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 hydrated water on protein unfolding

The conformational stability of a protein in aqueous solution is described in terms of the thermodynamic properties such as unfolding Gibbs free energy, which is the difference in the free energy (Gibbs function) between the native and random conformations in solution. The properties are composed of two contributions, one from enthalpy due to intramolecular interactions among constituent atoms and chain entropy of the backbone and side chains, and the other from the hydrated water around a protein molecule. The hydration free energy and enthalpy at a given temperature for a protein of known three-dimensional structure can be calculated from the accessible surface areas of constituent atoms according to a method developed recently. Since the hydration free energy and enthalpy for random conformations are computed from those for an extended conformation, the thermodynamic properties of unfolding are evaluated quantitatively. The evaluated hydration properties for proteins of known transition temperature (Tm) and unfolding enthalpy (delta Hm) show an approximately linear dependence on the number of constituent heavy atoms. Since the unfolding free energy is zero at Tm, the enthalpy originating from interatomic interactions of a polypeptide chain and the chain entropy are evaluated from an experimental value of delta Hm and computed properties due to the hydrated water around the molecule at Tm. The chain enthalpy and entropy thus estimated are largely compensated by the hydration enthalpy and entropy, respectively, making the unfolding free energy and enthalpy relatively small. The computed temperature dependences of the unfolding free energy and enthalpy for RNase A, T4 lysozyme, and myoglobin showed a good agreement with the experimental ones.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

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.     

Practical limitations on the use of thermodynamic data from isothermal processes

Enthalpy, entropy and volume data obtained for processes studied in aqueous solvents generally have been assumed to apply to the solute process without consideration of the coupling between the process and the two-state equilibrium of water. Walrafen's confirmation of the latter in 1983 shows that long-debated model to be correct so the enthalpy and entropy contributions to a free-energy change to give unambiguous information must be corrected for the water contribution. The situation is further complicated by differential chemical interaction of amphiphilic solutes with the two water species since experimental complications make correction difficult or impossible. A more general source of error in isothermal experiments is the linkage to the thermal-equilibrium device. That thermal problem discovered only in 1967 is not yet treated in textbooks although it is always a complication in isothermal processes and responsible for a hierarchy of thermodynamic quantities with different levels of reliability. Major consequences for several familiar thermodynamic and extra-thermodynamic methods are examined in terms of relative reliability. In most cases the thermal corrections are restricted by changes in phase state on cooling.     

The hydrophobic effect: a new insight from cold denaturation and a two-state water structure

Herein we provide a new insight into the hydrophobic effect in protein folding. Our proposition explains the molecular basis of cold denaturation, and of intermediate states in heat and their absence in cold denaturation. The exposure of non-polar surface reduces the entropy and enthalpy of the system, at low and at high temperatures. At low temperatures the favorable reduction in enthalpy overcomes the unfavorable reduction in entropy, leading to cold denaturation. At high temperatures, folding/unfolding is a two-step process: in the first, the entropy gain leads to hydrophobic collapse, in the second, the reduction in enthalpy due to protein-protein interactions leads to the native state. The different entropy and enthalpy contributions to the Gibbs energy change at each step at high, and at low, temperatures can be conveniently explained by a two-state model of the water structure. The model provides a clear view of the dominant factors in protein folding and stability. Consequently, it appears to provide a microscopic view of the hydrophobic effect and is consistently linked to macroscopic thermodynamic parameters.     

154 Protein folding and binding funnels: a common driving force and a common mechanism

Under the free energy landscape theory, both the protein-folding and protein–ligand binding processes are driven by the decrease in total Gibbs free energy of the protein-solvent or protein–ligand-solvent system, which involves the non-complementary changes between the entropy and enthalpy, ultimately leading to a global free energy minimization of these thermodynamic systems (Ji & Liu, 2011; Liu et al., 2012; Yang, Ji & Liu, 2012). In the case of protein folding, the lowering of the system free energy coupled with the gradual reduction in conformational degree of freedom of the folding intermediates determines that the shape of the free energy landscape for protein folding must be funnel-like (Dill & Chan, 1997), rather than non-funneled shapes (Ben-Naim, 2012). In the funnel-like free energy landscape, protein folding can be viewed as going down the hill via multiple parallel routes from a vast majority of individual non-native states on surface outside the funnel to the native states located around the bottom of the funnel. The first stage of folding, i.e. the rapid hydrophobic collapse process, is driven by the solvent entropy maximization. Concretely, the water molecules squeeze and sequestrate the hydrophobic amino acid side chains within the interior of the folding intermediates while exposing the polar and electrostatically charged side chains on the intermediate surface so as to minimize the solvent-accessible surface area of the solute and thus, the minimal contacts between the folding intermediates and the water molecules. This will maximize the entropy of the solvent, thus contributing substantially to lowering of the system free energy due to an absolute advantage of the solvent in both quantity and mass (Yang, Ji & Liu, 2012). The resulting molten globule states (Ohgushi & Wada, 1983), within which a few transient secondary structural components and tertiary contacts have been formed but many native contacts or close residue–residue interactions has yet to form, need to be further sculptured into the native states. This is a relatively slow “bottleneck” process because the competitive interactions between protein residues within the folding intermediates and between residues and water molecules may repeat many rounds to accumulate a large enough number of stable noncovalent bonds capable of counteracting the conformational entropy loss of the intermediates, thus putting this bottleneck stage under the enthalpy control (i.e. negative enthalpy change), contributing further to the lowering of the system free energy. Although the protein–ligand association occurs around the rugged bottom of the free energy landscape, the exclusion of water from the binding interfaces and the formation of noncovalent bonds between the two partners can still lower the system free energy. In conjunction with the loss of the rotational and translational degrees of freedom of the two partners as well as the loss of the conformational entropy of the protein, these processes could merge, downwards expand, and further narrow the free energy wells within which the protein–ligand binding process takes place, thereby making them look like a funnel, which we term the binding funnel. In this funnel, the free energy downhill process follows a similar paradigm to the protein-folding process. For example, if the initial collisions/contacts occur between the properly complementary interfaces of the protein and ligand, a large amount of water molecules (which usually form a water network around the solute surface) will be displaced to suit the need for maximizing the solvent entropy. This process is similar to that of the hydrophobic collapse during protein folding, resulting in a loosely associated protein–ligand complex that needs also to be further adapted into a tight complex, i.e. the second step which is mainly driven by the negative enthalpy change through intermolecular competitive interactions to gradually accumulate the noncovalent bonds and ultimately, to stabilize the complex at a tightly bound state. Taken together, we conclude that whether in the protein-folding or in the protein–ligand binding process, both the entropy-driven first step and the enthalpy-driven second step contribute to the lowering of the system free energy, resulting in the funnel-like folding or binding free energy landscape.     

On the dissection of the unfolding reaction by the dissolution thermodynamics of N-alkyl amides

Dissection of the unfolding thermodynamics based on small molecule dissolution led to controversial interpretations. It is proposed here that uncertainty about water transfer processes to be used in first approximation analyses of protein stability may be removed (i) separating liquid-dissolution-like effects from solid-like packing contributions; (ii) taking into account both peptide and side chain dissolution; and (iii) analysing the water-dependent part of the denaturation reaction by the dissolution thermodynamics of liquid N-alkyl amides. Based on these criteria, this paper analyses the entropy of the aqueous transfer of liquid N-alkyl amides filling a gap in a recent model of the unfolding energetics, which was limited to the enthalpy. Both enthalpic and entropic changes accompanying the liquid-dissolution-like immersion of internal amino acid residues in water during unfolding may be unambiguously described within this context. Although the model developed does not deepen our knowledge of protein unfolding, it may be of help in the analysis of whether liquid-dissolution-like effects or solid-like packing contributions play the major role in determining protein stability at elevated temperatures.     

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.     

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.     

Thermodynamics of binding water and solute to myosin

From the isopiestic measurements of the extents of adsorption of water vapour by fish myosin at various values of water activities at three different temperatures, the changes in free energy, enthalpy and entropy of dehydration of the protein have been calculated. Extents of excess binding of solvent and solute to myosin have also been determined from isopiestic experiments in the presence of different inorganic salts, sucrose and urea respectively. Mols of water and solute respectively bound in absolute amounts to myosin have been evaluated from these data in limited range of solute concentrations. Free energy changes at different concentrations of these solutes have also been evaluated and their relations with ‘salting-in’ and ‘salting-out’ phenomena have been discussed. The order of the values of the standard free energy change for excess binding calculated with respect to an unified thermodynamic scale are found to be consistent with relative reactivity of binding water to myosin in the presence of inorganic salts, sucrose and urea. Part of this work was presented at the 20th Annual Convention of Chemists of the Indian Chemical Society, Cuttack, 26th-30th December 1983.     

Linear free energy relationship for osmotic water flow through a membrane

A linear free-energy relationship has been found for the osmotic water flux through membranes in a broad variety of systems including electrolytes, organic compounds, intact biological cells and industrial scale filtration. In all cases, broad concentration ranges were found in which the equation In v = In m + β (v. flux (in kg cm⁻² min⁻¹: m. molarity)) was valid. The parameters and β were interpreted in terms of molecular weight, mean ionic radius, enthalpy of solvation. electronic structure and H-bonding propensity. The equation is independent of the membrane material and of the presence of other solutes and precipitates, as long as the latter are incompressible. Its parameters are only slightly dependent upon the temperature. The contributions from different solutes to the osmotic flux are at appreciable concentrations even additive. The relationship permits the prediction of the osmotic water flux and of the rate of filtration of systems of known composition. For simple systems it permits determination of the molecular weight, mean ionic radius, degree of hydration and enthalpy of solvalion. It is suggested that osmosis is primarily due to the shift of hydration equilibria and that guanidine hydrochloride. in a realistic concentration range, forms practically infinite clathrates with water. The properties of the urea and Gdn.HCl systems indicate that these solutes either reversibly change the membrane structure and/or display intrinsic hysteresis.     

Thermodynamics of the alkaline transition in phytocyanins

The thermodynamics of the alkaline transition which influences the spectral and redox properties of the type 1 copper center in phytocyanins has been determined spectroscopically. The proteins investigated include Rhus vernicifera stellacyanin, cucumber basic protein and its Met89Gln variant, and umecyanin, the stellacyanin from horseradish roots, along with its Gln95Met variant. The changes in reaction enthalpy and entropy within the protein series show partial compensatory behavior. Thus, the reaction free energy change (hence the pK _a value) is rather variable. This indicates that species-dependent differences in reaction thermodynamics, although containing an important contribution from changes in the hydrogen-bonding network of water molecules in the hydration sphere of the protein (which feature enthalpy–entropy compensation), are to a large extent protein-based. The data for axial ligand variants are consistent with the hypothesis of a copper-binding His as the deprotonating residue responsible for this transition.     

Physico-chemical aspects of solubility of myosin in aqueous media

Solubility of fish (Labio rohita) myosin has been studied at varying temperatures in presence of various inorganic salts like NaCl, KCl, NaBr, Na2SO4, KI, and organic solutes like sucrose and urea. The effect of pH on the solubility has also been studied both in absence and presence of NaCl. Thermal denaturation temperatures of myosin in presence of NaCl, KCl, NaBr and Na2SO4 were found to be 40 degrees, 40 degrees, 45 degrees and 50 degrees C respectively. Thermodynamic parameters like changes in standard free energy (delta G degrees), enthalpy (delta H degrees) and entropy (delta S degrees) for precipitation of myosin from solution phase to gel phase have been evaluated and the physico-chemical aspects have been critically discussed. The average delta G degrees for gel formation varied only between -30 and -40 kJ/mole of myosin, although the nature of solutes, temperature and folding state of protein have been grossly altered. A compensation effect has also been exhibited from the linear plot of average values of delta H degrees against T delta S degrees for various solutes.     

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.     

Thermodynamic Aspects of cAMP Dependent Protein Kinase Catalytic Subunit Allostery

Kinetics of thermal inactivation of acrylodan-labeled cAMP dependent protein kinase catalytic subunit, its binary complexes with ATP and peptide inhibitor PKI[5–24], respectively, and the ternary complex involving both of these ligands were studied at different temperatures (5–50 °C). The thermodynamic parameters ΔH and ΔS for ligand binding equilibria as well as for the allosteric interaction between the binding sites of these ligands were obtained by using the Van’t Hoff analysis. The results indicated that more inter- and intra-molecular non-covalent bonds were involved in ATP binding with the protein when compared to the peptide binding. Similarly, nucleotide and peptide binding steps were accompanied with different entropy effects, while almost no entropy change accompanied PKI[5–24] binding, suggesting that the protein flexibility was not affected in this case. Differently from the binary complex formation the ternary complex formation was accompanied by a significant entropy change and with intensive formation of new non-covalent interactions (ΔH). At the same time both ligand binding steps as well as the allosteric interaction between ligand binding sites could be described by a common entropy–enthalpy compensation plot, pointing to a similar mechanism of these phenomena. It was concluded that numerous weak interactions govern the allostery of cAMP dependent protein kinase catalytic subunit.     

Some ways of looking at compensatory kosmotropes and different water environments

Hydration of macromolecular structures determines biological activity. Stabilizing solutes are kosmotropic (increase order of water) rather than chaotropic (decrease order). Preferential hydration of surfaces is a thermodynamic consequence of the solution behavior of kosmotropic solutes, but inconsistencies imply interactions such as the hydration of specific sites within macromolecules. Thermodynamic measures require bulk pure solutes; here simpler measures of the effects on bulk water, water at surfaces and hydration water of probes have been applied to solutes including natural stabilizers, analogues and example chaotropes. Changes in the near-infrared spectra, water proton NMR chemical shifts and relaxation times measure changes in the bulk liquid; HPLC-column retention of solutes indicate interactions with hydration water at different surfaces, and fluorescence probes detect effects on functional group hydration water. Ab initio calculations and Monte-Carlo simulations of the solutes in water measure the energetics of the solute-water interactions, the dipole moments of these molecules, their charge distributions and the effect of the solute molecules on the structure of water. The rankings of the test solutes by these measures are not consistent. Thus, stabilizing solutes are not interchangeable in biological systems and the intracellular replacement of one by another could affect the integration of cell metabolism.     

Fluorescence energy transfer in one dimension: Frequency-domain fluorescence study of DNA–fluorophore complexes

The theory for the salt dependence of the free energy, entropy, and enthalpy of a polyelectrolyte in the PB (PB) model is extended to treat the nonspecific salt dependence of polyelectrolyte–ligand binding reactions. The salt dependence of the binding constant (K) is given by the difference in osmotic pressure terms between the react ants and the products. For simple 1-1 salts it is shown that this treatment is equivalent to the general preferential interaction model for the salt dependence of binding [C. Anderson and M. Record (1993) Journal of Physical Chemistry, Vol. 97, pp. 7116–7126]. The salt dependence, entropy, and enthalpy are compared for the PB model and one specific form of the preferential interaction coefficient model that uses counterion condensation/limiting law (LL) behavior. The PB and LL models are applied to three ligand–polyelectrolyte systems with the same net ligand charge: a model sphere–cylinder binding reaction, a drug–DNA binding reaction, and a protein–DNA binding reaction. For the small ligands both the PB and limiting law models give (ln K vs. In [salt]) slopes close in magnitude to the net ligand charge. However, the enthalpy/entropy breakdown of the salt dependence is quite different. In the PB model there are considerable contributions from electrostatic enthalpy and dielectric (water reorientation) entropy, compared to the predominant ion cratic (release) entropy in the limiting law model. The relative contributions of these three terms in the PB model depends on the ligand: for the protein, ion release entropy is the smallest contribution to the salt dependence of binding. The effect of three approximations made in the LL model is examined: These approximations are (1) the ligand behaves ideally, (2) the preferential interaction coefficient of the polyelectrolyte is unchanged upon ligand binding, and (3) the polyelectrolyte preferential interaction coefficient is given by the limiting law/counterion-condensation value. Analysis of the PB model shows that assumptions 2 and 3 break down at finite salt concentrations. For the small ligands the effects on the slope cancel, however, giving net slopes that are similar in the PB and LL models, but with a different entropy/enthalpy breakdown. For the protein ligand the errors from assumptions 2 and 3 in the LL model do not cancel. In addition, the ligand no longer behaves ideally due to its complex structure and charge distribution. Thus for the protein the slope is no longer related simply to the net ligand charge, and the PB model gives a much larger slope than the LL model. Additionally, in the PB model most of the salt dependence of the protein binding comes from the change in ligand activity, i.e. from nonspecific anion effects, in contrast to the small ligand case. While the absolute binding is sensitive to polyelectrolyte length, little length effect is seen on the salt dependence for the small ligands at 0.1M salt, and for lengths > 60 Å. Almost no DNA length dependenceis seen in the salt dependence of the protein binding, since this is determined primarily by the protein, not the DNA. © 1995 John Wiley & Sons, Inc.     

The physical origin of the low solubility of nonpolar solutes in water

Elementary but general statistical-mechanical relations are derived that relate the thermodynamic properties of the dissolution process to those of the pure solvent. A number of conclusions are drawn from qualitative arguments that these relations suggest. These include the following: (1) The low solubility of nonpolar solutes in water arises not from the fact that water molecules can form hydrogen bonds, but rather from the fact that they are small in size. (2) The large entropy decrease attending the transfer of an inert solute from a nonaqueous solvent to water is largely due to the decrease in entropy of the nonaqueous solvent as the solvent–solvent interaction is restored on removal of the solute from it. (3) It is improper to use values of thermodynamic quantities obtained from small-molecule transfer studies for those that involve macromolecular folding and interaction.