Theoretical Chemistry Accounts

, Volume 116, Issue 1–3, pp 297–306 | Cite as

Molecular Dynamics Simulation of Peptide Folding

Regular Article

Abstract

The simulation of peptide folding with atomic resolution has evolved remarkably during the last 7 years, i.e., from absolute skepticism on the capability of classical molecular dynamics (MD) methodology to reproduce complex biological phenomena such as the folding of even simple oligopeptides (6–15 residues) to the seemingly realistic representation of the thermodynamics and kinetics of folding of a rapidly increasing number of polypeptides (over 20 residues). Four factors permitted this rapid progress: the breakthrough of a second generation of force fields, a rapid and steady increase of (commodity) computer performance, a move from local computational resources to large distributed clusters and, last but not less important, a decision of particular groups to spend a large computational effort on projects that most other groups trusted unrealizable at the time. The present account goes over some aspects of peptide folding and its simulation with MD techniques while sweeping through the simulation landmarks of the last 7 years and conjecturing on the future.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Shortle D, Simons KT, Baker D (1998) Clustering of low-energy conformations near the native structures of small proteins. Proc Natl Acad Sci US Am 95:11158–11162CrossRefGoogle Scholar
  2. 2.
    Pappu RV, Srinivasan R, Rose GD (2000) The Flory isolated-pair hypothesis is not valid for polypeptide chains: implications for protein folding. Proc Natl Acad Sci US Am 97:12565–12570CrossRefGoogle Scholar
  3. 3.
    Wong KB, Clarke J, Bond CJ, Neira JL, Freund SMV, Fersht AR, Daggett V (2000) Towards a complete description of the structural and dynamic properties of the denatured state of barnase and the role of residual structure in folding. J Mol Biol 296:1257–1282CrossRefPubMedGoogle Scholar
  4. 4.
    Bai YW, Chung J, Dyson HJ, Wright PE (2001) Structural and dynamic characterization of an unfolded state of poplar apo-plastocyanin formed under nondenaturing conditions. Protein Sci 10:1056–1066CrossRefPubMedGoogle Scholar
  5. 5.
    Plaxco KW, Gross M (2001) Unfolded, yes, but random? Never! Nat Struct Biol 8:659–660CrossRefGoogle Scholar
  6. 6.
    Shortle D, Ackerman MS (2001) Persistence of native-like topology in a denatured protein in 8 M urea. Science 293:487–489CrossRefPubMedGoogle Scholar
  7. 7.
    van Gunsteren WF, Burgi P, Peter C, Daura X (2001) The key to solving the protein-folding problem lies in an accurate description of the denatured state. Angew Chem Int Ed 40:351–355CrossRefGoogle Scholar
  8. 8.
    Choy WY, Mulder FAA, Crowhurst KA, Muhandiram DR, Millett IS, Doniach S, Forman-Kay JD, Kay LE (2002) Distribution of molecular size within an unfolded state ensemble using small-angle X-ray scattering and pulse field gradient NMR techniques. J Mol Biol 316:101–112CrossRefPubMedGoogle Scholar
  9. 9.
    Klein-Seetharaman J, Oikawa M, Grimshaw SB, Wirmer J, Duchardt E, Ueda T, Imoto T, Smith LJ, Dobson CM, Schwalbe H (2002) Long-range interactions within a nonnative protein. Science 295:1719–1722CrossRefPubMedGoogle Scholar
  10. 10.
    Zagrovic B, Snow CD, Khaliq S, Shirts MR, Pande VS (2002) Native-like mean structure in the unfolded ensemble of small proteins. J Mol Biol 323:153–164CrossRefPubMedGoogle Scholar
  11. 11.
    Lei HX, Smith PE (2003) The role of the unfolded state in hairpin stability. Biophys J 85:3513–3520PubMedGoogle Scholar
  12. 12.
    Fitzkee NC, Fleming PJ, Gong HP, Panasik N, Street TO, Rose GD (2005) Are proteins made from a limited parts list? Trends Biochem Sci 30:73–80CrossRefPubMedGoogle Scholar
  13. 13.
    Dyer RB, Maness SJ, Franzen S, Fesinmeyer RM, Olsen KA, Andersen NH (2005) Hairpin folding dynamics: the cold-denatured state is predisposed for rapid refolding. Biochemistry 44:10406–10415CrossRefPubMedGoogle Scholar
  14. 14.
    Plattt GW, McParland VJ, Kalverda AP, Homans SW, Radford SE (2005) Dynamics in the unfolded state of beta(2)-microglobulin studied by NMR. J Mol Biol 346:279–294CrossRefPubMedGoogle Scholar
  15. 15.
    Pletneva EV, Gray HB, Winkler JR (2005) Many faces of the unfolded state: conformational heterogeneity in denatured yeast cytochrome c. J Mol Biol 345:855–867CrossRefPubMedGoogle Scholar
  16. 16.
    Vendruscolo M, Dobson CM (2005) Towards complete descriptions of the free-energy landscapes of proteins. Philos Trans R Soc Lond A Math Phys Eng Sci 363:433–450CrossRefGoogle Scholar
  17. 17.
    Kobayashi T, Ikeguchi M, Sugai S (2000) Molten globule structure of equine beta-lactoglobulin probed by hydrogen exchange. J Mol Biol 299:757–770CrossRefPubMedGoogle Scholar
  18. 18.
    Chakraborty S, Ittah V, Bai P, Luo L, Haas E, Peng ZY (2001) Structure and dynamics of the alpha-lactalbumin molten globule: fluorescence studies using proteins containing a single tryptophan residue. Biochemistry 40:7228–7238PubMedGoogle Scholar
  19. 19.
    Kim YJ, Kim YA, Park N, Son HS, Kim KS, Hahn JH (2005) Structural characterization of the molten globule state of apomyoglobin by limited proteolysis and HPLC-mass spectrometry. Biochemistry 44:7490–7496CrossRefPubMedGoogle Scholar
  20. 20.
    Troullier A, Reinstadler D, Dupont Y, Naumann D, Forge V (2000) Transient non-native secondary structures during the refolding of alpha-lactalbumin detected by infrared spectroscopy. Nat Struct Biol 7:78–86CrossRefPubMedGoogle Scholar
  21. 21.
    Matouschek A, Kellis JT, Serrano L, Fersht AR (1989) Mapping the transition-state and pathway of protein folding by protein engineering. Nature 340:122–126CrossRefPubMedGoogle Scholar
  22. 22.
    Fersht AR, Matouschek A, Serrano L (1992) The folding of an enzyme. 1. Theory of protein engineering analysis of stability and pathway of protein folding. J Mol Biol 224:771–782CrossRefPubMedGoogle Scholar
  23. 23.
    Sosnick TR, Dothager RS, Krantz BA (2004) Differences in the folding transition state of ubiquitin indicated by phi and psi analyses. Proc Natl Acad Sci US Am 101:17377–17382CrossRefGoogle Scholar
  24. 24.
    Horng JC, Cho JH, Raleigh DP (2005) Analysis of the pH-dependent folding and stability of histidine point mutants allows characterization of the denatured state and transition state for protein folding. J Mol Biol 345:163–173CrossRefPubMedGoogle Scholar
  25. 25.
    Raleigh DP, Plaxco KW (2005) The protein folding transition state: what are phi-values really telling us?. Prot Pept Lett 12:117–122CrossRefGoogle Scholar
  26. 26.
    Tollinger M, Kay LE, Forman-Kay JD (2005) Measuring pKa values in protein folding transition state ensembles by NMR spectroscopy. J Am Chem Soc 127:8904–8905CrossRefPubMedGoogle Scholar
  27. 27.
    Evans PA, Radford SE (1994) Probing the structure of folding intermediates. Curr Opin Struct Biol 4:100–106CrossRefGoogle Scholar
  28. 28.
    Plaxco KW, Dobson CM (1996) Time-resolved biophysical methods in the study of protein folding. Curr Opin Struct Biol 6:630–636CrossRefPubMedGoogle Scholar
  29. 29.
    Callender RH, Dyer RB, Gilmanshin R, Woodruff WH (1998) Fast events in protein folding: the time evolution of primary processes. Annu Rev Phys Chem 49:173–202CrossRefPubMedGoogle Scholar
  30. 30.
    Dobson CM, Hore PJ (1998) Kinetic studies of protein folding using NMR spectroscopy. Nat Struct Biol 5:504–507CrossRefPubMedGoogle Scholar
  31. 31.
    Dyson HJ, Wright PE (1998) Equilibrium NMR studies of unfolded and partially folded proteins. Nat Struct Biol 5:499–503CrossRefPubMedGoogle Scholar
  32. 32.
    Onuchic JN, LutheySchulten Z, Wolynes PG (1997) Theory of protein folding: the energy landscape perspective. Annu Rev Phys Chem 48:545–600CrossRefPubMedGoogle Scholar
  33. 33.
    Chan HS, Dill KA (1998) Protein folding in the landscape perspective: Chevron plots and non-Arrhenius kinetics. Proteins-Struct Funct Genet 30:2–33CrossRefPubMedGoogle Scholar
  34. 34.
    Thirumalai D, Klimov DK (1999) Deciphering the timescales and mechanisms of protein folding using minimal off-lattice models. Curr Opin Struct Biol 9:197–207CrossRefPubMedGoogle Scholar
  35. 35.
    Derreumaux P (2000) Ab initio polypeptide structure prediction. Theor Chem Acc 104:1–6Google Scholar
  36. 36.
    Dinner AR, Sali A, Smith LJ, Dobson CM, Karplus M (2000) Understanding protein folding via free-energy surfaces from theory and experiment. Trends Biochem Sci 25:331–339CrossRefPubMedGoogle Scholar
  37. 37.
    Ferrara P, Caflisch A (2000) Folding simulations of a three-stranded antiparallel beta-sheet peptide. Proc Natl Acad Sci US Am 97:10780–10785CrossRefGoogle Scholar
  38. 38.
    Wang HW, Sung SS (2000). Molecular dynamics simulations of three-strand beta-sheet folding. J Am Chem Soc 122:1999–2009CrossRefGoogle Scholar
  39. 39.
    Mirny L, Shakhnovich E (2001) Protein folding theory: from lattice to all-atom models. Annu Rev Biophy Biomol Struct 30:361–396CrossRefGoogle Scholar
  40. 40.
    De Mori GMS, Colombo G, Micheletti C (2005) Study of the villin headpiece folding dynamics by combining coarse-grained Monte Carlo evolution and all-atom molecular dynamics. Proteins-Struct Funct Bioinform 58:459–471CrossRefGoogle Scholar
  41. 41.
    Ding F, Buldyrev SV, Dokholyan NV (2005) Folding Trp-cage to NMR resolution native structure using a coarse-grained protein model. Biophys J 88:147–155CrossRefPubMedGoogle Scholar
  42. 42.
    Irback A, Mohanty S (2005) Folding thermodynamics of peptides. Biophys J 88:1560–1569CrossRefPubMedGoogle Scholar
  43. 43.
    Liwo A, Khalili M, Scheraga HA (2005) Ab initio simulations of protein-folding pathways by molecular dynamics with the united-residue model of polypeptide chains. Proc Natl Acad Sci US Am 102:2362–2367CrossRefGoogle Scholar
  44. 44.
    Daura X, Jaun B, Seebach D, van Gunsteren WF, Mark AE (1998) Reversible peptide folding in solution by molecular dynamics simulation. J Mol Biol 280:925–932CrossRefPubMedGoogle Scholar
  45. 45.
    Duan Y, Kollman PA (1998) Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. Science 282:740–744CrossRefPubMedGoogle Scholar
  46. 46.
    Takano M, Yamato T, Higo J, Suyama A, Nagayama K (1999) Molecular dynamics of a 15-residue poly(L-alanine) in water: helix formation and energetics. J Am Chem Soc 121:605–612CrossRefGoogle Scholar
  47. 47.
    Higo J, Galzitskaya OV, Ono S, Nakamura H (2001) Energy landscape of a beta-hairpin peptide in explicit water studied by multicanonical molecular dynamics. Chem Phys Lett 337:169–175CrossRefGoogle Scholar
  48. 48.
    Hummer G, Garcia AE, Garde S (2001) Helix nucleation kinetics from molecular simulations in explicit solvent. Proteins-Struct Funct Genet 42:77–84CrossRefPubMedGoogle Scholar
  49. 49.
    Garcia AE, Sanbonmatsu KY (2001) Exploring the energy landscape of a beta hairpin in explicit solvent. Proteins-Struct Funct Genet 42:345–354CrossRefPubMedGoogle Scholar
  50. 50.
    Snow CD, Nguyen N, Pande VS, Gruebele M (2002) Absolute comparison of simulated and experimental protein-folding dynamics. Nature 420:102–106CrossRefPubMedGoogle Scholar
  51. 51.
    Colombo G, De Mori GMS, Roccatano D (2003) Interplay between hydrophobic cluster and loop propensity in beta-hairpin formation: a mechanistic study. Protein Sci 12:538–550CrossRefPubMedGoogle Scholar
  52. 52.
    Shea JE, Brooks CL (2001) From folding theories to folding proteins: a review and assessment of simulation studies of protein folding and unfolding. Annu Rev Phys Chem 52:499–535PubMedGoogle Scholar
  53. 53.
    Daggett V (2002) Molecular dynamics simulations of the protein unfolding/folding reaction. Acc Chem Res 35:422–429CrossRefPubMedGoogle Scholar
  54. 54.
    Daggett V, Kollman PA, Kuntz ID (1991) A molecular-dynamics simulation of polyalanine – an analysis of equilibrium motions and helix coil transitions. Biopolymers 31:1115–1134CrossRefPubMedGoogle Scholar
  55. 55.
    Tobias DJ, Mertz JE, Brooks CL (1991) Nanosecond time scale folding dynamics of a pentapeptide in water. Biochemistry 30:6054–6058CrossRefPubMedGoogle Scholar
  56. 56.
    Shakhnovich EI (1997) Theoretical studies of protein-folding thermodynamics and kinetics. Curr Opin Struct Biol 7:29–40CrossRefPubMedGoogle Scholar
  57. 57.
    Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA (1995) A 2nd generation force-field for the simulation of proteins, nucleic-acids, and organic-molecules. J Am Chem Soc 117:5179–5197CrossRefGoogle Scholar
  58. 58.
    Jorgensen WL, Maxwell DS, TiradoRives J (1996) Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J Am Chem Soc 118:11225–11236CrossRefGoogle Scholar
  59. 59.
    MacKerell AD, Bashford D, Bellott M, Dunbrack RL, Evanseck JD, Field MJ, Fischer S, Gao J, Guo H, Ha S, Joseph-McCarthy D, Kuchnir L, Kuczera K, Lau FTK, Mattos C, Michnick S, Ngo T, Nguyen DT, Prodhom B, Reiher WE, Roux B, Schlenkrich M, Smith JC, Stote R, Straub J, Watanabe M, Wiorkiewicz- Kuczera J, Yin D, Karplus M (1998) All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B 102:3586–3616CrossRefGoogle Scholar
  60. 60.
    Daura X, Mark AE, van Gunsteren WF (1998) Parametrization of aliphatic CHn united atoms of GROMOS96 force field. J Comput Chem 19:535–547CrossRefGoogle Scholar
  61. 61.
    Daura X, vanGunsteren WF, Rigo D, Jaun B, Seebach D (1997) Studying the stability of a helical beta-heptapeptide by molecular dynamics simulations. Chem Eur J 3:1410–1417Google Scholar
  62. 62.
    Kubelka J, Eaton WA, Hofrichter J (2003) Experimental tests of villin subdomain folding simulations. J Mol Biol 329:625–630CrossRefPubMedGoogle Scholar
  63. 63.
    Berendsen HJC (1998) Protein folding – a glimpse of the holy grail?. Science 282:642–643CrossRefPubMedGoogle Scholar
  64. 64.
    Chipot C, Pohorille A (1998) Folding and translocation of the undecamer of poly-L-leucine across the water-hexane interface: a molecular dynamics study. J Am Chem Soc 120:11912–11924CrossRefPubMedGoogle Scholar
  65. 65.
    Bonvin A, van Gunsteren WF (2000) beta-Hairpin stability and folding: molecular dynamics studies of the first beta-hairpin of tendamistat. J Mol Biol 296:255–268CrossRefPubMedGoogle Scholar
  66. 66.
    Colombo G, Roccatano D, Mark AE (2002) Folding and stability of the three-stranded beta-sheet peptide betanova: insights from molecular dynamics simulations. Proteins-Struct Funct Genet 46:380–392CrossRefPubMedGoogle Scholar
  67. 67.
    Schaefer M, Bartels C, Karplus M (1998) Solution conformations and thermodynamics of structured peptides: molecular dynamics simulation with an implicit solvation model. J Mol Biol 284:835–848CrossRefPubMedGoogle Scholar
  68. 68.
    Lazaridis T, Karplus M (1999) Effective energy function for proteins in solution. Proteins-Struct Funct Genet 35:133–152CrossRefPubMedGoogle Scholar
  69. 69.
    Dinner AR, Lazaridis T, Karplus M (1999) Understanding beta-hairpin formation. Proc Natl Acad Sci US Am 96:9068–9073CrossRefGoogle Scholar
  70. 70.
    Ferrara P, Apostolakis J, Caflisch A (2002) Evaluation of a fast implicit solvent model for molecular dynamics simulations. Proteins-Struct Funct Genet 46:24–33CrossRefPubMedGoogle Scholar
  71. 71.
    Simmerling C, Strockbine B, Roitberg AE (2002) All-atom structure prediction and folding simulations of a stable protein. J Am Chem Soc 124:11258–11259CrossRefPubMedGoogle Scholar
  72. 72.
    Feig M, Brooks CL (2004) Recent advances in the development and application of implicit solvent models in biomolecule simulations. Curr Opin Struct Biol 14:217–224CrossRefPubMedGoogle Scholar
  73. 73.
    Ferrara P, Apostolakis J, Caflisch A (2000) Thermodynamics and kinetics of folding of two model peptides investigated by molecular dynamics simulations. J Phys Chem B 104:5000–5010CrossRefGoogle Scholar
  74. 74.
    Bursulaya BD, Brooks CL (2000) Comparative study of the folding free energy landscape of a three-stranded beta-sheet protein with explicit and implicit solvent models. J Phys Chem B 104:12378–12383CrossRefGoogle Scholar
  75. 75.
    Schafer H, Daura X, Mark AE, van Gunsteren WF (2001) Entropy calculations on a reversibly folding peptide: changes in solute free energy cannot explain folding behavior. Proteins-Struct Funct Genet 43:45– 56CrossRefPubMedGoogle Scholar
  76. 76.
    Shen MY, Freed KF (2002) Long time dynamics of met-enkephalin: comparison of explicit and implicit solvent models. Biophys J 82:1791–1808PubMedGoogle Scholar
  77. 77.
    Zhou RH, Berne BJ (2002) Can a continuum solvent model reproduce the free energy landscape of a beta-hairpin folding in water?. Proc Natl Acad Sci US Am 99:12777–12782CrossRefGoogle Scholar
  78. 78.
    Nymeyer H, Garcia AE (2003) Simulation of the folding equilibrium of alpha-helical peptides: a comparison of the generalized born approximation with explicit solvent. Proc Natl Acad Sci US Am 100:13934–13939CrossRefGoogle Scholar
  79. 79.
    Zhou RH (2003) Free energy landscape of protein folding in water: explicit vs. implicit solvent. Proteins-Struct Funct Genet 53:148–161CrossRefPubMedGoogle Scholar
  80. 80.
    Rhee YM, Sorin EJ, Jayachandran G, Lindahl E, Pande VS (2004) Simulations of the role of water in the protein-folding mechanism. Proc Natl Acad Sci US Am 101:6456–6461CrossRefGoogle Scholar
  81. 81.
    Stultz CM (2004) An assessment of potential of mean force calculations with implicit solvent models. J Phys Chem B 108:16525–16532CrossRefGoogle Scholar
  82. 82.
    Wagoner J, Baker NA (2004) Solvation forces on biomolecular structures: a comparison of explicit solvent and Poisson–Boltzmann models. J Comput Chem 25:1623–1629CrossRefPubMedGoogle Scholar
  83. 83.
    Snow CD, Sorin EJ, Rhee YM, Pande VS (2005) How well can simulation predict protein folding kinetics and thermodynamics?. Annu Rev Biophys Biomol Struct 34:43–69CrossRefPubMedGoogle Scholar
  84. 84.
    Sugita Y, Okamoto Y (1999) Replica-exchange molecular dynamics method for protein folding. Chem Phys Lett 314:141–151CrossRefGoogle Scholar
  85. 85.
    Swendsen RH, Wang JS (1986) Replica Monte-Carlo simulation of spin-glasses. Phys Rev Lett 57:2607–2609CrossRefPubMedGoogle Scholar
  86. 86.
    Berg BA, Neuhaus T (1991) Multicanonical algorithms for 1st order phase-transitions. Phys Lett B 267:249–253CrossRefGoogle Scholar
  87. 87.
    Nakajima N, Nakamura H, Kidera A (1997) Multicanonical ensemble generated by molecular dynamics simulation for enhanced conformational sampling of peptides. J Phys Chem B 101:817–824CrossRefGoogle Scholar
  88. 88.
    Voter AF (1998) Parallel replica method for dynamics of infrequent events. Phys Rev B 57:R13985–R13988CrossRefGoogle Scholar
  89. 89.
    Sugita Y, Okamoto Y (2000) Replica-exchange multicanonical algorithm and multicanonical replica-exchange method for simulating systems with rough energy landscape. Chem Phys Lett 329:261–270CrossRefGoogle Scholar
  90. 90.
    Rhee YM, Pande VS (2003) Multiplexed-replica exchange molecular dynamics method for protein folding simulation. Biophys J 84:775–786PubMedCrossRefGoogle Scholar
  91. 91.
    Paschek D, Garcia AE (2004) Reversible temperature and pressure denaturation of a protein fragment: a replica exchange molecular dynamics simulation study. Phys Rev Lett 93(23):238105CrossRefPubMedGoogle Scholar
  92. 92.
    Affentranger R, Tavernelli I, Di Iorio EE (2005) A novel Hamiltonian replica exchange MD protocol to enhance protein conformational space sampling. (submitted)Google Scholar
  93. 93.
    Zhou RH, Berne BJ, Germain R (2001) The free energy landscape for beta hairpin folding in explicit water. Proc Natl Acad Sci US Am 98:14931–14936CrossRefGoogle Scholar
  94. 94.
    Garcia AE, Onuchic JN (2003) Folding a protein in a computer: an atomic description of the folding/unfolding of protein A. Proc Natl Acad Sci US Am 100:13898–13903CrossRefGoogle Scholar
  95. 95.
    Pitera JW, Swope W (2003) Understanding folding and design: Replica-exchange simulations of “Trp-cage” fly miniproteins. Proc Natl Acad Sci US Am 100:7587–7592CrossRefGoogle Scholar
  96. 96.
    Rao F, Caflisch A (2003) Replica exchange molecular dynamics simulations of reversible folding. J Chem Phys 119:4035–4042CrossRefGoogle Scholar
  97. 97.
    Ohkubo YZ, Brooks CL (2003) Exploring Flory’s isolated-pair hypothesis: statistical mechanics of helix-coil transitions in polyalanine and the C-peptide from RNase A. Proc Natl Acad Sci US Am 100:13916–13921CrossRefGoogle Scholar
  98. 98.
    Swope WC, Pitera JW, Suits F (2004) Describing protein folding kinetics by molecular dynamics simulations. 1. Theory. J Phys Chem B 108:6571–6581CrossRefGoogle Scholar
  99. 99.
    Swope WC, Pitera JW, Suits F, Pitman M, Eleftheriou M, Fitch BG, Germain RS, Rayshubski A, Ward TJC, Zhestkov Y, Zhou R (2004) Describing protein folding kinetics by molecular dynamics simulations. 2. Example applications to alanine dipeptide and beta-hairpin peptide. J Phys Chem B 108:6582–6594CrossRefGoogle Scholar
  100. 100.
    Andrec M, Felts AK, Gallicchio E, Levy RM (2005) Protein folding pathways from replica exchange simulations and a kinetic network model. Proc Natl Acad Sci US Am 102:6801–6806CrossRefGoogle Scholar
  101. 101.
    Shirts M, Pande VS (2000) Computing – screen savers of the World unite!. Science 290:1903–1904CrossRefGoogle Scholar
  102. 102.
    Shirts MR, Pande VS (2001) Mathematical analysis of coupled parallel simulations. Phys Rev Lett 86:4983–4987CrossRefPubMedGoogle Scholar
  103. 103.
    Fersht AR (2002) On the simulation of protein folding by short time scale molecular dynamics and distributed computing. Proc Natl Acad Sci US Am 99:14122–14125CrossRefGoogle Scholar
  104. 104.
    Singhal N, Snow CD, Pande VS (2004) Using path sampling to build better Markovian state models: predicting the folding rate and mechanism of a tryptophan zipper beta hairpin. J Chem Phys 121:415–425CrossRefPubMedGoogle Scholar
  105. 105.
    Pande VS, Baker I, Chapman J, Elmer SP, Khaliq S, Larson SM, Rhee YM, Shirts MR, Snow CD, Sorin EJ, Zagrovic B (2003) Atomistic protein folding simulations on the submillisecond time scale using worldwide distributed computing. Biopolymers 68:91–109CrossRefPubMedGoogle Scholar
  106. 106.
    Seebach D, Beck AK, Bierbaum DJ (2004) The world of beta- and gamma-peptides comprised of homologated proteinogenic amino acids and other components. Chem Biodivers 1:1111–1239CrossRefGoogle Scholar
  107. 107.
    Daura X, Glattli A, Gee P, Peter C, Van Gunsteren WF (2002) Unfolded state of peptides. In: Unfolded proteins, vol 62, pp 341–360Google Scholar
  108. 108.
    Kritzer JA, Tirado-Rives J, Hart SA, Lear JD, Jorgensen WL, Schepartz A (2005) Relationship between side chain structure and 14-helix stability of beta(3)-peptides in water. J Am Chem Soc 127:167–178CrossRefPubMedGoogle Scholar
  109. 109.
    Wolynes PG (1995) Biomolecular folding in vacuo!!!?. Proc Natl Acad Sci US Am 92:2426–2427Google Scholar
  110. 110.
    Daura X, Mark AE, van Gunsteren WF (1999) Peptide folding simulations: no solvent required? Comput Phys Commun 123:97–102CrossRefGoogle Scholar
  111. 111.
    Velazquez I, Reimann CT, Tapia O (1999) Proteins in vacuo: relaxation of unfolded lysozyme leads to folding into native and non-native structures. A molecular dynamics study. J Am Chem Soc 121:11468–11477Google Scholar
  112. 112.
    Levy Y, Jortner J, Becker OM (2001) Solvent effects on the energy landscapes and folding kinetics of polyalanine. Proc Natl Acad Sci US Am 98:2188–2193CrossRefGoogle Scholar
  113. 113.
    Daura X, van Gunsteren WF, Mark AE (1999) Folding-unfolding thermodynamics of a beta-heptapeptide from equilibrium simulations. Proteins-Struct Funct Genet 34:269–280CrossRefPubMedGoogle Scholar
  114. 114.
    Zagrovic B, Pande VS (2004) How does averaging affect protein structure comparison on the ensemble level?. Biophys J 87:2240–2246CrossRefPubMedGoogle Scholar
  115. 115.
    de Groot BL, Daura X, Mark AE, Grubmuller H (2001) Essential dynamics of reversible peptide folding: memory-free conformational dynamics governed by internal hydrogen bonds. J Mol Biol 309:299–313CrossRefPubMedGoogle Scholar
  116. 116.
    Hamprecht FA, Peter C, Daura X, Thiel W, van Gunsteren WF (2001) A strategy for analysis of (molecular) equilibrium simulations: Configuration space density estimation, clustering, and visualization. J Chem Phys 114:2079–2089CrossRefGoogle Scholar
  117. 117.
    Ikeda K, Galzitskaya OV, Nakamura H, Higo J (2003) beta-hairpins, alpha-helices, and the intermediates among the secondary structures in the energy landscape of a peptide from a distal beta-Hairpin of SH3 domain. J Comput Chem 24:310–318CrossRefPubMedGoogle Scholar
  118. 118.
    Corcho FJ, Canto J, Perez JJ (2004) Comparative analysis of the conformational profile of substance P using simulated annealing and molecular dynamics. J Comput Chem 25:1937–1952CrossRefPubMedGoogle Scholar
  119. 119.
    Bursulaya BD, Brooks CL (1999) Folding free energy surface of a three-stranded beta-sheet protein. J Am Chem Soc 121:9947–9951CrossRefGoogle Scholar
  120. 120.
    Huisinga W, Best C, Roitzsch R, Schutte C, Cordes F (1999) From simulation data to conformational ensembles: structure and dynamics-based methods. J Comput Chem 20:1760–1774CrossRefGoogle Scholar
  121. 121.
    Onuchic JN, Wolynes PG (2004) Theory of protein folding. Curr Opin Struct Biol 14:70–75CrossRefPubMedGoogle Scholar
  122. 122.
    Daura X, Antes I, van Gunsteren WF, Thiel W, Mark AE (1999) The effect of motional averaging on the calculation of NMR-derived structural properties. Proteins-Struct Funct Genet 36:542–555CrossRefPubMedGoogle Scholar
  123. 123.
    Cardenas AE, Elber R (2003) Kinetics of cytochrome C folding: atomically detailed simulations. Proteins-Struct Funct Genet 51:245–257CrossRefPubMedGoogle Scholar
  124. 124.
    Kohn JE, Millett IS, Jacob J, Zagrovic B, Dillon TM, Cingel N, Dothager RS, Seifert S, Thiyagarajan P, Sosnick TR, Hasan MZ, Pande VS, Ruczinski I, Doniach S, Plaxco KW (2004) Random-coil behavior and the dimensions of chemically unfolded proteins. Proc Natl Acad Sci US Am 101:12491–12496CrossRefGoogle Scholar
  125. 125.
    Wei GH, Mousseau N, Derreumaux P (2004) Complex folding pathways in a simple beta-hairpin. Proteins-Struct Funct Bioinform 56:464–474CrossRefGoogle Scholar
  126. 126.
    van Gunsteren WF, Burgi R, Peter C, Daura X (2001) Comment on the communication “The key to solving the protein-folding problem lies in an accurate description of the denatured state” by van gunsteren et al. – reply. Angew Chem Int Ed 40:4616–4618CrossRefGoogle Scholar
  127. 127.
    Li MS, Klimov DK, Thirumalai D (2004) Thermal denaturation and folding rates of single domain proteins: size matters. Polymer 45:573–579CrossRefGoogle Scholar
  128. 128.
    Naganathan AN, Munoz V (2005) Scaling of folding times with protein size. J Am Chem Soc 127:480–481CrossRefPubMedGoogle Scholar
  129. 129.
    Kubelka J, Hofrichter J, Eaton WA (2004) The protein folding ‘speed limit’. Curr Opin Struct Biol 14:76–88CrossRefPubMedGoogle Scholar
  130. 130.
    Dinner AR, Karplus M (2001) Comment on the communication “The key to solving the protein-folding problem lies in an accurate description of the denatured state” by van gunsteren et al. Angew Chem Int Ed 40:4615–4616CrossRefGoogle Scholar
  131. 131.
    Cavalli A, Haberthur U, Paci E, Caflisch A (2003) Fast protein folding on downhill energy landscape. Protein Sci 12:1801–1803CrossRefPubMedGoogle Scholar
  132. 132.
    Strogatz SH (2001) Exploring complex networks. Nature 410:268–276CrossRefPubMedGoogle Scholar
  133. 133.
    Rao F, Caflisch A (2004) The protein folding network. J Mol Biol 342:299–306CrossRefPubMedGoogle Scholar
  134. 134.
    Kaminski GA, Friesner RA, Tirado-Rives J, Jorgensen WL (2001). Evaluation and reparametrization of the OPLS-AA force field for proteins via comparison with accurate quantum chemical calculations on peptides. J Phys Chem B 105:6474–6487CrossRefGoogle Scholar
  135. 135.
    Duan Y, Wu C, Chowdhury S, Lee MC, Xiong GM, Zhang W, Yang R, Cieplak P, Luo R, Lee T, Caldwell J, Wang JM, Kollman P. (2003) A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations. J Comput Chem 24:1999–2012CrossRefPubMedGoogle Scholar
  136. 136.
    Mackerell AD (2004) Empirical force fields for biological macromolecules: overview and issues. J Comput Chem 25:1584–1604CrossRefPubMedGoogle Scholar
  137. 137.
    Oostenbrink C, Villa A, Mark AE, Van Gunsteren WF (2004) A biomolecular force field based on the free enthalpy of hydration and solvation: the GROMOS force-field parameter sets 53A5 and 53A6. J Comput Chem 25:1656–1676PubMedGoogle Scholar
  138. 138.
    Hu H, Elstner M, Hermans J (2003) Comparison of a QM/MM force field and molecular mechanics force fields in simulations of alanine and glycine “dipeptides” (Ace-Ala-Nme and Ace-Gly-Nme) in water in relation to the problem of modeling the unfolded peptide backbone in solution. Proteins-Struct Funct Genet 50:451–463CrossRefPubMedGoogle Scholar
  139. 139.
    Mu YG, Kosov DS, Stock G (2003) Conformational dynamics of trialanine in water. 2. Comparison of AMBER, CHARMM, GROMOS, and OPLS force fields to NMR and infrared experiments. J Phys Chem B 107:5064–5073CrossRefGoogle Scholar
  140. 140.
    Okur A, Strockbine B, Hornak V, Simmerling C (2003) Using PC clusters to evaluate the transferability of molecular mechanics force fields for proteins. J Comput Chem 24:21–31CrossRefPubMedGoogle Scholar
  141. 141.
    Gnanakaran S, Garcia AE (2005) Helix-coil transition of alanine peptides in water: force field dependence on the folded and unfolded structures. Proteins-Struct Funct Bioinform 59:773–782CrossRefGoogle Scholar
  142. 142.
    Sorin EJ, Pande VS (2005) Empirical force-field assessment: the interplay between backbone torsions and noncovalent term scaling. J Comput Chem 26:682–690CrossRefPubMedGoogle Scholar
  143. 143.
    Glattli A, Daura X, van Gunsteren WF (2002) Derivation of an improved simple point charge model for liquid water: SPC/A and SPC/L. J Chem Phys 116:9811–9828CrossRefGoogle Scholar
  144. 144.
    Mahoney MW, Jorgensen WL (2000) A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions. J Chem Phys 112:8910–8922CrossRefGoogle Scholar
  145. 145.
    Rick SW (2004) A reoptimization of the five-site water potential (TIP5P) for use with Ewald sums. J Chem Phys 120:6085–6093CrossRefPubMedGoogle Scholar
  146. 146.
    Cieplak P, Caldwell J, Kollman P (2001) Molecular mechanical models for organic and biological systems going beyond the atom centered two body additive approximation: aqueous solution free energies of methanol and N-methyl acetamide, nucleic acid base, and amide hydrogen bonding and chloroform/water partition coefficients of the nucleic acid bases. J Comput Chem 22:1048–1057CrossRefGoogle Scholar
  147. 147.
    Kaminski GA, Stern HA, Berne BJ, Friesner RA (2004) Development of an accurate and robust polarizable molecular mechanics force field from ab initio quantum chemistry. J Phys Chem A 108:621–627CrossRefGoogle Scholar
  148. 148.
    Patel S, Brooks CL (2004) CHARMM fluctuating charge force field for proteins: I parameterization and application to bulk organic liquid simulations. J Comput Chem 25:1–15CrossRefPubMedGoogle Scholar
  149. 149.
    Patel S, Mackerell AD, Brooks CL (2004) CHARMM fluctuating charge force field for proteins: II – Protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model. J Comput Chem 25:1504–1514CrossRefPubMedGoogle Scholar
  150. 150.
    Borjesson U, Hunenberger PH (2001) Explicit-solvent molecular dynamics simulation at constant pH: methodology and application to small amines. J Chem Phys 114:9706–9719CrossRefGoogle Scholar
  151. 151.
    Baptista AM, Teixeira VH, Soares CM (2002) Constant-pH molecular dynamics using stochastic titration. J Chem Phys 117:4184–4200CrossRefGoogle Scholar
  152. 152.
    Burgi R, Kollman PA, van Gunsteren WF (2002) Simulating proteins at constant pH: an approach combining molecular dynamics and Monte Carlo simulation. Proteins-Struct Funct Genet 47:469–480CrossRefPubMedGoogle Scholar
  153. 153.
    Dlugosz M, Antosiewicz JM (2004) Constant-pH molecular dynamics simulations: a test case of succinic acid. Chem Phys 302:161–170CrossRefGoogle Scholar
  154. 154.
    Lee MS, Salsbury FR, Brooks CL (2004) Constant-pH molecular dynamics using continuous titration coordinates. Proteins-Struct Funct Bioinform 56:738–752CrossRefGoogle Scholar
  155. 155.
    Mongan J, Case DA, McCammon JA (2004) Constant pH molecular dynamics in generalized born implicit solvent. J Comput Chem 25:2038–2048CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Catalan Institution for Research and Advanced Studies (ICREA), Institute of Biotechnology and Biomedicine (IBB)Universitat Autónoma de BarcelonaBellaterraSpain

Personalised recommendations