Simple Accurate Verification of Enthalpy‐Entropy Compensation and Isoequilibrium Relationship

Abstract

In many experimental investigations of thermodynamic equilibrium or kinetic properties of series of similar reactions it is found that the enthalpies and entropies derived from Van ′t Hoff or Arrhenius plots exhibit a strong linear correlation. The origin of this Enthalpy‐Entropy compensation, which is strongly related to the coalescence tendency of Van ′t Hoff or Arrhenius plots, is not necessarily due to a physical/chemical/biological process. It can also be a merely statistical artefact. A new method, called Combined K‐CQF makes it possible both to quantify the degree of coalescence of experimental Van ‘t Hoff lines and to verify whether or not the Enthalpy‐Entropy Compensation is of a statistical origin at a desired confidence level. The method is universal and can handle data sets with any degree of coalescence of Van ‘t Hoff (or Arrhenius) plots. The new method requires only a standard least square fit of the enthalpyΔH versus entropy ΔS plot to determine the two essential dimensionless parameters K and CQF. The parameter K indicates the position (in inverse temperature) of the coalescence region of Van ‘t Hoff plots and CQF is a quantitative measure of the smallest spread of the Van ‘t Hoff plots. The position of the (K, CQF) couple with respect to universal confidence contours determined from a large number of simulations of random Van ‘t Hoff plots indicates straightforwardly whether or not the ΔH‐ΔS compensation is a statistical artefact.

Entropy-Enthalpy Compensation in Ti-V-Mn-Cr BCC Alloys Used as Hydrogen Storage Materials

“…This compensation effect has been reported in various systems in biology with protein ligand-receptor interactions [28][29][30] and in chemistry with the adsorption of molecules into microporous materials [31,32]. This phenomenon was also observed in various metal hydride systems as MSi/α-MSiH 3 (M = K, Rb, and Cs) [33], in the hydrogenation/dehydrogenation properties of Mg-Ti nanocomposites [34,35] and Pd-H nanocubes [35,36], and for H 2 permeation kinetics in PdAg membranes [37]. Anastasopol et al did not identify an exact mechanism for their results on Mg-Ti nanocomposites but tentatively explained it as being possibly due to lattice strains, the presence of interfaces between coherent Mg and TiH 2 nanodomains, the presence of hydrogen vacancies, and the formation of excess free volume due to local deformations of the material [34].…”

Enthalpy‐entropy compensation in the binding of quercetin to calf thymus DNA

“…where T C , compensation temperature in Kelvin, 4,5 is the slope of the fitting line, and β is the y-intercept (Figure 1B). The linear regression indicates that a significant correlation (R 2 = 0.9995) between ΔH and ΔS in the binding of the five forms of Qu to ctDNA.…”

“…The values and standard errors of T C and β are 297.3 ± 3.8 K and À26 ± 0.9 kJ/mol respectively. The correlation is known as enthalpy-entropy compensation, [4][5][6][7] which is an extra-thermodynamic phenomenon. 8 The phenomenon has been observed in various molecular association processes.…”

Comment on “Aggregation Interface and Rigid Spots Sustain the Stable Framework of a Thermophilic N-Demethylase”

“…In the t test, the degree of freedom (df) was calculated as df = ( n 1 – 2) + ( n 2 – 2), where n 1 and n 2 are the number of data points of TrSOX and BSOX, respectively: n 1 = 34, and n 2 = 21 (Figure A). T C can quantitatively measure the degree of compensation between Δ H and Δ S . The statistical difference in T C between TrSOX and BSOX (Table ) strongly suggests that denaturation of each protein follows a distinct mechanism.…”

“…Second, site-directed mutagenesis decreases both Δ H and Δ S in the case of TrSOX but increases them in the case of BSOX, in most cases. Third, linear regression using eq indicates a highly significant correlation between Δ H and Δ S in both proteins as the coefficients of determination ( R 2 ) are 0.9966 and 0.9992 for TrSOX and BSOX, respectively: normalΔ H = T normalC normalΔ S + β where T C , the compensation temperature, is the slope of the fitting line and β is the y -intercept (Figure A). The strong correlation between Δ H and Δ S is known as enthalpy–entropy compensation, often observed in a weakly coupled system. − Figure A clearly indicates that the denaturation of TrSOX and BSOX exhibits compensatory behavior, suggesting that the molecular components responsible for the denaturation of those proteins exhibit the property of a weakly coupled system.…”