Simulation of the Protein Folding Process

  • Roterman Irena
  • L. Konieczny
  • M. Banach
  • D. Marchewka
  • B. Kalinowska
  • Z. Baster
  • M. Tomanek
  • M. Piwowar
Part of the Springer Series in Bio-/Neuroinformatics book series (SSBN, volume 1)


This chapter introduces a novel protein folding simulation model which involves several stages. In particular, it distinguishes the so-called early stage (ES) and late state (LS) intermediates, though it can also account for a greater number of intermediates or — alternatively — using ES as the sole intermediate. The early stage intermediate is generated by geometric modeling of polypeptide bond chains, expressed as pairs of their relative binding angles (V-angle) and radii of curvature (R - which is dependent on V). Results of this process point to a limited conformational subspace, providing a convenient set of starting structures for subsequent free internal energy optimization algorithms. The late stage folding model acknowledges the influence of water on the folding process, with hydrophobic residues directed toward the center of the emerging protein body and hydrophilic residues exposed on its surface. Overall, the structure of the protein’s hydrophobic core can be modeled with a 3D Gauss function (hence the “fuzzy oil drop” designation). The presented algorithm reflects the influence of the aqueous environment on the protein’s structure as addition to the optimization of its internal free energy components.

Applying information theory concepts to the process of structural modeling justifies the need for a limited conformational subspace, comprising selected fragments of the Ramachandran map. Comparing the quantity of information present in the initial amino acid sequence with the quantity of information required to accurately describe the resulting 3D structure (pairs of Φ and Ψ angles) reveals a deficit and therefore calls for an additional source of information. We postulate that this information is contributed by the aqueous environment which triggers the generation of a hydrophobic core. In addition, deviations from the idealized “fuzzy oil drop” structure are found to correspond to active sites capable of binding ligands or forming protein complexes. Multicriteria optimization concept is applied to strike a balance between internal and external (environmental) optimization.


Hydrophobic Core Folding Process Folding Simulation Hydrophobicity Profile Elliptical Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Kim, P.S., Baldwin, R.L.: Specific intermediates in the folding reactions of small proteins and the mechanism of protein folding. Annu. Rev. Biochem. 51, 459–489 (1982)CrossRefGoogle Scholar
  2. 2.
    Kim, P.S., Baldwin, R.L.: Intermediates in the folding reactions of small proteins. Annu. Rev. Biochem. 59, 631–660 (1990)CrossRefGoogle Scholar
  3. 3.
    Ptitsyn, O.B., Rashin, A.A.: A model of myoglobin self-organization. Biophys. Chem. 3, 1–20 (1975)CrossRefGoogle Scholar
  4. 4.
    Karplus, M., Weaver, D.L.: Protein folding dynamics: the diffusion-collision model and experimental data. Protein Sci. 3(4), 650–668 (1994)CrossRefGoogle Scholar
  5. 5.
    Beck, C., Siemens, X., Weaver, D.L.: Diffusion-Collision Model Study of Misfolding in a Four-Helix Bundle Protein. Biophys. J. 81(6), 3105–3115 (2001)CrossRefGoogle Scholar
  6. 6.
    Islam, S.A., Karplus, M., Weaver, D.L.: Application of the diffusion-collision model to the folding of three-helix bundle proteins. J. Mol. Biol. 318(1), 199–215 (2002)CrossRefGoogle Scholar
  7. 7.
    Dill, K.A.: Theory for the folding and stability of globular proteins. Biochemistry 24, 1501–1509 (1985)CrossRefGoogle Scholar
  8. 8.
    Chan, H.S., Dill, K.A.: Protein folding in the landscape perspective: Chevron plots and non Arrhenius kinetics. Proteins 30, 2–33 (1998)CrossRefGoogle Scholar
  9. 9.
    Fiebig, K.M., Dill, K.A.: Protein core assembly processes. J. Chem. Phys. 98, 3475–3487 (1993)CrossRefGoogle Scholar
  10. 10.
    Weikl, T.R., Dill, K.A.: Folding rates and low-entropy loss routes of two-state proteins. J. Mol. Biol. 329, 585–598 (2003)CrossRefGoogle Scholar
  11. 11.
    Merlo, C., Dill, K.A., Weikl, T.R.: Phi values in protein-folding kinetics have energetic and structural components. Proc. Nat. Acad. Sci. USA 102, 10171–10175 (2005)CrossRefGoogle Scholar
  12. 12.
    Ozkan, S.B., Wu, G.A., Chodera, J.D., Dill, K.A.: Protein folding by zipping and assembly. Proc. Natl. Acad. Sci. USA 104(29), 11987–11992 (2007)CrossRefGoogle Scholar
  13. 13.
    Bowman, G.R., Pande, V.S.: Protein folded states are kinetic hubs. Proc. Nat. Acad. Sci. USA 107(24), 10890–10895 (2010)CrossRefGoogle Scholar
  14. 14.
    Creighton, T.E.: Protein folding. Biochem. J. 270, 1–16 (1990)Google Scholar
  15. 15.
    Roterman, I.: Modelling the optimal simulation path in the peptide chain folding - Studies based on geometry of alanine heptapeptide. J. Theoretical Biology 177, 283–288 (1995)CrossRefGoogle Scholar
  16. 16.
    Roterman, I.: The geometrical analysis of structural peptide backbone structure and its local deformations. Biochimie 77, 204–252 (1995)CrossRefGoogle Scholar
  17. 17.
    Roterman, I., Konieczny, L.: Geometrical analysis of structural changes in immunoglobin domains’ transition from native to molten state. Computers and Chemistry 19, 204–216 (1995)CrossRefGoogle Scholar
  18. 18.
    Konieczny, L., Bryliński, M., Roterman, I.: Gauss-function-based model of hydrophobicity density in proteins. In Silico. Biol. 6, 5–22 (2006)Google Scholar
  19. 19.
    Jurkowski, W., Wiśniowski, Z., Konieczny, L., Roterman, I.: The conformational sub-space in simulation of early-stage protein folding. Proteins: Structure, Function and Bioinformatics 55, 115–127 (2004)CrossRefGoogle Scholar
  20. 20.
    Dobson, C.M.: The structural basis of protein folding and its links with human disease. Phil. Trans. R. Soc. Lond. B 356, 133–143 (2001)CrossRefGoogle Scholar
  21. 21.
    Alonso, D.O., Daggett, V.: Molecular dynamics simulations of hydrophobic collapse of ubiquitin. Protein Sci. 7, 860–874 (1998)CrossRefGoogle Scholar
  22. 22.
    Ivankov, D.N., Finkelstein, A.V.: Prediction of protein folding rates from the amino acid sequence-predicted secondary structure. PNAS 101, 8942–8944 (2004)CrossRefGoogle Scholar
  23. 23.
    Kolinski, A., Skolnick, J., Yaris, R.: Monte Carlo studies on equilibrium globular protein folding. I. Homopolymeric lattice models of beta-barrel proteins. Biopolymers 26(6), 937–962 (1987)CrossRefGoogle Scholar
  24. 24.
    Rohl, C.A., Strauss, C.E., Misura, K.M.S., Baker, D.: Protein structure prediction using Rosetta. Methods in Enzymology 383, 66–93 (2004)CrossRefGoogle Scholar
  25. 25.
    Chothia, C., Lesk, A.M.: The relation between the divergence of sequence and structure in proteins. The EMBO Journal 5(4), 823–826 (1986)Google Scholar
  26. 26.
    Bystroff, C., Shao, Y.: Modeling protein pathways. In: Bujnicki, J. (ed.) Practical Bioinformatics, pp. 97–122. Springer (2004)Google Scholar
  27. 27.
    Kaczanowski, S., Zielenkiewicz, P.: Why similar protein sequences encode similar three-dimensional structures? Theoretical Chemistry Accounts 125, 543–550 (2010)CrossRefGoogle Scholar
  28. 28.
    Chenna, R., Sugawara, H., Koike, T., Lopez, R., Gibson, T.J., Higgins, D.G., Thompson, J.D.: Multiple sequence alignment with the Clustal series of programs. Nucleic Acids Res. 31(13), 3497–3500 (2003)CrossRefGoogle Scholar
  29. 29.
    Bryliński, M., Konieczny, L., Kononowicz, A., Roterman, I.: Conservative secondary structure motifs already present in early-stage folding (in silico) as found in the serpine family. J. Theor. Biol. 251, 275–285 (2008)CrossRefGoogle Scholar
  30. 30.
    Bryliński, M., Konieczny, L., Czerwonko, P., Jurkowski, W., Roterman, I.: Early-stage folding in proteins (in silico) – Sequence-to-structure relation. J. Biomed. Biotech. 2, 65–79 (2005)CrossRefGoogle Scholar
  31. 31.
    Bryliński, M., Konieczny, L., Roterman, I.: SPI-structure predictability index for protein sequence. In Silico. Biology 5(3), 227–237 (2005)Google Scholar
  32. 32.
    Kauzmann, W.: Some factors in the interpretation of protein denaturation. Adv. Protein Chem. 14, 1–63 (1959)CrossRefGoogle Scholar
  33. 33.
    Levitt, M.: A simplifed representation of protein conformations for rapid simulation of protein folding. J. Mol. Biol. 104, 59–107 (1976)CrossRefGoogle Scholar
  34. 34.
    Nalewajski, R.F.: Information theory of molecular systems. Elsevier, Amsterdam (2006)Google Scholar
  35. 35.
    Marchewka, D., Banach, M., Roterman, I.: Internal force field in proteins seen by divergence entropy. Bioinformation 6(8), 300–302 (2011)CrossRefGoogle Scholar
  36. 36.
    Banach, M., Prymula, K., Jurkowski, W., Konieczny, L., Roterman, I.: Fuzzy oil drop model to interpret the structure of antifreeze proteins and their mutants. J. Mol. Model. 18(1), 229–237 (2012)CrossRefGoogle Scholar
  37. 37.
    Bryliński, M., Prymula, K., Jurkowski, W., Kochańczyk, M., Stawowczyk, E., Konieczny, L., Roterman, I.: Prediction of functional sites based on the fuzzy oil drop model. PLoS Comput. Biol., e94 (2007)Google Scholar
  38. 38.
    Brylinski, M., Kochanczyk, M., Broniatowska, E., Roterman, I.: Localization of ligand binding site in proteins identified in silico. J. Mol. Model. 13(7), 665–675 (2007)CrossRefGoogle Scholar
  39. 39.
    Marchewka, D., Jurkowski, W., Banach, M., Roterman, I.: Prediction of protein-protein binding interfaces. In: Roterman, I. (ed.) Identification of Ligand Binding Site and Protein-Protein Interaction Area. Springer (2012)Google Scholar
  40. 40.
    Prymula, K., Jadczyk, T., Roterman, I.: Catalytic residues in hydrolases: analysis of methods designed for ligand-binding site prediction. J. Comput. Aided Mol. Des. 25(2), 117–133 (2011)CrossRefGoogle Scholar
  41. 41.
    Binkowski, A., Naghibzadeh, S., Liang, J.: CASTp: Computed atlas for surface topography of proteins. Nucleic Acids Res. 31, 3352–3355 (2003)CrossRefGoogle Scholar
  42. 42.
    Dundas, J., Ouyang, Z., Tseng, J., Binkowski, A., Turpaz, Y., et al.: CASTp: computed atlas of surface topography of proteins with structural and topographical mapping of functionally annotated residues. Nucleic Acids Res. 34, W116–W118 (2006)CrossRefGoogle Scholar
  43. 43.
    Hendlich, M., Rippmann, F., Barnickel, G.: LIGSITE: automatic and efficient detection of potential small molecule-binding sites in proteins. J. Mol. Graph. Model. 15(6), 359–363 (1997)CrossRefGoogle Scholar
  44. 44.
    Brady, G.P., Stouten, P.F.: Fast prediction and visualization of protein binding pockets with PASS. J. Computer Aided Mol. Des. 14, 383–401 (2000)CrossRefGoogle Scholar
  45. 45.
    Landau, M., Mayrose, I., Rosenberg, Y., Glaser, F., Martz, E., et al.: ConSurf 2005: the projection of evolutionary conservation scores of residues on protein structures. Nucleic Acids Res. 33, W299–W302 (2005)CrossRefGoogle Scholar
  46. 46.
    Mayrose, I., Graur, D., Ben-Tal, N., Pupko, T.: Comparison of site-specific rate-inference methods for protein sequences: empirical Bayesian methods are superior. Mol. Biol. Evol. 21(9), 1781–1791 (Epub June 16, 2004)CrossRefGoogle Scholar
  47. 47.
    Jambon, M., Imberty, A., Deléage, G., Geourjon, C.A.: A new bioinformatic approach to detect common 3D sites in protein structures. Proteins 52, 137–145 (2003)CrossRefGoogle Scholar
  48. 48.
    Jambon, M., Andrieu, O., Combet, C., Deléage, G., Delfaud, F., Geourjon, C.: The SuMo server: 3D search for protein functional sites. Bioinformatics 21(20), 3929–3930 (Epub September 1, 2005)CrossRefGoogle Scholar
  49. 49.
    Liang, J., Edelsbrunner, H., Woodward, C.: Anatomy of protein pockets and cavities: measurement of binding site geometry and implications for ligand design. Protein Sci. 7, 1884–1897 (1998)CrossRefGoogle Scholar
  50. 50.
    Wei, L., Altman, R.B.: Recognizing protein binding sites using statistical description of their 3D environments. In: Pac. Symp. Biocomput., pp. 497–508 (1998)Google Scholar
  51. 51.
    Liang, M.P., Banatao, D.R., Klein, T.E., Brutlag, D.L., Altman, R.B.: Webfeature: An interactive web tool for identifying and visualizing functional sites on macromolecular structures. Nucleic Acids Res. 31, 3324–3327 (2003)CrossRefGoogle Scholar
  52. 52.
    Banach, M., Marchewka, D., Piwowar, M., Roterman, I.: Divergence entropy characterizing the internal force field in proteins. In: Roterman-Konieczna, I. (ed.) Protein Folding in Silico. Woodhead Publishing (2012)Google Scholar
  53. 53.
    Alejster, P., Banach, M., Jurkowski, W., Marchewka, D., Roterman, I.: Comparative analysis od techniques oriented on the recognition of ligand binding area in proteins. In: Roterman, I. (ed.) Identification of Ligand Binding Site and Protein-Protein Interaction Area. Springer (2012)Google Scholar
  54. 54.
    Banach, M., Konieczny, L., Roterman, I.: Ligand binding site recognition. In: Roterman-Konieczna, I. (ed.) Protein Folding In Silico. Woodhead Publishing (2012)Google Scholar
  55. 55.
    Zobnina, V., Roterman, I.: Application of the fuzzy-oil-drop model to membrane protein simulation. Proteins Structure, Function, Bioinformatics 77, 378–394 (2009)CrossRefGoogle Scholar
  56. 56.
    Banach, M., Konieczny, L., Roterman, I.: Can the structure of the hydrophobic core determine the complexation site? In: Roterman, I. (ed.) Identification of Ligand Binding Site and Protein-Protein Interaction Area. Springer (2012)Google Scholar
  57. 57.
    Shannon, C.E.A.: Mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 (1948)MathSciNetzbMATHGoogle Scholar
  58. 58.
    Altschul, S., Madden, T., Schaffer, A., Zhang, J., Zhang, Z., Miller, W., Lipman, D.: Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucl. Acids Res. 25(17), 3389–3402 (1997)CrossRefGoogle Scholar
  59. 59.
    Król, M., Konieczny, L., Stąpor, K., Wiśniowski, Z., Ziajka, W., Szoniec, G., Roterman, I.: Misfolded proteins. In: Roterman-Konieczna, I. (ed.) Protein Folding In Silico. Woodhead Publishing (2012)Google Scholar
  60. 60.
    Orengo, C.A., Bray, J.E., Hubbard, T., LoConte, L., Silitoe, I.: Analysis of assessment of Abinitio three-dimesnional prediction. Secondary structure and contacts prediction. Proteins (suppl. 3), 149–170 (1999)Google Scholar
  61. 61.
    Liwo, A., Arłukowicz, 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(4), 1937–1942 (2002)CrossRefGoogle Scholar
  62. 62.
    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 Sci. 2(10), 1715–1731 (1993)CrossRefGoogle Scholar
  63. 63.
    Jurkowski, W., Bryliński, M., Konieczny, L., Roterman, I.: Lysozyme folder in silico according to the limited conformational sub-space. J. Biomol. Struct. Dynam. 22, 149–157 (2004)CrossRefGoogle Scholar
  64. 64.
    Brylinski, M., Konieczny, L., Roterman, I.: Fuzzy-oil-drop hydrophobic force field–a model to represent late-stage folding (in silico) of lysozyme. J. Biomol. Struct. Dyn. 23(5), 519–528 (2006)CrossRefGoogle Scholar
  65. 65.
    Bryliński, M., Konieczny, L., Roterman, I.: Hydrophobic collapse in (in silico) protein folding. Comp. Biol. Chem. 30, 255–267 (2006)zbMATHCrossRefGoogle Scholar
  66. 66.
    Brylinski, M., Jurkowski, W., Konieczny, L., Roterman, I.: Limitation of conformational space for proteins - early stage folding simulation of human α and β hemoglobin chains. TASK Quarterly 8, 413–422 (2004)Google Scholar
  67. 67.
    Brylinski, M., Konieczny, L., Roterman, I.: Is the protein folding an aim-oriented process? Human haemoglobin as example. Int. J. Bioinform. Res. Appl. 3(2), 234–260 (2007)CrossRefGoogle Scholar
  68. 68.
    Brylinski, M., Jurkowski, W., Konieczny, L., Roterman, I.: Limited conformational space for early-stage protein folding simulation. Bioinformatics 20, 199–205 (2004)CrossRefGoogle Scholar
  69. 69.
    Bryliński, M., Konieczny, L., Roterman, I.: Hydrophobic collapse in late-stage folding (in silico) of bovine pancreatic trypsin inhibitor. Biochimie 88, 1229–1239 (2006)CrossRefGoogle Scholar
  70. 70.
    Roterman, I., Konieczny, L., Banach, M., Jurkowski, W.: Intermediates in the protein folding process: a computational model. Int. J. Mol. Sci. 12(8), 4850–4860 (2011)CrossRefGoogle Scholar
  71. 71.
    Jurkowski, W., Kułaga, T., Roterman, I.: Geometric parameters defining the structure of proteins–relation to early-stage folding step. J. Biomol. Struct. Dyn. 29(1), 79–104 (2011)CrossRefGoogle Scholar
  72. 72.
    Roterman, I., Konieczny, L., Jurkowski, W., Prymula, K., Banach, M.: Two-intermediate model to characterize the structure of fast-folding proteins. J. Theor. Biol. 283(1), 60–70 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Roterman Irena
    • 1
  • L. Konieczny
    • 2
  • M. Banach
    • 3
  • D. Marchewka
    • 3
  • B. Kalinowska
    • 3
  • Z. Baster
    • 4
  • M. Tomanek
    • 5
  • M. Piwowar
    • 1
  1. 1.Department of Bioinformatics and Telemedicine – Medical CollegeJagiellonian UniversityKrakowPoland
  2. 2.Chair of Medical Biochemistry - Medical CollegeJagiellonian UniversityKrakówPoland
  3. 3.Faculty of Physics, Astronomy and Applied Computer ScienceJagiellonian UniversityKrakówPoland
  4. 4.Faculty of Physics AGHUniversity of Science and TechnologyKrakówPoland
  5. 5.Academic Computer CenterAGHKrakówPoland

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