. P., ed.), World Scientific, Singapore, pp. 59.

    Google Scholar 

  15. Lyubarsev, A. P., Martsinovski, A. A., Shevkunov, S. V., and Vorontsov-Velyaminov, P. N. (1992) New approach to monte-carlo calculation of the free-energy-method of expanded ensembles. J. Chem. Phys. 96, 1776–1793.

    Article  Google Scholar 

  16. Marinari, E. and Parisi, G. (1992) Simulated tempering: a new Monte Carlo scheme. Europhys. Lett. 19, 451–458.

    Article  CAS  Google Scholar 

  17. Stolovitzky, G. and Berne, B. J. (2000) Catalytic tempering: a method for sampling rough energy landscapes by monte carlo Proc. Natl. Acad. Sci. USA 97, 11,164–11,169.

    Article  CAS  PubMed  Google Scholar 

  18. Piela, L., Kostrowicki, J., and Scheraga, H. A. (1989) The multipleninima problem in the conformational analysis of molecules. Deformation of the protein energy hypersurface by the diffusion equation method. J. Phys. Chem. 93, 3339–3346.

    Article  CAS  Google Scholar 

  19. Kostrowicki J. A. and Scheraga, H. A. (1992) Application of the diffusion equiation method for global optimization to oligopeptides. J. Phys. Chem. 96, 7442–7449.

    Article  CAS  Google Scholar 

  20. Berne, B. J. and Straub, J. E. (1997) Novel methods of sampling phase space in the simulation of biological systems. Curr. Opin. Struct. Biol. 7, 181–189.

    Article  CAS  PubMed  Google Scholar 

  21. Sugita, Y. and Okamoto, Y. (2000) Replica-exchange multicanonical algorithm and multi-canonical replica-exchange method for simulating systems with rough energy landscape. Chem. Phys. Lett. 329, 261–270.

    Article  CAS  Google Scholar 

  22. Garcia, A. E. and Sanbonmatsu, K. Y. (2002) Alpha-helical stabilization by side chain shielding of backbone hydrogen bonds. Proc. Nat. Acad. Sci. USA 99, 2782–2787.

    Article  CAS  PubMed  Google Scholar 

  23. Zhou, R., Berne, B. J., and Germain, R. (2001) The free energy landscape for betahairpin folding in explicit water. Proc. Natl. Acad. Sci. USA 98, 14,931–14,936.

    Article  CAS  PubMed  Google Scholar 

  24. Rhee, Y. M. and Pande, V. S. (2003) Multiplexed-replica exchange molecular dynamics method for protein folding simulation. Biophys. J. 84, 775–786.

    Article  CAS  PubMed  Google Scholar 

  25. Ohkubo, Y. Z. and Brooks, C. L. (2003) Exploring flory’s isolated-pair hypothesis: Statistical mechanics of helixcoil transitions in polyalanine and the c-peptide from rnase a. Proc. Natl. Acad. Sci. USA 100, 13,916–13,921.

    Article  CAS  PubMed  Google Scholar 

  26. Zhou, R. (2003) Trp-cage: folding free energy landscape in explicit water. Proc. Natl. Acad. Sci. USA 100, 13,280–13,285.

    Article  CAS  PubMed  Google Scholar 

  27. Nymeyer, H. and Garcia, A. E. (2003) Interfacial folding of a membrane peptide: replica exchange simulations of walp in a dppc bilayer. Biophys. J. 84, 381A.

    Google Scholar 

  28. Zhou, R. (2003) Trp-cage: folding free energy landscape in explicit water. Proc. Natl. Acad. Sci. USA 100, 13,280–13,285.

    Article  CAS  PubMed  Google Scholar 

  29. Im, W., Feig, M., and Brooks, C. L. (2003) An implicit membrane generalized born theory for the study of structure, stability, and interactions of membrane proteins. Biophys. J. 85, 2900–2918.

    Article  CAS  PubMed  Google Scholar 

  30. Kokubo, H. and Okamoto, Y. (2004) Self-assembly of transmembrane helices of bacteriorhodopsin by a replica-exchange monte carlo simulation. Chem. Phys. Lett. 392, 168–175.

    Article  CAS  Google Scholar 

  31. Munoz, V., Thompson, P. A., Hofrichter, J., and Eaton, W. A. (1997) Folding dynamics and mechanism of β-hairpin formation. Nature 390, 196–199.

    Article  CAS  PubMed  Google Scholar 

  32. Zhou, R. (2004) Sampling protein folding free energy landscape: coupling replica exchange method with p3me/respa algorithm. J. Mol. Graph Model. 22, 451–463.

    Article  CAS  PubMed  Google Scholar 

  33. Williams, S., Causgrove, T. P., Gilmanshin, R., et al. (1996) Fast events in protein folding: Helix melting and formation in a small peptide. Biochemistry 35, 691–697.

    Article  CAS  PubMed  Google Scholar 

  34. Lockhart, D. J. and Kim, P. S. (1993) Electrostatic screening of charge and dipole interactions with the helix backbone. Science 260, 198–202.

    Article  CAS  PubMed  Google Scholar 

  35. Thompson, P. A., Eaton, W. A., and Hofrichter, J. (1997) Laser temperature jump study of the helix<=>coil kinetics of an alanine peptide interpreted with a kinetic zipper’ model. Biochemistry 36, 9200–9210.

    Article  CAS  PubMed  Google Scholar 

  36. Lednev, I. K., Karnoup, A. S., Sparrow, M. C., and Asher, S. A. (2001) Transient UV Raman spectroscopy finds no crossing barrier between the peptide alphahelix and fully random coil conformation. J. Am. Chem. Soc. 123, 2388–2392.

    Article  CAS  PubMed  Google Scholar 

  37. Kitchen, D. B., Hirata, F., Westbrook, J. D., Levy, R. M., Kofke, D., and Yarmush, M. (1990) Conserving energy during molecular dynamics simulations of water, proteins and proteins in water. J. Comp. Chem. 11, 1169–1180.

    Article  CAS  Google Scholar 

  38. Sayle, R. A. and Milner-White, E. J. (1995) Rasmol: biomolecular graphics for all. Trends Biochem. Sci. 20, 374–376.

    Article  CAS  PubMed  Google Scholar 

  39. Jorgensen, W. L., Maxwell, D., and Tirado-Rives, J. (1996) Development and testing of the opls all-atom force field on conformational energetics and properties of organic liquids. J. Am. Chem. Soc. 118, 11,225–11,236.

    Article  CAS  Google Scholar 

  40. Hockney, R. W. and Eastwood, J. W. (1989) Computer Simulation Using Particles. Adam Hilger, Bristol-New York, NY.

    Google Scholar 

  41. Tuckerman, M., Berne, B. J., and Martyna, G. J. (1992) Reversible multiple time scale molecular dynamics. J. Chem. Phys. 97, 1990–2001.

    Article  CAS  Google Scholar 

  42. Zhou, R. and Berne, B. J. (1995) A new molecular dynamics method combining the reference system propagator algorithm with a fast multipole method for simulating proteins and other complex systems. J. Chem. Phys. 103, 9444–9459.

    Article  CAS  Google Scholar 

  43. Zhou, R., Harder, E., Xu, H., and Berne, B. J. (2001) Efficient multiple time step method for use with ewald and particle mesh ewald for large biomolecular systems. J. Chem. Phys. 115, 2348–2358.

    Article  CAS  Google Scholar 

  44. Vila, J. A., Ripoll, D. R., and Scheraga, H. A. (2000) Physical reasons for the unusual alpha-helix stabilization afforded by charged or neutral polar residues in alanine-rich peptides. Proc. Natl. Acad. Sci. USA 97, 13,075–13,079.

    Article  CAS  PubMed  Google Scholar 

  45. Sundaralingam, M. and Sekharudu, Y. (1989) Water-inserted alpha-helical segments implicate reverse turns as folding intermediates. Science 244, 1333–1337.

    Article  CAS  PubMed  Google Scholar 

  46. Munoz, V., Henry, E. R., Hofrichter, J., and Eaton, W. A. (1998) A statistical mechanical model for β-hairpin kinetics. Proc. Natl. Acad. Sci. USA 95, 5872–5879.

    Article  CAS  PubMed  Google Scholar 

  47. Blanco, F. J., Rivas, G., and Serrano, L. (1994) A short linear peptide that folds in a native stable β-hairpin in aqueous solution. Nature Struc. Bio. 1, 584–590.

    Article  CAS  Google Scholar 

  48. Pande, V. S. and Rokhsar, D. S. (1999) Molecular dynamics simulations of unfolding and refolding of a β-hairpin fragment of protein g. Proc. Natl. Acad. Sci. USA 96, 9062–9067.

    Article  CAS  PubMed  Google Scholar 

  49. Zagrovic, B., Sorin, E. J., and Pande, V. S. (2001) β-hairpin folding simulation in atomistic detail using an implicit solvent model. J. Mol. Biol. 313, 151–169.

    Article  CAS  PubMed  Google Scholar 

  50. Dinner, A. R., Lazaridis, T., and Karplus, M. (1999) Understanding β-hairpin formation. Proc. Natl. Acad. Sci. USA 96, 9068–9073.

    Article  CAS  PubMed  Google Scholar 

  51. Garcia, A. E. and Sanbonmatsu, K. Y. (2001) Exploring the energy landscape of a β hairpin in explicit solvent. Proteins 42, 345–354.

    Article  CAS  PubMed  Google Scholar 

  52. Roccatano, D., Amadei, A., Nola, A. D., and Berendsen, H. J. (1999) A molecular dynamics study of the 41-56 β-hairpin from b1 domain of protein g. Protein Sci. 10, 2130–2143.

    Article  Google Scholar 

  53. Kolinski, A., Ilkowski, B., and Skolnick, J. (1999) Dynamics and thermodynamics of β-hairpin assembly: insights from various simulation techniques. Biophys. J. 77, 2942–2952.

    Article  CAS  PubMed  Google Scholar 

  54. Ma, B. and Nussinov, R. (2000) Molecular dynamics simulations of a β-hairpin fragment of protein G: balance between side-chain and backbone forces. J. Mol. Bio. 296, 1091–1104.

    Article  CAS  Google Scholar 

  55. Ferrenberg, A. M. and Swendsen, R. H. (1989) Optimized Monte Carlo data analysis. Phys. Rev. Lett. 63, 1195–1198.

    Article  CAS  PubMed  Google Scholar 

  56. Klimov, D. K. and Thirumalai, D. (2000) Mechanisms and kinetics of beta-hairpin formation. Proc. Natl. Acad. Sci. USA 97, 2544–2549.

    Article  CAS  PubMed  Google Scholar 

  57. Dinner, A. R. (1999) Monte carlo simulations of protein folding. PhD Thesis, Harvard University, Cambridge, MA.

    Google Scholar 

  58. Walser, P., Mark, A. E., and van Gunsteren, W. F. (2000) On the temperature and pressure dependence of a range of properties of a type of water model commonly used in high-temperature protein unfolding simulations. Biophys. J. 78, 2752–2760.

    Article  CAS  PubMed  Google Scholar 

  59. Zhou, R. and Berne, B. J. (2002) Can a continuum solvent model reproduce the free energy landscape of a β-hairpin folding in water? Proc. Natl. Acad. Sci. USA 99, 12,777–12,782.

    Article  CAS  PubMed  Google Scholar 

  60. Zhou, R. (2003) Free energy landscape of protein folding in water: explicit vs. implicit solvent. Proteins 53, 148–161.

    Article  CAS  PubMed  Google Scholar 

  61. Yoda, T., Sugita, Y., and Okamoto, Y. (2000) Comparisons of force fields for proteins by generalized-ensemble simulations. J. Chem. Phys. 113, 6042–6051.

    Article  Google Scholar 

  62. Zhou, R., Krilov, G., and Berne, B. J. (2004) Comment on “can a continuum solvent model reproduce the free energy landscape of a beta-hairpin folding in water?.” J. Phys. Chem. B. 108, 7528–7530.

    Article  CAS  Google Scholar 

  63. Sugita, Y. and Okamoto, Y. (1999) Replica-exchange molecular dynamics method for protein folding. Chem. Phys. Lett. 314, 141–151.

    Article  CAS  Google Scholar 

  64. Duane, S., Kennedy, A. D., Pendleton, B. J., and Roweth, D. (1987) Hybrid Monte Carlo. Phys. Lett. B 195, 216–222.

    Article  CAS  Google Scholar 

  65. Sugita, Y., Kitao, A., and Okamoto, Y. (2000) Multidimensional replica-exchange method for free-energy calculations. Chem. Phys. Lett. 329, 261–270.

    Article  CAS  Google Scholar 

  66. Whitfield, T. W., Bu, L., and Straub, J. E. (2002) Generalized parallel sampling. Physica A 305, 157–171.

    Article  Google Scholar 

  67. Liu, P., Huang, X., Zhou, R., and Berne, B. J. (2006) Hydrophobic aided replica exchange method. J. Chem. Phys. 110, in press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, Columbia University, New York, NY

    Ruhong Zhou

  2. Computational Biology Center, IBM Thomas J. Watson Research Center, Yorktown Heights, NY

    Ruhong Zhou

Authors
  1. Ruhong Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratory of Biochemistry, National Cancer Institute, National Institutes of Health, Bethesda, MD

    Yawen Bai

  2. Center for Cancer Research Nanobiology Program SAIC, National Cancer Institute-Frederick, Frederick, MD

    Ruth Nussinov

  3. Department of Human Genetics, Sackler School of Medicine, Tel Aviv University, Tel Aviv, Israel

    Ruth Nussinov

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Humana Press Inc.

About this protocol

Cite this protocol

Zhou, R. (2007). Replica Exchange Molecular Dynamics Method for Protein Folding Simulation. In: Bai, Y., Nussinov, R. (eds) Protein Folding Protocols. Methods in Molecular Biology™, vol 350. Humana Press. https://doi.org/10.1385/1-59745-189-4:205

Download citation

  • DOI: https://doi.org/10.1385/1-59745-189-4:205

  • Publisher Name: Humana Press

  • Print ISBN: 978-1-58829-622-1

  • Online ISBN: 978-1-59745-189-5

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics

Search

Navigation