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.
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- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- Karplus M., Weaver D. L. Protein-folding dynamics. Nature. 1976 Apr 1;260(5550):404–406. doi: 10.1038/260404a0. [DOI] [PubMed] [Google Scholar]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]