Enthalpy–entropy compensation phenomena in water solutions of proteins and small molecules: A ubiquitous properly of water

This article presents evidence for the existence of a specific linear relationship between the entropy change and the enthalpy change in a variety of processes of small solutes in water solution. The processes include solvation of ions and nonelectrolytes, hydrolysis, oxidation–reduction, ionization of weak electrolytes, and quenching of indole fluorescence among others. The values of the proportionality constant, called the compensation temperature, lie in a relatively narrow range, from about 250 to 315 °K, for all these processes. Such behavior can be a consequence of experimental errors but for a number of the processes the precision of the data is sufficient to show that the enthalpy–entropy compensation pattern is real. It is tentatively concluded that the pattern is real, very common and a consequence of the properties of liquid water as a solvent regardless of the solutes and the solute processes studied. As such the phenomenon requires that theoretical treatments of solute processes in water be expanded by inclusion of a specific treatment of the characteristic of water responsible for compensation behavior. The possible bases of the effect are proposed to be temperature-independent heat-capacity changes and/or shifts in concentrations of the two phenomenologically significant species of water. The relationship of these alternatives to the two-state process of water suggested by spectroscopic and relaxation studies is examined. The existence of a similar and probably identical relationship between enthalpy and entropy change in a variety of protein reactions suggests that liquid water plays a direct role in many protein processes and may be a common participant in the physiological function of proteins. It is proposed that the linear enthalpy–entropy relationship be used as a diagnostic test for the participation of water in protein processes. On this basis the catalytic processes of chymotrypsin and acetylcholinesterase are dominated by the properties of bulk water. The binding of oxygen by hemoglobin may fall in the same category. Similarities and differences in the behavior of small-solute and protein processes are examined to show how they may be related. No positive conclusions are established, but it is possible that protein processes are coupled to water via expansions and contractions of the protein and that in general the special pattern of enthalpy–entropy compensation is a consequent of the properties of water which require that expansions and contractions of solutes effect changes in the free volume of the nearby liquid water. It is shown that proteins can be expected to respond to changes in nearby water and interfacial free energy by expansions and contractions. Such responses may explain a variety of currently unexplained characteristics of protein solutions. More generally, the enthalpy–entropy compensation pattern appears to be the thermodynamic manifestation of “structure making” and “structure breaking,” operationally defined terms much used in discussions of water solutions. If so, the compensation pattern is ubiquitous and requires re-examination of a large body of molecular interpretations derived from quantitative studies of processes in water. Theories of processes in water may have to be expanded to accommodate this aspect of water behavior.     

Why water-soluble, compact, globular proteins have similar specific enthalpies of unfolding at 110 degrees C.

The changes in free energy, enthalpy, and entropy of unfolding have been measured for many water-soluble, compact, globular proteins by a number of workers. In principle, a wide range in stability could be achieved by proteins, as measured by the free energy of unfolding; in practice, evolution only allows a narrow range in this quantity. Proteins are only marginally stable at room temperature for many possible reasons, including ensuring that folding is reversible and polypeptide chains are not trapped in incorrectly folded structures. Many of these proteins have approximately the same values of enthalpy of unfolding around 110 degrees C. We show here that this arises because the change in entropy of unfolding at room temperature and the change in heat capacity on unfolding, which governs the temperature variation of the enthalpy and entropy, both vary with the magnitude of the hydrophobic effect in the protein. As all these proteins have evolved to achieve similar stabilities at room temperature, the enthalpy of unfolding will also vary with the size of the hydrophobic effect in the protein. A consequence of this is that curves of the specific unfolding enthalpy against temperature for different proteins intersect around 110 degrees C. A similar conclusion, on the basis of similar melting points rather than similar free energies of unfolding, has been reached independently by Baldwin and Muller (R. L. Baldwin, personal communication).     

Entropy—enthalpy compensation: Fact or artifact?

The phenomenon of entropy–enthalpy (S‐H) compensation is widely invoked as an explanatory principle in thermodynamic analyses of proteins, ligands, and nucleic acids. It has been suggested that this compensation is an intrinsic property of either complex, fluctuating, or aqueous systems. The questions examined here are whether the observed compensation is extra‐thermodynamic (i.e., reflects anything more than the well‐known laws of statistical thermodynamics) and if so, what does it reveal about the system? Compensation is rather variably defined in the literature and different usages are discussed. The most precise and interesting one, which is considered here, is a linear relationship between ΔH and ΔS for some series of perturbations or changes in experimental variable. Some recent thermodynamic data on proteins purporting to show compensation is analyzed and shown to be better explained by other causes. A general statistical mechanical model of a complex system is analyzed to explore whether and under what conditions extra‐thermodynamic compensation can occur and what it reveals about the system. This model shows that the most likely behavior to be seen is linear S‐H compensation over a rather limited range of perturbations with a compensation temperature Tc = dΔH/dΔS within 20% of the experimental temperature. This behavior is insensitive to the details of the model, thus revealing little extra‐thermodynamic or causal information about the system. In addition, it will likely be difficult to distinguish this from more trivial forms of compensation in real experimental systems.     

Two-dimensional differential scanning calorimetry: simultaneous resolution of intrinsic protein structural energetics and ligand binding interactions by global linkage analysis.

A general theoretical development for the design and analysis of two-dimensional thermal stability surfaces of proteins is presented. The surfaces are generated from multiple excess heat capacity profiles ( vs T) obtained at varying concentrations of an interacting ligand. The energetics of both the intrinsic protein stability and the protein-ligand interaction are simultaneously resolved by employing statistical thermodynamic models in global linkage analysis. This formalism allows resolution of the intrinsic protein folding-unfolding parameters (enthalpy, entropy, and heat capacity changes) as well as the ligand interaction parameters (binding stoichiometry, enthalpy, entropy, and heat capacity changes). The theory has been applied to the case of ribonuclease A and its interaction with cytidine-2'-monophosphate. The accuracy of the thermodynamic parameters obtained by this approach compares within error with those parameters that can be obtained by direct measurements.     

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.     

Effects of mutations on the thermodynamics of a protein folding reaction: implications for the mechanism of formation of the intermediate and transition states

We have measured changes in heat capacity, entropy, and enthalpy for each step in the folding reaction of CD2.d1 and evaluated the effects of core mutations on these properties. All wild-type and mutant forms fold through a rapidly formed intermediate state that precedes the rate-limiting transition state. Mutations have a pronounced effect on the enthalpy of both the intermediate and folded states, but in all cases a compensatory change in entropy results in a small net free-energy change. While the enthalpy change in the folded state can be attributed to a loss of van der Waals interactions, it has already been shown that changes in the stability of the intermediate are dominated by changes in secondary structure propensity [Lorch et al. (1999) Biochemistry 38, 1377-1385]. It follows that the thermodynamic basis of beta-propensity is enthalpic in origin. The effects of mutations on the enthalpy and entropy of the transition state are smaller than on the ground states. This relative insensitivity to mutation is discussed in the light of theories concerning the nature of the rate-limiting barrier in folding reactions.     

Thermodynamic consequences of the removal of a disulphide bridge from hen lysozyme.

Differential scanning calorimetry experiments as a function of pH have been carried out for native hen egg white lysozyme and a three-disulphide derivative (CM6,127-lysozyme). The results indicate that the enthalpy (delta H298) and heat capacity changes (delta Cp) for unfolding are closely similar for the two proteins. This shows that the substantial reduction (25 degrees C at pH 3.8) in Tm resulting from removal of the 6-127 disulphide bond can, to a good approximation, be attributed totally to an increase in the entropy difference between the native and denatured states. The significance of this result for understanding the factors influencing the stability of folded proteins is discussed.     

ProtSA: a web application for calculating sequence specific protein solvent accessibilities in the unfolded ensemble

Background  

The stability of proteins is governed by the heat capacity, enthalpy and entropy changes of folding, which are strongly correlated to the change in solvent accessible surface area experienced by the polypeptide. While the surface exposed in the folded state can be easily determined, accessibilities for the unfolded state at the atomic level cannot be obtained experimentally and are typically estimated using simplistic models of the unfolded ensemble. A web application providing realistic accessibilities of the unfolded ensemble of a given protein at the atomic level will prove useful.     

Observations on the origin of the non-linear van't Hoff behaviour of polypeptides in hydrophobic environments.

In this paper we describe a general procedure to determine the thermodynamic parameters associated with the interaction of polypeptides or proteins with immobilised lipophilic compounds such as non-polar n-octyl groups. To this end, the binding behaviour of an all L-alpha-polypeptide, 1, and its retro-inverso-isomer, 2, has been investigated with an n-octylsilica and water-organic solvent mixture containing different percentages of acetonitrile or methanol over the temperature range of 278-338 K. The results confirm that non-linear van'ts Hoff plots occur with this pair of polypeptide isomers, depending on the solvent composition. These findings are consistent with the changes in the thermodynamic parameters, enthalpy of association, delta Hoassoc,i, entropy of association, delta Soassoc,i, and heat capacity, delta Cop,i, all having significant temperature dependencies. Theoretical relationship linking the changes in the delta Hoassoc,i, delta Soassoc,i and delta Cop,i values of these polypeptide-non-polar ligate systems, as a function of temperature, T, have been validated. Significant differences were observed in the magnitudes of these thermodynamic quantities when acetonitrile or methanol was employed as the organic solvent. The origin of these solvent-dependent effects can be attributed to the hydrogen-bonding propensity of the respective solvent. Involvement of enthalpy-entropy compensation effects associated with the interaction of these polypeptides with the hydrophobic ligates has also been documented. Analysis of empirical extra-thermodynamic relationships associated with molecular structural properties of these polypeptides, such as the slope term, S, derived from the plots of the logarithmic capacity factor, log k'i, of these polypeptides vs. the volume fraction of the organic solvent, [symbol: see text] as a function of temperature, T, has also revealed similar correlations in terms of the interactive behaviour of polypeptides 1 and 2 under these experimental conditions. These findings provide an extended thermodynamic and extra-thermodynamic framework to examine the solvational, conformational and other equilibrium processes that polypeptides (or proteins) can undergo in the presence of n-alkylsilicas or other classes of immobilised hydrophobic surfaces. The experimental approach utilised in this study with these topologically similar polypeptides thus represents a generic procedure to explore the behaviour of polypeptides or proteins in non-polar environments in terms of their molecular properties and the associated linear free energy relationships that determine their interactive behaviour.     

Searching for quantitative entropy-enthalpy compensation among protein variants

Entropy-enthalpy (SH) compensation occurs when a small change in DeltaG is caused by large, and nearly compensatory, changes in DeltaH and DeltaS. It is considered a ubiquitous property of reactions in water. Because water is intimately involved in protein stability, SH compensation among protein variants, if it exists, could lead to important knowledge about protein-water interactions. In light of recent theoretical work on SH compensation, we gathered thermodynamic data for >200 protein variants to seek evidence for the simplest quantitative model of SH compensation (i.e., The van't Hoff denaturation enthalpy divided by the van't Hoff denaturation entropy is a constant). We conclude that either the data are insufficient to support the idea that quantitative SH compensation is a general feature of variant proteins or that such compensation does not exist. This study reinforces the idea that DeltaH-versus-DeltaS plots should not be used to provide evidence for SH compensation.     

Linear free-energy model description of the conformational stability of uracil-DNA glycosylase inhibitor A thermodynamic characterization of interaction with denaturant and cold denaturation.

The equilibrium unfolding of uracil DNA glycosylase inhibitor (Ugi), a small acidic protein of molecular mass 9474 Da, has been studied by a combination of thermal-induced and guanidine hydrochloride (GdnCl)-induced denaturation. The analysis of the denaturation data provides a measure of the changes in conformational free energy, enthalpy, entropy and heat capacity DeltaCp that accompany the equilibrium unfolding of Ugi over a wide range of temperature and GdnCl concentration. The unfolding of Ugi is a simple two-state, reversible process. The protein undergoes both low-temperature and high-temperature unfolding even in the absence of GdnCl but more so in the presence of denaturant. The data are consistent with the linear free-energy model and with a temperature independent DeltaCp over the large temperature range of unfolding. The small DeltaCp (6.52 kJ.mol-1.K-1) for the unfolding of Ugi, is perhaps a reflection of a relatively small, buried hydrophobic core in the folded form of this small monomeric protein. Despite a relatively low value of DeltaG(H2O), 7.40 kJ.mol-1 at pH 8.3, Ugi displays considerable stability with the temperature of maximum stability being 301.6 K.     

Rigidity Emerges during Antibody Evolution in Three Distinct Antibody Systems: Evidence from QSFR Analysis of Fab Fragments

The effects of somatic mutations that transform polyspecific germline (GL) antibodies to affinity mature (AM) antibodies with monospecificity are compared among three GL-AM Fab pairs. In particular, changes in conformational flexibility are assessed using a Distance Constraint Model (DCM). We have previously established that the DCM can be robustly applied across a series of antibody fragments (VL to Fab), and subsequently, the DCM was combined with molecular dynamics (MD) simulations to similarly characterize five thermostabilizing scFv mutants. The DCM is an ensemble based statistical mechanical approach that accounts for enthalpy/entropy compensation due to network rigidity, which has been quite successful in elucidating conformational flexibility and Quantitative Stability/Flexibility Relationships (QSFR) in proteins. Applied to three disparate antibody systems changes in QSFR quantities indicate that the VH domain is typically rigidified, whereas the VL domain and CDR L2 loop become more flexible during affinity maturation. The increase in CDR H3 loop rigidity is consistent with other studies in the literature. The redistribution of conformational flexibility is largely controlled by nonspecific changes in the H-bond network, although certain Arg to Asp salt bridges create highly localized rigidity increases. Taken together, these results reveal an intricate flexibility/rigidity response that accompanies affinity maturation.     

Comparisons of pressure and temperature activation parameters for amide hydrogen exchange in T4 lysozyme

Activation enthalpies and entropies are reported for proton-deuteron exchange at 42 amide sites in T4 lysozyme and compared with activation volumes for the same residues obtained earlier [Hitchens, T. K., and Bryant, R. G. (1998) Biochemistry 37, 5878-5887]. There is no correlation found between activation volume and activation entropy or activation enthalpy. The activation enthalpy is linearly related to the activation entropy in part as a consequence of a relatively narrow sampling window for the rate constants that corresponds to a narrow range of activation free energy. A consequence of the entropy-enthalpy compensation is preservation of rank order of proton exchange. Variations in DeltaH, DeltaS, and DeltaV for residues that are structurally close together in the folded protein suggest that there may be a variety of energetically distinct pathways for the access of solvent to these structurally related exchange sites.     

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.     

Investigating Homology between Proteins using Energetic Profiles

Accumulated experimental observations demonstrate that protein stability is often preserved upon conservative point mutation. In contrast, less is known about the effects of large sequence or structure changes on the stability of a particular fold. Almost completely unknown is the degree to which stability of different regions of a protein is generally preserved throughout evolution. In this work, these questions are addressed through thermodynamic analysis of a large representative sample of protein fold space based on remote, yet accepted, homology. More than 3,000 proteins were computationally analyzed using the structural-thermodynamic algorithm COREX/BEST. Estimated position-specific stability (i.e., local Gibbs free energy of folding) and its component enthalpy and entropy were quantitatively compared between all proteins in the sample according to all-vs.-all pairwise structural alignment. It was discovered that the local stabilities of homologous pairs were significantly more correlated than those of non-homologous pairs, indicating that local stability was indeed generally conserved throughout evolution. However, the position-specific enthalpy and entropy underlying stability were less correlated, suggesting that the overall regional stability of a protein was more important than the thermodynamic mechanism utilized to achieve that stability. Finally, two different types of statistically exceptional evolutionary structure-thermodynamic relationships were noted. First, many homologous proteins contained regions of similar thermodynamics despite localized structure change, suggesting a thermodynamic mechanism enabling evolutionary fold change. Second, some homologous proteins with extremely similar structures nonetheless exhibited different local stabilities, a phenomenon previously observed experimentally in this laboratory. These two observations, in conjunction with the principal conclusion that homologous proteins generally conserved local stability, may provide guidance for a future thermodynamically informed classification of protein homology.     

Contribution of translational and rotational motions to molecular association in aqueous solution

Much uncertainty and controversy exist regarding the estimation of the enthalpy, entropy, and free energy of overall translational and rotational motions of solute molecules in aqueous solutions, quantities that are crucial to the understanding of molecular association/recognition processes and structure-based drug design. A critique of the literature on this topic is given that leads to a classification of the various views. The major stumbling block to experimentally determining the translational/rotational enthalpy and entropy is the elimination of vibrational perturbations from the measured effects. A solution to this problem, based on a combination of energy equi-partition and enthalpy-entropy compensation, is proposed and subjected to verification. This method is then applied to analyze experimental data on the dissociation/unfolding of dimeric proteins. For one translational/rotational unit at 1 M standard state in aqueous solution, the results for enthalpy (H degrees (tr)), entropy (S degrees (tr)), and free energy (G degrees (tr)) are H (degrees) (tr) = 4.5 +/- 1.5RT, S (degrees) (tr) = 5 +/- 4R, and G (degrees) (tr) = 0 +/- 5RT. Therefore, the overall translational and rotational motions make negligible contribution to binding affinity (free energy) in aqueous solutions at 1 M standard state.     

Extent of enthalpy-entropy compensation in protein-ligand interactions

The extent of enthalpy-entropy compensation in protein-ligand interactions has long been disputed because negatively correlated enthalpy (ΔH) and entropy (TΔS) changes can arise from constraints imposed by experimental and analytical procedures as well as through a physical compensation mechanism. To distinguish these possibilities, we have created quantitative models of the effects of experimental constraints on isothermal titration calorimetry (ITC) measurements. These constraints are found to obscure any compensation that may be present in common data representations and regression analyses (e.g., in ΔH vs. -TΔS plots). However, transforming the thermodynamic data into ΔΔ-plots of the differences between all pairs of ligands that bind each protein diminishes the influence of experimental constraints and representational bias. Statistical analysis of data from 32 diverse proteins shows a significant and widespread tendency to compensation. ΔΔH versus ΔΔG plots reveal a wide variation in the extent of compensation for different ligand modifications. While strong compensation (ΔΔH and -TΔΔS opposed and differing by < 20% in magnitude) is observed for 22% of modifications (twice that expected without compensation), 15% of modifications result in reinforcement (ΔΔH and -TΔΔS of the same sign). Because both enthalpy and entropy changes arise from changes to the distribution of energy states on binding, there is a general theoretical expectation of compensated behavior. However, prior theoretical studies have focussed on explaining a stronger tendency to compensation than actually found here. These results, showing strong but imperfect compensation, will act as a benchmark for future theoretical models of the thermodynamic consequences of ligand modification.     

Binding of bovine pancreatic trypsin inhibitor to trypsinogen: spectroscopic and volumetric studies

We have investigated the binding of bovine pancreatic trypsin inhibitor (BPTI) to bovine trypsinogen by combining ultrasonic velocimetry, high precision densimetry, and fluorescence spectroscopy. We report the changes in volume, adiabatic compressibility, van't Hoff enthalpy, entropy, and free energy that accompany the association of the two proteins at 25 degrees C and pH 8.0. We have used the measured changes in volume and compressibility in conjunction with available structural data to characterize the binding-induced changes in the hydration properties and intrinsic packing of the two proteins. Our estimate reveals that 110 +/- 40 water molecules become released to the bulk from the hydration shells of BPTI and trypsinogen. Furthermore, we find that the intrinsic coefficient of adiabatic compressibility of the two proteins decreases by 14 +/- 2%, which is suggestive of the binding-induced rigidification of the proteins' interior. BPTI-trypsinogen association is an entropy-driven event which proceeds with an unfavorable change in enthalpy. The favorable change in entropy results from partial compensation between two predominant terms. Namely, a large favorable change in hydrational entropy slightly prevails over a close in magnitude but opposite in sign change in configurational entropy. The reduction in configurational entropy and, consequently, protein dynamics is consistent with the observed decrease in intrinsic compressibility. In general, results of this work emphasize the vital role that water plays in modulating protein recognition events.     

Thermodynamics of the complex formation in pyridine between gold(i) and ligands coordinating via N,P, As or Sb

The thermodynamics of complex formation between gold(I) and the ligands tricyclohexylphosphine, triphenylamine, -phosphine, -arsine, and -stibine has been determined in pyridine solution by potentiometric and calorimetric measurements. As expected, the very soft gold(I) displays a more marked stability (b)-sequence N ⪡ P > As > Sb than its lighter, and less soft, congener silver(I). Like all complexes of these ligands so far studied, the present ones are strongly enthalpy stabilized while the entropy changes are generally unfavourable. The stepwise entropy changes show quite peculiar differences between the various ligands, however. The thermodynamics of these complexes is in striking contrast to that of the gold(I) halido complexes in pyridine which are strongly entropy stabilized, while the enthalpy changes are small.     

Polarity as a criterion in protein design

Hypothetical proteins can be tested computationally by determining whether or not the designed sequence-structure pair has the characteristics of a typical globular protein. We have developed such a test by deriving quantities with approximately constant value for all globular proteins, based on empirical analysis of the exposed and buried surfaces of 128 structurally known proteins. The characteristic quantities that best appear to segregate badly designed or deliberately misfolded proteins from their properly folded natural relatives are the polar fraction of side chains on the protein surface and, independently, in the protein interior. Three of the seven hypothetical structures tested here can be rejected as having too many polar side-chain groups in the interior or too few on the protein surface. In addition, a recently designed nutritional protein is identified as being very much unlike globular proteins. These database-derived characteristic quantities are useful in screening designed proteins prior to experiment and may be useful in screening experimentally determined (X-ray, NMR) protein structures for possible errors.