Toward an accurate theoretical framework for describing ensembles for proteins under strongly denaturing conditions

Biophysical Journal

Volumn 91, Issue 5, 2006, Pages 1868-1886

  Tran, Hoang T ^a   Pappu, Rohit V ^a  

^a WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

POLYMER; PROTEIN;

AMINO ACID SEQUENCE; ARTICLE; DENATURATION; MEDICAL LITERATURE; MEDICAL RESEARCH; PROTEIN STRUCTURE;

EID: 33748454896     PISSN: 00063495     EISSN: None     Source Type: Journal    
DOI: 10.1529/biophysj.106.086264     Document Type: Article

References (138)

1. Kauzmann, W. 1959. Some factors in the interpretation of protein denaturation. Adv. Protein Chem. 14:1-63.
2. Miller, W. G., and C. V. Goebel. 1968. Dimensions of protein random coils. Biochemistry. 7:3925-3935.
3. Tanford, C. 1968. Protein denaturation. Adv. Protein Chem. 23:121-282.
4. Dill, K. A., and D. Shortle. 1991. Deantured states of proteins. Annu. Rev. Biochem. 60:795-825.
5. Shortle, D. 1996. The denatured state (the other half of the folding equation) and its role in protein stability. FASEB J. 10:27-34.
6. Smith, L. J., K. M. Fiebig, H. Schwalbe, and C. M. Dobson. 1996. The concept of a random coil: residual structure in peptides and denatured proteins. Fold. Des. 1:R95-R106.
7. Wong, K. B., J. Clarke, C. J. Bond, J. L. Neira, S. M. V. Freund, A. R. Fersht, and V. Daggett. 2000. Towards a complete description of the structural and dynamic properties of the denatured state of barnase and the role of residual structure in folding. J. Mol. Biol. 296:1257-1282.
8. van Gunsteren, W. F., R. Burgi, C. Peter, and X. Daura. 2001. The key to solving the protein-folding problem lies in an accurate description of the denatured state. Angew. Chem. Int. Ed. Engl. 40:351-355.
9. Schellman, J. A. 2002. Fifty years of solvent denaturation. Biophys. Chem. 96:91-101.
10. Baldwin, R. L. 2002. A new perspective on unfolded proteins. Adv. Protein Chem. 62:361-367.
11. Kohn, J. E., I. S. Millett, J. Jacob, B. Zagrovic, T. M. Dillon, N. Cingel, R. S. Dothager, S. Seifert, P. Thiyagarajan, T. R. Sosnick, M. Z. Hasan, V. S. Pande, I. Ruzcinski, S. Doniach, and K. W. Plaxco. 2004. Random-coil behavior and the dimensions of chemically unfolded proteins. Proc. Natl. Acad. Sci. USA. 101:12491-12496.
12. Fleming, P. J., and G. D. Rose. 2005. Conformational properties of unfolded proteins. In Protein Folding Handbook, Vol. 2. J. Buchner and T. Kiefhaber, editors. Wiley-VCH, Weinheim, Germany. 710-736.
13. Dill, K. A., and D. Stigter. 1995. Modeling protein stability as heteropolymer collapse. Adv. Protein Chem. 46:59-104.
14. Robertson, A. D., and K. P. Murphy. 1997. Protein structure and the energetics of protein stability. Chem. Rev. 97:1251-1267.
15. Laziridis, T., and M. Karplus. 2003. Thermodynamics of protein folding: a microscopic view. Biophys. Chem. 100:367-395.
16. Garcia-Moreno, B., and C. A. Fitch. 2004. Structural interpretation of pH and salt-dependent processes in proteins with computational methods. Methods Enzymol. 380:20-51.
17. Zhou, H.-X. 2004. Polymer models of protein stability, folding, and interactions. Biochemistry. 43:2141-2154.
18. Pace, C. N., G. R. Grimsley, and J. M. Scholtz. 2005. Denaturant-induced protein unfolding. In Protein Folding Handbook, Vol. 1. J. Buchner and T. Kiefhaber, editors. Wiley-VCH, Weinheim, Germany. 45-69.
19. Bryngelson, J. D., J. N. Onuchic, N. D. Socci, and P. G. Wolynes. 1995. Funnels, pathways, and the energy landscape of protein folding: a synthesis. Proteins.. 21:167-195.
20. Dill, K. A., and H. S. Chan. 1997. From Levinthal to pathways to funnels. Nat. Struct. Biol. 4:10-19.
21. Baldwin, R. L., and G. D. Rose. 1999. Is protein folding hierarchic? II. Trends Biochem. Sci. 24:77-83.
22. Dinner, A. R., A. Sali, L. J. Smith, C. M. Dobson, and M. Karplus. 2000. Understanding protein folding via free energy surfaces from theory and experiments. Trends Biochem. Sci. 25:331-339.
23. Daggett, V. 2002. Molecular dynamics simulations of the protein unfolding/folding reaction. Acc. Chem. Res. 35:422-429.
24. Religa, T. L., J. S. Markson, U. Mayor, S. M. V. Freund, and A. R. Fersht. 2005. Solution structure of a protein denatured state and folding intermediate. Nature. 437:1053-1056.
25. Mendes, J., R. Guerois, and L. Serrano. 2002. Energy estimation in protein design. Curr. Opin. Struct. Biol. 12:441-446.
26. Anil, B., R. Craig-Schapiro, and D. P. Raleigh. 2006. Design of a hyperstable protein by rational consideration of unfolded state interactions. J. Am. Chem. Soc. 128:3144-3145.
27. Dobson, C. M. 2004. Principles of protein folding, misfolding, and aggregation. Semin. Cell Dev. Biol. 15:3-16.
28. Ohnishi, S., and K. Takano. 2004. Amyloid fibrils from the viewpoint of protein folding. Cell. Mol. Life Sci. 61:511-524.
29. Uversky, V. N., and A. L. Fink. 2004. Conformational constraints for amyloid formation: the importance of being unfolded. Biochim. Biophys. Acta. 1698:131-153.
30. Tanford, C. 1970. Protein denaturation: C. Theoretical models for the mechanism of denaturation. Adv. Protein Chem. 24:1-95.
31. Makhatadze, G. I. 1999. Thermodynamics of protein interactions with urea and guanidinium hydrochloride. J. Phys. Chem. B. 103:4781-4785.
32. Schellman, J. A. 2003. Protein stability in mixed solvents: A balance of contact interactions and excluded volume. Biophys. J. 85:108-125.
33. Ferreon, A. C. M., and D. W. Bolen. 2004. Thermodynamics of denaturant-induced unfolding of a protein that exhibits variable two-state denaturation. Biochemistry. 43:13357-13369.
34. Felitsky, D. J., and M. T. Record. 2004. Application of the local-bulk partitioning and competitive binding models to interpret preferential interactions of glycine betaine and urea with protein surface. Biochemistry. 43:9276-9288.
35. Rösgen, J., B. M. Pettitt, and D. W. Bolen. 2005. Bolen. Protein folding, stability, and solvation structure in osmolyte solutions. Biophys. J. 89:2988-2997.
36. Auton, M., and D. W. Bolen. 2005. Predicting the energetics of osmolyte-induced protein folding/unfolding. Proc. Natl. Acad. Sci. USA. 102:15065-15068.
37. Chan, H. S., and K. A. Dill. 1991. Polymer principles in protein structure and stability. Annu. Rev. Biophys. Biophys. Chem. 20:447-490.
38. Rubenstein, M., and R. H. Colby. 2003. Polymer Physics. Oxford University Press, New York.
39. Schäfer, L. 1999. Excluded Volume Effects in Polymer Solutions as Explained by the Renormalization Group. Springer, Berlin.
40. Grosberg, A. Y., and A. R. Khokhlov. 1994. Statistical Physics of Macromolecules. AIP Series in Polymers and Complex Materials. American Institute of Physics, New York.
41. des Cloizeaux, J., and G. Janink. 1990. Polymers in Solution: Their Modeling and Structure. Oxford University Press, Oxford, UK.
42. de Gennes, P. G. 1979. Scaling Concepts in Polymer Physics. Cornell University Press, Ithaca, NY.
43. Flory, P. J. 1969. Statistical Mechanics of Chain Molecules. Hanser Publishers, Munich.
44. Flory, P. J. 1953. Principles of Polymer Chemistry. Cornell University Press, Ithaca, NY.
45. Sanchez, I. C. 1979. Phase transition behavior of the isolated polymer chain. Macromolecules. 12:980-988.
46. Wilkins, D. K., S. B. Grimshaw, V. Receveur, C. M. Dobson, J. A. Jones, and L. J. Smith. 1999. Hydrodynamic radii of native and denatured proteins measured by pulse field gradient NMR techniques. Biochemistry. 38:16424-16431.
47. Millett, I. S., S. Doniach, and K. W. Plaxco. 2002. Toward a taxonomy of the denatured state: small angle scattering studies of unfolded proteins. Adv. Protein Chem. 62:241-262.
48. Tran, H. T., X. Wang, and R. V. Pappu. 2005. Reconciling sequence-specific conformational preferences with generic behavior of denatured proteins. Biochemistry. 44:11369-11380.
49. Le Guillou, J. C., and J. Zinn-Justin. 1980. Critical exponents from field theory. Phys. Rev. B. 21:3976-3998.
50. Receveur, V., D. Durand, M. Desmadril, and P. Calmattes. 1998. Repulsive interparticle interactions in a denatured protein solution revealed by small angle neutron scattering. FEBS Lett. 426:57-61.
51. Hansen, J.-P., and I. R. McDonald. 1986. Theory of Simple Liquids. Academic Press, London.
52. Chandler, D., J. D. Weeks, and H. C. Andersen. 1983. van der Waals picture of liquids, solids, and phase transformations. Science. 220:787-794.
53. Hoover, W. G., S. G. Gray, and K. W. Johnson. 1971. Thermodynamic properties of the fluid and solid phases for inverse power potentials. J. Chem. Phys. 55:1128-1136.
54. Hopfinger, A. J. 1973. Conformational Properties of Macromolecules. Academic Press, New York.
55. rd ed.. W. H. Freeman Press, San Francisco.
56. Slater, J. C., and J. G. Kirkwood. 1931. The van der Waals forces in gases. Phys. Rev. 37:682-696.
57. Stillinger, F. H., and T. A. Weber. 1985. Inherent structure theory of liquids in the hard-sphere limit. J. Chem. Phys. 83:4767-4775.
58. Pappu, R. V., and G. D. Rose. 2002. A simple model for poly-proline II structure in unfolded states of alanine-based peptides. Protein Sci. 11:2437-2455.
59. Engh, R. A., and R. Huber. 1991. Accurate bond and angle parameters for X-ray protein structure refinement. Acta Crystallogr. 47:392-400.
60. Frenkel, D., and B. Smit. 2002. Understanding Molecular Simulation. From Algorithms to Applications. Academic Press, London, UK.
61. Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. 1953. Equation of state calculations by fast computing machines. J. Chem. Phys. 21:1087-1092.
62. Glatter, O., and O. Kratky. 1982. Small Angle X-Ray Scattering. Academic Press, London.
63. Doniach, S. 2001. Changes in biomolecular conformation seen by small angle X-ray scattering. Chem. Rev. 101:1763-1778.
64. Higgins, J. L., and H. C. Benoit. 1994. Polymers and Neutron Scattering. Oxford Science Publications, Clarendon Press, Oxford.
65. Steinhauser, M. O. 2005. A molecular dynamics study on universal properties of polymer chains in different solvent qualities. Part I. A review of linear chain properties. J. Chem. Phys. 122:094901.
66. Dima, R. I., and D. Thirumalai. 2004. Asymmetry in the shapes of folded and denatured states of proteins. J. Phys. Chem. B. 108:6564-6570.
67. Jackson, S. E. 1998. How to small single-domain proteins fold? Fold. Des. 3:R81-R91.
68. Plaxco, K. W., K. T. Simons, I. Ruczinski, and D. Baker. 2000. Topology, stability, sequence, and length: defining the determinants of two-state protein folding kinetics. Biochemistry. 39:11177-11183.
69. Lumry, R., and R. Biltonen. 1966. Validity of the "two-state" hypothesis for conformational transitions for proteins. Biopolymers. 4:917-944.
70. Jackson, W. M., and J. F. Brandts. 1970. Thermodynamics of protein denaturation. A calorimetric study of the reversible denaturation of chymotrypsinogen and conclusions regarding the validity of the two-state approximation. Biochemistry. 9:2294-2301.
71. Gillespie, J., and D. Shortle. 1997. Characterization of long-range structure in the denatured state of staphylococcal nuclease. 1. Paramagnetic relaxation enhancement by nitroxide spin labels. J. Mol. Biol. 268:158-169.
72. Kristjansdottir, S., K. Lindorff-Larsen, W. Fieber, C. M. Dobson, M. Vendruscolo, and F. M. Poulsen. 2005. Formation of native and non-native interactions in ensembles of ACBP molecules from paramagnetic spin relaxation enhancement studies. J. Mol. Biol. 347:1053-1062.
73. Lindorff-Larsen, K., S. Kristjansdottir, K. Teilum, W. Fieber, C. M. Dobson, F. M. Poulsen, and M. Vendruscolo. 2004. Determination of an ensemble of structures representing the denatured state of the bovine acyl-coenzyme A binding protein. J. Am. Chem. Soc. 126:3291-3299.
74. Chattopadhyay, K., S. Safarian, E. L. Elson, and C. Frieden. 2005. Measuring unfolding of proteins in the presence of denaturant using fluorescence correlation spectroscopy. Biophys. J. 88:1413-1422.
75. McCarney, E. R., J. H. Werner, S. L. Bernstein, I. Ruczinski, D. E. Makarov, P. M. Goodwin, and K. W. Plaxco. 2005. Site-specific dimensions across a highly denatured protein: A single molecule study. J. Mol. Biol. 352:672-682.
76. Sinha, K. K., and J. B. Udgaonkar. 2005. Dependence of the size of the initially collapsed form during the refolding of barstar on denaturant concentration: Evidence for a continuous transition. J. Mol. Biol. 353:704-718.
77. Bhavesh, N. S., J. Juneja, J. B. Udgaonkar, and R. V. Hosur. 2004. Native and nonnative conformational preferences in the urea-unfolded state of barstar. Protein Sci. 13:3085-3091.
78. Zagrovic, B., and V. S. Pande. 2003. Structural correspondence between the α-helix and the random-flight chain resolves how unfolded proteins can have native-like properties. Nat. Struct. Biol. 10:955-961.
79. Thirumalai, D., and B.-Y. Ha. 1998. Statistical mechanics of semi-flexible chains: A mean field variational approach. In Theoretical and Mathematical Models in Polymer Research. A. Grosberg, editor. Academic Press, Boston. 1-35.
80. Damaschun, G., H. Damaschun, K. Gast, R. Misselwitz, J. J. Muller, W. Pfeil, and D. Zirwer. 1993. Cold denaturation-induced conformational changes in phosphoglycerate kinase from yeast. Biochemistry. 32:7739-7746.
81. Schwalbe, H., K. M. Fiebig, M. Buck, J. A. Jones, S. B. Grimshaw, A. Spencer, S. J. Glaser, L. J. Smith, and C. M. Dobson. 1997. Structural and dynamical properties of a denatured protein. Heteronuclear 3D NMR experiments and theoretical simulations of lysozyme in 8M urea. Biochemistry. 36:8977-8991.
82. Damaschun, G., H. Damaschun, K. Gast, and D. Zirwer. 1999. Proteins can adopt totally different folded conformations. J. Mol. Biol. 291:715-725.
83. Schwarzinger, S., P. E. Wright, and H. J. Dyson. 2002. Molecular hinges in protein folding: The urea-denatured state of apomyoglobin. Biochemistry. 41:12681-12686.
84. Mohana-Borges, R., N. K. Goto, G. J. A. Kroon, H. J. Dyson, and P. E. Wright. 2004. Structural characterization of unfolded states of apomyoglobin using residual dipolar couplings. J. Mol. Biol. 340:1131-1142.
85. Ohkubo, Y. Z., and C. L. Brooks. 2003. Exploring Flory's isolated-pair hypothesis: statistical mechanics of helix-coil transitions in polyalanine and the C-peptide from RNase A. Proc. Natl. Acad. Sci. USA. 100:13916-13921.
86. Thompson, J. B., H. G. Hansma, P. K. Hansma, and K. W. Plaxco. 2002. The backbone conformational entropy of protein folding: experimental measures from atomic force microscopy. J. Mol. Biol. 322:645-652.
87. Richards, F. M. 1977. Areas, volumes, packing and protein structure. Annu. Rev. Biophys. Bioeng. 6:151-176.
88. Zhou, Y., D. Vitkup, and M. Karplus. 1999. Native proteins are surface-molten solids: application of the Lindemann criterion for the solid versus liquid state. J. Mol. Biol. 285:1371-1375.
89. Liang, J., and K. A. Dill. 2001. Are proteins well packed? Biophys. J. 81:751-766.
90. Myers, J. K., C. N. Pace, and J. M. Scholtz. 1995. Denaturant m-values and heat capacity changes: relation to changes in accessible surface areas of protein unfolding. Protein Sci. 4:2138-2148.
91. Khokhlov, A. R. 1981. Influence of excluded volume effect on the rates of polymer-polymer interactions. Macromol. Rapid Commun. 2:633-636.
92. Grosberg, A. Y., P. G. Khalatur, and A. R. Khokhlov. 1983. Polymer coils with excluded volume in dilute solution: The invalidity of the model of impenetrable spheres and the influence of excluded volume on the rates of diffusion-controlled intermolecular reactions. Macromol. Rapid Commun. 3:709-713.
93. Leavell, M. D., P. Novak, C. R. Behrens, J. S. Schoeniger, and G. H. Kruppa. 2004. Strategy for selective chemical cross-linking of tyrosine and lysine residues. J. Am. Soc. Mass Spectrom. 15:1604-1611.
94. Ohnishi, S., A. L. Lee, M. H. Edgell, and D. Shortle. 2004. Direct demonstration of structural similarity between native and denatured eglin C. Biochemistry. 43:4064-4070.
95. Ackerman, M. S., and D. Shortle. 2002. Robustness of the long-range structure in denatured staphylococcal nuclease to changes in amino acid sequence. Biochemistry. 41:13791-13797.
96. Hodsdon, M. E., and C. Frieden. 2001. Intestinal fatty acid binding protein: The folding mechanism as determined by NMR studies. Biochemistry. 40:732-742.
97. Klein-Seetharaman, J., M. Oikawa, S. B. Grimshaw, J. Wirmer, E. Duchardt, T. Ueda, T. Imoto, L. J. Smith, C. M. Dobson, and H. Schwalbe. 2002. Long-range interactions within a non-native protein. Science. 295:1719-1722.
98. Koepf, E. K., H. M. Petrassi, M. Sudol, and J. W. Kelly. 1999. An isolated three-stranded antiparallel b-sheet domain that unfolds and refolds reversibly: Evidence for a structured hydrophobic cluster in urea and GdnHCl and a disordered thermal unfolded state. Protein Sci. 8:841-853.
99. Ferguson, N., R. Day, C. M. Johnson, M. D. Allen, V. Daggett, and A. R. Fersht. 2005. Simulation and experiment at high temperatures: ultrafast folding of a thermophilic protein by nucleation-condensation. J. Mol. Biol. 347:855-870.
100. Fitzkee, N. C., and G. D. Rose. 2004. Reassessing random-coil statistics in unfolded proteins. Proc. Natl. Acad. Sci. USA. 101:12497-12502.
101. Fitzkee, N. C., and G. D. Rose. 2005. Sterics and solvation winnow accessible conformational space for unfolded proteins. J. Mol. Biol. 353:873-887.
102. II conformation. J. Am. Chem. Soc. 125:8092-8093.
103. Li, H., and C. Frieden. 2005. Phenylalanine side chain behavior of the intestinal fatty acid-binding protein: the effect of urea on backbone and side chain stability. J. Biol. Chem. 280:38556-38561.
104. Plaxco, K. W., K. T. Simons, and D. Baker. 1998. Contact order, transition state placement, and the refolding rates of single domain proteins. J. Mol. Biol. 277:985-994.
105. Shea, J.-E., J. N. Onuchic, and C. L. Brooks. 1999. Exploring the origins of topological frustration: design of a minimally frustrated fragment of the B domain of protein A. Proc. Natl. Acad. Sci. USA. 96:12512-12517.
106. Clementi, C., P. A. Jennings, and J. N. Onuchic. 2000. How native-state topology affects the folding of dihydrofolate reductase and interleukin-1β. Proc. Natl. Acad. Sci. USA. 97:5871-5876.
107. Go, N. 1983. Theoretical studies of protein folding. Annu. Rev. Biophys. Bioeng. 12:183-210.
108. Fisher, M. E. 1966. Shape of a self-avoiding walk of a polymer chain. J. Chem. Phys. 44:616-622.
109. McKenzie, D. S., and M. A. Moore. 1971. Shape of a self-avoiding walk or polymer chain. J. Phys. A. Math. Gen. 4:L82-L86.
110. McKenzie, D. S. 1973. The end-to-end length distribution of self-avoiding walks. J. Phys. A.: Math. Nucl. Gen. 6:338-352.
111. des Cloizeaux, J. 1974. Lagrangian theory of a self-avoiding random chain. Phys. Rev. A. 10:1665-1669.
112. Bishop, M., and J. H. R. Clarke. 1991. Investigation of the end-to-end distance distribution function for random and self-avoiding walks in two and three dimensions. J. Chem. Phys. 94:3936-3942.
113. Valleau, J. P. 1996. Distribution of end-to-end length of an excluded volume chain. J. Chem. Phys. 104:3071-3074.
114. Zhou, H.-X. 2002. Dimensions of denatured protein chains from hydrodynamic data. J. Phys. Chem. B. 106:5769-5775.
115. Zhou, H.-X. 2002. A Gaussian-chain model for treating residual charge-charge interactions in the unfolded state of proteins. Proc. Natl. Acad. Sci. USA. 99:3569-3574.
116. Zhou, H.-X. 2003. Direct test of the Gaussian-chain model for treating residual charge-charge interactions in the unfolded state of proteins. J. Am. Chem. Soc. 125:2060-2061.
117. Brewer, S. H., D. M. Vu, Y. F. Tang, S. Franzen, D. P. Raleigh, and R. B. Dyer. 2005. Effect of modulating unfolded state structure on the folding kinetics of the villin headpiece subdomain. Proc. Natl. Acad. Sci. USA. 102:16662-16667.
118. Horng, J. C., J. H. Cho, and D. P. Raleigh. 2005. Analysis of pH-dependent folding and stability of histidine point mutants allows characterization of the denatured state and transition state for protein folding. J. Mol. Biol. 345:163-173.
119. Trefethen, J. M., C. N. Pace, J. M. Scholtz, and D. N. Brems. 2005. Charge-charge interactions in the denatured state influence the folding kinetics of ribonuclease Sa. Protein Sci. 14:1934-1938.
120. Cho, J. H., and D. P. Raleigh. 2005. Mutational analysis demonstrates that specific electrostatic interactions can play a key role in the denatured ensembles of proteins. J. Mol. Biol. 353:174-185.
121. Li, Y., F. Picart, and D. P. Raleigh. 2005. Direct characterization of the folded, unfolded, and urea-denatured states of the C-terminal domain of the ribosomal protein L9. J. Mol. Biol. 349:839-846.
122. Cho, J. H., S. Sato, and D. P. Raleigh. 2004. Thermodynamics and kinetics of non-native interactions in protein folding: a single point mutant significantly stabilizes the N-terminal domain of L9 by modulating non-native interactions in the denatured state. J. Mol. Biol. 338:827-837.
123. Reference deleted in proof.
124. Jha, A. K., A. Colubri, K. F. Freed, and T. R. Sosnick. 2005. Statistical coil model of the unfolded state: resolving the reconciliation problem. Proc. Natl. Acad. Sci. USA. 102:13099-13104.
125. Jha, A. K., A. Colubri, M. H. Zaman, S. Koide, T. R. Sosnick, and K. F. Freed. 2005. Helix, sheet, and polyproline II frequencies and strong nearest neighbor effects in a restricted coil library. Biochemistry. 44:9691-9702.
126. Goldenberg, D. P. 2003. Computational simulation of the statistical properties of unfolded proteins. J. Mol. Biol. 326:1615-1633.
127. Ding, F., R. K. Jha, and N. V. Dokholyan. 2005. Scaling behavior and structure of denatured proteins. Structure. 13:1047-1054.
128. Smith, L. J., K. A. Bolin, H. Schwalbe, M. W. MacArthur, J. M. Thornton, and C. M. Dobson. 1996. Analysis of main chain torsion angles in proteins: prediction of NMR coupling constants for native and random coil conformations. J. Mol. Biol. 255:494-506.
129. Creamer, T. P., R. Srinivasan, and G. D. Rose. 1995. Modeling unfolded proteins of peptides and proteins. Biochemistry. 34:16245-16250.
130. Shortle, D., and M. S. Ackerman. 2001. Persistence of native-like topology in a denatured protein in 8M urea. Science. 293:487-489.
131. Choy, W. Y., and J. D. Forman-Kay. 2001. Calculation of ensembles of structures representing the unfolded state of an SH3 domain. J. Mol. Biol. 308:1011-1032.
132. McCarney, E. R., J. E. Kohn, and K. W. Plaxco. 2005. Is there or isn't there? The case for (and against) residual structure in chemically denatured proteins. Crit. Rev. Biochem. Mol. Biol. 40:181-189.
133. Rose, G. D. Getting to know u. 2002. Adv. Protein. Chem. 62:xv-xxi.
134. Zagrovic, B., C. D. Snow, S. Khaliq, M. R. Shirts, and V. S. Pande. 2002. Native-like mean structure in the unfolded ensemble of small proteins. J. Mol. Biol. 323:153-164.
135. Lakshmikanth, G. S., K. Sridevi, G. Krishnamoorthy, and J. B. Udgaonkar. 2001. Structure is lost incrementally during the unfolding of barstar. Nat. Struct. Biol. 8:799-804.
136. Feibig, K. M., H. Schwalbe, M. Buck, L. J. Smith, and C. M. Dobson. 1996. Toward a description of the conformations of denatured states of proteins. Comparison of a random coil model with NMR measurements. J. Phys. Chem. B. 100:2661-2666.
137. Calmettes, P., D. Durand, M. Desmadril, P. Minard, V. Receveur, and J. C. Smith. 1994. How random is a highly denatured protein. Biophys. Chem. 53:105-113.
138. Whittington, S. J., B. W. Chellgren, V. M. Hermann, and T. P. Creamer. 2005. Urea promotes polyproline II helix formation: implications for protein denatured states. Biochemistry. 44:6269-6275.