Dual Effect of Secondary Solutes on Binding Equilibria: Contributions from Solute-Reactant Interactions and Solute-Water Interactions

Abstract

This study examines the role of water in binding equilibria with a special focus on secondary solutes (cosolutes) that influence the equilibrium but are not constituents of the final product. Using a thermodynamic framework that includes an explicit term for the release of water molecules upon binding, this investigation reveals how solutes may alter equilibria by changing the activity of the reactants, reflected in ΔG°^(obs), and by changing the chemical potential of the solvent, reflected in ΔG^S. The framework is applied to four experimental binding systems that differ in the degree of electrostatic contributions. The model systems include the chelation of Ca²⁺ by EDTA and three host-guest reactions; the pairings of p-sulfonatocalix[4]arene with tetramethylammonium ion, cucurbit[7]uril with N-acetyl-phenylalanine-amide, and β-cyclodextrin with adamantane carboxylate are tested. Each reaction pair is examined by isothermal titration calorimetry at 25 °C in the presence of a common osmolyte, sucrose, and a common chaotrope, urea. Molar solutions of trehalose and phosphate were also tested with selected models. In general, cosolutes that enhance binding tend to reduce the solvation free energy penalty and cosolutes that weaken binding tend to increase the solvation free energy penalty. Notably, the nonpolar-nonpolar interaction between adamantane carboxylate and β-cyclodextrin is characterized by a ΔG^S value near zero. The results with β-cyclodextrin, in particular, prompt further discussions of the hydrophobic effect and the biocompatible properties of trehalose. Other investigators are encouraged to test and refine the approach taken here to further our understanding of solvent effects on molecular recognition.

Scheme 1. Model Binding Reactions

Figure 1

Steps in analyzing binding data for solutions of a secondary solute at high concentration. The control experiment is shown as a black dashed line, and the cosolute experiment is given by the purple solid line in each panel, accompanied by the corresponding linear fit. (a) K values obtained from ITC measurements are plotted as −RTlnK versus the molar concentration of complex at the 1:1 titration point in the calorimeter. A linear fit indicates agreement with eq 8. (b) The concentration of the complex and the measured K value for each ITC trial are converted to units of molality. This alters both the x and y values for each (x, y) data point in the graph. At this stage, one calculates γ^rxn from the y-intercepts (ΔG°) and eq 11. In this example, T = 298.15 K, ΔΔG° = +0.30, and γ^rxn = 0.60. (c) The x-value of each data point is converted to thermodynamic activity by multiplying the molal concentration of the complex by the activity coefficient, γ^rxn. The slope of each line from this plot is ΔG^S for the reaction in the corresponding solution.

Figure 2

Binding analysis for Ca²⁺/EDTA in the presence of secondary solutes at 25 °C. Solutions from top to bottom: 8.0 M urea (red circles), 4.0 M urea (purple open triangles), 2.0 M urea (blue diamonds), control (black squares, dashed line), 1.0 M trehalose (brown open circles), and 1.0 M sucrose (green open diamonds). The linear fit is given next to each line for which the slope corresponds to ΔG^S and the y-intercept is ΔG°^(observed). Error bars are approximately the same size as symbols but omitted for clarity.

Figure 3

Binding analysis for SC4/TMA⁺ in the presence of secondary solutes. Solutions from top to bottom: 4 M urea (purple, triangles), control (black squares, dashed line), and 1 M sucrose (green, diamonds). Error bars are shown, but small.

Figure 4

Binding analysis for CB7/AcPheNH₂ in the presence of secondary solutes. Solutions from top to bottom: 4 M urea (purple, triangles), 1 M sucrose (green, diamonds), and control (black squares, dashed line). Error bars are shown.

Figure 5

Binding analysis for βCD/AC^– in the presence of secondary solutes. Solutions from top to bottom: 1.0 M trehalose (brown, open circles), 4.0 M urea (purple, open triangles), 1.0 M sucrose (green, open diamonds), control (black, open squares, dashed line), 1.0 M cesium phosphate buffer (blue, filled diamonds), and 1.0 M potassium phosphate buffer (red, filled circles). The horizontal line for the control indicates ΔG^S ≈0.

Figure 6

Raising the bar for bulk water in defining the change in solvation free energy. (a) Common view of solvation free energy for which the release of water from nonpolar solutes and surfaces is negative and favorable (red region) and release from polar solutes and surfaces is positive and unfavorable (blue region). At some intermediate point in polarity, there must exist a surface that corresponds to ΔG^S = 0, labeled here as the aqua indifferens point. (b) Alternative view of solvation free energy in a dilute solution for which the value of G^bulk is raised (horizontal dashed line) until the change in solvation free energy for a surface of low polarity (i.e., hydrophobic surface) is near the aqua indifferens point. The ranking of hydration energies as a function of surface chemistry (diagonal line) is the same for both panels.

Figure 7

Inclusion of bulk water in thermodynamic cycles. The generic binding reaction defined in the gas (phase 1) is modified to acknowledge the release of a subset of water molecules when transferred to a dilute aqueous solution (phase 2). The change in chemical potential for this subset of water molecules is not captured by the transfer free energies of the reactants and products from the gas phase. When comparing the reaction in two aqueous solutions (phases 2 and 3), the transfer free energy for this subset of bulk water molecules should be included in the thermodynamic cycle (red arrow).