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Surmounting the Multiple-Minima Problem in Protein Folding

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Abstract

Protein folding is a very difficult global optimization problem. Furthermore it is coupled with the difficult task of designing a reliable force field with which one has to search for the global minimum. A summary of a series of optimization methods developed and applied to various problems involving polypeptide chains is described in this paper. With recent developments, a computational treatment of the folding of globular proteins of up to 140 residues is shown to be tractable.

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References

  1. Wales, D.J. and Scheraga, H.A. (1999), Global optimization of clusters, crystals and biomolecules, Science, 285: 1368–1372.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  5. Némethy, G., Gibson, K.D., Palmer, K.A., Yoon, C.N., Paterlini, G., Zagari, A., Rumsey, S. and Scheraga, H.A. (1992), Energy parameters in polypeptides. X. 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.

    Google Scholar 

  6. Liwo, A., Pincus, M.R., Wawak, R.J., Rackovsky, S. and Scheraga, H.A. (1993), Calculation of protein backbone geometry from -carbon coordinates based on peptide-group dipole alignment, Protein Science 2: 1697–1714.

    Google Scholar 

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

    Google Scholar 

  8. Liwo, A., Oldziej, 6S., Pincus, M.R., Wawak, R.J., Rackovsky, S. and Scheraga, H.A. (1997), 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.

    Google Scholar 

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

    Google Scholar 

  10. Liwo, A., Kazmierkiewicz, R., Czaplewski, C., Groth, M., Oldziej, S., Wawak, R.J., Rackovsky, S., Pincus, M.R. and Scheraga, H.A. (1998), A united-residue force field for off-lattice proteinSURMOUNTING THE MULTIPLE-MINIMA PROBLEM 257 structure simulations. III. Origin of backbone hydrogen-bonding cooperativity in united-residue potentials, J. Comput. Chem. 19: 259–276.

    Google Scholar 

  11. Scheraga, H.A. (1974), Prediction of protein conformation, in C.B. Anfinsen and A.N. Schechter (eds.), Current Topics in Biochemistry(pp. 1–42), Academic Press, New York.

    Google Scholar 

  12. Simon, I., Némethy, 0G. and Scheraga, H.A. (1978), Conformational energy calculations of the effects of sequence variations on the conformations of two tetrapeptides, Macromolecules11: 797–804.

    Google Scholar 

  13. Pincus, M.R., Klausner, R.D. and Scheraga, H.A. (1982), Calculation of the three-dimensional structure of the membrane-bound portion of melittin from its amino acid sequence, Proc. Natl. Acad. Sci., USA 79: 5107–5110.

    Google Scholar 

  14. Scheraga, H.A. (1983), Recent progress in the theoretical treatment of protein folding, Biopolymers22: 1–14.

    Google Scholar 

  15. Vásquez, M. and Scheraga, H.A. (1985), Use of buildup and energy-minimization procedures to compute low-energy structures of the backbone of enkephalin, Biopolymers 24: 1437–1447.

    Google Scholar 

  16. Gibson, K.D. and Scheraga, H.A. (1987), Revised algorithms for the build-up procedure for predicting protein conformations by energy minimization, J. Comput. Chem. 8: 826–834.

    Google Scholar 

  17. Vásquez, M., Némethy, G. and Scheraga, H.A. (1983), Computed conformational states of the 20 naturally occurring amino acid residues and of the prototype residue -aminobutyric acid, Macromolecules 16: 1043–1049.

    Google Scholar 

  18. Zimmerman, S.S., Pottle, M.S., Némethy, G. and Scheraga, H.A. (1977), Conformational analysis of the twenty naturally occurring amino acid residus using ECEPP, Macromolecules10:1–9. e

    PubMed  Google Scholar 

  19. Vásquez, M. and Scheraga, H.A. (1988), Calculation of protein conformation by the build-up procedure. Application to bovine pancreatic trypsin inhibitor using limited simulated nuclear magnetic resonance data, J. Biomol. Struct. & Dyn 5: 705–755.

    Google Scholar 

  20. Vásquez, M. and Scheraga, H.A. (1988), Variable-target-function and build-up procedures for the calculation of protein conformation. Application to bovine pancreatic trypsin inhibitor using limited simulated nuclear magnetic resonance data, J. Biomol. Struct. & Dyn. 5: 757–784.

    Google Scholar 

  21. Dygert, M., G¯o, N. and Scheraga, H.A. (1975), Use of a symmetry condition to compute the conformation of gramicidin S, Macromolecules 8: 750–761.

    PubMed  Google Scholar 

  22. Némethy, G. and Scheraga, H.A. (1984), Hydrogen bonding involving the ornithine side chain of gramicidin S, Biochem. Biophys. Res. Commun. 118: 643–647.

    Google Scholar 

  23. Miller, M.H. and Scheraga, H.A. (1976), Calculation of the structures of collagen models. Role of interchain interactions in determining the triple-helical coiled-coil conformation. 1. Poly(glycyl-prolyl-prolyl), J. Polymer Sci.: Polymer Symposia No. 54, pp. 171–200.

  24. Miller, M.H., Némethy, G. and Scheraga, H.A. (1980), Calculation of the structures of collagen models. Role of interchain interactions in determining the triple-helical coiled-coil conformation. 2. Poly(glycyl-prolyl-hydroxyprolyl), Macromolecules13: 470–478.

    Google Scholar 

  25. Miller, M.H., Némethy, G. and Scheraga, H.A. (1980), Calculation of the structures of collagen models. Role of interchain interactions in determining the triple-helical coiled-coil conformation. 3. Poly(glycyl-prolyl-alanyl), Macromolecules13: 910–913.

    Google Scholar 

  26. Levitt, M. and Chothia, C. (1976), Structural patterns in globular proteins, Nature 261: 552–558.

    PubMed  Google Scholar 

  27. Wada, A. (1976), The-helix as an electric macro-dipole, Adv. Biophys. 9: 1–63.

    Google Scholar 

  28. Perutz, M.F. (1978), Electrostatic effects in proteins, Science 201: 1187–1191.

    Google Scholar 

  29. Hol, W.G.J., Halie, L.M. and Sander, C. (1981), Dipoles of the -helix and -sheet: their role in protein folding, Nature 294: 532–536.

    Google Scholar 

  30. Chou, K.-C., Némethy, G. and Scheraga, H.A. (1983), Energetic approach to the packing of -helices. 1. Equivalent helices, J. Phys. Chem.8

  31. Hol, W.G.J. (1985), The role of the α-helix dipole in protein function and structure, Prog.Biophys. molec. Biol. 45: 149–195.

    Google Scholar 

  32. Piela, L. and Scheraga, H.A. (1987), On the multiple-minima problem in the conformational analysis of polypeptides. I. Backbone degrees of freedom for a perturbed -helix, Biopolymers 26: S33-S58.

    Google Scholar 

  33. Ripoll, D.R., Piela, L., Vásquez, M. and Scheraga, H.A. (1991), On the multiple-minima problem in the conformational analysis of polypeptides. V. Application of the self-consistent electrostatic field and the electrostatically driven Monte Carlo methods to bovine pancreatic trypsin inhibitor, Proteins: Struc., Func., and Gen. 10: 188–198.

    Google Scholar 

  34. Li, Z. and Scheraga, H.A. (1987), Monte Carlo-minimization approach to the multiple-minima problem in protein folding, Proc. Natl. Acad. Sci., USA 84

  35. Li, Z. and Scheraga, H.A. (1988), Structure and free energy of complex thermodynamicsystems, J. Molec. Str. (Theochem) 179: 333–352.

    Google Scholar 

  36. Bharucha-Reid, A.T. (1960), Elements of the theory of Markov processes and their applications, McGraw-Hill, New York.

  37. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E. (1953), Equation of state calculations by fast computing machines, J. Chemical Physics 21: 1087–1092.

    Google Scholar 

  38. Hagler, A.T., Stern, P.S., Sharon, R., Becker, J.M. and Naider, F. (1979), Computer simlulation of the conformational properties of oligopeptides. Comparison of theoretical methods and anlaysis of experimental results, J. Am. Chem. Soc 101:6842–6852.

    Google Scholar 

  39. Rapaport, D.C. and Scheraga, H.A. (1981), Evolution and stability of polypeptide chain conformation: a simulation study, Macromolecules 14: 1238–1246.

    Google Scholar 

  40. Paine, G.H. and Scheraga, H.A. (1985), Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. I. Backbone structure of enkephalin,Biopolymers 24:1391–1436

    Google Scholar 

  41. Gay, D.M. (1983), Algorithm 611. Subroutines for unconstrained minimization using a model/trust-region approach, ACM Trans. Math. Software 9: 503–524.

    Google Scholar 

  42. Ripoll, D.R. and Scheraga, H.A. (1988), On the multiple-minima problem in the conformational analysis of polypeptides. II. An electrostatically driven Monte Carlo method-tests on poly(Lalanine), Biopolymers 28: 263–287.

    Google Scholar 

  43. Ripoll, D.R. and Scheraga, H.A. (1989), The multiple-minima problem in the conformational analysis of polypeptides. III. An electrostatically driven Monte Carlo method; tests on enkephalin, J. Protein Chem. 8: 263–287.

    PubMed  Google Scholar 

  44. Ripoll, D.R., Liwo, A. and Scheraga, H.A. (1998), New developments of the electrostatically driven Monte Carlo method-Test on the membrane bound portion of melittin, Biopolymers 46: 117–126.

    PubMed  Google Scholar 

  45. Liwo, A., Tempczyk, A., Oldziej, S., Shenderovich, M.D., Hruby, V.J., Talluri, S., Ciarkowski, J., Kasprzykowski, F., Lankiewicz, L. and Grzonka, Z. (1996), Exploration of the conformational space of oxytocin and arginine-vasopressin using the electrostatically-driven Monte Carlo and molecular dynamics methods, Biopolymers 38: 157–175.

    PubMed  Google Scholar 

  46. Ripoll, D.R., Vásquez, M.J. and Scheraga, H.A. (1991), The electrostatically driven Monte Carlo method: Application to conformational analysis of decaglycine, Biopolymers 31: 319–330.

    Google Scholar 

  47. Ripoll, D.R. (1992), Conformational study of a peptide epitope shows large preferences for -turn conformations, Int. J. Pepide Protein Res.40: 575–581.

    Google Scholar 

  48. Faerman, C.H. and Ripoll, D.R. (1992), Conformational analysis of a twelve-residue analogue of mastoparan and mastoparan X, Proteins 12: 111–116.

    Google Scholar 

  49. Liwo, A., Gibson, K.D., Scheraga, H.A., Brandt-Rauf, P.W., Monaco, R. and Pincus, M.R. (1994), Comparison of the low energy conformations of an oncogenic and a non-oncogenic p21 protein, neither of which binds GTP or GDP, J. Protein Chem. 13: 237–251.

    PubMed  Google Scholar 

  50. Ashkenazi, G., Ripoll, D.R., Lotan, N. and Scheraga, H.A. (1997), A molecular switch for biological logic gates: conformational studies, Biosensors & Bioelectronics 12: 85–95.

    Google Scholar 

  51. Ripoll, D.R., Vorobjev, Y.N., Liwo, A., Vila, J.A. and Scheraga, H.A. (1996), Coupling between folding and ionization equilibria. Effects of pH on the conformational preferences of polypeptides, J. Mol. Biol.2 770–783.

    Google Scholar 

  52. Vila, J.A., Ripoll, D.R., Villegas, M.E., Vorobjev, Y.N. and Scheraga, H.A. (1998), Role of hydrophobicity and solvent-mediated charge-charge interactions in stabilizing -helices, Biophys. J. 75: 2637–2646.

    PubMed  Google Scholar 

  53. Vila, J.A., Ripoll, D.R., Vorobjev, Y.N. and Scheraga, H.A. (1998), Computation of the structure-dependent pka shifts in a polypentapeptide of the Poly[fv(IPGVG), fe(IPGEG)] family, J. Phys. Chem. B 102: 3065–3067.

    Google Scholar 

  54. Olszewski, K.A., Piela, L. and Scheraga, H.A. (1992), Mean-field theory as a tool for intramolecular conformational optimization. 1. Tests on terminally-blocked alanine and Metenkephalin, J. Phys. Chem. 96: 4672–4676.

    Google Scholar 

  55. Olszewski, K.A., Piela, L. and Scheraga, H.A. (1993), Mean field theory as a tool for intramolecular conformational optimization. 2. Tests on the homopolypeptides decaglycine and icosalanine, J.Phys. Chem. 97: 260–266.

    Google Scholar 

  56. Olszewski, K.A., Piela, L. and Scheraga, H.A. (1993), Mean field theory as a tool for intramolecular conformational optimization. 3. Test on melittin, J. Phys. Chem. 97: 267–270.

    Google Scholar 

  57. Piela, L., Kostrowicki, J. and Scheraga, H.A. (1989), The multiple-minima problem in the conformational analysis of molecules. Deformation of the potential energy hypersurface by the diffusion equation method, J. Phys. Chem. 93: 3339–3346.

    Google Scholar 

  58. Pillardy, J., Olszewski, K.A. and Piela, L. (1992), Performance of the shift method of global minimization in searches for optimum structures of clusters of Lennard-Jones atoms, J. Phys. Chem. 96: 4337–4341.

    Google Scholar 

  59. Pillardy, J. and Piela, L. (1995), Molecular dynamics on deformed potential energy hypersurfaces, J. Phys. Chem. 99: 11805–11812.

    Google Scholar 

  60. Wawak, R.J., Gibson, K.D., Liwo, A. and Scheraga, H.A. (1996), Theoretical prediction of a crystal structure, Proc. Natl. Acad. Sci., USA 93: 1743–1746.

    Google Scholar 

  61. Wawak, R.J., Pillardy, J., Liwo, A., Gibson, K.D. and Scheraga, H.A. (1998), Diffusion equation and distance scaling methods of global optimization; Applications to crystal structure prediction, J. Phys. Chem. 102: 2904–2918.

    Google Scholar 

  62. Pillardy, J., Liwo, A., Groth, M. and Scheraga, H.A., An efficient deformation-based global optimization method for off-lattice polymer chains; self-consistent basin-to-deformed-basin mapping (SCBDBM). Application to united-residue polypeptide chains, J. Phys. Chem. B103: 7353–7366.

  63. Pillardy, J., Liwo, A. and Scheraga, H.A. An efficient deformation-based global optimization method [self-consistent basin-to-deformed-basin mapping (SCBDBM)]; Application to Lennard-Jones atomic clusters, J. Phys. Chem., in press.

  64. Kostrowicki, J., Piela, L., Cherayil, B.J. and Scheraga, H.A. (1991), Performance of the diffusion equation method in searches for optimum structures of clusters of Lennard-Jones atoms, J. Phys. Chem. 95: 4113–4119.

    Google Scholar 

  65. Wawak, R.J., Wimmer, M.M. and Scheraga, H.A. (1992), Application of the diffusion equation method of global optimization to water clusters, J. Phys. Chem. 96: 5138–5145.

    Google Scholar 

  66. Kostrowicki, J. and Scheraga, H.A. (1992), Application of the diffusion equation method for global optimization to oligopeptides, J. Phys. Chem. 96: 7442–7449.

    Google Scholar 

  67. Pillardy, J., Olszewski, K.A. and Piela, L. (1992), Theoretically predicted lowest-energy structures of water clusters, J. Mol. Struct. 270: 277–285.

    Google Scholar 

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

  69. Lee, J., Scheraga, H.A. and Rackovsky, S. (1998), Conformational analysis of the 20-residue membrane-bound portion of melittin by conformational space annealing, Biopolymers 46:103–115

    Google Scholar 

  70. Lee, J. and Scheraga, H.A. (1999), Conformational space annealing by parallel computations: extensive conformational search of Met-enkephalin and of the 20-residue membrane-bound portion of melittin, Int. J. Quant. Chem. 75: 255–265.

    Google Scholar 

  71. Goldberg, D.E. (1989), Genetic Algorithms in Search, Optimization & Machine Learning, Addison-Wesley, Reading, MA.

    Google Scholar 

  72. Lee, J., Liwo, A. and Scheraga, H.A. (1999), Energy-based de novo protein folding by conformational space annealing and an off-lattice united-residue force field: Application to the 10–55 fragment of staphylococcal protein A and to apo calbindin D9K., Proc. Natl. Acad. Sci. USA 96: 2025–2030.

    Google Scholar 

  73. Ye, Y.-J. and Scheraga, H.A. (1999), Kinetics of protein folding, in “Slow Dynamics in Complex Systems: Eighth Tohwa University International Symposium”, Eds. M. Tokuyama and I. Oppenheim. AIP Conference Proceedings469, pp. 452–475, Amer. Inst. Phys.

  74. Ye, Y.-J., Ripoll, D.R. and Scheraga, H.A. (1999), Kinetics of cooperative protein folding involving two separate conformational families, Computational and Theoretical Polymer Science, 9: 359–370.

    Google Scholar 

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

    Google Scholar 

  76. G¯o, N. and Scheraga, H.A. (1970), Ring closure and local conformational deformations of chain molecules, Macromolecules3:178–187.

    Google Scholar 

  77. Palmer, K.A. and Scheraga, H.A. (1991), Standard-geometry chains fitted to X-ray derived structures; Validation of the rigid-geometry approximation. I. Chain closure through a limited search of 'loop' conformations, J. Comput. Chem. 12: 505–526.

    Google Scholar 

  78. Vila, J., Williams, R.L., Vásquez, M. and Scheraga, H.A. (1991), Empirical solvation models can be used to differentiate native from near-native conformations of bovine pancreatic trypsin inhibitor, Proteins: Struc., Func., and Gen 1.

  79. Third Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction; http://predictioncenter.llnl.gov/casp3/Casp3.html, (1999).A.,Calculation of protein conformation by global optimization of a potential energy function, Proteins:Struc., Func., and Gen., suppl. 3:204–208.

    Google Scholar 

  80. Lee, J., Liwo, A., Ripoll, D.R., Pillardy, J. and Scheraga, H.A. (1999), Calculation of proteinconformation by global optimization of a potential energy function, Proteins: Struc., Func.,and Gen., suppl. 3: 204–208.

    Google Scholar 

  81. Yang, F., Gustafson, K.R., Boyd, M.R. and Wlodawer, A. (1998), Crystal structure of Escherichia coli HdeA, Nature Struct. Biol. 5: 763–764.

    Google Scholar 

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Authors
  1. Harold A. Scheraga
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  2. Jooyoung Lee
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  3. Jarosław Pillardy
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  4. Yuan-Jie Ye
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  5. Adam Liwo
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  6. Daniel Ripoll
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Scheraga, H.A., Lee, J., Pillardy, J. et al. Surmounting the Multiple-Minima Problem in Protein Folding. Journal of Global Optimization 15, 235–260 (1999). https://doi.org/10.1023/A:1008328218931

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