Entropy in molecular recognition by proteins

Abstract

Molecular recognition by proteins is fundamental to molecular biology. Dissection of the thermodynamic energy terms governing protein-ligand interactions has proven difficult, with determination of entropic contributions being particularly elusive. NMR relaxation measurements have suggested that changes in protein conformational entropy can be quantitatively obtained through a dynamical proxy, but the generality of this relationship has not been shown. Twenty-eight protein-ligand complexes are used to show a quantitative relationship between measures of fast side-chain motion and the underlying conformational entropy. We find that the contribution of conformational entropy can range from favorable to unfavorable, which demonstrates the potential of this thermodynamic variable to modulate protein-ligand interactions. For about one-quarter of these complexes, the absence of conformational entropy would render the resulting affinity biologically meaningless. The dynamical proxy for conformational entropy or "entropy meter" also allows for refinement of the contributions of solvent entropy and the loss in rotational-translational entropy accompanying formation of high-affinity complexes. Furthermore, structure-based application of the approach can also provide insight into long-lived specific water-protein interactions that escape the generic treatments of solvent entropy based simply on changes in accessible surface area. These results provide a comprehensive and unified view of the general role of entropy in high-affinity molecular recognition by proteins.

Keywords: NMR relaxation; binding thermodynamics; entropy; molecular recognition; protein dynamics.

Fig. 1.

Calibration of the dynamical proxy for protein conformational entropy. Fitting of Eq. 3 to data provided by 28 protein–ligand associations (blue, green, and magenta circles) is shown. The difference in the measured total binding entropy and calculated solvent entropy is plotted against the change in the dynamical proxy upon binding of ligand. The dynamical proxy is the difference of the average Lipari–Szabo squared generalized order parameters of methyl group symmetry axes (Δ<O²_axis>) scaled by the number of total torsion angles (Nχ) in the protein. Horizontal error bars include the SD of <O²_axis>, which is less than ±0.01 for our data. For complexes involving small peptides or oligonucleotides, the uncertainty of the ligand contributes to the abscissa error bars (SI Appendix). The ordinate error bars are from the propagated quadrature errors of experimental ΔS_total and the precision of the fitted coefficients used to determine ΔS_solvent, and ΔS_r-t. In many cases, the ordinate error is less than the size of the symbol. The fitted slope (s_d) of −0.0048 ± 0.0005 kJ⋅mol⁻¹⋅K⁻¹ allows for the conversion of measured changes in methyl-bearing side-chain motion and the associated contribution to the total conformational entropy. Other parameters determined for Eq. 3 are summarized in Table 1. Also shown are the values for the barnase/dCGAC complex without addition of a net contribution from long-lived water with the protein (red diamond) and with a net contribution from water rigidly associated only in the complex added (gray diamond). The latter is calculated using the entropy of fusion for the immobilization of nine water molecules in the complex only (9 × −22 J⋅mol⁻¹⋅K⁻¹). Further details are provided in the main text. The orange square represents the HBP(D24R)–histamine binary complex binding to serotonin. The CaM and CAP data subsets are shown in green and blue, respectively.

Fig. 2.

Contribution of protein conformational entropy to the free energy of ligand binding to proteins. The broad range of contributions available to proteins for high-affinity binding of ligands is illustrated by the protein–ligand complexes used to calibrate the parameters of Eq. 3. The 28 protein–ligand complexes are arranged in descending order of the contribution of conformational entropy (red bars) to the total free energy of binding (blue bars). Conformational entropy contributed by the response of amino acid side chains to the binding of a ligand can vary from highly unfavorable, to negligible, to highly favorable. In some cases, conformational entropy is essential for high-affinity binding. The structural origins of the variable utilization of conformational entropy in molecular recognition are unknown. In most cases, the change in solvent entropy remains a dominant contribution. Note that −TΔS_r-t, ΔS_ligand, and ΔS_solvent are not shown here. The thermodynamics of each complex are summarized in SI Appendix, Tables S2 and S4.

Fig. 3.

Identification of rigidly held water in free barnase. Expansion of the 2D slice at the water resonance of 3D ¹⁵N-resolved NOE spectroscopy (NOESY) spectra of barnase in bulk aqueous solution (A, 50-ms NOE mixing time) and barnase encapsulated in CTAB/hexanol reverse micelles prepared in pentane (B, 40-ms NOE mixing time) is illustrated. These cross-peaks correspond to NOEs between amide hydrogens of barnase and local hydration water. The detection of hydration water in bulk aqueous solution is potentially corrupted by various mechanisms, most notably hydrogen exchange. These artifacts are suppressed in the reverse micelle. The correspondence of cross-peaks indicated by annotated assignments confirms those cross-peaks in the aqueous spectrum as genuine NOEs. Comparison of NOE and ROE cross-peak intensities indicates that these waters are rigidly held in free barnase. Additional NOEs in the reverse micelle spectrum result from the general slowing of water that brings motion of additional waters in the hydration layer into a detectable time regime. (C) Structural mapping of NOE cross-peaks between the protein and water in free barnase in bulk solution. Sites with long-lived hydration interactions are shown as green spheres. Crystallographic waters of free barnase in the binding site are shown as blue spheres.