Entropy−Enthalpy Compensation in Chemical Reactions and Adsorption: An Exactly Solvable Model

The Nature of the Enthalpy-Entropy Compensation and "Exotic" Arrhenius Parameters in the Denaturation Kinetics of Proteins

Protein unfolding is a ubiquitous process responsible for the loss of protein functionality (denaturation), which, in turn, can be accompanied by the death of cells and organisms. The nature of enthalpy-entropy compensation (EEC) in the kinetics of protein unfolding is a subject of debate. In order to investigate the nature of EEC, the "completely loose" transition state (TS) model has been applied to calculate the Arrhenius parameters for the unfolding of polyglycine dimers as a model process. The calculated Arrhenius parameters increase with increasing dimer length and demonstrate enthalpy-entropy compensation. It is shown that EEC results from the linear correlations of enthalpy and entropy of activation with dimer length, which are derived directly from the properties of the transition state. It is shown that EEC in solvated (hydrated, etc.) proteins is a direct consequence of EEC in proteins themselves. The suggested model allows us also to reproduce and explain "exotic" very high values of the pre-exponential factor measured for the proteins unfolding, which are drastically higher than those known for unimolecular reactions of organic molecules. A similar approach can be applied to analyzing the nature of EEC phenomena observed in other areas of chemistry.

Enthalpy-Entropy Compensation Effect in Saturated Solutions on an Example of Polynuclear Aromatics According to Thermodynamics at Melting Temperature

A thermodynamic the influence of temperature on the logarithm of the considered quantity is expressed by bifunctional functional terms (1/T, lnT). For this purpose, the Apelblat & Manzurola (A&M) equation was used for extended model dissolution analysis of 12 aromatic hydrocarbons in tetralin and decalin vs. temperature for saturated solutions. The A&M equation was found to be thermodynamically compensatory in the sense of Enthalpy-Entropy-Compensation (EEC) while limiting melting temperature Tm=∆mH∆mS. The coefficients for the functional terms A1 vs. A2 are a linear relationship, with a slope called the compensation temperature Tc, as ratio of average enthalpy to average entropy. From this dependence, it has been shown that the approximation of ∆cp=∆mS¯ is justified, also assuming the average entropy. Regarding the term representing the activity coefficients, modifications to the A&M equation were proposed by replacing the intercept and it was shown that the new form correctly determines ∆mH. However, the condition is that the molar fraction of the solute exceeds x > 0.5 moles. It has been shown that the simplest equation referred to van ’t Hoff’s isobar also allows the simultaneous determination of enthalpy and entropy, but these quantities do not always come down to melting temperature.

"In-water" Dehydration Reaction of an Aromatic Diol on an Inorganic Surface

The effect of a synthetic saponite surface on the "in-water" dehydration reaction of diol was examined using 4-formyl-1-methylquinolinium salt (MQu⁺) as a substrate. The equilibrium between aldehyde (MQu⁺-Aldehyde) and diol (MQu⁺-Diol) was affected by the surrounding environment. The equilibrium behavior was observed by ¹H nuclear magnetic resonance (NMR) and UV-vis absorption measurements. Although MQu⁺ was completely in the form of MQu⁺-Diol in water, the equilibrium almost shifted to the MQu⁺-Aldehyde side when MQu⁺ was adsorbed on the saponite surface in water. In addition, the MQu⁺-Aldehyde ratio depended on the negative charge density of saponite. The factors that determine MQu⁺-Aldehyde: MQu⁺-Diol ratio were discussed from the thermodynamic analysis of the system. These data indicate that the electrostatic interaction between the charged saponite surface and MQu⁺ stabilized the aldehyde side enthalpically and destabilized it entropically. The major reason for these results is considered to be the difference in adsorption stabilization between MQu⁺-Aldehyde and MQu⁺-Diol on saponite surfaces.

Kinetic compensation effect of isoconversional methods

For experimental data obtained under different reaction/process conditions over time or temperature, the kinetic compensation effect (KCE) can be expected. Under dynamic (nonisothermal) conditions, at least two analytical pathways forming the KCE were found. Constant heating rate (q = const) and variable conversion degrees (α = var) lead to a vertical source of the KCE, called the isochronal effect. In turn, for a variable heating rate (q = var) and constant conversion degree (α = const), we can obtain an isoconversional compensation effect. In isothermal conditions (analyzed as polyisothermal), the KCE appears only as an isoconversional source of the compensating effect. The scattering of values for the determined isokinetic temperatures is evidence of a strong influence of the experimental conditions and the calculation methodology. The parameters of the Arrhenius law have been shown to allow the determination of the KCE and further the isokinetic temperature. In turn, using the Eyring equations for the same parameters, we can determine the enthalpy–entropy compensation (EEC) for the activation process and the compensation temperature, which is often treated as an isokinetic temperature. KCE effects have also been shown to be able to be amplified or dissipated, but isokinetic temperature is not a compensating quantity in the literal sense in isoconversional methods because $${T}_{iso}\to \infty .$$ T iso → ∞ . Thus, in isoconversional methods, isoconversional KCE values are characterized by strong variability of activation energy corresponding to the weak variation of the pre-exponential factor, which in practice means that $${\text{ln}}\mathit {A}\to {\text{const}}.$$ ln A → const . This is completely in line with the classical Arrhenius law.

The origin of extrathermodynamic compensations

The way of analysis of thermodynamic systems, which takes into consideration systems’ phase volumes, is suggested. A validity of such approach was verified by the example of studying of extrathermodynamic compensations. Several types of exact linear extrathermodynamic compensations as well as their peculiar type, which peculiarity is indefinable compensation temperature, are established. The criteria that specify these types are stated. These results are illustrated by the identified exact extrathermodynamic compensations in formation of pyrene excimers.

The impact of water molecules on binding affinity of the anti-diabetic thiazolidinediones for catalase: Kinetic and mechanistic approaches

Water molecules play a vital role in efficient drug binding to its target. Thiazolidinediones (TZDs), a class of anti-diabetic drugs, are widely used for treatment of type 2 diabetes mellitus. In the present study, the possible contribution of water molecules to the binding of TZDs to catalase, a potential target in the liver, was investigated by different experimental and theoretical methods. These studies indicated that TZDs could significantly improve the catalase catalytic function with a significant contribution from water molecules. As a probe for the differential number of released water molecules during the catalase transition from E to E* states, the activity of TZDs-catalase complexes was demonstrated to be mainly dependent on water activity. However, free catalase decomposed the substrate more independently. In addition, the spectrofluorimetry studies showed that the binding of TZDs to catalase needed the release of water molecules from the enzyme's binding pocket. The thermodynamic studies indicated that the binding enthalpy and entropy of TZDs for catalase were decreased with lower water activity. The favorable process contributes to release of water molecules from the binding pocket through the formation of hydrophobic interactions between catalase and TZDs in an enthalpic manner. Molecular docking simulations confirmed that the depletion of water molecules from the binding cavity is essential for effective interactions between TZDs and catalase.

Mathematical Models of Cell Response Following Heating

The cells of the cardiovascular system can experience temperature excesses of a few degrees during a diseased state or of tens of degrees during a thermal therapy treatment. These raised temperatures may be acute or of long duration. The multiple cell lines that compose each tissue then react, in approximate order of increasing thermal insult, by expressing heat shock proteins, undergoing apoptosis, or suffering necrosis. Mathematical models of the response of cells could aid in planning and designing thermal therapies. The multi-factor nature of the cell response makes it challenging to develop such models. The models most used clinically are mathematically simple and based on the response of representative tissues. The model that might provide the most fundamental understanding of the biochemical response of cells requires many parameters, some of which are difficult to measure. None of the semi-empirical models that provide improved prediction of cell fate have been widely accepted to plan therapies. There remain great opportunities for developing mathematical models cell response.

Molecular rigidity and enthalpy-entropy compensation in DNA melting

Enthalpy-entropy compensation (EEC) is observed in diverse molecular binding processes of importance to living systems and manufacturing applications, but this widely occurring phenomenon is not sufficiently understood from a molecular physics standpoint. To gain insight into this fundamental problem, we focus on the melting of double-stranded DNA (dsDNA) since measurements exhibiting EEC are extensive for nucleic acid complexes and existing coarse-grained models of DNA allow us to explore the influence of changes in molecular parameters on the energetic parameters by using molecular dynamics simulations. Previous experimental and computational studies have indicated a correlation between EEC and changes in molecular rigidity in certain binding-unbinding processes, and, correspondingly, we estimate measures of DNA molecular rigidity under a wide range of conditions, along with resultant changes in the enthalpy and entropy of binding. In particular, we consider variations in dsDNA rigidity that arise from changes of intrinsic molecular rigidity such as varying the associative interaction strength between the DNA bases, the length of the DNA chains, and the bending stiffness of the individual DNA chains. We also consider extrinsic changes of molecular rigidity arising from the addition of polymer additives and geometrical confinement of DNA between parallel plates. All our computations confirm EEC and indicate that this phenomenon is indeed highly correlated with changes in molecular rigidity. However, two distinct patterns relating to how DNA rigidity influences the entropy of association emerge from our analysis. Increasing the intrinsic DNA rigidity increases the entropy of binding, but increases in molecular rigidity from external constraints decreases the entropy of binding. EEC arises in numerous synthetic and biological binding processes and we suggest that changes in molecular rigidity might provide a common origin of this ubiquitous phenomenon in the mutual binding and unbinding of complex molecules.

The equation of state of polymers. Part III: Relation with the compensation law

The properties of amorphous polymers and of organic compounds under pressure are interpreted in the framework of the modified Van der Walls Equation of State (mVW-EOS) the Vogel-Fulcher-Tamann (VFT) law and of the compensation law. We have shown recently that polymers and organic compounds in amorphous liquid and crystalline states verify the mVW-EOS which depends on three parameters, [Formula: see text] [Formula: see text] and [Formula: see text]. In this paper we compare the characteristic pressure [Formula: see text] of the mVW-EOS to the various pressures [Formula: see text] deduced from thermodynamic and kinetic properties of polymers in the liquid and solid states. [Formula: see text] and [Formula: see text] are: a) the enthalpy and volume change at the melting and glass transitions (the glass being isotropic or oriented and annealed below [Formula: see text] at various aging conditions); b) the activation parameters of individual [Formula: see text] and cooperative [Formula: see text] motions in crystalline liquid and amorphous polymers studied by dielectric or mechanical spectroscopy; and c) the activation parameters of amorphous (solid and liquid) polymers submitted to a deformation depending on the time frequency temperature and strain rate. For a same material, whatever its state and whatever the experimental properties analyzed (dielectric and mechanical relaxation, viscosity, auto-diffusion, yielding under hydrostatic pressure), we demonstrate that [Formula: see text], ([Formula: see text] Grüneisen parameter, [Formula: see text] compressibility). In all polymers and organic compounds (and water), these pressures, weakly dependent on T and P near [Formula: see text] and [Formula: see text] at low pressure are characteristic of the H-H inter-molecular interactions. It is shown that the two empirical Lawson and Keyes relations of the compensation law can be deduced from the mVW-EOS.

The Roles of Water in the Protein Matrix: A Largely Untapped Resource for Drug Discovery

The value of thoroughly understanding the thermodynamics specific to a drug discovery/design study is well known. Over the past decade, the crucial roles of water molecules in protein structure, function, and dynamics have also become increasingly appreciated. This Perspective explores water in the biological environment by adopting its point of view in such phenomena. The prevailing thermodynamic models of the past, where water was seen largely in terms of an entropic gain after its displacement by a ligand, are now known to be much too simplistic. We adopt a set of terminology that describes water molecules as being "hot" and "cold", which we have defined as being easy and difficult to displace, respectively. The basis of these designations, which involve both enthalpic and entropic water contributions, are explored in several classes of biomolecules and structural motifs. The hallmarks for characterizing water molecules are examined, and computational tools for evaluating water-centric thermodynamics are reviewed. This Perspective's summary features guidelines for exploiting water molecules in drug discovery.

Variable temperatures 1H NMR technique on the kinetics and thermodynamic parameters of equilibrium between the Z and E isomers in a stable phosphorus ylide involving an imidazole

Analysis of ¹H NMR spectra of a special ylide involving an imidazole at variable temperatures has been employed to study the kinetics of the interchangeable process in the equilibrium between the two Z- and E-isomers of a stable phosphorus ylide.

Kinetic and density functional theory (DFT) studies of in vitro reactions of acrylamide with the thiols: captopril, l-cysteine, and glutathione

In vitro kinetic studies with DFT computations to explain the potential of acrylamide metabolism/toxicity with thiols in vivo.

Evaluation of the three-phase equilibrium method for measuring temperature dependence of internally consistent partition coefficients (K(OW), K(OA), and K(AW)) for volatile methylsiloxanes and trimethylsilanol

Partitioning equilibria and their temperature dependence of chemicals between different environmental media are important in determining the fate, transport, and distribution of contaminants. Unfortunately, internally consistent air/water (K(AW)), 1-octanol/air (K(OA)), and 1-octanol/water (K(OW)) partition coefficients, as well as information on their temperature dependence, are scarce for organosilicon compounds because of the reactivity of these compounds in water and octanol and their extreme partition coefficients. A newly published 3-phase equilibrium method was evaluated for simultaneous determination of the temperature dependence of (K(OW), K(OA), and K(AW)) of 5 volatile methylsiloxanes (VMS) and trimethylsilanol (TMS) in a temperature range from 4 °C to 35 °C. The measured partition coefficients at the different temperatures for any given compound, and the enthalpy and entropy changes for the corresponding partition processes, were all internally consistent, suggesting that the 3-phase equilibrium method is suitable for this type of measurement. Compared with common environmental contaminants reported in the literature, VMS have enthalpy and entropy relationships similar to those of alkanes for air/water partitioning and similar to those of polyfluorinated compounds for octanol/air partitioning, but more like those for benzoates and phenolic compounds for octanol/water partitioning. The temperature dependence of the partition coefficients of TMS is different from those of VMS and is more like that of alcohols, phenols, and sulfonamides.

Critical review and interpretation of environmental data for volatile methylsiloxanes: partition properties

Volatile methylsiloxanes (VMS) enter the environment through industrial activities and the use of various consumer products. Reliable measurements of environmental partition properties for these compounds are critical for accurate prediction of their environmental fate, distribution, transport, exposure and potential effects. In this study, the measured partition properties including air/water (K(AW)), octanol/water (K(OW)), and octanol/air partitioning coefficients (K(OA)), soil organic carbon/water distribution coefficient (K(OC)), and biological medium/fluid partition coefficients, and their temperature dependence were critically reviewed. Based on these results, organosilicon compounds such as methylsiloxanes are expected to behave differently in the environment compared to conventional hydrophobic environmental contaminants, as a result of their inherent characteristics related to molecular size and capacity for different types of molecular interactions that control partitioning. The differences are critical and need to be taken into consideration in environmental exposure and risk analyses of these compounds.

Glass: Kohlrausch exponent, fragility, anharmonicity

The thermodynamical and mechanical properties of (fragile and strong) glass are modeled based on a generalised activation energy relationship log( τ ) = ΔG ( β )/RTn(T') process of glass-forming liquids. This cooperative process involves 1/n(T') elementary β motions of activation Gibbs energy ΔG ( β ) dependent on the equivalent temperature T', the temperature of the liquid in equilibrium having the volume of the glass, function of temperature and aging conditions. From this modified VFT law the relaxation of any properties (V , H , stress, creep) can be calculated and approximated by the Kohlrausch function. This model predicts consistency relationships for: a) the temperature (and aging time) variation of the Kohlrausch exponent; b) the temperature dependence of the stabilisation time domain of strong and fragile glass; c) the linear relation between the activation parameters (E (*) energy, S (*) entropy, V (*) volume) of the α and β transition. The Lawson and Keyes (LK) relations are recalled and it is shown that these relations (somewhat equivalant to the compensation law or Meyer-Neldel rule) are observed generally in glass. Morever the (macroscopic) ratios ΔH/ΔV observed during aging or after a temperature jump and the (microscopic) ratio E (*)/V (*) are found equal to κγ (κ compressibily, γ Grüneisen parameter), in agreement with the LK predictions. From various experiments and in agreement with predictions of this model we conclude that the Grüneisen parameter γ ( B ) (pressure derivative of the bulk modulus) and the Mean Square Displacement (MSD) characterising the anharmonicity of solids (and liquids) are the main parameters which govern the relaxation properties of the glass state. Linear relations between the parameters γ ( B ), the fragility m, and the Kohlrausch exponent n ( g ) at T ( g ) are explained. These correlations underscore a strong relationship between the fragilty of glass formers and the extent of the anharmonicity in the interatomic interactions.