Conformational entropy in molecular recognition by proteins

Abstract

Molecular recognition by proteins is fundamental to almost every biological process, particularly the protein associations underlying cellular signal transduction. Understanding the basis for protein-protein interactions requires the full characterization of the thermodynamics of their association. Historically it has been virtually impossible to experimentally estimate changes in protein conformational entropy, a potentially important component of the free energy of protein association. However, nuclear magnetic resonance spectroscopy has emerged as a powerful tool for characterizing the dynamics of proteins. Here we employ changes in conformational dynamics as a proxy for corresponding changes in conformational entropy. We find that the change in internal dynamics of the protein calmodulin varies significantly on binding a variety of target domains. Surprisingly, the apparent change in the corresponding conformational entropy is linearly related to the change in the overall binding entropy. This indicates that changes in protein conformational entropy can contribute significantly to the free energy of protein-ligand association.

Figure 1. Calmodulin-binding peptides

a, Sequence alignment of the six calmodulin-binding peptides. Note that CaMKKαp binds in opposite orientation to CaM relative to the other five peptides. For PDEp, a C15S mutation has been used to avoid complications with oxidation. b, Thermodynamic parameters. The Gibbs free energy (ΔG), enthalpy (ΔH) and entropy (−TΔS) for the formation of the six calcium-saturated CaM-peptide complexes at 35 °C. Values are tabulated in the Supplementary Information.

Figure 2. Correlation of the change in residual conformational entropy of calmodulin with the change in the total entropy of binding of a target domain

The change in conformational entropy was estimated using Equation 2 as described in the Methods and Supplementary Information. Propagation of measurement error in fitted order parameters results in uncertainties in conformational entropy less than the size of the symbols used. The fitted linear correlation coefficient (R²) of conformational entropy versus the entropy of binding is 0.78 with a slope of 0.51.

Figure 3. Distribution of the amplitude of methyl-bearing side chain motion of calmodulin in complex with target domains and correlation with the change in total entropy of binding

Shown are histograms of the squared generalized order parameters for calmodulin methyl group symmetry axes obtained at 35 °C. The solid lines represent fitted 3-Gaussian distributions centred on $O_{\mathit{axis}}^2$ values of 0.35 (J-class, red), 0.58 (α-class, green) and 0.78 (ω-class, blue). The relative populations of each class were derived from the fitted 3-Gaussian distributions for each complex. The change in population of the J, α and ω classes with the $-T\mathrm{\Delta }{S}_{\mathit{binding}}^{\mathit{system}}$ have fitted linear correlation coefficients (R²) of −0.83, +0.74 and +0.70, respectively. Correlation of the number of sites assigned to each class by simple binning, as colour-coded, yielded similar results (see Supplementary Information). Error bars reflect the variation of the population of each motional class that results from an increase or decrease in the measured $O_{\mathit{axis}}^2$ values by two standard deviations (see Figure 2).