Characterization of rare events in molecular dynamics

Entropy

Volumn 16, Issue 1, 2014, Pages 350-376

  Hartmann, Carsten ^a   Banisch, Ralf ^a   Sarich, Marco ^a   Badowski, Tomasz ^a   Scḧutte, Christof ^a,b  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

Change of measure; Cumulant generating function; Dynamic programming; Molecular dynamics; Optimal pathways; Rare events; Stochastic control

Indexed keywords

EID: 84893162671     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e16010350     Document Type: Article

References (61)

1. Eyring, H. The activated complex in chemical reactions. J. Chem. Phys. 1935, 3, 107-115.
2. Wigner, E. Calculation of the rate of elementary association reactions. J. Chem. Phys. 1937, 5, 720-725.
3. Bolhuis, P.G.; Chandler, D.; Dellago, C.; Geissler, P. Transition path sampling: Throwing ropes over rough mountain passes, in the dark. Annu. Rev. Phys. Chem. 2002, 59, 291-318.
4. E, W.; Ren, W.; Vanden-Eijnden, E. String method for the study of rare events. Phys. Rev. B 2002, 66, 052301.
5. Beccara, S.; Skrbic, T.; Covino, R.; Faccioli, P. Dominant folding pathways of a WW domain. Proc. Natl. Acad. Sci. USA 2012, 109, 2330-2335.
6. Faccioli, P.; Lonardi, A.; Orland, H. Dominant reaction pathways in protein folding: A direct validation against molecular dynamics simulations. J. Chem. Phys. 2010, 133, 045104.
7. Pinski, F.; Stuart, A. Transition paths in molecules: Gradient descent in path space. J. Chem. Phys. 2010, 132, 184104.
8. Allen, R.; Warren, P.; ten Wolde, P.R. Sampling rare switching events in biochemical networks. Phys. Rev. Lett. 2005, 94, 018104.
9. Moroni, D.; van Erp, T.; Bolhuis, P. Investigating rare events by transition interface sampling. Physica A 2004, 340, 395-401.
10. Faradjian, A.K.; Elber, R. Computing time scales from reaction coordinates by milestoning. J. Chem. Phys. 2004, 120, 10880-10889.
11. Olender, R.; Elber, R. Calculation of classical trajectories with a very large time step: Formalism and numerical examples. J. Chem. Phys. 1996, 105, 9299-9315.
12. Jarzynski, C. Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 1997, 78, 2690-2693.
13. Crooks, G. Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. Phys. Rev. E 1999, 60, 2721-2726.
14. Sarich, M.; Bansich, R.; Hartmann, C.; Scḧutte, C. Markov state models for rare events in molecular dynamics. Entropy 2014, 16, 258-286.
15. Allen, R.J.; Valeriani, C.; Tanase-Nicola, S.; tenWolde, P.R.; Frenkel, D. Homogeneous nucleation under shear in a two-dimensional Ising model: Cluster growth, coalescence, and breakup. J. Chem. Phys. 2008, 129, 134704.
16. Berryman, J.T.; Schilling, T. Sampling rare events in nonequilibrium and nonstationary systems. J. Chem. Phys. 2010, 133, 244101.
17. E,W.; Vanden-Eijnden, E. Towards a theory of transition paths. J. Stat. Phys. 2006, 123, 503-523.
18. E, W.; Vanden-Eijnden, E. Metastability, Conformation Dynamics, and Transition Pathways in Complex Systems. In Multiscale Modeling and Simulation; Springer: Berlin, Germany, 2004; pp. 35-68.
19. Metzner, P.; Scḧutte, C.; Vanden-Eijnden, E. Illustration of transition path theory on a collection of simple examples. J. Chem. Phys. 2006, 125, 084110.
20. E, W.; Vanden-Eijnden, E. Transition-path theory and path-finding algorithms for the study of rare events. Annu. Rev. Phys. Chem. 2010, 61, 391-420.
21. Metzner, P.; Scḧutte, C.; Vanden-Eijnden, E. Transition path theory for Markov jump processes. Multiscale Model. Sim. 2009, 7, 1192-1219.
22. Metzner, P. Transition Path Theory for Markov Processes: Application to Molecular Dynamics. Ph.D. Thesis, Freie Universiẗat Berlin, Berlin, Germany, 2007.
23. Nóe, F.; Scḧutte, C.; Vanden-Eijnden, E.; Reich, L.; Weikl, T. Constructing the full ensemble of folding pathways from short off-equilibrium trajectories. Proc. Natl. Acad. Sci. USA 2009, 106, 19011-19016.
24. Chandler, D. Finding Transition Pathways: Throwing Ropes over Rough Montain Passes, in the Dark; World Scientific: Singapore, Singapore, 1998.
25. D̈urr, D.; Bach, A. The Onsager-Machlup function as Lagrangian for the most probable path of a diffusion process. Commun. Math. Phys. 1978, 60, 153-170.
26. Berkowitz, M.; Morgan, J.D.; McCammon, J.A.; Northrup, S.H. Diffusion-controlled reactions: A variational formula for the optimum reaction coordinate. J. Chem. Phys. 1983, 79, 5563-5565.
27. Huo, S.; Straub, J.E. The MaxFlux algorithm for calculating variationally optimized reaction paths for conformational transitions in many body systems at finite temperature. J. Chem. Phys. 1997, 107, 5000-5006.
28. Zhao, R.; Shen, J.; Skeel, R.D. Maximum flux transition paths of conformational change. J. Chem. Theory Comput. 2010, 6, 2411-2423.
29. Cameron, M. Estimation of reactive fluxes in gradient stochastic systems using an analogy with electric circuits. J. Comput. Phys. 2013, 247, 137-152.
30. Vanden-Eijnden, E.; Heymann, M. The geometric minimum action method for computing minimum energy paths. J. Chem. Phys. 2008, 128, 061103.
31. Jonsson, H.; Mills, G.; Jacobsen, K. Nudged Elastic Band Method for Finding Minimum Energy Paths of Transitions. In Classical and Quantum Dynamics in Condensed Phase Simulations; Berne, B.J., Ciccotti, G., Coker, D.F., Eds.; World Scientific: Singapore, Singapore, 1998.
32. Freidlin, M.; Wentzell, A.D. Random Perturbations of Dynamical Systems; Springer, New York, NY, USA, 1998.
33. E, W.; Ren, W.; Vanden-Eijnden, E. Finite temperature string method for the study of rare events. J. Phys. Chem. B 2005, 109, 6688-6693.
34. Ren, W.; Vanden-Eijnden, E.; Maragakis, P; E, W. Transition pathways in complex systems: Application of the finite-temperature string method to the alanine dipeptide. J. Phys. Chem. 2005, 123, 134109.
35. Vanden-Eijnden, E.; Venturoli, M. Revisiting the finite temperature string method for the calculation of reaction tubes and free energies. J. Phys. Chem. 2009, 130, 194103.
36. Allen, R.; Frenkel, D.; ten Wolde, P.R. Simulating rare events in equilibrium or nonequilibrium stochastic systems. J. Chem. Phys. 2006, 124, 024102.
37. Allen, R.; Frenkel, D.; ten Wolde, P.R. Forward flux sampling-type schemes for simulating rare events: Efficiency analysis. J. Chem. Phys. 2006, 124, 194111.
38. Becker, N.B.; Allen, R.J.; ten Wolde, P.R. Non-stationary forward flux sampling. J. Chem. Phys. 2012, 136, 174118.
39. Kratzer, K.; Arnold, A.; Allen, R.J. Automatic, optimized interface placement in forward flux sampling simulations. J. Chem. Phys. 2013, 138, 164112.
40. Vanden-Eijnden, E.; Venturoli, M.; Ciccotti, G.; Elber, R. On the assumptions underlying milestoning. J. Chem. Phys. 2008, 129, 174102.
41. Latorre, J.; Hartmann, C.; Scḧutte, C. Free energy computation by controlled Langevin processes. Procedia Comput. Sci. 2010, 1, 1591-1600.
42. Leliévre, T.; Stoltz, G.; Rousset, M. Free Energy Computations: A Mathematical Perspective; Imperial College Press: London, UK, 2010.
43. Isralewitz, B.; Gao, M.; Schulten, K. Steered molecular dynamics and mechanical functions of proteins. Curr. Opin. Struct. Biol. 2001, 11, 224-230.
44. Vaikuntanathan, S.; Jarzynski, C. Escorted free energy simulations: Improving convergence by reducing dissipation. Phys. Rev. Lett. 2008, 100, 190601.
45. Oberhofer, H.; Dellago, C. Optimum bias for fast-switching free energy calculations. Comput. Phys. Commun. 2008, 179, 41-45.
46. Dai Pra, P.; Meneghini, L.; Runggaldier, W. Connections between stochastic control and dynamic games. Math. Control Signals Syst. 1996, 9, 303-326.
47. Fleming,W.; Soner, H. Controlled Markov Processes and Viscosity Solutions; Springer: New York, NY, USA, 2006.
48. Awad, H.; Glynn, P.; Rubinstein, R. Zero-variance importance sampling estimators for markov process expectations. Math. Oper. Res. 2013, 38, 358-388.
49. Badowski, T. Importance Sampling Using Discrete Girsanov Estimators. Ph.D. Thesis, Freie Universiẗat Berlin, Berlin, Germany, 2013, in preparation.
50. Fleming, W. Risk sensitive stochastic control and differential games. Commun. Inf. Syst. 2006, 6, 161-178.
51. Day, M. Conditional exits for small noise diffusions with characteristic boundary. Ann. Probab. 1992, 20, 1385-1419.
52. Hartmann, C.; Scḧutte, C. Efficient rare event simulation by optimal nonequilibrium forcing. J. Stat. Mech. Theor. Exp. 2012, 2012, P11004.
53. Darve, E.; Rodriguez-Gomez, D.; Pohorille, A. Adaptive biasing force method for scalar and vector free energy calculations. J. Chem. Phys. 2008, 128, 144120.
54. Leliévre, T.; Rousset, M.; Stoltz, G. Computation of free energy profiles with parallel adaptive dynamicss. J. Chem. Phys. 2007, 126, 134111.
55. Leliévre, T.; Rousset, M.; Stoltz, G. Long-time convergence of an adaptive biasing force methods. Nonlinearity 2008, 21, 1155-1181.
56. Zhang, W.; Latorre, J.; Pavliotis, G.; Hartmann, C. Optimal control of multiscale diffusions using reduced-order models. J. Comput. Dynam. 2013, submitted.
57. Dupuis, P.; Wang, H. Importance sampling, large deviations, and differential games. Stochast. Stochast. Rep. 2004, 76, 481-508.
58. Dupuis, P.; Wang, H. Subsolutions of an isaacs equation and efficient schemes for importance sampling. Math. Oper. Res. 2007, 32, 723-757.
59. Zhang, W.; Hartmann, C.; Weber, M.; Scḧutte, C. Importance sampling in path space for diffusion processes. Multiscale Model. Sim. 2013, submitted.
60. Banisch, R.; Hartmann, C. Meshless Discretizations of LQ-type stochastic control problems. SIAM J. Control Optim. 2013, submitted.
61. Vanden-Eijnden, E.; Weare, J. Rare event simulation of small noise diffusions. Commun. Pure Appl. Math. 2012, 65, 1770-1803.