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.     

Effects of ligand binding on the stability of aldo–keto reductases: Implications for stabilizer or destabilizer chaperones

Ligands such as enzyme inhibitors stabilize the native conformation of a protein upon binding to the native state, but some compounds destabilize the native conformation upon binding to the non‐native state. The former ligands are termed “stabilizer chaperones” and the latter ones “destabilizer chaperones.” Because the stabilization effects are essential for the medical chaperone (MC) hypothesis, here we have formulated a thermodynamic system consisting of a ligand and a protein in its native‐ and non‐native state. Using the differential scanning fluorimetry and the circular dichroism varying the urea concentration and temperature, we found that when the coenzyme NADP⁺ was absent, inhibitors such as isolithocholic acid stabilized the aldo–keto reductase AKR1A1 upon binding, which showed actually the three‐state folding, but destabilized AKR1B10. In contrast, in the presence of NADP⁺, they destabilized AKR1A1 and stabilized AKR1B10. To explain these phenomena, we decomposed the free energy of stabilization (ΔΔG) into its enthalpy (ΔΔH) and entropy (ΔΔS) components. Then we found that in a relatively unstable protein showing the three‐state folding, native conformation was stabilized by the negative ΔΔH in association with the negative ΔΔS, suggesting that the stabilizer chaperon decreases the conformational fluctuation of the target protein or increase its hydration. However, in other cases, ΔΔG was essentially determined by the delicate balance between ΔΔH and ΔΔS. The proposed thermodynamic formalism is applicable to the system including multiple ligands with allosteric interactions. These findings would promote the development of screening strategies for MCs to regulate the target conformations.     

Kinetic and thermodynamic analysis for lipase-catalyzed hydrolytic resolution of (R,S)-alcohols though their azolyl carbamates

A new approach to the lipase-catalyzed hydrolytic resolution of (R,S)-azolyl carbamates for obtaining chiral azolyl carbamates and alcohol is described. With (R,S)-1-phenylethyl azolyl carbamates as the model substrates, the best reaction condition of using (R,S)-1-phenylethyl 4-bromopyrazole carbamate (1) as the substrate in water-saturated diisopropyl ether at 45?°C is selected. The kinetic constants, and hence enantiomeric ratio of 124, are then estimated from the kinetic analysis by considering the alcohol inhibition effect, with which theoretical time-course conversions for both enantiomers are numerically solved and agree with the experimental data. The thermodynamic parameters -ΔΔH and -ΔΔS satisfying a linear enthalpy-entropy compensation relationship of -ΔΔS?=?-38.84?+?3.29(-ΔΔH) are further estimated. An extension of the resolution platform to (R,S)-4-bromopyrazole carbamates derived from other (R,S)-alcohols (4, 5, 7) is also addressed.     

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.     

Role of the heat capacity change in understanding and modeling melting thermodynamics of complementary duplexes containing standard and nucleobase-modified LNA

Melting thermodynamic data obtained by differential scanning calorimetry (DSC) are reported for 43 duplexed oligonucleotides containing one or more locked nucleic acid (LNA) substitutions. The measured heat capacity change (ΔC(p)) for the helix-to-coil transition is used to compute the changes in enthalpy and entropy for melting of an LNA-bearing duplex at the T(m) of its corresponding isosequential unmodified DNA duplex to allow rigorous thermodynamic analysis of the stability enhancements provided by LNA substitutions. Contrary to previous studies, our analysis shows that the origin of the improved stability is almost exclusively a net reduction (ΔΔS° < 0) in the entropy gain accompanying the helix-to-coil transition, with the magnitude of the reduction dependent on the type of nucleobase and its base pairing properties. This knowledge and our average measured value for ΔC(p) of 42 ± 11 cal mol(-1) K(-1) bp(-1) are then used to derive a new model that accurately predicts melting thermodynamics and the increased melting temperature (ΔT(m)) of heteroduplexes formed between an unmodified DNA strand and a complementary strand containing any number and configuration of standard LNA nucleotides A, T, C, and G. This single-base thermodynamic (SBT) model requires only four entropy-related parameters in addition to ΔC(p). Finally, DSC data for 20 duplexes containing the nucleobase-modified LNAs 2-aminoadenine (D) and 2-thiothymine (H) are reported and used to determine SBT model parameters for D and H. The data and model suggest that along with the greater stability enhancement provided by D and H bases relative to their corresponding A and T analogues, the unique pseudocomplementary properties of D-H base pairs may make their use appealing for in vitro and in vivo applications.     

Thermodynamic compensation upon binding to exosite 1 and the active site of thrombin

Several lines of experimental evidence including amide exchange and NMR suggest that ligands binding to thrombin cause reduced backbone dynamics. Binding of the covalent inhibitor dPhe-Pro-Arg chloromethyl ketone to the active site serine, as well as noncovalent binding of a fragment of the regulatory protein, thrombomodulin, to exosite 1 on the back side of the thrombin molecule both cause reduced dynamics. However, the reduced dynamics do not appear to be accompanied by significant conformational changes. In addition, binding of ligands to the active site does not change the affinity of thrombomodulin fragments binding to exosite 1; however, the thermodynamic coupling between exosite 1 and the active site has not been fully explored. We present isothermal titration calorimetry experiments that probe changes in enthalpy and entropy upon formation of binary ligand complexes. The approach relies on stringent thrombin preparation methods and on the use of dansyl-l-arginine-(3-methyl-1,5-pantanediyl)amide and a DNA aptamer as ligands with ideal thermodynamic signatures for binding to the active site and to exosite 1. Using this approach, the binding thermodynamic signatures of each ligand alone as well as the binding signatures of each ligand when the other binding site was occupied were measured. Different exosite 1 ligands with widely varied thermodynamic signatures cause a similar reduction in ΔH and a concomitantly lower entropy cost upon DAPA binding at the active site. The results suggest a general phenomenon of enthalpy-entropy compensation consistent with reduction of dynamics/increased folding of thrombin upon ligand binding to either the active site or exosite 1.     

Analysis of protein-ligand interactions by fluorescence polarization

Quantification of the associations between biomolecules is required both to predict and understand the interactions that underpin all biological activity. Fluorescence polarization (FP) provides a nondisruptive means of measuring the association of a fluorescent ligand with a larger molecule. We describe an FP assay in which binding of fluorescein-labeled inositol 1,4,5-trisphosphate (IP(3)) to N-terminal fragments of IP(3) receptors can be characterized at different temperatures and in competition with other ligands. The assay allows the standard Gibbs free energy (ΔG°), enthalpy (ΔH°) and entropy (ΔS°) changes of ligand binding to be determined. The method is applicable to any purified ligand-binding site for which an appropriate fluorescent ligand is available. FP can be used to measure low-affinity interactions in real time without the use of radioactive materials, it is nondestructive and, with appropriate care, it can resolve ΔH° and ΔS°. The first part of the protocol, protein preparation, may take several weeks, whereas the FP measurements, once they have been optimized, would normally take 1-6 h.     

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.     

Thermodynamics of insertion and self-association of a transmembrane helix: a lipophobic interaction by phosphatidylethanolamine

Thermodynamic parameters for the insertion and self-association of transmembrane helices are important for understanding the folding of helical membrane proteins. The lipid composition of bilayers would significantly affect these fundamental processes, although how is not well understood. Experimental systems using model transmembrane helices and lipid bilayers are useful for measuring and interpreting thermodynamic parameters (ΔG, ΔH, ΔS, and ΔC(p)) for the processes. In this study, the effect of the charge, phase, acyl chain unsaturation, and lateral pressure profile of bilayers on the membrane partitioning of the transmembrane helix (AALALAA)(3) was examined. Furthermore, the effect of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylethanolamine (POPE) on the thermodynamics for insertion and self-association of the helix in host membranes composed of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) was investigated in detail. Interbilayer transfer of the helix monomer from POPC to POPC/POPE (1/1) bilayers was unfavorable (ΔG = +4.5 ± 2.9 kJ mol(-1) at 35 °C) due to an increase in enthalpy (ΔH = +31.1 ± 2.1 kJ mol(-1)). On the other hand, antiparallel dimerization of the helices in POPC/POPE (1/1) bilayers was enhanced compared with that in POPC bilayers (ΔΔG = -4.9 ± 0.2 kJ mol(-1) at 35 °C) due to a decrease in enthalpy (ΔΔH = -33.2 ± 1.5 kJ mol(-1)). A greater thickness of POPC/POPE bilayers only partially explained the observed effects. The residual effects could be related to changes in other physical properties such as higher lateral pressure in the hydrocarbon core in the PE-containing membrane. The origin of the enthalpy-driven "lipophobic" force that modulates the insertion and association of transmembrane helices will be discussed.     

Accounting for conformational entropy in predicting binding free energies of protein-protein interactions

Protein-protein interactions are governed by the change in free energy upon binding, ΔG = ΔH - TΔS. These interactions are often marginally stable, so one must examine the balance between the change in enthalpy, ΔH, and the change in entropy, ΔS, when investigating known complexes, characterizing the effects of mutations, or designing optimized variants. To perform a large-scale study into the contribution of conformational entropy to binding free energy, we developed a technique called GOBLIN (Graphical mOdel for BiomoLecular INteractions) that performs physics-based free energy calculations for protein-protein complexes under both side-chain and backbone flexibility. Goblin uses a probabilistic graphical model that exploits conditional independencies in the Boltzmann distribution and employs variational inference techniques that approximate the free energy of binding in only a few minutes. We examined the role of conformational entropy on a benchmark set of more than 700 mutants in eight large, well-studied complexes. Our findings suggest that conformational entropy is important in protein-protein interactions--the root mean square error (RMSE) between calculated and experimentally measured ΔΔGs decreases by 12% when explicit entropic contributions were incorporated. GOBLIN models all atoms of the protein complex and detects changes to the binding entropy along the interface as well as positions distal to the binding interface. Our results also suggest that a variational approach to entropy calculations may be quantitatively more accurate than the knowledge-based approaches used by the well-known programs FOLDX and Rosetta--GOBLIN's RMSEs are 10 and 36% lower than these programs, respectively.     

Second-contact shell mutation diminishes streptavidin-biotin binding affinity through transmitted effects on equilibrium dynamics

We report a point mutation in the second contact shell of the high-affinity streptavidin-biotin complex that appears to reduce binding affinity through transmitted effects on equilibrium dynamics. The Y54F streptavidin mutation causes a 75-fold loss of binding affinity with 73-fold faster dissociation, a large loss of binding enthalpy (ΔΔH = 3.4 kcal/mol at 37 °C), and a small gain in binding entropy (TΔΔS = 0.7 kcal/mol). The removed Y54 hydroxyl is replaced by a water molecule in the bound structure, but there are no observable changes in structure in the first contact shell and no additional changes surrounding the mutation. Molecular dynamics simulations reveal a large increase in the atomic fluctuation amplitudes for W79, a key biotin contact residue, compared to the fluctuation amplitudes in the wild-type. The increased W79 atomic fluctuation amplitudes are caused by loss of water-mediated hydrogen bonds between the Y54 hydroxyl group and peptide backbone atoms in and near W79. We propose that the increased atomic fluctuation amplitudes diminish the integrity of the W79-biotin interaction and represents a loosening of the "tryptophan collar" that is critical to the slow dissociation and high affinity of streptavidin-biotin binding. These results illustrate how changes in protein dynamics distal to the ligand binding pocket can have a profound impact on ligand binding, even when equilibrium structure is unperturbed.     

Synthesis,Characterization, and Cytotoxicity Studies of a Novel Palladium(II) Complex and Evaluation of DNA-Binding Aspects

A new water-soluble palladium(II) complex, [Pd(bpy)(pyr-Ac]NO₃ in which bpy = 2,2′-bipyridine and pyr-Ac is 1-pyrrolacetato, has been synthesized and characterized by spectroscopic methods (¹H NMR, FT-IR, and UV-Vis), molar conductivity measurements, and elemental analysis. The results obtained from elemental analysis and conductivity measurements confirmed the stoichiometry of ligand and its complex while the characteristic peaks in UV-Vis and FT-IR and resonance peaks in ¹H NMR spectra confirmed the formation of ligand frameworks around the palladium ion. The 50% cytotoxic concentration (Ic₅₀) of new synthesized Pd(II) complex was determined by using MTT assay against human breast cancer cell line, T47D. The interaction between the Pd(II) complex with calf thymus DNA was studied at different temperatures by using absorption spectroscopy, fluorescence titration spectra, ethidium bromide displacement, and gel chromatography studies. The results obtained by absorption spectroscopy revealed that the Pd(II) complex can bind to DNA cooperatively at low concentrations. Several binding parameters in the above interaction were calculated by the fluorescence quenching method. The quenching mechanism was suggested to be the static quenching. The thermodynamic parameters: enthalpy change (ΔH °), entropy change (ΔS °), and Gibbs free energy (ΔG °), showed that van der Waals and hydrogen binding are predominant intermolecular forces between Pd(II) complex and DNA. These results were also consistent with the results obtained from Scatchard's plots.     

Thermodynamics of oligosaccharide binding to a monoclonal antibody specific for a Salmonella O-antigen point to hydrophobic interactions in the binding site.

The thermodynamic characteristics of oligosaccharide binding to an antibody binding site that is dominated by aromatic amino acids suggest that the hydrophobic effect contributes substantially to complex formation as well as hydrogen bonding and van der Waals interactions. A detailed titration microcalorimetric study on the temperature dependence of the binding of a trisaccharide, representing the epitope of a Salmonella O-antigen, showed that its maximum binding to the monoclonal antibody Se155-4 occurs just below room temperature and both enthalpy and entropy changes are strongly dependent on temperature in a mutually compensating manner. The heat capacity change also shows an unusually strong temperature dependence being large and negative above room temperature and positive below. van't Hoff analysis of the temperature dependence of the binding constant yielded a biphasic curve with two apparent intrinsic enthalpy estimations (approximately -100 kJ mol-1 above 18 degrees C and approximately +100 kJ mol-1 below), each very different from the calorimetrically determined enthalpies (ranging from about -60 kJ mol-1 to -20 kJ mol-1). This was interpreted as being due to large enthalpy contributions from concomitant reactions, most notably changes in solvation. Linear plots, -delta H0 versus -T delta S0, observed for temperature-dependent measurements mirror the behavior seen for a series of functional group replacements, suggesting that the molecular and physical origin of these phenomena are closely related and linked to the role of water in complex formation. The thermodynamic results are compared to the mode of binding determined from a 2.05-A resolution structure of the Fab-oligosaccharide complex, and with literature data for the heat capacities of sugars in aqueous solution and for the thermodynamics of carbohydrate binding to transport proteins and lectins.     

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.     

Contribution of the trifluoroacetyl group in the thermodynamics of antigen–antibody binding

We analyzed the binding of the 7C8 antibody to the chloramphenicol phosphonate antigens—one containing a trifluoroacetyl group (CP‐F) and the other containing an acetyl group (CP‐H)—by using isothermal titration calorimetry (ITC). The thermodynamic difference due to the substitution of F by H was evaluated using free energy calculations based on molecular dynamics (MD) simulations. We have previously shown that another antibody, namely, 6D9, binds more weakly to CP‐H than to CP‐F, mainly due to the different hydration free energies of the dissociated state and not due to the unfavorable hydrophobic interactions with the antibody in the bound state. Unlike in the binding of the trifluoroacetyl group with 6D9, in its binding with 7C8, it is exposed to the solvent, as seen in the crystal structure of the complex of 7C8 with CP‐F. The thermodynamic analysis performed in this study showed that the binding affinity of 7C8 for CP‐H is similar to that for CP‐F, but this binding to CP‐H is accompanied with less favorable enthalpy and more favorable entropy changes. The free energy calculations indicated that, upon the substitution of F by H, enthalpy and entropy changes in the associated and dissociated states were decreased, but the magnitude of enthalpy and entropy changes in the dissociated state was larger than that in the associated state. The differences in binding free energy, enthalpy, and entropy changes determined by the free energy calculations for the substitution of F by H are in good agreement with the experimental results. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Thermodynamic Parameters of Frog Brain κ-Opioid Receptors

Abstract: The thermodynamic parameters for [³H]-ethylketocyclazocine binding in frog ( Rana esculenta ) brain membranes have been examined. Computer-based nonlinear regression analysis of the untransformed equilibrium displacement data showed that this ligand bound to two sites with different affinities and capacities in this tissue. K _A values derived from equilibrium displacement curves have been used for calculating the changes in the standard Gibbs energy, enthalpy, and entropy during the binding process. Van't Hoff plots are bipartite, with transitions occurring at 18°C for both the high- and the low-affinity sites. For the high-affinity site, the reaction appears to be associated with a decrease in enthalpy below the transition temperature and a significant gain in entropy above this temperature. The reverse appears to be true for the low-affinity site. We conclude that this profile fairly approximates the mixed agonist-antagonist nature of this ligand and surmise that thermodynamic analysis could be a very useful tool for characterization of the nature of cloned opioid receptors in vitro.     

Adsorption thermodynamics to clean up wastewater; critical review

The current review paper deals with critical evaluation of the thermodynamic parameters of adsorption equilibrium uptakes of heavy metals, dyes and other organic pollutants from the wastewater using low-cost adsorbents, activated carbon derived from agricultural waste, industrial wastes and other important adsorbent materials. Present review paper focus the spontaneity of adsorption processes when the thermodynamic parameters were assessed with the compensation effects of standard enthalpy change (ΔH^o) and standard entropy change (ΔS^o) with temperature. This paper also investigates the spontaneity of adsorption on the basis of thermodynamic criteria of spontaneity and the temperature range to predict feasibility of the adsorption processes.     

Thermodynamic analysis of the interaction of factor VIII with von Willebrand factor

Factor VIII (FVIII) is a glycoprotein that plays an important role in the intrinsic pathway of coagulation. In circulation, FVIII is protected upon binding to von Willebrand factor (VWF), a chaperone molecule that regulates its half-life, distribution, and activity. Despite the biological significance of this interaction, its molecular mechanisms are not fully characterized. We determined the equilibrium and activation thermodynamics of the interaction between FVIII and VWF. The equilibrium affinity determined by surface plasmon resonance was temperature-dependent with a value of 0.8 nM at 35 °C. The FVIII-VWF interaction was characterized by very fast association (8.56 × 10(6) M(-1) s(-1)) and fast dissociation (6.89 × 10(-3) s(-1)) rates. Both the equilibrium association and association rate constants, but not the dissociation rate constant, were dependent on temperature. Binding of FVIII to VWF was characterized by favorable changes in the equilibrium and activation entropy (TΔS° = 89.4 kJ/mol, and -TΔS(++) = -8.9 kJ/mol) and unfavorable changes in the equilibrium and activation enthalpy (ΔH° = 39.1 kJ/mol, and ΔH(++) = 44.1 kJ/mol), yielding a negative change in the equilibrium Gibbs energy. Binding of FVIII to VWF in solid-phase assays demonstrated a high sensitivity to acidic pH and a sensitivity to ionic strength. Our data indicate that the interaction between FVIII and VWF is mediated mainly by electrostatic forces, and that it is not accompanied by entropic constraints, suggesting the absence of conformational adaptation but the presence of rigid "pre-optimized" binding surfaces.