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Simulations of the Folding of Proteins: A Historical Perspective

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Computational Methods to Study the Structure and Dynamics of Biomolecules and Biomolecular Processes

Part of the book series: Springer Series in Bio-/Neuroinformatics ((SSBN,volume 1))

Abstract

Highlights of the evolutionary development of the physical approach to biology during the last 80 years are traced in this chapter. The historical sequence of events that led to the introduction of modern simulation methods to treat biological processes is described in detail.

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References

  1. Cohn, E.J., Edsall, J.T.: Proteins, Amino Acids and Peptides as Ions and Dipolar Ions. Reinhold publishers, New York (1943)

    Google Scholar 

  2. Linderstrøm-Lang, K.U.: On the ionisation state of proteins. Compt. Rend. Trav. Lab., Carlsberg 15, 1–29 (1924)

    Google Scholar 

  3. Debye, P., Hückel, E.: Zur Theorie der Electrolyte. Phys. Zeit. 24, 185–206 (1923)

    MATH  Google Scholar 

  4. Svedberg, T., Pederson, K.O.: The Ultracentrifuge. Clarendon Press, Oxford (1940)

    Google Scholar 

  5. Neurath, H., Saum, A.M.: The denaturation of serum albumin: Diffusion and viscosity measurements of serum albumin in the presence of urea. J. Biol. Chem. 128, 347–362 (1939)

    Google Scholar 

  6. Oncley, J.L.: Evidence from physical chemistry regarding the size and shape of protein molecules from ultra-centrifugation, diffusion, viscosity, dielectric dispersion, and double refraction of flow. Annals, N.Y. Acad. of Sci. 41, 121–150 (1941)

    Article  Google Scholar 

  7. Edsall, J.T.: On the laboratory that produced the book, Proteins, Amino Acids and Peptides. AICHE Journal 44, 949–953 (1995)

    Article  Google Scholar 

  8. Anfinsen, C.B.: Principles that govern the Folding of Protein Chains. Science 181, 223–230 (1973)

    Article  Google Scholar 

  9. Scheraga, H.A., Edsall, J.T., Gadd Jr., J.O.: Double refraction of flow: Numerical evaluation of extinction angle and birefringence as a function of velocity gradient. J. Chem. Phys. 19, 1101–1108 (1951)

    Article  Google Scholar 

  10. Scheraga, H.A., Mandelkern, L.: Consideration of the hydrodynamic properties of proteins. J. Am. Chem. Soc. 75, 179–184 (1953)

    Article  Google Scholar 

  11. Flory, P.J., Fox Jr., T.G.: Treatment of intrinsic viscosities. J. Am. Chem. Soc. 73, 1904–1908 (1951)

    Article  Google Scholar 

  12. Mandelkern, L., Krigbaum, W.R., Scheraga, H.A., Flory, P.J.: Sedimentation behavior of flexible chain molecules: polyisobutylene. J. Chem. Phys. 20, 1392–1397 (1952)

    Article  Google Scholar 

  13. Pauling, L., Corey, R.B., Brauson, H.R.: The structure of proteins: Two hydrogen-bonded helical configurations of the polypeptide chain. Proc. Natl. Acad. Sci. USA 37, 205–211 (1951)

    Article  Google Scholar 

  14. Pauling, L., Corey, R.B.: Configurations of polypeptide chains with favored orientations around single bonds: Two new pleated sheets. Proc. Natl. Acad. Sci. USA 37, 729–740 (1951)

    Article  Google Scholar 

  15. Sanger, F.: The arrangement of amino acids in proteins. Adv. Protein Chem. 7, 1–66 (1952)

    Article  Google Scholar 

  16. Ryle, A., Sanger, F., Smith, I.F., Kitai, R.: The disulfide bonds of insulin. Biochem. J. 60, 542–556 (1955)

    Google Scholar 

  17. Perutz, M.F., Rossman, M.G., Cullis, A.F., Muirhead, H., Will, G., North, A.C.T.: Structure of Haemoglobin, A three-dimensional Fourier synthesis at 5.5 Å resolution, obtained by x-ray analysis. Nature 185, 416–422 (1960)

    Article  Google Scholar 

  18. Kendrew, J.C., Dickerson, R.E., Strandberg, B.E., Hart, R.G., Davies, D.R., Philips, D.C., Shore, V.C.: Structure of myoglobin, A three-dimensional Fourier synthesis at 2 Å resolution. Nature 185, 422–427 (1960)

    Article  Google Scholar 

  19. Laskowski Jr., M., Scheraga, H.A.: Thermodynamic considerations of protein reactions. I. Modified reactivity of polar groups. J. Am. Chem. Soc. 76, 6305–6319 (1954)

    Article  Google Scholar 

  20. Laskowski Jr., M., Scheraga, H.A.: Thermodynamic considerations of protein reactions. II. Modified reactivity of primary valence bonds. J. Am. Chem. Soc. 78, 5793–5798 (1956)

    Article  Google Scholar 

  21. Némethy, G., Scheraga, H.A.: The structure of water and hydrophobic bonding in proteins. III. The thermodynamic properties of hydrophobic bonds in proteins. J. Phys. Chem. 66, 1773–1789 (1962); Erratum: J. Phys. Chem. 67, 2888 (1963)

    Google Scholar 

  22. Griffith, J.H., Scheraga, H.A.: Statistical thermodynamics of aqueous solutions. I. Water structure, solutions with non-polar solutes, and hydrophobic interactions. J. Molec. Str. 682, 97–113 (2004)

    Google Scholar 

  23. Owicki, J.C., Scheraga, H.A.: Monte Carlo calculations in the isothermal isobaric ensemble. 2. Dilute aqueous solution of methane. J. Am. Chem. Soc. 99, 7413–7418 (1977)

    Article  Google Scholar 

  24. Rapaport, D.C., Scheraga, H.A.: Hydration of inert solutes. A molecular dynamics study. J. Phys. Chem. 86, 873–880 (1982)

    Article  Google Scholar 

  25. Kendrew, J.C.: The structure of globular proteins. Comp. Biochem. Physiol. 4, 249–252 (1962)

    Article  Google Scholar 

  26. Scheraga, H.A.: Theory of hydrophobic interactions. J. Biomolec. Structure and Dynamics 16, 447–460 (1998)

    Article  Google Scholar 

  27. Sturtevant, J.M., Laskowski Jr., M., Donnelly, T.H., Scheraga, H.A.: Equilibria in the fibrinogen-fibrin conversion. III. Heats of polymerization and clotting of fibrin monomer. J. Am. Chem. Soc. 77, 6168–6172 (1955)

    Article  Google Scholar 

  28. Scheraga, H.A.: Structural studies of pancreatic ribonuclease. Fed. Proc. 26, 1380–1387 (1967)

    Google Scholar 

  29. Wlodawer, A., Svensson, L.A., Sjölin, L., Gilliland, G.L.: Structure of phosphate-free ribonuclease A refined at 1.26Å. Biochemistry 27, 2705–2717 (1988)

    Article  Google Scholar 

  30. Némethy, G., Scheraga, H.A.: Theoretical determination of sterically allowed conformations of a polypeptide chain by a computer method. Biopolymers 3, 155–184 (1965)

    Article  Google Scholar 

  31. Scheraga, H.A.: Calculations of conformations of polypeptides. Adv. Phys. Org. Chem. 6, 103–184 (1968)

    Article  Google Scholar 

  32. Ramachandran, G.N., Ramakrishnan, C., Sasisekharan, V.: Stereochemistry of polypeptide chain configurations. J. Mol. Biol. 7, 95–99 (1963)

    Article  Google Scholar 

  33. Scheraga, H.A., Leach, S.J., Scott, R.A., Némethy, G.: Intramolecular forces and protein conformation. Disc Faraday Soc. 40, 268–277 (1965)

    Article  Google Scholar 

  34. Némethy, G., Leach, S.J., Scheraga, H.A.: The influence of amino acid side chains on the free energy of helix coil transitions. J. Phys. Chem. 70, 998–1004 (1966)

    Article  Google Scholar 

  35. Leach, S.J., Némethy, G., Scheraga, H.A.: Computation of the sterically allowed conformations of peptides. Biopolymers 4, 369–407 (1966)

    Article  Google Scholar 

  36. de Santis, P., Giglio, E., Liquori, A.M., Ripamonti, A.: Stability of helical conformations of simple linear polymers. J. Polym. Sci. Part A 1, 1383–1404 (1963)

    Google Scholar 

  37. Brant, D.A., Flory, P.J.: The configuration of random polypeptide chains. II. Theory. J. Am. Chem. Soc. 87, 2791–2800 (1965)

    Article  Google Scholar 

  38. Ooi, T., Scott, R.A., Vanderkooi, G., Scheraga, H.A.: Conformational analysis of macromolecules. IV. Helical structures of poly-L-alanine, poly-L-valine, poly-β-methyl L-aspartate, poly-γ-methyl-L-glutamate, and poly-L-tyrosine. J. Chem. Phys. 46, 4410–4426 (1967)

    Article  Google Scholar 

  39. Gibson, K.D., Scheraga, H.A.: Minimization of polypeptide energy. II. Preliminary structures of oxytocin, vasopressin and an octapeptide from ribonuclease. Proc. Natl. Acad. Sci. USA 58, 1317–1323 (1967)

    Article  Google Scholar 

  40. Gibson, K.D., Scheraga, H.A.: Minimization of polypeptide energy. VII. Second derivatives and statistical weights of energy minima for deca L alanine. Proc. Natl. Acad. Sci. USA 63, 242–245 (1969)

    Article  Google Scholar 

  41. Scott, R.A., Vanderkooi, G., Tuttle, R.W., Shames, P.M., Scheraga, H.A.: Minimization of polypeptide energy. III. Application of a rapid energy minimization technique to the calculation of preliminary structures of gramicidin-S. Proc. Natl. Acad. Sci. 58, 2204–2211 (1967)

    Article  Google Scholar 

  42. Yan, J.F., Vanderkooi, G., Scheraga, H.A.: Conformational analysis of macromolecules. V. Helical structures of poly-L-aspartic acid and poly-L glutamic acid, and related compounds. J. Chem. Phys. 49, 2713–2726 (1968)

    Article  Google Scholar 

  43. Yan, J.F., Momany, F.A., Scheraga, H.A.: Conformational analysis of macromolecules. VI. Helical Structures of o-, m-, and p- chlorobenzyl esters of poly-L-aspartic acid. J. Am. Chem. Soc. 92, 1109–1115 (1970)

    Article  Google Scholar 

  44. Momany, F.A., Vanderkooi, G., Scheraga, H.A.: Determination of intermolecular potentials from crystal data. I. General theory and application to crystalline benzene at several temperatures. Proc. Natl. Acad. Sci. USA 61, 429–436 (1968)

    Article  Google Scholar 

  45. Momany, F.A., McGuire, R.F., Yan, J.F., Scheraga, H.A.: Energy parameters in polypeptides. IV. Semiempirical molecular orbital calculations of conformational dependence of energy and partial charge in di- and tripeptides. J. Phys. Chem. 75, 2286–2297 (1971)

    Article  Google Scholar 

  46. Levitt, M., Lifson, S.: Refinement of protein confirmations using a macromolecular energy minimization procedure. J. Mol. Biol. 46, 269–279 (1969)

    Article  Google Scholar 

  47. Hagler, A.T., Huler, E., Lifson, S.: Energy functions for peptides and proteins. I. Derivation of a consistent force field including the hydrogen bond from amide crystals. J. Am. Chem. Soc. 96, 5319–5327 (1974)

    Article  Google Scholar 

  48. Momany, F.A., McGuire, R.F., Burgess, A.W., Scheraga, H.A.: Energy parameters in polypeptides. VII. Geometric parameters, partial atomic charges, nonbonded interactions, hydrogen bond interactions, and intrinsic torsional potentials for the naturally occurring amino acids. J. Phys. Chem. 79, 2361–2381 (1975)

    Article  Google Scholar 

  49. Némethy, G., Pottle, M.S., Scheraga, H.A.: Energy parameters in polypeptides. 9. Updating of geometrical parameters, nonbonded interactions, and hydrogen bond interactions for the naturally occurring amino acids. J. Phys. Chem. 87, 1883–1887 (1983)

    Article  Google Scholar 

  50. Sippl, M.J., Némethy, G., Scheraga, H.A.: Intermolecular potentials from crystal data. 6. Determination of empirical potentials for O-H∙∙∙O=C hydrogen bonds from packing configurations. J. Phys. Chem. 88, 6231–6233 (1984)

    Article  Google Scholar 

  51. Némethy, G., Gibson, K.D., Palmer, K.A., Yoon, C.N., Paterlini, G., Zagari, A., Rumsey, S., Scheraga, H.A.: Energy parameters in polypeptides. 10. Improved geometrical parameters and nonbonded interactions for use in the ECEPP/3 algorithm, with application to proline containing peptides. J. Phys. Chem. 96, 6472–6484 (1992)

    Article  Google Scholar 

  52. Arnautova, Y.A., Jagielska, A., Scheraga, H.A.: A new force field (ECEPP-05) for peptides, proteins and organic molecules. J. Phys. Chem. B 110, 5025–5044 (2006)

    Article  Google Scholar 

  53. Brooks, B.R., Bruccoleri, R.E., Olafson, B.D., States, D.J., Swaminathan, S., Karplus, M.: CHARMM: A program for macromolecular energy, minimization, and dynamics calculations. J. Comput. Chem. 4, 187–217 (1983)

    Article  Google Scholar 

  54. Cornell, W.D., Cieplak, P., Bayley, C.I., Gould, I.R., Merz Jr., K.M., Ferguson, D.M., Spellmeyer, D.C., Fox, T., Caldwell, J.W., Kollman, P.A.: A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules. J. Am. Chem. Soc. 117, 5179–5197 (1995)

    Article  Google Scholar 

  55. Scott, W.R.P., Huenenberger, P.H., Tironi, I.G., Mark, A.E., Billeter, S.R., Fennen, J., Torda, A.E., Huber, T., Krueger, P., van Gusteren, W.F.: The GROMOS biomolecular simulation program package. J. Phys. Chem. A 103, 3596–3607 (1999)

    Article  Google Scholar 

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

    Article  Google Scholar 

  57. Ooi, T., Oobatake, M., Némethy, G., Scheraga, H.A.: Accessible surface areas as a measure of the thermodynamic parameters of hydration of peptides. Proc. Natl. Acad. Sci. USA 84, 3086–3090 (1987); Erratum: ibid, 84, 6015 (1987)

    Google Scholar 

  58. Vila, J., Williams, R.L., Vasquez, M., Scheraga, H.A.: Empirical solvation models can be used to differentiate native from near native conformations of bovine pancreatic trypsin inhibitor. Proteins: Structure, Function, and Genetics 10, 199–218 (1991)

    Article  Google Scholar 

  59. Nicholls, A., Honig, B.: A rapid finite difference algorithm, utilizing successive over-relaxation to solve the Poisson-Boltzmann equation. J. Comp. Chem. 12, 435–445 (1991)

    Article  Google Scholar 

  60. Nicholls, A., Sharp, K.A., Honig, B.: Protein folding and association: Insights from the interfacial and thermodynamic properties of hydrocarbons. Proteins: Struct. Funct. Genet. 11, 281–296 (1991)

    Article  Google Scholar 

  61. Vorobjev, Y.N., Vila, J.A., Scheraga, H.A.: FAMBE-pH: a fast and accurate method to compute the total solvation free energies of proteins. J. Phys. Chem. B 112, 11122–11136 (2008)

    Article  Google Scholar 

  62. Still, W.C., Tempczyk, A., Hawley, R.C., Henderickson, T.: Semianalytical treatment of solvation for molecular mechanics and dynamics. J. Am. Chem. Soc. 112, 6127–6129 (1990)

    Article  Google Scholar 

  63. Bashford, D., Case, D.: Generalized Born models of macromolecular solvation effects. Annu. Rev. Phys. Chem. 51, 129–152 (2000)

    Article  Google Scholar 

  64. Ferrara, P., Apostolakis, J., Caflisch, A.: Evolution of a fast implicit solvent model for molecular dynamics simulations. Proteins 46, 24–33 (2002)

    Article  Google Scholar 

  65. Bursulaya, B., Brooks III, C.I.: Comparative study of folding free energy landscape of a three-stranded-sheet protein with explicit and implicit solvent models. J. Phys. Chem. B 104, 12378–12383 (2002)

    Article  Google Scholar 

  66. Im, W., Lee, M., Brooks, C.: Generalized Born model with a simple smoothing function. J. Comp. Chem. 24, 1691–1702 (2003)

    Article  Google Scholar 

  67. Scheraga, H.A., Pillardy, J., Liwo, A., Lee, J., Czaplewski, C., Ripoll, D.R., Wedemeyer, W.J., Arnautova, Y.A.: Evolution of physics-based methodology for exploring the conformational energy landscape of proteins. J. Comput. Chem. 23, 28–34 (2002)

    Article  Google Scholar 

  68. Alder, B.J., Wainwright, T.: Molecular dynamics by electronic computers. In: Prigogine, I. (ed.) Proc. Int. Symp. Transp. Process. Stat. Mech., pp. 97–131. Interscience, New York (1957)

    Google Scholar 

  69. McCammon, J.A., Gelin, B.R., Karplus, M.: Dynamics of folded proteins. Nature 267, 585–590 (1977)

    Article  Google Scholar 

  70. Scheraga, H.A., Khalili, M., Liwo, A.: Protein folding dynamics: Overview of molecular simulation techniques. Annual Rev. Phys. Chem. 58, 57–83 (2007)

    Article  Google Scholar 

  71. Shirts, M., Pande, V.S.: Screen Savers of the World Unite! Science 290, 1903–1904 (2000)

    Article  Google Scholar 

  72. Shaw, D.E., et al.: Structure and dynamics of an unfolded protein examined by molecular dynamics simulation. J. Am. Chem. Soc. 336, 3787–3791 (2012)

    Google Scholar 

  73. Li, Z., Scheraga, H.A.: Monte Carlo minimization approach to the multiple minima problem in protein folding. Proc. Natl. Acad. Sci. USA 84, 6611–6615 (1987)

    Article  MathSciNet  Google Scholar 

  74. Hansmann, U.H.E., Masuya, M., Okamoto, Y.: Characteristic temperatures of folding of a small peptide. Proc. Natl. Acad. Sci. USA 94, 10652–10656 (1997)

    Article  Google Scholar 

  75. Dygert, M., Go, N., Scheraga, H.A.: Use of a symmetry condition to compute the conformation of gramicidin-S. Macromolecules 8, 750–761 (1975)

    Article  Google Scholar 

  76. Gō, N., Scheraga, H.A.: Ring closure in chain molecules with C n , I or S 2n symmetry. Macromolecules 6, 273–281 (1973)

    Article  Google Scholar 

  77. Mirau, R.A., Bovey, F.A.: 2D and 3D NMR studies of polypeptide structure and function. In: Abstracts, 199th ACS Meeting. Polymer Division, Boston, vol. 206 (1990)

    Google Scholar 

  78. Ripoll, D.R., Vila, J.A., Scheraga, H.A.: Folding of the villin headpiece subdomain from random structures. Analysis of the charge distribution as a function of pH. J. Mol. Biol. 339, 915–925 (2004)

    Article  Google Scholar 

  79. Vila, J.A., Ripoll, D.R., Scheraga, H.A.: Atomically detailed folding simulation of the B domain of staphylococcal protein A from random structures. Proc. Natl. Acad. Sci. USA 100, 14812–14816 (2003)

    Article  Google Scholar 

  80. Vila, J.A., Arnautova, Y.A., Martin, O.A., Scheraga, H.A.: Quantum-mechanics-derived 13Cα chemical shift server (Che Shift) for protein structure validation. Proc. Natl. Acad. Sci., USA 106, 16972–16977 (2009)

    Article  Google Scholar 

  81. Vila, J.A., Scheraga, H.A.: Assessing the accuracy of protein structures by quantum mechanical computations of 13Cα chemical shifts. Accounts of Chem. Res. 42, 1545–1553 (2009)

    Article  Google Scholar 

  82. Miller, M.H., Scheraga, H.A.: Calculation of the structures of collagen models. Role of interchain interactions in determining the triple-helical coiled coil conformation. I. Poly(glycyl-prolyl-prolyl). J. Polymer Sci.: Polymer Symposia 54, 171–200 (1976)

    Google Scholar 

  83. Miller, M.H., Némethy, G., Scheraga, H.A.: Calculation of the structures of collagen models. Role of interchain interactions in determining the triple-helical coiled-coil conformation. 2. Poly(glycyl-prolyl-hydroxyprolyl). Macromolecules 13, 470–478 (1980)

    Article  Google Scholar 

  84. Miller, M.H., Némethy, G., Scheraga, H.: Calculation of the structures of collagen models. Role of interchain interactions in determining the triple-helical-coiled coil conformation. 3. Poly(glycyl-prolyl-alanyl). Macromolecules 13, 910–913 (1980)

    Article  Google Scholar 

  85. Némethy, G., Miller, M.H., Scheraga, H.A.: Calculation of the structures of collagen models. Role of interchain interactions in determining the triple-helical coiled-coil conformation. 4. Poly(glycyl-alanyl-prolyl). Macromolecules 13, 914–919 (1980)

    Article  Google Scholar 

  86. Pincus, M.R., Scheraga, H.A.: Conformational energy calculations of enzyme-substrate and enzyme-inhibitor complexes of lysozyme. 2. Calculation of the structures of complexes with a flexible enzyme. Macromolecules 12, 633–644 (1979)

    Article  Google Scholar 

  87. Smith-Gill, S.J., Rupley, J.A., Pincus, M.R., Carty, R.P., Scheraga, H.A.: Experimental identification of a theoretically predicted “left sided” binding mode for (GlcNAc)6 in the active site of lysozyme. Biochemistry 23, 993–997 (1984)

    Article  Google Scholar 

  88. Simon, I., Glasser, L., Scheraga, H.A., Manley, R.S.J.: Structure of cellulose. 2. Low-energy crystalline arrangements. Macromolecules 21, 990–998 (1988)

    Article  Google Scholar 

  89. Kolinski, A.: Protein modeling and structure prediction with a reduced representation. Acta Biochim. Biol. 51, 349–371 (2004)

    Google Scholar 

  90. Voth, G.A.: Coarse-graining of condensed phase and biomolecular symmetry. CRC Press, Boca Raton (2009)

    Google Scholar 

  91. Levitt, M., Warshel, A.: Computer simulation of protein folding. Nature 253, 694–698 (1975)

    Article  Google Scholar 

  92. Pincus, M.R., Scheraga, H.A.: An approximate treatment of long range interactions in proteins. J. Phys. Chem. 81, 1579–1583 (1977)

    Article  Google Scholar 

  93. Sieradzan, A.K., Hansmann, U.H.E., Scheraga, H.A., Liwo, A.: Extension of UNRES force field to treat polypeptide chains with D-amino-acid residues. J. Chem. Theory and Computation (submitted)

    Google Scholar 

  94. Liwo, A., Pincus, M.R., Wawak, R.J., Rackovsky, S., Scheraga, H.A.: Prediction of protein conformation on the basis of a search for compact structures; test on avian pancreatic polypeptide. Protein Science 2, 1715–1731 (1993)

    Article  Google Scholar 

  95. Liwo, A., Oldziej, S., Pincus, M.R., Wawak, R.J., Rackovsky, S., Scheraga, H.A.: A united-residue force field for off-lattice protein-structure simulations. I. Functional forms and parameters of long-range side-chain interaction potentials from protein crystal data. J. Comput. Chem. 18, 849–873 (1997)

    Article  Google Scholar 

  96. Liwo, A., Pincus, M.R., Wawak, R.J., Rackovsky, S., Oldziej, S., Scheraga, H.A.: A united-residue force field for off-lattice protein-structure simulations. II. Parameterization of short-range interactions and determination of weights of energy terms by Z-score optimization. J. Comput. Chem. 18, 874–887 (1997)

    Article  Google Scholar 

  97. Liwo, A., Kazmierkiewicz, R., Czaplewski, C., Groth, M., Oldziej, S., Wawak, R.J., Rackovsky, S., Pincus, M.R., Scheraga, H.A.: United-residue force field for off-lattice protein-structure simulations. III. Origin of backbone hydrogen-bonding cooperativity in united-residue potentials. J. Comput. Chem. 19, 259–276 (1998)

    Article  Google Scholar 

  98. Liwo, A., Czaplewski, C., Pillardy, J., Scheraga, H.A.: Cumulant-based expressions for the multibody terms for the correlation between local and electrostatic interactions in the united-residue force field. J. Chem. Phys. 115, 2323–2347 (2001)

    Article  Google Scholar 

  99. Liwo, A., Arlukowicz, P., Czaplewski, C., Ołdziej, S., Pillardy, J., Scheraga, H.A.: A method for optimizing potential-energy functions by a hierarchical design of the potential-energy landscape: Application to the UNRES force field. Proc. Natl. Acad. Sci. USA 99, 1937–1942 (2002)

    Article  Google Scholar 

  100. Liwo, A., Ołdziej, S., Czaplewski, C., Kosłowska, U., Scheraga, H.A.: Parameterization of backbone-electrostatic and multibody contributions to the UNRES force field for protein-structure prediction from ab initio energy surfaces of model systems. J. Phys. Chem. B 108, 9421–9438 (2004)

    Article  Google Scholar 

  101. Liwo, A., Arłukowicz, P., Ołdziej, S., Czaplewski, C., Makowski, M., Scheraga, H.A.: Optimization of the UNRES force field by hierarchical design of the potential-energy landscape. 1. Tests of the approach using simple lattice protein models. J. Phys. Chem. B 108, 16918–16933 (2004)

    Article  Google Scholar 

  102. Ołdziej, S., Liwo, A., Czaplewski, C., Pillardy, J., Scheraga, H.A.: Optimization of the UNRES force field by hierarchical design of the potential-energy landscape. 2. Off-lattice tests of the method with single proteins. J. Phys. Chem. B 108, 16934–16949 (2004)

    Article  Google Scholar 

  103. Ołdziej, S., Lagiewka, J., Liwo, A., Czaplewski, C., Chinchio, M., Nanias, M., Scheraga, H.A.: Optimization of the UNRES force field by hierarchical design of the potential-energy landscape. 3. Use of many proteins in optimization. J Phys. Chem. B 108, 16950–16959 (2004)

    Article  Google Scholar 

  104. Liwo, A., Khalili, M., Scheraga, H.A.: Ab initio simulations of protein-folding pathways by molecular dynamics with the united-residue model of polypeptide chains. Proc. Natl. Acad. Sci. USA 102, 2362–2367 (2005)

    Article  Google Scholar 

  105. Khalili, M., Liwo, A., Rakowski, F., Grochowski, P., Scheraga, H.A.: Molecular dynamics with the united-residue model of polypeptide chains. I. Lagrange equations of motion and tests of numerical stability in the microcanonical mode. J. Phys. Chem. B 109, 13785–13797 (2005)

    Article  Google Scholar 

  106. Khalili, M., Liwo, A., Jagielska, A., Scheraga, H.A.: Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model α-helical systems. J. Phys. Chem. B 109, 13798–13810 (2005)

    Article  Google Scholar 

  107. Liwo, A., Khalili, M., Czaplewski, C., Kalinowski, S., Ołdziej, S., Wachucik, K., Scheraga, H.A.: Modification and optimization of the united-residue (UNRES) potential-energy function for canonical simulations. I. Temperature dependence of the effective energy function and tests of the optimization method with single training proteins. J. Phys. Chem. B 111, 260–285 (2007)

    Article  Google Scholar 

  108. Kozlowska, U., Liwo, A., Scheraga, H.A.: Determination of virtual-bond-angle potentials of mean force for coarse-grained simulations of protein structure and folding from ab initio energy surfaces of terminally-blocked glycine, alanine, and proline. J Physics: Condensed Matter 19, 285203-1—285203-15 (2007)

    Google Scholar 

  109. Liwo, A., Czaplewski, C., Ołdziej, S., Rojas, A.V., Kazmierkiewicz, R., Makowski, M., Murarka, R.K., Scheraga, H.A.: Simulation of protein structure and dynamics with the coarse-grained UNRES force field. In: Voth, G.A. (ed.) Coarse-Graining of Condensed Phase and Biomolecular Systems, pp. 107–122. CRC Press, Boca Raton (2008)

    Google Scholar 

  110. Ołdziej, S., Czaplewski, C., Liwo, A., Scheraga, H.A.: Towards temperature dependent coarse-grained potential of side-chain interactions for protein folding simulations. In: IEEE International Conference on Bioinformatics and Bioengineering, BIBE, pp. 263–266 (2010)

    Google Scholar 

  111. Liwo, A., Ołdziej, S., Czaplewski, C., Kleinerman, D.S., Blood, P., Scheraga, H.A.: Implementation of molecular dynamics and its extensions with the coarse-grained UNRES force field on massively parallel systems; towards millisecond-scale simulations of protein structure, dynamics, and thermodynamics. J. Chem. Theory and Comput. 6, 890–909 (2010)

    Article  Google Scholar 

  112. Maisuradze, G.G., Senet, P., Czaplewski, C., Liwo, A., Scheraga, H.A.: Investigation of protein folding by coarse-grained molecular dynamics with the UNRES force field. J. Phys. Chem. A 114, 4471–4485 (2010)

    Article  Google Scholar 

  113. Makowski, M., Liwo, A., Scheraga, H.A.: Simple physics-based analytical formulas for the potentials of mean force of the interaction of amino-acid side chains in water. VI. Oppositely-charged side chains. J. Phys. Chem. 115, 6130–6137 (2011)

    Article  Google Scholar 

  114. Sieradzan, A.K., Scheraga, H.A., Liwo, A.: Determination of effective potentials for the stretching of Cα…Cα virtual bonds in polypeptide chains for coarse-grained simulations of proteins from ab initio energy surfaces of N-methylacetamide and N-acetylpyrrolidine. J. Chem. Theory and Computation 8, 1334–1343 (2012)

    Article  Google Scholar 

  115. Shen, H., Liwo, A., Scheraga, H.A.: An improved functional form for the temperature, scaling factors of the components of the mesoscopic UNRES force field for simulations of protein structure and dynamics. J. Phys. Chem. B 113, 8738–8744 (2009)

    Article  Google Scholar 

  116. Kolinski, A., Skolnick, J.: Discretized model of proteins: I. Monte Carlo study of cooperativity in homopolypeptides. J. Chem. Phys. 97, 9412–9426 (1992)

    Article  Google Scholar 

  117. He, Y., Xiao, Y., Liwo, A., Scheraga, H.A.: Exploring the parameter space of the coarse-grained UNRES force field by random search: Selecting a transferable medium-resolution force field. J. Comput. Chem. 30, 2127–2135 (2009)

    Article  Google Scholar 

  118. Lee, J., Scheraga, H.A., Rackovsky, S.: New optimization method for conformational energy calculations on polypeptides: Conformational space annealing. J. Comput. Chem. 18, 1222–1232 (1997)

    Article  Google Scholar 

  119. Kazmierkiewicz, R., Liwo, A., Scheraga, H.A.: Energy-based reconstruction of a protein backbone from its α-carbon trace by a Monte-Carlo method. J. Comput. Chem. 23, 715–723 (2002)

    Article  Google Scholar 

  120. Kazmierkiewicz, R., Liwo, A., Scheraga, H.A.: Addition of side chains to a known backbone with defined side-chain centroids. Biophys. Chem. 100, 261–280 (2003); Erratum: Biophys Chem. 106, 91 (2003)

    Google Scholar 

  121. Elber, R., Ghosh, A., Cardenas, A.: Long time dynamics of complex systems. Acc. Chem. Res. 35, 396–403 (2002)

    Article  Google Scholar 

  122. Ghosh, A., Elber, R., Scheraga, H.A.: An atomically detailed study of the folding pathways of protein A with the stochastic difference equation. Proc. Natl. Acad. Sci. USA 99, 10394–10398 (2002)

    Article  Google Scholar 

  123. Kubo, R.: Generalized Cumulant Expansion Method. J. Phys. Soc. Jpn 17, 1100–1120 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  124. Rojas, A.V., Liwo, A., Scheraga, H.A.: Molecular dynamics with the united-residue (UNRES) force field. Ab initio folding simulations of multi-chain proteins. J. Phys. Chem. B 111, 293–309 (2007)

    Article  Google Scholar 

  125. Liwo, A., Lee, J., Ripoll, D.R., Pillardy, J., Scheraga, H.A.: Protein structure prediction by global optimization of a potential energy function. Proc. Natl. Acad. Sci. USA 96, 5482–5485 (1999)

    Article  Google Scholar 

  126. Khalili, M., Liwo, A., Scheraga, H.A.: Kinetic studies of folding of the B-domain of staphylococcal protein A with molecular dynamics and a united-residue (UNRES) model of polypeptide chains. J. Mol. Biol. 355, 536–547 (2006)

    Article  Google Scholar 

  127. Swendsen, R.H., Wang, J.S.: Replica Monte Carlo simulations of spin-glasses. Phys. Rev. Lett. 57, 2607–2609 (1986)

    Article  MathSciNet  Google Scholar 

  128. Sugita, Y., Okamoto, Y.: Replica-exchange molecular dynamics method for protein folding. Chem. Phys. Lett. 314, 141–151 (1999)

    Article  Google Scholar 

  129. Nanias, M., Chinchio, M., Ołdziej, S., Czaplewski, C., Scheraga, H.A.: Protein structure prediction with the UNRES force-field using Replica-Exchange Monte Carlo-with-Minimization; Comparison with MCM, CSA and CFMC. J. Comput. Chem. 26, 1472–1486 (2005)

    Article  Google Scholar 

  130. Rhee, Y.M., Pande, V.S.: Multiplexed-Replica Exchange Molecular Dynamics Method for Protein Folding Simulation. Biophys. J. 84, 775–786 (2003)

    Article  Google Scholar 

  131. Czaplewski, C., Kalinowski, S., Liwo, A., Scheraga, H.A.: Application of multiplexed replica exchange molecular dynamics to the UNRES force field: tests with α and α + β proteins. J. Chem. Theory and Comput. 5, 627–640 (2009)

    Article  Google Scholar 

  132. Rojas, A., Liwo, A., Browne, D., Scheraga, H.A.: Mechanism of fiber assembly; treatment of Aβ-peptide aggregation with a coarse-grained united-residue force field. J. Mol. Biol. 404, 537–552 (2010)

    Article  Google Scholar 

  133. He, Y., Liwo, A., Weinstein, H., Scheraga, H.A.: PDZ binding to the BAR domain of PICK1 is elucidated by coarse-grained molecular dynamics. J. Mol. Biol. 405, 298–314 (2011)

    Article  Google Scholar 

  134. Golas, E., Maisuradze, G.G., Senet, P., Ołdziej, S., Czaplewski, C., Scheraga, H.A., Liwo, A.: Simulation of the opening and closing of Hsp70 chaperones by coarse-grained molecular dynamics. J. Chem. Theory and Computation 8, 1750–1764 (2012)

    Article  Google Scholar 

  135. Marmur, J., Doty, P.: Thermal renaturation of deoxyribonucleic acids. J. Mol. Biol. 3, 585–594 (1961)

    Article  Google Scholar 

  136. Peyrard, M., Bishop, A.R.: Statistical Mechanics of a Nonlinear Model for DNA Denaturation. Phys. Rev. Lett. 62, 2755–2758 (1989)

    Article  Google Scholar 

  137. Olson, W.K.: Simulating DNA at low resolution. Curr. Opinion Struct. Biol. 6, 242–256 (1996)

    Article  Google Scholar 

  138. Hyeon, C., Thirumalai, D.: Mechanical unfolding of RNA hairpins. Proc. Natl. Acad. Sci. U S A 102, 6789–6794 (2005)

    Article  Google Scholar 

  139. Knotts, T., Rathore, N., Schwartz, D.C., de Pablo, J.J.: A coarse grain model for DNA. J. Chem. Phys. 126, 084901– 084901-12 (2007)

    Google Scholar 

  140. Voltz, K., Trylska, J., Tozzini, V., Kurkal-Siebert, V., Langowski, J., Smith, J.: Coarse-Grained Force Field for the Nucleosome from Self-Consistent Multiscaling. J. Comput. Chem. 29, 1429–1439 (2008)

    Article  Google Scholar 

  141. Ouldridge, T.E., Louis, A.A., Doye, J.P.K.: DNA Nanotweezers Studied with a Coarse-Grained Model of DNA. Phys. Rev. Lett. 104, 178101-1–178101-4 (2010)

    Google Scholar 

  142. Maciejczyk, M., Spasic, A., Liwo, A., Scheraga, H.A.: Coarse-grained model of nucleic acid bases. J. Comput. Chem. 31, 1644–1655 (2010)

    Google Scholar 

  143. He, Y., Maciejczyk, M., Ołdziej, S., Scheraga, H.A., Liwo, A.: Mean-field interactions between nucleic-acid-base dipoles can drive the formation of the double helix. Phys. Rev. Lett. 110, 098101 (2013)

    Google Scholar 

  144. Pollack, L.: Fashioning NAMD, a History of Risk and Reward: Klaus Schulten Reminisces. In: Schlick, T. (ed.) Innovations in Biomolecular Modeling and Simulations, vol. 1., Royal Society of Chemistry, Cambridge (2012)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  146. Yang, L., Song, G., Jernigan, R.L.: How well can we understand large-scale protein motions using normal modes of elastic network models? Biophys. J. 93, 920–929 (2007)

    Article  Google Scholar 

  147. Senet, P., Maisuradze, G.G., Foulie, C., Delarue, P., Scheraga, H.A.: How main-chains of proteins explore the free-energy landscape in native states. Proc. Natl. Acad. Sci. USA 105, 19708–19713 (2008)

    Article  Google Scholar 

  148. Cote, Y., Senet, P., Delarue, P., Maisuradze, G.G., Scheraga, H.A.: Nonexponential decay of internal rotational correlation functions of native proteins and self-similar structural fluctuations. Proc. Natl. Acad. Sci. USA 107, 19844–19849 (2010)

    Article  Google Scholar 

  149. Cote, Y., Senet, P., Delarue, P., Maisuradze, G.G., Scheraga, H.A.: Anomalous diffusion and dynamical correlation between the side chains and the main chain of proteins in their native state. Proc. Natl. Acad. Sci. 109, 10346–10351 (2012)

    Article  Google Scholar 

  150. Schlick, T. (ed.): Innovations in Biomolecular Modeling and Simulations, vols. 1 and 2. Royal Society of Chemistry, Cambridge (2012)

    Google Scholar 

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  1. Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, 14853-1301, U.S.A.

    Harold A. Scheraga

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    Adam Liwo

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Scheraga, H.A. (2014). Simulations of the Folding of Proteins: A Historical Perspective. In: Liwo, A. (eds) Computational Methods to Study the Structure and Dynamics of Biomolecules and Biomolecular Processes. Springer Series in Bio-/Neuroinformatics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28554-7_1

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