Stability parameters for one-step mechanism of irreversible protein denaturation: a method based on nonlinear regression of calorimetric peaks with nonzero deltaCp

Thermal transitions of many proteins have been found to be calorimetrically irreversible and scan-rate dependent. Calorimetric determinations of stability parameters of proteins which unfold irreversibly according to a first-order kinetic scheme have been reported. These methods require the approximation that the increase in heat capacity upon denaturation deltaCp is zero. A method to obtain thermodynamic parameters and activation energy for the two-state irreversible process N --> D from nonlinear fitting to calorimetric traces is proposed here. It is based on a molar excess heat capacity function which considers irreversibility and a nonzero constant deltaCp. This function has four parameters: (1) temperature at which the calorimetric profile reaches its maximal value (Tm), (2) calorimetric enthalpy at Tm (deltaHm), (3) deltaCp, and (4) activation energy (E). The thermal irreversible denaturation of subtilisin BPN' from Bacillus amyloliquefaciens was studied by differential scanning calorimetry at pH 7.5 to test our model. Transitions were found to be strongly scanning-rate dependent with a mean deltaCp value of 5.7 kcal K(-1)mol(-1), in agreement with values estimated by accessible surface area and significantly higher than a previously reported value.     

Denaturant mediated unfolding of both native and molten globule states of maltose binding protein are accompanied by large deltaCp's.

Maltose binding protein (MBP) is a large, monomeric two domain protein containing 370 amino acids. In the absence of denaturant at neutral pH, the protein is in the native state, while at pH 3.0 it forms a molten globule. The molten globule lacks a tertiary circular dichroism signal but has secondary structure similar to that of the native state. The molten globule binds 8-anilino-1-naphthalene sulfonate (ANS). The unfolding thermodynamics of MBP at both pHs were measured by carrying out a series of isothermal urea melts at temperatures ranging from 274-329 K. At 298 K, values of deltaGdegrees , deltaCp, and Cm were 3.1+/-0.2 kcal mol(-1), 5.9+/-0.8 kcal mol(-1) K(-1) (15.9 cal (mol-residue)(-1) K(-1)), and 0.8 M, respectively, at pH 3.0 and 14.5+/-0.4 kcal mol(-1), 8.3+/-0.7 kcal mol(-1) K(-1) (22.4 kcal (mol-residue)(-1) K(-1)), and 3.3 M, respectively, at pH 7.1. Guanidine hydrochloride denaturation at pH 7.1 gave values of deltaGdegrees and deltaCp similar to those obtained with urea. The m values for denaturation are strongly temperature dependent, in contrast to what has been previously observed for small globular proteins. The value of deltaCp per mol-residue for the molten globule is comparable to corresponding values of deltaCp for the unfolding of typical globular proteins and suggests that it is a highly ordered structure, unlike molten globules of many small proteins. The value of deltaCp per mol-residue for the unfolding of the native state is among the highest currently known for any protein.     

A mechanistic analysis of the increase in the thermal stability of proteins in aqueous carboxylic acid salt solutions

The stability of proteins is known to be affected significantly in the presence of high concentration of salts and is highly pH dependent. Extensive studies have been carried out on the stability of proteins in the presence of simple electrolytes and evaluated in terms of preferential interactions and increase in the surface tension of the medium. We have carried out an in-depth study of the effects of a series of carboxylic acid salts: ethylene diamine tetra acetate, butane tetra carboxylate, propane tricarballylate, citrate, succinate, tartarate, malonate, and gluconate on the thermal stability of five different proteins that vary in their physico-chemical properties: RNase A, cytochrome c, trypsin inhibitor, myoglobin, and lysozyme. Surface tension measurements of aqueous solutions of the salts indicate an increase in the surface tension of the medium that is very strongly correlated with the increase in the thermal stability of proteins. There is also a linear correlation of the increase in thermal stability with the number of carboxylic groups in the salt. Thermal stability has been found to increase by as much as 22 C at 1 M concentration of salt. Such a high thermal stability at identical concentrations has not been reported before. The differences in the heat capacities of denaturation, deltaCp for RNase A, deduced from the transition curves obtained in the presence of varying concentrations of GdmCl and that of carboxylic acid salts as a function of pH, indicate that the nature of the solvent medium and its interactions with the two end states of the protein control the thermodynamics of protein denaturation. Among the physico-chemical properties of proteins, there seems to be an interplay of the hydrophobic and electrostatic interactions that lead to an overall stabilizing effect. Increase in surface free energy of the solvent medium upon addition of the carboxylic acid salts appears to be the dominant factor in governing the thermal stability of proteins.     

Kinetic coupling between protein folding and prolyl isomerization. II. Folding of ribonuclease A and ribonuclease T1.

The folding and unfolding kinetics within the transition region were measured for RNase A and for RNase T1. The data were used to evaluate the theoretical models for the influence of prolyl isomerization on the observed folding kinetics. These two proteins were selected, since the folding reaction of RNase A is faster than prolyl isomerization, whereas in RNase T1, folding is slower than isomerization in the transition region. Folding of RNase T1 was investigated for three variants with different numbers of cis prolyl residues. The results indicate that in the transition region the folding rates are indeed strongly dependent on the number of prolyl residues. The variant of RNase T1 that contains only one cis prolyl residue folds about ten times faster than two variants that contain two cis prolyl residues. For both RNase A and RNase T1, the apparent rates of folding and unfolding as well as the corresponding amplitudes depend on the concentration of denaturant in a manner that was predicted by the model calculations. When refolding was started from the fast-folding species, additional kinetic phases could be observed in the transition region for both proteins. The obtained values could be used to calculate the microscopic rate constants of folding and isomerization on the basis of theoretical models.     

Effect of D-amino acids on the functional activity and conformational stability of ribonuclease-A

Using cytidine 2':3' cyclic monophosphate as a substrate, Km and k(cat) of ribonuclease-A in the presence of different concentrations of D-amino acids (Ala, Ser, Pro and Lys) and their L-isomers were measured at pH 6.0 and 25 degrees C. These kinetic parameters remained unchanged in the presence and absence of D-and L-amino acids. This is the first experimental evidence showing that D-amino acids are compatible with the enzyme function. Values of Tm (midpoint of denaturation), deltaHm (enthalpy change at Tm) and deltaCp (constant-pressure heat capacity change) were also determined from the heat-induced denaturation curves of the protein, measured in the presence and absence of D- and L-isomers of an amino acid at four different pH values. It is shown for the first time that these thermodynamic parameters, within experimental errors, do not depend on the stereospecificity of an amino acid. Estimates of deltaGDo with the help of Gibbs-Helmoltz equation (deltaGDo = deltaHm (1-298.15/Tm)--deltaCp [(Tm-298.15) + 298.15 In (298.15/Tm)]) using known values of Tm, deltaHm and deltaCp suggested that D- and L-amino acids are compatible with protein stability, for deltaGDo remained unchanged in the presence of amino acids.     

Low molecular mass pectate lyase from Fusarium moniliforme: similar modes of chemical and thermal denaturation

A low molecular mass pectate lyase from Fusarium moniliforme was unfolded reversibly by urea and Gdn-HCl at its optimum pH of 8.5, as monitored by intrinsic fluorescence, circular dichroism, and enzymatic activity measurements. Equilibrium unfolding studies yielded a deltaG(H(2)O) of 1.741 kcal/mol, D1/2 of 2.3M, and m value of 0.755kcal/molM with urea and a deltaG(H(2)O) of 1.927kcal/mol, D1/2 of 1.52M, and m value of 1.27 kcal/molM with Gdn-HCl as the denaturant. Thermal denaturation of the pectate lyase at, pH 8.5, was also reversible even after exposure to 75 degrees C for 10 min. Thermodynamic parameters calculated from thermal denaturation curves at pH values from 5.0 to 8.5 yielded a deltaCp of 0.864kcal/(molK). The deltaG(25 degrees C) at, pH 8.5, was 2.06kcal/mol and was in good agreement with the deltaG(H(2)O) values obtained from chemical denaturation curves. There was no exposure of hydrophobic pockets during chemical or thermal denaturation as indicated by the inability of ANS to bind the pectate lyase.     

Mutational and structural-based analyses of the osmolyte effect on protein stability

It is known that several naturally occurring substances known as osmolytes increase the conformational stability of proteins. Bolen and co-worker proposed the osmophobic theory, which asserts the osmolyte effect occurs because of an unfavorable interaction of osmolytes mainly with the protein backbone, based on the results on the transfer Gibbs energy of amino acids (Deltag) [Bolen and Baskakov (2001) J. Mol. Biol. 310, 955-963]. In this paper, we report the effect of sarcosine on the conformational stability (DeltaG) of RNase Sa (96 residues and one disulfide bond) and four mutant proteins. The thermal denaturation curves for RNase Sa in sarcosine fitted a two-state model on nonlinear least-squares analysis. All the RNase Sa proteins were stabilized by sarcosine. For example, the increase in stability of the wild-type protein in 4 M sarcosine due to the osmolyte effect (Delta(o)DeltaG) is 3.2 kcal/mol. Mutational analysis of the osmolyte effect indicated that the changed Delta(o)DeltaG values upon mutation (Delta(m)Delta(o)DeltaG), as estimated from the Deltag values, are similar to the experimental values. Structural-based analysis of the osmolyte effect was also performed using model denatured structures: (a) a fully extended model (single chain) with no disulfide bond, (b) two-part, unfolded models (two chains) with a disulfide bond constructed through molecular dynamic (MD) simulation, and (c) a two-part, folded model (two chains). The two-part, unfolded models were expected to be more suitable as denatured structures. The Delta(o)DeltaG values calculated using the two-part, unfolded models were more consistent with experimental values than those calculated using the fully extended and two-part, folded models. This suggests that MD simulation is useful for testing denatured structures. These results indicate that the osmophobic theory can explain the osmolyte effect on protein stability.     

Refinement of noncalorimetric determination of the change in heat capacity, DeltaC(p), of protein unfolding and validation across a wide temperature range

The change in heat capacity, DeltaC(p), on protein unfolding has been usually determined by calorimetry. A noncalorimetric method which employs the Gibbs-Helmholtz relationship to determine DeltaC(p) has seen some use. Generally, in this method the free energy change on unfolding of the protein is determined at a variety of temperatures and the temperature at which DeltaG is zero, T(m), and change in enthalpy at T(m) are determined by thermal denaturation and DeltaC(p) is then calculated using the Gibbs-Helmholtz equation. We show here that an abbreviated method with stability determinations at just two temperatures gives values of DeltaC(p) consistent with values from free energy change on unfolding determination at a much wider range of temperatures. Further, even the free energy change on unfolding from a single solvent denaturation at the proper temperature, when coupled with the melting temperature, T(m), and the van't Hoff enthalpy, DeltaH(vH), from a thermal denaturation, gives a reasonable estimate of DeltaC(p), albeit with greater uncertainty than solvent denaturations at two temperatures. We also find that nonlinear regression of the Gibbs-Helmholtz equation as a function of stability and temperature while simultaneously fitting DeltaC(p), T(m), and DeltaH(vH) gives values for the last two parameters that are in excellent agreement with experimental values.     

Heat capacity change for ribonuclease A folding.

The change in heat capacity deltaCp for the folding of ribonuclease A was determined using differential scanning calorimetry and thermal denaturation curves. The methods gave equivalent results, deltaCp = 1.15+/-0.08 kcal mol(-1) K(-1). Estimates of the conformational stability of ribonuclease A based on these results from thermal unfolding are in good agreement with estimates from urea unfolding analyzed using the linear extrapolation method.     

Thermal stability and enzymatic activity of RNase A in the presence of cationic gemini surfactants

The thermal stability and enzymatic activity of bovine pancreatic ribonuclease A (RNase A) have been investigated in the presence of a homologous series of cationic gemini surfactants (alkanediyl-α,ω-bis(hydroxyethyl methyl hexadecyl ammonium bromide)). UV, circular dichorism and fluorescence spectroscopies have been used for this study. The denaturation curves at various surfactant concentrations were analyzed on basis of a two-transition model to obtain values of T(m) (temperature at the midpoint of denaturation) and ΔH(m) (enthalpy change at T(m)) of each transition. The main conclusion of this study is that these cationic gemini surfactants slightly activate and stabilize RNase A below their critical micelle concentrations at pH 5.0. The cationic gemini surfactant with the shorter spacer interacts more efficiently with RNase A than those with longer spacers.     

Charge-charge interactions are key determinants of the pK values of ionizable groups in ribonuclease Sa (pI=3.5) and a basic variant (pI=10.2)

The pK values of the titratable groups in ribonuclease Sa (RNase Sa) (pI=3.5), and a charge-reversed variant with five carboxyl to lysine substitutions, 5K RNase Sa (pI=10.2), have been determined by NMR at 20 degrees C in 0.1M NaCl. In RNase Sa, 18 pK values and in 5K, 11 pK values were measured. The carboxyl group of Asp33, which is buried and forms three intramolecular hydrogen bonds in RNase Sa, has the lowest pK (2.4), whereas Asp79, which is also buried but does not form hydrogen bonds, has the most elevated pK (7.4). These results highlight the importance of desolvation and charge-dipole interactions in perturbing pK values of buried groups. Alkaline titration revealed that the terminal amine of RNase Sa and all eight tyrosine residues have significantly increased pK values relative to model compounds.A primary objective in this study was to investigate the influence of charge-charge interactions on the pK values by comparing results from RNase Sa with those from the 5K variant. The solution structures of the two proteins are very similar as revealed by NMR and other spectroscopic data, with only small changes at the N terminus and in the alpha-helix. Consequently, the ionizable groups will have similar environments in the two variants and desolvation and charge-dipole interactions will have comparable effects on the pK values of both. Their pK differences, therefore, are expected to be chiefly due to the different charge-charge interactions. As anticipated from its higher net charge, all measured pK values in 5K RNase are lowered relative to wild-type RNase Sa, with the largest decrease being 2.2 pH units for Glu14. The pK differences (pK(Sa)-pK(5K)) calculated using a simple model based on Coulomb's Law and a dielectric constant of 45 agree well with the experimental values. This demonstrates that the pK differences between wild-type and 5K RNase Sa are mainly due to changes in the electrostatic interactions between the ionizable groups. pK values calculated using Coulomb's Law also showed a good correlation (R=0.83) with experimental values. The more complex model based on a finite-difference solution to the Poisson-Boltzmann equation, which considers desolvation and charge-dipole interactions in addition to charge-charge interactions, was also used to calculate pK values. Surprisingly, these values are more poorly correlated (R=0.65) with the values from experiment. Taken together, the results are evidence that charge-charge interactions are the chief perturbant of the pK values of ionizable groups on the protein surface, which is where the majority of the ionizable groups are positioned in proteins.     

Heme and pH-dependent stability of an anionic horseradish peroxidase

Horseradish peroxidase A1 thermal stability was studied by steady-state fluorescence, circular dichroism and differential scanning calorimetry at pH values of 4, 7 and 10. Changes in the intrinsic protein probes, tryptophan fluorescence, secondary structure, and heme group environment are not coincident. The T(m) values measured from the visible CD data are higher than those measured from Trp fluorescence and far-UV CD data at all pH values showing that the heme cavity is the last structural region to suffer significant conformational changes during thermal denaturation. However ejection of the heme group leads to an irreversible unfolding behavior at pH 4, while at pH 7 and 10 refolding is still observed. This is putatively correlated with the titration state of the heme pocket. Thermal transitions of HRPA1 showed scan rate dependence at the three pH values, showing that the denaturation process was kinetically controlled. The denaturation process was interpreted in terms of the classic scheme, N<-->U-->D and fitted to far-UV CD ellipticity. A good agreement was obtained between the experimental and theoretical T(m) values and percentages of irreversibility. However the equilibrium between N and U is probably more complex than just a two-state process as revealed by the multiple T(m) values.     

Denaturant m values and heat capacity changes: relation to changes in accessible surface areas of protein unfolding.

Denaturant m values, the dependence of the free energy of unfolding on denaturant concentration, have been collected for a large set of proteins. The m value correlates very strongly with the amount of protein surface exposed to solvent upon unfolding, with linear correlation coefficients of R = 0.84 for urea and R = 0.87 for guanidine hydrochloride. These correlations improve to R = 0.90 when the effect of disulfide bonds on the accessible area of the unfolded protein is included. A similar dependence on accessible surface area has been found previously for the heat capacity change (delta Cp), which is confirmed here for our set of proteins. Denaturant m values and heat capacity changes also correlate well with each other. For proteins that undergo a simple two-state unfolding mechanism, the amount of surface exposed to solvent upon unfolding is a main structural determinant for both m values and delta Cp.     

Compatibility of osmolytes with Gibbs energy of stabilization of proteins

This study led to the conclusion that naturally occurring osmolytes which are known to protect proteins against denaturing stresses, do not perturb the Gibbs energy of stabilization of proteins at 25 degrees C (DeltaG(D) degrees ) which has been shown to control the in vivo rate of degradative protein turnover (Pace et al., Acta Biol. Med. Germ 40 (1981) 1385-1392). This conclusion has been reached from our studies of heat-induced denaturation of lysozyme, ribonuclease A, cytochrome c and myoglobin in the presence of different concentrations of osmolytes, namely, glycine, proline, sarcosine and glycine-betaine. At a fixed concentration of osmolyte a heat-induced denaturation curve measured by following changes in the molar absorption coefficient of the protein, was analyzed for T(m), the midpoint of the denaturation and DeltaH(m), the enthalpy change of denaturation at T(m). Values of DeltaG(D) degrees were determined with Gibbs-Helmoltz equation using known values of T(m), DeltaH(m) and DeltaC(p), the constant-pressure heat capacity change. It has been observed that T(m) increases with the osmolyte concentration, whereas DeltaG(D) degrees remains unaffected in the presence of the osmolyte. This observation on DeltaG(D) degrees in the presence of osmolytes has been considered in the physiological context.     

A Gaussian statistical mechanical model for the equilibrium thermodynamics of barnase folding

Given an all non-hydrogen-atom potential function that implicitly includes solvation effects, it is possible to adjust its parameters to favor the correct native structure for several proteins over decoys produced by ungapped threading. It is also possible to further train it to reproduce the experimental free energy of unfolding in aqueous solution at 298 K for wild-type barnase and 66 mutants. For this, the native state is represented by the crystal structure at a single energy level with a calculated low degeneracy; the denatured state is represented by the extended conformation and a high calculated degeneracy. The same two-state model can be extended to account for the stability of all 67 sequences toward urea denaturation at 298 K by building in a solvation term that depends on urea concentration. With the addition of one more parameter set to give the correct heat capacity of unfolded barnase in solution, it is possible to approximate the experimental thermodynamics of barnase thermal denaturation: melting temperature, width of thermal transition, deltaG, deltaH, deltaS, and deltaCp. This requires a novel sort of statistical mechanical model where the two states each have a Gaussian density of microscopic state distribution as a function of energy.     

Osmolytes stabilize ribonuclease S by stabilizing its fragments S protein and S peptide to compact folding-competent states

Osmolytes stabilize proteins to thermal and chemical denaturation. We have studied the effects of the osmolytes sarcosine, betaine, trimethylamine-N-oxide, and taurine on the structure and stability of the protein.peptide complex RNase S using x-ray crystallography and titration calorimetry, respectively. The largest degree of stabilization is achieved with 6 m sarcosine, which increases the denaturation temperatures of RNase S and S pro by 24.6 and 17.4 degrees C, respectively, at pH 5 and protects both proteins against tryptic cleavage. Four crystal structures of RNase S in the presence of different osmolytes do not offer any evidence for osmolyte binding to the folded state of the protein or any perturbation in the water structure surrounding the protein. The degree of stabilization in 6 m sarcosine increases with temperature, ranging from -0.52 kcal mol(-1) at 20 degrees C to -5.4 kcal mol(-1) at 60 degrees C. The data support the thesis that osmolytes that stabilize proteins, do so by perturbing unfolded states, which change conformation to a compact, folding competent state in the presence of osmolyte. The increased stabilization thus results from a decrease in conformational entropy of the unfolded state.     

Hydrogen-exchange stabilities of RNase T1 and variants with buried and solvent-exposed Ala --> Gly mutations in the helix

Hydrogen-exchange rates were measured for RNase T1 and three variants with Ala --> Gly substitutions at a solvent-exposed (residue 21) and a buried (residue 23) position in the helix: A21G, G23A, and A21G + G23A. These results were used to measure the stabilities of the proteins. The hydrogen-exchange stabilities (DeltaG(HX)) for the most stable residues in each variant agree with the equilibrium conformational stability measured by urea denaturation (DeltaG(U)), if the effects of D(2)O and proline isomerization are included [Huyghues-Despointes, B. M. P., Scholtz, J. M., and Pace, C. N. (1999) Nat. Struct. Biol. 6, 210-212]. These residues also show similar changes in DeltaG(HX) upon Ala --> Gly mutations (DeltaDeltaG(HX)) as compared to equilibrium measurements (DeltaDeltaG(U)), indicating that the most stable residues are exchanging from the globally unfolded ensemble. Alanine is stabilizing compared to glycine by 1 kcal/mol at a solvent-exposed site 21 as seen by other methods for the RNase T1 protein and peptide helix [Myers, J. K., Pace, C. N., and Scholtz, J. M. (1997) Proc. Natl. Acad. Sci. U.S.A. 94, 3833-2837], while it is destabilizing at the buried site 23 by the same amount. For the A21G variant, only local NMR chemical shift perturbations are observed compared to RNase T1. For the G23A variant, large chemical shift changes are seen throughout the sequence, although X-ray crystal structures of the variant and RNase T1 are nearly superimposable. Ala --> Gly mutations in the helix of RNase T1 at both helical positions alter the native-state hydrogen-exchange stabilities of residues throughout the sequence.     

Conformational stability of legume lectins reflect their different modes of quaternary association: solvent denaturation studies on concanavalin A and winged bean acidic agglutinin

Thermodynamic parameters associated with the unfolding of the legume lectin, WBA II, were determined by isothermal denaturation. The analysis of isothermal denaturation data provided values for conformational stability and heat capacity for WBA II unfolding. To explore the role of intersubunit contact in stability, we carried out similar studies under identical conditions on Concanavalin A, a legume lectin of nearly similar size, buried hydrophobic surface area and tertiary structure to that of WBA II but with a different oligomerization pattern. Both proteins showed a reversible two-state unfolding with guanidine hydrochloride. As expected, the change in heat capacity upon unfolding was similar for both proteins at 3.5 and 3.7 kcal mol(-1) K(-1) for Concanavalin A and WBA II, respectively. Although the deltaG(H20) at the maximum stability of both proteins is around 16 kcal/mol, Concanavalin A exhibits greater stability at higher temperatures. The T(g) obtained for Concanavalin A and WBA II were 21 degrees C apart at 87.2 and 66.6 degrees C, respectively. The higher conformational stability at higher temperatures and the T(g) of Concanavalin A as compared to that of WBA II are largely due to substantial differences in the degree of subunit contact in these dimeric proteins. Ionic interactions and hydrogen bonding between the monomers of the two proteins also seem to play a significant role in the observed stability differences between these two proteins.     

A thermodynamic analysis of a family of small globular proteins: SH3 domains.

The stability and folding thermodynamics of two SH3-domains, belonging to Fyn and Abl proteins, have been studied by scanning calorimetry and urea-induced unfolding. They undergo an essentially two-state unfolding with parameters similar to those of the previously studied alpha-spectrin SH3 domain. The correlations between the thermodynamic parameters (heat capacity increment, delta Cp,U, the proportionality factor, m, and the Gibbs energy, delta Gw298) of unfolding and some integral structural parameters, such as polar and non-polar areas exposed upon domain denaturation, have been analyzed. The experimental data on delta Cp,U and the m-factor of the linear extrapolation model (LEM) obey the simple empirical correlations deduced elsewhere. The Gibbs energies calculated from the DSC data were compared with those found by fitting urea-unfolding curves to the LEM and the denaturant-binding model (DBM). The delta Gw298 values found with DBM correlate better with the DSC data, while those obtained with LEM are systematically smaller. The systematic difference between the parameters calculated with LEM and DBM are explained by an inherent imperfection of the LEM.