ARTICLE PUBLISHED ONLINE: 11 APRIL 2010 | DOI: 10.1038/NCHEMBIO.347 The role of conformational entropy in molecular recognition by calmodulin Michael S Marlow1–3, Jakob Dogan1–3, Kendra K Frederick1,2, Kathleen G Valentine1,2 & A Joshua Wand1,2* 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 modifica- tion of our understanding of the energetics of protein-ligand interactions. he formation of protein complexes involves a complicated with high affinity15. Using NMR relaxation methods, we have manifold of interactions that often includes dozens of amino shown that calcium-saturated calmodulin (CaM) is an unusually acids and thousands of square Ångstroms of contact area1. dynamic protein and is characterized by a broad distribution of T 10 The origins of high-affinity interactions are quite diverse and com- the amplitudes of fast side chain dynamics . The binding of target plex and are reflected in the difficulty of computing the energet- domains causes a redistribution of these motions in calmodulin10,11. ics of interactions between proteins using molecular structure Interpretation of the changes in motion using a simple harmonic alone2. Indeed, structure-based design of pharmaceuticals has been oscillator model13 yielded a linear correlation between the appar- impeded by this barrier3. Of interest here is the role of protein con- ent change in conformational entropy of CaM and the total bind- formational entropy in modulating the free energy of the associa- ing entropy11. Taken at face value, this suggested a considerable tion of a protein with a ligand. Decomposition of the total binding contribution from conformational entropy to the total binding free energy emphasizes that the entropy of binding is comprised of entropy and indicated a role for conformational entropy in ‘tun- contributions from the protein, the ligand and the solvent: ing’ calmodulin’s high-affinity interactions. However, the analytical strategy used suffers from several 11,12 © 2010 Nature America, Inc. All rights reserved. All rights Inc. America, Nature © 2010 ∆∆GHtott=−ot TS∆∆totb=−HTindp( ∆∆ SS rotein ++ ligand ∆ S so lven t ) (1) potential limitations . That approach effectively takes an inven- tory of the change in motion at a limited number of sites and inter- Historically, the contributions by solvent entropy have taken center prets this within the context of a simple physical model such as stage and are usually framed in terms of the so-called hydrophobic the harmonic oscillator13. This raises several issues including the effect4. Hydrophobic solvation by water continues to be the subject effects of correlated motion, the operation of a more complex of extensive analysis5,6. In principle, the entropic contributions of a potential energy function, the completeness of the oscillator count, 12 structured protein to the binding of a ligand (∆Sprotein) include both and so on . Although the presence of a linear correlation between changes in its internal conformational entropy (∆Sconf) and changes the apparent change in conformational entropy and total binding 7 in rotational and translational entropy (∆SRT) . Equation (1) empha- entropy is a compelling indication of the importance of the former, sizes that the measurement of the entropy of binding does not resolve the quantitative scale of the interpreted ∆Sconf is potentially suspect. contributions from internal protein conformational entropy. Despite Here we resolve this issue by taking a different approach based on the suggestion that the conformational entropy of structured pro- an empirical calibration of the dynamical proxy for conformational teins is significant8,9, it is only recently that experimental evidence entropy. Rather than attempt a model-dependent interpretation has become available to indicate that it is sufficiently responsive to of an inventory of changes in local dynamics, we use experimen- influence the thermodynamics of protein association10,11. tal measures of local dynamics as a proxy for local disorder and Experimental measurement of ∆Sconf has been difficult. Motion seek an empirical scaling between them. The aim is to effectively between different microscopic structural states has been devel- solve for each term of equation (1). An essential component of oped as an indirect measure of or proxy for conformational this approach is knowledge of the dynamics of the target domains, entropy12. Motion expressed on the subnanosecond timescale cor- which are determined here. The availability of these data allows responds to significant entropy13, and NMR relaxation methods for the quantitative calibration of the dynamical proxy for confor- are particularly well suited for its characterization12. Previously, we mational entropy. We found that the conformational entropy of used calmodulin as a model system to investigate the role of con- calmodulin not only contributes significantly to the free energy formational entropy in the high-affinity association of proteins11. of binding of target domains but also appears to be the dominant Calmodulin is central to calcium-mediated signal transduction factor in tuning the affinity of calmodulin for the various target pathways of eukaryotes14 and interacts with hundreds of proteins domains examined. 1Johnson Research Foundation and 2Department of Biochemistry and Biophysics, University of Pennsylvania, Philadelphia, Pennsylvania, USA. 3These authors contributed equally to this work. *e-mail: [email protected] 352 NATURE CHEMICAL BIOLOGY | VOL 6 | MAY 2010 | www.nature.com/naturechemicalbiology NatURE CHEMICAL BIOLOGY DOI: 10.1038/NCHEMBIO.347 ARTICLE 10 2 smMLCK(p) are heterogeneously distributed, with O axis values ranging from 0.05 to 0.95 (Fig. 1). The distribution is non-uniform and reminis- CaMKI(p) cent of the multimodal distributions of the calmodulin component eNOS(p) of these complexes11. 8 CaMKKα(p) PDE(p) Variable and counterintuitive motion at the interface nNOS(p) The methyl-bearing side chains of the target domains are distri- buted throughout the CaM-peptide interface, thereby providing an 6 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 Occurrences 4 localize to hydrophobic pockets formed by the N-terminal and C-terminal domains of CaM. Typically, one anchor resi- due is aromatic (tryptophan or phenylalanine) and the other is aliphatic. Anchor residues are believed to be essential for com- 2 plex formation21. The aliphatic side chain anchors of the bound target domains were localized to the N-terminal domain of CaM (Fig. 2). Surprisingly, most aliphatic peptide side chains histori- cally identified as anchor residues were more dynamic than one 0 2 might expect. Specifically, the O axis values of the eNOS(p) and 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 nNOS(p) leucine δ methyls and the CaMKI(p) methionine ε 2 O axis methyl were at or below the residue-specific averages for the CaM complexes (Supplementary Table 3). With Leu19 of smMLCK(p) Figure 1 | Distribution of methyl symmetry axis generalized order providing the lone exception, the binding within the pocket need parameters for the target domains bound to calcium-saturated wild- not significantly confine the motion of the anchor residues of the type calmodulin. We determined the parameters using deuterium NMR bound target domain. relaxation (see Methods). Complex formation results in a pattern of the dynamics of the CaM methyl-bearing residues that form the binding pocket (Ile27, Leu32, Met51, Ile52, Val55, Ile63 and Met71). For example, in every RESULTS complex, Ile27δ and Ile63δ exhibit relatively restricted motion, 2 Dynamics of the target domains in complex with CaM with an average O axis of 0.69 (n = 12), which is 0.19 greater than Using deuterium NMR relaxation methods16, we examined fast the residue average for isoleucine δ methyls in the CaM complexes. 2 motion of the methyl-bearing side chains of the target domains in In contrast, the O axis for the δ methyl of Ile52 averages 0.36 (n = 6), the six CaM complexes examined previously11. These include com- which is 0.14 less than the residue average in the CaM complexes. 2 plexes between calmodulin and the calmodulin-binding domains The average O axis for the δ methyls of Leu32 of 0.50 (n = 12) is of the endothelial and neuronal nitric oxide synthases (eNOS and also substantially smaller than the residue average of 0.60. We © 2010 Nature America, Inc. All rights reserved. All rights Inc. America, Nature © 2010 nNOS, respectively), calmodulin kinase kinase-α