Transition-path theory and path-finding algorithms for the study of rare events

Annual Review of Physical Chemistry

Volumn 61, Issue , 2010, Pages 391-420

  E, Weinan ^a   Vanden Eijnden, Eric ^b  

^a PRINCETON UNIVERSITY   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

Activated process; Minimum free energy path; String method; Transition state theory

Indexed keywords

ACTIVATED PROCESS; ENERGY PATHS; MINIMUM FREE ENERGIES; MINIMUM FREE ENERGY PATH; NUMERICAL ALGORITHMS; PATH-FINDING ALGORITHMS; STRING METHODS; THEORETICAL FRAMEWORK; TRANSITION PATH THEORIES; TRANSITION STATE THEORIES;

FREE ENERGY;

EID: 77951688892     PISSN: 0066426X     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev.physchem.040808.090412     Document Type: Article

References (91)

1. Eyring H. 1935. The activated complex and the absolute rate of chemical reactions. Chem. Rev. 17:65-77
2. Horiuti J. 1938. On the statistical mechanical treatment of the absolute rate of chemical reaction. Bull. Chem. Soc. Jpn. 13:210-216
3. Wigner E. 1938. The transition state method. Trans. Faraday Soc. 34:29-41
4. Bennett CH. 1975. Exact defect calculations in model substances. In Diffusion in Solids: Recent Developments, ed. AS Nowick, JJ Burton, pp. 73-113. New York: Academic
5. Chandler D. 1978. Statistical mechanics of isomerization dynamics in liquids and the transition state approximation. J. Chem. Phys. 68:2959-2970
6. Keck J. 1962. Statistical investigation of dissociation cross-sections for diatoms. Discuss. Faraday Soc. 33:173-182
7. Yamamoto T. 1960. Quantum statistical mechanical theory of the rate of exchange chemical reactions in the gas phase. J. Chem. Phys. 33:281-289
8. E W, Vanden-Eijnden E. 2009. Transition path theory and path-finding algorithms for the study of rare events. Extended version available from the ArXiv
9. Pratt L. 1986. A statistical method for identifying transition states in high dimensional problems. J. Chem. Phys. 85:5045-5048
10. Bolhuis P. 2003. Transition-path sampling of β-hairpin folding. Proc. Natl. Acad. Sci. USA 100:12129-12134
11. Bolhuis P, Chandler D, Dellago C, Geissler P. 2002. Transition path sampling: throwing ropes over rough mountain passes, in the dark. Annu. Rev. Phys. Chem. 53:291-318
12. E W, Vanden-Eijnden E. 2006. Towards a theory of transition paths. J. Stat. Phys. 123:503-523
13. Metzner P, Schütte C, Vanden-Eijnden E. 2006. Illustration of transition path theory on a collection of simple examples. J. Chem. Phys. 125:084110
14. Metzner P, Schütte C, Vanden-Eijnden E. 2009. Transition path theory for Markov jump processes. Multiscale Model. Sim. 7:1192-1219
15. Vanden-Eijnden E. 2006. Transition path theory. In Computer Simulations in Condensed Matter: From Materials to Chemical Biology, Vol. 1, ed. M Ferrario, G Ciccotti, K Binder, pp. 439-478 Berlin: Springer
16. E W, Ren W, Vanden-Eijnden E. 2002. String method for the study of rare events. Phys. Rev. B 66:052301
17. E W, Ren W, Vanden-Eijnden E. 2005. Finite temperature string method for the study of rare events. J. Phys. Chem. B 109:6688-6693
18. E W, Ren W, Vanden-Eijnden E. 2005. Transition pathways in complex systems: reaction coordinates, isocommittor surfaces, and transition tubes. Chem. Phys. Lett. 413:242-247
19. Maragliano L, Fischer A, Vanden-Eijnden E, Ciccotti G. 2006. String method in collective variables: minimum free energy paths and isocommittor surfaces. J. Chem. Phys. 125:024106
20. Maragliano L, Vanden-Eijnden E. 2007. On-the-fly string method for minimum free energy paths calculation. Chem. Phys. Lett. 446:182-190
21. Ren W, Vanden-Eijnden E, Maragakis P, E W. 2005. Transition pathways in complex systems: application of the finite-temperature string method to the alanine dipeptide. J. Chem. Phys. 123:134109
22. Vanden-Eijnden E, Venturoli M. 2009. Revisiting the finite temperature string method for the calculation of reaction tubes and free energies. J. Chem. Phys. 130:194103
23. Bussi G, Donadio D, Parrinello M. 2007. Canonical sampling through velocity rescaling. J. Chem. Phys. 126:014101
24. Leimkuhler B, Legoll F, NoorizadehE. 2008. Atemperature control technique for nonequilibrium molecular simulation. J. Chem. Phys. 128:074105
25. Bussi G, Zykova-Timan T, Parrinello M. 2009. Isothermal-isobaric molecular dynamics using stochastic velocity rescaling. J. Chem. Phys. 130:074101
26. Doob JL. 2001 (1984). Classical Potential Theory and Its Probabilistic Counterpart. Berlin: Springer-Verlag
27. Sznitman A-S. 1998. Brownian Motion, Obstacles and Random Media. Springer Monogr. Math. Berlin: Springer-Verlag
28. Bass RF. 1997. Diffusions and Elliptic Operators: Probability and Its Applications. New York: Springer Verlag
29. Hummer G. 2004. From transition paths to transition states and rate coefficients. J. Chem. Phys. 120:516-523
30. Berezhkovskii A, Hummer G, Szabo A. 2009. Reactive flux and folding pathways in network models of coarse-grained protein dynamics. J. Chem. Phys. 130:205102
31. Venturoli M, Vanden-Eijnden E, Ciccotti G. 2009. Kinetics of phase transitions in two dimensional Ising models studied with the string method. J. Math. Chem. 45:188-222
32. Buchete N, Hummer G. 2008. Coarse master equations for peptide folding dynamics. J. Phys. Chem. B 112:6057-6069
33. Chodera JD, Singhal N, Pande VS, Dill KA, Swope WC. 2007. Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics. J. Chem. Phys. 126:155101
34. Hummer G, Kevrekidis IG. 2003. Coarse molecular dynamics of a peptide fragment: free energy, kinetics, and long-time dynamics computation. J. Chem. Phys. 118:10762-10773
35. Krivov S, Karplus M. 2004. Free energy disconnectivity graphs: application to peptide models. J. Chem. Phys. 117:10894-10903
36. Noe F, Horenko I, Schü tte C, Smith J. 2007. Hierarchical analysis of conformational dynamics in biomolecules: transition networks of metastable states. J. Chem. Phys. 126:155102
37. Pan AC, Roux B. 2008. Building Markov state models along pathways to determine free energies and rates of transitions. J. Chem. Phys. 129:064107
38. Shalloway D. 1996. Macrostates of classical stochasic systems. J. Chem. Phys. 105:9986-10007
39. Sriraman S, Kevrekidis IG, Hummer G. 2005. Coarse master equation from Bayesian analysis of replica molecular dynamics simulations. J. Phys. Chem. B 109:6479-6484
40. Swope W, Pitera J, Suits F. 2004. Describing protein folding kinetics by molecular dynamics simulations. 1. Theory. J. Phys. Chem. B 108:6571-6581
41. Swope W, Pitera J, Suits F, Pitman M, Eleftheriou M, et al. 2004. Describing protein folding kinetics by molecular dynamics simulations. 2. Example applications to alanine dipeptide and β-hairpin peptide. J. Phys. Chem. B 108:6582-6594
42. Tal F, Vanden-Eijnden E. 2006. Transition state theory and dynamical corrections in ergodic systems. Nonlinearity 19:501-510
43. Vanden-Eijnden E, Tal F. 2005. Transition state theory: variational formulation, dynamical corrections, and error estimates. J. Chem. Phys. 123:184103
44. Vanden-Eijnden E, Venturoli M, Ciccotti G, Elber R. 2008. On the assumptions underlying milestoning. J. Chem. Phys. 129:174102
45. Branduardi D, Gervasio FL, Parrinello M. 2007. From a to b in free energy space. J. Chem. Phys. 126:054103
46. Berkowitz M, Morgan JD, McCammon JA, Northrup SH. 1983. Diffusion-controlled reactions: a varia-tional formula for the optimum reaction coordinate. J. Chem. Phys. 79:5563-5565
47. E W, Vanden-Eijnden E. 2004. Metastability, conformation dynamics, and transition pathways in complex systems. In Multiscale Modelling and Simulation, ed. S Attinger, P Koumoutsakos, pp. 35-68. New York: Springer
48. Hastie T. 1984. Principal curves and surfaces. PhD thesis. Stanford Univ.
49. Hastie T, Tibshirani R, Friedman JH. 2001. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. New York: Springer
50. Nocedal J, Wright S. 1999. Numerical Optimization. New York: Springer
51. Henkelman G, Jó nsson H. 1999. A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J. Chem. Phys. 111:7010-7022
52. Fischer S, Karplus M. 1992. Conjugate peak refinement: an algorithm for finding reaction paths and accurate transition states in systems with many degrees of freedom. Chem. Phys. Lett. 194:252-261
53. Brower RC, Kessler DA, Koplik J, Levine H. 1983. Geometrical approach to moving-interface dynamics. Phys. Rev. Lett. 51:1111-1114
54. Brower RC, Kessler DA, Koplik J, Levine H. 1984. Geometrical models of interface evolution. Phys. Rev. A 29:1335-1342
55. E W, Ren W, Vanden-Eijnden E. 2007. Simplified and improved string method for computing the minimum energy paths in barrier-crossing events. J. Chem. Phys. 126:164103
56. Ren W. 2003. Higher order string method for finding minimum energy paths. Comm. Math. Sci. 1:377-384
57. Henkelman G, Jónsson H. 2000. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys. 113:9978-9985 (Pubitemid 32076892) (Pubitemid 32076892)
58. Burger S, Yang W. 2006. Quadratic string method for determining the minimum-energy path based on multiobjective optimization. J. Chem. Phys. 124:054109
59. Peters B, Heyden A, Bell AT, Chakraborty A. 2004. A growing string method for determining transition states: comparison to the nudged elastic band and string methods. J. Chem. Phys. 120:7877-7886
60. Kanai Y, Tilocca A, Selloni A, Car R. 2004. First-principles string molecular dynamics: an efficient approach for finding chemical reaction pathways. J. Chem. Phys. 121:3359-3367
61. Miller TF III, Vanden-Eijnden E, Chandler D. 2007. Solvent coarse-graining and the string method applied to the hydrophobic collapse of a hydrated chain. Proc. Natl. Acad. Sci. USA 104:14559-14564
62. Khavrutskii IV, Arora K, Brooks CL 3rd. 2006. Harmonic Fourier beads method for studying rare events on rugged energy surfaces. J. Chem. Phys. 125:174108
63. Khavrutskii IV, McCammon JA. 2007. Generalized gradient-augmented harmonic Fourier beads method with multiple atomic and/or center-of-mass positional restraints. J. Chem. Phys. 127:124901
64. Pan AC, Sezer D, Roux B. 2008. Finding transition pathways using the string method with swarms of trajectories. J. Phys. Chem. B 112:3432-3440
65. OlenderR,Elber R. 1997. Yet another lookatthe steepest descent path. J. Mol. Struct. Theochem. 398:63-71
66. Vanden-Eijnden E, Heymann M. 2008. The geometric minimum action method for computing minimum energy paths. J. Chem. Phys. 128:061103
67. Dellago C, Bolhuis PG, Geissler PL. 2002. Transition path sampling. Adv. Chem. Phys. 123:1-78
68. Elber R, Karplus M. 1987. A method for determining reaction paths in large molecules: application to myoglobin. Chem. Phys. Lett. 139:375-380
69. Ulitsky A, Elber R. 1990. A new technique to calculate steepest descent paths in flexible polyatomic systems. J. Chem. Phys. 92:1510-1511
70. Gillilan RE, Lilien RH. 2004. Optimization and dynamics of protein-protein complexes using b-splines. J. Comput. Chem. 25:1630-1646
71. Henkelman G, Jóhannesson G, Jónsson H. 2000. Methods for finding saddle points and minimum energy paths. Prog. Theor. Chem. Phys. 111:269-300
72. Jónsson H, Mills G, Jacó bsen KW. 1998. Nudged elastic band method for finding minimum energy paths of transitions. In Classical and Quantum Dynamics in Condensed Phase Simulations, ed. BJ Berne, G Ciccotti, DF Coker, pp. 385-404. Singapore: World Sci.
73. Sheppard D, Terrell R, Henkelman G. 2008. Optimization methods for finding minimum energy paths. J. Chem. Phys. 128:134106
74. Henkelman G, Uberuaga BP, Jónsson H. 2000. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 113:9901-9904 (Pubitemid 32076883) (Pubitemid 32076883)
75. Vanden-EijndenE. 2009. Some recent techniques for free energy calculations. J. Comput. Phys. 30:1737-1747
76. ElberR. 2007. Amilestoning studyofthe kinetics ofanallosteric transition: atomically detailed simulations of deoxy Scapharca hemoglobin. Biophys. J. 92:L85-87
77. Faradjian AK, Elber R. 2004. Computing time scales from reaction coordinates by milestoning. J. Chem. Phys. 120:10880-10889
78. Shalloway D, Faradijan AK. 2006. Efficient computation of the first passage time distribution of the generalized master equation by steady-state relaxation. J. Chem. Phys. 124:054112
79. Vanden-Eijnden E, Venturoli M. 2009. Markovian milestoning with Voronoi tessellations. J. Chem. Phys. 130:194101
80. West AMA, Elber R, Shalloway D. 2007. Extending molecular dynamics timescales with milestoning: example of complex kinetics in a solvated peptide. J. Chem. Phys. 126:145104
81. Moroni D, Bolhuis PG, van Erp TS. 2004. Rate constants for diffusive processes by partial path sampling. J. Chem. Phys. 120:4055-4065
82. Moroni D, van Erp TS, Bolhuis PG. 2004. Investigating rare events by transition interface sampling. Phys. A 340:395-401
83. van Erp TS, Moroni D, Bolhuis PG. 2003. A novel path sampling method for the calculation of rate constants. J. Chem. Phys. 118:7762-7774
84. Allen RJ, Frenkel D, ten Wolde PR. 2006. Forward flux sampling-type schemes for simulating rare events: efficiency analysis. J. Chem. Phys. 124:194111
85. Allen RJ, Frenkel D, ten Wolde PR. 2006. Simulating rare events in equilibrium or nonequilibrium stochastic systems. J. Chem. Phys. 124:024102
86. Valeriani C, Allen RJ, Morelli MJ, Frenkel D, ten Wolde PR. 2007. Computing stationary distributions in equilibrium and nonequilibrium systems with forward flux sampling. J. Chem. Phys. 127:114109
87. Vanden-Eijnden E, Venturoli M. 2009. Exact rate calculations by trajectory parallelization and tilting. J. Chem. Phys. 131:044120
88. Dickson A, Warmflash A, Dinner AR. 2009. Nonequilibrium umbrella sampling in spaces of many order parameters. J. Chem. Phys. 130:074104
89. Warmflash A, Bhimalapuram P, Dinner AR. 2007. Umbrella sampling for nonequilibrium processes. J. Chem. Phys. 127:154112
90. Parr RG, Yang W. 1989. Density Functional Theory of Atoms and Molecules. New York: Oxford Univ. Press
91. Friesecke G, Junge O, Koltai P. 2009. Mean field approximation in conformation dynamics. Multiscale Model. Simul. In press