Topological Quantities Determining the Folding/Unfolding Rate of Two-state Folding Proteins

Abstract

We investigate various topological and energy parameters from the protein native structure and find combinations of some parameters that are well correlated with the rate of folding/unfolding. For folding, the topological quantity that combines the clustering coefficient and the long-range order (or total contact distance/contact order) has a high correlation with the folding rate, expressed as ln k F , obtained from standard experimental conditions. For unfolding, a combination of the impact of edge removal, obtained from the protein structure, and the stability of the native protein structure, as expressed by the free energy change ΔG, gives a good correlation with unfolding rate, ln k U .

This is a preview of subscription content, access via your institution.

References

  1. 1.

    Jackson, S.E.: How do small single-domain proteins fold? Fold. Des. 3, R81–R91 (1998)

    Article  CAS  Google Scholar 

  2. 2.

    Fersht, A.: Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding. Freeman, New York (1999)

    Google Scholar 

  3. 3.

    Huang, G., Oas, T.: Structure and stability of monomeric gamma repressor: NMR evidence for two-state folding. Biochemistry 34, 3884–3892 (1995)

    Article  CAS  Google Scholar 

  4. 4.

    Burton, R.E., Huang, G.S., Daugherty, M.A., Fullbright, P.W., Oas, T.G.: Microsecond protein folding through a compact transition state. J. Mol. Biol. 263, 311–322 (1996)

    Article  CAS  Google Scholar 

  5. 5.

    Kragelund, B.B., Robinson, C.V., Knudsen, J., Dobson, C.M., Poulsen, F.M.: Folding of a four-helix bundle: studies of acyl-coenzyme A binding protein. Biochemistry 34, 7217–7224 (1995)

    Article  CAS  Google Scholar 

  6. 6.

    Kragelund, B.B., Højrup, P., Jensen, M.S., Schjerling, C.K., Juul, E., Knudsen, J., Poulsen, M.: Fast and one-step folding of closely and distantly related homologous proteins of a four-helix bundle family. J. Mol. Biol. 256, 187–200 (1996)

    Article  CAS  Google Scholar 

  7. 7.

    Chan, C., Hu, Y., Takahashi, S., Rousseau, D.L., Eaton, W.A., Hofrichter, J.: Submillisecond protein folding kinetics studied by ultrarapid mixing. Proc. Natl. Acad. Sci. USA 94, 1779–1784 (1997)

    Google Scholar 

  8. 8.

    Schindler, T., Herrler, M., Marahiel, M.A., Schmid, F.X.: Extremely rapid protein folding in the absence of intermediates. Nat. Struct. Biol. 2, 663–673 (1995)

    Article  CAS  Google Scholar 

  9. 9.

    Viguera, A.R., Martinez, J.C., Filimonov, V.V., Mateo, P.L., Serrano, L.: Thermodynamic and kinetic analysis of the SH3 domain of spectrin shows a two-state folding transition. Biochemistry 33, 2142–2150 (1994)

    Article  CAS  Google Scholar 

  10. 10.

    Viguera, A.R., Serrano, L., Wilmanns, M.: Different folding transition states may result in the same native structure. Nat. Struct. Biol. 3, 874–880 (1996)

    Article  CAS  Google Scholar 

  11. 11.

    Grantcharova, V.P., Baker, D.: Folding dynamics of the src SH3 domain. Biochemistry 36, 15685–15692 (1997)

    Article  CAS  Google Scholar 

  12. 12.

    Guijarro, J.I., Morton, C.J., Plaxco, K.W., Campbell, I.D., Dobson, C.M.: Folding kinetics of the SH3 domain of PI3 kinase by real-time NMR combined with optical spectroscopy. J. Mol. Biol. 276, 657–667 (1998)

    Article  CAS  Google Scholar 

  13. 13.

    Plaxco, K.W., Guijarro, J.I., Morton, C.J., Pitkeathly, M., Campbell, I.D., Dobson, C.M.: The folding kinetics and thermodynamics of the Fyn-SH3 domain. Biochemistry 37, 2529–2537 (1998)

    Article  CAS  Google Scholar 

  14. 14.

    Ferguson, N., Capaldi, A.P., James, R., Kleanthous, C., Radford, S.E.: Rapid folding with and without populated intermediates in the homologous four-helix proteins Im7 and Im9. J. Mol. Biol. 286, 1597–1608 (1999)

    Article  CAS  Google Scholar 

  15. 15.

    Clarke, J., Cota, E., Fowler, S.B., Hamill, S.J.: Folding studies of immunoglobulin-like β-sandwich proteins suggest that they share a common folding pathway. Structure 7, 1145–1153 (1999)

    Article  CAS  Google Scholar 

  16. 16.

    Villegas, V., Azuaga, A., Catasus, L.I., Reverter, D., Mateo, P.L., Aviles, F.X., Serrano, L.: Evidence for a two-state transition in the folding process of the activation domain of human procarboxypeptidase A2. Biochemistry 34, 15105–15110 (1995)

    Article  CAS  Google Scholar 

  17. 17.

    Nuland, N.V., Meijberg, W., Warner, J., Forge, V., Scheek, R.M., Robillard, G.T., Dobson, C.M.: Slow cooperative folding of a small globular protein HPr. Biochemistry 37, 622–637 (1998)

    Article  Google Scholar 

  18. 18.

    Plaxco, K.W., Simons, K.T., Baker, D.: Contact order, transition state placement and the refolding rates of single domain proteins. J. Mol. Biol. 277, 985–994 (1998)

    Article  CAS  Google Scholar 

  19. 19.

    Plaxco, K.W., Simons, K.T., Ruczinski, I., Baker, D.: Topology, stability, sequence, and length: defining the determinants of two-state protein folding kinetics. Biochemistry 39, 11171–11183 (2000)

    Article  Google Scholar 

  20. 20.

    Gromiha, M.M., Selvaraj, S.: Comparison between long-range interactions and contact order in determining the folding rate of two-state proteins: application of long-range order to folding rate prediction. J. Mol. Biol. 310, 27–32 (2001)

    Article  CAS  Google Scholar 

  21. 21.

    Zhou, H., Zhou, Y.: Folding rate prediction using total contact distance. Biophys. J. 82, 458–463 (2002)

    Article  CAS  Google Scholar 

  22. 22.

    Fersht, A.R.: Transition-state structure as a unifying basis in protein-folding mechanisms: contact order, chain topology, stability, and the extended nucleus mechanism. Proc. Natl. Acad. Sci. USA 97, 1525–1529 (2000)

    Article  CAS  Google Scholar 

  23. 23.

    Munoz, V., Eaton, W.A.: A simple model for calculating the kinetics of protein folding from three-dimensional structures. Proc. Natl. Acad. Sci. USA 96, 11311–11316 (1999)

    Article  CAS  Google Scholar 

  24. 24.

    Jung, J., Lee, J., Moon, H.: Topological determinants of protein unfolding rates. Proteins 58, 389–395 (2005)

    Article  CAS  Google Scholar 

  25. 25.

    Maxwell, K.L., Wildes, D., Zarrine-Afsar, A., Delosrios, M.A., Browin, A.G., Friel, C.T., Hedberg, L., Horng, J., Bona, D., Miller, E.J., Vallée-Bélisle, A., Main, E.R.G., Bemporad, F., Qiu, L., Teilum, K., Vu, N., Edwards, A.M., Ruczinski, I., Poulsen, F.M., Kragelund, B.B., Michnick, S.W., Chiti, F., Bai, Y., Hagen, S.J., Serrano, L., Oliverberg, M., Raleigh, D.P., Wittung-Stafshede, P., Radford, S.E., Jackson, S.E., Sosnick, T.R., Marqusee, S., Davidson, A.R., Plaxco, K.W.: Protein folding: defining a “standard” set of experimental conditions and a preliminary kinetic data set of two-state proteins. Protein Sci. 14, 602–616 (2005)

    Article  CAS  Google Scholar 

  26. 26.

    Xu, G., Narayan, M., Kurinov, I., Ripoll, D.R., Welker, E., Khalili, M., Ealick, S.E., Scheraga, H.A.: A localized specific interaction alters the unfolding pathways of structural homologues. J. Am. Chem. Soc. 128, 1204–1213 (2006)

    Article  CAS  Google Scholar 

  27. 27.

    Jejera, E., Machado, A., Rebelo, I., Nieto-Villar, J.: Fractal protein structure revisited: topological kinetic and thermodynamic relationships. Physica A 388, 4600–4608 (2009)

    Article  Google Scholar 

  28. 28.

    Hvidt, A., Westh, P.: Different views on the stability of protein conformations and hydrophobic effects. J. Solution Chem. 27, 395–402 (1998)

    Article  CAS  Google Scholar 

  29. 29.

    Yu, L., Hu, X., Lin, R., Xu, G.: Enthalpic interaction of amino acids with 2-chloroenthanol in aqueous solutions at 298.15 K. J. Solution Chem. 33, 131–141 (2004)

    Article  CAS  Google Scholar 

  30. 30.

    Yu, L., Lin, R., Hu, X., Xu, G.: Enthalpic interaction of amino acids with ethanol in aqueous solutions at 25°C. J. Solution Chem. 32, 273–281 (2003)

    Article  CAS  Google Scholar 

  31. 31.

    Liu, H., Lin, R., Zhang, H.: Enthalpic interactions of amino acids with glucose in aqueous solutions at 298.15 K. J. Solution Chem. 32, 977–985 (2003)

    Article  CAS  Google Scholar 

  32. 32.

    Dokholyan, N.V., Li, L., Shakhnovich, E.I.: Topological determinants of protein folding. Proc. Natl. Acad. Sci. USA 99, 8637–8641 (2002)

    Article  CAS  Google Scholar 

  33. 33.

    Greene, L.H., Higman, V.A.: Uncovering network systems within protein structures. J. Mol. Biol. 334, 781–791 (2003)

    Article  CAS  Google Scholar 

  34. 34.

    Li, J., Wang, J., Wang, W.: Identifying folding nucleus on residue contact networks of proteins. Proteins 71, 1899–1907 (2008)

    Google Scholar 

  35. 35.

    Watts, D.J., Strogatz, S.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)

    Article  CAS  Google Scholar 

  36. 36.

    Newman, M.E.J., Strogatz, S.H., Watts, D.J.: Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64, 026118 (2001)

    Article  CAS  Google Scholar 

  37. 37.

    Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45, 167–256 (2003)

    Article  Google Scholar 

  38. 38.

    Albert, R., Jeong, H., Barabasi, A.: Error and attack tolerance of complex networks. Nature 406, 378–382 (2000)

    Article  CAS  Google Scholar 

  39. 39.

    Jone, K., Wittung-Stafshede, P.: The largest protein observed to fold by two-state kinetic mechanism does not obey contact-order correlation. J. Am. Chem. Soc. 125, 9607–9608 (2003)

    Google Scholar 

  40. 40.

    Micheletti, C.: Prediction of folding rates and transition-state placement from native-state geometry. Proteins 51, 74–84 (2003)

    Article  CAS  Google Scholar 

  41. 41.

    Bagler, G., Sinha, S.: Assortative mixing in protein contact networks and protein folding kinetics. Bioinformatics 23, 1760–1767 (2007)

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jaewoon Jung.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Jung, J., Buglass, A.J. & Lee, EK. Topological Quantities Determining the Folding/Unfolding Rate of Two-state Folding Proteins. J Solution Chem 39, 943–958 (2010). https://doi.org/10.1007/s10953-010-9556-3

Download citation

Keywords

  • Protein folding
  • Contact order
  • Long-range order
  • Total contact distance
  • Clustering coefficient
  • Impact of edge removal