Skip to main content
Protein Science : A Publication of the Protein Society logoLink to Protein Science : A Publication of the Protein Society
. 2000 Mar;9(3):452–465. doi: 10.1110/ps.9.3.452

Entropic barriers, transition states, funnels, and exponential protein folding kinetics: a simple model.

D J Bicout 1, A Szabo 1
PMCID: PMC2144570  PMID: 10752607

Abstract

This paper presents an analytically tractable model that captures the most elementary aspect of the protein folding problem, namely that both the energy and the entropy decrease as a protein folds. In this model, the system diffuses within a sphere in the presence of an attractive spherically symmetric potential. The native state is represented by a small sphere in the center, and the remaining space is identified with unfolded states. The folding temperature, the time-dependence of the populations, and the relaxation rate are calculated, and the folding dynamics is analyzed for both golf-course and funnel-like energy landscapes. This simple model allows us to illustrate a surprising number of concepts including entropic barriers, transition states, funnels, and the origin of single exponential relaxation kinetics.

Full Text

The Full Text of this article is available as a PDF (2.2 MB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Bryngelson J. D., Onuchic J. N., Socci N. D., Wolynes P. G. Funnels, pathways, and the energy landscape of protein folding: a synthesis. Proteins. 1995 Mar;21(3):167–195. doi: 10.1002/prot.340210302. [DOI] [PubMed] [Google Scholar]
  2. Chan H. S., Dill K. A. Protein folding in the landscape perspective: chevron plots and non-Arrhenius kinetics. Proteins. 1998 Jan;30(1):2–33. doi: 10.1002/(sici)1097-0134(19980101)30:1<2::aid-prot2>3.0.co;2-r. [DOI] [PubMed] [Google Scholar]
  3. Chen Y. D., Rubin R. J., Szabo A. Fluorescence dequenching kinetics of single cell-cell fusion complexes. Biophys J. 1993 Jul;65(1):325–333. doi: 10.1016/S0006-3495(93)81076-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Dill K. A., Bromberg S., Yue K., Fiebig K. M., Yee D. P., Thomas P. D., Chan H. S. Principles of protein folding--a perspective from simple exact models. Protein Sci. 1995 Apr;4(4):561–602. doi: 10.1002/pro.5560040401. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Fersht A. R. Optimization of rates of protein folding: the nucleation-condensation mechanism and its implications. Proc Natl Acad Sci U S A. 1995 Nov 21;92(24):10869–10873. doi: 10.1073/pnas.92.24.10869. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Jackson S. E., Fersht A. R. Folding of chymotrypsin inhibitor 2. 1. Evidence for a two-state transition. Biochemistry. 1991 Oct 29;30(43):10428–10435. doi: 10.1021/bi00107a010. [DOI] [PubMed] [Google Scholar]
  7. Karplus M., Sali A. Theoretical studies of protein folding and unfolding. Curr Opin Struct Biol. 1995 Feb;5(1):58–73. doi: 10.1016/0959-440x(95)80010-x. [DOI] [PubMed] [Google Scholar]
  8. Karplus M. The Levinthal paradox: yesterday and today. Fold Des. 1997;2(4):S69–S75. doi: 10.1016/s1359-0278(97)00067-9. [DOI] [PubMed] [Google Scholar]
  9. Karplus M., Weaver D. L. Protein-folding dynamics. Nature. 1976 Apr 1;260(5550):404–406. doi: 10.1038/260404a0. [DOI] [PubMed] [Google Scholar]
  10. Leopold P. E., Montal M., Onuchic J. N. Protein folding funnels: a kinetic approach to the sequence-structure relationship. Proc Natl Acad Sci U S A. 1992 Sep 15;89(18):8721–8725. doi: 10.1073/pnas.89.18.8721. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Muñoz V., Henry E. R., Hofrichter J., Eaton W. A. A statistical mechanical model for beta-hairpin kinetics. Proc Natl Acad Sci U S A. 1998 May 26;95(11):5872–5879. doi: 10.1073/pnas.95.11.5872. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Muñoz V., Thompson P. A., Hofrichter J., Eaton W. A. Folding dynamics and mechanism of beta-hairpin formation. Nature. 1997 Nov 13;390(6656):196–199. doi: 10.1038/36626. [DOI] [PubMed] [Google Scholar]
  13. Oliveberg M., Tan Y. J., Fersht A. R. Negative activation enthalpies in the kinetics of protein folding. Proc Natl Acad Sci U S A. 1995 Sep 12;92(19):8926–8929. doi: 10.1073/pnas.92.19.8926. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Onuchic J. N., Luthey-Schulten Z., Wolynes P. G. Theory of protein folding: the energy landscape perspective. Annu Rev Phys Chem. 1997;48:545–600. doi: 10.1146/annurev.physchem.48.1.545. [DOI] [PubMed] [Google Scholar]
  15. Onuchic J. N., Wolynes P. G., Luthey-Schulten Z., Socci N. D. Toward an outline of the topography of a realistic protein-folding funnel. Proc Natl Acad Sci U S A. 1995 Apr 11;92(8):3626–3630. doi: 10.1073/pnas.92.8.3626. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Pande V. S., Grosberg AYu, Tanaka T., Rokhsar D. S. Pathways for protein folding: is a new view needed? Curr Opin Struct Biol. 1998 Feb;8(1):68–79. doi: 10.1016/s0959-440x(98)80012-2. [DOI] [PubMed] [Google Scholar]
  17. Shakhnovich E. I. Theoretical studies of protein-folding thermodynamics and kinetics. Curr Opin Struct Biol. 1997 Feb;7(1):29–40. doi: 10.1016/s0959-440x(97)80005-x. [DOI] [PubMed] [Google Scholar]
  18. Wolynes P. G., Onuchic J. N., Thirumalai D. Navigating the folding routes. Science. 1995 Mar 17;267(5204):1619–1620. doi: 10.1126/science.7886447. [DOI] [PubMed] [Google Scholar]
  19. Zwanzig R. Diffusion in a rough potential. Proc Natl Acad Sci U S A. 1988 Apr;85(7):2029–2030. doi: 10.1073/pnas.85.7.2029. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Zwanzig R. Simple model of protein folding kinetics. Proc Natl Acad Sci U S A. 1995 Oct 10;92(21):9801–9804. doi: 10.1073/pnas.92.21.9801. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Zwanzig R., Szabo A., Bagchi B. Levinthal's paradox. Proc Natl Acad Sci U S A. 1992 Jan 1;89(1):20–22. doi: 10.1073/pnas.89.1.20. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Protein Science : A Publication of the Protein Society are provided here courtesy of The Protein Society

RESOURCES