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Part of the book series: Lecture Notes in Physics ((LNP,volume 703))

Abstract

This chapter summarizes several computational strategies to study the kinetics of two-state protein folding using all atom models. After explaining the background of two state folding using energy landscapes I introduce common protein models and computational tools to study folding thermodynamics and kinetics. Free energy landscapes are able to capture the thermodynamics of two-state protein folding, and several methods for efficient sampling of these landscapes are presented. An accurate estimate of folding kinetics, the main topic of this chapter, is more difficult to achieve. I argue that path sampling methods are well suited to overcome the problems connected to the sampling of folding kinetics. Some of the major issues are illustrated in the case study on the folding of the GB1 hairpin.

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References

  1. C. M. Dobson (2004) Principles of protein folding, misfolding and aggregation. Semin. Cell. Dev. Biol. 15, pp. 3–16

    Article  Google Scholar 

  2. A. Fersht 1999 Structure and Mechanism in Protein Science, Freeman, New York

    Google Scholar 

  3. M. S. Cheung, L. L. Chavez, J. N. Onuchic (2004) The energy langscape for protein folding and possible connections to function. Polymer 45, pp. 547–55

    Article  Google Scholar 

  4. J. Kubelka, J. Hofrichter, W. A. Eaton (2004) The protein folding ’speed limit’.Curr. Opin. Struc. Biol. 14, pp. 76–88

    Article  Google Scholar 

  5. L. Mirny, E. Shakhnovich (2001) Protein folding theory: From lattice to allatom models. Annu. Rev. Biophys. Biom. 30, pp. 361–396

    Article  Google Scholar 

  6. J. E. Shea, C. L. Brooks (2001) From folding theories to folding proteins: A review and assessment of simulation studies of protein folding and unfolding. Annu. Rev. Phys. Chem. 52 pp. 499–535

    Article  ADS  Google Scholar 

  7. S. Gnanakaran, H. Nymeyer, J. Portman, K. Y. Sanbonmatsu, A. E. Garcia (2003) Peptide folding simulations. Curr. Opin. Struc. Biol. 13, pp. 168–174

    Article  Google Scholar 

  8. C. D. Snow, E. J. Sorin, Y. M. Rhee, V. Pande (2005) How well can simulation predict protein folding kinetics and thermodynamics? Annu. Rev. Biophys. Biomol. Struct. 34, pp. 43–69

    Article  Google Scholar 

  9. C. B. Anfinsen (1973) Principles that govern the folding of protein chains., Science 181, pp. 223–230

    Google Scholar 

  10. D. Chandler, (1987) Introduction to Modern Statistical Mechanics, Oxford University Press, New York

    Google Scholar 

  11. A. Grosberg (2004) Statistical mechanics of protein folding: some outstanding problems, in: N. Attig, K. Binder, H. Grubmüller, K. Kremer (Eds.), Computational Soft Matter: from Synthetic Polymers to Proteins, Vol. 23 of NIC Series, Graphische Betriebe, Jülich, pp. 375–399

    Google Scholar 

  12. J. N. Onuchic, Z. Luthey-Schulten, P. G. Wolynes (1997) Theory of protein folding: The energy landscape perspective. Annu. Rev. Phys. Chem. 48, pp. 545–600

    Article  ADS  Google Scholar 

  13. D. Wales (2003) Energy Landscapes, Cambridge University Press, Cambridge

    Google Scholar 

  14. V. S. Pande, A. Y. Grosberg, T. Tanaka (2000) Heteropolymer freezing and design: Towards physical models of protein folding. Rev. Mod. Phys. 72, pp. 259– 314

    Article  ADS  Google Scholar 

  15. A. R. Dinner, A. Sali, L. J. Smith, C. M. Dobson, M. Karplus (2000) Understanding protein folding via free-energy surfaces from theory and experiment. Trends Biochem. Sci. 25, pp. 331–339

    Article  Google Scholar 

  16. S. Gianni, N. R. Guydosh, F. Khan, T. D. Caldas, U. Mayor, G. W. N. White, M. L. DeMarco, V. Daggett, A. R. Fersht (2003) Unifying features in proteinfolding mechanisms. P. Natl. Acad. Sci. USA 100, pp. 13286–13291

    Article  ADS  Google Scholar 

  17. S. Islam, M. Karplus, D. Weaver (2002) Application of the diffusion-collision model to the folding of three-helix bundle proteins. J. Mol. Biol. 318, pp. 199– 215

    Article  Google Scholar 

  18. A. Akmal, V. Munoz (2004) The nature of the free energy barriers to two-state folding. Proteins: Struc. Funct. Bio. 47, pp. 142–152

    Article  Google Scholar 

  19. Y. Harano, M. Kinoshita (2005) Translational-entropy gain of solvent upon protein folding. Biophys. J. 89, pp. 2701–2710

    Article  Google Scholar 

  20. B. Gillespie, K. W. Plaxco (2004) Using protein folding rates to test protein folding theories. Annu. Rev. Biochem. 73. pp. 837–859

    Article  Google Scholar 

  21. D. Frenkel, B. Smit (2002) Understanding molecular simulation. 2nd ed., Academic Press, San Diego, CA

    Google Scholar 

  22. J. Norberg, L. Nilsson (2003) Advances in biomolecular simulations: methodology and recent applications. Q. Rev. Biophys. 36, pp. 257–306

    Article  Google Scholar 

  23. M. P. Allen, D. J. Tildesley (1987) Computer Simulation of Liquids. Oxford University Press, Oxford

    MATH  Google Scholar 

  24. A. Ricci, G. Ciccotti. (2003) Algorithms for brownian dynamics. Mol. Phys. 101, pp. 1927–1931

    Article  ADS  Google Scholar 

  25. K. Binder, D. Heermann (2002) Monte Carlo simulation in statistical physics, Springer, Berlin

    MATH  Google Scholar 

  26. K. Kikuchi, M. Yoshida, T. Maekawa, H. Watanabe (1991) Metropolis Monte-Carlo method as a numerical technique to solve the Fokker-Planck equation. Chem. Phys. Lett. 185, pp. 335–338

    Article  ADS  Google Scholar 

  27. W. Wang, O. Donini, C. M. Reyes, P. A. Kollman (2001) Biomolecular simulations: Recent developments in force fields, simulations of enzyme catalysis, protein-ligand, protein-protein, and protein-nucleic acid noncovalent interactions. Annu. Rev. Biophys. Biom. 30, pp. 211–243

    Article  Google Scholar 

  28. M. Levitt, (1983) Molecular dynamics of native protein .1. Computer simulation of trajectories. J. Mol. Biol. 168, pp. 595–620

    Article  Google Scholar 

  29. M. Levitt, M. Hirschberg, R. Sharon, V. Daggett (1995) Potential-energy function and parameters for simulations of the molecular-dynamics of proteins and nucleic-acids in solution. Comput. Phys. Commun. 91, pp. 215–231

    Article  ADS  Google Scholar 

  30. W. Cornell, P. Cieplak, C. I. Bayly, I. R. Gould, M. K. M. (1995) A 2nd generation force-field for the simulation of proteins, nucleic-acids, and organicmolecules. J. Am. Chem. Soc. 117, pp. 5179–5197

    Google Scholar 

  31. A. D. MacKerell Jr., D. Bashford, M. Bellott, R. Dunbrack Jr., J. Evanseck, M. Field, S. Fischer, J. Gao, H. Guo, S Ha et al. (1998) All-atom empirical potential for molecular modeling and dynamics studies of proteins. J. Phys. Chem. B 102, pp. 3586–3616

    Article  Google Scholar 

  32. W. van Gunsteren (1987) H. Berendsen, Gromos-87 manual, Biomos BV, Groningen, The Netherlands

    Google Scholar 

  33. W. L. Jorgensen, D. S. Maxwell, J. Tirado-Rives (1996) Development and testing of the opls all-atom force field on conformational energetics and properties of organic liquids. J. Am. Chem. Soc. 118, pp. 11225–11236

    Article  Google Scholar 

  34. J. Jorgensen, W.L. and Chandrasekhar, J. Madura, R. Impey, M. Klein (1983) Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 79, pp. 926–935

    Google Scholar 

  35. H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, J. Hermans (1981) Intermolecular Forces, D. Reidel Publishing Company, Dordrecht, Ch. Interaction models for water in relation to protein hydration, pp. 331–342

    Google Scholar 

  36. J. Banks, G. Kaminski, R. Zhou, D. Mainz, B. Berne, R. Friesner (1999) Parametrizing a polarizable force field from ab initio data. i. the fluctuating point charge model. J. Chem. Phys. 110, pp. 741–754

    Article  ADS  Google Scholar 

  37. H. Andersen (1983) Rattle: a “velocity” version of the shake algorithm for molecular dynamics. J. Comput. Phys. 52, pp. 24–34

    Article  MATH  ADS  Google Scholar 

  38. B. Hess, B. Bekker (1997) H. J. C. Berendsen, J. G. E. M. Fraaije, LINCS: a linear constraints solver for molecular simulations. J. Comp. Chem. 18, pp. 1463– 1472

    Article  Google Scholar 

  39. M. Tuckerman, G. Martyna, B. Berne (1992) Reversible multiple time scale molecular dynamics. J. Chem. Phys. 97, pp. 1990–2001

    Article  ADS  Google Scholar 

  40. B. Lindahl, E. Hess, D. van der Spoel (2001) Gromacs 3.0: a package for molecular simulation and trajectory analysis. J. Mol. Mod. 7, pp. 306–317

    Google Scholar 

  41. Y. Duan, P. A. Kollman (1998) Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. Science 282, pp. 740– 744

    Article  ADS  Google Scholar 

  42. S. Miyamoto, P. A. Kollman (1997) SETTLE: an analytical version of the SHAKE and the RATTLE algorithms for rigid water molecules. J. Comp. Chem. 13, pp. 952–962

    Article  Google Scholar 

  43. T. Lazaridis, M. Karplus (1999) Effective energy function for proteins in solution. Prot. Struct. Func. Gen. 35, pp. 133–152

    Article  Google Scholar 

  44. D. Qiu, P. S. Shenkin, F. P. Hollinger, W. C. Still (1997) The GB/SA continuum model for solvation. a fast analytical method for the calculation of approximate born radii. J. Phys. Chem. A 101, pp. 3005–3014

    Article  Google Scholar 

  45. M. Y. Shen, K. F. Freed (2002) Long time dynamics of met-enkephalin: Comparison of explicit and implicit solvent models. Biophys. J. 82, pp. 1791–1808

    Article  ADS  Google Scholar 

  46. H. Nymeyer, A. E. Garcia (2003) Simulation of the folding equilibrium of alpha-helical peptides: A comparison of the generalized born approximation with explicit solvent. P. Natl. Acad. Sci. USA 100, pp. 13934–13939

    Article  ADS  Google Scholar 

  47. R. H. Zhou, B. J. Berne (2002) Can a continuum solvent model reproduce the free energy landscape of a beta-hairpin folding in water? P. Natl. Acad. Sci. USA 99, pp. 12777–12782

    Article  ADS  Google Scholar 

  48. H. Taketomi, Y. Ueda, N. Go (1975) Studies on protein folding, unfolding and fluctuations by computer-simulation. 1. effect of specific amino-acid sequence represented by specific inter-unit interactions. Int. J. Pept. Protein Res. 7, p. 445

    Google Scholar 

  49. C. Clementi, A. E. Garcia, J. N. Onuchic (2003) Interplay among tertiary contacts, secondary structure formation and side-chain packing in the protein folding mechanism: All-atom representation study of protein L. J. Mol. Biol. 326, pp. 933–954

    Article  Google Scholar 

  50. A. Liwo, M. Khalili, H. A. Scheraga (2005) Ab initio simulations of proteinfolding pathways by molecular dynamics with the united-residue model of polypeptide chains. P. Natl. Acad. Sci. USA 102, pp. 2362–2367

    Article  ADS  Google Scholar 

  51. S. Oldziej, C. Czaplewski, A. Liwo, M. Chinchio, M. Nanias, J. A. Vila, M. Khalili, Y. A. Arnautova, A. Jagielska, M. Makowski, H. D. Schafroth, R. Kazmierkiewicz, D. R. Ripoll, J. Pillardy, J. A. Saunders, Y. K. Kang, K. D. Gibson, H. A. Scheraga, (2005) Physics-based protein-structure prediction using a hierarchical protocol based on the unres force field: Assessment in two blind tests. P. Natl. Acad. Sci. USA 102, pp. 7547–7552

    Article  ADS  Google Scholar 

  52. K. A. Dill, S. Bromberg, K.Yue, K. M. Fiebig, D. P. Yee, P. Thomas, H. S. Chan (1995) Principles of protein-folding - a perspective from simple exact models. Prot. Science 4, pp. 561–602

    Article  Google Scholar 

  53. H. S. Chan, K. A. Dill (1998) Protein folding in the landscape perspective: Chevron plots and non-arrhenius kinetics. Proteins 30, pp. 2–33

    Article  Google Scholar 

  54. P. de Gennes (1979) Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca NY

    Google Scholar 

  55. S. Miyazawa, R. Jernigan (1985) Estimation of e.ective interresidue contact energies from protein crystal-structures - quasi-chemical approximation. Macromolecules 18, p. 534

    Article  ADS  Google Scholar 

  56. I. Coluzza, H. G. Muller, D. Frenkel (2003) Designing refoldable model molecules. Phys. Rev. E 68, p. 046703

    Article  ADS  Google Scholar 

  57. S. S. Plotkin, J. N. Onuchic (2002) Understanding protein folding with energy landscape theory - part ii: Quantitative aspects. Q. Rev. Biophys. 35, pp. 205–286

    Article  Google Scholar 

  58. I. Coluzza, D. Frenkel (2005) Designing specificity of protein-substrate interactions. Phys. Rev. E 70, p. 051917

    Article  ADS  Google Scholar 

  59. I. Coluzza, S. van der Vies, D. Frenkel (2006) Translocation boost proteinfolding efficiency of double-barreled chaperonins. Biophys. J. 90, pp. 3375– 3381.

    Google Scholar 

  60. A. Ferrenberg, R. Swendsen (1989) Optimized monte-carlo data-analysis. Phys. Rev. Lett. 63, pp. 1195–1198

    Article  ADS  Google Scholar 

  61. A. Laio, M. Parrinello (2002) Escaping free-energy minima. P. Natl. Acad. Sci. USA 99, pp. 12562-12567

    Article  ADS  Google Scholar 

  62. H. Grubmüller (1995) Predicting slow structural transitions in macromolecular systems - conformational flooding. Phys. Rev. E 52, pp. 2893–2906

    Article  ADS  Google Scholar 

  63. A. Voter (1997) Hyperdynamics: Accelerated molecular dynamics of infrequent events. Phys. Rev. Lett. 78, pp. 3908–3911

    Article  ADS  Google Scholar 

  64. B. Berg, T. Neuhaus (1992) Multicanonical ensemble - a new approach to simulate 1st-order phase-transitions. Phys. Rev. Lett. 68, pp. 9–12

    Article  ADS  Google Scholar 

  65. A. Mitsutake, Y. Sugita, Y. Okamoto (2001) Generalized-ensemble algorithms for molecular simulations of biopolymers. Biopolymers 60, pp. 96–123

    Article  Google Scholar 

  66. E. J. Sorin, V. S. Pande (2005) Exploring the helix-coil transition via all-atom equilibrium ensemble simulations. Biophys. J. 88, pp. 2472–2493

    Article  ADS  Google Scholar 

  67. P. Liu, B. Kim, R. Friensner, B. Berne (2005) Replica exchange with solute tempering: A method for sampling biological systems in explicit water. P. Natl. Acad. Sci. USA 102, pp. 13749–13754

    Article  ADS  Google Scholar 

  68. I. Coluzza, D. Frenkel (2005) Virtual-move parallel tempering. Phys. Chem. Phys 6, pp. 1779–1783

    Google Scholar 

  69. D. Frenkel (2004) Speed-up of monte carlo simulations by sampling of rejected states. P. Natl. Acad. Sci. USA 101, pp. 17571–17575

    Article  ADS  Google Scholar 

  70. P. Ferrara, J. Apostolakis, A. Caflisch (2000) Thermodynamics and kinetics of folding of two model peptides investigated by molecular dynamics simulations. J.Phys. Chem. B. 104, pp. 5000–5010

    Article  Google Scholar 

  71. V. S. Pande, I. Baker, J. Chapman, S. P. Elmer, S. Khaliq, S. M. Larson, Y. M. Rhee, M. R. Shirts, C. D. Snow, E. J. Sorin, B. Zagrovic (2003) Atomistic protein folding simulations on the submillisecond time scale using worldwide distributed computing. Biopolymers 68, pp. 91–109

    Article  Google Scholar 

  72. D. A. C. Beck, V. Dagget (2004) Methods for molecular dynamics simulation of protein folding/unfolding in solution. Methods 34, pp. 112–120

    Article  Google Scholar 

  73. N. Ferguson, R. Day, C. M. Johnson, M. D. Allen, V. Dagget, A. Fersht (2005) Simulation and experiment at high temperatures: Ultrafast folding of a thermophilic protein by nucleation-condensation. J. Mol. Biol. 347, pp. 855–870

    Article  Google Scholar 

  74. V. S. Pande, D. S. Rokhsar (1999) Molecular dynamics simulations of unfolding and refolding of a beta-hairpin fragment of protein G. P. Natl. Acad. Sci. USA 96, pp. 9062–9067

    Article  ADS  Google Scholar 

  75. D. Chandler (1978) Statistical mechanics of isomerization dynamics in liquids and the transition state. J. Chem. Phys. 68, pp. 2959–2970

    Article  ADS  Google Scholar 

  76. C. H. Bennett (1977) Molecular dynamics and transition state theory: the simulation of infrequent events, in: R. Christofferson (Ed.), Algorithms for Chemical Computations, ACS Symposium Series No. 46, American Chemical Society, Washington, D.C., pp. 63–97

    Google Scholar 

  77. C. Dellago, P. G. Bolhuis, P. L. Geissler (2002) Transition path sampling. Adv. Chem. Phys. 123, pp. 1–78

    Article  Google Scholar 

  78. R. Du, V. S. Pande, A. Y. Grosberg, T. Tanaka, E. S. Shakhnovich (1998) On the transition coordinate for protein folding. J. Chem. Phys. 108, pp. 334–350

    Article  ADS  Google Scholar 

  79. Y. Rhee, V. Pande (2005) One-dimensional reaction coordinate and the corresponding potential of mean force from commitment probability distribution. J. Phys. Chem. B 109, pp. 6780–6786 432.

    Google Scholar 

  80. L. R. Pratt (1986) A statistical-method for identifying transition-states in high dimensional problems. J. Chem. Phys. 85, p. 5045

    Article  ADS  MathSciNet  Google Scholar 

  81. R. Olender, R. Elber (1996) Calculation of classical trajectories with a very large time step: Formalism and numerical examples. J. Chem. Phys. 105, pp. 9299–9315

    Article  ADS  Google Scholar 

  82. R. Elber, A. Ghosh, A. Cardenas, H. Stern (2003) Bridging the gap between long time trajectories and reaction pathways. Adv. Chem. Phys. 126, pp. 93– 129

    Article  Google Scholar 

  83. P. Eastman, N. Gronbech-Jensen, S. Doniach (2001) Simulation of protein folding by reaction path annealing. J. Chem. Phys. 114, pp. 3823–3841

    Article  ADS  Google Scholar 

  84. P. G. Bolhuis, D. Chandler, C. Dellago, P. L. Geissler (2002) Transition path sampling: Throwing ropes over rough mountain passes, in the dark. Annu. Rev. Phys. Chem. 53, pp. 291–318

    Article  ADS  Google Scholar 

  85. P. G. Bolhuis (2003) Transition path sampling on diffusive barriers. J. Phys.- Condens. Mat. 15, pp. S113–S120

    Article  ADS  Google Scholar 

  86. H. C. Andersen (1980) Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys. 72, pp. 2384–2389

    Article  ADS  Google Scholar 

  87. T. S. van Erp, D. Moroni, P. G. Bolhuis (2003) A novel path sampling method for the calculation of rate constants. J. Chem. Phys. 118, pp. 7762–7774

    Article  ADS  Google Scholar 

  88. P. G. Bolhuis (2005) Kinetic pathways of beta-hairpin (un)folding in explicit solvent. Biophys. J. 88, pp. 50–61

    Article  ADS  Google Scholar 

  89. D. Moroni, P. G. Bolhuis, T. S. van Erp (2004) Rate constants for diffusive processes by partial path sampling. J. Chem. Phys. 120, pp. 4055–4065

    Article  ADS  Google Scholar 

  90. A. Faradjian, R. Elber (2004) Computing time scales from reaction coordinates by milestoning. J. Chem. Phys. 120, pp. 10880–10889

    Article  ADS  Google Scholar 

  91. N. Singhal, C. D. Snow, V. S. Pande (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, pp. 415–425

    Article  ADS  Google Scholar 

  92. N. M. Amato, G. Song (2002) Using motion planning to study protein folding pathways. J. Comput. Biol. 9, pp. 149–168

    Article  Google Scholar 

  93. N. M. Amato, K. A. Dill, G. Song (2003) Using motion planning to map protein folding landscapes and analyze folding kinetics of known native structures. J. Comput. Biol. 10, pp. 239–255

    Article  Google Scholar 

  94. S. V. Krivov, M. Karplus (2004) Hidden complexity of free energy surfaces for peptide (protein) folding. P. Natl. Acad. Sci. USA 101, pp. 14766–14770

    Article  ADS  Google Scholar 

  95. A. B. Bortz, M. H. Kalos, J. L. Lebowitz (1975) New algorithm for monte-carlo simulation of ising spin systems. J. Comput. Phys. 17, p. 10

    Article  ADS  Google Scholar 

  96. V. Munoz, P. A. Thompson, J. Hofrichter, W. A. Eaton (1997) Folding dynamics and mechanism of beta-hairpin formation. Nature 390, pp. 196–199

    Article  ADS  Google Scholar 

  97. V. Munoz, E. R. Henry, J. Hofrichter, W. A. Eaton (1998) A statistical mechanical model for beta-hairpin kinetics. P. Natl. Acad. Sci. USA 95, pp. 5872–5879

    Article  ADS  Google Scholar 

  98. A. Kolinski, B. Ilkowski, J. Skolnick (1999) Dynamics and thermodynamics of beta-hairpin assembly: Insights from various simulation techniques. Biophys. J. 77, pp. 2942–2952

    Article  Google Scholar 

  99. D. K. Klimov, D. Thirumalai (2000) Mechanisms and kinetics of beta-hairpin formation. P. Natl. Acad. Sci. USA 97, pp. 2544–2549

    Article  ADS  Google Scholar 

  100. G. H. Wei, P. Derreumaux, N. Mousseau (2004) Complex folding pathways in a simple beta-hairpin. Prot. Struct. Func. Bio. 56, pp. 464–474

    Article  Google Scholar 

  101. A. R. Dinner, T. Lazaridis, M. Karplus (1999) Understanding beta-hairpin formation. P. Natl. Acad. Sci. USA 96, pp. 9068–9073

    Google Scholar 

  102. B. Zagrovic, E. Sorin, V. S. Pande (2001) Beta-hairpin folding simulations in atomistic detail using an implicit solvent model. J. Mol. Biol. 313, pp. 151–169

    Article  Google Scholar 

  103. D. Roccatano, A. Amadei, A. Di Nola, H. J. C. Berendsen (1999) A molecular dynamics study of the 41-56 beta-hairpin from B1 domain of protein G. Protein Sci. 8, pp. 2130–2143

    Article  Google Scholar 

  104. B. Y. Ma, R. Nussinov (2000) Molecular dynamics simulations of a beta-hairpin fragment of protein G: Balance between side-chain and backbone forces. J. Mol. Biol. 296, pp. 1091–1104

    Article  Google Scholar 

  105. A. E. Garcia, K. Y. Sanbonmatsu (2001) Exploring the energy landscape of a beta hairpin in explicit solvent. Proteins 42, pp. 345–354

    Article  Google Scholar 

  106. R. H. Zhou, B. J. Berne, R. Germain (2001) The free energy landscape for beta hairpin folding in explicit water. P. Natl. Acad. Sci. USA 98, pp. 14931–14936

    Google Scholar 

  107. J. Tsai, M. Levitt (2002) Evidence of turn and salt bridge contributions to beta-hairpin stability: MD simulations of C-terminal fragment from the B1 domain of protein G. Biophys. Chem. 101, pp. 187–201

    Article  Google Scholar 

  108. F. B. Sheinerman, C. L. Brooks (1998) Calculations on folding of segment B1 of streptococcal protein G. J. Mol. Biol. 278, pp. 439–456

    Article  Google Scholar 

  109. F. B. Sheinerman, C. L. Brooks (1998) Molecular picture of folding of a small alpha/beta protein. P. Natl. Acad. Sci. USA 95, pp. 1562–1567

    Article  ADS  Google Scholar 

  110. M. S. Cheung, A. E. Garcia, J. N. Onuchic (2002) Protein folding solvation: Water expulsion and formation of the hydrophobic core occur after the structural collapse. P. Natl. Acad. Sci. USA 99, pp. 685–690

    Article  ADS  Google Scholar 

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Bolhuis, P. (2006). Sampling Kinetic Protein Folding Pathways using All-Atom Models. In: Ferrario, M., Ciccotti, G., Binder, K. (eds) Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology Volume 1. Lecture Notes in Physics, vol 703. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-35273-2_11

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