Pressure- and Urea-Induced Denaturation of Bovine Serum Albumin: Considerations about Protein Heterogeneity

Douglas Ricardo Norberto, Joelma Mauricio Vieira, Ancelmo Rabelo de Souza, Jose Ailton Conceicao Bispo, Carlos Francisco Sampaio Bonafe

.

DOI: 10.4236/ojbiphy.2012.21002                

Abstract

Urea denatures proteins at different concentrations, depending on the experimental conditions and the protein. We in-vestigated the pressure-induced denaturation of bovine serum albumin (BSA) in the presence of subdenaturing concen-trations of urea based on a two-state equilibrium. Pressure-induced denaturation was enhanced at urea concentrations ([U]) of 3.5 M to 8.0 M, with the free energy of denaturation at atmospheric pressure ranging from +5.0 to –2.5 kJ/mol of BSA. The m values appeared to be biphasic, with m1 and m2 of 0.92 and 2.35 kJ mol–1?M–1, respectively. Plots of versus ln[U] yielded values of u, the apparent stoichiometric coefficient, of 1.68 and 6.67 mol of urea/mol of BSA for m1 and m2, respectively. These values were compared with the m and u values of other monomeric proteins reported in or calculated from the literature. The very low values of u systematically observed for proteins were suggestive of heterogeneity in the free energy of denaturation. Thus, a u value of 140 mol of urea/mol of BSA may indicate the existence of a heterogeneous molecular population with respect to the free energy of dena-turation.

Keywords

Apparent Stoichiometric Coefficient; Bovine Serum Albumin; High Pressure-Induced Denaturation; Protein Heterogeneity; Urea-Induced Denaturation

1. Introduction

Knowledge of protein denaturation is fundamental for understanding numerous biological processes. Historically, this phenomenon has been studied by using denaturing agents such as urea and guanidine hydrochloride [1]. Denaturation can also be induced by an increase in temperature, which leads to the weakening of interactions in the proteins and consequent exposure of previously hidden hydrophobic groups. In contrast, the use of pressure favors processes that involve a negative change in volume, such as the transfer of solvent to the hydrophobic core of proteins that disturbs hydrophobic interactions between nonpolar side chains, resulting in denaturation. The hydration of internal groups within a protein can also contribute to a change in volume in the unfolded state [2]. High hydrostatic pressure increases the susceptibility to urea induced denaturation and allows the determination of thermodynamic parameters such as the change in volume associated with denaturation and the free energy of denaturation [3,4].

More recently, hydrostatic pressure and urea have been used to study the dissociation and denaturation of proteins and viruses. Hydrostatic pressure is particularly useful for studying viral inactivation, especially with regard to its application in the development of vaccines [5]. High pressure has been used to determine the thermodynamic parameters and properties of dissociation in multimeric proteins [3,4] and the conditions of reassociation [6]. Previous work examined the effect of protons and pressure on the dissociation of tobacco mosaic virus (TMV) and giant multimeric hemoglobin, with the quantification and stoichiometric analysis of proton release [7,8]. Similar experiments in the presence of urea concentrations up to 7.0 M demonstrated a significantly greater involvement of urea in denaturation than in dissociation. The initial step of TMV dissociation can be clearly identified by light scattering, whereas the denaturation phases can be monitored by changes in the fluorescence properties [4]. Similar fluorescence and light scattering measurements at various urea concentrations have been reported for other viruses. Most values for the apparent stoichiometry of urea during dissociation range from 0.5 mol to 1.5 mol of urea/mol of subunit, while those for denaturation range from 4.0 to 11.0 mol of urea/mol of subunit [4]. Studies of protein denaturation have examined protein-solvent interactions during the denaturation transition [9-15]. More recently, Auton and Bolen [16] suggested that the peptide backbone provided a major contribution to urea-induced denaturation.

Several decades ago it was shown that the analysis of plots of the DG⁰ of denaturation versus ln of the denaturant concentration systematically yielded a very low value for the stoichiometry of the denaturant during protein denaturation, with the final equilibrium being considered as a reaction involving protein and denaturant. These lower-than-expected values led to alternative ways of analyzing protein denaturation. For example, in studies of protein denaturation by chemicals, an important point is whether the free energy of denaturation should be considered to be linearly dependent on [D] (denaturant concentration) or ln[D]. Pace [17] described a theoretical approach based on a linear relationship that has since been applied to most of the proteins investigated. However, Schellman [18] observed that there was no reason to expect the free energy of protein denaturation to be strictly linear with the denaturant concentration.

The aim of this work was to investigate whether the denaturation of bovine serum albumin (BSA) by urea and pressure was linearly or logarithmically related to the urea concentration. This relationship was assessed by calculating the m-values and several other thermodynamic parameters. In contrast to the 2130 capsid subunits associated with the RNA of TMV, BSA is a monomeric protein and therefore a much simpler system. Our results were compared with those for other monomeric proteins reported in the literature. Based on our findings, we propose an alternative explanation for the very low value consistently found in plots of the DG⁰ of denaturation versus ln[D], i.e., that this discrepancy is based on the heterogeneity of the DG⁰ of denaturation in protein populations.

2. Materials and Methods

2.1. Chemicals

All reagents were of analytical grade. Distilled water was filtered and deionized through a Millipore water puri- fication system (18 MΩ resistance). Unless stated otherwise, the experiments were done at 5˚C in 100 mMTrisHCl buffer, pH 7.0. Ultrapure urea and essentially fatfree BSA were obtained from Sigma. The concentration of urea used varied from 3.5 M to 8.0 M.

2.2. Fluorescence under Pressure

The high pressure system used has been described elsewhere [19]. An ISS model high-pressure (HP) cell with sapphire windows connected to a pressure generator (HIP) was used, with pressures of up to 250 MPa being studied. Fluorescence was recorded with an Edinburgh FL 900 spectrofluorometer equipped with a xenon lamp source. The pressure system was automated and detailed by Santos et al. [7]. The fluorescence data were obtained by excitation of BSA at 280 nm and emission was recorded at 300 nm - 450 nm. Changes in the fluorescence spectra resulting from the exposure of tryptophan residues were quantified by the spectral center of mass (n_p),

(1)

where F_i is the fluorescence emitted at wave number n_i and the summation is carried out over the range of appreciable values of F. The degree of denaturation at pressure p(a_p) is related to n by the expression

(2)

where Q is the ratio of the quantum yields of denatured and native forms, n_p is the center of mass at pressure p, and n_des and n_n are the corresponding quantities for the denatured and native forms, respectively [3]. The software “Mathematica” was used to obtain the fitted curves of denaturation.

2.3. Theory

Equilibrium denaturation profiles were analyzed based on the binding equilibrium for the interaction of protein with the solvent and by using a two-state model (see Discussion below). Since the conformation of denatured proteins changes with the concentration of urea and guanidine hydrochloride, the evaluation of over a large solvent concentration range can be quite informative [18, 20].

Analysis of the effect of urea on BSA in this work was done by using an approach similar to that previously described for the effect of this co-solvent and protons on protein aggregates [4,7,8]. Thus, the apparent constant of denaturation at urea concentration [U], K_[U], is correlated to the apparent constant of denaturation K as K_[U] = K[U]^u [4]. The corresponding apparent free energy of denaturation on a molar basis, , is given by:

(3)

where U₁ indicates a urea concentration of 1 M and u is the apparent stoichiometry of urea. Note that the equilibrium constant at 1 M urea, , is equal to K * 1^u = K, so.

Plotting versus ln[U] should produce a straight line with a slope corresponding to –uRT. Calculation of the equilibrium constant at pressure p and a given urea concentration [U], K_[U],p, is based on the relationship [4]

(4)

where DV is the volume change associated with denaturation and the index [U], p represents the corresponding urea concentration and pressure. The calculation of K_[U],p can be done based on the respective degree of denaturation, a_[U],p, as

(5)

The Equation (5) thus yields the denaturation constant K. The logarithmic form of Equation (4) furnishes the respective free energy of denaturation at pressure p

(6)

Plotting DG_[U],p versus p furnishes DV as the slope and as the free energy of denaturation at atmospheric pressure. A marked change in the slope of the plot versus ln[U] at different urea concentrations is indicative of distinct urea sensitivities. Consequently, the overall or global denaturation reflects a summation of the responses of a population of BSA molecules with different susceptibilities and furnishes the general equilibrium constant K_i[U]^u, where K_i,[U]= K_i[U]^u and i represents each BSA population.

Based on this idea, the experimental data correspond to the sum of the distinct populations involved and the degree of denaturation a^* is partitioned as follows

(7)

where the coefficient f_i represents the fraction of species i. The corresponding free energy of denaturation as a function of the equilibrium constants is expressed as

(8)

This alternative approach for assessing denaturation is based on the assumption of a heterogeneous protein population. As will be seen, this approach yields high values of u^*.

3. Results

We investigated the changes in the fluorescence of BSA at different concentrations of urea and pressure (Figure 1)

and attempted to correlate them with structural alterations. Compared to the fluorescence emission spectrum obtained in the absence of urea, a high urea concentration produced a significant red shift that intensified as the hy-

Figure 1. Normalized fluorescence spectra of BSA at several urea concentrations and pressures, expressed in wave number. Excitation at 285 nm and emission at 300 nm - 450 nm. The BSA concentration was 0.5 mg/mL in 100 mMTrisHCl buffer, pH 7.4, at 22˚C. Curve a: no urea and atmospheric pressure, curve b: 7.0 M urea and atmospheric pressure, curve c: 7.0 M urea and 250 MPa, and curve d: 7.0 M urea and atmospheric pressure after return from 250 MPa. A.U. = arbitrary units.

drostatic pressure increased. The fluorescence spectrum obtained after returning to atmospheric pressure was very similar to that obtained before the increase in pressure, indicating that the phenomenon was reversible under these experimental conditions.

The centers of mass of the fluorescence emission spectra for BSA measured in wavenumber and calculated according to Equation (1) yielded values that revealed the degree of exposure of aromatic amino acids, especially tryptophan. This parameter reflects the extent of denaturation. The effect of pressure on the center of mass at urea concentrations up to 8.0 M is shown in Figure 2(a). Pressure produced a marked red shift in the fluorescence spectra at all urea concentrations, indicating enhanced denaturation in the presence of urea. The center of mass values obtained upon returning to atmospheric pressure were identical to those obtained before pressure application for all urea concentrations (not shown), indicating that the pressure-induced denaturation was reversible. This finding also corroborated the validity of the thermodynamic parameters obtained.

The inset in Figure 2(a) shows the effect of urea on the center of mass values at different pressures. A more intense red shift was observed in the fluorescence spectra at lower pressures. Figure 2(b) shows the respective correlation between the degree of denaturation and pressure at different urea concentrations by applying Equation (2) to the fluorescence data, and Figure 2(b) shows the corresponding plots of lnK versus pressure.

Figure 3 shows the free energy of denaturation at different pressures as a function of urea concentration

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	C. Camilloni, A. G. Rocco, I. Eberini, E. Gianazza, R. A. Broglia and G. Tiana, “Urea and Guanidinium Chloride Denature Protein L in Different Ways in Molecular Dynamics Simulations,” Biophysical Journal, Vol. 94, Mo. 12, 2008, pp. 4654-4661.
[2]	K. L. Schweiker, V. W. Fitz and G. I. Makhatadze, “Universal Convergence of the Specific Volume Changes of Globular Proteins upon Unfolding,” Biochemistry, Vol. 48, No. 46, 2009, pp. 10846-10851. doi:10.1021/bi901220u
[3]	C. F. S. Bonafe, C. M. R. Vital, R. C. B. Telles, M. C. Gon?alves, M. S. A. Matsuura, F. B. T. Pessine, D. R. C. Freitas and J. Vega, “Tobacco Mosaic Virus Disassembly by High Hydrostatic Pressure in Combination with Urea and Low Temperature,” Biochemistry, Vol. 37, No. 31, 1998, pp. 11097-11105. doi:10.1021/bi980349n
[4]	J. L. R. Santos, R. Aparicio, I. Joekes, J. L. Silva, J. A. C. Bispo and C. F. S. Bonafe, “Different Urea Stoichiometries between the Dissociation and Denaturation of Tobacco Mosaic Virus as Probed by Hydrostatic Pressure,” Biophysical Chemistry, Vol. 134, No. 3, 2008, pp. 214-224. doi:10.1016/j.bpc.2008.02.010
[5]	C. F. S. Bonafe, M. Glaser, E. W. Voss, G. Weber and J. L. Silva, “Virus Inactivation by Anilinonaphthalene Sulfonate Compounds and Comparison with Other Ligands,” Biochemical and Biophysical Research Communications, Vol. 275, No. 3, 2000, pp. 955-961. doi:10.1006/bbrc.2000.3402
[6]	C. F. S. Bonafe, M. Villas-Boas, M. C. Suarez and J. L. Silva, “Reassembly of a Large Multisubunit Protein Promoted by Nonprotein Factors. Effects of Calcium and Glycerol on the Association of Extracellular Hemoglobin,” Journal Biological Chemistry, Vol. 266, 1991, pp. 13210-13216.
[7]	J. L. R. Santos, J. A. C. Bispo, G. F. Landini and C. F. S. Bonafe, “Proton Dependence of Tobacco Mosaic Virus Dissociation by Pressure,” Biophysical Chemistry, Vol. 111, No. 1, 2004, pp. 53-61. doi:10.1016/j.bpc.2004.04.003
[8]	J. A. C. Bispo, J. L. R. Santos, G. F. Landini, J. M. Gon?alves and C. F. S. Bonafe, “pH Dependence of the Dissociation of Multimeric Hemoglobin Probed by High Hydrostatic Pressure,” Biophysical Chemistry, Vol. 125, 2007, No. 2-3, pp. 341-349.
[9]	R. Simpson and W. Kauzmann, “The Kinetics of Protein Denaturation, 1. The Behavior of the Optical Rotation of Ovalbumin in Urea Solutions,” Journal of the American Chemical Society, Vol. 75, 1953, pp. 5139-5152. doi:10.1021/ja01117a001
[10]	C. Tanford, “Physical Chemistry of Macromolecules,” John Wiley & Sons, New York, 1961.
[11]	J. Wyman, “Linked Functions and Reciprocal Effects in Hemoglobin—A Second Look,” Advances in Protein Chemistry, Vol. 19, 1964, pp. 223-286.
[12]	J. A. Schellman, “Solvent Denaturation,” Biopolymers, Vol. 17, 1978, pp. 1305-1322. doi:10.1002/bip.1978.360170515
[13]	J. A. Schellman, “Macromolecular Binding,” Biopolymers, Vol. 14, No. 5, 1975, pp. 999-1018. doi:10.1002/bip.1975.360140509
[14]	I. V. Baskakov and D. W. Bolen, “Monitoring the Sizes of Denatured Ensembles of Staphylococcal Nuclease Proteins: Implications Regarding M Values, Intermediates, and Thermodynamics,” Biochemistry, Vol. 37, 1998, pp. 18010-18017. doi:10.1021/bi981849j
[15]	Y. Kita, T. Arakawa, T. Y. Lin and S. N. Timasheff, “Contribution of the Surface Free Energy Perturbation to Protein-Solvent Interactions,” Biochemistry, Vol. 33, No. 50, 1994, pp. 15178-15189. doi:10.1021/bi00254a029
[16]	M. Auton and D. W. Bolen, “Predicting the Energetics of Osmolyte-Induced Protein Folding/Unfolding,” Proceedings of the National Academy of Sciences, Vol. 102, No. 42, 2005, pp. 15065-15068. doi:10.1073/pnas.0507053102
[17]	R. F. Greene and C. N. Pace, “Urea and Guanidine Hydrochloride Denaturation of Ribonuclease, lysozyme, a-Chymotrypsin, and β-Lactoglobulin,” Journal of Biological Chemistry, Vol. 249, No. 17, 1974, pp. 5388-5393.
[18]	J. A. Schellman, “The Thermodynamic Stability of Proteins,” Annual Review of Biophysics and Biophysical Chemistry, Vol. 16, No. 1, 1987, pp. 115-137. doi:10.1146/annurev.bb.16.060187.000555
[19]	A. A. Paladini and G. Weber, “Absolute Measurements of Fluorescence Polarization at High Pressures,” Review of Scientific Instruments, Vol. 52, No. 3, 1981, pp. 419-427. doi:10.1063/1.1136596
[20]	J. A. Schellman, “Protein Stability in Mixed Solvents: A Balance of Contact Interaction and Excluded Volume,” Biophysical Journal, Vol. 85, No. 1, 2003, pp. 108-125. doi:10.1016/S0006-3495(03)74459-2
[21]	E. F. Casassa and H. Eisenberg, “Thermodynamic Analysis of Multicomponent Solutions,” Advances in Protein Chemistry, Vol. 19, 1964, pp. 287-395. doi:10.1016/S0065-3233(08)60191-6
[22]	E. P. Hade and C. Tanford, “Isopiestic Compositions as a Measure of Preferential Interactions of Macromolecules in Two-Component Solvents. Application to Proteins in Concentrated Aqueous Cesium Chloride and Guanidine Hydrochloride,” Journal of the American Chemical Society, USA, Vol. 89, No. 19, 1967, pp. 5034-5040. doi:10.1021/ja00995a036
[23]	I. V. Baskakov and D. W. Bolen, “The Paradox between M Values and Delta Cp’S for Denaturation of Ribonuclease T1 with Disulfide Bonds Intact and Broken,” Protein Science, Vol. 8, No. 6, 1999, pp. 1314-1319. doi:10.1110/ps.8.6.1314
[24]	P. Banerjee, S. Pramanik, A. Sarkar and S. C. Bhattacharya, “Deciphering the Fluorescence Resonance Energy Transfer Signature of 3-Pyrazolyl 2-Pyrazoline in Transport Proteinous Environment,” Journal of Physical Chemistry B, Vol. 113, No. 33, 2009, pp 11429-11436. doi:10.1021/jp811479r
[25]	H. Wu, P. Wang, X. Hu, Z. Dai and X. Zou, “Site-Selective Probe for Investigating the Asynchronous Unfolding of Domains in Bovine Serum Albumin,” Talanta, Vol. 84, No. 3, 2011, pp. 881-886. doi:10.1016/j.talanta.2011.02.027
[26]	R. Kumaran and P. Ramamurthy, “Denaturation Mechanism of Bsa by Urea Derivatives: Evidence for Hydrogen-Bonding Mode from Fluorescence Tools,” Journal of Fluorescence, Vol. 21, No. 4, 2011, pp. 1499-1508. doi:10.1007/s10895-011-0836-0
[27]	D. Barrick, “What Have We Learned from the Studies of Two-State Folders, and What Are the Unanswered Questions about Two-State Protein Folding?” Physical Biology, Vol. 6, No. 1, 2009, pp. 1-9. doi:10.1088/1478-3975/6/1/015001
[28]	D. Barrick, D. U. Ferreiro and E. A. Komives, “Folding Landscapes of Ankyrin Repeat Proteins: Experiments Meet Theory,” Current Opinion in Structural Biology, Vol. 18, No. 1, 2008, pp. 27-34. doi:10.1016/j.sbi.2007.12.004
[29]	C. N. Pace, E. J. Hebert, K. L. Shaw, D. Schell, V. Both, D. Krajcikova, J. Sevcik, K. S. Wilson, Z. Dauter, R. W. Hartley and G. R. Grimsley, “Conformational Stability and Thermodynamics of Folding of Ribonucleases Sa, Sa2 and Sa3,” Journal of Molecular Biology, Vol. 279, No. 1, 1998, pp. 271-286. doi:10.1006/jmbi.1998.1760
[30]	R. F. Latypov, T. S. Harvey, D. Liu, P. V. Bondarenko, T. Kohno, R. A. Fachini, R. D. Rosenfeld, R. R. Ketchem, D. N. Brems and A. A. Raibekas, “Biophysical Characterization of Structural Properties and Folding of Interleukin-1 Receptor Antagonist,” Journal of Molecular Biology, Vol. 368, No. 4, 2007, pp. 1187-1201. doi:10.1016/j.jmb.2007.02.031
[31]	B. Farruggia and G. A. Picó, “Thermodynamic Features of the Chemical and Thermal Denaturations of Human Serum Albumin,” International Journal of Biological Macromolecules, Vol. 26, No. 5, 1999, pp. 317-323. doi:10.1016/S0141-8130(99)00054-9
[32]	J. H. Carra, E. A. Anderson and P. L. Privalov, “Thermodynamics of Staphylococcal Nuclease Denaturation. I. the Acid-Denatured State,” Protein Science, Vol. 3, No. 6, 1994, pp. 944-951. doi:10.1002/pro.5560030609
[33]	P. Sen, B. Ahmad and R. H. Khan, “Formation of a Molten Globule Like State in Bovine Serum Albumin at Alkaline pH,” European Biophysical Journal, Vol. 37, No. 8, 2008, pp. 1303-1308. doi:10.1007/s00249-008-0335-7
[34]	M. Y. Khan, S. K. Agarwal and S. Hangloo, “Urea- Induced Structural Transformations in Bovine Serum Albumin,” The Journal of Biochemistry, Vol. 102, No. 2, 1987, pp. 313-317.
[35]	C. A. Royer, “Revisiting Volume Changes in Pressure-Induced Protein Unfolding,” Biochimica et Biophysica Acta, Vol. 1595, No. 1-2, 2002, pp. 201-209. doi:10.1016/S0167-4838(01)00344-2
[36]	I. Luque, S. Leavitt and E. Freire, “The Linkage between Protein Folding and Functional Cooperativity: Two Sides of the Same Coin?” Annual Review of Biophysics & Biomolecular Structure, Vol. 31, 2002, pp. 235-256. doi:10.1146/annurev.biophys.31.082901.134215
[37]	N. Tanaka, H. Nishizawa and S. Kunugi, “Structure of Pressure-Induced Denatured State of Human Serum Albumin: A Comparison with the Intermediate in Urea- Induced Denaturation,” Biochimica et Biophysica Acta, Vol. 1338, No. 1, 1997, pp. 13-20. doi:10.1016/S0167-4838(96)00175-6
[38]	B. Ahmad, M .K. A. Khan, S. K. Haq and R. H. Khan, “Intermediate Formation at Lower Urea Concentration in B Isomer of Human Serum Albumin: A Case Study Using Domain Specific Ligands,” Biochemical and Biophysical Research Communications, Vol. 314, No. 1, 2004, pp. 166-173. doi:10.1016/j.bbrc.2003.12.069
[39]	B. Ahmad, Ankita and R. H. Khan, “Urea Induced Unfolding of F Isomer of Human Serum Albumin: A Case Study Using Multiple Probes,” Archives of Biochemistry and Biophysics, Vol. 437, No. 2, 2005, pp. 159-167. doi:10.1016/j.abb.2005.03.013
[40]	D. A. Egan, T. M. Logan, H. Liang, E. Matayoshi, S. W. Fesik and T. F. Holzman, “Equilibrium Denaturation Of Recombinant Human FK Binding Protein in Urea,” Biochemistry, Vol. 32, No. 8, 1993, pp. 1920-1927. doi:10.1021/bi00059a006
[41]	C. N. Pace, “Determination and Analysis of Urea and Guanidine Hydrochloride Denaturation Curves,” Methods in Enzymology, Vol. 131, 1986, pp. 266-280. doi:10.1016/0076-6879(86)31045-0
[42]	C. N. Pace, D. V. Laurents and R. E. Erickson, “Urea Denaturation of Barnase: Ph Dependence and Characterization of the Unfolded State,” Biochemistry, Vol. 31, No. 10, 1992, pp. 2728-2734. doi:10.1021/bi00125a013
[43]	M. H. Brumano and M. G. Oliveira, “Urea-Induced Denaturation of b-trypsin: An Evidence for a Molten Globule State,” Protein and Peptide Letters, Vol. 11, No. 2, 2004, pp. 133-140. doi:10.2174/0929866043478257
[44]	T. A. Dar, L. R. Singh, A. Islam, F. Anjum, A. A. Moo- savi-Movahedi and F. Ahmad, “Guanidinium Chloride and Urea Denaturations of b-Lactoglobulin at pH 2.0 and 25?C: The Equilibrium Intermediate Contains Non-Native Structures (Helix, Tryptophan and Hydrophobic Patches),” Biophysical Chemistry, Vol. 127, No. 3, 2007, pp. 140-148. doi:10.1016/j.bpc.2007.01.006
[45]	Y. J. Shiu, U. S. Jeng, Y. S. Huang, Y. H. Lai, H. F. Lu, C. T. Liang, I. J. Hsu, C. H. Su, C. Su, I. Chao, A. C. Su and S. H. Lin, “Global and Local Structural Changes of Cytochrome C and Lysozyme Characterized by a Multigroup Unfolding Process,” Biophysical Journal, Vol. 94, No. 12, 2008, pp. 4828-4836. doi:10.1529/biophysj.107.124214
[46]	A. R. H. Babbes, E. T. Powers and J. W. Kelly, “Quanti?cation of the Thermodynamically Linked Quaternary and Tertiary Structural Stabilities of Transthyretin And Its Disease-Associated Variants: The Relationship between Stability and Amyloidosi,” Biochemistry, Vol. 7, 2008, pp. 6969-6984. doi:10.1021/bi800636q
[47]	A. C. Ferreon and D. W. Bolen, “Thermodynamics of Denaturant-Induced Unfolding of a Protein That Exhibits Variable Two-State Denaturation,” Biochemistry, Vol. 43, No. 42, 2004, pp. 13357-13369. doi:10.1021/bi048666j
[48]	H. Kokubo, J. R?sgen, D. W. Bolen and B. M. Pettitt, “Molecular Basis of the Apparent Near Ideality of Urea Solutions,” Biophysical Journal, Vol. 93, No. 10, 2007, pp. 3392-3407. doi:10.1529/biophysj.107.114181
[49]	M. C. Stumpe and H. Grubmüller, “Interaction of Urea with Amino Acids: Implications for Urea-Induced Protein Denaturation,” Journal of the American Chemical Society, Vol. 129, No. 51, 2007, pp. 16126-16131. doi:10.1021/ja076216j
[50]	T. E. Creighton, “Toward a Better Understanding of Protein Folding Pathways,” Proceedings of the National Academy of Sciences, USA, Vol. 85, No. 14, 1988, pp. 5082-5086.