Unfolding free energy changes determined by the linear extrapolation method. 2. Incorporation of delta G degrees N-U values in a thermodynamic cycle

The linear extrapolation method was used to evaluate the unfolding free energy changes (delta G degrees N-U) for phenylmethanesulfonyl chymotrypsin (PMS-Ct) at pH 6.0. The nonlinear least-squares fits of difference spectral data using urea and guanidinium chloride as denaturants gave identical values for delta G degrees N-U and delta epsilon degrees U, the latter being extinction coefficient differences between native and unfolded forms of the protein in the limit of zero concentration of denaturant. The independence of these parameters from the nature of solvent suggests strongly that they are characteristic properties of the protein alone. The delta G degrees N-U data at pH 6.0 and 4.0, which differ by more than 100-fold in stability of the protein, were incorporated into a thermodynamic cycle involving free energy changes for titration of native and unfolded PMS-Ct from pH 4.0 to 6.0. The purpose of the cycle was to test whether delta G degrees N-U obtained by use of the linear extrapolation method exhibits the characteristics required of a thermodynamic function of state. Within error, the thermodynamic cycle was found to accommodate the delta G degrees N-U quantities obtained at pH 4.0 and 6.0 for PMS-Ct.     

Thermodynamics of ribonuclease T1 denaturation.

Differential scanning calorimetry has been used to investigate the thermodynamics of denaturation of ribonuclease T1 as a function of pH over the pH range 2-10, and as a function of NaCl and MgCl2 concentration. At pH 7 in 30 mM PIPES buffer, the thermodynamic parameters are as follows: melting temperature, T1/2 = 48.9 +/- 0.1 degrees C; enthalpy change, delta H = 95.5 +/- 0.9 kcal mol-1; heat capacity change, delta Cp = 1.59 kcal mol-1 K-1; free energy change at 25 degrees C, delta G degrees (25 degrees C) = 5.6 kcal mol-1. Both T1/2 = 56.5 degrees C and delta H = 106.1 kcal mol-1 are maximal near pH 5. The conformational stability of ribonuclease T1 is increased by 3.0 kcal/mol in the presence of 0.6 M NaCl or 0.3 M MgCl2. This stabilization results mainly from the preferential binding of cations to the folded conformation of the protein. The estimates of the conformational stability of ribonuclease T1 from differential scanning calorimetry are shown to be in remarkably good agreement with estimates derived from an analysis of urea denaturation curves.     

Low-temperature unfolding of a mutant of phage T4 lysozyme. 2. Kinetic investigations

A disulfide-bridged variant of bacteriophage T4 lysozyme has been found to undergo a low- as well as high-temperature unfolding transition in guanidinium chloride [see Chen and Schellman (1989)]. The kinetics for this process have been followed for several temperatures, a range of guanidinium chloride concentrations, and a number of values of pH. Microscopic rate constants for protein unfolding and refolding were extracted from these data to explore the nature of the cold unfolding transition. The data were interpreted using transition-state theory. It was found that the Arrhenius energy is temperature dependent. The transition state is characterized by (1) a high energy and low entropy compared to the native state, (2) a heat capacity which is closer to the native state than to the unfolded state, and (3) a low exposure to solvent compared to the unfolded state, as judged by its interaction with guanidinium chloride. With increasing concentration of guanidinium chloride, the low-temperature unfolding rate increases strongly, and the refolding rate decreases very strongly.     

Conformational stability and mechanism of folding of ribonuclease T1

Urea and thermal unfolding curves for ribonuclease T1 (RNase T1) were determined by measuring several different physical properties. In all cases, steep, single-step unfolding curves were observed. When these results were analyzed by assuming a two-state folding mechanism, the plots of fraction unfolded protein versus denaturant were coincident. The dependence of the free energy of unfolding, delta G (in kcal/mol), on urea concentration is given by delta G = 5.6 - 1.21 (urea). The parameters characterizing the thermodynamics of unfolding are: midpoint of the thermal unfolding curve, Tm = 48.1 degrees C, enthalpy change at Tm, delta Hm = 97 kcal/mol, and heat capacity change, delta Cp = 1650 cal/mol deg. A single kinetic phase was observed for both the folding and unfolding of RNase T1 in the transition and post-transition regions. However, two slow kinetic phases were observed during folding in the pre-transition region. These two slow phases account for about 90% of the observed amplitude, indicating that a faster kinetic phase is also present. The slow phases probably result from cis-trans isomerization at the 2 proline residues that have a cis configuration in folded RNase T1. These results suggest that RNase T1 folds by a highly cooperative mechanism with no structural intermediates once the proline residues have assumed their correct isomeric configuration. At 25 degrees C, the folded conformation is more stable than the unfolded conformations by 5.6 kcal/mol at pH 7 and by 8.9 kcal/mol at pH 5, which is the pH of maximum stability. At pH 7, the thermodynamic data indicate that the maximum conformational stability of 8.3 kcal/mol will occur at -6 degrees C.     

Thermodynamics of alligator metmyoglobin unfolding

The conformational free energy of alligator metmyoglobin was examined over a pH range of 4.4-8.0, a temperature range of 18-48 degrees C, and a guanidinium chloride concentration of 0-2.3 M. For isothermal unfolding at 25 degrees C essentially the same value was obtained for the conformational free energy from all the data: 7.0 +/- 0.5 kcal/mol. The cooperativity of the unfolding with respect to denaturant is considerably less than for mammalian myoglobins. On unfolding three to four side chains with a pKa of 6.3 in the unfolded protein are protonated instead of the six expected. The temperature at which delta H (unfolding) is zero is much lower than for previously characterized myoglobins. Alligator metmyoglobin, considerably less stable than other previously characterized myoglobins, may not be as compactly folded.     

Unfolding free energy changes determined by the linear extrapolation method. 1. Unfolding of phenylmethanesulfonyl alpha-chymotrypsin using different denaturants

Characteristics and properties of the unfolding free energy change, delta G degrees N-U, as determined by the linear extrapolation method are assessed for the unfolding of phenylmethanesulfonyl chymotrypsin (PMS-Ct). Difference spectral measurements at 293 nm were used to define PMS-Ct unfolding brought about with guanidinium chloride, urea, and 1,3-dimethylurea. All three denaturants were shown to give identical extinction coefficient differences (delta epsilon N-U) between native and unfolded forms of the protein in the limit of zero concentration of denaturant. The independence of delta epsilon N-U on denaturant supports the linear extension of pre- and postdenaturational base lines into the transition zone, allowing evaluation of unfolding equilibrium constants based on the two-state assumption. An expression, based on the linear extrapolation method, was used to provide estimates of delta G degrees N-U for the three denaturants using nonlinear least-squares fitting of the primary data, delta epsilon versus [denaturant]. The three delta G degrees N-U values were identical, within error, suggesting that the free energy change is a property of the protein system and independent of denaturant. It is suggested that the error in delta G degrees N-U determined from use of the linear extrapolation method is significantly larger than commonly reported in the literature.     

Stability of a homo-dimeric Ca(2+)-binding member of the beta gamma-crystallin superfamily: DSC measurements on spherulin 3a from Physarum polycephalum.

Spherulin 3a (S3a) from Physarum polycephalum represents the only known single-domain member of the superfamily of beta gamma eye-lens crystallins. It shares the typical two Greek-key motif and is stabilized by dimerization and Ca(2+)-binding. The temperature and denaturant-induced unfolding of S3a in the absence and in the presence of Ca2+ were investigated by differential scanning calorimetry and fluorescence spectroscopy. To accomplish reversibility without chemical modification of the protein during thermal denaturation, the only cysteine residue (Cys4) was substituted by serine; apart from that, the protein was destabilized by adding 0.5-1.8 M guanidinium chloride (GdmCl). The Cys4Ser mutant was found to be indistinguishable from natural S3a. The equilibrium unfolding transitions obey the two-state model according to N2-->2 U, allowing thermodynamic parameters to be determined by linear extrapolation to zero GdmCl concentration. The corresponding transition temperatures TM for the Ca(2+)-free and Ca(2+)-loaded protein were found to be 65 and 85 degrees C, the enthalpy changes delta Hcal, 800 and 1280 kJ/mol(dimer), respectively. The strong dependencies of TM and delta Hcal on the GdmCl concentration allow the molar heat capacity change delta Cp to be determined. As a result, delta Cp = 18 kJ/(K mol(dimer)) was calculated independent of Ca2+. No significant differences were obtained between the free energy delta G degree calculated from delta Hcal and TM, and extrapolated from the stability curves in the presence of different amounts of denaturant. The free energy derived from thermal unfolding was confirmed by the spectral results obtained from GdmCl-induced equilibrium transitions at different temperatures for the Ca(2+)-free or the Ca(2+)-loaded protein, respectively. Within the limits of error, the delta G degree values extrapolated from the transitions of chemical denaturation to zero denaturant concentration are identical with the calorimetric results.     

The thermodynamics of protein stability. Cold destabilization as a general phenomenon

A theoretical analysis of the temperature/stability profiles of proteins shows that, where a two-state model represents the denaturation, and where the free energy of denaturation delta G(T) shows a strong temperature dependence, then the protein becomes subject to both high- and low-temperature destabilization. In the simplest case delta G(T) is parabolic, therefore the high temperature TH, where delta (G(TH) = 0, is complemented by a low temperature TL, where delta G(TL) = 0. It is generally stated that the partial molal heat capacity change delta C accompanying the heat denaturation is positive and independent of the temperature. This implies that heating the protein through TL results in a negative delta C which seems physically unsatisfactory. The constant delta C model is explored and a physically more realistic model is advanced which allows for a temperature-dependent delta C which changes sign at some temperature within the range of stability of the native protein; delta G(T) then has the form of a skewed parabola. Experimental heat capacity data for native lysozyme and for a flexible polymer lend support to this model. The molecular basis of cold inactivation of proteins is discussed in the light of the thermodynamic analysis.     

The volume and compressibility changes of lysozyme associated with guanidinium chloride and pressure-assisted unfolding.

The apparent specific volumes and isentropic compressibilities of hen egg white lysozyme were measured in aqueous guanidinium chloride solutions at 25 degrees C by means of a vibrational densimeter and a sing-around ultrasonic velocimeter. Little transition attributable to a protein unfolding was detected in the partial specific volume, while the partial specific isentropic compressibility decreased slightly around the transition region. The pressure-assisted unfolding was also investigated in aqueous guanidinium chloride solutions by means of ultraviolet spectroscopy. Assuming a two-state transition model, it was found that the free energy change of unfolding depends almost linearly on pressure and the unfolding reaction is accompanied by a small decrease in volume. The compressibility behavior is in conflict with the notion that a protein structure is almost completely unfolded by guanidinium chloride and most of the amino acid residues in the protein interior are exposed to solvent. These results support the current view that globular proteins have some residual structures even in the unfolded state induced by a strong denaturant.     

High- and low-temperature unfolding of human high-density apolipoprotein A-2.

Human plasma apolipoprotein A-2 (apoA-2) is the second major protein of the high-density lipoproteins that mediate the transport and metabolism of cholesterol. Using CD spectroscopy and differential scanning calorimetry, we demonstrate that the structure of lipid-free apoA-2 in neutral low-salt solutions is most stable at approximately 25 degrees C and unfolds reversibly both upon heating and cooling from 25 degrees C. High-temperature unfolding of apoA-2, monitored by far-UV CD, extends from 25-85 degrees C with midpoint Th = 56 +/- 2 degrees C and vant Hoff's enthalpy delta H(Th) = 17 +/- 2 kcal/mol that is substantially lower than the expected enthalpy of melting of the alpha-helical structure. This suggests low-cooperativity apoA-2 unfolding. The apparent free energy of apoA-2 stabilization inferred from the CD analysis of the thermal unfolding, delta G(app)(25 degrees) = 0.82 +/- 0.15 kcal/mol, agrees with the value determined from chemical denaturation. Enhanced low-temperature stability of apoA-2 observed upon increase in Na2HPO4 concentration from 0.3 mM to 50 mM or addition of 10% glycerol may be linked to reduced water activity. The close proximity of the heat and cold unfolding transitions, that is consistent with low delta G(app)(25 degrees), indicates that lipid-free apoA-2 has a substantial hydrophobic core but is only marginally stable under near-physiological solvent conditions. This suggests that in vivo apoA-2 transfer is unlikely to proceed via the lipid-free state. Low delta H(Th) and low apparent delta Cp approximately 0.52 kcal/mol.K inferred from the far-UV CD analysis of apoA-2 unfolding, and absence of tertiary packing interactions involving Tyr groups suggested by near-UV CD, are consistent with a molten globular-like state of lipid-free apoA-2.     

Conformational stability of HPr: the histidine-containing phosphocarrier protein from Bacillus subtilis.

The conformational stability of the histidine-containing phosphocarrier protein (HPr) from Bacillus subtilis has been determined using a combination of thermal unfolding and solvent denaturation experiments. The urea-induced denaturation of HPr was monitored spectroscopically at fixed temperatures and thermal unfolding was performed in the presence of fixed concentrations of urea. These data were analyzed in several different ways to afford a measure of the cardinal parameters (delta Hg, Tg, delta Sg, and delta Cp) that describe the thermodynamics of folding for HPr. The method of Pace and Laurents (Pace CN, Laurents DV, 1989, Biochemistry 28:2520-2525) was used to estimate delta Cp as was a global analysis of the thermal- and urea-induced unfolding data. Each method used to analyze the data gives a similar value for delta Cp (1,170 +/- 50 cal mol-1K-1). Despite the high melting temperature for HPr (Tg = 73.5 degrees C), the maximum stability of the protein, which occurs at 26 degrees C, is quite modest (delta Gs = 4.2 kcal mol-1). In the presence of moderate concentrations of urea, HPr exhibits cold denaturation, and thus a complete stability curve for HPr, including a measure of delta Cp, can be achieved using the method of Chen and Schellman (Chen B, Schellman JA, 1989, Biochemistry 28:685-691). A comparison of the different methods for the analysis of solvent denaturation curves is provided and the effects of urea on the thermal stability of this small globular protein are discussed. The methods presented will be of general utility in the characterization of the stability curve for many small proteins.     

Thermodynamics of maltose binding protein unfolding.

The maltose binding protein (MBP or MalE) of Escherichia coli is the periplasmic component of the transport system for malto-oligosaccharides. It is used widely as a carrier protein for the production of recombinant fusion proteins. The melting of recombinant MBP was studied by differential scanning and titration calorimetry and fluorescence spectroscopy under different solvent conditions. MBP exhibits a single peak of heat absorption with a delta(Hcal)/delta(HvH) ratio in the range of 1.3-1.5, suggesting that the protein comprises two strongly interacting thermodynamic domains. Binding of maltose resulted in elevation of the Tm by 8-15 degrees C, depending of pH. The presence of ligand at neutral pH, in addition to shifting the melting process to higher temperature, caused it to become more cooperative. The delta(Hcal)/delta(HvH) ratio decreased to unity, indicating that the two domains melt together in a single two-state transition. This ligand-induced merging of the two domains appears to occur only at neutral pH, because at low pH maltose simply stabilized MBP and did not cause a decrease of the delta(Hcal)/delta(HvH) ratio. Binding of maltose to MBP is characterized by very low enthalpy changes, approximately -1 kcal/mol. The melting of MBP is accompanied by an exceptionally large change in heat capacity. 0.16 cal/K-g, which is consistent with the high amount of nonpolar surface--0.72 A2/g--that becomes accessible to solvent in the unfolded state. The high value of delta Cp determines a very steep delta G versus T profile for this protein and predicts that cold denaturation should occur above freezing temperatures. Evidence for this was provided by changes in fluorescence intensity upon cooling the protein. A sigmoidal cooperative transition with a midpoint near 5 degrees C was observed when MBP was cooled at low pH. Analysis of the melting of several fusion proteins containing MBP illustrated the feasibility of assessing the folding integrity of recombinant products prior to separating them from the MBP carrier protein.     

A new method for determining the heat capacity change for protein folding

In order to use results from calorimetry or thermal unfolding curves to estimate the free energy change for protein unfolding at 25 degrees C, it is necessary to know the change in heat capacity for unfolding, delta Cp. We describe a new method for measuring delta Cp which is based on results from urea and thermal unfolding curves but does not require a calorimeter. We find that delta Cp = 1650 +/- 200 cal/(deg.mol) for the unfolding of ribonuclease T1 and that delta Cp = 2200 +/- 300 cal/(deg.mol) for the unfolding of ribonuclease A.     

Thermodynamic analysis of the folding of the streptococcal protein G IgG-binding domains B1 and B2: why small proteins tend to have high denaturation temperatures.

We have cloned, expressed, and characterized two naturally occurring variations of the IgG-binding domain of streptococcal protein G. The domain is a stable cooperative folding unit of 56 amino acids, which maintains a unique folded structure without disulfide cross-links or tight ligand binding. We have studied the thermodynamics of the unfolding reaction for the two versions of this domain, designated B1 and B2, which differ by six amino acids. They have denaturation temperatures of 87.5 degrees C and 79.4 degrees C, respectively at pH 5.4, as determined by differential scanning calorimetry. Thermodynamic state functions for the unfolding reaction (delta G, delta H, delta S, and delta Cp) have been determined and reveal several interesting insights into the behavior of very small proteins. First, though the B1 domain has a heat denaturation point close to 90 degrees C, it is not unusually stable at physiologically relevant temperatures (delta G = 25 kJ/mol at 37 degrees C). This behavior occurs because the stability profile (delta G vs temperature) is flat and shallow due to the small delta S and delta Cp for unfolding. Related to this point is the second observation that small changes in the free energy of unfolding of the B-domain due to mutation or change in solvent conditions lead to large shifts in the heat denaturation temperature. Third, the magnitude and relative contributions of hydrophobic vs nonhydrophobic forces (per amino acid residue) to the total free energy of folding of the B-domain are remarkably typical of other globular proteins of much larger size.     

Two types of arrestins expressed in medaka rod photoreceptors

Globular protein thermostability is characterized the cold denaturation, maximal stability (Tms) and heat denaturation temperatures. For mesophilic globular proteins, Tms typically ranges from -25 degrees C to +35 degrees C. We show that the indirect estimate of Tms from calorimetry and the direct estimate from chemical denaturation performed in a range of temperatures are in close agreement. The heat capacity change of unfolding per mol residue (delta Cp) alone is shown to accurately predict Tms. Delta Cp and hence Tms can be predicted solely from the protein sequence. The average difference in free energy of unfolding at the observed and predicted values of Tms is 1.0 kcal mol(-1), which is small compared to typical values of the total free energy of unfolding.     

Pressure-induced unfolding of lysozyme in aqueous guanidinium chloride solution.

The pressure-induced unfolding of lysozyme was investigated in an aqueous guanidinium chloride solution by means of ultraviolet spectroscopy. Assuming a two-state transition model, volume changes were calculated from the slope of free energy vs. pressure plots over a temperature range of 10 to 60 degrees C. Between 25 and 60 degrees C, almost constant volume changes were observed in the transition region, which was reflected in almost identical slopes of the free energy change vs. pressure plots. On the other hand, the different slopes were observed in the pressure dependence of free energy change at temperatures lower than 25 degrees C. These data were interpreted as suggesting that a two-state model is not appropriate at low temperature, but instead one or more intermediates are present under these conditions. The volume changes for unfolding became less negative at temperatures higher than 25 degrees C.     

Conformational free energy of armadillo metmyoglobin

The conformational free energy of armadillo metmyoglobin was examined over a pH range of 4.4-8.0 and a guanidinium chloride concentration of 0-2.3 M. For isothermal unfolding at 25 degrees essentially the same value was obtained for the conformational free energy from all the data: 27 +/- 2 kJ/mol. These data suggest that the armadillo has the least stable metmyoglobin of any mammal thus far examined. The cooperativity of the unfolding with respect to denaturant is considerably less than for other mammalian myoglobins. On unfolding only three to four side chains with a pKA of 6 in the unfolded protein are protonated instead of the six found for horse and sperm whale myoglobins.     

Conformational properties of streptokinase--differential scanning calorimetric investigations.

The two-domain structure of streptokinase (Sk) was demonstrated by scanning calorimetric investigations at neutral pH and low ionic strength. The melting pattern of the protein is composed of two two-state transitions at TtrS1 = 45.9 +/- 0.4 degrees C with delta H1 = 431 +/- 18 kJ/mol, and TtrS2 = 60.1 +/- 1.3 degrees C with delta H2 = 306 +/- 16 kJ/mol. The partial specific heat capacity of native Sk was determined to be Cp = 1.42 +/- 0.17 J/K/g and the denaturational heat capacity change associated with the two transitions, delta Cp1 = 0.21 J/K/g and delta Cp2 = 0.38 J/K/g, respectively. The overall melting pattern of Sk remains almost unchanged at a variety of tested solvent compositions, except at pH 4 (and below) and in the presence of denaturants. The two domains show different susceptibility to urea. It is proposed that the less thermostable domain is located within the N-terminal part (residues 1-230), and the more thermostable one, within the C-terminal region.