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Specialized Methods for Improving Ergodic Sampling Using Molecular Dynamics and Monte Carlo Simulations

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Free Energy Calculations

Part of the book series: Springer Series in CHEMICAL PHYSICS ((CHEMICAL,volume 86))

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References

  1. Eckmann, J.P.; Ruelle, D., Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 1985, 57, 617-656

    CAS  Google Scholar 

  2. Berne, B.J.; Straub, J.E., Novel methods of sampling phase space in the simulation of biological systems, Curr. Opin. Struct. Biol. 1997, 7, 181-189

    CAS  Google Scholar 

  3. Hodel, A.; Simonson, T.; Fox, R.O.; Brunger, A.T., Conformational substates and uncertainty in macromolecular free-energy calculations, J. Phys. Chem. 1993, 97, 3409-3417

    CAS  Google Scholar 

  4. Mountain, R.D.; Thirumalai, D., Measures of effective ergodic convergence in liquids, J. Phys. Chem. 1989, 93, 6975-6979

    CAS  Google Scholar 

  5. Mountain, R.D.; Thirumalai, D., Quantitative measure of efficiency of Monte-Carlo simulations, Physica A 1994, 210, 453-460

    CAS  Google Scholar 

  6. Straub, J.E.; Thirumalai, D., Exploring the energy landscape in proteins, Proc. Natl Acad. Sci. USA 1993, 90, 809-813

    CAS  Google Scholar 

  7. Straub, J.E.; Rashkin, A.; Thirumalai, D., Dynamics in rugged energy landscapes with applications to the S-peptide and Ribonuclease A, J. Am. Chem. Soc. 1994, 116, 2049

    Google Scholar 

  8. Siepmann, J.I.; Sprik, M., Folding of model heteropolymers by configurational-bias Monte Carlo, Chem. Phy. Lett. 1992, 199, 220

    CAS  Google Scholar 

  9. Rossky, P.J.; Doll, J.D.; Friedman, H.L., Brownian dynamics as smart Monte Carlo simulation, J. Chem. Phys. 1978, 69, 4628

    CAS  Google Scholar 

  10. Cao, J.; Berne, B.J., Monte Carlo methods for accelerating barrier crossing: anti-force-bias and variable step algorithms, J. Chem. Phys. 1990, 92, 1980

    CAS  Google Scholar 

  11. Frantz, D.D.; Freeman, D.L.; Doll, J.D., Reducing quasi-ergodic behavior in Monte Carlo simulation by J-walking: Applications to atomic clusters, J. Chem. Phys. 1990, 93,2769

    Google Scholar 

  12. Tsai, C.J.; Jordan, K.D., Use of the histogram and jump-walking methods for overcom-ing slow barrier crossing behavior in Monte Carlo simulations: applications to the phase transitions in the (Ar)13 and (H2 O)8 clusters, J. Chem. Phys. 1993, 99, 6957

    CAS  Google Scholar 

  13. Marinari, E.; Parisi, G., Simulated tempering - a new Monte-Carlo scheme, Europhys. Lett. 1992, 19, 451-458

    CAS  Google Scholar 

  14. Geyer, C.J.; Thompson, E.A., Annealing Markov-chain Monte-Carlo with applications to ancestral inference, J. Am. Stat. Assoc. 1995, 90, 909-920

    Google Scholar 

  15. Hukushima, K.; Nemoto, K., Exchange Monte Carlo method and application to spin glass simulations, J. Phys. Soc. Jpn. 1996, 65, 1604-1608

    CAS  Google Scholar 

  16. Berg, B.A.; Neuhaus, T., Multicanonical algorithms for 1st order phase-transitions, Phys. Lett. B 1991, 267, 249-253

    Google Scholar 

  17. Berg, B.A.; Neuhaus, T., Multicanonical ensemble - a new approach to simulate 1st-order phase-transitions, Phys. Rev. Lett. 1992, 68, 9-12

    Google Scholar 

  18. Swendsen, R.H.; Wang, J.S., Nonuniversal critical-dynamics in Monte-Carlo simulations, Phys. Rev. Lett. 1987, 58, 86-88

    Google Scholar 

  19. Hansmann, U.H.E.; Okamoto, Y.; Eisenmenger, F., Molecular dynamics, Langevin and hybrid Monte Carlo simulations in a multicanonical ensemble, Chem. Phys. Lett. 1996, 259,321-330

    CAS  Google Scholar 

  20. Torrie, G.M.; Valleau, J.P., Non-physical sampling distributions in Monte-Carlo free-energy estimation - umbrella sampling, J. Comput. Phys. 1977, 23, 187-199

    Google Scholar 

  21. Carter, E.A.; Ciccotti, G.; Haynes, J.T.; Kapral, R., Constrained reaction coordinate dynamics for the simulation of rare events, Chem. Phys. Lett. 1989, 156, 472-477

    CAS  Google Scholar 

  22. Darve, E.; Pohorille, A., Calculating free energies using average force, J. Chem. Phys. 2001,115,9169-9183

    CAS  Google Scholar 

  23. Torrie, G.M.; Valleau, J.P., Monte Carlo free energy estimates using non-Boltzmann sampling: Application to the subcritical Lennard-Jones fluid, Chem. Phys. Lett. 1974, 28,578-581

    CAS  Google Scholar 

  24. Lee, J., New Monte-Carlo algorithm - entropic sampling, Phys. Rev. Lett. 1993, 71, 211-214

    CAS  Google Scholar 

  25. Nakajima, N.; Nakamura, H.; Kidera, A., Multicanonical ensemble generated by mole-cular dynamics simulation for enhanced conformational sampling of peptides, J. Phys. Chem. B 1997, 101, 817-824

    CAS  Google Scholar 

  26. Lyubartsev, A.P.; Martsinovski, A.A.; Shevkunov, S.V.; Vorontsovvelyaminov, P.N., New approach to Monte-Carlo calculation of the free-energy - method of expanded ensembles, J. Chem. Phys. 1992, 96, 1776-1783

    CAS  Google Scholar 

  27. Hesselbo, B.; Stinchcombe, R.B., Monte-Carlo simulation and global optimization without parameters, Phys. Rev. Lett. 1995, 74, 2151-2155

    CAS  Google Scholar 

  28. Bartels, C.; Karplus, M., Multidimensional adaptive umbrella sampling: applications to main chain and side chain peptide conformations, J. Comput. Chem. 1997, 18, 1450-1462

    CAS  Google Scholar 

  29. Darve, E.; Wilson, M.A.; Pohorille, A., Calculating free energies using a scaled-force molecular dynamics algorithm, Mol. Simul. 2002, 28, 113-144

    CAS  Google Scholar 

  30. Kumar, S.; Bouzida, D.; Swendsen, R.H.; Kollman, P.A.; Rosenberg, J.M., The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method, J. Comput. Chem. 1992, 13, 1011-1021

    CAS  Google Scholar 

  31. Tsallis, C., Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 1988, 52,479-487

    Google Scholar 

  32. Curado, E.M.F.; Tsallis, C., Generalized statistical mechanics: Connection with ther-modynamics, J. Phys. A: Math. Gen. 1991, 24, L69

    Google Scholar 

  33. Andricioaei, I.; Straub, J.E., Generalized simulated annealing algorithms using Tsallis statistics: application to conformational optimization of a tetrapeptide, Phys. Rev. E 1996,53, R3055-R3058

    CAS  Google Scholar 

  34. Andricioaei, I.; Straub, J.E.; Karplus, M., Simulation of quantum systems using path integrals in a generalized ensemble, Chem. Phys. Lett. 2001, 346, 274-282

    CAS  Google Scholar 

  35. Andricioaei, I.; Straub, J.E., On Monte Carlo and molecular dynamics methods inspired by Tsallis statistics: methodology, optimization, and application to atomic clusters, J. Chem. Phys. 1997, 107, 9117-9124

    CAS  Google Scholar 

  36. Bhattacharya, K.K.; Sethna, J.P., Multicanonical methods, molecular dynamics, and Monte Carlo methods: comparison for Lennard-Jones glasses, Phys. Rev. E 1998, 57, 2553-2562

    CAS  Google Scholar 

  37. Swendsen, R.H.; Wang, J.S., Replica Monte-Carlo simulation of spin-glasses, Phys. Rev. Lett. 1986, 57, 2607-2609

    Google Scholar 

  38. Manousiouthakis, V.I.; Deem, M.W., Strict detailed balance is unnecessary in Monte Carlo simulation, J. Chem. Phys. 1999, 110, 2753-2756

    CAS  Google Scholar 

  39. Kofke, D.A., On the acceptance probability of replica-exchange Monte Carlo trials, J. Chem. Phys. 2002, 117, 6911-6914

    CAS  Google Scholar 

  40. Predescu, C.; Predescu, M.; Ciobanu, C.V., On the efficiency of exchange in parallel tempering Monte Carlo simulations, J. Phys. Chem. B 2005, 109, 4189-4196

    CAS  Google Scholar 

  41. Schug, A.; Herges, T.; Wenzel, W., All-atom folding of the three-helix HIV accessory protein with an adaptive parallel tempering method, Proteins-Struct. Funct. Bioinform. 2004,57,792-798

    CAS  Google Scholar 

  42. . Rathore, N.; Chopra, M.; de Pablo, J.J., Optimal allocation of replicas in parallel tempering simulations, J. Chem. Phys. 2005, 122

    Google Scholar 

  43. Sugita, Y.; Okamoto, Y., Replica-exchange molecular dynamics method for protein folding, Chem. Phys. Lett. 1999, 314, 141-151

    CAS  Google Scholar 

  44. . Calvo, F., All-exchanges parallel tempering, J. Chem. Phys. 2005, 123

    Google Scholar 

  45. Calvo, F.; Neirotti, J.P.; Freeman, D.L.; Doll, J.D., Phase changes in38-atom Lennard-Jones clusters. II. A parallel tempering study of equilibrium and dynamic properties in the molecular dynamics and microcanonical ensembles, J. Chem. Phys. 2000, 112,10350-10357

    CAS  Google Scholar 

  46. Yan, Q.L.; de Pablo, J.J., Hyper-parallel tempering Monte Carlo: Application to the Lennard-Jones fluid and the restricted primitive model, J. Chem. Phys. 1999, 111, 9509-9516

    CAS  Google Scholar 

  47. Andricioaei, I.; Straub, J.E., On Monte Carlo and molecular dynamics methods in-spired by Tsallis statistics: methodology, optimization, and application to atomic clus-ters, J. Chem. Phys. 1997, 107, 9117-9124

    CAS  Google Scholar 

  48. Whitfield, T.W.; Bu, L.; Straub, J.E., Generalized parallel sampling, Physica A - Stat. Mech. Appl. 2002, 305, 157-171

    Google Scholar 

  49. . Jang, S.M.; Shin, S.; Pak, Y., Replica-exchange method using the generalized effective potential, Phys. Rev. Lett. 2003, 91

    Google Scholar 

  50. Liu, H.B.; Jordan, K.D., On the convergence of parallel tempering Monte Carlo simu-lations of LJ(38), J. Phys. Chem. A 2005, 109, 5203-5207

    CAS  Google Scholar 

  51. Sugita, Y.; Kitao, A.; Okamoto, Y., Multidimensional replica-exchange method for free-energy calculations, J. Chem. Phys. 2000, 113, 6042-6051

    CAS  Google Scholar 

  52. Fukunishi, H.; Watanabe, O.; Takada, S., On the Hamiltonian replica exchange method for efficient sampling of biomolecular systems: application to protein structure predic-tion, J. Chem. Phys. 2002, 116, 9058-9067

    CAS  Google Scholar 

  53. Sugita, Y.; Okamoto, Y., Replica-exchange multicanonical algorithm and multicanoni-cal replica-exchange method for simulating systems with rough energy landscape, Chem. Phys. Lett. 2000, 329, 261-270

    CAS  Google Scholar 

  54. Faller, R.; Yan, Q.L.; de Pablo, J.J., Multicanonical parallel tempering, J. Chem. Phys. 2002,116,5419-5423

    CAS  Google Scholar 

  55. Hansmann, U.H.E., Parallel tempering algorithm for conformational studies of biologi-cal molecules, Chem. Phys. Lett. 1997, 281, 140-150

    CAS  Google Scholar 

  56. Garcia, A.E.; Onuchic, J.N., Folding a protein in a computer: An atomic description of the folding/unfolding of protein A, Proc. Natl Acad. Sci. USA 2003, 100, 13898-13903

    CAS  Google Scholar 

  57. Falcioni, M.; Deem, M.W., A biased Monte Carlo scheme for zeolite structure solution, J. Chem. Phys. 1999, 110, 1754-1766

    CAS  Google Scholar 

  58. Haliloglu, T.; Kolinski, A.; Skolnick, J., Use of residual dipolar couplings as restraints in ab initio protein structure prediction, Biopolymers 2003, 70, 548-562

    CAS  Google Scholar 

  59. Earl, D.J.; Deem, M.W., Parallel tempering: theory, applications, and new perspectives, Phys. Chem. Chem. Phys. 2005, 7, 3910-3916

    CAS  Google Scholar 

  60. Frantz, D.D.; Freeman, D.L.; Doll, J.D., Reducing quasi-ergodic behavior in Monte-Carlo simulations by J-walking - applications to atomic clusters, J. Chem. Phys. 1990,93,2769-2784

    CAS  Google Scholar 

  61. Neirotti, J.P.; Calvo, F.; Freeman, D.L.; Doll, J.D., Phase changes in 38-atom Lennard-Jones clusters. I. A parallel tempering study in the canonical ensemble, J. Chem. Phys. 2000,112,10340-10349

    CAS  Google Scholar 

  62. Stolovitzky, G.; Berne, B.J., Catalytic tempering: A method for sampling rough energy landscapes by Monte Carlo, Proc. Natl Acad. Sci. USA 2000, 97, 11164-11169

    CAS  Google Scholar 

  63. Purisima, E.O.; Scheraga, H.A., An approach to the multiple-minima problem by relax-ing dimensionality, Proc. Natl Acad. Sci. USA 1986, 83, 2782-2786

    CAS  Google Scholar 

  64. Faken, D.B.; Voter, A.F.; Freeman, D.L.; Doll, J.D., Dimensional strategies and the minimization problem: barrier-avoiding algorithms, J. Phys. Chem. A 1999, 103, 9521-9526

    CAS  Google Scholar 

  65. Stillinger, F.H.; Weber, T.A., Hidden structure in liquids, Phys. Rev. A 1982, 25, 978-989

    CAS  Google Scholar 

  66. Stillinger, F.H.; Weber, T.A., Packing structures and transitions in liquids and solids, Science 1984, 225, 983-989

    CAS  Google Scholar 

  67. Zhou, R.; Berne, B.J., Smart walking: A new method for Boltzmann sampling of protein conformations, J. Chem. Phys. 1997, 107, 9185

    CAS  Google Scholar 

  68. Li, Z.Q.; Scheraga, H.A., Monte-Carlo-minimization approach to the multiple-minima problem in protein folding, Proc. Natl Acad. Sci. USA 1987, 84, 6611-6615

    CAS  Google Scholar 

  69. Rahman, J.A.; Tully, J.C., Puddle-jumping: A flexible sampling algorithm for rare event systems, Chem. Phys. 2002, 285, 277-287

    CAS  Google Scholar 

  70. . Bogdan, T.V.; Wales, D.J.; Calvo, F., Equilibrium thermodynamics from basin-sampling, J. Chem. Phys. 2006, 124

    Google Scholar 

  71. . Nigra, P.; Freeman, D.L.; Doll, J.D., Combining smart darting with parallel tempering using Eckart space: Application to Lennard-Jones clusters, J. Chem. Phys. 2005, 122

    Google Scholar 

  72. Amadei, A.; Linssen, A.B.M.; Berendsen, H.J.C., Essential dynamics of proteins, Proteins 1993, 17, 412-425

    CAS  Google Scholar 

  73. Balsera, M.A.; Wriggers, W.; Oono, Y.; Schulten, K., Principal component analysis and long time protein dynamics, J. Phys. Chem. 1996, 100, 2567-2572

    CAS  Google Scholar 

  74. Duane, S.; Kennedy, A.D.; Pendleton, B.J.; Roweth, D., Hybrid Monte Carlo, Phys. Lett. B 1987, 195, 216-222

    CAS  Google Scholar 

  75. Mehlig, B.; Heermann, D.W.; Forrest, B.M., Hybrid Monte Carlo method for condensed-matter systems, Phys. Rev. B 1992, 45, 679-685

    Google Scholar 

  76. Metropolis, N.; Rosenbluth, A.W.; Rosenbluth, N.N.; Teller, A.H.; Teller, E., Equation of state calculations by fast computing machines, J. Chem. Phys. 1953, 21, 1087-1092

    CAS  Google Scholar 

  77. Miller, M.A.; Amon, L.M.; Reinhardt, W.P., Should one adjust the maximum step size in a Metropolis Monte Carlo simulation? Chem. Phys. Lett. 2000, 331, 278-284

    CAS  Google Scholar 

  78. Bouzida, D.; Kumar, S.; Swendsen, R.H., Efficient Monte Carlo methods for the computer simulation of biological systems, Phys. Rev. A 1992, 45, 8894-8901

    CAS  Google Scholar 

  79. Ryckaert, J.P.; Ciccotti, G.; Berendsen, H.J.C., Numerical integration of the Cartesian equations of motion of a system with constraints: Molecular dynamics of n-alkanes, J. Comput. Phys. 1977, 23, 327-341

    CAS  Google Scholar 

  80. 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.; Farmer, B.L., MBO(N)D: A multibody method for long-time molecular dynamics simulations, J. Comput. Chem. 2000, 21, 159-184

    CAS  Google Scholar 

  81. Tuckerman, M.E.; Martyna, G.J.; Berne, B.J., Molecular-dynamics algorithm for condensed systems with multiple time scales, J. Chem. Phys. 1990, 93, 1287-1291

    CAS  Google Scholar 

  82. Elber, R.; Meller, J.; Olender, R., Stochastic path approach to compute atomically detailed trajectories: application to the folding of C peptide, J. Phys. Chem. B 1999, 103,899-911

    CAS  Google Scholar 

  83. Elber, R.; Ghosh, A.; Cardenas, A., Long time dynamics of complex systems, Acc. Chem. Res. 2002, 35, 396-403

    CAS  Google Scholar 

  84. Nadler, W.; Schulten, K., Generalized moment expansion for Brownian relaxation processes, J. Chem. Phys. 1985, 82, 151-160

    CAS  Google Scholar 

  85. Kostov, K.S.; Freed, K.F., Mode coupling theory for calculating the memory func-tions of flexible chain molecules: influence on the long time dynamics of oligoglycines, J. Chem. Phys. 1997, 106, 771-783

    CAS  Google Scholar 

  86. Space, B.; Rabitz, H.; Askar, A., Long time scale molecular dynamics subspace inte-gration method applied to anharmonic crystals and glasses, J. Chem. Phys. 1993, 99, 9070-9079

    CAS  Google Scholar 

  87. Dauber-Osguthorpe, P.; Maunder, C.M.; Osguthorpe, D.J., Molecular dynamics: Deci-phering the data, J. Comput. Aided Mol. Des. 1996, 10, 177-185

    CAS  Google Scholar 

  88. Phillips, S.C.; Essex, J.W.; Edge, C.M., Digitally filtered molecular dynamics: the fre-quency specific control of molecular dynamics simulations, J. Chem. Phys. 2000, 112, 2586-2597

    CAS  Google Scholar 

  89. Elber, R.; Karplus, M., Enhanced sampling in molecular-dynamics - use of the time-dependent Hartree approximation for a simulation of carbon-monoxide diffusion through myoglobin, J. Am. Chem. Soc. 1990, 112, 9161-9175

    CAS  Google Scholar 

  90. Ulitsky, A.; Elber, R., Application of the locally enhanced sampling (LES) and a mean-field with a binary collision correction (CLES) to the simulation of Ar diffusion and NO recombination in myoglobin, J. Phys. Chem. 1994, 98, 1034-1043

    CAS  Google Scholar 

  91. Huber, T.; van Gunsteren, W.F., SWARM-MD: searching conformational space by cooperative molecular dynamics, J. Phys. Chem. A 1998, 102, 5937-5943

    CAS  Google Scholar 

  92. Simmerling, C.; Fox, T.; Kollman, P.A., Use of locally enhanced sampling in free energy calculations: Testing and application to the alpha → beta anomerization of glucose, J. Am. Chem. Soc. 1998, 120, 5771-5782

    CAS  Google Scholar 

  93. Piela, L.; Kostrowicki, J.; Scheraga, H.A., The multiple-minima problem in the conformational-analysis of molecules - deformation of the potential-energy hypersur-face by the diffusion equation method, J. Phys. Chem. 1989, 93, 3339-3346

    CAS  Google Scholar 

  94. Liu, Z.H.; Berne, B.J., Method for accelerating chain folding and mixing, J. Chem. Phys. 1993, 99, 6071-6077

    CAS  Google Scholar 

  95. Whitfield, T.W.; Bu, L.; Straub, J.E., Generalized parallel sampling, Physica A 2002, 305,157-171

    Google Scholar 

  96. Krivov, S.V.; Chekmarev, S.F.; Karplus, M., Potential energy surfaces and conforma-tional transitions in biomolecules: A successive confinement approach applied to a solvated tetrapeptide, Phys. Rev. Lett. 2002, 88, 038101

    Google Scholar 

  97. Andricioaei, I.; Straub, J.E., On Monte Carlo and molecular dynamics methods inspired by Tsallis statistics: methodology, optimization, and application to atomic clusters, J. Chem. Phys. 1997, 107, 9117-9124

    CAS  Google Scholar 

  98. Hansmann, U.H.E.; Okamoto, Y., Generalized-ensemble Monte Carlo method for systems with rough energy landscapes, Phys. Rev. E 1997, 56, 2228-2233

    CAS  Google Scholar 

  99. Frantz, D.D.; Freeman, D.L.; Doll, J.D., Reducing quasi-ergodic behavior in Monte Carlo simulations by J-walking: applications to atomic clusters, J. Chem. Phys. 1990, 93,2769-2784

    CAS  Google Scholar 

  100. Marinari, E.; Parisi, G., Simulated tempering - A new Monte Carlo scheme, Europhys. Lett. 1992, 19, 451-458

    CAS  Google Scholar 

  101. Hansmann, U.H.E., Parallel tempering algorithm for conformational studies of biological molecules, Chem. Phys. Lett. 1997, 281, 140-150

    CAS  Google Scholar 

  102. Hess, B., Similarities between principal components of protein dynamics and random diffusion, Phys. Rev. E 2000, 62, 8438-8448

    CAS  Google Scholar 

  103. Tuckerman, M.; Berne, B.J.; Martyna, G.J., Reversible multiple time scale molecular dynamics, J. Chem. Phys. 1992, 97, 1990-2001

    CAS  Google Scholar 

  104. Jarzynski, C., Nonequilibrium equality for free energy differences, Phys. Rev. Lett. 1997,78,2690-2693

    CAS  Google Scholar 

  105. Jorgensen, W.L.; Ravimohan, C., Monte Carlo simulation of differences in free energies of hydration, J. Chem. Phys. 1985, 83, 3050-3054

    CAS  Google Scholar 

  106. Hummer, G.; Szabo, A., Free energy reconstruction from nonequilibrium single-molecule pulling experiments, Proc. Natl Acad. Sci. USA 2001, 98, 3659-3661

    Google Scholar 

  107. Dellago, C.; Bolhuis, P.G.; Csajka, F.S.; Chandler, D., Transition path sampling and the calculation of rate constants, J. Chem. Phys. 1998, 108, 1964-1977

    CAS  Google Scholar 

  108. Dellago, C.; Bolhuis, P.G.; Chandler, D., On the calculation of reaction rate constants in the transition path ensemble, J. Chem. Phys. 1999, 110, 6617-6625

    CAS  Google Scholar 

  109. Oberhofer, H.; Dellago, C.; Geissler, P.L., Biased sampling of nonequilibrium trajectories: can fast switching simulations outperform conventional free energy calculation methods?, J. Phys. Chem. B 2005, 109, 6902-6915

    CAS  Google Scholar 

  110. Corcelli, S.A.; Rahman, J.A.; Tully, J.C., Efficient thermal rate constant calculation for rare event systems, J. Chem. Phys. 2003, 118, 1085-1088

    CAS  Google Scholar 

  111. Voter, A.F., Hyperdynamics: Accelerated molecular dynamics of infrequent events, Phys. Rev. Lett. 1997, 78, 3908-3911

    CAS  Google Scholar 

  112. Voter, A.F., A method for accelerating the molecular dynamics simulation of infrequent events, J. Chem. Phys. 1997, 106, 4665-4677

    CAS  Google Scholar 

  113. Hamelberg, D.; Mongan, J.; McCammon, J.A., Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules, J. Chem. Phys. 2004, 120, 11919-11929

    CAS  Google Scholar 

  114. Laio, A.; Parrinello, M., Escaping free-energy minima, Proc. Natl Acad. Sci. USA 2002, 99,12562-12566

    Google Scholar 

  115. Huber, G.A.; Kim, S., Weighted-ensemble Brownian dynamics simulations for protein association reactions, Biophys. J. 1996, 70, 97-110

    CAS  Google Scholar 

  116. Grubmuller, H., Predicting slow structural transitions in macromolecular systems -conformational flooding, Phys. Rev. E 1995, 52, 2893-2906

    Google Scholar 

  117. MacFadyen, J.; Andricioaei, I., A skewed-momenta method to efficiently generate conformational-transition trajectories, J. Chem. Phys. 2005, 123, 074107

    Google Scholar 

  118. Brooks, B.R.; Janezic, D.; Karplus, M., Harmonic-analysis of large systems. 1. Methodology, J. Comput. Chem. 1995, 16, 1522-1542

    CAS  Google Scholar 

  119. Andricioaei, I.; Dinner, A.R.; Karplus, M., Self-guided enhanced sampling methods for thermodynamic averages, J. Chem. Phys. 2003, 118, 1074-1084

    CAS  Google Scholar 

  120. Go, N.; Noguti, T.; Nishikawa, T., Dynamics of a small globular protein in terms of low-frequency vibrational-modes, Proc. Natl Acad. Sci. USA - Biol. Sci. 1983, 80, 3696-3700

    CAS  Google Scholar 

  121. Levitt, M.; Sander, C.; Stern, P.S., Protein normal-mode dynamics - trypsin-inhibitor, crambin, ribonuclease and lysozyme, J. Mol. Biol. 1985, 181, 423-447

    CAS  Google Scholar 

  122. Brooks, B.; Karplus, M., Normal-modes for specific motions of macromolecules -application to the hinge-bending mode of lysozyme, Proc. Natl Acad. Sci. USA 1985, 82,4995-4999

    CAS  Google Scholar 

  123. Ma, J.P.; Karplus, M., Ligand-induced conformational changes in ras p21: a normal mode and energy minimization analysis, J. Mol. Biol. 1997, 274, 114-131

    CAS  Google Scholar 

  124. Cui, Q.; Li, G.H.; Ma, J.P.; Karplus, M., A normal mode analysis of structural plasticity in the biomolecular motor F-1-ATPase, J. Mol. Biol. 2004, 340, 345-372

    CAS  Google Scholar 

  125. Tama, F.; Sanejouand, Y.H., Conformational change of proteins arising from normal mode calculations, Protein Eng. 2001, 14, 1-6

    CAS  Google Scholar 

  126. Krebs, W.G.; Alexandrov, V.; Wilson, C.A.; Echols, N.; Yu, H.Y.; Gerstein, M., Normal mode analysis of macromolecular motions in a database framework: developing mode concentration as a useful classifying statistic, Proteins-Struct. Funct. Gene. 2002, 48, 682-695

    CAS  Google Scholar 

  127. Delarue, M.; Sanejouand, Y.H., Simplified normal mode analysis of conformational transitions in DNA-dependent polymerases: the elastic network model, J. Mol. Biol. 2002,320,1011-1024

    CAS  Google Scholar 

  128. Tama, F.; Valle, M.; Frank, J.; Brooks, C.L., Dynamic reorganization of the functionally active ribosome explored by normal mode analysis and cryo-electron microscopy, Proc. Natl Acad. Sci. USA 2003, 100, 9319-9323

    CAS  Google Scholar 

  129. . Braun, O.; Hanke, A.; Seifert, U., Probing molecular free energy landscapes by periodic loading, Phys. Rev. Lett. 2004, 93

    Google Scholar 

  130. Sun, S.X., Equilibrium free energies from path sampling of nonequilibrium trajectories, J. Chem. Phys. 2003, 118, 5769-5775

    CAS  Google Scholar 

  131. Ytreberg, F.M.; Zuckerman, D.M., Single-ensemble nonequilibrium path-sampling estimates of free energy differences, J. Chem. Phys. 2004, 120, 10876-10879

    CAS  Google Scholar 

  132. . Mukamel, S., Quantum extension of the Jarzynski relation: analogy with stochastic dephasing, Phys. Rev. Lett. 2003, 90

    Google Scholar 

  133. Lua, R.C.; Grosberg, A.Y., Practical applicability of the Jarzynski relation in statistical mechanics: a pedagogical example, J. Phys. Chem. B 2005, 109, 6805-6811

    CAS  Google Scholar 

  134. Palmer, A.G., NMR characterization of the dynamics of biomacromolecules, Chem. Rev. 2004, 104, 3623-3640

    CAS  Google Scholar 

  135. Kleinert, H., Path Integrals in Quantum Mechanics, Statistics, Polymer Physics and Financial Markets, (3rd edition), World Scientific, Singapore

    Google Scholar 

  136. Onsager, L.; Machlup, S., Fluctuations and irreversible processes, Phys. Rev. 1953, 91, 1505-1512

    CAS  Google Scholar 

  137. Elber, R.; Meller, J.; Olender, R., Stochastic path approach to compute atomically detailed trajectories: application to the folding of C peptide, J. Phys. Chem. B 1999, 103,899-911

    CAS  Google Scholar 

  138. Zuckerman, D.M.; Woolf, T.B., Efficient dynamic importance sampling of rare events in one dimension, Phys. Rev. E 2001, 6302, 016702

    Google Scholar 

  139. Chandler, D.; Wolynes, P.G., Exploiting the isomorphism between quantum theory and classical statistical mechanics of polyatomic fluids, J. Chem. Phys. 1981, 74, 4078-4095

    CAS  Google Scholar 

  140. Berne, B.J.; Thirumalai, D., On the simulation of quantum systems: path integral meth-ods, Annu. Rev. Phys. Chem. 1986, 37, 401-424

    CAS  Google Scholar 

  141. Feynman, R.P.; Hibbs, A.R., Quantum Mechanics and Path Integrals, McGraw-Hill: New York, 1965

    Google Scholar 

  142. Barker, J.A., A quantum-statistical Monte Carlo method: Path integrals with boundary conditions, J. Chem. Phys. 1979, 70, 2914-2918

    CAS  Google Scholar 

  143. Parrinello, M.; Rahman, A., Study of an F center in molten KCl, J. Chem. Phys. 1980, 80,860-867

    Google Scholar 

  144. Kuharski, R.A.; Rossky, P.J., Quantum mechanical contributions to the structure of liquid water, Chem. Phys. Lett. 1984, 103, 357-362

    CAS  Google Scholar 

  145. Thirumalai, D.; Wallqvist, A.; Berne, B.J., Path-integral Monte Carlo simulations of electron localization in water clusters, J. Stat. Phys. 1986, 43, 973-984

    Google Scholar 

  146. Hinsen, K.; Roux, B., Potential of mean force and reaction rates for proton transfer in acetylacetone, J. Chem. Phys. 1997, 106, 3567-3577

    CAS  Google Scholar 

  147. Ceperley, D.M., Path-integrals in the theory of condensed helium, Rev. Mod. Phys. 1995, 67,279-355

    CAS  Google Scholar 

  148. Schweizer, K.S.; Stratt, R.M.; Chandler, D.; Wolynes, P.G., Convenient and accurate discretized path integral methods for equilibrium quantum mechanical calculations, J. Chem. Phys. 1981, 75, 1347-1364

    CAS  Google Scholar 

  149. Pollock, E.L.; Ceperley, D.M., Simulation of quantum many-body systems by path-integral methods, Phys. Rev. B 1984, 30, 2555-2568

    CAS  Google Scholar 

  150. Raedt, H.De; Raedt, B.De, Applications of the generalized Trotter formula, Phys. Rev. A 1983, 28, 3575-3580

    Google Scholar 

  151. Sprik, M.; Klein, M.L.; Chandler, D., Staging: A sampling technique for the Monte Carlo evaluation of path integrals, Phys. Rev. B 1985, 31, 4234-4244

    CAS  Google Scholar 

  152. Herman, M.F.; Bruskin, E.J.; Berne, B.J., On path integral Monte Carlo simulations, J. Chem. Phys. 1982, 76, 5150-5155

    CAS  Google Scholar 

  153. Friesner, R.A.; Levy, R.M., An optimized harmonic reference system for the evaluation of discretized path integrals, J. Chem. Phys. 1984, 80, 4488-4495

    CAS  Google Scholar 

  154. Straub, J.E.; Andricioaei, I., Computational methods inspired by Tsallis statistics: Monte Carlo and molecular dynamics algorithms for the simulation of classical and quantum systems, Braz. J. Phys. 1999, 29, 179-186

    Google Scholar 

  155. Andricioaei, I.; Straub, J.E., Computational methods for the simulation of classical and quantum many body systems sprung from the nonextensive thermostatistics. In Nonextensive Statistical Mechanics and Its Application, Abe, S.; Okamoto, Y., Eds., Lecture Notes in Physics. Springer: Berlin, Heidelberg, New York, 2001, ch. IV, pp. 195-235

    Google Scholar 

  156. Tsallis, C., Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 1988, 52,479-487

    Google Scholar 

  157. Chandler, D. Quantum processes in liquids. In Liquids, Freezing and Glass Transition, Levesque, D.; Hansen, J.; Zinn-Justin, J., Eds. Elsevier: New York, 1990, pp. 195-285

    Google Scholar 

  158. Cao, J.; Voth, G.A., The formulation of quantum statistical mechanics based on Feynman path centroid density, J. Chem. Phys. 1994, 100, 5093-5105

    CAS  Google Scholar 

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  1. Department of Chemistry, Center for Computational Medicine and Biology University of Michigan, 48109-1055, Ann Arbor, Michigan

    Ioan Andricioaei

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  1. Equipe de Dynamique des Assemblages Membranaires UMR CNRS/UHP 7565, Universite Henri Poincare, BP 239, 54506, Vandoe uvre-l s-Nancy cedex, France

    Christophe Chipot

  2. Department of Pharmaceutical Chemistry, University of California San Francisco, 600 16th Street, CA 94143, San Francisco, USA

    Andrew Pohorille

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Andricioaei, I. (2007). Specialized Methods for Improving Ergodic Sampling Using Molecular Dynamics and Monte Carlo Simulations. In: Chipot, C., Pohorille, A. (eds) Free Energy Calculations. Springer Series in CHEMICAL PHYSICS, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38448-9_8

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