Experimental support for a desolvation energy term in governing equations for binding equilibria

Abstract

This study introduces a new thermodynamic framework for aqueous reaction equilibria that treats water as a coreactant in the development of a general binding equation. The approach features an explicit consideration for the change in hydration that occurs when two solvated surfaces come into contact. As an outcome of this framework, the standard-state free energy of binding is defined by the summation of two terms: the traditional term (-RT ln Ki) plus a desolvation free-energy term that is weighted by the number of complexes formed at equilibrium. The new formalism suggests that the equilibrium ratio, Ki, is not a constant and that the observed concentration dependence of Ki may be used to obtain the molar desolvation energy and the standard-state free energy at infinite dilution. The governing equation is supported by results from isothermal titration calorimetry using the chelation of calcium(II) by EDTA as a model binding reaction. This work may have far-reaching implications for solution thermodynamics, including an explanation for the oft-noted discrepancy between the enthalpy values obtained by calorimetry and those from the van't Hoff approach.

Figure 1

Sample calorimetry experiment for binding of Ca²⁺ to EDTA in 150 mM MES buffer, pH 6.2. The top panel is a thermogram showing the heat released per injection versus time, and the bottom panel is the binding isotherm showing the integrated peak results plotted against the corresponding molar ratio of Ca²⁺/EDTA. Experimental conditions are 5.00 mM CaCl₂ in syringe, 0.500 mM EDTA in sample cell, and 25 °C. Additional ITC runs are given in Figure S1.

Figure 2

Calorimetry data support inclusion of desolvation energy term in governing equation for binding equilibria. Each K_i value in Table 1 was utilized to calculate −RTlnK and plotted against the corresponding concentration of calcium, also given in Table 1. The linear relationship at each temperature is consistent with Eq. 11, for which the y-intercept is ΔG° and the slope is ΔG^H2O.

Figure 3

Temperature-dependent analysis of the desolvation energy for binding of Ca²⁺ to EDTA. Values of ΔH^H2O = +324 kcal/mol and ΔS^H2O = +0.87 kcal/mol·K are obtained from the slope and y-intercept of the line, respectively. These quantities represent the energetic contributions of water per mole of complex formed. See Table 2 for values of ΔG^H2O versus temperature.

Figure 4

Comparison of binding enthalpies obtained by three different methods. The ΔH° value (gray bar) was calculated from a van’t Hoff plot using Eq. 11 and the ΔG° values in Table 2. The ΔH^vH values (black bars) were calculated from a van’t Hoff plot using the traditional free energy relationship, ΔG° = −RTlnK, and the K_i values obtained at a single starting concentration. The ΔH^ITC values (white bars) were obtained from the calorimeter output at 25 °C after subtracting the corresponding control run at each concentration; the ΔH^ITC values were weakly dependent on temperature and nearly constant with concentration (Table S1). The numbers on the graph above each pair of bars denote the starting concentrations of EDTA in mM.