Skip to main content
SpringerLink
Log in

Transition Pathways, Rare Events and Related Questions

  • Reference work entry
  • First Online:
Encyclopedia of Applied and Computational Mathematics

  • 100 Accesses

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 999.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 999.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 999.99
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. Allen, R.J., Warren, P.B., ten Wolde, P.R.: Sampling rare switching events in biochemical networks. Phys. Rev. Lett. 94(1), 018104 (2005)

    Article  Google Scholar 

  2. Bhatt, D., Zhang, B.W., Zuckerman, D.M.: Steady-state simulations using weighted ensemble path sampling. J. Chem. Phys. 133(1), 014110 (2010)

    Article  Google Scholar 

  3. Bolhuis, P.G., Chandler, D., Dellago, C., Geissler, P.L.: Transition path sampling: throwing ropes over rough mountain passes, in the dark. Annu. Rev. Phys. Chem. 53, 291–318 (2002)

    Article  Google Scholar 

  4. Chandler, D.: Statistical mechanics of isomerization dynamics in liquids and the transition state approximation. J. Chem. Phys. 68(6), 2959 (1978)

    Article  MathSciNet  Google Scholar 

  5. Chandler, D.: Introduction to Modern Statistical Mechanics, vol 1. Oxford University Press, New York (1987)

    Google Scholar 

  6. Chodera, J.D., Singhal, N., Pande, V.S., Dill, K.A., Swope, W.C.: Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics. J. Chem. Phys. 126, 155101 (2007)

    Article  Google Scholar 

  7. Church, B.W., Orešič, M., Shalloway, D.: Tracking metastable states to free-energy global minima. In: Pardalos, P.M., Shalloway, D., Xue, G. (eds.) DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding, pp. 41–64. American Mathematical Society, Providence (1996)

    Google Scholar 

  8. Darve, E., Pohorille, A.: Calculating free energies using average force. J. Chem. Phys. 115(2), 9169–9183 (2001)

    Article  Google Scholar 

  9. Darve, E., Rodríguez-Gómez, D., Pohorille, A.: Adaptive biasing force method for scalar and vector free energy calculations. J. Chem. Phys. 128(14), 144120 (2008)

    Article  Google Scholar 

  10. Dellago, C., Bolhuis, P.G.: Transition path sampling and other advanced simulation techniques for rare events. Adv. Polym. Sci. 221, 167–233 (2009)

    Google Scholar 

  11. Dellago, C., Bolhuis, P.G., Csajka, F.S., Chandler, D.: Transition path sampling and the calculation of rate constants. J. Chem. Phys. 108(5), 1964–1977 (1998)

    Article  Google Scholar 

  12. Dellago, C., Bolhuis, P.G., Geissler, P.L.: Transition path sampling. Adv. Chem. Phys. 123, 1–78 (2002)

    Google Scholar 

  13. Deuflhard, P.: From molecular dynamics to conformation dynamics in drug design. In: Kirkilionis, M., Krömker, S., Rannacher, R., Tomi, F. (eds.) Trends in Nonlinear Analysis, p. 269. Springer, Berlin/Heidelberg (2003)

    Google Scholar 

  14. Deuflhard, P., Dellnitz, M., Junge, O., Schütte, C.: Computation of Essential Molecular Dynamics by Subdivision Techniques I: Basic Concept, vol SC 96-45. Konrad-Zuse-Zentrum für Informationstechnik Berlin, Berlin (1996)

    Google Scholar 

  15. Dickson, A., Warmflash, A., Dinner, A.R.: Nonequilibrium umbrella sampling in spaces of many order parameters. J. Chem. Phys. 130(7), 074104 (2009)

    Article  Google Scholar 

  16. van Erp, T.S., Moroni, D., Bolhuis, P.G.: A novel path sampling method for the calculation of rate constants. J. Chem. Phys. 118(17), 7762 (2003)

    Article  Google Scholar 

  17. Faradjian, A.K., Elber, R.: Computing time scales from reaction coordinates by milestoning. J. Chem. Phys. 120(23), 10880 (2004)

    Article  Google Scholar 

  18. Gardiner, C.W.: Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2nd edn. Springer, Berlin (1997)

    MATH  Google Scholar 

  19. Hänggi, P., Borkovec, M.: Reaction-rate theory: fifty years after Kramers. Rev. Mod. Phys. 62(2), 251–341 (1990)

    Article  MathSciNet  Google Scholar 

  20. Hénin, J., Chipot, C.: Overcoming free energy barriers using unconstrained molecular dynamics simulations. J. Chem. Phys. 121(7), 2904–2914 (2004)

    Article  Google Scholar 

  21. Huber, G.A., Kim, S.: Weighted-ensemble Brownian dynamics simulations for protein association reactions. Biophys. J. 70(1), 97–110 (1996)

    Article  Google Scholar 

  22. Lelièvre, T., Rousset, M., Stoltz, G.: Computation of free energy differences through nonequilibrium stochastic dynamics: the reaction coordinate case. J. Comput. Phys. 222(2), 624–643 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  23. Lelièvre, T., Stoltz, G., Rousset, M.: Free Energy Computations. A Mathematical Perspective. Imperial College Press, London (2010)

    Book  MATH  Google Scholar 

  24. Noé, F., Horenko, I., Schütte, C., Smith, J.C.: Hierarchical analysis of conformational dynamics in biomolecules: transition networks of metastable states. J. Chem. Phys. 126(15), 155102 (2007)

    Article  Google Scholar 

  25. Orešič, M., Shalloway, D.: Hierarchical characterization of energy landscapes using Gaussian packet states. J. Chem. Phys. 101(11), 9844 (1994)

    Article  Google Scholar 

  26. Rodríguez-Gómez, D., Darve, E., Pohorille, A.: Assessing the efficiency of free energy calculation methods. J. Chem. Phys. 120(8), 3563–3578 (2004)

    Article  Google Scholar 

  27. Schütte, C., Huisinga, W.: Biomolecular conformations can be identified as metastable sets of molecular dynamics. In: Handbook of Numerical Analysis, vol. X, pp. 699–744. North-Holland, Amsterdam (2003)

    Google Scholar 

  28. Schütte, C., Huisinga, W., Deuflhard, P.: Transfer operator approach to conformational dynamics in biomolecular systems. In: Fiedler, B. (ed.) Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pp. 191–223. Springer, Berlin (2001)

    Chapter  Google Scholar 

  29. Shalloway, D.: Macrostates of classical stochastic systems. J. Chem. Phys. 105(22), 9986 (1996)

    Article  Google Scholar 

  30. Singhal, N., Snow, C.D., Pande, V.S.: Using path sampling to build better Markovian state models: predicting the folding rate and mechanism of a tryptophan zipper beta hairpin. J. Chem. Phys. 121(1), 415 (2004)

    Article  Google Scholar 

  31. Swope, W.C., Pitera, J.W., Suits, F.: Describing protein folding kinetics by molecular dynamics simulations. 1. Theory. J. Phys. Chem. B 108(21), 6571–6581 (2004)

    Google Scholar 

  32. Truhlar, D.: Variational transition state theory. Annu. Rev. Phys. Chem. 35(1), 159–189 (1984)

    Article  MathSciNet  Google Scholar 

  33. Tucker, S.C.: Variational transition state theory in condensed phases. In: Talkner, P., Hänggi, P. (eds.) New Trends in Kramers’ Reaction Rate Theory, Kluwer Academic, The Netherlands, pp. 5–46. (1995)

    Chapter  Google Scholar 

  34. Vanden-Eijnden, E., Venturoli, M.: Markovian milestoning with Voronoi tessellations. J. Chem. Phys. 130(19), 194101 (2009)

    Article  Google Scholar 

  35. Vanden-Eijnden, E., Venturoli, M., Ciccotti, G., Elber, R.: On the assumptions underlying milestoning. J. Chem. Phys. 129(17), 174102 (2008)

    Article  Google Scholar 

  36. Warmflash, A., Bhimalapuram, P., Dinner, A.R.: Umbrella sampling for nonequilibrium processes. J. Chem. Phys. 127(15), 154112 (2007)

    Article  Google Scholar 

  37. West, A.M.A., Elber, R., Shalloway, D.: Extending molecular dynamics time scales with milestoning: example of complex kinetics in a solvated peptide. J. Chem. Phys. 126(14), 145104 (2007)

    Article  Google Scholar 

  38. Zhang, B.W., Jasnow, D., Zuckerman, D.M.: The “weighted ensemble” path sampling method is statistically exact for a broad class of stochastic processes and binning procedures. J. Chem. Phys. 132(5), 054107 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA

    Eric Darve

Authors
  1. Eric Darve
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Texas at Austin, Austin, TX, USA

    Björn Engquist

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this entry

Cite this entry

Darve, E. (2015). Transition Pathways, Rare Events and Related Questions. In: Engquist, B. (eds) Encyclopedia of Applied and Computational Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70529-1_266

Download citation

Publish with us

Policies and ethics

Search

Navigation