Fast Relaxation Methods

Protein Folding Handbook

Volumn 1, Issue , 2008, Pages 454-490

  Gruebele, Martin ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Dissociation; Methods; Pressure; Protonation; Relaxation

Indexed keywords

EID: 84889808538     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9783527619498.ch14     Document Type: Chapter

References (170)

1. Eigen, M. & Maeyer, L. D. (1963). Relaxation methods. In Technique of Organic Chemistry (Weissberger, A., ed.), pp. 895-1054. Interscience, New York.
2. Valentine, J. S. (1998). Special Issue on Protein Folding. In Acc. Chem. Research (Valentine, J. S., ed.), Vol. 31, pp. 697-780.
3. Jacob, M., Holtermann, G., Perl, D. et al. (1999). Microsecond folding of the cold shock protein measured by a pressure-jump technique. Biochemistry 38, 2882-91.
4. Gruebele, M. (1999). The physical chemistry of protein folding. Annu. Rev. Phys. Chem. 50, 485-516.
5. Callender, R. & Dyer, D. B. (2002). Probing protein dynamics using temperature jump relaxation spectroscopy. Curr. Opin. Struct. Biol. 12, 628-33.
6. Jennings, P. & Wright, P. (1993). Formation of a molten globule intermediate early in the kinetic folding pathway of apomyoglobin. Science 262, 892-5.
7. Huang, G. S. & Oas, T. G. (1995). Submillisecond folding of monomeric l repressor. Proc. Natl Acad. Sci. USA 92, 6878-82.
8. Eigen, M., Hammes, G. G. & Kustin, K. (1960). Fast reactions of imidazole studied with relaxation spectrometry. J. Am. Chem. Soc. 82, 3482-3.
9. Turner, D. H., Flynn, G. W., Lundberg, S. K., Faller, L. D. & Sutin, N. (1972). Dimerization of proflavin by the laser Raman temperaturejump method. Nature 239, 215-17.
10. Holzwarth, J. F., Eck, V. & Genz, A. (1985). Iodine laser temperature-jump: relaxation processes in phospholipid bilayers on the picosecond to millisecond time-scale. In Spectroscopy and the Dynamics of Molecular Biological Systems (Bayley, P. M. & Dale, R. E., eds), pp. 351-377. Academic Press, London.
11. Williams, A. P., Longfellow, C. E., Freier, S. M., Kierzek, R. & Turner, D. H. (1989). Laser temperature-jump, spectroscopic, and thermodynamic study of salt effects on duplex formation by dGCATGC. Biochemistry 28, 4283-91.
12. Jones, C. M., Henry, E. R., Hu, Y. et al. (1993). Fast events in protein folding initiated by pulsed laser photolysis. Proc. Natl Acad. Sci. USA 90, 11860-64.
13. Phillips, C. M., Mizutani, Y. & Hochstrasser, R. M. (1995). Ultrafast thermally induced unfolding of RNase A. Proc. Natl Acad. Sci. USA 92, 7292-6.
14. Nölting, B., Golbik, R. & Fersht, A. R. (1995). Submillisecond events in protein folding. Proc. Natl Acad. Sci. USA 92, 10668-72.
15. Williams, S., Causgrove, T. P., Gilmanshin, R. et al. (1996). Fast events in protein folding: helix melting and formation in a small peptide. Biochemistry 35, 691-7.
16. Ballew, R. M., Sabelko, J. & Gruebele, M. (1996). Direct observation of fast protein folding: The initial collapse of apomyoglobin. Proc. Natl Acad. Sci. USA 93, 5759-64.
17. Pascher, T., Chesick, J. P., Winkler, J. R. & Gray, H. B. (1996). Protein folding triggered by electron transfer. Science 271, 1558-60.
18. Schwarz, G. & Seelig, J. (1968). Kinetic properties and the electric field effect of the helix-coil transition of poly(g-benzyl l-glutamate) determined from dielectric relaxation measurements. Biopolymers 6, 1263-77.
19. Hawley, S. A. (1971). Reversible pressure-temperature unfolding of chymotrypsinogen. Biochemistry 10, 2436-42.
20. Royer, C. A. (2002). Revisiting volume changes in pressure-induced protein unfolding. Biochim. Biophys. Acta 1595, 201-9.
21. Desai, G., Panick, G., Zein, M., Winter, R. & Royer, C. A. (1999). Pressure-jump Studies of the Folding/Unfolding of trp Repressor. J. Mol. Biol. 288, 461-7.
22. Clegg, R. M., Elson, E. L. & Maxfield, B. W. (1975). New technique for optical observation of the kinetics of chemical reactions perturbed by small pressure changes. Biopolymers 14, 883-7.
23. Hoffman, G. W. (1971). A nanosecond temperature-jump apparatus. Rev. Sci. Instrum. 42, 1643-7.
24. Rigler, R., Rabl, C. R. & Jovin, T. M. (1974). A temperature-jump apparatus for fluorescence measurements. Rev. Sci. Instrum. 45.
25. Nölting, B., Golbik, R., Neira, J. L., Soler-Gonzalez, A. S., Schreiber, G. & Fersht, A. R. (1997). The folding pathway of a protein at high resolution from microseconds to seconds. Proc. Natl Acad. Sci. USA 94, 826-30.
26. Ferguson, N., Johnson, C. M., Macias, M., Oschkinat, H. & Fersht, A. (2001). Ultrafast folding of WW domains without structured aromatic clusters in the denatured state. Proc. Natl Acad. Sci. USA 98, 13002-7.
27. Ferguson, N., Pires, J. R., Toepert, F. et al. (2001). Using flexible loop mimetics to extend Phi-value analysis to secondary structure interactions. Proc. Natl Acad. Sci. USA 98, 13008-13.
28. Mayor, U., Johnson, C. M., Daggett, V. & Fersht, A. R. (2000). Protein folding and unfolding in microseconds to nanoseconds by experiment and simulation. Proc. Natl Acad. Sci. USA 97, 13518-22.
29. Gillespie, B., Vu, D. M., Shah, P. S. et al. (2003). NMR and temperaturejump measurements of de novo designed proteins demonstrate rapid folding in the absence of explicit selection for kinetics. J. Mol. Biol. 4.
30. Mayor, U., Guydosh, N. R., Johnson, C. M. et al. (2003). The complete folding pathway of a protein from nanoseconds to microseconds. Nature 421, 863-7.
31. Rabl, C. R., Martin, S. R., Neumann, E. & Bayley, P. M. (2002). Temperature jump kinetic study of the stability of apo-calmodulin. Biophys. Chem. 101, 553-464.
32. Sanchez, I. E. & Kiefhaber, T. (2003). Hammond behavior versus ground state effects in protein folding: Evidence for narrow free energy barriers and residual structure in unfolded states. J. Mol. Biol. 327, 867-84.
33. Ansari, A., Jones, C. M., Henry, E. R., Hofrichter, J. & Eaton, W. A. (1992). The role of solvent viscosity in the dynamics of protein conformational changes. Science 256, 1796-8.
34. Mines, G. A., Pascher, T., Lee, S. C., Winkler, J. R. & Gray, H. B. (1996). Cytochrome c folding triggered by electron transfer. Chem. Biol. 3, 491-7.
35. Wittung-Stafshede, P., Gray, H. B. & Winkler, J. R. (1997). Rapid formation of a four-helix bundle, cytochrome b562 folding triggered by electron transfer. J. Am. Chem. Soc. 119, 9562-3.
36. Telford, J. R., Wittung-Stafshede, P., Gray, H. B. & Winkler, J. R. (1998). Protein folding triggered by electron transfer. Acc. Chem. Res. 31, 755-63.
37. Lee, J. C., Gray, H. B. & Winkler, J. R. (2001). Cytochrome c0 folding triggered by electron transfer: fast and slow formation of four-helix bundles. Proc. Natl Acad. Sci. USA 98, 7760-4.
38. Chang, I. J., Lee, J. C., Winkler, J. R. & Gray, H. B. (2003). The proteinfolding speed limit: Intrachain diffusion times set by electron-transfer rates in denatured Ru(NH3)(5)(His-33)-Zn-cytochrome c. Proc. Natl Acad. Sci. USA 100, 3838-40.
39. Gutman, M., Huppert, D. & Pines, E. (1981). The pH jump: a rapid modulation of pH of aqueous solutions by a laser pulse. J. Am. Chem. Soc. 103, 3709-13.
40. Pines, E. & Huppert, D. (1983). pH jump: a relaxation approach. J. Phys. Chem. 87, 4471-8.
41. George, M. V. & Scaiano, J. C. (1980). Photochemistry of o-nitrobenzaldehyde and related studies. J. Phys. Chem. 84, 492-5.
42. Abbruzzetti, S., Crema, E., Masino, L. et al. (2000). Fast events in protein folding: Structural volume changes accompanying the early events in the N ! I transition of apomyoglobin induced by ultrafast pH jump. Biophys. J. 78, 405-15.
43. Choi, J., Hirota, N. & Terazima, M. (2001). Enthalpy and volume changes on the pH jump process studied by the transient grating technique. Anal. Sci. 17, s13-s15.
44. Volk, M., Kholodenko, Y., Lu, H. S. M., Gooding, E. A., DeGrado, W. F. & Hochstrasser, R. M. (1997). Peptide conformational dynamics and vibrational stark effects following photoinitiated disulfide cleavage. J. Phys. Chem. 101, 8607-16.
45. Metzler, R., Klafter, J., Jortner, J. & Volk, M. (1998). Multiple time scales for dispersive kinetics in early events of peptide folding. Chem. Phys. Lett. 293, 477-84.
46. Hagen, S. J., Hofrichter, J., Szabo, A. & Eaton, W. A. (1996). Diffusionlimited contact formation in unfolded cytochrome c: Estimating the maximum rate of protein folding. Proc. Natl Acad. Sci. USA 93, 11615-17.
47. Hagen, S. J., Hofrichter, J. & Eaton, W. A. (1997). Rate of intrachain diffusion of unfolded cytochrome c. J. Phys. Chem. B 101, 2352-65.
48. Bieri, O. & Kiefhaber, T. (1999). Elementary steps in protein folding. Biol. Chem. 380, 923-9.
49. Lapidus, L. J., Eaton, W. A. & Hofrichter, J. (2000). Measuring the rate of intramolecular contact formation in polypeptides. Proc. Natl Acad. Sci. USA 97, 7220-5.
50. Lapidus, L., Eaton, W. & Hofrichter, J. (2001). Dynamics of intramolecular contact formation in polypeptides: distance dependence of quenching rates in room temperature glass. Phys. Rev. Lett. 87.
51. Bieri, O. & Kiefhaber, T. (2000). Kinetic models in protein folding. In Mechanisms of Protein Folding, 2nd edn (Pain, R. H., ed.), Vol. 32, pp. 34-64. Oxford University Press, Oxford.
52. Ballew, R. M., Sabelko, J. & Gruebele, M. (1996). Observation of distinct nanosecond and microsecond protein folding events. Nat. Struct. Biol. 3, 923-6.
53. Gilmanshin, R., Williams, S., Callender, R. H., Woodruff, W. H. & Dyer, R. B. (1997). Fast events in protein folding: Relaxation dynamics of secondary and tertiary structure in native apomyoglobin. Proc. Natl Acad. Sci. USA 94, 3709-13.
54. Thompson, P. A., Eaton, W. A. & Hofrichter, J. (1997). Laser temperature jump study of the helix reversible arrow coil kinetics of an alanine peptide interpreted with a 'kinetic zipper' model. Biochemistry 36, 9200-10.
55. Dyer, R. B., Gai, F., Woodruff, W. H., Gilmanshin, R. & Callender, R. H. (1998). Infrared studies of fast events in protein folding. Acc. Chem. Res. 31, 709-16.
56. Sabelko, J., Ervin, J. & Gruebele, M. (1999). Observation of strange kinetics in protein folding. Proc. Nat. Acad. Sci. USA 96, 6031-6.
57. Crane, J. C., Koepf, E. K., Kelly, J. W. & Gruebele, M. (2000). Mapping the transition state of the WW domain beta sheet. J. Mol. Biol. 298, 283-92.
58. Leeson, D. T., Gai, F., Rodriguez, H. M., Gregoret, L. M. & Dyer, R. B. (2000). Protein Folding on a Complex Energy Landscape. Proc. Natl Acad. Sci. USA 97, 2527-32.
59. Jäger, M., Nguyen, H., Crane, J., Kelly, J. & Gruebele, M. (2001). The folding mechanism of a b-sheet: The WW domain. J. Mol. Biol. 311, 373-93.
60. Gulotta, M., Gilmanshin, R., Buscher, T. C., Callender, R. H. & Dyer, R. B. (2001). Core formation in apomyoglobin: probing the upper reaches of the folding energy landscape. Biochemistry 40, 5137-43.
61. Snow, C., Nguyen, H., Pande, V. & Gruebele, M. (2002). Absolute comparison of simulated and experimental protein folding dynamics. Nature 420, 102-6.
62. Osváth, S. & Gruebele, M. (2003). Proline can have opposite effects on fast and slow protein folding phases. Biophys. J. 85, 1215-22.
63. Osváth, S., Sabelko, J. & Gruebele, M. (2003). Tuning the heterogeneous early folding dynamics of phosphoglycerate kinase. J. Mol. Biol. 333, 187-99.
64. Pandit, A., Ma, H., Stokkum, I. v., Gruebele, M. & Grondelle, R. v. (2003). The time resolved dissociation reaction of the light-harvesting 1 complex of Rhodospirillum rubrum, studied with an infrared laser-pulse temperature jump. Biochemistry 41, 15115-20.
65. Yang, W. & Gruebele, M. (2003). Folding at the speed limit. Nature 423, 193-7.
66. Nguyen, H., Jäger, M., Gruebele, M. & Kelly, J. (2003). Tuning the freeenergy landscape of a WW domain by temperature, mutation and truncation. Proc. Natl Acad. Sci. USA 100, 3948-53.
67. Ballew, R. M., Sabelko, J., Reiner, C. & Gruebele, M. (1996). A singlesweep, nanosecond time resolution laser temperature-jump apparatus. Rev. Sci. Instrum. 67, 3694-9.
68. Eaton, W. A., Muñoz, V., Thompson, P. A., Henry, E. R. & Hofrichter, J. (1998). Kinetics and dynamics of loops, a-helices, b-hairpins, and fastfolding proteins. Acc. Chem. Res. 31, 745-53.
69. Muñoz, V., Thompson, P. A., Hofrichter, J. & Eaton, W. A. (1997). Folding dynamics and mechanism of b-hairpin formation. Nature 390, 196-9.
70. Muñoz, V., Henry, E. R., Hofrichter, J. & Eaton, W. A. (1998). A Statistical Mechanical Model for b-Hairpin Kinetics. Proc. Natl Acad. Sci. USA 95, 5872-9.
71. Huang, C. Y., Getahun, Z., Wang, T., DeGrado, W. F. & Gai, F. (2001). Time-resolved infrared study of the helix-coil transition using C-13-labeled helical peptides. J. Am. Chem. Soc. 123, 12111-12.
72. Getahun, Z., Huang, C. Y., Wang, T., Leon, B. D., DeGrado, W. F. & Gai, F. (2003). Using nitrile-derivated amino acids as infrared probes of local environment. J. Am. Chem. Soc. 125.
73. Klimov, D. K. & Thirumalai, D. (2000). Mechanisms and kinetics of beta-hairpin formation. Proc. Natl Acad. Sci. USA 97, 2544-9.
74. Yang, W., Prince, R., Sabelko, J., Moore, J. S. & Gruebele, M. (2000). Transition from exponential to nonexponential kinetics during formation of an artificial helix. J. Am. Chem. Soc. 122, 3248-9.
75. Hummer, G., Garcia, A. E. & Garde, S. (2000). Conformational diffusion and helix formation kinetics. Phys. Rev. Lett. 85, 2637-40.
76. Gilmanshin, R., Callender, R. H. & Dyer, R. B. (1998). The core of apomyoglobin E-form folds at the diffusion limit. Nat. Struct. Biol. 5, 363-5.
77. Low, D. W., Winkler, J. R. & Gray, H. B. (1996). Photoinduced oxidation of microperoxidase-9: generation of ferryl and cation-radical prophyrins. J. Am. Chem. Soc. 118, 117-20.
78. Pollack, L., Tate, M. W., Darnton, N. C., Knight, J. B., Gruner, S. M., Eaton, W. A. & Austin, R. H. (1999). Compactness of the denatured state of a fast-folding protein measured by submillisecond small-angle X-ray scattering. Proc. Natl Acad. Sci. USA 96, 10115.
79. Gilmanshin, R., Callender, R. H., Dyer, R. B. & Woodruff, W. H. (1998). Fast event in protein folding: the time evolution of primary processes. Annu. Rev. Phys. Chem. 49, 173-202.
80. Wang, J. & El-Sayed, M. A. (1999). Temperature jump-induced secondary structural change of the membrane protein bacteriorhodopsin in the premelting temperature region: a nanosecond time-resolved Fourier transform infrared study. Biophys. J. 76, 2777-83.
81. Ma, H., Ervin, J. & Gruebele, M. (2003). Multichannel, single-sweep infrared detection for nanosecond relaxation kinetics experiments. Rev. Sci. Inst. 75, 486-491.
82. Chen, E. F. & Kliger, D. S. (1996). Time-resolved near UV circular dichroism and absorption studies of carbonmonoxymyoglobin photolysis intermediates. Inorg. Chim. Acta 242, 149-58.
83. Chen, E. F., Goldbeck, R. A. & Kliger, D. S. (1997). Nanosecond time-resolved spectroscopy of biomolecular processes. Annu. Rev. Biophys. Biomol. Struct. 26, 327-55.
84. Chen, E., Wood, M. J., Fink, A. L. & Kliger, D. S. (1998). Time-resolved circular dichroism studies of protein folding intermediates of cytochrome c. Biochemistry 37, 5589-98.
85. Chen, E. F., Gensch, T., Gross, A. B., Hendriks, J., Hellingwerf, K. J. & Kliger, D. S. (2003). Dynamics of protein and chromophore structural changes in the photocycle of photoactive yellow protein monitored by time-resolved optical rotatory dispersion. Biochemistry 42, 2062-71.
86. Lednev, I. K., Karnoup, A. S., Sparrow, M. C. & Asher, S. A. (1999). a-Helix peptide folding and unfolding activation barriers: a nanosecond UV resonance study. J. Am. Chem. Soc. 121, 8074-86.
87. Lednev, I. K., Karnoup, A. S., Sparrow, M. C. & Asher, S. A. (1999). Nanosecond UV resonance raman examination of initial steps in a-helix secondary structure evolution. J. Am. Chem. Soc. 121, 4076-7.
88. Yamamoto, K., Mizutani, Y. & Kitagawa, T. (2000). Nanosecond temperature jump and time-resolved Raman study of thermal unfolding of ribonuclease A. Biophys. J. 79, 485-95.
89. Yeh, S., Han, S. & Rousseau, D. L. (1998). Cytochrome c Folding and Unfolding: A Biphasic Mechanism. Acc. Chem. Res. 31, 727-36.
90. Lakowicz, J. R. (1986). Fluorescence studies of structural flucturations in macromolecules as observed by fluorescence spectroscopy in the time, lifetime, and frequency domains. In Methods in Enzymology, Vol. 131, pp. 518-567. Academic Press, New York.
91. Chen, Y. & Barkley, M. D. (1998). Toward understanding tryptophan fluorescence in proteins. Biochemistry 37, 9976-82.
92. Förster, T. (1948). Zwischenmoleku ̈lare Energiewanderung und Fluoreszenz. Ann. Physik 2, 55-75.
93. Rischel, C. & Poulsen, F. M. (1995). Modification of a specific tyrosine enables tracing of the end-to-end distance during apomyoglobin folding. FEBS Lett. 374, 105-9.
94. Ballew, R. M. (1996). Direct observation of fast protein folding: distinct nanosecond and microsecond events in the folding of apomyoglobin. Thesis, University of Illinois.
95. Gruebele, M., Sabelko, J., Ballew, R. & Ervin, J. (1998). Laser temperature jump induced protein refolding. Acc. Chem. Res. 31, 699-707.
96. Garcia, P., Desmadril, M., Minard, P. & Yon, J. M. (1995). Evidence for residual structures in an unfolded from of yeast phosphoglycerate kinase. Biochemistry 34, 397-404.
97. Ervin, J., Larios, E., Osvath, S., Schulten, K. & Gruebele, M. (2002). What causes hyperfluorescence: Folding intermediates or conformationally flexible native states? Biophys. J. 83, 473-83.
98. Ervin, J., Sabelko, J. & Gruebele, M. (2000). Submicrosecond real-time fluorescence detection: application to protein folding. J. Photochem. Photobiol. B54, 1-15.
99. Henry, E. R. & Hofrichter, J. (1992). Singular value decomposition: application to analysis of experimental data. Methods Enzymol. 210, 129-92.
100. Bryngelson, J. D. & Wolynes, P. G. (1987). Spin glasses and the statistical mechanics of protein folding. Proc. Natl Acad. Sci. USA 84, 7524-8.
101. Onuchic, J. N., Wolynes, P. G., Luthey-Schulten, Z. & Socci, N. D. (1995). Toward an outline of the topography of a realistic protein folding funnel. Proc. Natl Acad. Sci. USA 92, 3626-30.
102. Kiefhaber, T., Schmid, F. X., Willaert, K., Engelborghs, Y. & Chaffotte, A. (1992). Structure of a rapidly formed intermediate in ribonuclease T1 folding. Protein Sci. 1, 1162-72.
103. Pappenberger, G., Aygun, H., Engels, J. W., Reimer, U., Fischer, G. & Kiefhaber, T. (2001). Nonprolyl cis peptide bonds in unfolded proteins cause complex folding kinetics. Nat. Struct. Biol. 8, 452-8.
104. Kelley, R. F. & Richards, F. M. (1987). Replacement of proline-76 with alanine eliminates the slowest kinetic phase in thioredoxin folding. Biochemsitry 26, 6765-74.
105. Plaxco, K. W., Guijarro, J. I., Morton, C. J., Pitkeathly, M., Campbell, I. D. & Dobson, C. M. (1998). The folding kinetics and thermodynamics of the Fyn-SH3 domain. Biochemistry 37, 2529-37.
106. Onuchic, J. N., Luthey-Schulten, Z. & Wolynes, P. G. (1997). Theory of protein folding: the energy landscape perspective. Annu. Rev. Phys. Chem. 48, 545-600.
107. Pappu, R. V., Srinivasan, R. & Rose, G. D. (2000). The Flory isolated-pair hypothesis is not valid for polypeptide chains: Implications for protein folding. Proc. Natl Acad. Sci. USA 97, 12565-70.
108. Bromberg, S. & Dill, K. A. (1994). Side-chain entropy and packing in proteins. Protein Sci. 3, 997-1009.
109. Bryngelson, J. D. & Wolynes, P. G. (1989). Intermediates and barrier crossing in random energy model (with applications to protein folding). J. Phys. Chem. 93, 6902-15.
110. Kim, P. S. & Baldwin, R. L. (1990). Intermediates in the folding reactions of small proteins. Annu. Rev. Biochem. 59, 631-60.
111. Bachmann, A. & Kiefhaber, T. (2001). Apparent two-state tendamistat folding is a sequential process along a defined route. J. Mol. Biol. 306, 375-86.
112. Creighton, T. E. (1988). Toward a better understanding of protein folding pathways. Proc. Natl Acad. Sci. USA 85, 5082-6.
113. Zwanzig, R. (1997). Two-state models of protein folding kinetics. Proc. Natl Acad. Sci. USA 94, 148-50.
114. Nymeyer, H., García, A. E. & Onuchic, J. N. (1998). Folding funnels and frustration in off-lattice minimalist protein landscapes. Proc. Natl Acad. Sci. USA 95, 5921-8.
115. Plotkin, S. S., Wang, J. & Wolynes, P. G. (1997). Statistical mechanics of a correlated energy landscape model for protein folding funnels. J. Chem. Phys. 106, 2932-48.
116. Go, N. (1983). Theoretical studies of protein folding. Annu. Rev. Biophys. Bioeng. 12, 183-210.
117. Thompson, P. A., Eaton, W. A. & Hofrichter, J. (1997). Laser temperature jump study of the helix x coil kinetics of an alanine peptide interpreted with a 'kinetic zipper' model. Biochemistry 36, 9200-10.
118. Zwanzig, R. (1988). Diffusion in a rough potential. Proc. Natl Acad. Sci., USA 85, 2029-30.
119. Shea, J. E., Onuchic, J. N. & C L Brooks, I. (2000). Energetic frustration and the nature of the transition state ensemble in protein folding. J. Chem. Phys. 113, 7663-71.
120. Portman, J. J., Takada, S. & Wolynes, P. G. (2001). Microscopic theory of protein folding rates. II. Local reaction coordinates and chain dynamics. J. Chem. Phys. 114, 5082-96.
121. Thirumalai, D., Klimov, D. K. & Dima, R. I. (2002). Insights into specific problems in protein folding using simple concepts. Adv. Chem. Phys. 120, 35-76.
122. Alm, E. & Baker, D. (1999). Prediction of protein-folding mechanisms from free energy landscapes derived from native structures. Proc. Natl Acad. Sci. USA 96, 11305-10.
123. Muñoz, V. & Eaton, W. A. (1999). A simple model for calculating the kinetics of protein folding from threedimenstional structures. Proc. Natl Acad. Sci. USA 96, 11311-16.
124. Koga, N. & Takada, S. (2001). Roles of native topology and chain-length scaling in protein folding: a simulation study with a Go-like model. J. Mol. Biol. 313, 171-80.
125. Silow, M. & Oliveberg, M. (1997). High-energy channeling in protein folding. Biochemistry 36, 7633-7.
126. Wagner, C. & Kiefhaber, T. (1999). Intermediates can accelerate protein folding. Proc. Natl Acad. Sci. USA 96, 6716-21.
127. Skorobogatiy, M., Guo, H. & Zuckerman, M. (1998). Non-Arrhenius modes in the relaxation of model proteins. J. Chem. Phys. 109, 2528-35.
128. Metzler, R., Klafter, J. & Jortner, J. (1999). Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems. Proc. Natl Acad. Sci. USA 96, 11085-9.
129. Becker, O. M. & Karplus, M. (1997). The topology of multidimensional potential energy surfaces: theory and application to peptide structure and kinetics. J. Chem. Phys. 22, 1495-517.
130. Becker, O. M. (1998). Principal coordinate maps of molecular potential energy surfaces. J. Comput. Chem. 19, 1255-67.
131. Kramers, H. A. (1940). Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284.
132. Plaxco, K. W. & Baker, D. (1998). Limited internal friction in the ratelimiting step of a two-state protein folding reaction. Proc. Natl Acad. Sci. USA 95, 13591-6.
133. Jacob, M., Schindler, T., Balbach, J. & Schmid, F. X. (1997). Diffusion control in an elementary protein folding reaction. Proc. Natl Acad. Sci. USA 94, 5622-7.
134. Jacob, M., Geeves, M., Holtermann, G. & Schmid, F. X. (1999). Diffusional barrier crossing in a two-state protein folding reaction. Proc. Natl Acad. Sci. USA 94, 5622-7.
135. Bhattacharyya, R. P. & Sosnick, T. R. (1999). Viscosity dependence of the folding kinetics of a dimeric and monomeric coiled coil. Biochemistry 38, 2601-9.
136. Bieri, O., Wirz, J., Hellrung, B., Schutkowski, M., Drewello, M. & Kiefhaber, T. (1999). The speed limit of protein folding measure by triplettriplet energy transfer. Proc. Natl Acad. Sci. USA 96, 9597-601.
137. Pappenberger, G., Saudan, C., Becker, M., Merbach, A. E. & Kiefhaber, T. (2000). Denaturantinduced movement of the transition state of protein folding revealed by high-pressure stopped-flow measurements. Proc. Natl Acad. Sci. USA 97, 17-22.
138. Khorasanizadeh, S., Peters, I. & Roder, H. (1996). Evidence for a three-state model of protein folding from kinetic analysis of ubiquitin variants with altered core residues. Nat. Struct. Biol. 3, 193-205.
139. Shastry, M. C. R. & Roder, H. (1998). Evidence for barrier-limited protein folding kinetics on the microsecond time scale. Nat. Struct. Biol. 5, 385-92.
140. Hagen, S. J. & Eaton, W. A. (2000). Two-state expansion and collapse of a polypeptide. J. Mol. Biol. 297, 781-9.
141. Qin, Z., Ervin, J., Larios, E., Gruebele, M. & Kihara, H. (2002). Formation of a compact structured ensemble without fluorescence signature early during ubiquitin folding. J. Phys. Chem. B 106, 13040-6.
142. Finkelstein, A. V. & Shakhnovich, E. I. (1989). Theory of cooperative transitions in protein molecules. ii. phase diagram for a protein molecule in solution. Biopolymers 28, 1681-94.
143. Parker, M. J. & Marqusee, S. (1999). The cooperativity of burst phase reactions explored. J. Mol. Biol. 293, 1195-210.
144. Englander, S. W., Sosnick, T. R., Mayne, L. C., Shtilerman, M., Qi, P. X. & Bai, Y. (1998). Fast and slow folding in cytochrome c. Acc. Chem. Res. 31, 767-74.
145. Krantz, B. A. & Sosnick, T. R. (2000). Distinguishing between twostate and three-state models for ubiquitin folding. Biochemistry 39, 11696-701.
146. Capaldi, A. P., Shastry, M. C. R., Kleanthous, C., Roder, H. & Radford, S. E. (2001). Ultrarapid mixing experiments reveal that Im7 folds via an on-pathway intermediate. Nat. Struct. Biol. 8, 68-72.
147. Miller, W. G. & Goebel, C. V. (1968). Dimensions of protein random coils. Biochemistry 7, 3925-34.
148. Ervin, J. & Gruebele, M. (2002). Quantifying protein folding transition states with Phi-T. J. Biol. Phys. 28, 115-28.
149. Pain, R. H., ed. (2000). Mechanisms of Protein Folding, Vol 32. Frontiers in Molecular Biology. Oxford University Press, Oxford.
150. Berne, B. J. (1993). Theoretical and numerical methods in rate theory. In Activated Barrier Crossing: Applications in Physics, Chemistry and Biology (Hänggi, P. & Fleming, G. R., eds), pp. 82-119. World Scientific, Singapore.
151. Muñoz, V. (2002). Thermodynamics and kinetics of downhill protein folding investigated with a simple statistical mechanical model. Int. J. Quantum Chem. 90, 1522-8.
152. Poland, D. & Scheraga, H. A. (1970). Theory of Helix-Coil Transitions in Biopolymers, Academic Press, New York.
153. Dill, K. A. (1985). Theory for the folding and stability of globular proteins. Biochemistry 24, 1501-9.
154. Yue, K., Fiebig, K. M., Thomas, P. D., Chan, H. S., Shakhnovich, E. I. & Dill, K. A. (1995). A test of lattice protein folding algorithms. Proc. Natl Acad. Sci. USA 92, 325-9.
155. Shakhnovich, E., Farztdinov, G., Gutin, A. M. & Karplus, M. (1991). Protein folding bottlenecks: a lattice Monte Carlo simulation. Phys. Rev. Lett. 67, 1665-8.
156. Onuchic, J. N., Nymeyer, H., Garcia, A. E., Chahine, J. & Socci, N. D. (2000). The energy landscape theory of protein folding: Insights into folding mechanisms and scenarios. Adv. Protein Chem. 53, 87-152.
157. Kaya, H. & Chan, H. S. (2000). Energetic components of cooperative protein folding. Phys. Rev. Lett. 85, 4823-6.
158. Guo, Z. & Thirumalai, D. (1996). Kinetics and thermodynamics of folding of a de novo designed fourhelix bundle protein. J. Mol. Biol. 263, 323-43.
159. Klimov, D. K. & Thirumalai, D. (1997). Viscosity dependence of the folding rates of proteins. Phys. Rev. Lett. 79, 317-20.
160. Srinivas, G., Yethiraj, A. & Bagchi, B. (2001). Nonexponentiality of time dependent survival probability and the fractional viscosity dependence of the rate in diffusion controlled reactions in a polymer chain. J. Chem. Phys. 114, 9170-8.
161. Duan, Y. & Kollman, P. A. (1998). Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. Science 282, 740-4.
162. Ladurner, A. G., Itzhaki, L. S., Daggett, V. & Fersht, A. R. (1998). Synergy between simulation and experiment in describing the energy landscape of protein folding. Proc. Natl Acad. Sci. USA 95, 8473-8.
163. Karanicolas, J. & III, C. L. B. (2003). The structural basis for biphasic kinetics in the folding of the WW domain from a formin-binding protein: lessons for protein design. Proc. Natl Acad. Sci. USA 100, 3954-9.
164. Kaya, H. & Chan, H. S. (2000). Polymer principles of protein calorimetric two-state cooperativity. Proteins Struct. Funct. Genet. 40, 637-61.
165. Shea, J. & Brooks, C. L. (2001). From folding theories to folding proteins: a review and assessment of simulation studies of protein folding and unfolding. Annu. Rev. Phys. Chem. 52, 499-535.
166. Clementi, C., Nymeyer, H. & Onuchic, J. N. (2000). Topological and energetic factors: What deter-mines the structural details of the transition state ensemble and "en-route" intermediates for protein folding? An investigation for small globular proteins. J. Mol. Biol. 298, 937-53.
167. Burton, R. E., Huang, G. S., Daugherty, M. A., Calderone, T. L. & Oas, T. G. (1997). The energy landscape of a fast-folding protein mapped by Ala ! Gly Substitutions. Nat. Struct. Biol. 4, 305-10.
168. Garcia, C., Nishimura, C., Cavagnero, S., Dyson, H. J. & Wright, P. E. (2000). Changes in the apomyoglobin folding pathway caused by mutation of the distal histidine residue. Biochemistry 39, 11227-37.
169. Jäger, M., Nguyen, H., Kelly, J. & Gruebele, M. (2003). Redesigning the turns of WW domain: the functionfolding relationship. Submitted.
170. Fersht, A. (1999). Structure & Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding. WH Freeman, New York.