Chapter 3 Methods for Monte Carlo Simulations of Biomacromolecules

Annual Reports in Computational Chemistry

Volumn 5, Issue , 2009, Pages 49-76

  Vitalis, Andreas ^a   Pappu, Rohit V ^a  

^a Center for Computational Biology   (United States)

Author keywords

concerted rotations; Monte Carlo simulations; multicanonical ensemble; polynucleotides; polypeptides; torsional space

Indexed keywords

EID: 69449096819     PISSN: 15741400     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1574-1400(09)00503-9     Document Type: Review

References (145)

1. Plotkin S.S., and Onuchic J.N. Understanding protein folding with energy landscape theory. Part I: Basic concepts. Q. Rev. Biophys. 35 (2002) 111-167
2. Plotkin S.S., and Onuchic J.N. Understanding protein folding with energy landscape theory part II: Quantitative aspects. Q. Rev. Biophys. 35 (2002) 205-286
3. McCammon J.A., Gelin B.R., and Karplus M. Dynamics of folded proteins. Nature 267 (1977) 585-590
4. Jorgensen W.L., and Tirado-Rives J. Monte Carlo vs molecular dynamics for conformational sampling. J. Phys. Chem. 100 (1996) 14508-14513
5. Baker N.A. Improving implicit solvent simulations: a Poisson-centric view. Curr. Opin. Struct. Biol. 15 (2005) 137-143
6. Chen J., Brooks Iii C.L., and Khandogin J. Recent advances in implicit solvent-based methods for biomacromolecular simulations. Curr. Opin. Struct. Biol. 18 (2008) 140-148
7. Onufriev A. Implicit solvent models in molecular dynamics simulations: a brief overview. In: Wheeler R.A., and Spellmeyer D.C. (Eds). Annual Reports in Computational Chemistry Vol. 4 (2008), Elsevier, Amsterdam 125-137
8. Frenkel D., and Smit B. Understanding Molecular Simulation. 2nd ed. (2002), Academic Press, San Diego
9. Binder K. Monte Carlo Simulation in Statistical Physics. 3rd ed. (1997), Springer-Verlag, Berlin
10. Allen M.P., and Tildesley D.J. Computer Simulation of Liquids (1989), Oxford University Press, Oxford, NY
11. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., and Teller E. Equation of state calculations by fast computing machines. J. Chem. Phys. 21 (1953) 1087-1092
12. Borovinskiy A.L., and Grosberg A.Y. Design of toy proteins capable of rearranging conformations in a mechanical fashion. J. Chem. Phys. 118 (2003) 5201-5212
13. Mazenko G.A. Equilibrium Statistical Mechanics (2000), Wiley Interscience, New York
14. Jorgensen W.L., and Tirado-Rives J. Molecular modeling of organic and biomacromolecular systems using BOSS and MCPRO. J. Comput. Chem. 26 (2005) 1689-1700
15. Hess B., Kutzner C., Van Der Spoel D., and Lindahl E. GROMACS 4: algorithms for highly efficient, load-balanced, and scalable molecular simulation. J. Chem. Theory Comput. 4 (2008) 435-447
16. Phillips J.C., Braun R., Wang W., Gumbart J., Tajkhorshid E., Villa E., Chipot C., Skeel R.D., Kalé L., and Schulten K. Scalable molecular dynamics with NAMD. J. Comput. Chem. 26 (2005) 1781-1802
17. Ponder, J.W. (2004). TINKER-Software Tools for Molecular Design (http://dasher.wustl.edu/tinker), 4.2 ed.
18. Case D.A., Darden T.A., Cheatham T.E., Simmerling C.L., Wang J., Duke R.E., Luo R., Crowley M., Walker R.C., Zhang W., Merz K.M., Wang B., Hayik S., Roitberg A., Seabra G., Kolossváry I., Wong K.F., Paesani F., Vanicek J., Wu X., Brozell S.R., Steinbrecher T., Gohlke H., Yang L., Tan C., Mongan J., Hornak V., Cui G., Mathews D.H., Seetin M.G., Sagui C., Babin V., and Kollman P.A. AMBER 10. (2008), University of California, San Francisco
19. Brooks B.R., Bruccoleri R.E., Olafson B.D., States D.J., Swaminathan S., and Karplus M. CHARMM: a program for macromolecular energy, minimization, and dynamics calculations. J. Comput. Chem. 4 (1983) 187-217
20. Hu J., Ma A., and Dinner A.R. Monte Carlo simulations of biomacromolecules: the MC module in CHARMM. J. Comput. Chem. 27 (2006) 203-216
21. Martin, M.G. (2008). MCCCS Towhee (http://towhee.sourceforge.net/).
22. Irbäck A., and Mohanty S. PROFASI: a Monte Carlo simulation package for protein folding and aggregation. J. Comput. Chem. 27 (2006) 1548-1555
23. Kutteh R., and Straatsma T.P. Molecular dynamics with general holonomic constraints and application to internal coordinate constraints. In: Lipkowitz L.D., and Boyd D.B. (Eds). Reviews in Computational Chemistry Vol. 12 (1998), Wiley, New York 75-136
24. Patriciu A., Chirikjian G.S., and Pappu R.V. Analysis of the conformational dependence of mass-metric tensor determinants in serial polymers with constraints. J. Chem. Phys. 121 (2004) 12708-12720
25. Fixman M. Classical statistical mechanics of constraints: a theorem and application to polymers. Proc. Natl. Acad. Sci. U.S.A. 71 (1974) 3050-3053
26. Ulmschneider J.P., Ulmschneider M.B., and Di Nola A. Monte Carlo vs molecular dynamics for all-atom polypeptide folding simulations. J. Phys. Chem. B 110 (2006) 16733-16742
27. Cahill S., Cahill M., and Cahill K. On the kinematics of protein folding. J. Comput. Chem. 24 (2003) 1364-1370
28. Karplus M., and Kushick J.N. Method for estimating the configurational entropy of macromolecules. Macromolecules 14 (1981) 325-332
29. Fitzgerald J.E., Jha A.K., Sosnick T.R., and Freed K.F. Polypeptide motions are dominated by peptide group oscillations resulting from dihedral angle correlations between nearest neighbors. Biochemistry 46 (2007) 669-682
30. Vitalis A., and Pappu R.V. ABSINTH: a new continuum solvation model for simulations of polypeptides in aqueous solutions. J. Comput. Chem. 30 (2009) 673-699
31. Kaminski G.A., Friesner R.A., Tirado-Rives J., and Jorgensen W.L. Evaluation and reparametrization of the OPLS-AA force field for proteins via comparison with accurate quantum chemical calculations on peptides. J. Phys. Chem. B 105 (2001) 6474-6487
32. Skeel R.D., and Izaguirre J.A. An impulse integrator for Langevin dynamics. Mol. Phys. 100 (2002) 3885-3891
33. Duan Y., Wu C., Chowdhury S., Lee M.C., Xiong G., Zhang W., Yang R., Cieplak P., Luo R., Lee T., Caldwell J., Wang J., and Kollman P. A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations. J. Comput. Chem. 24 (2003) 1999-2012
34. Foloppe N., and MacKerell Jr. A.D. All-atom empirical force field for nucleic acids: I. Parameter optimization based on small molecule and condensed phase macromolecular target data. J. Comput. Chem. 21 (2000) 86-104
35. MacKerell Jr. A.D., Bashford D., Bellott M., Dunbrack Jr. R.L., Evanseck J.D., Field M.J., Fischer S., Gao J., Guo H., Ha S., Joseph-McCarthy D., Kuchnir L., Kuczera K., Lau F.T.K., Mattos C., Michnick S., Ngo T., Nguyen D.T., Prodhom B., Reiher Iii W.E., Roux B., Schlenkrich M., Smith J.C., Stote R., Straub J., Watanabe M., Wiórkiewicz-Kuczera J., Yin D., and Karplus M. All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. B 102 (1998) 3586-3616
36. Oostenbrink C., Villa A., Mark A.E., and Van Gunsteren W.F. A biomacromolecular force field based on the free enthalpy of hydration and solvation: the GROMOS force-field parameter sets 53A5 and 53A6. J. Comput. Chem. 25 (2004) 1656-1676
37. Darden T., York D., and Pedersen L. Particle mesh Ewald: an N·log(N) method for Ewald sums in large systems. J. Chem. Phys. 98 (1993) 10089-10092
38. Mallik B., Masunov A., and Lazaridis T. Distance and exposure dependent effective dielectric function. J. Comput. Chem. 23 (2002) 1090-1099
39. Michel J., Taylor R.D., and Essex J.W. Efficient generalized born models for Monte Carlo simulations. J. Chem. Theory Comput. 2 (2006) 732-739
40. Nilmeier J., and Jacobson M. Multiscale Monte Carlo sampling of protein sidechains: application to binding pocket flexibility. J. Chem. Theory Comput. 4 (2008) 835-846
41. Gelb L.D. Monte Carlo simulations using sampling from an approximate potential. J. Chem. Phys. 118 (2003) 7747-7750
42. Hetényi B., Bernacki K., and Berne B.J. Multiple "time step" Monte Carlo. J. Chem. Phys. 117 (2002) 8203-8207
43. Essmann U., Perera L., Berkowitz M.L., Darden T., Lee H., and Pedersen L.G. A smooth particle mesh Ewald method. J. Chem. Phys. 103 (1995) 8577-8593
44. Bernacki K., Hetényi B., and Berne B.J. Multiple "time step" Monte Carlo simulations: application to charged systems with Ewald summation. J. Chem. Phys. 121 (2004) 44-50
45. Ewald P.P. Die Berechnung optischer und elektrostatischer Gitterpotentiale. Annalen der Physik 369 (1921) 253-287
46. Brush S.G., Sahlin H.L., and Teller E. Monte-Carlo study of a one-component plasma. I. J. Chem. Phys. 45 (1966) 2102-2118
47. Hansen J.P. Statistical mechanics of dense ionized matter. I. Equilibrium properties of the classical one-component plasma. Phys. Rev. A 8 (1973) 3096-3109
48. Adams D.J., and Dubey G.S. Taming the Ewald sum in the computer simulation of charged systems. J. Comput. Phys. 72 (1987) 156-176
49. Toukmaji A.Y., and Board Jr. J.A. Ewald summation techniques in perspective: a survey. Comput. Phys. Commun. 95 (1996) 73-92
50. Tironi I.G., Sperb R., Smith P.E., and Van Gunsteren W.F. A generalized reaction field method for molecular dynamics simulations. J. Chem. Phys. 102 (1995) 5451-5459
51. Hockney R.W., and Eastwood J.W. Computer Simulations Using Particles (1981), McGraw-Hill, New York
52. Verlet L. Computer "experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 159 (1967) 98-103
53. Murthy V.L., Srinivasan R., Draper D.E., and Rose G.D. A complete conformational map for RNA. J. Mol. Biol. 291 (1999) 313-327
54. Lal M. 'Monte Carlo' computer simulation of chain molecules. I. Mol. Phys. 17 (1969) 57-64
55. Dunbrack Jr. R.L. Rotamer libraries in the 21st century. Curr. Opin. Struct. Biol. 12 (2002) 431-440
56. Ho B.K., Coutsias E.A., Seok C., and Dill K.A. The flexibility in the proline ring couples to the protein backbone. Protein Sci. 14 (2005) 1011-1018
57. Vitagliano L., Berisio R., Mastrangelo A., Mazzarella L., and Zagari A. Preferred proline puckerings in cis and trans peptide groups: implications for collagen stability. Protein Sci. 10 (2001) 2627-2632
58. Saenger W. Principles of Nucleic Acid Structure. 1st ed. (1984), Springer, New York
59. Sklenar H., Wüstner D., and Rohs R. Using internal and collective variables in Monte Carlo simulations of nucleic acid structures: chain breakage/closure algorithm and associated Jacobians. J. Comput. Chem. 27 (2006) 309-315
60. Binder K., Baschnagel J., and Paul W. Glass transition of polymer melts: test of theoretical concepts by computer simulation. Prog. Polymer Sci. (Oxford) 28 (2003) 115-172
61. Tanaka M., Grosberg A.Y., and Tanaka T. Molecular dynamics simulations of polyampholytes. Langmuir 15 (1999) 4052-4055
62. Takada S., and Wolynes P.G. Glassy dynamics of random heteropolymers. Prog. Theor. Phys. Suppl. (1997) 49-52
63. Vitalis A., Wang X., and Pappu R.V. Quantitative characterization of intrinsic disorder in polyglutamine: insights from analysis based on polymer theories. Biophys. J. 93 (2007) 1923-1937
64. Frisch T., and Verga A. Slow relaxation and solvent effects in the collapse of a polymer. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66 (2002) 041807
65. Ziv G., Thirumalai D., and Haran G. Collapse transition in proteins. Phys. Chem. Chem. Phys. 11 (2009) 83-93
66. Straub J.E., and Thirumalai D. Exploring the energy landscape in proteins. Proc. Natl. Acad. Sci. U.S.A. 90 (1993) 809-813
67. Van Gunsteren W.F., Bakowies D., Baron R., Chandrasekhar I., Christen M., Daura X., Gee P., Geerke D.P., Glättli A., Hünenberger P.H., Kastenholz M.A., Oostenbrink C., Schenk M., Trzesniak D., Van Der Vegt N.F.A., and Yu H.B. Biomacromolecular modeling: goals, problems, perspectives. Angew. Chem. Int. Ed. 45 (2006) 4064-4092
68. Hess B. Convergence of sampling in protein simulations. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65 (2002) 031910
69. Frickenhaus S., Kannan S., and Zacharias M. Efficient evaluation of sampling quality of molecular dynamics simulations by clustering of dihedral torsion angles and sammon mapping. J. Comput. Chem. 30 (2009) 479-492
70. Son W.J., Jang S., and Shin S. A simple method of estimating sampling consistency based on free energy map distance. J. Mol. Graph. Model. 27 (2008) 321-325
71. Monticelli L., Sorin E.J., Tieleman D.P., Pande V.S., and Colombo G. Molecular simulation of multistate peptide dynamics: a comparison between microsecond timescale sampling and multiple shorter trajectories. J. Comput. Chem. 29 (2008) 1740-1752
72. Karney C.F.F. Quaternions in molecular modeling. J. Mol. Graph. Model. 25 (2007) 595-604
73. Franklin J., and Doniach S. Adaptive time stepping in biomacromolecular dynamics. J. Chem. Phys. 123 (2005) 124909
74. Barth E., Leimkuhler B., and Reich S. Time-reversible variable-stepsize integrator for constrained dynamics. SIAM J. Sci. Comput. 21 (1999) 1027-1044
75. Izaguirre J.A., Catarello D.P., Wozniak J.M., and Skeel R.D. Langevin stabilization of molecular dynamics. J. Chem. Phys. 114 (2001) 2090-2098
76. Vitalis A., Wang X., and Pappu R.V. Atomistic simulations of the effects of polyglutamine chain length and solvent quality on conformational equilibria and spontaneous homodimerization. J. Mol. Biol. 384 (2008) 279-297
77. Sokal A.D. Monte Carlo methods for the self-avoiding walk. In: Binder K. (Ed). In Monte Carlo and Molecular Dynamics Simulations in Polymer Science (1995), Oxford University Press, New York 47-124
78. Podtelezhnikov A.A., and Wild D.L. Exhaustive Metropolis Monte Carlo sampling and analysis of polyalanine conformations adopted under the influence of hydrogen bonds. Protein. Struct. Funct. Genet. 61 (2005) 94-104
79. Go N., and Scheraga H.A. Ring closure and local conformational deformations of chain molecules. Macromolecules 3 (1970) 178-187
80. Bruccoleri R.E., and Karplus M. Chain closure with bond angle variations. Macromolecules 18 (1985) 2767-2773
81. Ulmschneider J.P., and Jorgensen W.L. Monte Carlo backbone sampling for polypeptides with variable bond angles and dihedral angles using concerted rotations and a Gaussian bias. J. Chem. Phys. 118 (2003) 4261-4271
82. Dodd L.R., Boone T.D., and Theodorou D.N. A concerted rotation algorithm for atomistic Monte Carlo simulation of polymer melts and glasses. Mol. Phys. 78 (1993) 961-996
83. Hoffmann D., and Knapp E.W. Polypeptide folding with off-lattice Monte Carlo dynamics: the method. Eur. Biophys. J. 24 (1996) 387-403
84. Dinner A.R. Local deformations of polymers with nonplanar rigid main-chain internal coordinates. J. Comput. Chem. 21 (2000) 1132-1144
85. Mezei M. Efficient Monte Carlo sampling for long molecular chains using local moves, tested on a solvated lipid bilayer. J. Chem. Phys. 118 (2003) 3874-3879
86. Favrin G., Irbäck A., and Sjunnesson F. Monte Carlo update for chain molecules: biased Gaussian steps in torsional space. J. Chem. Phys. 114 (2001) 8154-8158
87. Coutsias E.A., Seok C., Jacobson M.P., and Dill K.A. A kinematic view of loop closure. J. Comput. Chem. 25 (2004) 510-528
88. Kolodny R., Guibas L., Levitt M., and Koehl P. Inverse kinematics in biology: the protein loop closure problem. Int. J. Robot. Res. 24 (2005) 151-163
89. Swendsen R.H., and Wang J.S. Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett. 58 (1987) 86-88
90. Wolff U. Collective Monte Carlo updating for spin systems. Phys. Rev. Lett. 62 (1989) 361-364
91. Luijten E. Introduction to cluster Monte Carlo algorithms. In: Ferrario M., Ciccotti G., and Binder K. (Eds). Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology Vol. 1-703 (2006), Springer, Berlin 13-38
92. Liu J., and Luijten E. Rejection-free geometric cluster algorithm for complex fluids. Phys. Rev. Lett. 92 (2004) 035504
93. Dress C., and Krauth W. Cluster algorithm for hard spheres and related systems. J. Phys. A Gen. Phys. 28 (1995) L597-L601
94. Whitelam S., and Geissler P.L. Avoiding unphysical kinetic traps in Monte Carlo simulations of strongly attractive particles. J. Chem. Phys. 127 (2007) 154101
95. Bhattacharyay A., and Troisi A. Self-assembly of sparsely distributed molecules: an efficient cluster algorithm. Chem. Phys. Lett. 458 (2008) 210-213
96. Liu J., and Luijten E. Generalized geometric cluster algorithm for fluid simulation. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71 (2005) 066701
97. Maggs A.C. Multiscale Monte Carlo algorithm for simple fluids. Phys. Rev. Lett. 97 (2006) 197802
98. Pangali C., Rao M., and Berne B.J. On a novel Monte Carlo scheme for simulating water and aqueous solutions. Chem. Phys. Lett. 55 (1978) 413-417
99. Rossky P.J., Doll J.D., and Friedman H.L. Brownian dynamics as smart Monte Carlo simulation. J. Chem. Phys. 69 (1978) 4628-4633
100. Heyes D.M., and Branka A.C. Monte Carlo as Brownian dynamics. Mol. Phys. 94 (1998) 447-454
101. Kotelyanskii M.J., and Suter U.W. A dynamic Monte Carlo method suitable for molecular simulations. J. Chem. Phys. 96 (1992) 5383-5388
102. Duane S., Kennedy A.D., Pendleton B.J., and Roweth D. Hybrid Monte Carlo. Phys. Lett. B 195 (1987) 216-222
103. Kennedy A.D., and Pendleton B. Acceptances and autocorrelations in hybrid Monte Carlo. Nucl. Phys. B (Proc. Suppl.) 20 (1991) 118-121
104. Mackenzie P.B. An improved hybrid Monte Carlo method. Phys. Lett. B 226 (1989) 369-371
105. Faller R., and De Pablo J.J. Constant pressure hybrid molecular dynamics - Monte Carlo simulations. J. Chem. Phys. 116 (2002) 55-59
106. Izaguirre J.A., and Hampton S.S. Shadow hybrid Monte Carlo: an efficient propagator in phase space of macromolecules. J. Comput. Phys. 200 (2004) 581-604
107. Akhmatskaya E., Bou-Rabee N., and Reich S. A comparison of generalized hybrid Monte Carlo methods with and without momentum flip. J. Comput. Phys. 228 (2009) 2256-2265
108. Kennedy A.D. Higher order hybrid Monte Carlo. Nucl. Phys. B (Proc. Suppl.) 9 (1989) 457-462
109. Berendsen H.J.C., Postma J.P.M., Van Gunsteren W.F., Di Nola A., and Haak J.R. Molecular dynamics with coupling to an external bath. J. Chem. Phys. 81 (1984) 3684-3690
110. Kremer K., and Binder K. Monte Carlo simulation of lattice models for macromolecules. Comput. Phys. Rep. 7 (1988) 259-310
111. Nidras P.P., and Brak R. New Monte Carlo algorithms for interacting self-avoiding walks. J. Phys. A Math. Gen. 30 (1997) 1457-1469
112. Siepmann J.I., and Frenkel D. Configurational bias Monte Carlo: a new sampling scheme for flexible chains. Mol. Phys. 75 (1992) 59-70
113. O'Toole E.M., and Panagiotopoulos A.Z. Monte Carlo simulation of folding transitions of simple model proteins using a chain growth algorithm. J. Chem. Phys. 97 (1992) 8644-8652
114. Frenkel D., Mooij G.C.A.M., and Smit B. Novel scheme to study structural and thermal properties of continuously deformable molecules. J. Phys. Condens. Matter 4 (1992) 3053-3076
115. Vendruscolo M. Modified configurational bias Monte Carlo method for simulation of polymer systems. J. Chem. Phys. 106 (1997) 2970-2976
116. Vlugt T.J.H., Martin M.G., Smit B., Siepmann J.I., and Krishna R. Improving the efficiency of the configurational-bias Monte Carlo algorithm. Mol. Phys. 94 (1998) 727-733
117. Zhang J., Kou S.C., and Liu J.S. Biopolymer structure simulation and optimization via fragment regrowth Monte Carlo. J. Chem. Phys. 126 (2007) 225101
118. Escobedo F.A., and De Pablo J.J. Extended continuum configurational bias Monte Carlo methods for simulation of flexible molecules. J. Chem. Phys. 102 (1995) 2636-2652
119. Houdayer J. The wormhole move: a new algorithm for polymer simulations. J. Chem. Phys. 116 (2002) 1783-1787
120. Laso M., Karayiannis N.C., and Müller M. Min-map bias Monte Carlo for chain molecules: biased Monte Carlo sampling based on bijective minimum-to-minimum mapping. J. Chem. Phys. 125 (2006) 164108
121. Grassberger P. Pruned-enriched Rosenbluth method: simulations of θ polymers of chain length up to 1 000 000. Phys. Rev. E -Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 56 (1997) 3682-3693
122. Consta S., Vlugt T.J.H., Hoeth J.W., Smit B., and Frenkel D. Recoil growth algorithm for chain molecules with continuous interactions. Mol. Phys. 97 (1999) 1243-1254
123. Prentiss M.C., Wales D.J., and Wolynes P.G. Protein structure prediction using basin-hopping. J. Chem. Phys. 128 (2008) 225106
124. Sugita Y., Mitsutake A., and Okamoto Y. Generalized-ensemble algorithms for protein folding simulations. In: Janke W. (Ed). Rugged Free Energy Landscapes Vol. 736 (2008), Springer, Berlin 369-407
125. Frantz D.D., Freeman D.L., and Doll J.D. Reducing quasi-ergodic behavior in Monte Carlo simulations by J-walking: applications to atomic clusters. J. Chem. Phys. 93 (1990) 2769-2784
126. Zhou R., and Berne B.J. Smart walking: a new method for Boltzmann sampling of protein conformations. J. Chem. Phys. 107 (1997) 9185-9196
127. Xu H., and Berne B.J. Multicanonical jump walking: a method for efficiently sampling rough energy landscapes. J. Chem. Phys. 110 (1999) 10299-10306
128. Brown S., and Head-Gordon T. Cool walking: a new Markov chain Monte Carlo sampling method. J. Comput. Chem. 24 (2003) 68-76
129. Andricioaei I., Straub J.E., and Voter A.F. Smart darting Monte Carlo. J. Chem. Phys. 114 (2001) 6994-7000
130. Nigra P., Freeman D.L., and Doll J.D. Combining smart darting with parallel tempering using Eckart space: application to Lennard-Jones clusters. J. Chem. Phys. 122 (2005) 1
131. Wang F., and Landau D.P. Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett. 86 (2001) 2050
132. Shell M.S., Debenedetti P.G., and Panagiotopoulos A.Z. Generalization of the Wang-Landau method for off-lattice simulations. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66 (2002) 056703
133. Wüst T., and Landau D.P. The HP model of protein folding: a challenging testing ground for Wang-Landau sampling. Comput. Phys. Commun. 179 (2008) 124-127
134. Thomas G.L., Sessions R.B., and Parker M.J. Density guided importance sampling: application to a reduced model of protein folding. Bioinformatics 21 (2005) 2839-2843
135. Shimada J., Kussell E.L., and Shakhnovich E.I. The folding thermodynamics and kinetics of crambin using an all-atom Monte Carlo simulation. J. Mol. Biol. 308 (2001) 79-95
136. Shimada J., and Shakhnovich E.I. The ensemble folding kinetics of protein G from an all-atom Monte Carlo simulation. Proc. Natl. Acad. Sci. U.S.A. 99 (2002) 11175-11180
137. Nivón L.G., and Shakhnovich E.I. All-atom Monte Carlo simulation of GCAA RNA folding. J. Mol. Biol. 344 (2004) 29-45
138. Shental-Bechor D., Kirca S., Ben-Tal N., and Haliloglu T. Monte Carlo studies of folding, dynamics, and stability in α-helices. Biophys. J. 88 (2005) 2391-2402
139. Irbäck A. Protein folding, unfolding and aggregation studied using an all-atom model with a simplified interaction potential. In: Janke W. (Ed). Rugged Free Energy Landscapes Vol. 736 (2008), Springer, Berlin 269-291
140. Li D.W., Mohanty S., Irbäck A., and Huo S. Formation and growth of oligomers: a Monte Carlo study of an amyloid tau fragment. PLoS Comput. Biol. 4 (2008) e1000238
141. Mitternacht S., Luccioli S., Torcini A., Imparato A., and Irbäck A. Changing the mechanical unfolding pathway of FnIII10 by tuning the pulling strength. Biophys. J. 96 (2009) 429-441
142. Ulmschneider J.P., Ulmschneider M.B., and Di Nola A. Monte Carlo folding of trans-membrane helical peptides in an implicit generalized Born membrane. Protein. Struct. Funct. Genet. 69 (2007) 297-308
143. Ulmschneider J.P., and Ulmschneider M.B. Folding simulations of the transmembrane helix of virus protein U in an implicit membrane model. J. Chem. Theory Comput. 3 (2007) 2335-2346
144. De Mori G.M.S., Colombo G., and Micheletti C. Study of the villin headpiece folding dynamics by combining coarse-grained Monte Carlo evolution and all-atom molecular dynamics. Protein. Struct. Funct. Genet. 58 (2005) 459-471
145. Meli M., Morra G., and Colombo G. Investigating the mechanism of peptide aggregation: insights from mixed Monte Carlo-molecular dynamics simulations. Biophys. J. 94 (2008) 4414-4426