Characteristic thermodynamic properties of hydrated water for 20 amino acid residues in globular proteins

Thermodynamic properties associated with hydrated water of proteins of known three-dimensional structure were computed and average values of hydration free energy, enthalpy, and heat capacity of unfolding for every amino acid residue were obtained. Each amino acid residue had characteristic values; in particular, the quantities for a side chain reflected the character of the amino acid, while those for the main chain were more or less the same except for glycine, alanine, and proline. The major contribution to the quantities was from the end group(s) of a side chain. The following interesting features were found. 1) The hydration quantity of unfolding derived from the native and extended conformations for a protein was approximately equal to the sum of the corresponding average quantities of component amino acid residues in the protein. 2) The profile of a quantity such as hydration free energy of unfolding along the sequence computed from the accessible surface areas of the native and extended conformations showed a strong correlation with the profile obtained by allocating the average value for the amino acid residue at every position on the sequence. The correlation coefficients between two profiles for unfolding quantities of hydration, i.e., free energy, enthalpy, heat capacity, and free energy of side chain are 0.72, 0.62, 0.80, and 0.75, respectively. Thus, every amino acid residue in the native conformation of a globular protein seems to be located in such a position that a thermodynamic quantity for each residue is approximately equal to its average value.     

Thermodynamics of the temperature-induced unfolding of globular proteins.

The heat capacity, enthalpy, entropy, and Gibbs energy changes for the temperature-induced unfolding of 11 globular proteins of known three-dimensional structure have been obtained by microcalorimetric measurements. Their experimental values are compared to those we calculate from the change in solvent-accessible surface area between the native proteins and the extended polypeptide chain. We use proportionality coefficients for the transfer (hydration) of aliphatic, aromatic, and polar groups from gas phase to aqueous solution, we estimate vibrational effects, and we discuss the temperature dependence of each constituent of the thermodynamic functions. At 25 degrees C, stabilization of the native state of a globular protein is largely due to two favorable terms: the entropy of non-polar group hydration and the enthalpy of interactions within the protein. They compensate the unfavorable entropy change associated with these interactions (conformational entropy) and with vibrational effects. Due to the large heat capacity of nonpolar group hydration, its stabilizing contribution decreases quickly at higher temperatures, and the two unfavorable entropy terms take over, leading to temperature-induced unfolding.     

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.     

Thermodynamic properties of globular proteins and the principle of stabilization of their native structure

A semi-empirical method has been used to estimate the thermodynamic parameters of hydration of buried surface areas of ribonuclease S, lysozyme and myoglobin from the model of complete unfolding according to Ooi et al. ((1987) Proc. Natl. Acad. Sci. USA 84, 3086-3090). The buried surface area of proteins is considered as the difference between the accessible surface area of native protein and the completely extended polypeptide chain according to Lee and Richards ((1971) J. Mol. Biol. 55, 379-400). The contributions of nonpolar and polar protein groups to the general value of Gibbs energy, enthalpy, entropy and heat capacity of hydration have been determined. The obtained results on the thermodynamic behavior of proteins in the process of complete unfolding are in good agreement with the results of microcalorimetric studies of thermal denaturation.     

Thermodynamics of unfolding for turkey ovomucoid third domain: thermal and chemical denaturation.

We have used thermal and chemical denaturation to characterize the thermodynamics of unfolding for turkey ovomucoid third domain (OMTKY3). Thermal denaturation was monitored spectroscopically at a number of wave-lengths and data were subjected to van't Hoff analysis; at pH 2.0, the midpoint of denaturation (Tm) occurs at 58.6 +/- 0.4 degrees C and the enthalpy of unfolding at this temperature (delta Hm) is 40.8 +/- 0.3 kcal/mol. When Tm was perturbed by varying pH and denaturant concentration, the resulting plots of delta Hm versus Tm yield a mean value of 590 +/- 120 cal/(mol.K) for the change in heat capacity upon unfolding (delta Cp). A global fit of the same data to an equation that includes the temperature dependence for the enthalpy of unfolding yielded a value of 640 +/- 110 cal/(mol.K). We also performed a variation of the linear extrapolation method described by Pace and Laurents, which is an independent method for determining delta Cp (Pace, C.N. & Laurents, D., 1989, Biochemistry 28, 2520-2525). First, OMTKY3 was thermally denatured in the presence of a variety of denaturant concentrations. Linear extrapolations were then made from isothermal slices through the transition region of the denaturation curves. When extrapolated free energies of unfolding (delta Gu) were plotted versus temperature, the resulting curve appeared linear; therefore, delta Cp could not be determined. However, the data for delta Gu versus denaturant concentration are linear over an extraordinarily wide range of concentrations. Moreover, extrapolated values of delta Gu in urea are identical to values measured directly.     

Thermodynamics of unfolding of the alpha-amylase inhibitor tendamistat. Correlations between accessible surface area and heat capacity.

Unfolding of the small alpha-amylase inhibitor tendamistat (74 residues, 2 disulfide bridges) has been characterized thermodynamically by high sensitivity scanning microcalorimetry. To link the stability parameters with structural information we use heat capacity group parameters and water accessible surface areas to calculate the change in heat capacity on unfolding of tendamistat. Our results show that both the group parameter and surface area approaches provide a reasonable, though not perfect, basis for delta Cp calculations. When using the experimentally determined temperature-independent heat capacity increase of 2.89 kJ mol-1 K-1 tendamistat exhibits convergence of thermodynamic parameters at about 140 degrees C, in agreement with recent predictions of the temperature at which the hydrophobic hydration is supposed to disappear. Despite the apparent support of this new view of the hydrophobic effect, there are inconsistencies in the interpretation of the thermodynamic parameters and these are addressed in the Discussion. The specific stability of tendamistat is similar to that of modified bovine pancreatic trypsin inhibitor, with only two of the native three disulfide bridges intact. This observation confirms our previous conclusion that disulfide bridges affect significantly the enthalpy and entropy of unfolding. The recent study by Doig & Williams provides additional convincing support for this conclusion. The predictive scheme proposed by these authors permits a fair estimate of the Gibbs free energy and enthalpy changes of these two proteins.     

Basic pancreatic trypsin inhibitor has unusual thermodynamic stability parameters

The stability parameters delta Gst, delta Hst and delta Sst of native basic pancreatic trypsin inhibitor (BPTI) have been characterized by microcalorimetric unfolding studies in various buffer solutions, at different pH values and in the presence of guanidine hydrochloride. The unfolding enthalpy of BPTI, in contrast ot other globular proteins, exhibits a very small dependence on temperature, which results in a characteristic different temperature dependence of the Gibbs energy of stabilization. BPTI has a very high specific Gibbs energy of stabilization, which renders the slow exchange rates of amide protons understandable. Comparison of the unfolding entropy of BPTI at 110 degrees C with corresponding values of other proteins, revealed that the delta S values of BPTI are lower by 2.9 J/(K X residue). This lower value of the unfolding entropy is in good agreement with predictions of a theoretical study by Poland & Scheraga (1965) where the influence of crosslinks on the configurational entropy has been studied. Additionally, we were able to calculate an interaction enthalpy per site of -5.6 kJ/mol based on the measurements of unfolding of BPTI in 6 M-guanidine hydrochloride.     

A study on the enthalpy-entropy compensation in protein unfolding

A large number of thermodynamic data including the free energy, enthalpy, entropy, and heat capacity changes were collected for the denaturation of various proteins. Regression indicated that remarkable enthalpy-entropy compensation occurred in protein unfolding, which meant that the change in enthalpy was almost compensated by a corresponding change in entropy resulting in a smaller net free energy change. This behavior was proposed to result from the water molecule reorganization, which contributed significantly to the enthalpy and entropy changes but little to the free energy change in protein unfolding. It turned out that the enthalpy-entropy compensation could provide novel insights into the problem of enthalpy and entropy convergence in protein unfolding.     

Temperature dependence of the preferential interactions of ribonuclease A in aqueous co-solvent systems: thermodynamic analysis.

The temperature dependence of preferential solvent interactions with ribonuclease A in aqueous solutions of 30% sorbitol, 0.6 M MgCl2, and 0.6 M MgSO4 at low pH (1.5 and 2.0) and high pH (5.5) has been investigated. This protein was stabilized by all three co-solvents, more so at low pH than high pH (expect 0.6 M MgCl2 at pH 5.5). The preferential hydration of protein in all three co-solvents was high at temperatures below 30 degrees C and decreased with a further increase in temperature (for 0.6 M MgCl2 at pH 5.5, this was not significant), indicating a greater thermodynamic instability at low temperature than at high temperature. The preferential hydration of denatured protein (low pH, high temperature) was always greater than that of native protein (high pH, high temperature). In 30% sorbitol, the interaction passed to preferential binding at 45% for native ribonuclease A and at 55 degrees C for the denatured protein. Availability of the temperature dependence of the variation with sorbitol concentration of the chemical potential of the protein, (delta mu(2)/delta m3)T,p,m2, permitted calculation of the corresponding enthalpy and entropy parameters. Combination with available data on sorbitol concentration dependence of this interaction parameter gave (approximate) values of the transfer enthalpy, delta H2,tr, and transfer entropy delta S2,tr. Transfer of ribonuclease A from water into 30% sorbitol is characterized by positive values of the transfer free energy, transfer enthalpy, transfer entropy, and transfer heat capacity. On denaturation, the transfer enthalpy becomes more positive. This increment, however, is small relative to both the enthalpy of unfolding in water and to the transfer enthalpy of the native protein from water a 30% sorbitol solution.     

Differential scanning calorimetry of thermal unfolding of the methionine repressor protein (MetJ) from Escherichia coli.

The thermal stability of the methionine repressor protein from Escherichia coli (MetJ) has been examined over a wide range of pH (pH 3.5-10) and ionic strength conditions using differential scanning calorimetry. Under reducing conditions, the transitions are fully reversible, and thermograms are characteristic of the cooperative unfolding of a globular protein with a molecular weight corresponding to the MetJ dimer, indicating that no dissociation of this dimeric protein occurs before unfolding of the polypeptide chains under most conditions. In the absence of reducing agent, repeated scans in the calorimeter show only partial reversibility, though the thermodynamic parameters derived from the first scans are comparable to those obtained under fully reversible conditions. The protein is maximally stable (Tm 58.5 degrees C) at about pH 6, close to the estimated isoelectric point, and stability is enhanced by increasing ionic strength in the range I = 0.01-0.4 M. The average calorimetric transition enthalpy (delta Hm) for the dimer is 505 +/- 28 kJ mol-1 under physiological conditions (pH 7, I = 0.125, Tm = 53.2 degrees C) and shows a small temperature dependence which is consistent with an apparent denaturational heat capacity change (delta Cp) of about +8.9 kJ K-1 mol-1. The effects of both pH and ionic strength on the transition temperature and free energy of MetJ unfolding are inconsistent with any single amino acid contribution and are more likely the result of more general electrostatic interactions, possibly including significant contributions from electrostatic repulsion between the like-charged monomers which can be modeled by a Debye-Hückel screened potential.     

Thermodynamics of the hydrophobic effect. III. Condensation and aggregation of alkanes, alcohols, and alkylamines

Knowledge of the energetics of the low solubility of non-polar compounds in water is critical for the understanding of such phenomena as protein folding and biomembrane formation. Solubility in water can be considered as one leg of the three-part thermodynamic cycle - vaporization from the pure liquid, hydration of the vapor in aqueous solution, and aggregation of the substance back into initial pure form as an immiscible phase. Previous studies on the model compounds n-alkanes, 1-alcohols, and 1-aminoalkanes have noted that the thermodynamic parameters (Gibbs free energy, DeltaG; enthalpy, DeltaH; entropy, DeltaS; and heat capacity, DeltaC(p)) associated with these three processes are generally linear functions of the number of carbons in the alkyl chains. Here we assess the accuracy and limitations of the assumption of additivity of CH(2) group contributions to the thermodynamic parameters for vaporization, hydration, and aggregation. Processes of condensation from pure gas to liquid and aqueous solution to aggregate are compared. Hydroxy, amino, and methyl headgroup contributions are estimated, liquid and solid aggregates are distinguished. Most data in the literature were obtained for compounds with short aliphatic hydrocarbon tails. Here we emphasize long aliphatic chain behavior and include our recent experimental data on long chain alkylamine aggregation in aqueous solution obtained by titration calorimetry and van't Hoff analysis. Contrary to what is observed for short compounds, long aliphatic compound aggregation has a large exothermic enthalpy and negative entropy.     

Calculation of the thermodynamic quantities of solvation for lysozyme and β-lactoglobulin a in guanidinium chloride

The thermodynamic quantities of solvation, that is, Gibbs free energy, enthalpy, and entropy for the transfer of lysozyme and β-lactoglobulin A from water to 6M guanidinium chloride solution, were calculated from the respective contributions of constituent groups. Comparison of the calculated values with the experimental ones reveals satisfactory agreement for lysozyme, whereas for β-lactoglobulin A, it is semiquantitative. Thus the method of calculation appears to be fundamentally sound. The reasons for the differences in calculated and experimental value are briefly discussed.     

Energetics of interactions of aromatic hydrocarbons with water

The thermodynamics of transfer of aromatic (benzene, toluene) and aliphatic (ethane, propane, butane) hydrocarbons from the gas phase into water in the temperature range 5–125°C have been analyzed in order to determine the net hydration effect of these compounds. In the case of the aromatic hydrocarbons the enthalpic contribution predominates over the entropic contribution to the Gibbs energy of hydration. This results in a negative value of the hydration Gibbs energy of aromatic hydrocarbons, in contrast to the positive Gibbs energy of hydration of aliphatic hydrocarbons. The different sign of the hydration Gibbs energies indicates that the mechanism causing hydrophobicity of aromatic hydrocarbons has different nature than that causing the hydrophobicity of aliphatic hydrocarbons. The comparison of hydration of aliphatic and aromatic hydrocarbons leads to the following thermodynamic parameters for these additional interactions between the benzene ring and water at 25°C: enthalpy −5.4 kJ/mol, entropy 26.8 J/K mol and Gibbs energy −13.4 kJ/mol. The large enthalpic contribution to the Gibbs energy of hydration of aromatic hydrocarbons probably comes from the ability of the aromatic ring to accept hydrogens from water, forming hydrogen bonds.     

Thermodynamics of globular proteins

The analysis of temperature-induced unfolding of proteins in aqueous solutions was performed. Based on the data of thermodynamic parameters of protein unfolding and using the method of semi-empirical calculations of hydration parameters at reference temperature 298 K, we obtained numerical values of enthalpy, free energy, and entropy which characterize the unfolding of proteins in the ‘gas phase’. It was shown that specific values of the energy of weak intramolecular bonds (?H^int), conformational free energy (?G^conf) and entropy (?S^conf) are the same for proteins with molecular weight 7–25 kDa. Using the energy value (?H^int) and the proposed approach for estimation of the conformational entropy of native protein (S^NC), numerical values of the absolute free energy (G^NC) were obtained.     

Calorimetric study of the complexes between polyuridylic acid and adenylic nucleotides.

Soluble complexes of poly (U) and adenylic nucleotides in NaCl solutions were studied by scanning microcalorimetry. The melting enthalpies, delta Hm, of poly (U) complexes with adenosine, 2',3' -cAMP, 2'(3')-AMP, 5-AMP, ADP, ATP in 1 M NaCl are 50.5; 45.0; 42.9; 28.6; 26.1 and 25.6 kJ/mole triplets, respectively. Delta Hm is independent of the complex melting temperature, Tm. The calorimetric enthalpies are considerably lower than the apparent delta Hv.H. obtained from Tm dependence on free monomer concentration. The enthalpy of complex formation in 1 M NaCl depends neither ob the number nor on the degree of ionization of the phosphate groups but is essentially determined by their 5' - or 2'(3')-position. In contrast to 2'(3')- AMP. 2 poly (U), delta Hm of 5'AMP. 2 poly (U) increases considerably at lowering Na+ concentration. The enthalpy of poly (U) double helix melting in 1 M NaCl is 8.8 kJ/mole pairs which is 2.5 times lower than that in MgCl2 solutions.     

Thermodynamic Characterization of the Unfolding of the Prion Protein

The prion protein appears to be unusually susceptible to conformational change, and unlike nearly all other proteins, it can easily be made to convert to alternative misfolded conformations. To understand the basis of this structural plasticity, a detailed thermodynamic characterization of two variants of the mouse prion protein (moPrP), the full-length moPrP (23–231) and the structured C-terminal domain, moPrP (121–231), has been carried out. All thermodynamic parameters governing unfolding, including the changes in enthalpy, entropy, free energy, and heat capacity, were found to be identical for the two protein variants. The N-terminal domain remains unstructured and does not interact with the C-terminal domain in the full-length protein at pH 4. Moreover, the enthalpy and entropy of unfolding of moPrP (121–231) are similar in magnitude to values reported for other proteins of similar size. However, the protein has an unusually high native-state heat capacity, and consequently, the change in heat capacity upon unfolding is much lower than that expected for a protein of similar size. It appears, therefore, that the native state of the prion protein undergoes substantial fluctuations in enthalpy and hence, in structure.     

Non-linear effects of temperature and urea on the thermodynamics and kinetics of folding and unfolding of hisactophilin

Extensive measurements and analysis of thermodynamic stability and kinetics of urea-induced unfolding and folding of hisactophilin are reported for 5-50 degrees C, at pH 6.7. Under these conditions hisactophilin has moderate thermodynamic stability, and equilibrium and kinetic data are well fit by a two-state transition between the native and the denatured states. Equilibrium and kinetic m values decrease with increasing temperature, and decrease with increasing denaturant concentration. The betaF values at different temperatures and urea concentrations are quite constant, however, at about 0.7. This suggests that the transition state for hisactophilin unfolding is native-like and changes little with changing solution conditions, consistent with a narrow free energy profile for the transition state. The activation enthalpy and entropy of unfolding are unusually low for hisactophilin, as is also the case for the corresponding equilibrium parameters. Conventional Arrhenius and Eyring plots for both folding and unfolding are markedly non-linear, but these plots become linear for constant DeltaG/T contours. The Gibbs free energy changes for structural changes in hisactophilin have a non-linear denaturant dependence that is comparable to non-linearities observed for many other proteins. These non-linearities can be fit for many proteins using a variation of the Tanford model, incorporating empirical quadratic denaturant dependencies for Gibbs free energies of transfer of amino acid constituents from water to urea, and changes in fractional solvent accessible surface area of protein constituents based on the known protein structures. Noteworthy exceptions that are not well fit include amyloidogenic proteins and large proteins, which may form intermediates. The model is easily implemented and should be widely applicable to analysis of urea-induced structural transitions in proteins.     

Conformational study of angiotensin II

Conformational free energy calculations using an empirical potential ECEPP/3 (Empirical Conformational Energy Program for Peptides, Version 3) were carried out on angiotensin II (AII) of sequence Asp-Arg-Val-Tyr-Ile-His-Pro-Phe to find the stable conformations of the free state in the unhydrated and the hydrated states. A conformational analysis of the unhydrated state was carried out using the buildup procedure. The free energy calculation using the hydration shell model was also carried out to obtain the stable conformation of the hydrated state. The calculated stable conformations of AII in both states have a partially right-handed α-helical structure stabilized by short- and medium-range interactions. The similarity between the lowest free energy conformations of the unhydrated and hydrated states suggests that the hydration might not be important to stabilize the overall conformation of AII in a free state. The absence of any intramolecular interaction of the Tyr side chain suggests the possible interaction of this residue with the receptor. In this study, we found that the low free energy conformations contain both the parallel-plate and the perpendicular-plate geometries of the His and Phe rings, suggesting the coexistence of both conformations. © 1996 John Wiley & Sons, Inc.     

Elucidating protein thermodynamics from the three-dimensional structure of the native state using network rigidity

Given the three-dimensional structure of a protein, its thermodynamic properties are calculated using a recently introduced distance constraint model (DCM) within a mean-field treatment. The DCM is constructed from a free energy decomposition that partitions microscopic interactions into a variety of constraint types, i.e., covalent bonds, salt-bridges, hydrogen-bonds, and torsional-forces, each associated with an enthalpy and entropy contribution. A Gibbs ensemble of accessible microstates is defined by a set of topologically distinct mechanical frameworks generated by perturbing away from the native constraint topology. The total enthalpy of a given framework is calculated as a linear sum of enthalpy components over all constraints present. Total entropy is generally a nonadditive property of free energy decompositions. Here, we calculate total entropy as a linear sum of entropy components over a set of independent constraints determined by a graph algorithm that builds up a mechanical framework one constraint at a time, placing constraints with lower entropy before those with greater entropy. This procedure provides a natural mechanism for enthalpy-entropy compensation. A minimal DCM with five phenomenological parameters is found to capture the essential physics relating thermodynamic response to network rigidity. Moreover, two parameters are fixed by simultaneously fitting to heat capacity curves for histidine binding protein and ubiquitin at five different pH conditions. The three free parameter DCM provides a quantitative characterization of conformational flexibility consistent with thermodynamic stability. It is found that native hydrogen bond topology provides a key signature in governing molecular cooperativity and the folding-unfolding transition.