Dynamics of the target domains in complex with CaM
Using deuterium NMR relaxation methods16
, we examined fast motion of the methyl-bearing side-chains of the target domains in the six CaM complexes examined previously11
. These include complexes between calmodulin and the calmodulin-binding domains of the endothelial and neuronal nitric oxide synthases (eNOS and nNOS, respectively), calmodulin kinase kinase alpha (CaMKKα), calmodulin kinase I (CaMKI), phosphodiesterase (PDE) and the smooth muscle myosin light chain kinase (smMLCK). The calmodulin-binding domains are represented here as peptides and we will use the nomenclature eNOS(p), for example, to emphasize this fact. All peptide domains have a basic amphiphillic sequences, typical of CaM binding domains (Supplementary Table 1
). These domains have been found by isothermal titration calorimetry at 308 K to bind with roughly the same affinity to CaM but with widely different thermodynamic parameters defining the free energy of association11,17,18
. In the case of the CaMKKα(p) and smMLCK(p) domains, binding is driven by a large favorable change in total binding enthalpy overcoming a large unfavorable change in total binding entropy. At the other extreme, nNOS(p) binding is driven by a favorable change in total enthalpy accompanied by a small favorable change in entropy. The other domains represent intermediate cases. The entropy of binding of these domains varies by 90 kJ/mole and changes sign (Supplementary Table 2
All bound target domain methyl resonances are well resolved in 13
C- NMR spectra and deuterium relaxation parameters could be measured with high precision (Supplementary Fig. 1
). The degree of spatial restriction of each motional probe was assigned a number between 0, corresponding to complete isotropic disorder, and 1, corresponding to a fixed orientation within the molecular frame. This parameter is the so-called model-free squared generalized order parameter19
as it applies to the methyl symmetry axis (O2axis
). A recent re-evaluation of the model-free treatment of Lipari & Szabo reinforces confidence in its robustness with respect to highly asymmetric side chain motion 20
. The 80 methyl O2axis
parameters from 53 residues of the target domains in the six wild-type CaM complexes are heterogeneously distributed with O2axis
values ranging from 0.05 to 0.95 (). The distribution is non-uniform and reminiscent of the multi-modal distributions of the calmodulin component of these complexes11
Figure 1 Distribution of methyl symmetry axis generalized order parameters () for the target domains bound to calcium-saturated wild-type calmodulin (CaM). Determined using deuterium NMR relaxation (see Methods).
Variable and counter-intuitive motion at the interface
The methyl bearing side-chains of the target domains are distributed throughout the CaM-peptide interface providing an excellent system to examine the intricacies of structure-dynamics relationships. The structures of all but the complex with PDE(p) are known. CaM-target complexes have “anchor” residues that localize to hydrophobic pockets formed by the amino and carboxy-terminal domains of CaM. Typically, one anchor residue is aromatic (Trp or Phe) and the other aliphatic. Anchor residues are believed to be essential for complex formation21
. The aliphatic side-chain anchors of the bound target domains are localized to the amino-terminal domain of CaM (). Surprisingly, most aliphatic peptide side chains historically identified as “anchor” residues are more dynamic than one might expect. Specifically, the O2axis
values of eNOS(p) and nNOS(p) leucine δ methyls and the CaMKI(p) methionine ε methyl are at or below the residue-specific averages for the CaM complexes (Supplementary Table 3
). With L19 of smMLCK(p) providing the lone exception, the binding within the pocket need not significantly confine the motion of the anchor residues of the bound target domain.
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 (more ...)
Complex formation results in a striking pattern of the dynamics of the CaM methyl-bearing residues that form the binding pocket (I27, L32, M51, I52, V55, I63, and M71). For example, in every complex I27δ and I63δ exhibit relatively restricted motion with an average O2axis
of 0.69 (n = 12), which is 0.19 greater than the residue average for isoleucine δ-methyls in the CaM complexes. In contrast, the O2axis
for the δ-methyl of I52 averages 0.36 (n = 6), which is 0.14 less than the residue average in the CaM complexes. The average O2axis
for the δ-methyls of L32 of 0.50 (n = 12) is also significantly smaller than the residue average of 0.60. A similar pattern is seen in the residues found in the carboxy-terminal pocket that bind aromatic peptide anchor residues. Some residues, such as L105 and V136, have methyl group dynamics at their residue specific averages in the CaM complexes. Others are highly constrained such as I100δ (n = 5) and A128 (n = 5), which show average O2axis
that are 0.3 and 0.23 larger than the residue averages. Clearly, binding does not induce a uniform reduction in side-chain motion within the hydrophobic pockets. More nuanced responses are also seen. This may be a feature of proteins that have evolved to bind numerous targets. Such responses motivates extending the view of hot spot interactions 22
to include resolution of dynamical (entropic) from specific enthalpic contributions.
Calibration of the “entropy meter”
We now turn to the insights into the thermodynamic origins of binding offered by the characterization of internal motion in the calmodulin complexes. A main goal is to empirically calibrate the dynamical proxy of conformational entropy for the calmodulin system. We first decompose the entropy of binding in terms of contributions from calmodulin, the target domains and solvent:
Contributions from rotational and translational entropy of CaM and the peptide (ΔSRT
) have been grouped. The similarity in peptide lengths, the structures of the complexes, and the binding affinities suggest that ΔSRT
is essentially constant across the complexes. We further postulate that the contribution of changes in the conformational entropy of CaM and the target domains are linearly related to local disorder represented by the squared generalized order parameters determined by NMR relaxation in methyl groups:
The parameter m
defines the scaling between average changes in residue weighted generalized order parameters for calmodulin and the target domain upon binding (i.e.
are the number of residues in CaM and a given target domain, respectively, used in the entropy calibration (See Supplementary Table 1
for further explanation). Equation (3)
includes potential contributions ( ΔSother
) from other sources conformational entropy of the protein that are not sensed (directly or indirectly) by the deuterium NMR relaxation probes used here. This includes, for example, vibrational entropy involving motion that does not average the angle of the methyl symmetry axis with the magnetic field and motion slower than overall tumbling of the macromolecule 12
. We assume that these other contributions ( ΔSother
) are the same for all target peptides and complexes, which is not unreasonable given that the peptides all have roughly the same number of degrees of freedom. This leads to the prediction of a linear relationship between the difference of the total binding entropy and the solvent entropy and the apparent change in conformational entropy measured by NMR relaxation:
Some of the assumptions leading to Equation (4)
may appear drastic. However, should any of them be violated, a significant deviation from linearity should be observed.
As suggested by Equation (4)
, to compare dynamics in the various complexes we employ a normalization procedure to account for variation in the number of methyl sites in CaM whose motion could be quantified and to account for the fact that, although fully resolved, the number of residues in the target domains vary. A simple average was employed (see Equation (4)
and Supplementary Table 4
). The apparent change in conformational entropy due to fast motion was then calculated without explicit consideration of the classical entropy due to rotamer interconversion11,23
. This entropy will be contained within the calibrated dynamical proxy (i.e., within the scalar m
). As the free target states cannot be assessed using the model-free formalism19
, we assume that the dynamics of the free unstructured target domains are uniform and correspond to an O2axis
of 0.05. This limiting value is seen, for example, in Val-3 of CaMKKα(p) bound to CaM, which is completely solvent exposed and hence provides a internal reference for unrestricted motion that meets the criteria of the model-free treatment.
parameter only detects motion on a timescales significantly shorter than the macromolecular tumbling, which for these complexes is on the order of 8.5 ns11
. States that interconvert on the μs-ms timescale are illuminated by chemical shift averaging effects24
. Methyl dispersion experiments of the CaM:smMLCK(p) and CaM:nNOS(p) complexes indicate that these complexes are silent in this time regime. States that are not averaged on the chemical shift times scale are indicated by the presence of minor components in the NMR spectrum. A small amount of micro-heterogeneity was observed in CaM in some of the complexes11
. This is a small contribution that we ignore. There is no micro-heterogeneity of side-chain conformations of the bound target domains evident in their 13
C-HSQC spectra and the corresponding contribution to the conformational entropy was taken to be zero.
To solve equation (4)
, we use the binding entropies obtained by isothermal titration calorimetry11
and calculate the change in solvent entropy using the known structures of free CaM25
and the five complexes for which high resolution structures are available26-29
. The empirical relationship between changes in accessible surface area and the entropy of solvent30
is employed and calculated assuming a fully solvated structure for the dissociated target domains (see Methods and Supplementary Table 5
). Not included are changes in solvent entropy due to electrostriction of water by solvation of explicit charge (however, see below). To further test this approach, we also examined the complex of a mutant CaM with the smMLCKp domain. Of several examined previously, we chose to examine the CaM(E84K):smMLCK(p) complex as it showed the most varied dynamical response compared to the wild-type complex31
. The entropy of binding was determined by isothermal titration calorimetry to be +41 ± 1 kJ/mole at 308 K, which is significantly less unfavorable than the wild-type complex. The binding free energy and enthalpy were also determined be −43.6 ± 0.5 and −84.3 ± 0.8 kJ/mole, respectively. The methyl O2axis
parameters were previously determined for the complex31
. To use this complex for calibration required measurement of the dynamics of the bound smMLCK(p) domain and characterization of the dynamics of the free CaM(E84K) mutant.
a quantitative linear relationship and is plotted for the six complexes (). Five given an excellent linear relationship (R = 0.95) and a slope of −0.037 ± 0.007 kJ K −1
and an ordinate intercept of 0.26 ± 0.18 K kJ−1
(). The CaMKKα(p) complex is a clear outlier (). This is not surprising. The primary sequence is unusually hydrophobic (Supplementary Table 1
) and the peptide has limited solubility17
. Hydrophobic cluster analysis32
illuminates a hydrophobic patch and suggests that the dissociated domain exists in a collapsed, less hydrated state than is assumed for the solvent entropy calculations. A simple correction based on the size of the predicted hydrophobic cluster shows that this is not an unreasonable explanation for the apparent discrepancy ().
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 (more ...)
Excluding the CaMKKα(p) complex, the quantitative linearity of the remaining points strongly suggests that the assumptions underlying Equation (4)
are largely valid and that a self-consistent view of the origin of the thermodynamics of binding in the calmodulin system has been established. Most important is the apparent validity of employing measures of motion as a quantitative proxy for conformational entropy. Furthermore, the quantitative consistency also suggests that the contribution of vibrational entropy, which is largely contained in the constant intercept in , is not variable
across the calmodulin complexes. In this respect, it is interesting to note that the corresponding ordinate intercept is nominally positive even though the loss of rotational and translational entropy would result in a negative contribution to the ordinate intercept (see Equation 2
). This apparent discrepancy is easily explained by recognizing that the formation of the each of the complexes results in the burial of 6 charged side-chains through the formation of ion pairs. The removal of charge from bulk water will result in a significant increase in solvent entropy33
. The degree of electrostriction in the free state can be estimated from the pressure dependence of the formation of the CaM:smMLCK(p) complex, which has been measured using hydrogen exchange based methods34
. Comparison to solvent entropy values for model charged species33
suggests that this effect is comparable to the predicted positive contribution to the free energy of binding by ΔSRT
. Furthermore, vibrational entropy has also been suggested to provide a favorable contribution to the binding of ligands to proteins in some cases, dihydrofolate reductase being one such example35
. It is possible that an increase in vibrational entropy upon formation of the calmodulin complexes also diminishes the counter-balances the contribution of the loss of rotational and translational entropy to the ordinate intercept of . Regardless, the linear regression statistics indicates that these contributions are constant across the five well-behaved complexes.
The possible exception of the CaM:CaMKKα(p) complex to the linear relationship defined by the other five complexes () has several interesting implications. As noted above, this domain is expected to form a collapsed hydrophobic cluster in the free state. A simple calculation suggests that such a dehydrated cluster could significantly reduce the apparent discrepancy (see Supplementary Table 5
and ). The resulting chain compaction would cause an opposing correction but in this situation is predicted to be relatively small36
. It should be noted that the isothermal titration calorimetry profile of the formation of this complex is simple and unremarkable and does not indicate the presence of a more complex equilibrium involving the disassembly of aggregates of the target, for example17
. In addition, calmodulin interacts with this domain in reverse orientation from the others, which may be reflected in the apparently anomalously higher motion of the bound domain. Despite these uncertainties about the nature of the solvent and free target domain contributions to the binding entropy of the formation of this complex, the contribution of CaM to the binding of the CaMKKα(p) target is consistent with the other complexes, as we will now show below.