Transition path sampling and forward flux sampling. Applications to biological systems

Journal of Physics Condensed Matter

Volumn 21, Issue 33, 2009, Pages

  Escobedo, Fernando A ^a   Borrero, Ernesto E ^a   Araque, Juan C ^a  

^a Cornell University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONFORMATIONAL TRANSITIONS; ENZYME CATALYSIS; MECHANISM AND KINETICS; NANO SCALE; PATH SAMPLING METHOD; POTENTIAL EFFICIENCY; RAPID GROWTH; SAMPLING METHOD; SIMULATION METHODS; TRANSITION PATH SAMPLING; TRANSITION PATHWAY; TRANSITIONAL EVENTS;

BIOLOGICAL SYSTEMS; BIOMOLECULES; SYSTEMS ENGINEERING;

PROTEIN FOLDING;

EID: 70349291211     PISSN: 09538984     EISSN: 1361648X     Source Type: Journal    
DOI: 10.1088/0953-8984/21/33/333101     Document Type: Review

References (116)

1. Sethuraman A, Vedantham G, Imoto T, Przybycien T and Belfort G 2004 Protein unfolding at interfaces: slow dynamics of α-helix to β-sheet transition Proteins: Struct. Funct. Bioinform. 56 669-78
2. Tsumoto K, Ejima D, Kumagai I and Arakawa T 2003 Practical considerations in refolding proteins from inclusion bodies Protein Expr. Purif. 28 1-8
3. Snow C D, Sorin E J, Rhee Y M and Pande V S 2005 How well can simulation predict protein folding kinetics and thermodynamics? Annu. Rev. Biophys. Biomol. Struct. 34 43-69
4. Allen R J, Frenkel D and ten Wolde P R 2006 Forward flux sampling-type schemes for simulating rare events: efficiency analysis J. Chem. Phys. 124 194111
5. Allen R J, Frenkel D and ten Wolde P R 2006 Simulating rare events in equilibrium or nonequilibrium stochastic systems J. Chem. Phys. 124 024102
6. Bolhuis P G 2003 Transition-path sampling of β-hairpin folding Proc. Natl Acad. Sci. USA 100 12129-34
7. Dellago C and Bolhuis P G 2007 Atomistic Approaches in Modern Biology: from Quantum Chemistry to Molecular Simulations (Berlin: Springer) pp291-317
8. Juraszek J and Bolhuis P G 2006 Sampling the multiple folding mechanisms of Trp-cage in explicit solvent Proc. Natl Acad. Sci. USA 103 15859-64
9. Ma A and Dinner A R 2005 Automatic method for identifying reaction coordinates in complex systems J. Phys. Chem. B 109 6769-79
10. Peters B and Trout B L 2006 Obtaining reaction coordinates by likelihood maximization J. Chem. Phys. 125 054108
11. van Erp T S 2006 Efficiency analysis of reaction rate calculation methods using analytical models I: the two-dimensional sharp barrier J. Chem. Phys. 125 174106
12. Dellago C and Bolhuis P G 2008 Advanced Computer Simulation Approaches for Soft Matter Sciences III ed C Holmer and K Kremer (Berlin: Springer) pp167-233
13. Dellago C, Bolhuis P G and Chandler D 1999 On the calculation of reaction rate constants in the transition path ensemble J. Chem. Phys. 110 6617-25
14. Dellago C, Bolhuis P G, Csajka F S and Chandler D 1998 Transition path sampling and the calculation of rate constants J. Chem. Phys. 108 1964-77
15. Dellago C, Bolhuis P G and Geissler P L 2002 Transition path sampling Adv. Chem. Phys. 123 1-78
16. Bolhuis P G, Chandler D, Dellago C and Geissler P L 2002 Transition path sampling: throwing ropes over rough mountain passes, in the dark Annu. Rev. Phys. Chem. 53 291-318
17. Bolhuis P G 2003 Transition path sampling on diffusive barriers J. Phys.: Condens. Matter 15 S113-20
18. Geyer C J and Thompson E A 1995 Annealing Markov chain Monte Carlo with applications to ancestral inference J. Am. Stat. Assoc. 90 909-20
19. Vlugt T J H and Smit B 2001 On the efficient sampling of pathways in the transition path ensemble PhysChemComm 2 1
20. Chopra M, Malshe R, Reddy A S and de Pablo J J 2008 Improved transition path sampling methods for simulation of rare events J. Chem. Phys. 128 144104
21. Grunwald M, Rabani E and Dellago C 2006 Mechanisms of the wurtzite to rocksalt transformation in CdSe nanocrystals Phys. Rev. Lett. 96 255701
22. Hu J, Ma A and Dinner A R 2006 Bias annealing: a method for obtaining transition paths de novo J. Chem. Phys. 125 114101
23. Moroni D, van Erp T S and Bolhuis P G 2004 Investigating rare events by transition interface sampling Physica A 340 395-401
24. van Erp T S and Bolhuis P G 2005 Elaborating transition interface sampling methods J. Comput. Phys. 205 157-81
25. van Erp T S, Moroni D and Bolhuis P G 2003 A novel path sampling method for the calculation of rate constants J. Chem. Phys. 118 7762-74
26. Bolhuis P G 2008 Rare events via multiple reaction channels sampled by path replica exchange J. Chem. Phys. 129 114108
27. van Erp T S 2007 Reaction rate calculation by parallel path swapping Phys. Rev. Lett. 98 268301
28. Rogal J and Bolhuis P G 2008 Multiple state transition path sampling J. Chem. Phys. 129 224107
29. Moroni D, van Erp T S and Bolhuis P G 2005 Simultaneous computation of free energies and kinetics of rare events Phys. Rev. E 71 056709
30. Allen R J, Warren P B and ten Wolde P R 2005 Sampling rare switching events in biochemical networks Phys. Rev. Lett. 94 018104
31. Juraszek J and Bolhuis P G 2008 Rate constant and reaction coordinate of Trp-cage folding in explicit water Biophys. J. 95 4246-57
32. Borrero E E and Escobedo F A 2009 Simulating the kinetics and thermodynamics of transitions via forward flux/umbrella sampling J. Phys. Chem. B 113 6434-45
33. Valeriani C, Allen R J, Morelli M J, Frenkel D and ten Wolde P R 2007 Computing stationary distributions in equilibrium and nonequilibrium systems with forward flux sampling J. Chem. Phys. 127 114109
34. Borrero E E and Escobedo F A 2007 Reaction coordinates and transition pathways of rare events via forward flux sampling J. Chem. Phys. 127 164101-17
35. Borrero E E and Escobedo F A 2008 Optimizing the sampling and staging for simulations of rare events via forward flux sampling schemes J. Chem. Phys. 129 024115-16
36. Huber G A and Kim S 1996 Weighted-ensemble Brownian dynamics simulations for protein association reactions Biophys. J. 70 97-110
37. Dickson A, Warmflash A and Dinner A R 2009 Nonequilibrium umbrella sampling in spaces of many order parameters J. Chem. Phys. 130 074104
38. Farkas L 1927 The speed of germinitive formation in over saturated vapours Z. Phys. Chem. 125 236-42
39. Hänggi P, Talkner P and Borkovec M 1990 Reaction-rate theory: fifty years after Kramers Rev. Mod. Phys. 62 251
40. Northrup S H, Allison S A and McCammon J A 1984 Brownian dynamics simulation of diffusion-influenced bimolecular reactions J. Chem. Phys. 80 1517-26
41. Gabdoulline R R and Wade R C 2002 Biomolecular diffusional association Curr. Opin. Struct. Biol. 12 204-13
42. Rojnuckarin A, Livesay D R and Subramaniam S 2000 Bimolecular reaction simulation using weighted ensemble Brownian dynamics and the University of Houston Brownian Dynamics program Biophys. J. 79 686-93
43. Zhang B W, Jasnow D and Zuckerman D M 2007 Efficient and verified simulation of a path ensemble for conformational change in a united-residue model of calmodulin Proc. Natl Acad. Sci. USA 104 18043-8
44. Rojnuckarin A, Kim S and Subramaniam S 1998 Brownian dynamics simulations of protein folding: access to milliseconds timescale and beyond Proc. Natl Acad. Sci. USA 95 4288-92
45. Fisher E W, Rojnuckarin A and Kim S 2001 Kinetic effects of mutations of charged residues on the surface of a dimeric hemoglobin: insights from Brownian dynamics simulations J. Mol. Struct. 549 47-54
46. Fisher E W, Rojnuckarin A and Kim S 2002 Effects of local repositioning of charged surface residues on the kinetics of protein dimerization probed by Brownian dynamics simulations J. Mol. Struct. 592 37-45
47. Fisher E W, Rojnuckarin A and Kim S 2002 Exhaustive enumeration of the effects of point charge mutations on the electrostatically driven association of hemoglobin subunits, using weighted-ensemble Brownian dynamics simulations Struct. Chem. 13 193-202
48. Faradjian A K and Elber R 2004 Computing timescales from reaction coordinates by milestoning J. Chem. Phys. 120 10880-9
49. West A M A, Elber R and Shalloway D 2007 Extending molecular dynamics timescales with milestoning: example of complex kinetics in a solvated peptide J. Chem. Phys. 126 145104
50. Vanden-Eijnden E, Venturoli M, Ciccotti G and Elber R 2008 On the assumptions underlying milestoning J. Chem. Phys. 129 174102
51. Montroll E W and Weiss G H 1965 Random walks on lattices. 2 J. Math. Phys. 6 167
52. Kampen N G v 1992 Stochastic Processes in Physics and Chemistry (Amsterdam: North-Holland)
53. Elber R 2007 A milestoning study of the kinetics of an allosteric transition: atomically detailed simulations of deoxy Scapharca hemoglobin Biophys. J. 92 L85-L7
54. E W, Ren W Q and Vanden-Eijnden E 2005 Finite temperature string method for the study of rare events J. Phys. Chem. B 109 6688-93
55. E W and Vanden-Eijnden E 2006 Towards a theory of transition paths J. Stat. Phys. 123 503-23
56. Vanden-Eijnden E and Tal F A 2005 Transition state theory: variational formulation, dynamical corrections, and error estimates J. Chem. Phys. 123 184103
57. E W, Ren W Q and Vanden-Eijnden E 2002 String method for the study of rare events Phys. Rev. B 66 052301
58. Henkelman G and Jonsson H 2000 Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points J. Chem. Phys. 113 9978
59. Henkelman G, Uberuaga B P and Jonsson H 2000 A climbing image nudged elastic band method for finding saddle points and minimum energy paths J. Chem. Phys. 113 9901
60. E W, Ren W Q and Vanden-Eijnden E 2005 Transition pathways in complex systems: reaction coordinates, isocommittor surfaces, and transition tubes Chem. Phys. Lett. 413 242-7
61. Gardiner C W 2004 Handbook of Stochastic Methods: for Physics, Chemistry, and the Natural Sciences (Berlin: Springer)
62. Ren W, Vanden-Eijnden E, Maragakis P and E W 2005 Transition pathways in complex systems: application of the finite-temperature string method to the alanine dipeptide J. Chem. Phys. 123 134109
63. Maragliano L, Fischer A, Vanden-Eijnden E and Ciccotti G 2006 String method in collective variables: minimum free energy paths and isocommittor surfaces J. Chem. Phys. 125 024106
64. Maragliano L and Vanden-Eijnden E 2007 On-the-fly string method for minimum free energy paths calculation Chem. Phys. Lett. 446 182-90
65. Hummer G 2004 From transition paths to transition states and rate coefficients J. Chem. Phys. 120 516-23
66. E W, Ren W Q and Vanden-Eijnden E 2005 Transition pathways in complex systems: reaction coordinates, isocommittor surfaces, and transition tubes Chem. Phys. Lett. 413 242-7
67. Peters B, Beckham G T and Trout B L 2007 Extensions to the likelihood maximization approach for finding reaction coordinates J. Chem. Phys. 127 034109
68. Best R B and Hummer G 2005 Reaction coordinates and rates from transition paths Proc. Natl Acad. Sci. USA 102 6732-7
69. Dinner A R, So S S and Karplus M 1998 Use of quantitative structure-property relationships to predict the folding ability of model proteins Proteins: Struct. Funct. Bioinform. 33 177-203
70. Dinner A R, So S S and Karplus M 2002 Computational Methods for Protein Folding pp1-34
71. So S S and Karplus M 1997 Three-dimensional quantitative structure-activity relationships from molecular similarity matrices and genetic neural networks. 1. Method and validations J. Med. Chem. 40 4347-59 (Pubitemid 28042314)
72. Metzner P, Schutte C and Vanden-Eijnden E 2006 Illustration of transition path theory on a collection of simple examples J. Chem. Phys. 125 084110
73. Velez-Vega C, Borrero E E and Escobedo F A 2009 Kinetics and reaction coordinate for the isomerization of alanine dipeptide by a forward flux sampling protocol J. Chem. Phys. 130 225101
74. ten Wolde P R and Chandler D 2002 Drying-induced hydrophobic polymer collapse Proc. Natl Acad. Sci. USA 99 6539-43
75. Bolhuis P G, Dellago C and Chandler D 2000 Reaction coordinates of biomolecular isomerization Proc. Natl Acad. Sci. USA 97 5877-82
76. Bolhuis P G 2005 Examining the folding of small two-state proteins in explicit water using path sampling techniques Biophys. Soc. Mtg Abstr. 88 182A
77. Bolhuis P G 2005 Kinetic pathways of beta-hairpin (un)folding in explicit solvent Biophys. J. 88 50-61
78. Evans D A and Wales D J 2004 Folding of the GB1 hairpin peptide from discrete path sampling J. Chem. Phys. 121 1080-90
79. Hagan M F, Dinner A R, Chandler D and Chakraborty A K 2003 Atomistic understanding of kinetic pathways for single base-pair binding and unbinding in DNA Proc. Natl Acad. Sci. USA 100 13922-7
80. Basner J E and Schwartz S D 2005 How enzyme dynamics helps catalyze a reaction in atomic detail: a transition path sampling study J. Am. Chem. Soc. 127 13822-31
81. Radhakrishnan R and Schlick T 2004 Orchestration of cooperative events in DNA synthesis and repair mechanism unraveled by transition path sampling of DNA polymerase β 's closing Proc. Natl Acad. Sci. USA 101 5970-5
82. Radhakrishnan R and Schlick T 2005 Fidelity discrimination in DNA polymerase β: differing closing profiles for a mismatched (G:A) versus matched (G:C) base pair J. Am. Chem. Soc. 127 13245-52
83. Radhakrishnan R, Yang L J, Arora K and Schlick T 2004 Exploring DNA polymerase beta mechanisms by advanced sampling techniques Biophys. Soc. Mtg Abstr. 86 34A
84. Marti J 2004 A molecular dynamics transition path sampling study of model lipid bilayer membranes in aqueous environments J. Phys.: Condens. Matter 16 5669-78
85. Marti J and Csajka F S 2004 Transition path sampling study of flip-flop transitions in model lipid bilayer membranes Phys. Rev. E 69 061918
86. Borrero E E and Escobedo F A 2006 Folding kinetics of a lattice protein via a forward flux sampling approach J. Chem. Phys. 125 164904-14
87. Fersht A R 1997 Nucleation mechanisms in protein folding Curr. Opin. Struct. Biol. 7 3-9
88. Vendurscolo M, Paci E, Dobson C M and Karplus M 2001 Three key residues form a critical network in a protein folding transition state Nature 409 641-5
89. Martinez L M C, Quintana E E B, Escobedo F A and DeLisa M P 2008 In silico protein fragmentation reveals the importance of critical nuclei on domain reassembly Biophys. J. 94 1575-88
90. Bolhuis P G 2009 Two-state protein folding kinetics through all-atom molecular dynamics based sampling Front. Biosci. 14 2801-28
91. Chopra M, Reddy A S, Abbott N L and de Pablo J J 2008 Folding of polyglutamine chains J. Chem. Phys. 129 135102
92. Sambriski E J, Ortiz V and de Pablo J J 2009 Sequence effects in the melting and renaturation of short DNA oligonucleotides: structure and mechanistic pathways J. Phys.: Condens. Matter 21 034105
93. Hu J, Ma A and Dinner A R 2008 A two-step nucleotide-flipping mechanism enables kinetic discrimination of DNA lesions by AGT Proc. Natl Acad. Sci. USA 105 4615-20
94. Wang Y L and Schlick T 2007 Distinct energetics and closing pathways for DNA polymerase beta with 8-oxoG template and different incoming nucleotides BMC Struct. Biol. 7 7
95. Dimelow R J, Bryce R A, Masters A J, Hillier I H and Burton N A 2006 Exploring reaction pathways with transition path and umbrella sampling: application to methyl maltoside J. Chem. Phys. 124 114113
96. Pan A C, Sezer D and Roux B 2008 Finding transition pathways using the string method with swarms of trajectories J. Phys. Chem. B 112 3432-40
97. Khalili M and Wales D J 2008 Pathways for conformational change in nitrogen regulatory protein C from discrete path sampling J. Phys. Chem. B 112 2456-65
98. Wales D J 2002 Discrete path sampling Mol. Phys. 100 3285-305
99. Ma L and Cui Q 2007 Activation mechanism of a signaling protein at atomic resolution from advanced computations J. Am. Chem. Soc. 129 10261-8
100. Quaytman S L and Schwartz S D 2007 Reaction coordinate of an enzymatic reaction revealed by transition path sampling Proc. Natl Acad. Sci. USA 104 12253-8
101. Saen-oon S, Quaytman-Machleder S, Schramm V L and Schwartz S D 2008 Atomic detail of chemical transformation at the transition state of an enzymatic reaction Proc. Natl Acad. Sci. USA 105 16543-8
102. Crehuet R and Field M J 2007 A transition path sampling study of the reaction catalyzed by the enzyme chorismate mutase J. Phys. Chem. B 111 5708-18
103. Morelli M J, Tanase-Nicola S, Allen R J and ten Wolde P R 2008 Reaction coordinates for the flipping of genetic switches Biophys. J. 94 3413-23
104. Morelli M J, ten Wolde P R and Allen R J 2009 DNA looping provides stability and robustness to the bacteriophase lambda switch Proc. Natl Acad. Sci. USA 106 18101-6
105. Huang L and Makarov D E 2008 The rate constant of polymer reversal inside a pore J. Chem. Phys. 128 114903
106. Hernandez-Ortiz J P and de Pablo J J 2008 Hydrodynamic effects on the translocation rate of a polymer through a narrow pore J. Chem. Phys. at press
107. Chekmarev D S, Ishida T and Levy R M 2004 Long-time conformational transitions of alanine dipeptide in aqueous solution: continuous and discrete-state kinetic models J. Phys. Chem. B 108 19487-95
108. de Oliveira C A F, Hamelberg D and McCammon J A 2007 Estimating kinetic rates from accelerated molecular dynamics simulations: alanine dipeptide in explicit solvent as a case study J. Chem. Phys. 127 175105-8
109. Chun H M, Padilla C E, Chin D N, Watanabe M, Karlov V I, Alper H E, Soosaar K, Blair K B, Becker O M, Caves L S D, Nagle R, Haney D N and Farmer B L 2000 MBO(N)D: a multibody method for long-time molecular dynamics simulations J. Comput. Chem. 21 159-84
110. Vedell P and Wu Z 2008 The solution of the boundary-value problems for the simulation of transition of protein conformation Int. J. Numer. Anal. Model. submitted
111. Frenkel D and Smit B 2002 Understanding Molecular Simulation: from Algorithms to Applications (Boston: Academic)
112. Neidigh J W, Fesinmeyer R M and Andersen N H 2002 Designing a 20-residue protein Nat. Struct. Biol. 9 425-30
113. Linhananta A, Boer J and MacKay I 2005 The equilibrium properties and folding kinetics of an all-atom Go model of the Trp-cage J. Chem. Phys. 122 114901
114. Ota M, Ikeguchi M and Kidera A 2004 Phylogeny of protein-folding trajectories reveals a unique pathway to native structure Proc. Natl Acad. Sci. USA 101 17658-63
115. Simmerling C, Strockbine B and Roitberg A E 2002 All-atom structure prediction and folding simulations of a stable protein J. Am. Chem. Soc. 124 11258-9
116. Snow C D, Zagrovic B and Pande V S 2002 The Trp cage: folding kinetics and unfolded state topology via molecular dynamics simulations J. Am. Chem. Soc. 124 14548-9