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Influence of Glycerol on the Structure and Thermal Stability of Lysozyme: A Dynamic Light Scattering and Circular Dichroism Study Alessandro Esposito,† Lucia Comez,*,†,‡ Stefania Cinelli,† Filippo Scarponi,† and Giuseppe Onori† Dipartimento di Fisica, UniVersita` di Perugia, Via Pascoli, I-06123 Perugia, Italy, and CRS SOFT INFM-CNR, c/o Dipartimento di Fisica, UniVersita` “La Sapienza”, I-00185 Roma, Italy ReceiVed: July 16, 2009; ReVised Manuscript ReceiVed: October 17, 2009
Photon correlation spectroscopy and circular dichroism have been used to study the role of hydration in the structure and thermostability of the model protein lysozyme in water-glycerol mixtures. Two cases have been considered: water-rich and glycerol-rich regimes of concentrations. We follow the thermal denaturation both by optical spectral changes and hydrodynamic radius variations. This methodology allows us to emphasize the relevant role played by hydrophobic interactions during the process in aqueous solutions and, in glycerol, to distinguish the non-cooperative melting of secondary structure, supporting the view of a protein transition to a molten globule-like state. I. Introduction Even if the concept that proteins should remain folded and active in nonaqueous solvents is counterintuitive and even if several works have stressed the uniqueness of water in its properties as solvent for biological processes, it has been recently proved that proteins are stable in organic solvents and that even multicomponent enzymes retain catalytic activity in nonaqueous solvents.1 The case of polyols is particularly relevant: it has been shown that the addition of glycerol or sucrose to a protein solution results in preferentially hydrated protein molecules and, as a consequence, in a stabilization of the native structure against thermal denaturation.2-5 The protein folding problem, which remains in fact one of the key unresolved issues in biophysics, should be also mentioned. To provide critical insights into the mechanisms and pathways of protein folding, increasing attention has been focused on protein denatured and partially folded states. It has been suggested generally that the surrounding solvent, water, is involved inextricably in the protein folding process.6 The key issue in rationalizing all these striking findings, as well as in answering the question if proteins dissolve and conduct their normal biological functions in some nonaqueous solvents, is that of protein structure and conformational stability in different solvent conditions. The physico-chemical properties of proteins depend markedly on the role of the water in various non-covalent interactions, including solvation of ionic groups and dipoles, hydrogen bonding, and hydrophobic interactions.7,8 In particular, the presence of cosolvents as sugars and polyols in aqueous solution can stabilize the protein against both chemical or physical denaturation. The mechanism regulating such a process is still an argument of scientific investigation.9 The case of lysozyme in water/glycerol mixtures is of particular interest: it has been shown that this protein correctly regains its catalytic activity even in nearly anhydrous glycerol with an efficiency comparable with that in aqueous solutions.6 In addition, a two-dimensional * To whom correspondence should be addressed. E-mail: lucia.comez@ fisica.unipg.it. † Universita` di Perugia. ‡ Universita` “La Sapienza”.
1H-NMR and circular dichroism (CD) spectroscopy study has revealed that secondary and tertiary structures of lysozyme in glycerol are similar to those observed in water10,11 and that upon heating it cooperatively unfolds not into a random coil (as in water) but apparently into a molten globule. Actually, thermal melting of lysozyme in glycerol followed by CD spectral changes indicated unfolding of the tertiary structure with a Tm of 76 °C and no appreciable loss of the secondary structure up to 85 °C. Such conformational states that are devoid of the tertiary structure but contain extensive secondary structure may be viewed as molten globulelike states.10 It was reasonably supposed that the melting of secondary structure of lysozyme in glycerol occurs for temperatures above 90 °C. In effect, in a recent differential calorimetry study it has been observed that lysozyme dissolved in glycerol undergoes an additional cooperative transition with a marginal endothermic heat effect at temperatures of 120-130 °C.12 Nevertheless, as suggested by the same authors, this transition cannot be ascribed to the loss of secondary structure of lysozyme because helix-coil transitions cannot provide the cooperation needed in the unfolding of globular proteins.13,14 Thus, the problem is still not clear and the importance of studying this second structural transition using a structurally sensitive method becomes evident. Glycerol appears as one interesting nonaqueous system to investigate the modifications in the structure and thermostability of proteins in solution. Recently, some of us have focused on lysozyme in water/glycerol mixtures to study the role of hydration in the structure, dynamics, and thermostability of this model protein.15-19 In the present work, we utilize photon correlation spectroscopy (PCS) to investigate the thermal denaturation of lysozyme in water/glycerol mixtures. The estimate of the diffusion coefficient in solution obtained from PCS experiments can be used to calculate the average hydrodynamic radius of the protein. This same technique was employed by Nicoli et al. to study the thermal denaturation of lysozyme in water20 and by Dubin et al. to investigate the denaturation of lysozyme by guanidine chloride.21 In the first work, modifications in the hydrodynamic radius were studied in the temperature range 20-70 °C at various values of pH in the range 1-3 at ionic strengths from 0.01 to 0.2 M; in the
10.1021/jp906739v 2009 American Chemical Society Published on Web 11/19/2009
Structure and Thermal Stability of Lysozyme second optical mixing spectroscopy was employed to measure the translational diffusion coefficient of lysozyme (pH 4.2 and protein concentration 1%) in buffered guanidine hydrochloride (Gdn-HCl) solutions at different concentrations of Gdn-HCl. Recently, PCS was utilized to investigate the native conformation of lysozyme in water/ethanol22 and water/glycerol mixtures.23 As a function of ethanol concentration, in the waterrich region of composition (cosolvent mole fraction less than 0.08, pH ) 3), a nontrivial behavior of the hydrodynamic radius was observed, similar to that of partial molar volume reflecting changes in the alcohol/water structure, while it was shown that the protein structure remains practically unaffected by glycerol. But, it is the first time that dynamic light scattering is used for studying the effect of glycerol on the thermal unfolding of lysozyme. Specifically, we present new PCS data on lysozymewater/glycerol mixtures and supplement them with new CD measurements in the 20-115 °C temperature range, extending to a wider interval previous CD data. For our analysis, we consider two different compositions of solutions: (i) a waterrich mixture (20% weight in glycerol) and (ii) a glycerol-rich mixture (98% weight in glycerol).
J. Phys. Chem. B, Vol. 113, No. 51, 2009 16421
Figure 1. Photon correlation function, g2(t), of lysozyme in a water-glycerol mixture (water 80 wt %) (pH 3) at T ) 30 °C: (3) experimental data; (solid line) fitting by a single-exponential function.
glycerol-rich solutions (water 2 wt %), respectively. CD results are expressed in terms of mean residual ellipticity, [θ], (deg cm2/dmol). III. Results and Discussion
II. Experimental Section Samples. Hen egg-white lysozyme was obtained from Fluka Chemie and used without further purification. Distilled, deionized water and glycerol (99.9%) from Carlo Erba were used. Samples for both PCS and CD measurements were prepared dissolving the dry powder in a 18 mM NaCl-water solution and adding concentrated HCl dropwise until the pH reached 3.0 ( 0.1, as monitored by a pH meter. At this value of pH, the protein is in the native state and it has a positive net charge. Final samples were prepared by diluting adequate volumes of protein water solution into glycerol in order to achieve mixtures of water/glycerol having the requested final compositions. The concentration of protein in the sample solution was determined by weighting the components and in some cases by spectrophotometry using the extinction coefficient of 2.63 mg-1 mL cm-1 at 280 nm. Both methods gave identical results within experimental error. The concentration used varied from 0.5 to 10% by weight. The sample was placed in a 10 mm diameter cell through a 0.22 µm filter. PCS. The cell was placed in a thermostatic bath, whose temperature was regulated within 0.1 °C by a Haake DC-50 thermostatic circulator. The effective bath temperature was also monitored during the measurement by means of a type-k thermocouple placed in the fluid near the sample. Since the relatively dilute solutions of small protein scatter light weakly, an intense laser source was required to produce an acceptable count rate. A Coherent Model 532-400 diode pumped solid state laser was used at a power of approximately 400 mW at a wavelength of 532 nm. A scattering angle of 90° was employed. The scattered light was analyzed with a Brookhaven BI 2000 autocorrelator. PCS data were collected on water-rich (water 80 wt %) and glycerol-rich (water 2 wt %) solutions in the temperatures range from 30 to 82.5 °C. CD. Circular dichroism experiments were performed on a JASCO J-810 spectropolarimeter. CD in the far-UV region (190-250 nm) was monitored using a quartz cell of 0.1 cm path length with a protein concentration of about 10 µM. CD in the near-UV region was monitored using a 1.0 cm cell with a protein concentration of about 40 µM. Spectra were collected in the 20-95 °C and 20-115 °C temperature range on water-rich solutions (water 80 wt %) and
Effect of Intermolecular Interactions on Hydrodynamic Radius of Lysozyme. When laser light is scattered from a suspension of diffusing particles, the intensity autocorrelation function of the scattered light, g2(t), decays with time exponentially to a constant background. The time constant of the decay, the correlation time τ, is given by
τ ) (2Dq2)-1
(1)
where D is the Stokes-Einstein diffusion constant
D ) kT/6πηRh
(2)
and q is the scattering wave vector
q ) (4πn/λ)sin(φ/2)
(3)
In the above, k is Boltzmann’s constant, T the temperature, η the solvent viscosity, Rh the radius of the equivalent hydrodynamic sphere (apparent hydrodynamic radius), n is the refractive index of the scattering medium, λ the wavelength, and φ the scattering angle. Lysozyme is one of the earliest characterized and most studied globular proteins. It is globular in shape with highly compact conformation. For all the water/glycerol compositions, protein concentration and temperature here investigated, the correlation functions have always been fitted by a single exponential. This is indicative of the presence of one diffusing species only. A representative PCS spectrum together with the fitting curve is shown in Figure 1. As described above, measurements of τ allow for the determination of the hydrodynamic radius Rh using eqs 1-3. Refractive index and viscosity of the mixtures, used in obtaining Rh, have been taken from literature.24,25 However, it must be noted that measured diffusion coefficients, D, can be greatly affected by interparticle interactions of the scattering system. As a consequence, the values of Rh strongly depend on protein and salt concentration, linearly decreasing, in a first approximation, as the concentration of lysozyme is increased or salt concentration decreased. Therefore, to study the dependence of the apparent hydrodynamic radius from the solution ionic strength, we performed a systematic study of Rh for lysozyme in aqueous solutions as a function of the salt concentration. Figure 2 shows the results for mixtures with NaCl concentration ranging from about 4 to 20 mM. At low ionic strengths, strong
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Figure 2. Dependence of Rh on salt concentration from 4 to 20 mM, for a 5 mg/mL lysozyme aqueous solution, pH ) 3.0, at 25 °C. The line is to guide the eye.
electrostatic repulsion dominates protein-protein interactions. With an increase in ionic strength, electrostatic repulsion is screened and Rh increases up to a constant value of about 20 Å reached approximately at 15 mM. The ratio (Rh)20mM/(Rh)4mM is found to be close to 3, equal to the factor obtained on bovine serum albumin for the reciprocal of the diffusion coefficient at similar ionic strengths.26 The estimated value of 20 Å is in agreement with literature data.22 Following these indications, all samples used for this study have been prepared by adding a quantity of salt of about 18 mM, where Coulombic repulsion between lysozyme molecules is considered to be well shielded. Another significant aspect for the experiment is the choice of the pH of the solution, which contributes in determining the state of a protein. During the last several decades there have been numerous publications on studies of pH-induced changes in proteins. It was found that at 25 °C lysozyme does not denature at any pH, and only smooth and gradual changes in the protein structure by variations of pH were observed. Smooth changes are connected with the titration of groups with a pH not very different from that of free amino acids. pH also modifies the stability of the protein, which is disturbed by a decrease in its net positive charge as the solution becomes less acidic.27 Moreover, at high pH values a growing tendency toward aggregation of unfolded lysozyme was observed,28 while at lower pH values repulsive intermolecular interactions prevent this phenomenon. In the case of PCS measurements, which are particularly sensitive to aggregation processes, the expedient to work at low pH values results very crucial. For this reason all our measurements have been done using pH ) 3.0. Thermal Unfolding of Lysozyme: CD and PCS Analysis. Lysozyme was chosen as model protein for our study because it is a typical globular protein of modest size (129 amino acid residues, molecular weight 14445), and its thermal unfolding has been shown to be a two-state process both in aqueous solution29 and in glycerol.19 CD analysis of lysozyme dissolved in a water-rich (20% glyc) and in a glycerol-rich (98% glyc) solution was carried out in the far- and near-UV region. The former reflects the secondary structure, whereas the latter arises from the tertiary structure of the protein. At ambient temperature, aqueous and glycerol farand near-UV CD spectra resulted similar, in agreement with previous observations,10 showing that secondary and tertiary structures of lysozyme are comparable, and the native structure is likely the same in both solutions (not shown). We studied the structural stability of the protein in solution by monitoring the thermal denaturation of lysozyme both at 222 nm (secondary structure) and at 288 nm (tertiary structure) (Figures 3 and 4). The influence of temperature is apparent from
Esposito et al.
Figure 3. Percentage variation of ellipticity reported for two specific wavelenghts: [∆θ/θ]222 and [∆θ/θ]288 referring, respectively, to the temperature evolution of secondary and tertiary structure of lysozyme in water-rich solution. The fitting curve with a two-state denaturation model on tertiary structure is also reported as a solid line.
Figure 4. Percentage variation of ellipticity reported for two specific wavelenghts: [∆θ/θ]222 and [∆θ/θ]288 referring, respectively, to the temperature evolution of secondary and tertiary structure of lysozyme in glycerol-rich solution. The fitting curve with a two-state denaturation model on tertiary structure is also reported as a solid line.
the very beginning of the heating of the solution, consistent with a gradual change in the premelting state of the protein followed by a cooperative transition associated with the denaturation. In accord with previous observations,10 the data show that in the aqueous sample thermal unfolding of the secondary and tertiary structures of lysozyme occurs concurrently with a Tm of about 74 °C (Figure 3). CD spectral changes for glycerol, reported in Figure 4, conversely indicate a cooperative unfolding of the tertiary structure at nearly the same melting temperature as in the aqueous sample (Tm ≈ 78 °C) and no loss of secondary structure up to 80-85 °C (Figure 3), in agreement with previous literature data.10 At higher temperatures, a noncooperative melting of secondary structure becomes incipient. A quantitative analysis of CD thermal curves was undertaken according to the two state equilibrium model N T U.30,31 To apply the two-state approximation in the analysis of the lysozyme denaturation, additional experiments were performed to check the reversibility of the thermally induced transition. Actually, it is well-known that the denaturation of small globular proteins (like lysozyme) represents a process in which essentially only two macroscopic states are displayed, native and denatured (N and U) and generally can be regarded as a two-state transition. It should emphasized that the N and U states of a protein depend on the environmental conditions (pH, temperature, solvent, etc.), but these surroundings modify the protein states gradually and cannot be considered as phase transitions,
Structure and Thermal Stability of Lysozyme
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Figure 5. CD data referring to the temperature evolution of tertiary structure of lysozyme in water-rich solution shown together with the hydrodynamic radius estimated via PCS measurements for the same solution.
i.e., as transitions between macroscopic state, but only as transitions between microscopic states, corresponding to the same macroscopic state.32 On the basis of the two-state model, the CD thermal unfolding profiles may be well approximated by the equation
∆θ ) θ
[ ]
[ ∆θθ ]
N
[ ∆θθ ]
+K
U
1+K
(4)
where [(∆θ)/(θ)]N and [(∆θ)/(θ)]U are the variation of molar ellipticities for native (N) and unfolded (U) states, respectively, and [(∆θ)/(θ)] that observed in the transition region. Here, [(∆θ)/(θ)]N and [(∆θ)/(θ)]U were assumed depend linearly on temperature. The unfolding equilibrium constant K changes with temperature as given by the following van’t Hoff equation
[ (
K(T) ) exp -
∆H 1 1 R T Tm
)]
(5)
where ∆H is the van’t Hoff unfolding enthalpy and Tm is the denaturation temperature. The thermodynamic parameters of lysozyme unfolding were provided by the least-squares fit of eq 4, together with eq 5, to the experimental unfolding profiles; the fitting curves are shown in Figure 3 and 4. It is evident that the transition profiles are well approximated by the two-state model. The values obtained from the fitting procedure are ∆H ) (400 ( 30) kJ/mol; Tm ) (78.6 ( 0.3) °C and ∆H ) (480 ( 30) kJ/mol; Tm ) (73.6 ( 0.3) °C for water 2 and 80 wt % samples respectively, in agreement with calorimetric results.12,19,29 A qualitative interpretation of our results has been achieved by comparing the different behaviors obtained from water-rich and glycerol-rich solutions by means of DC and PCS. To this end, representative results for the thermal denaturation of lysozyme in the aqueous solution obtained by light scattering are shown in Figure 5. The average protein radius as deduced from the diffusion coefficient is plotted as a function of increasing temperature, over the range 20 to 85 °C. These data show two distinct behaviors as a function of temperature: a first trend in the premelting region where continuous gradual changes of the effective hydrodynamic radius are evident and a second, major, change near the melting region. At melting, the large increase of hydrodynamic radius is observed with a trend strongly resembling the results of optical measurements. Both techniques clearly show evidence for a transition of the macromolecule from the native to a denatured state at around 74 °C. The increase of Rh occurs concurrently
with the thermal unfolding of tertiary and secondary structure (Figure 3). By comparison of the shapes of the transitions represented by the three distinct measurements, we see that they are essentially coincident. That is, the “swelling” of the macromolecule as obtained from diffusion coefficient measurements strictly follows the change in CD at 288 nm caused by the alteration in the local environments of the aromatic residues as well as the change at 222 nm caused by the variation of the secondary structure of the protein upon denaturation. In particular, the hydrodynamic radius Rh increases from 19.5 ( 0.6 Å at 30 °C to 25.4 ( 0.8 Å at 82.6 °C. The estimated variations of Rh indicate that no dramatic dismantling of lysozyme occurs. A partially open threedimensional conformation is consistent with our PCS results. Actually, lysozyme has four disulfide bonds distributed over the polypeptide chain, which limit the freedom of expansion of the polypeptide coil. The overall observed increase of Rh is about 30%, in reasonable agreement with the enhance (about 40%) of the radius of gyration calculated by SAXS measurements performed on lysozyme unfolded by urea (pH ) 2.9),33 where Rg was found as 15.3 ( 0.2 Å and 21.8 ( 0.3 Å for the native and unfolded protein, respectively. By focusing further on the premelting region, numerical results are in accordance with dielectric measurements at radiofrequencies on lysozyme aqueous solution in the temperature interval 5-55 °C (pH ) 3.5).34 From the analysis of the dielectric relaxation of the protein solution, the effective hydrodynamic radius was calculated. Interestingly, the results show that temperature causes continuous gradual changes of Rh with a trend exceptionally similar to that found in the present work by using PCS. While a conclusive explanation for the above behavior is difficult to deduce, an hypothesis can be proposed. At a first, a tentative correlation with the temperature changes in the thermodynamic parameters could be underlined. In a series of papers, Pfeil and Privalov28 presented an experimental approach to provide standard thermodynamic functions of native and denatured protein using experimental data achieved by scanning calorimetry, isothermal calorimetry, and potentiometric titration. In these papers, values of the enthalpy, entropy and Gibbs free energy (G) for native and denatured lysozyme are reported in the range 0-100 °C and pH 1.5-7.0. All these thermodynamic quantities appear to be temperature-dependent functions. In particular, the Gibbs free energy, in the native state, shows a broad maximum as a function of temperature, weekly pH dependent. Intriguingly, the same analogous trend is here observed in the hydrodynamic radius of native lysozyme in the premelting region. It is likely that these variations of free energy are possibly correlated with continuous changes of the interactions responsible for the stabilization of the native protein structure and, in particular, with the modifications of hydrophobic interactions which, as it is well-known, strongly depend on temperature. Such variations in the interactions should promote gradual changes of the protein conformational properties and of the hydration degree even in the range of physiological temperatures. The primary contribution to the strength of hydrophobic interactions derives from changes in the structure of water when nonpolar groups interact with one another. Hydrophobic interactions are believed to play an important role in stabilizing the native structure of proteins. Such interactions arise from the unique three-dimensional structure of water and should be changed considerably by variations in the solvent structure due to addition of glycerol. In fact, in glycerol, the hydrophobic effect is no longer present, and consistent with our hypothesis,
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Figure 6. CD data referring to the temperature evolution of tertiary structure of lysozyme in glycerol-rich solution shown together with the hydrodynamic radius estimated via PCS measurements for the same solution. No evident variations are seen for Rh in the temperature range where the melting of tertiary structure is observed.
no variations of hydrodynamic radius in the premelting region is observed (see Figure 6). Further, in consonance with indications obtained from CD data on a noncooperative transition of the protein which could be connected to a molten globulelike state (Figure 4), we perceive only a small increase of the hydrodynamic radius in correspondence to the melting of the tertiary structure. IV. Conclusions In the present work we have used two independent experimental methodologies, PCS and far- and near-UV CD spectroscopy, to investigate the role of hydration in the structure and thermostability of proteins in solution. The studied system is the model protein lysozyme, dissolved in a water-glycerol mixture. Two limiting cases have been analyzed: water-rich and glycerol-rich solutions. The experimental data referring to water-rich solutions show that variations of temperature in a region of great biological interest cause continuous gradual changes of the effective hydrodynamic radius Rh of the protein. As a matter of fact, the effective hydrodynamic radius of lysozyme shows a maximum where an analogous maximum in the Gibbs free energy also occurs. The variations of Rh and G as a function of temperature appear strictly correlated. A tentative interpretation of these effects can be done in terms of variations with the temperature of the hydration of hydrophobic groups and of the hydrophobic interactions. Specifically, the presence of the maximum in the Rh temperature-trend could be associated to the competition of two opposite effects. The initial growth of the hydrodynamic radius could be attributed to a decrease of hydrophobic effects due to a loss of water structure, while the subsequent decline to a change in the hydration shell, which precedes the melting of the protein. This interpretation is in line with what was observed by means of wide-angle X-ray scattering measurements where the small tendency of the radius of gyration to decrease during the thermal unfolding process is ascribed to the collapse of the hydration shell prior to the unfolding.35 Furthermore, the view that the special behavior of the hydrodynamic radius as a function of temperature is associated to modifications of hydrophobic interactions, which promote gradual changes of the protein conformational properties, is here sustained by the result obtained in glycerol, where the hydrophobic effect is lacking, and this effect is not visible.
Esposito et al. Moreover, the experimental results for glycerol-rich solutions allow us to obtain precious information about the melting of secondary structure of lysozyme in glycerol. Circular dichroism spectral changes indicate a cooperative unfolding of the tertiary structure at nearly the same melting temperature as in the aqueous sample (average value at Tm ≈ 76 °C) and no loss of secondary structure up to 80-85 °C, confirming previous literature data. As a new result, we show an extension of CD data to higher temperatures, which allows us to follow a noncooperative melting of secondary structure that onsets above 85 °C. Coherently with the indications obtained from optical spectra, we perceive only a little increase of the hydrodynamic radius in correspondence to the melting of the tertiary structure, supporting the view of a protein transition to a molten globule-like state. Acknowledgment. F.S. acknowledges support from CNISM. References and Notes (1) Oppenheim, S. F.; Studts, J. M.; Fox, B. G.; Dordick, J. S. Appl. Biochem. Biotechnol. 2001, 90, 187. (2) Timasheff, S. N. Stability of Protein Pharmaceuticals. Part B. In ViVo Pathways of Degradation and Strategies for Protein Stabilization; Ahern, T. J., Manning, M. C., Eds.; Plenum, New York, 1992; pp 265-285. (3) Lee, J. C.; Timasheff, S. N. J. Biol. Chem. 1981, 256, 7193. (4) Gekko, K.; Timasheff, S. N. Biochemistry 1981, 20, 4677. (5) Xie, G.; Timasheff, S. N. Protein Sci. 1997, 6, 211. (6) Rariy, R. V.; Klibanov, A. M. Proc. Natl. Acad. Sci. 1997, 13520. (7) Tanford, C. Physical Chemistry of Macromolecules; Wiley: New York, 1961. (8) Bellissent-Funel, M. C. Hydration processes in biology; IOS Press: Amsterdam, 1999. (9) Zou, Q.; Bennion, B. J.; Daggett, V.; Murphy, K. P. J. Am. Chem. Soc. 2002, 124, 1192. (10) Knubovets, T.; Osterhout, J. J.; Connolly, P. J.; Klibanov, A. M. Proc. Natl. Acad. Sci. 1999, 96, 1262. (11) Knubovets, T.; Osterhout, J. J.; Klibanov, A. M. Biotechnol. Bioengineer. 1999, 63, 242. (12) Burova, T. V.; Grinberg, N. V.; Grinberg, V. Y.; Rariy, R. V.; Klibanov, A. M. Biochim. Biophys. Acta 2000, 1478, 308. (13) Dill, K. A.; Stigter, D. AdV. Protein Chem. 1995, 46, 59. (14) Honig, B.; Yang, A. S. AdV. Protein Chem. 1995, 46, 27. (15) Paciaroni, A.; Cinelli, S.; Onori, G. Biophys. J. 2002, 83, 1157. (16) Paciaroni, A.; Orecchini, A.; Cinelli, S.; Onori, G.; Lechner, R. E.; Pieper, J. J. Chem. Phys. 2003, 292, 397. (17) Cinelli, S.; De Francesco, A.; Onori, G.; Paciaroni, A. Phys. Chem. Chem. Phys. 2004, 6, 3591. (18) Sinibaldi, R.; Ortore, M. G.; Spinozzi, F.; Carsughi, F.; Frielinghaus, H.; Cinelli, S.; Onori, G.; Mariani, P. J. Chem. Phys. 2007, 126, 235101. (19) Spinozzi, F.; Ortore, M. G.; Sinibaldi, R.; Mariani, P.; Esposito, A.; Cinelli, S.; Onori, G. J. Chem. Phys. 2008, 129, 035101. (20) Nicoli, D. F.; Benedek, G. B. Biopolymers 1976, 15, 2421. (21) Dubin, S. B.; Feher, G.; Benedek, G. B. Biochemistry 1973, 12, 714. (22) Calandrini, V.; Fioretto, D.; Onori, G.; Santucci, A. Chem. Phys. Lett. 2000, 324, 344–348. (23) Bonincontro, A.; Calandrini, V.; Onori, G. Colloids Surf. B 2001, 21, 311–316. (24) Yin, D. C.; Inatomi, Y.; Wakayama, N. I.; Huang, W. D. Cryst. Res. Technol. 2003, 38, 785–792. (25) Segur, J. B.; Oberstar, H. E. Ind. Eng. Chem. 1951, 43, 2117. (26) Doherty, P.; Benedek, G. J. Chem. Phys. 1974, 61, 5426. (27) Tsong, T. Y.; Hearn, R. P.; Wrathall, D. P.; Sturtevant, J. M. Biochemistry 1970, 9, 2666. (28) Pfeil, W.; Privalov, P. L. Biophys. Chem. 1976, 4, 23. Pfeil, W.; Privalov, P. L. Biophys. Chem. 1976, 4, 33. Pfeil, W.; Privalov, P. L. Biophys. Chem. 1976, 4, 41. (29) Cinelli, S.; Onori, G.; Santucci, A. J. Phys. Chem. B, 1997, 101, 8029. (30) Brandts, J. F. J. Am. Chem. Soc. 1964, 86, 4291. (31) Biltonen, R.; Lumry, R. J. Am. Chem. Soc. 1965, 87, 4208. (32) Privalov, P. L. AdV. Protein Chem. 1979, 33, 167–2044. (33) Chen, L.; Hodgson, K. O.; Doniach, S. J. Mol. Biol. 1996, 261, 658–671. (34) Bonincontro, A.; De Francesco, A.; Onori, G. Chem. Phys. Lett. 1999, 301, 189–192. (35) Koizumi, M.; Hirai, H.; Onai, T.; Inoue, K.; Hirai, M. J. Appl. Crystallogr. 2007, 40, 175.
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