Solvation free energy in governing equations for DNA hybridization, protein-ligand binding, and protein folding

Abstract

This work examines the thermodynamics of model biomolecular interactions using a governing equation that accounts for the participation of bulk water in the equilibria. In the first example, the binding affinities of two DNA duplexes, one of nine and one of 10 base pairs in length, are measured and characterized by isothermal titration calorimetry (ITC) as a function of concentration. The results indicate that the change in solvation free energy that accompanies duplex formation (ΔG^S) is large and unfavorable. The duplex with the larger number of G:C pairings yields the largest change in solvation free energy, ΔG^S = +460 kcal·mol^-1per base pair at 25 °C. A van't Hoff analysis of the data is complicated by the varying degree of intramolecular base stacking within each DNA strand as a function of temperature. A modeling study reveals how the solvation free energy alters the output of a typical ITC experiment and leads to a good, though misleading, fit to the classical equilibrium equation. The same thermodynamic framework is applied to a model protein-ligand interaction, the binding of ribonuclease A with the nucleotide inhibitor 3'-UMP, and to a conformational equilibrium, the change in tertiary structure of α-lactalbumin in molar guanidinium chloride solutions. The ribonuclease study yields a value of ΔG^S = +160 kcal·mol^-1, whereas the folding equilibrium yields ΔG^S ≈ 0, an apparent characteristic of hydrophobic interactions. These examples provide insight on the role of solvation energy in binding equilibria and suggest a pivot in the fundamental application of thermodynamics to solution chemistry.

Keywords: DNA duplex; bulk water; calorimetry; desolvation; hydration; ribonuclease inhibitor.

Fig. 1

Hybridization of oligo9 with oligo9c at 25 °C. Equilibrium binding quotients were obtained by ITC as a function of concentration. The linear fit is indicated on the graph, from which the slope corresponds to ΔG ^S and the y‐intercept corresponds to ΔG°, in accord with Eqn (7). Error bars represent standard deviation values (n = 3). See Table S1 for corresponding values of K and ΔH ^ITC.

Fig. 2

Hybridization of oligo10 with oligo10c. The corresponding temperatures and goodness of fits to Eqn (7) are shown on the graph. Note that the starting conformations of the oligonucleotides vary with temperature due to different amounts of intramolecular stacking. Error bars represent standard deviation values (n = 4). See Fig. S1 for sample ITC data and Table S2 for corresponding values of K and ΔH ^ITC.

Fig. 3

Revised analysis of oligo10/10c hybridization. (A) Schematic diagram of two‐step process for unstacking of intramolecular bases prior to duplex formation; Δ_itc G° = Δ_un G° + ΔG°. (B) Updated graph for hybridization of oligo10/10c using ΔG° values in Table 1. Error bars represent standard deviation values, n = 4. (C) A van't Hoff analysis of the ΔG° values in Table 1.

Fig. 4

Modeling of titration results for oligo10/10c at 0.20 mm concentration and 25 °C. (A) Equilibrium quotients as a function of ΔG° and ΔG ^S, as obtained from Eqn (6) using WolframAlpha to calculate the unknown concentration of duplex after each injection. The x‐axis represents the molar ratio of total injected species (X _t) to total binding partner in the ITC cell (M _t). For the three solid curves, ΔG° = −9.30 kcal·mol⁻¹, and ΔG ^S is given next to each curve in kcal·mol⁻¹. Simulations for ΔG ^S = 0 correspond to a constant value of K. The gray dotted line represents a constant K value of 2.03 × 10⁶, and the vertical arrow indicates the intersection with the dataset for ΔG ^S = +4000, just prior to exceeding a molar ratio of 1.0. (B) Simulated ITC enthalpy curves corresponding to datasets in panel (A). The gray dots represent K = 2.03 × 10⁶ (ΔG ^S = 0, ΔG° = −8.60 kcal·mol⁻¹) and nearly coincide with the red curve (for which ΔG ^S = +4000, ΔG° = −9.30 kcal·mol⁻¹).

Fig. 5

Binding analysis of 3′‐UMP/RNase A and 2′‐CMP/RNase A as a function of concentration. Binding of the 3′‐UMP inhibitor was measured in 25 mm KCl and 25 mm Bis‐Tris buffer, pH 6.0, at 25 °C (top, black squares). The K values for 2′‐CMP are tabulated in Wiseman et al., as measured in 200 mm KCl and 200 mm potassium acetate buffer, pH 5.5, at 28 °C (bottom, red circles) [15]. Error bars represent standard deviation values (n = 4). For 3′‐UMP, see Fig. S2 for sample ITC data and Table S3 for corresponding values of K and ΔH ^ITC.

Fig. 6

The two‐state equilibrium for α‐lactalbumin in guanidinium chloride does not change with protein concentration. The near‐UV CD profiles of α‐lactalbumin in 1.25 m GuHCl, 10 mm EDTA, and 10 mm Tris at 25 °C are shown as a function of protein concentration. The native structure (lower spectrum) corresponds to 5 mg·mL⁻¹ in the absence of GuHCl. The path length of the cuvet (l) was varied from 0.01 to 1.0 cm to maintain a constant number of protein molecules in the path of the light source for all samples (l·c = 1 cm·mg·mL⁻¹).

Fig. 7

The change in solvation energy for waters released from a surface depends on the average free energy of bulk water. The y‐axis represents the solvation energy for a given surface, and the x‐axis represents a generic hydrophilicity scale that corresponds to the chemistry of the surface. A nonpolar (low hydrophilicity) surface is characterized by a high solvation energy that approaches the free energy of the bulk water, denoted here as the aqua indifferens point (red circle).