pH corrections and protein ionization in water/guanidinium chloride.

More than 30 years ago, Nozaki and Tanford reported that the pK values for several amino acids and simple substances in 6 M guanidinium chloride differed little from the corresponding values in low salt (Nozaki, Y., and C. Tanford. 1967. J. Am. Chem. Soc. 89:736-742). This puzzling and counter-intuitive result hinders attempts to understand and predict the proton uptake/release behavior of proteins in guanidinium chloride solutions, behavior which may determine whether the DeltaG(N-D) values obtained from guanidinium chloride-induced denaturation data can actually be interpreted as the Gibbs energy difference between the native and denatured states (Bolen, D. W., and M. Yang. 2000. Biochemistry. 39:15208-15216). We show in this work that the Nozaki-Tanford result can be traced back to the fact that glass-electrode pH meter readings in water/guanidinium chloride do not equal true pH values. We determine the correction factors required to convert pH meter readings in water/guanidinium chloride into true pH values and show that, when these corrections are applied, the effect of guanidinium chloride on the pK values of simple substances is found to be significant and similar to that of NaCl. The results reported here allow us to propose plausible guanidinium chloride concentration dependencies for the pK values of carboxylic acids in proteins and, on their basis, to reproduce qualitatively the proton uptake/release behavior for the native and denatured states of several proteins (ribonuclease A, alpha-chymotrypsin, staphylococcal nuclease) in guanidinium chloride solutions. Finally, the implications of the pH correction for the experimental characterization of protein folding energetics are briefly discussed.

Heat capacity analysis of oxidized Escherichia coli thioredoxin fragments (1--73, 74--108) and their noncovalent complex. Evidence for the burial of apolar surface in protein unfolded states.

We have calculated the absolute heat capacities of fragments 1--73 (N fragment) and 74--108 (C fragment) from thioredoxin, their complex and the uncleaved protein, from the concentration dependence of the apparent heat capacities of the solutions determined by differential scanning calorimetry. We find that, while the absolute heat capacities of uncleaved, unfolded thioredoxin and the C fragment are in good agreement with the theoretical values expected for fully solvated chains (calculated as the sum of the contributions of the constituent amino acids), the absolute heat capacities of the N fragment and the unfolded complex are about 2 kJ x K(-1) x mol(-1) lower than the fully solvated-chain values. We attribute this discrepancy to burial of the apolar surface in the N fragment (as burial of the polar area is expected to lead to an increase in heat capacity). Illustrative calculations suggest that burial of about 1000--1600 A(2) of apolar surface takes place in the N fragment (probably accompanied by the burial of a smaller amount of polar surface). In general, this work is supportive of heat capacity measurements on protein fragments being useful as probes of surface burial in studies to characterize protein unfolded states and the high regions of protein folding landscapes.

Native hydrogen bonds in a molten globule: the apoflavodoxin thermal intermediate.

The structure and energetics of protein-folding intermediates are poorly understood. We have identified, in the thermal unfolding of the apoflavodoxin from Anabaena PCC 7119, an equilibrium intermediate with spectroscopic properties of a molten globule and substantial enthalpy and heat capacity of unfolding. The structure of the intermediate is probed by mutagenesis (and phi analysis) of polar residues involved in surface-exposed hydrogen bonds connecting secondary-structure elements in the native protein. All hydrogen bonds analysed are formed in the molten globule intermediate, either with native strength or debilitated. This suggests the overall intermediate's topology and surface tertiary interactions are close to native, and indicates that hydrogen bonding may contribute significantly to shape the conformation and energetics of folding intermediates.

To charge or not to charge?

The ability to engineer proteins with increased thermostability will profoundly broaden their practical applications. Recent experimental results show that optimization of charge-charge interactions on the surface of proteins can be a useful strategy in the design of thermostable enzymes. Results also indicate a possibility that such optimized interactions provide structural determinants for enhanced stability of proteins from thermophilic organisms. In this article, the general strategy for design of thermostable proteins and perspectives for future studies are discussed.

Energetics of myo-inositol hexasulfate binding to human acidic fibroblast growth factor effect of ionic strength and temperature.

The binding of myo-inositol hexasulfate to an N-terminal truncated 132-amino-acid human acidic fibroblast growth factor form was studied by isothermal titration calorimetry. The technique yields values for the enthalpy change and equilibrium constant, from which the Gibbs energy and entropy change can also be calculated. Experiments in different buffers and pH values show that the proton balance in the reaction is negligible. Experiments at pH 7.0 in the presence of 0.2-0.6 M NaCl showed that the enthalpy and Gibbs energy changes parallel behaviour with ionic strength change, with values in the -21 to -11 kJ x mol(-1) range in the first case and in the -31 to -22 kJ x mol(-1) range in the second. No dependence of entropy on ionic strength was found, with a constant value of approximately 35 J x K(-1) x mol(-1) at all ionic strengths studied. The results can be interpreted in molecular terms by a model in which competitive binding of 3-4 chloride ions to the myo-inositol-binding site is assumed. Isothermal titration calorimetry was also performed at different temperatures and yielded a value of -142+/-13 J x K(-1) x mol(-1) for the heat-capacity change at pH 7.0 and 0.4 M NaCl. Using different parametric equations in the literature, changes on ligand binding in the range -100 to -200 A2 in solvent-accessible surface areas, both polar and apolar, were calculated from thermodynamic data. These values suggest a negligible overall conformational change in the protein when the ligand binds and agree closely with calculations performed with NMR structural data, in which it is shown that the most important negative change in total solvent-accessible surface area occurs in the amino acids Ile56, Gln57, Leu58 and Leu149, in the high-affinity receptor-binding region of the protein.

The sarcosine effect on protein stability: a case of nonadditivity?

We have used differential scanning calorimetry to determine the effect of low concentrations (C = 0-2 M) of the osmolyte sarcosine on the Gibbs energy changes (deltaG) for the unfolding of hen-egg-white lysozyme, ribonuclease A, and ubiquitin, under the same buffer and pH conditions. We have also computed this effect on the basis of the additivity assumption and using published values of the transfer Gibbs energies for the amino acid side chains and the peptide backbone unit. The values thus predicted for the slope delta deltaG/deltaC agree with the experimental ones, but only if the unfolded state is assumed to be compact (that is, if the accessibility to solvent of the unfolded state is modeled using segments excised from native structures). The additivity-based calculations predict similar delta deltaG/deltaC values for the three proteins studied. We point out that, to the extent that this approximate constancy of delta deltaG/deltaC holds, osmolyte-induced increases in denaturation temperature will be larger for proteins with low unfolding enthalpy (small proteins that bury a large proportion of apolar surface). The experimental results reported here are consistent with this hypothesis.

Lower kinetic limit to protein thermal stability: a proposal regarding protein stability in vivo and its relation with misfolding diseases.

In vitro thermal denaturation experiments suggest that, because of the possibility of irreversible alterations, thermodynamic stability (i.e., a positive value for the unfolding Gibbs energy) does not guarantee that a protein will remain in the native state during a given timescale. Furthermore, irreversible alterations are more likely to occur in vivo than in vitro because (a) some irreversible processes (e.g., aggregation, "undesirable" interactions with other macromolecular components, and proteolysis) are expected to be fast in the "crowded" cellular environment and (b) in many cases, the relevant timescale in vivo (probably related to the half-life for protein degradation) is expected to be longer than the timescale of the usual in vitro experiments (of the order of minutes). We propose, therefore, that many proteins (in particular, thermophilic proteins and "complex" proteins systems) are designed (by evolution) to have significant kinetic stability when confronted with the destabilizing effect of irreversible alterations. We show that, as long as these alterations occur mainly from non-native states (a Lumry-Eyring scenario), the required kinetic stability may be achieved through the design of a sufficiently high activation barrier for unfolding, which we define as the Gibbs energy barrier that separates the native state from the non-native ensemble (unfolded, partially folded, and misfolded states) in the following generalized Lumry-Eyring model: Native State <--> Non-Native Ensemble --> Irreversibly Denatured Protein. Finally, using familial amyloid polyneuropathy (FAP) as an illustrative example, we discuss the relation between stability and amyloid fibril formation in terms of the above viewpoint, which leads us to the two following tentative suggestions: (a) the hot spot defined by the FAP-associated amyloidogenic mutations of transthyretin reflects the structure of the transition state for unfolding and (b) substances that decrease the in vitro rate of transthyretin unfolding could also be inhibitors of amyloid fibril formation.

Comparative calorimetric study of non-amyloidogenic and amyloidogenic variants of the homotetrameric protein transthyretin.

Familial amyloidotic polyneuropathy (FAP) is an autosomal dominant hereditary type of amyloidosis involving amino acid substitutions in transthyretin (TTR). V30M-TTR is the most frequent variant, and L55P-TTR is the variant associated with the most aggressive form of FAP. The thermal stability of the wild-type, V30M-TTR, L55P-TTR and a non-amyloidogenic variant, T119M-TTR, was studied by high-sensitivity differential scanning calorimetry (DSC). The thermal unfolding of TTR is a spontaneous reversible process involving a highly co-operative transition between folded tetramers and unfolded monomers. All variants of transthyretin are very stable to the thermal unfolding that occurs at very high temperatures, most probably because of their oligomeric structure. The data presented in this work indicated that for the homotetrameric form of the wild-type TTR and its variants, the order of stability is as follows: wild-type TTR approximately > T119M-TTR > L55P-TTR > V30M-TTR, which does not correlate with their known amyloidogenic potential.

Engineering a thermostable protein via optimization of charge-charge interactions on the protein surface.

A simple theoretical model for increasing the protein stability by adequately redesigning the distribution of charged residues on the surface of the native protein was tested experimentally. Using the molecule of ubiquitin as a model system, we predicted possible amino acid substitutions on the surface of this protein which would lead to an increase in its stability. Experimental validation for this prediction was achieved by measuring the stabilities of single-site-substituted ubiquitin variants using urea-induced unfolding monitored by far-UV CD spectroscopy. We show that the generated variants of ubiquitin are indeed more stable than the wild-type protein, in qualitative agreement with the theoretical prediction. As a positive control, theoretical predictions for destabilizing amino acid substitutions on the surface of the ubiquitin molecule were considered as well. These predictions were also tested experimentally using correspondingly designed variants of ubiquitin. We found that these variants are less stable than the wild-type protein, again in agreement with the theoretical prediction. These observations provide guidelines for rational design of more stable proteins and suggest a possible mechanism of structural stability of proteins from thermophilic organisms.

Thermal versus guanidine-induced unfolding of ubiquitin. An analysis in terms of the contributions from charge-charge interactions to protein stability.

We have characterized the guanidine-induced unfolding of both yeast and bovine ubiquitin at 25 degrees C and in the acidic pH range on the basis of fluorescence and circular dichroism measurements. Unfolding Gibbs energy changes calculated by linear extrapolation from high guanidine unfolding data are found to depend very weakly on pH. A simple explanation for this result involves the two following assumptions: (1) charged atoms of ionizable groups are exposed to the solvent in native ubiquitin (as supported by accessible surface area calculations), and Gibbs energy contributions associated with charge desolvation upon folding (a source of pK shifts) are small; (2) charge-charge interactions (another source of pK shifts upon folding) are screened out in concentrated guanidinium chloride solutions. We have also characterized the thermal unfolding of both proteins using differential scanning calorimetry. Unfolding Gibbs energy changes calculated from the calorimetric data do depend strongly on pH, a result that we attribute to the pH dependence of charge-charge interactions (not eliminated in the absence of guanidine). In fact, we find good agreement between the difference between the two series of experimental unfolding Gibbs energy changes (determined from high guanidine unfolding data by linear extrapolation and from thermal denaturation data in the absence of guanidine) and the theoretical estimates of the contribution from charge-charge interactions to the Gibbs energy change for ubiquitin unfolding obtained by using the solvent-accessibility-corrected Tanford-Kirkwood model, together with the Bashford-Karplus (reduced-set-of-sites) approximation. This contribution is found to be stabilizing at neutral pH, because most charged groups on the native protein interact mainly with groups of the opposite charge, a fact that, together with the absence of large charge-desolvation contributions, may explain the high stability of ubiquitin at neutral pH. In general, our analysis suggests the possibility of enhancing protein thermal stability by adequately redesigning the distribution of solvent-exposed, charged residues on the native protein surface.

Cold denaturation of ubiquitin.

Temperature induced unfolding of bovine ubiquitin in solutions with different concentrations of guanidinium hydrochloride (GdmCl) has been measured using differential scanning calorimetry. It has been shown that at high concentrations of GdmCl the ubiquitin molecule can undergo both heat and cold induced denaturation. Analysis of the enthalpy of unfolding of ubiquitin in the presence of GdmCl shows a good agreement with the thermodynamic denaturant binding model. The unfolding Gibbs energy is found to change linearly with guanidine concentration up to zero denaturant concentration.

Are there equilibrium intermediate states in the urea-induced unfolding of hen egg-white lysozyme?

Protein folding intermediates that are sometimes populated at equilibrium under mild denaturing conditions have attracted much attention as plausible models for the kinetic intermediates transiently populated in the refolding kinetic pathways. Hen egg-white lysozyme is often considered as a typical example of close adherence to the equilibrium, two-state unfolding mechanism. However, recent small-angle X-ray scattering studies suggest that an equilibrium intermediate state is significantly populated in the urea-induced unfolding of this protein at moderately acidic pH. In this work, we analyze the urea-induced unfolding of hen egg-white lysozyme on the basis of steady-state fluorescence measurements, characterization of the folding-unfolding kinetics, double-jump unfolding assays for the amount of native protein, and double-jump refolding assays for the amount of unfolded protein. Our results do not provide support for the presence of an intermediate state and, in particular, disfavor that the following two types of intermediates be significantly populated at equilibrium: (1) intermediates showing a substantial quenching of the tryptophan fluorescence (such as that observed in the transient intermediates found in the refolding kinetic pathway under strongly native conditions) and (2) associating intermediates. Also, the deconvolution of the radius of gyration unfolding profile by using the values for the amount of native state derived from our double-jump unfolding assays is consistent with a two-state unfolding equilibrium and suggests, furthermore, that, in this case, large alterations in the average structure of the unfolded ensemble do not take place in response to changes in urea concentration. This work points up possible pitfalls in the experimental detection of equilibrium folding intermediates and suggests procedures to circumvent them.

Maximum entropy, analysis of kinetic processes involving chemical and folding-unfolding changes in proteins.

We show that numerical inversion of the Laplace transform by using the maximum entropy method can be successfully applied to the analysis of complex kinetic processes involving chemical and folding-unfolding changes in proteins. First, we present analyses of simulated data which support that: (i) the maximum entropy calculation of rate distributions, combined with Monte Carlo analyses of the associated uncertainties, yields results consistent with the information actually supplied by the data, thus preventing their over-interpretation; (ii) maximum entropy analysis may be used to extract discrete rates (corresponding to individual exponential contributions), as well as broad rate distributions (provided, of course, that the adequate information is supplied by the data). We further illustrate the applicability of the maximum entropy analysis with experimental data corresponding to two nontrivial model processes: (a) the kinetics of chemical modification of sulfhydryl groups in glycogen synthase by reaction with Ellman's reagent; (b) the kinetics of folding of ribonuclease a under strongly folding conditions, as monitored by fluorescence and optical absorption. Finally, we discuss that the maximum entropy approach should be particularly useful in studies on protein folding kinetics, which generally involve the comparison between several complex kinetic profiles obtained by using different physical probes. Thus, protein folding kinetics is usually interpreted in terms of kinetic mechanisms involving a comparatively small number of kinetic steps between well-defined protein states. According to this picture, rate distributions derived from experimental kinetic profiles by maximum entropy analysis are expected to show a small number of comparatively narrow peaks, from which we can determine, without a priori assumptions, the number of exponential contributions required to describe each experimental kinetic profile (the number of peaks), together with their amplitudes (from the peak areas), time constant values (from the peak positions), and associated Monte Carlo uncertainties. On the other hand, recent theoretical studies describe protein folding kinetics in terms of the protein energy landscape (the multidimensional surface of energy versus conformational degrees of freedom), emphasize the difficulty in defining a single reaction coordinate for folding, and point out that individual chains may fold by multiple pathways. This indicates that, in some cases at least, folding kinetics might have to be described in terms of broad rate distributions (rather than in terms of a small number of discrete exponential contributions related to kinetic steps between well-defined protein states). We suggest that the maximum entropy procedures described in this work may provide a method to detect this situation and to derive such broad rate distributions from experimental data.

Analysis of differential scanning calorimetry data for proteins. Criteria of validity of one-step mechanism of irreversible protein denaturation.

We consider in this work the analysis of the excess heat capacity C(p)(ex) versus temperature profiles in terms of a model of thermal protein denaturation involving one irreversible step. It is shown that the dependences of ln C(p)(ex) on 1 T (T is the absolute temperature) obtained at various temperature scanning rates have the same form. Several new methods for estimation of parameters of the Arrhenius equation are explored. These new methods are based on the fitting of theoretical equations to the experimental heat capacity data, as well as on the analysis of the dependence d(ln C (p)(ex)) d ( 1 T ) on 1 T . We have applied the proposed methods to calorimetric data corresponding to the irreversible thermal denaturation of Torpedo californica acetylcholinesterase, cellulase from Streptomyces halstedii JM8, and lentil lectin. Criteria of validity for the one-step irreversible denaturation model are discussed.

A model-independent, nonlinear extrapolation procedure for the characterization of protein folding energetics from solvent-denaturation data.

We have characterized the guanidine-induced denaturation of hen egg white lysozyme within the 30-75 degrees C temperature range on the basis of equilibrium fluorescence measurements, unfolding assays, kinetic fluorescence measurements, and differential scanning calorimetry. Analysis of the guanidine denaturation profiles according to the linear extrapolation method yields values for the denaturation Gibbs energy which are about 15 kJ/mol lower than those derived from differential scanning calorimetry. Our results strongly suggest that this discrepancy is not due to deviations from the two-state denaturation mechanism. We propose a new method for the determination of denaturation Gibbs energies from solvent-denaturation data (the constant-delta G extrapolation procedure). It employs several solvent-denaturation profiles (obtained at different temperatures) to generate the protein stability curve at zero denaturant concentration within the -8 to 8 kJ/mol delta G range. The method is model-independent and provides a practical, nonlinear alternative to the commonly employed linear extrapolation procedure. The application of the constant-delta G method to our data suggests that the guanidine-concentration dependence of the denaturation Gibbs energy is approximately linear over an extended concentration range but, also, that strong deviations from linearity may occur at low guanidine concentrations. We tentatively attribute these deviations to the abrupt change of the contribution to protein stability that arises from pairwise charge-charge electrostatic interactions. This contribution may be positive, negative, or close to zero, depending on the pH value and the charge distribution on the native protein surface [Yang, A.-S., & Honig, B. (1993) J. Mol. Biol. 231, 459-474], which may help to explain why disparate effects have been found when studying protein denaturation at low guanidine concentrations. Kinetic m values for lysozyme denaturation depend on temperature, in a manner which appears consistent with Hammond behavior.

An osmolyte effect on the heat capacity change for protein folding.

We have carried out a differential scanning calorimetry study into the pH effect on the thermal denaturation of ribonuclease A at several concentrations of the osmolyte sarcosine. In order to properly analyze these data, we have elaborated the thermodynamic theory of the linkage between temperature, cosolvent, and pH effects. The denaturation heat capacity increases with sarcosine concentration. The effects of temperature and sarcosine concentration on the denaturation enthalpy and entropy values are well described by convergence equations, with convergence temperatures of around 100 degrees C for the enthalpy and around 112 degrees C for the entropy; we suggest that these effects might be related to a solvent-induced alteration of the apolar-group-hydration contribution to the folding thermodynamics. From our data, we estimate that about 70 extra molecules of water are thermodynamically bound upon ribonuclease denaturation in diluted aqueous solutions of sarcosine; this number is 6-9 times smaller than that predicted on the basis of the following two premises: (a) the osmolyte is strongly excluded from the surface of both the native and the denatured protein and (b) the denatured state is a fully solvated chain. We suggest that at least one of these two premises does not hold. We briefly comment on the potential use of cosolvent effects on thermal denaturation to evaluate the degree of hydration of denatured proteins (thus providing an independent measure of the consequence of their possible residual structure) and, also, on the possibility of finding substances that are more efficient protein stabilizers than known osmolytes are.

The molecular basis of cooperativity in protein folding. Thermodynamic dissection of interdomain interactions in phosphoglycerate kinase.

In the presence of guanidine hydrochloride, phosphoglycerate kinase from yeast can be reversibly denatured by either heating or cooling the protein solution above or below room temperature [Griko, Y. V., Venyaminov, S. Y., & Privalov, P. L. (1989) FEBS Lett. 244, 276-278]. The heat denaturation of PGK is characterized by the presence of a single peak in the excess heat capacity function obtained by differential scanning calorimetry. The transition curve approaches the two-state mechanism, indicating that the two domains of the molecule display strong cooperative interactions and that partially folded intermediates are not largely populated during the transition. On the contrary, the cold denaturation is characterized by the presence of two peaks in the heat capacity function. Analysis of the data indicates that at low temperatures the two domains behave independently of each other. The crystallographic structure of PGK has been used to identify the nature of the interactions between the two domains. These interactions involve primarily the apposition of two hydrophobic surfaces of approximately 480 A2 and nine hydrogen bonds. This information, in conjunction with experimental thermodynamic values for hydrophobic, hydrogen bonding interactions and statistical thermodynamic analysis, has been used to quantitatively account for the folding/unfolding behavior of PGK. It is shown that this type of analysis accurately predicts the cooperative behavior of the folding/unfolding transition and its dependence on GuHCl concentration.

Theoretical analysis of Lumry-Eyring models in differential scanning calorimetry.

A theoretical analysis of several protein denaturation models (Lumry-Eyring models) that include a rate-limited step leading to an irreversibly denatured state of the protein (the final state) has been carried out. The differential scanning calorimetry transitions predicted for these models can be broadly classified into four groups: situations A, B, C, and C'. (A) The transition is calorimetrically irreversible but the rate-limited, irreversible step takes place with significant rate only at temperatures slightly above those corresponding to the transition. Equilibrium thermodynamics analysis is permissible. (B) The transition is distorted by the occurrence of the rate-limited step; nevertheless, it contains thermodynamic information about the reversible unfolding of the protein, which could be obtained upon the appropriate data treatment. (C) The heat absorption is entirely determined by the kinetics of formation of the final state and no thermodynamic information can be extracted from the calorimetric transition; the rate-determining step is the irreversible process itself. (C') same as C, but, in this case, the rate-determining step is a previous step in the unfolding pathway. It is shown that ligand and protein concentration effects on transitions corresponding to situation C (strongly rate-limited transitions) are similar to those predicted by equilibrium thermodynamics for simple reversible unfolding models. It has been widely held in recent literature that experimentally observed ligand and protein concentration effects support the applicability of equilibrium thermodynamics to irreversible protein denaturation. The theoretical analysis reported here disfavors this claim.

Differential scanning calorimetric study of carboxypeptidase B, procarboxypeptidase B and its globular activation domain.

High-sensitivity differential scanning calorimetry has been applied to the study of porcine pancreatic carboxypeptidase B, the proenzyme and its 81-residue activation domain. The thermal study has been carried out over a range of scan rates, ionic strengths and pH values. The thermal unfolding of the isolated activation domain has been found to be reversible and corresponds to that of a typical compact globular structure, with melting temperatures higher than those of the enzyme and proenzyme. Both proteins, on the other hand, undergo an irreversible, highly scan-rate-dependent thermal denaturation under all the experimental conditions investigated. The denaturation of the enzyme at pH 7.5 and the proenzyme at pH 7.5 and 9.0 follows the two-state irreversible model [Sánchez-Ruiz, J.M., López-Lacomba, J.L., Cortijo, M. & Mateo, P.L. (1988) Biochemistry 27, 1648-1652]. Thus the kinetic constants and activation parameters of the denaturation process could be obtained and compared to those for other proteins, particularly those of the closely related carboxypeptidase A system.