Journal of Chemical Physics
Feedback | Help | Exit
The Journal of Chemical Physics
   
 
 
 
Previous Article
Nonadiabatic simulation study of photoisomerization of azobenzene: Detailed mechanism and load-resisting capacity
Nonadiabatic dynamical simulations were carried out to study cis-to-trans isomerization of azobenzene under laser irradiation and/or external mechanical loads. We used a semiclassical electron-radiati...
Next Article
Phase diagram of a model of nanoparticles in electrolyte solutions
We obtain accurate fluid-fluid coexistence curves for a recent simple model of interacting nanoparticles that includes the effects of ion-dispersion forces. It has been proposed that these ion-dispers...

Preserving the Boltzmann ensemble in replica-exchange molecular dynamics

J. Chem. Phys. 129, 164112 (2008); doi:10.1063/1.2989802

Published 27 October 2008

You are not logged in to this journal. Log in

Ben Cooke1 and Scott C. Schmidler2
1Department of Mathematics, Duke University, Durham, North Carolina 27708-0251, USA
2Department of Statistical Science, Program in Computational Biology and Bioinformatics, and Program in Structural Biology and Biophysics, Duke University, Durham, North Carolina 27708-0251, USA
We consider the convergence behavior of replica-exchange molecular dynamics (REMD) [Sugita and Okamoto, Chem. Phys. Lett. 314, 141 (1999)] based on properties of the numerical integrators in the underlying isothermal molecular dynamics (MD) simulations. We show that a variety of deterministic algorithms favored by molecular dynamics practitioners for constant-temperature simulation of biomolecules fail either to be measure invariant or irreducible, and are therefore not ergodic. We then show that REMD using these algorithms also fails to be ergodic. As a result, the entire configuration space may not be explored even in an infinitely long simulation, and the simulation may not converge to the desired equilibrium Boltzmann ensemble. Moreover, our analysis shows that for initial configurations with unfavorable energy, it may be impossible for the system to reach a region surrounding the minimum energy configuration. We demonstrate these failures of REMD algorithms for three small systems: a Gaussian distribution (simple harmonic oscillator dynamics), a bimodal mixture of Gaussians distribution, and the alanine dipeptide. Examination of the resulting phase plots and equilibrium configuration densities indicates significant errors in the ensemble generated by REMD simulation. We describe a simple modification to address these failures based on a stochastic hybrid Monte Carlo correction, and prove that this is ergodic. ©2008 American Institute of Physics
History: Received 16 April 2008; accepted 5 September 2008; published 27 October 2008
Permalink: http://link.aip.org/link/?JCPSA6/129/164112/1
BUY THIS ARTICLE   (US$28)
Download HTML Download Sectioned HTML Download PDF (3936 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 31.15.xv
    Molecular dynamics and other numerical methods in atomic and molecular physics
  • 02.70.Ns
    Molecular dynamics and particle methods
  • YEAR: 2008

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (52)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. Y. Sugita and Y. Okamoto, Chem. Phys. Lett. 314, 141 (1999).
  2. C. J. Geyer, Markov chain Monte Carlo maximum likelihood, in Computing Science and Statistics: Proceedings of the 23rd Symposium on Interface, 1991, pp. 156–163.
  3. P. H. Nguyen, Y. Mu, and G. Stock, Proteins: Struct., Funct., Genet. 60, 485 (2005).
  4. M. M. Seibert, A. Patriksson, B. Hess, and D. van der Spoel, J. Mol. Biol. 354, 173 (2005).
  5. W. Zhang, C. Wu, and Y. Duan, J. Chem. Phys. 123, 154105 (2005).
  6. B. Cooke and S. C. Schmidler, “Statistical prediction and molecular dynamics simulation,” Biophys. J. (in press).
  7. D. A. Beck, G. W. White, and V. Daggett, J. Struct. Biol. 157, 514 (2007).
  8. X. Periole and A. E. Mark, J. Chem. Phys. 126, 014903 (2007).
  9. A. E. Roitberg, A. Okur, and C. Simmerling, J. Phys. Chem. B 111, 2415 (2007).
  10. N. Madras and Z. Zheng, Random Struct. Algorithms 1, 66 (2003).
  11. D. Woodard, S. C. Schmidler, and M. Huber, “Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions,” Ann. Appl. Probab. (to be published).
  12. N. Bhatnagar and D. Randall, “Torpid mixing of simulated tempering on the Potts model,” in Proceedings of the 15th ACM/SIAM Symposium on Discrete Algorithms (SODA), 2004, pp. 478–487.
  13. D. Woodard, S. C. Schmidler, and M. Huber, “Sufficient conditions for torpid mixing of parallel and simulated tempering on multimodal distributions,” Electron. J. Probab. (submitted).
  14. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, New York, 1987).
  15. D. J. Evans and G. P. Morriss, Statistical Mechanics of Non-Equilibrium Liquids (Academic, New York, 1990).
  16. D. Frenkel and B. Smit, Understanding Molecular Simulation (Academic, New York, 1996).
  17. A. R. Leach, Molecular Modelling: Principles and Applications (Addison Wesley Longman, New York, 1996).
  18. P. Billingsley, Probability and Measure, 3rd ed. (Wiley, New York, 1995).
  19. G. H. Choe, Computational Ergodic Theory (Springer-Verlag, Berlin, 2005).
  20. For ease of exposition we suppress formal statement of certain technical conditions; e.g., all sets and transformations considered are assumed to be pi-measurable, and limits hold pi-almost everywhere.
  21. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).
  22. V. I. Arnold, Mathematical Methods of Classical Mechanics 2nd ed. (Springer-Verlag, Berlin, 1989).
  23. P. J. Channell and C. Scovel, Nonlinearity 3, 231 (1990).
  24. H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsterenand, A. DiNola, and J. R. Haak, J. Chem. Phys. 81, 3684 (1984).
  25. X. Daura, B. Juan, D. Seebach, W. F. van Gunsteren, and A. E. Mark, J. Mol. Biol. 280, 925 (1998).
  26. X. Daura, K. Gademann, B. Jaun, D. Seebach, and W. F. van Gunsteren, Angew. Chem., Int. Ed. 38, 236 (1999).
  27. A. E. Garcia and K. Y. Sanbonmatsu, Proc. Natl. Acad. Sci. U.S.A. 99, 2782 (2002).
  28. L. J. Smith, X. Daura, and W. F. van Gunsteren, Proteins: Struct., Funct., Genet. 48, 487 (2002).
  29. H. Nymeyer and A. E. Garcia, Proc. Natl. Acad. Sci. U.S.A. 100, 13934 (2003).
  30. D. A. Pearlman et al., Comput. Phys. Commun. 91, 1 (1995).
  31. J. C. Phillips et al., J. Comput. Chem. 26, 1781 (2005).
  32. E. Lindahl, B. Hess, and D. van der Spoel, J. Mol. Model. 7, 306 (2001).
  33. T. Morishita, J. Chem. Phys. 113, 2976 (2000).
  34. S. Nosé, J. Chem. Phys. 81, 511 (1984).
  35. W. G. Hoover, Phys. Rev. A 31, 1695 (1985).
  36. R. G. Winkler, V. Kraus, and P. Reineker, J. Chem. Phys. 102, 9018 (1995).
  37. G. J. Martyna, M. L. Klein, and M. Tuckerman, J. Chem. Phys. 97, 2635 (1992).
  38. S. D. Bond, B. J. Leimkuhler, and B. B. Laird, J. Comput. Phys. 151, 114 (1999).
  39. S. Nosé, J. Phys. Soc. Jpn. 70, 75 (2001).
  40. B. B. Laird and B. J. Leimkuhler, Phys. Rev. E 68, 016704 (2003).
  41. B. J. Leimkuhler and C. R. Sweet, J. Chem. Phys. 121, 108 (2004).
  42. S. Duane, A. D. Kennedy, B. J. Pendleton, and D. Roweth, Phys. Lett. B 195, 216 (1987).
  43. R. W. Pastor, in The Molecular Dynamics of Liquid Crystals, edited by G. R. Luckhurst and C. A. Veracini (Kluwer Academic, Dordrecht, 1994), pp. 85–138.
  44. W. K. Hastings, Biometrika 57, 97 (1970).
  45. R. M. Neal, “Probabilistic inference using Markov chain Monte Carlo methods,” Technical Report No. CRG-TR-93-1, University of Toronto, 1993.
  46. J. S. Liu, Monte Carlo Strategies in Scientific Computing (Springer-Verlag, Berlin, 2001).
  47. S. P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability (Springer-Verlag, Berlin, 1993).
  48. A. Brünger, C. Brooks III, and M. Karplus, Chem. Phys. Lett. 105, 495 (1984).
  49. J. Mattingly, A. M. Stuart, and D. J. Higham, Stochastic Proc. Appl. 101, 185 (2002).
  50. G. O. Roberts and R. L. Tweedie, Bernoulli 2, 341 (1996).
  51. G. O. Roberts and J. S. Rosenthal “Examples of adaptive MCMC,” J. Comp. Graph. Stat. (unpublished).
  52. S. Toxvaerd, Phys. Rev. E 47, 343 (1993).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics