The role of conformational entropy in molecular recognition by calmodulin

Abstract

The physical basis for high-affinity interactions involving proteins is complex and potentially involves a range of energetic contributions. Among these are changes in protein conformational entropy, which cannot yet be reliably computed from molecular structures. We have recently used changes in conformational dynamics as a proxy for changes in conformational entropy of calmodulin upon association with domains from regulated proteins. The apparent change in conformational entropy was linearly related to the overall binding entropy. This view warrants a more quantitative foundation. Here we calibrate an 'entropy meter' using an experimental dynamical proxy based on NMR relaxation and show that changes in the conformational entropy of calmodulin are a significant component of the energetics of binding. Furthermore, the distribution of motion at the interface between the target domain and calmodulin is surprisingly noncomplementary. These observations promote modification of our understanding of the energetics of protein-ligand interactions.

Figure 1

Distribution of methyl symmetry axis generalized order parameters ($O_{\text{axis}}^2$) for the target domains bound to calcium-saturated wild-type calmodulin (CaM). Determined using deuterium NMR relaxation (see Methods).

Figure 2

Dynamical character of the hydrophobic anchor in the N-terminal domain of CaM. Shown are the heavy atom surface representations of CaM residues 78-144 and the associated target domains. The target domains were flipped 180° and translated to the right to show the binding interface. Circled areas indicate the hydrophobic pockets of CaM. Methyl groups are color coded according to their mobility. The arrows point to the so-called anchor residues. The figure was generated using PyMol.

Figure 3

Calibration of the dynamical proxy for protein conformational entropy. Simple considerations lead to the prediction of a quantitative linear relationship between the total binding entropy and the entropy of solvent to the conformational entropy by NMR relaxation parameters derived from methyl bearing amino acids (see Equation 4). The error bars represent the average standard deviation of the difference of the average $O_{\text{axis}}^2$ parameters between free CaM and the complex with each target (see text). Each $O_{\text{axis}}^2$ parameter was derived from T₁ and T_1ρ values obtained at two magnetic field strengths. The average dynamics of wild-type and E84K CaM were based on 52 resolved methyl sites. The average dynamics of the six complexes shown were based on 73 to 88 resolved methyl sites (see Supplementary Table 7 for further details). The lower CaM:CaMKKα(p) datum is a clear outlier (Jackknife distance 8.8, all others < 2.3). The upper CaM:CaMKKα(p) point results from a simple correction to the solvent entropy arising from a postulated hydrophobic cluster in the free state of this target domain (see Supplementary Table 5). Excluding the CaM:CaMKKα(p) points results in a linear regression statistic R of 0.95. This regression line is shown. The slope (m = −0.037 ± 0.007 kJ K⁻¹ mol res⁻¹) allows for empirical calibration of the conversion of changes in side-chain dynamics to a quantitative estimate of changes in conformational entropy. The ordinate intercept is 0.26 ± 0.18 kJ K⁻¹ mol res ⁻¹.

Figure 4

Decomposition of the entropy of binding of target domains to calcium-saturated calmodulin. Based on Equation 4 and the calibration of the dynamical proxy (see Fig. 3) Solid diamonds are the solvent entropies calculated from the changes in accessible surface area and include the correction resulting from the postulated hydrophobic cluster of the free CaMKα(p) target domain (see text and Supplementary Table 5). The uncorrected value for CaMKα(p) is shown as an open diamond. No structure is available for the CaM:PDE(p) complex so the corresponding solvent entropy cannot be calculated. Solid circles and triangles are the contributions to the binding entropy by the conformational entropy of CaM and the target domains, respectively. Solid squares are the contributions to the binding entropy not reflected in the measured dynamics i.e. (ΔS_other + ΔS_RT ) (see Equation 4), which is obtained from linear regression (see Fig. 3). Though not required, there are interesting linear correlations between the total binding entropy and its components. There is a significant (R = 0.94) but weakly dependent (slope = −0.25 ± 0.04) negative linear correlation between solvent entropy and total binding entropy. In contrast, there is a significant (R = 0.91) and relatively strong positive dependence (slope = +1.0 ± 0.2) observed between the change of conformational entropy of CaM and the total binding entropy. The apparent negative correlation between target binding entropy and the total binding entropy is not statistically significant (R = 0.045).