Entropy in molecular recognition by proteins
José A. Caroa,1, Kyle W. Harpolea,1, Vignesh Kasinatha,1, Jackwee Lima,1, Jeffrey Granjaa, Kathleen G. Valentinea, Kim A. Sharpa, and A. Joshua Wanda,2
aJohnson Research Foundation and Department of Biochemistry and Biophysics, University of Pennsylvania Perelman School of Medicine, Philadelphia, PA 19104-6059
Edited by G. Marius Clore, National Institutes of Health, National Institute of Diabetes and Digestive and Kidney Diseases, Bethesda, MD, and approved May 9, 2017 (received for review December 26, 2016)
Molecular recognition by proteins is fundamental to molecular free energy (ΔGtotal) of binding are measured and the total biology. Dissection of the thermodynamic energy terms governing binding entropy (ΔStotal) is determined by: protein–ligand interactions has proven difficult, with determina- tion of entropic contributions being particularly elusive. NMR re- ΔG = ΔH − TΔS = ΔH laxation measurements have suggested that changes in protein total total total total conformational entropy can be quantitatively obtained through − Δ protein + Δ ligand + Δ + Δ + Δ T Sconf Sconf Ssolvent Sr−t Sother . a dynamical proxy, but the generality of this relationship has [1] 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. Here and throughout the main text, the thermodynamic values We find that the contribution of conformational entropy can range refer to a standard 1 M state of concentration. The challenge is to from favorable to unfavorable, which demonstrates the potential quantify the various microscopic contributions to the free energy of of this thermodynamic variable to modulate protein–ligand inter- binding. Detailed atomic resolution structural models provide great actions. For about one-quarter of these complexes, the absence of insight into the origins of the enthalpy of binding. Much less certain conformational entropy would render the resulting affinity biolog- are the various contributions to the total binding entropy. In principle, several types of entropy are potentially important (right ically meaningless. The dynamical proxy for conformational entropy 1 or “entropy meter” also allows for refinement of the contributions side of Eq. ). Historically, entropy has most often entered the discussion in terms of the changes in the entropy of solvent water of solvent entropy and the loss in rotational-translational entropy Δ “ accompanying formation of high-affinity complexes. Furthermore, ( Ssolvent) and framed in terms of the so-called hydrophobic ef- fect” (10, 11). ΔSsolvent has, with some success, been related empir- structure-based application of the approach can also provide insight Δ into long-lived specific water–protein interactions that escape the ically to changes in accessible surface area ( ASA) of the protein and ligand upon complexation (12). Changes in the conformational generic treatments of solvent entropy based simply on changes in Δ Δ accessible surface area. These results provide a comprehensive and entropy ( Sconf) and the rotational-translation entropy ( Sr-t) (13) unified view of the general role of entropy in high-affinity molecu- of the interacting species have received far less attention, presum- lar recognition by proteins. ably because they have resisted experimental measurement. Con- tributions to binding entropy from unrecognized sources (ΔSother) 1 entropy | molecular recognition | binding thermodynamics | arealsoincludedinEq. and discussed below. protein dynamics | NMR relaxation Significance ost biological processes are controlled using molecular Mrecognition by proteins. Protein–ligand interactions regu- Molecular recognition by proteins is a key element of biology. late enzyme function, signaling pathways, and cellular events Appreciation of the underlying thermodynamics has been in- essential to life, particularly through allosteric mechanisms (1). complete because of uncertainty in several contributions to the Indeed, efforts at pharmaceutical intervention in disease have entropy. Here, we demonstrate a way to measure changes in largely centered on the manipulation of molecular recognition by protein conformational entropy using a dynamical proxy pro- vided by NMR relaxation methods. We find that conforma- proteins. The physical origin of high-affinity interactions in- tional entropy can contribute significantly and variably to the volving proteins has been the subject of intense investigation for thermodynamics of binding. In addition, we determine the con- decades. Structural analysis at atomic resolution has helped il- tribution of rotational-translational entropy loss upon forming a luminate in great detail the role played by enthalpy. On the other high-affinity complex involving a protein. The contribution of hand, the role of entropy in modulating the free energy of as- solvent entropy is also recalibrated. Thus, a more complete view sociation of a protein with a ligand has remained elusive. Of of entropy in binding has been established and shows that in- prime interest here is the conformational entropy of the protein, clusion of conformational entropy is necessary to understanding which is defined by the distribution of conformational states the origins of high-affinity interactions involving proteins. populated by the protein. A binding event can result in a re- distribution of populated states, and such differences are effec- Author contributions: A.J.W. designed research; J.A.C., K.W.H., V.K., J.L., K.G.V., and tively invisible in a static, monolithic view of proteins. It remains A.J.W. performed research; V.K., J.G., K.G.V., and A.J.W. contributed new reagents/ analytic tools; J.A.C., K.W.H., V.K., J.L., K.G.V., K.A.S., and A.J.W. analyzed data; and a challenge for structure-based efforts, agnostic to the confor- J.A.C., K.W.H., V.K., K.G.V., K.A.S., and A.J.W. wrote the paper. mational landscape available to the protein, to relate the inter- The authors declare no conflict of interest. actions of a few amino acids at a specific interface to the global, This article is a PNAS Direct Submission. experimentally measured free energies (2–4). The potential role Data deposition: The NMR chemical shifts and obtained order parameters have been for conformational entropy in protein function has been specu- deposited in the BioMagResBank, www.bmrb.wisc.edu (accession nos. 26667, 26670, lated about and simulated for some time (4–9), but a compre- 25728, 25727, 26983, 26619, and 26620). hensive, quantitative, and experimental evaluation of the extent 1J.A.C., K.W.H., V.K., and J.L. contributed equally to this work. and variation of its importance has been lacking. 2To whom correspondence should be addressed. Email: [email protected]. Experimental insight into binding entropy often begins from a This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. BIOPHYSICS AND
calorimetric perspective where the heat or enthalpy (ΔHtotal) and 1073/pnas.1621154114/-/DCSupplemental. COMPUTATIONAL BIOLOGY
www.pnas.org/cgi/doi/10.1073/pnas.1621154114 PNAS | June 20, 2017 | vol. 114 | no. 25 | 6563–6568 Downloaded by guest on October 2, 2021 Some time ago, it was realized that fast subnanosecond time constant]. There are now roughly two dozen published studies of scale motion between conformational states might provide ac- the change in methyl-bearing side-chain dynamics that are suf- cess to various thermodynamic features (14), especially confor- ficiently complete to use to test this idea (SI Appendix, Table S1). mational entropy (15, 16). Application of this idea has been Criteria for selection of these complexes included the availability thwarted by several technical limitations (17, 18), but has nev- of comprehensive assignments and relaxation data in both free ertheless led to the strong suggestion that dynamical proxies and complexed protein states, as well as a largely dry interface made available by NMR relaxation measurements could provide in the complex. We have augmented many of these NMR re- access to measures of conformational entropy (19). More re- laxation studies by measuring the binding thermodynamics using cently, efforts have been taken to overcome these technical isothermal titration calorimetry (ITC) under corresponding barriers and limitations and to render this approach to protein NMR solution conditions (i.e., buffer, pH, temperature). Com- entropy quantitative (20, 21). The resulting NMR-based dy- pletely new examples were also examined. The curated dataset is – namical proxy for conformational entropy or “entropy meter” summarized in SI Appendix, Tables S1 S4. takes a simple form that requires a few assumptions, particularly Previously, the empirically determined coefficients relating about the precise nature of the underlying motion (21): changes in accessible polar and apolar surface area to the sol- vation entropies of these two types of surface had to be derived h i Δ = proteinΔ 2 protein + ligandΔ 2 ligand subject to various assumptions about the nature of conforma- Stotal sd Nχ Oaxis Nχ Oaxis tional entropy (12). The unprecedented amount of dynamical data used here now allows us to determine the area coefficients + ΔSsolvent + ΔSr−t + ΔSother. directly. The data on the 28 proteins used here were obtained at [2] somewhat different temperatures (298–308 K). Significant heat 2 capacity changes accompany hydration of apolar and polar The first two terms contain the dynamical proxy, where O axis is a groups. Fortunately, the corresponding temperature variation of measure of the degree of spatial restriction of the methyl group the desolvation entropy is well described experimentally by the symmetry axis and ranges between 0, which represents complete relations ΔS = ΔCp ·ln(T/385K)·ΔASA (27) and isotropic disorder, and 1, which corresponds to no internal mo- apolar apolar apolar ΔSpolar = ΔCppolar·ln(T/176K)·ΔASApolar (28), where ΔCpapolar tion within the molecular frame (22), and is measured in various and ΔCp are the changes in hydration heat capacities per ways (17). Numerous models and simulations indicate that polar unit area of apolar (ΔASAapolar) and polar (ΔASApolar) surface, changes in entropy will be linearly related to changes in the respectively, and 385 K and 176 K are reference temperatures at relevant O2, varying between 0.1 and 0.9 (14–17, 21, 23). This which the apolar and polar solvation entropies extrapolate to linearity is the basis for the simple form of the entropy meter (20, 0 (27, 28). The intercept of Eq. 2 contains the loss in rotational- 21). Measurement of fast internal side-chain motion in proteins translational entropy upon formation of the complex. We there- is largely restricted to the methyl group, which, due to its fast fore recast Eq. 2 as: rotation, can be used as a relaxation probe in even very large h i proteins (17). The change in the average methyl group symmetry protein ligand 2 Δ = proteinΔ 2 + ligandΔ 2 axis order parameter (Δ
6564 | www.pnas.org/cgi/doi/10.1073/pnas.1621154114 Caro et al. Downloaded by guest on October 2, 2021 and it is often a large determinant of the thermodynamics of binding (Fig. 2). Indeed, for approximately one-quarter of the complexes used in the calibration of the entropy, the absence of the contribution of conformational entropy to the binding ther- modynamics would result in biologically ineffective affinities. The calibrated entropy meter allows the determination of the contribution of conformational entropy to a binding process using only the dynamical information; that is, for a heterodimer (AB): h i A B ΔS = s NAΔ O2 + NBΔ O2 ; conf d χ axis χ axis [4] −3 −1 −1 sd = −ð4.8 ± 0.5Þ × 10 kJ mol K .
Importantly, other entropic contributions to protein–ligand associations are also made accessible by the approach summa- rized in Fig. 1 and Eq. 3. Eq. 3 allows for other unknown sources of entropy. These sources might include, for example, (de)pro- tonation or (de)solvation of charge associated with binding (29). Clearly, if ΔSother is both significant and varies between com- plexes, then the linearity of Eq. 3 will be degraded. The observed linear correlation strongly suggests that such is not the case. Thus, if ΔSother is small relative to ΔSconf and ΔSsolvent, then the ordinate intercept represents the loss in rotational-translational entropy upon formation of high-affinity complexes. ΔSr-t has Fig. 1. Calibration of the dynamical proxy for protein conformational en- been the subject of extensive theoretical debate but, like con- tropy. Fitting of Eq. 3 to data provided by 28 protein–ligand associations formational entropy, has resisted experimental definition. The (blue, green, and magenta circles) is shown. The difference in the measured −1 −1 apparent ΔSr-t is −0.10 ± 0.01 kJ·mol ·K (standard state of total binding entropy and calculated solvent entropy is plotted against the 1 M), which compares reasonably well with the apparent ΔS change in the dynamical proxy upon binding of ligand. The dynamical proxy r-t is the difference of the average Lipari–Szabo squared generalized order obtained through molecular dynamics simulations (30). 2 The contribution of solvent entropy to processes involving parameters of methyl group symmetry axes (Δ
Table 1. Calibration of the entropy meter using only the two protein systems, catabolite activator protein Parameter Value and calmodulin, used previously for calibration (21) (Fig. 1, − − Intercept (ΔS + ΔS )/kJ·mol 1·K 1 −0.10 ± 0.01 green and blue circles, respectively). Although it is likely that sd r-t other −3 · −1· −1 − ± will vary in detail between different proteins, the precision cap- Slope (sd)*/10 kJ mol K 4.8 0.5 Δ −4 · −1· −1· −2 + ± tured by Fig. 1 indicates that this variability is limited. Cpapolar/10 kJ mol K Å 3.7 1.1 Δ −5 · −1· −1· −2 − ± In this treatment, we have ignored the contribution to the Cppolar/10 kJ mol K Å 5.2 1.0 −5 · −1· −1· −2 − ± binding entropy from the backbone of the protein. Recent sim- aapolar (298 K)/10 kJ mol K Å 9.6 2.9 −5 · −1· −1· −2 − ± ulations suggest that the binding of ligands by structured proteins apolar (298 K)/10 kJ mol K Å 2.7 0.5 will involve little contribution from the backbone of the poly- Calibration of the entropy meter is derived from a global fit for the
peptide chain (25). Unfortunately, only six of the complexes used parameters ΔCpapolar, ΔCppolar, ΔSr-t, and sd of Eq. 3 using the experimental have sufficiently characterized dynamics to allow backbone motion binding entropy changes, order parameter changes, and known experimen- to be fully included in our analysis. However, when analyzed in a tal temperatures for the 28 complexes summarized in Fig. 1 (R = −0.85, R2 = −7 similar fashion, this subset indicates that the contribution by the 0.72, P < 10 ). Uncertainties were determined by Monte Carlo sampling. SDs backbone to the binding entropy is indeed small (<5%). Using the are shown. The average covariance matrix is provided in SI Appendix, Table S6. Values for the hydration entropy coefficients per unit area are also tab- determined value of sd, we can now establish quantitatively that ulated at the standard temperature of 298 K. Calibration is performed with the contribution of conformational entropy to molecular recog- reference to a standard state concentration of 1 M. nition by proteins is quite variable. Conformational entropy can *Entropic contribution of the backbone is not directly included (as discussed BIOPHYSICS AND
highly disfavor, have no effect on, or strongly favor association, in the main text). COMPUTATIONAL BIOLOGY
Caroetal. PNAS | June 20, 2017 | vol. 114 | no. 25 | 6565 Downloaded by guest on October 2, 2021 (43, 44), and a calmodulin–peptide complex (45). Early NMR studies suggested that the backbone contributed less to the heat capacity of folded proteins than side chains (41). Using the en- tropy meter, we find that the amino acid side chains contribute only a small fraction (∼5–6%) to the total heat capacity measured by differential scanning calorimetry of the latter two proteins (SI Appendix,TableS6). This finding reinforces the proposal that most of the heat capacity comes from solvent–protein interactions (10, 40, 46). In addition to exploring the role of conformational entropy in protein function, the entropy meter can be used to illuminate other important manifestations of entropy. For example, the complexes used for calibration of the entropy meter largely have dry interfaces. The presence of retained “structural” water at the buried surface comprising the interface would affect the solvent entropy but would be masked by the standard method to calcu- late it based on accessible surface area. Following calibration (Fig. 1), the entropy associated with the organization of water within a protein complex can be explored. To illustrate this view, we examined the complex between the extracellular ribonuclease barnase of Bacillus amyloliquefaciens and an oligonucleotide dCGAC model substrate. Barnase is a 110-residue ribonuclease and is inhibited by the 89-residue barstar to suppress its poten- Fig. 2. Contribution of protein conformational entropy to the free energy tially lethal activity inside the cell. The barnase/dCGAC complex of ligand binding to proteins. The broad range of contributions available to has nine fully buried and crystallographically well-defined struc- proteins for high-affinity binding of ligands is illustrated by the protein– tural water molecules at the interface (47) (Fig. 3). Determina- ligand complexes used to calibrate the parameters of Eq. 3. The 28 protein– tion of the binding thermodynamics by direct titration monitored ligand complexes are arranged in descending order of the contribution of by NMR spectroscopy and ITC indicates that the free energy of conformational entropy (red bars) to the total free energy of binding (blue binding of dCGAC to barnase is essentially provided by a gain in bars). Conformational entropy contributed by the response of amino acid entropy (SI Appendix, Fig. S3 and Table S2). Dynamic analysis side chains to the binding of a ligand can vary from highly unfavorable, to indicates a corresponding increase in side-chain motion upon negligible, to highly favorable. In some cases, conformational entropy is binding of the oligonucleotide that corresponds to a favorable essential for high-affinity binding. The structural origins of the variable utilization of conformational entropy in molecular recognition are un- contribution to the binding entropy (SI Appendix, Fig. S3 and known. In most cases, the change in solvent entropy remains a dominant Table S4). An inventory of the entropy contributions as outlined 3 contribution. Note that −TΔSr-t, ΔSligand, and ΔSsolvent are not shown here. by Eq. results in good agreement, which is in apparent con- The thermodynamics of each complex are summarized in SI Appendix, Tables tradiction to the implications of the structure of the complex S2 and S4. noted above. This contradiction arises because rigidification of nine water molecules is not accommodated by the solvation term − − of Eq. 3. Using the entropy of fusion of water (−22 J·mol 1·K 1) hydrophobic effect. Concomitantly, burial of the polar area also (48), the rigidification of these waters in the complex is be pre- stabilizes the complex via release of its hydrating water into the dicted to result in a distinct deviation from the calibration line bulky, less ordered state (31). The coefficients are smaller than (Fig. 1, gray and blue diamonds). Thus, either the structural obtained previously (12, 33) and, in part, reflect the impact of waters retain considerable Sr-t in the complex and/or they are inadequately assessing the contribution of residual side-chain en- rigidified in free barnase. To answer this question, we turned to tropy in the folded state of proteins in prior work. It is also in- an approach introduced some time ago by Wüthrich and co- teresting to note that the smaller magnitude likely arises from a workers (49), where the nuclear Overhauser effect (NOE), and difference in the nature of solvation. Prior solvation entropies have its rotating frame counterpart (ROE), between hydrogens of the been estimated from group transfers between water and organic protein and hydrogens of long-lived associated water can provide solvents or global unfolding of globular proteins (e.g., refs. 12, 27, information about protein–water dynamics. An unprecedented 28, 33–36), which involves complete solvation of side chains. In number of NOE contacts consistent with the long-lived attach- contrast, the studies here focus on the (de)solvation of more ex- ment of the nine waters buried at the interface in the complex tended protein surfaces and may reflect differences in length scale, are seen in free barnase (4). It is noted that artifacts can po- detailed geometry, and inherent dynamics of protein surfaces tentially occur when using this approach in bulk solution (50). (e.g., refs. 37–39). This issue remains to be explored further. However, encapsulation of proteins within the protective water Several fundamental properties of protein molecules in solu- core of a reverse micelle suppresses hydrogen exchange and tion are related to their heat capacity, which, in turn, is related to other processes that can corrupt the NOE and ROE (51). Di- the underlying entropy. The most pertinent definition of Cp here polar contacts consistent with nine of the buried waters of the is the derivative of the entropy with respect to the natural log- crystallographic structure are also observed from encapsulated arithm of the temperature. Thus, the determined sd parameter of barnase (Fig. 3). The average NOE/ROE ratio of these water– the entropy meter, along with suitable temperature dependence protein contacts in bulk solution is approximately −0.15, indicating data, allows the protein conformational contribution to Cp that the waters are relatively rigidly held to the protein. Thus, the changes to be determined. The relative importance of confor- rigidly held water by free barnase appears to nullify the entropic cost mational and solvation contributions to ΔCp of binding, as for of using water as a structural element in the complex. ΔS, has been the subject of considerable debate (40), because, A second example of the further insights that can be garnered previously, there was no experimental way to isolate the different from the entropy meter centers on the idea that the loss of contributions. The temperature dependence of fast methyl-bearing rotation-translational entropy will diminish for weaker interac- side-chain motion has been examined for only a few proteins: for tions (i.e., Kd > 100 μM) due to significant residual motion in the example, the drkN (41) and α-spectrin (42) SH3 domains, ubiquitin complex. To explore this idea, we examined the interaction of
6566 | www.pnas.org/cgi/doi/10.1073/pnas.1621154114 Caro et al. Downloaded by guest on October 2, 2021 Fig. 3. Identification of rigidly held water in free barnase. Expansion of the 2D slice at the water reso- nance 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 hydro- gens of barnase and local hydration water. The de- tection 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.
histamine and serotonin with the histamine-binding protein role in the formation of complexes involving proteins: It can (HBP) from the Rhipicephalus appendiculatus tick. HBP is a favor, disfavor, or have no impact on the free energy of binding. member of the lipocalin family of proteins, which have been There are no obvious structural correlates apparent for this be- shown to bind to histamine and serotonin (52). These hetero- havior. The connection between structure, the enthalpy that it cyclic molecules serve as primary mediators of the inflammatory represents, conformational entropy, and internal motion pre- response upon tissue damage (53). HBP is a 171-residue, sents an immediate challenge to our current understanding of β-barrel protein that, unlike most other lipocalin family proteins, protein thermodynamics and function. In this vein, the view has evolved to possess two histamine-binding sites, with one emerging from crystallographic analysis of minor conformers in having high affinity (H-site) and one having low affinity (L-site) proteins (55–57), combined with the dynamical proxy validated (52). The tick secretes HBP to interfere with the defensive in- here, provides a means to quantify the role of conformational flammatory response of the host. For our studies, we have used entropy in protein structure and function. the D24R mutation located in the L-site that largely abolishes the binding of the second histamine molecule while retaining Methods the primary high-affinity histamine binding (H-site) (54). ITC Various proteins and their complexes (47, 52, 58–61) were prepared as de- established that histamine binds with very high affinity to scribed in detail in SI Appendix. Some published NMR relaxation and ther- = ± HBP(D24R) [Kd 3.2 0.7 nM, consistent with earlier mea- modynamic studies were used without further analysis (SI Appendix, Table 2 surements using trace radiolabeling (52)] and is accompanied by S1). Macromolecular rotational correlation times and backbone O NH were a large favorable change in enthalpy and an unfavorable total determined (62) from 15N relaxation obtained at two magnetic fields. binding entropy (SI Appendix, Table S2). NMR relaxation analysis Model-free parameters (22) were determined using a grid search approach ++ indicates a heterogeneous response of the protein to the binding of (63) using a version of Relxn2A (64) implemented in the C /AMP language. histamine (SI Appendix,Fig.S4). These results give a datum very The 15N-relaxation analysis used an effective N-H bond length of 1.04 Å (65) 15 close to the consensus fitted line of the entropy meter. Titration of and a general N tensor breadth of 170 ppm (66). Tumbling models were 2 the HBP(D24R)•histamine complex with serotonin reveals a weak identified through standard statistical analysis (67). Methyl group O axis binding site largely centered on residues Y30, V49, V51, A53, F67, parameters were determined from measured (68) deuterium T1 and T1ρ re- E82, which are near the L-site (SI Appendix,Fig.S5). This finding laxation. A quadrupolar coupling constant of 167 kHz was used (69). Analysis of NMR relaxation in these systems is summarized in SI Appendix, Tables S3, could be indicative of residual binding activity at the L-site. ITC S4, and S7. Changes in polar and apolar accessible surface area were calcu- reveals no detectable heat, indicating that the modest binding free − lated using AREAIMOL (70) as described previously (20) (SI Appendix, Table energy ( 13.7 kJ/mol) is driven entirely by entropy. NMR relaxation S4). BioMagResBank accession numbers are summarized in SI Appendix, analysis indicates an increase in side-chain dynamics that corre- Table S8. Studies of protein hydration dynamics used 3D 15N-resolved 1H-1H −1 −1 sponds to a very modest ΔSconf of 3 ± 1J·mol ·K . Interestingly, NOE spectroscopy and ROE spectroscopy (7.2-kHz spin lock field) experiments when completing the inventory of entropy, one finds only a small (51, 71). Perdeuterated barnase prepared in 25 mM imidazole (pH 6.2) and deviation from the entropy predicted (Fig. 1). This deviation is 10 mM KCl was encapsulated by defined volume injection (72) into 75 mM likely traced to an uncertainty in the solvation parameters for this deuterated hexadecyltrimethylammonium bromide (CTAB) and 190 mM complex and perhaps to a small residual Sr-t of the serotonin ligand deuterated hexanol in deuterated pentane to a molar ratio of water to CTAB (W or water loading) of 20. Structural fidelity of encapsulated barnase was in the complex. Thus, ΔSr-t estimated in Fig. 1 is likely valid down 0 confirmed by comparison of 15N-HSQC spectra. These experiments were per- to relatively low affinities corresponding to dissociation constants in 1 the millimolar range. formed at 25 °C and 500 MHz ( H). In summary, the coefficients relating changes in fast protein ACKNOWLEDGMENTS. We thank Professor Mark Greene for generous access side-chain motion to changes in conformational entropy, changes to the isothermal titration calorimeter. We thank Veronica Moorman and in accessible surface area to changes in solvent entropy, and the Kendra Frederick for preliminary calorimetry experiments and initial cura- loss of rotational-translational entropy in high-affinity complexes tion of published studies. This work was supported by the Mathers have been determined. The range of ligand types used here Foundation (A.J.W.), NIH Grants GM102447 and GM100910 (to A.J.W.), demonstrates that the relationship between fast internal side-chain and National Science Foundation Grant MCB-1158038 (to A.J.W.). K.A.S. acknowledges support from the Johnson Research Foundation. J.L. grate- motion and the underlying conformational entropy is universal fully acknowledges a Biomedical Research Council (A*STAR) Singapore post-
and represents a fundamental property of soluble proteins. It is doctoral fellowship. J.A.C. gratefully acknowledges an NIH postdoctoral BIOPHYSICS AND fellowship (GM117878). demonstrated that conformational entropy has a highly variable COMPUTATIONAL BIOLOGY
Caroetal. PNAS | June 20, 2017 | vol. 114 | no. 25 | 6567 Downloaded by guest on October 2, 2021 1. Motlagh HN, Wrabl JO, Li J, Hilser VJ (2014) The ensemble nature of allostery. Nature 37. Sharp KA, Nicholls A, Fine RF, Honig B (1991) Reconciling the magnitude of the mi- 508:331–339. croscopic and macroscopic hydrophobic effects. Science 252:106–109. 2. Clackson T, Wells JA (1995) A hot spot of binding energy in a hormone-receptor in- 38. Chandler D (2005) Interfaces and the driving force of hydrophobic assembly. Nature terface. Science 267:383–386. 437:640–647. 3. Wodak SJ, Janin J (2002) Structural basis of macromolecular recognition. Adv Protein 39. Wang L, Berne BJ, Friesner RA (2011) Ligand binding to protein-binding pockets with Chem 61:9–73. wet and dry regions. Proc Natl Acad Sci USA 108:1326–1330. 4. Zhou HX, Gilson MK (2009) Theory of free energy and entropy in noncovalent 40. Prabhu NV, Sharp KA (2005) Heat capacity in proteins. Annu Rev Phys Chem 56: binding. Chem Rev 109:4092–4107. 521–548. 5. Welch GR, Somogyi B, Damjanovich S (1982) The role of protein fluctuations in en- 41. Yang D, Mok YK, Forman-Kay JD, Farrow NA, Kay LE (1997) Contributions to protein zyme action: a review. Prog Biophys Mol Biol 39:109–146. entropy and heat capacity from bond vector motions measured by NMR spin re- 6. Cooper A, Dryden DTF (1984) Allostery without conformational change. A plausible laxation. J Mol Biol 272:790–804. model. Eur Biophys J 11:103–109. 42. Xue Y, Pavlova MS, Ryabov YE, Reif B, Skrynnikov NR (2007) Methyl rotation barriers 7. Gilson MK, Given JA, Bush BL, McCammon JA (1997) The statistical-thermodynamic in proteins from 2H relaxation data. Implications for protein structure. J Am Chem Soc basis for computation of binding affinities: A critical review. Biophys J 72:1047–1069. 129:6827–6838. 8. Luo H, Sharp K (2002) On the calculation of absolute macromolecular binding free 43. Song XJ, Flynn PF, Sharp KA, Wand AJ (2007) Temperature dependence of fast dy- energies. Proc Natl Acad Sci USA 99:10399–10404. namics in proteins. Biophys J 92:L43–L45. 9. Singh N, Warshel A (2010) A comprehensive examination of the contributions to the 44. Sabo TM, et al. (2012) Thermal coefficients of the methyl groups within ubiquitin. binding entropy of protein-ligand complexes. Proteins 78:1724–1735. Protein Sci 21:562–570. 10. Sturtevant JM (1977) Heat capacity and entropy changes in processes involving pro- 45. Lee AL, Wand AJ (2001) Microscopic origins of entropy, heat capacity and the glass teins. Proc Natl Acad Sci USA 74:2236–2240. transition in proteins. Nature 411:501–504. 11. Dill KA (1990) Dominant forces in protein folding. Biochemistry 29:7133–7155. 46. Wintrode PL, Privalov PL (1997) Energetics of target peptide recognition by calmod- 12. Hilser VJ, García-Moreno EB, Oas TG, Kapp G, Whitten ST (2006) A statistical ther- ulin: a calorimetric study. J Mol Biol 266:1050–1062. modynamic model of the protein ensemble. Chem Rev 106:1545–1558. 47. Buckle AM, Fersht AR (1994) Subsite binding in an RNase: Structure of a barnase- 13. Steinberg IZ, Scheraga HA (1963) Entropy changes accompanying association reac- tetranucleotide complex at 1.76-A resolution. Biochemistry 33:1644–1653. tions of proteins. J Biol Chem 238:172–181. 48. Giauque WF, Stout JW (1936) The entropy of water and the third law of thermody- 14. Akke M, Brüschweiler R, Palmer AGI (1993) NMR order parameters and free-energy - namics. The heat capacity of ice from 15 to 273°K. J Am Chem Soc 58:1144–1150. an analytical approach and its application to cooperative Ca2+ binding by calbindin- 49. Otting G, Liepinsh E, Wüthrich K (1991) Protein hydration in aqueous solution. D(9k). J Am Chem Soc 115:9832–9833. Science 254:974–980. 15. Li Z, Raychaudhuri S, Wand AJ (1996) Insights into the local residual entropy of 50. Halle B (2004) Protein hydration dynamics in solution: A critical survey. Philos Trans R proteins provided by NMR relaxation. Protein Sci 5:2647–2650. Soc Lond B Biol Sci 359:1207–1223, discussion 1223–1224, 1323–1328. 16. Yang D, Kay LE (1996) Contributions to conformational entropy arising from bond 51. Nucci NV, Pometun MS, Wand AJ (2011) Site-resolved measurement of water-protein vector fluctuations measured from NMR-derived order parameters: Application to interactions by solution NMR. Nat Struct Mol Biol 18:245–249. protein folding. J Mol Biol 263:369–382. 52. Paesen GC, Adams PL, Harlos K, Nuttall PA, Stuart DI (1999) Tick histamine-binding 17. Igumenova TI, Frederick KK, Wand AJ (2006) Characterization of the fast dynamics of proteins: Isolation, cloning, and three-dimensional structure. Mol Cell 3:661–671. protein amino acid side chains using NMR relaxation in solution. Chem Rev 106: 53. Sangamnatdej S, Paesen GC, Slovak M, Nuttall PA (2002) A high affinity serotonin- 1672–1699. and histamine-binding lipocalin from tick saliva. Insect Mol Biol 11:79–86. 18. Wand AJ (2013) The dark energy of proteins comes to light: conformational entropy 54. Syme NR, Dennis C, Bronowska A, Paesen GC, Homans SW (2010) Comparison of and its role in protein function revealed by NMR relaxation. Curr Opin Struct Biol 23: entropic contributions to binding in a “hydrophilic” versus “hydrophobic” ligand- 75–81. protein interaction. J Am Chem Soc 132:8682–8689. 19. Frederick KK, Marlow MS, Valentine KG, Wand AJ (2007) Conformational entropy in 55. Fraser JS, et al. (2011) Accessing protein conformational ensembles using room- molecular recognition by proteins. Nature 448:325–329. temperature X-ray crystallography. Proc Natl Acad Sci USA 108:16247–16252. 20. Marlow MS, Dogan J, Frederick KK, Valentine KG, Wand AJ (2010) The role of con- 56. Keedy DA, et al. (2015) Mapping the conformational landscape of a dynamic enzyme formational entropy in molecular recognition by calmodulin. Nat Chem Biol 6: by multitemperature and XFEL crystallography. eLife 4:e07574. 352–358. 57. Woldeyes RA, Sivak DA, Fraser JS (2014) E pluribus unum, no more: From one crystal, 21. Kasinath V, Sharp KA, Wand AJ (2013) Microscopic insights into the NMR relaxation- many conformations. Curr Opin Struct Biol 28:56–62. based protein conformational entropy meter. J Am Chem Soc 135:15092–15100. 58. Seeholzer SH, Wand AJ (1989) Structural characterization of the interactions between 22. Lipari G, Szabo A (1982) Model-free approach to the interpretation of nuclear calmodulin and skeletal muscle myosin light chain kinase: Effect of peptide (576-594)G magnetic-resonance relaxation in macromolecules.1. Theory and range of validity. binding on the Ca2+-binding domains. Biochemistry 28:4011–4020. J Am Chem Soc 104:4546–4559. 59. Kranz JK, Lee EK, Nairn AC, Wand AJ (2002) A direct test of the reductionist approach 23. Lee AL, Sharp KA, Kranz JK, Song XJ, Wand AJ (2002) Temperature depen- to structural studies of calmodulin activity: Relevance of peptide models of target dence of the internal dynamics of a calmodulin-peptide complex. Biochemistry 41: proteins. J Biol Chem 277:16351–16354. 13814–13825. 60. Finerty PJ, Jr, Muhandiram R, Forman-Kay JD (2002) Side-chain dynamics of the SAP 24. Karplus M, Ichiye T, Pettitt BM (1987) Configurational entropy of native proteins. SH2 domain correlate with a binding hot spot and a region with conformational Biophys J 52:1083–1085. plasticity. J Mol Biol 322:605–620. 25. Sharp KA, O’Brien E, Kasinath V, Wand AJ (2015) On the relationship between NMR- 61. Bhabha G, Tuttle L, Martinez-Yamout MA, Wright PE (2011) Identification of en- derived amide order parameters and protein backbone entropy changes. Proteins 83: dogenous ligands bound to bacterially expressed human and E. coli dihydrofolate 922–930. reductase by 2D NMR. FEBS Lett 585:3528–3532. 26. Tzeng SR, Kalodimos CG (2012) Protein activity regulation by conformational entropy. 62. Tjandra N, Feller SE, Pastor RW, Bax A (1995) Rotational diffusion anisotropy of hu- Nature 488:236–240. man ubiquitin from 15N NMR relaxation. J Am Chem Soc 117:12562–12566. 27. Baldwin RL (1986) Temperature dependence of the hydrophobic interaction in pro- 63. Dellwo MJ, Wand AJ (1989) Model-independent and model-dependent analysis of tein folding. Proc Natl Acad Sci USA 83:8069–8072. the global and internal dynamics of cyclosporine-A. J Am Chem Soc 111:4571–4578. 28. Makhatadze GI, Privalov PL (1993) Contribution of hydration to protein folding 64. Kasinath V, Valentine KG, Wand AJ (2013) A 13C labeling strategy reveals a range of thermodynamics. I. The enthalpy of hydration. J Mol Biol 232:639–659. aromatic side chain motion in calmodulin. J Am Chem Soc 135:9560–9563. 29. Leavitt S, Freire E (2001) Direct measurement of protein binding energetics by iso- 65. Ottiger M, Bax A (1998) Determination of relative N-HN, N-C¢, CR-C¢, and CR-HR thermal titration calorimetry. Curr Opin Struct Biol 11:560–566. effective bond lengths in a protein by NMR in a dilute liquid crystalline phase. 30. Harpole KW, Sharp KA (2011) Calculation of configurational entropy with a J Am Chem Soc 120:12334–12341. Boltzmann-quasiharmonic model: The origin of high-affinity protein-ligand binding. 66. Lee AL, Wand AJ (1999) Assessing potential bias in the determination of rotational J Phys Chem B 115:9461–9472. correlation times of proteins by NMR relaxation. J Biomol NMR 13:101–112. 31. Ben-Naim A, Marcus Y (1984) Solvation thermodynamics of nonionic solutes. J Chem 67. Moorman VR, et al. (2014) Dynamic and thermodynamic response of the Ras protein Phys 81:2016–2027. Cdc42Hs upon association with the effector domain of PAK3. J Mol Biol 426: 32. Marcus Y (1994) A simple empirical model describing the thermodynamics of hydra- 3520–3538. 2 tion of ions of widely varying charges, sizes, and shapes. Biophys Chem 51:111–127. 68. Muhandiram DR, Yamazaki T, Sykes BD, Kay LE (1995) Measurement of HT1 and T1ρ 33. Gómez J, Hilser VJ, Xie D, Freire E (1995) The heat capacity of proteins. Proteins 22: relaxation-times in uniformly 13C-labeled and fractionally 2H-labeled proteins in so- 404–412. lution. J Am Chem Soc 117:11536–11544. 34. Spolar RS, Livingstone JR, Record MT, Jr (1992) Use of liquid hydrocarbon and amide 69. Mittermaier A, Kay LE (1999) Measurement of methyl 2H quadrupolar couplings in transfer data to estimate contributions to thermodynamic functions of protein oriented proteins. How uniform is the quadrupolar coupling constant? J Am Chem folding from the removal of nonpolar and polar surface from water. Biochemistry 31: Soc 121:10608–10613. 3947–3955. 70. Bailey S; Collaborative Computational Project, Number 4 (1994) The CCP4 suite: 35. Privalov PL, Makhatadze GI (1992) Contribution of hydration and non-covalent in- Programs for protein crystallography. Acta Crystallogr D Biol Crystallogr 50:760–763. teractions to the heat capacity effect on protein unfolding. J Mol Biol 224:715–723. 71. Otting G (1997) NMR studies of water bound to biological molecules. Prog Nucl Magn 36. Privalov PL, Makhatadze GI (1993) Contribution of hydration to protein folding Reson Spectrosc 31:259–285. thermodynamics. II. The entropy and Gibbs energy of hydration. J Mol Biol 232: 72. Nucci NV, Valentine KG, Wand AJ (2014) High-resolution NMR spectroscopy of en- 660–679. capsulated proteins dissolved in low-viscosity fluids. J Magn Reson 241:137–147.
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