Temperature dependence of dynamics and thermodynamics of the regulatory domain of human cardiac troponin C

Binding of Ca(2+) to the regulatory domain of troponin C (TnC) in cardiac muscle initiates a series of protein conformational changes and modified protein-protein interactions that initiate contraction. Cardiac TnC contains two Ca(2+) binding sites, with one site being naturally defunct. Previously, binding of Ca(2+) to the functional site in the regulatory domain of TnC was shown to lead to a decrease in conformational entropy (TDeltaS) of 2 and 0.5 kcal mol(-1) for the functional and nonfunctional sites, respectively, using (15)N nuclear magnetic resonance (NMR) relaxation studies [Spyracopoulos, L., et al. (1998) Biochemistry 37, 18032-18044]. In this study, backbone dynamics of the Ca(2+)-free regulatory domain are investigated by backbone amide (15)N relaxation measurements at eight temperatures from 5 to 45 degrees C. Analysis of the relaxation measurements yields an order parameter (S(2)) indicating the degree of spatial restriction for a backbone amide H-N vector. The temperature dependence of S(2) allows estimation of the contribution to protein heat capacity from pico- to nanosecond time scale conformational fluctuations on a per residue basis. The average heat capacity contribution (C(p,j)) from backbone conformational fluctuations for regions of secondary structure for the regulatory domain of cardiac apo-TnC is 6 cal mol(-1) K(-1). The average heat capacity for Ca(2+) binding site 1 is larger than that for site 2 by 1.3 +/- 0.8 cal mol(-1) K(-1), and likely represents a mechanism where differences in affinity between Ca(2+) binding sites for EF hand proteins can be modulated.     

Conformational entropy changes upon lactose binding to the carbohydrate recognition domain of galectin-3

The conformational entropy of proteins can make significant contributions to the free energy of ligand binding. NMR spin relaxation enables site-specific investigation of conformational entropy, via order parameters that parameterize local reorientational fluctuations of rank-2 tensors. Here we have probed the conformational entropy of lactose binding to the carbohydrate recognition domain of galectin-3 (Gal3), a protein that plays an important role in cell growth, cell differentiation, cell cycle regulation, and apoptosis, making it a potential target for therapeutic intervention in inflammation and cancer. We used ¹⁵N spin relaxation experiments and molecular dynamics simulations to monitor the backbone amides and secondary amines of the tryptophan and arginine side chains in the ligand-free and lactose-bound states of Gal3. Overall, we observe good agreement between the experimental and computed order parameters of the ligand-free and lactose-bound states. Thus, the ¹⁵N spin relaxation data indicate that the molecular dynamics simulations provide reliable information on the conformational entropy of the binding process. The molecular dynamics simulations reveal a correlation between the simulated order parameters and residue-specific backbone entropy, re-emphasizing that order parameters provide useful estimates of local conformational entropy. The present results show that the protein backbone exhibits an increase in conformational entropy upon binding lactose, without any accompanying structural changes.     

Prediction of methyl-side Chain Dynamics in Proteins

A simple analytical model is presented for the prediction of methyl-side chain dynamics in comparison with S(2) order parameters obtained by NMR relaxation spectroscopy. The model, which is an extension of the local contact model for backbone order parameter prediction, uses a static 3D protein structure as input. It expresses the methyl-group S(2) order parameters as a function of local contacts of the methyl carbon with respect to the neighboring atoms in combination with the number of consecutive mobile dihedral angles between the methyl group and the protein backbone. For six out of seven proteins the prediction results are good when compared with experimentally determined methyl-group S(2) values with an average correlation coefficient r = 0.65+/-0.14. For the unusually rigid cytochrome c(2) no significant correlation between prediction and experiment is found. The presented model provides independent support for the reliability of current side-chain relaxation methods along with their interpretation by the model-free formalism.     

Characterizing a partially folded intermediate of the villin headpiece domain under non-denaturing conditions: contribution of His41 to the pH-dependent stability of the N-terminal subdomain

The contribution of interactions involving the imidazole ring of His41 to the pH-dependent stability of the villin headpiece (HP67) N-terminal subdomain has been investigated by nuclear magnetic resonance (NMR) spin relaxation. NMR-derived backbone N-H order parameters (S2) for wild-type (WT) HP67 and H41Y HP67 indicate that reduced conformational flexibility of the N-terminal subdomain in WT HP67 is due to intramolecular interactions with the His41 imidazole ring. These interactions, together with desolvation effects, contribute to significantly depress the pKa of the buried imidazole ring in the native state. 15N R1rho relaxation dispersion data indicate that WT HP67 populates a partially folded intermediate state that is 10.9 kJ mol(-1) higher in free energy than the native state under non-denaturing conditions at neutral pH. The partially folded intermediate is characterized as having an unfolded N-terminal subdomain while the C-terminal subdomain retains a native-like fold. Although the majority of the residues in the N-terminal subdomain sample a random-coil distribution of conformations, deviations of backbone amide 1H and 15N chemical shifts from canonical random-coil values for residues within 5A of the His41 imidazole ring indicate that a significant degree of residual structure is maintained in the partially folded ensemble. The pH-dependence of exchange broadening is consistent with a linear three-state exchange model whereby unfolding of the N-terminal subdomain is coupled to titration of His41 in the partially folded intermediate with a pKa,I=5.69+/-0.07. Although maintenance of residual interactions with the imidazole ring in the unfolded N-terminal subdomain appears to reduce pKa,I compared to model histidine compounds, protonation of His41 disrupts these interactions and reduces the difference in free energy between the native state and partially folded intermediate under acidic conditions. In addition, chemical shift changes for residues Lys70-Phe76 in the C-terminal subdomain suggest that the HP67 actin binding site is disrupted upon unfolding of the N-terminal subdomain, providing a potential mechanism for regulating the villin-dependent bundling of actin filaments.     

Structure, dynamics, and thermodynamics of the structural domain of troponin C in complex with the regulatory peptide 1-40 of troponin I

The structure of the calcium-saturated C-domain of skeletal troponin C (CTnC) in complex with a regulatory peptide comprising residues 1-40 (Rp40) of troponin I (TnI) was determined using nuclear magnetic resonance (NMR) spectroscopy. The solution structure determined by NMR is similar to the structure of the C-domain from intact TnC in complex with TnI(1)(-)(47) determined by X-ray crystallography [Vassylyev, D. G., Takeda, S., Wakatsuki, S., Maeda, K., and Maeda, Y. (1998) Proc. Natl. Acad. Sci. U.S.A. 95, 4847-4852]. Changes in the dynamic properties of CTnC.2Ca2+ induced by Rp40 binding were investigated using backbone amide (15)N NMR relaxation measurements. Analysis of NMR relaxation data allows for extraction of motional order parameters on a per residue basis, from which the contribution of changes in picosecond to nanosecond time scale motions to the conformational entropy associated with complex formation can be estimated. The results indicate that binding of Rp40 decreases backbone flexibility in CTnC, particularly at the end of the C-terminal helix. The backbone conformational entropy change (-TDeltaS) associated with binding of Rp40 to CTnC.2Ca2+ determined from (15)N relaxation data is 9.6 +/- 0.7 kcal mol(-1) at 30 degrees C. However, estimation of thermodynamic quantities using a structural approach [Lavigne, P., Bagu, J. R., Boyko, R., Willard, L., Holmes, C. F., and Sykes, B. D. (2000) Protein Sci. 9, 252-264] reveals that the change in solvation entropy upon complex formation is dominant and overcomes the thermodynamic "cost" associated with "stiffening" of the protein backbone upon Rp40 binding. Additionally, backbone amide (15)N relaxation data measured at different concentrations of CTnC.2Ca2+.Rp40 reveal that the complex dimerizes in solution. Fitting of the apparent global rotational correlation time as a function of concentration to a monomer-dimer equilibrium yields a dimerization constant of approximately 8.3 mM.     

NMR structural and dynamic characterization of the acid-unfolded state of apomyoglobin provides insights into the early events in protein folding

Apomyoglobin forms a denatured state under low-salt conditions at pH 2.3. The conformational propensities and polypeptide backbone dynamics of this state have been characterized by NMR. Nearly complete backbone and some side chain resonance assignments have been obtained, using a triple-resonance assignment strategy tailored to low protein concentration (0.2 mM) and poor chemical shift dispersion. An estimate of the population and location of residual secondary structure has been made by examining deviations of (13)C(alpha), (13)CO, and (1)H(alpha) chemical shifts from random coil values, scalar (3)J(HN,H)(alpha) coupling constants and (1)H-(1)H NOEs. Chemical shifts constitute a highly reliable indicator of secondary structural preferences, provided the appropriate random coil chemical shift references are used, but in the case of acid-unfolded apomyoglobin, (3)J(HN,H)(alpha) coupling constants are poor diagnostics of secondary structure formation. Substantial populations of helical structure, in dynamic equilibrium with unfolded states, are formed in regions corresponding to the A and H helices of the folded protein. In addition, the deviation of the chemical shifts from random coil values indicates the presence of helical structure encompassing the D helix and extending into the first turn of the E helix. The polypeptide backbone dynamics of acid-unfolded apomyoglobin have been investigated using reduced spectral density function analysis of (15)N relaxation data. The spectral density J(omega(N)) is particularly sensitive to variations in backbone fluctuations on the picosecond to nanosecond time scale. The central region of the polypeptide spanning the C-terminal half of the E helix, the EF turn, and the F helix behaves as a free-flight random coil chain, but there is evidence from J(omega(N)) of restricted motions on the picosecond to nanosecond time scale in the A and H helix regions where there is a propensity to populate helical secondary structure in the acid-unfolded state. Backbone fluctuations are also restricted in parts of the B and G helices due to formation of local hydrophobic clusters. Regions of restricted backbone flexibility are generally associated with large buried surface area. A significant increase in J(0) is observed for the NH resonances of some residues located in the A and G helices of the folded protein and is associated with fluctuations on a microsecond to millisecond time scale that probably arise from transient contacts between these distant regions of the polypeptide chain. Our results indicate that the equilibrium unfolded state of apomyoglobin formed at pH 2.3 is an excellent model for the events that are expected to occur in the earliest stages of protein folding, providing insights into the regions of the polypeptide that spontaneously undergo local hydrophobic collapse and sample nativelike secondary structure.     

Effects of calcium binding on the side-chain methyl dynamics of calbindin D9k: a 2H NMR relaxation study

The effects of Ca(2+) binding on the side-chain methyl dynamics of calbindin D(9k) have been characterized by (2)H NMR relaxation rate measurements. Longitudinal, transverse in-phase, quadrupolar order, transverse anti-phase and double quantum relaxation rates are reported for both the apo and Ca(2+)-loaded states of the protein at two magnetic field strengths. The relatively large size of the data set allows for a detailed analysis of the underlying conformational dynamics by spectral density mapping and model-free fitting procedures. The results reveal a correlation between a methyl group's distance from the Ca(2+) binding sites and its conformational dynamics. Several methyl groups segregate into two limiting classes, one proximal and the other distal to the binding sites. Methyl groups in these two classes respond differently to Ca(2+) binding, both in terms of the timescale and amplitude of their fluctuations. Ca(2+) binding elicits a partial immobilization among methyl groups in the proximal class, which is consistent with previous studies of calbindin's backbone dynamics. The distal class, however, exhibits a trend that could not be inferred from the backbone data in that its mobility actually increases with Ca(2+) binding. We have introduced the term polar dynamics to describe this type of organization across the molecule. The trend may represent an important mechanism by which calbindin D(9k) achieves high affinity binding while minimizing the corresponding loss of conformational entropy.     

Conformational dynamics and thermodynamics of protein-ligand binding studied by NMR relaxation

Protein conformational dynamics can be critical for ligand binding in two ways that relate to kinetics and thermodynamics respectively. First, conformational transitions between different substates can control access to the binding site (kinetics). Secondly, differences between free and ligand-bound states in their conformational fluctuations contribute to the entropy of ligand binding (thermodynamics). In the present paper, I focus on the second topic, summarizing our recent results on the role of conformational entropy in ligand binding to Gal3C (the carbohydrate-recognition domain of galectin-3). NMR relaxation experiments provide a unique probe of conformational entropy by characterizing bond-vector fluctuations at atomic resolution. By monitoring differences between the free and ligand-bound states in their backbone and side chain order parameters, we have estimated the contributions from conformational entropy to the free energy of binding. Overall, the conformational entropy of Gal3C increases upon ligand binding, thereby contributing favourably to the binding affinity. Comparisons with the results from isothermal titration calorimetry indicate that the conformational entropy is comparable in magnitude to the enthalpy of binding. Furthermore, there are significant differences in the dynamic response to binding of different ligands, despite the fact that the protein structure is virtually identical in the different protein-ligand complexes. Thus both affinity and specificity of ligand binding to Gal3C appear to depend in part on subtle differences in the conformational fluctuations that reflect the complex interplay between structure, dynamics and ligand interactions.     

Increased backbone mobility in beta-barrel enhances entropy gain driving binding of N-TIMP-1 to MMP-3

The high-affinity inhibition of stromelysin 1 (MMP-3) by tissue inhibitor of metalloproteinases 1 (TIMP-1) helps control tissue remodeling and tumor development. The interaction of N-TIMP-1 with the catalytic domain of MMP-3 has been investigated by titration calorimetry and 15N NMR. Their unfavorable enthalpy of binding of +6.5 kcal mol(-1) is unusual among protein-protein associations, deviates from structure-based prediction, and is compensated by a net entropy increase providing at least 18 kcal mol(-1) of favorable free energy of binding at a 1M reference state. The small heat capacity of binding agrees well with the heat capacity predicted from 65% of the surface buried on binding being polar, and suggests that the hydrophobic effect can account for only part of the entropy of binding. Using NMR, binding-induced changes in the backbone of N-TIMP-1 were checked as one possible source of conformational entropy changes. MMP binding slightly increases rigidity in some contact sites in TIMP-1 but increases mobility remotely in the otherwise rigid beta-barrel core of N-TIMP-1, increasing 15N relaxation evidence of pico- to nanosecond and micro- to millisecond fluctuations of beta-strands A-F. Residual dipolar couplings suggest dynamic deviations from X-ray coordinates of the complex. These suggest that the beta-barrel has small backbone conformational fluctuations, while segments of strands betaB, betaE and betaF might experience fluctuations only in their backbone environment. This is a distinctive example of affinity between two well-structured proteins being enhanced by increased conformational entropy in the reservoir of a folding core.     

The backbone conformational entropy of protein folding: experimental measures from atomic force microscopy

The energy dissipated during the atomic force microscopy-based mechanical unfolding and extension of proteins is typically an order of magnitude greater than their folding free energy. The vast majority of the "excess" energy dissipated is thought to arise due to backbone conformational entropy losses as the solvated, random-coil unfolded state is stretched into an extended, low-entropy conformation. We have investigated this hypothesis in light of recent measurements of the energy dissipated during the mechanical unfolding of "polyproteins" comprised of multiple, homogeneous domains. Given the assumption that backbone conformational entropy losses account for the vast majority of the energy dissipated (an assumption supported by numerous lines of experimental evidence), we estimate that approximately 19(+/-2)J/(mol K residue) of entropy is lost during the extension of three mechanically stable beta-sheet polyproteins. If, as suggested by measured peak-to-peak extension distances, pulling proceeds to near completion, this estimate corresponds to the absolute backbone conformational entropy of the unfolded state. As such, it is exceedingly close to previous theoretical and semi-empirical estimates that place this value at approximately 20J/(mol K residue). The estimated backbone conformational entropy lost during the extension of two helical polyproteins, which, in contrast to the mechanically stable beta-sheet polyproteins, rupture at very low applied forces, is three- to sixfold less. Either previous estimates of the backbone conformational entropy are significantly in error, or the reduced mechanical strength of the helical proteins leads to the rupture of a subsequent domain before full extension (and thus complete entropy loss) is achieved.     

Structural and dynamic characterization of an unfolded state of poplar apo-plastocyanin formed under nondenaturing conditions

Plastocyanin is a predominantly beta-sheet protein containing a type I copper center. The conformational ensemble of a denatured state of apo-plastocyanin formed in solution under conditions of low salt and neutral pH has been investigated by multidimensional heteronuclear NMR spectroscopy. Chemical shift assignments were obtained by using three-dimensional triple-resonance NMR experiments to trace through-bond heteronuclear connectivities along the backbone and side chains. The (3)J(HN,Halpha) coupling constants, (15)N-edited proton-proton nuclear Overhauser effects (NOEs), and (15)N relaxation parameters were also measured for the purpose of structural and dynamic characterization. Most of the residues corresponding to beta-strands in the folded protein exhibit small upfield shifts of the (13)C(alpha) and (13)CO resonances relative to random coil values, suggesting a slight preference for backbone dihedral angles in the beta region of (phi,psi) space. This is further supported by the presence of strong sequential d(alphaN)(i, i + 1) NOEs throughout the sequence. The few d(NN)(i, i + 1) proton NOEs that are observed are mostly in regions that form loops in the native plastocyanin structure. No medium or long-range NOEs were observed. A short sequence, between residues 59 and 63, was found to populate a nonnative helical conformation in the unfolded state, as indicated by the shift of the (13)C(alpha), (13)CO, and (1)H(alpha) resonances relative to random coil values and by the decreased values of the (3)J(HN,Halpha) coupling constants. The (15)N relaxation parameters indicate restriction of motions on a nanosecond timescale in this region. Intriguingly, this helical conformation is present in a sequence that is close to but not in the same location as the single short helix in the native folded protein. The results are consistent with earlier NMR studies of peptide fragments of plastocyanin and confirm that the regions of the sequence that form beta-strands in the native protein spontaneously populate the beta-region of (phi,psi) space under folding conditions, even in the absence of stabilizing tertiary interactions. We conclude that the state of apo-plastocyanin present under nondenaturing conditions is a noncompact unfolded state with some evidence of nativelike and nonnative local structuring that may be initiation sites for folding of the protein.     

Multiple time scale backbone dynamics of homologous thermophilic and mesophilic ribonuclease HI enzymes

Backbone conformational fluctuations on multiple time scales in a cysteine-free Thermus thermophilus ribonuclease HI mutant (ttRNH(*)) are quantified using (15)N nuclear magnetic spin relaxation. Laboratory-frame relaxation data acquired at 310 K and at static magnetic field strengths of 11.7, 14.1 and 18.8 T are analysed using reduced spectral density mapping and model-free approaches. Chemical exchange line broadening is characterized using Hahn-echo transverse and multiple quantum relaxation data acquired over a temperature range of 290-320 K and at a static magnetic field strength of 14.1 T. Results for ttRNH(*) are compared to previously published data for a mesophilic homologue, Escherichia coli ribonuclease HI (ecRNH). Intramolecular conformational fluctuations on the picosecond-to-nanosecond time scale generally are similar for ttRNH(*) and ecRNH. beta-Strands 3 and 5 and the glycine-rich region are more rigid while the substrate-binding handle region and C-terminal tail are more flexible in ttRNH(*) than in ecRNH. Rigidity in the two beta-strands and the glycine-rich region, located along the periphery of the central beta-sheet, may be associated with the increased thermodynamic stability of the thermophilic enzyme. Chemical exchange line broadening, reflecting microsecond-to-millisecond time scale conformational changes, is more pronounced in ttRNH(*) than in ecRNH, particularly for residues in the handle and surrounding the catalytic site. The temperature dependence of chemical exchange show an increase of approximately 15 kJ/mol in the apparent activation energies for ttRNH(*) residues in the handle compared to ecRNH. Increased activation barriers, coupled with motion between alpha-helices B and C not present in ecRNH, may be associated with the reduced catalytic activity of the thermophilic enzyme at 310 K.     

Slow motions in chicken villin headpiece subdomain probed by cross-correlated NMR relaxation of amide NH bonds in successive residues

The villin headpiece subdomain (HP36) is a widely used system for protein-folding studies. Nuclear magnetic resonance cross-correlated relaxation rates arising from correlated fluctuations of two N-H^N dipole-dipole interactions involving successive residues were measured at two temperatures at which HP36 is at least 99% folded. The experiment revealed the presence of motions slower than overall tumbling of the molecule. Based on the theoretical analysis of the spectral densities we show that the structural and dynamic contributions to the experimental cross-correlated relaxation rate can be separated under certain conditions. As a result, dynamic cross-correlated order parameters describing slow microsecond-to-millisecond motions of N-H bonds in neighboring residues can be introduced for any extent of correlations in the fluctuations of the two bond vectors. These dynamic cross-correlated order parameters have been extracted for HP36. The comparison of their values at two different temperatures indicates that when the temperature is raised, slow motions increase in amplitude. The increased amplitude of these fluctuations may reflect the presence of processes directly preceding the unfolding of the protein.     

Distinct phases of free α-synuclein--a Monte Carlo study

The α-synuclein protein (αS), implicated in Parkinson's disease, shows conformational versatility. It aggregates into β-sheet-rich fibrils, occurs in helical membrane-bound forms, is disordered as a free monomer, and has recently been suggested to have a folded helical tetramer as its main physiological form. Here, we use implicit solvent all-atom Monte Carlo methods to explore the conformational ensemble sampled by the free αS monomer. We analyze secondary structure propensities, size, and topological properties and compare with existing experimental data. Our study suggests that free αS has two distinct phases. One phase has the expected disordered character. The other phase also shows large conformational variability. However, in this phase, the β-strand content is substantial, and the backbone fold shows statistical similarities with that in αS fibrils. Presence of this phase is consistent with data from low-temperature experiments. Conversion of disordered αS to this fibril-like form requires the crossing of a rather large apparent free-energy barrier.     

Relationship of DNA structure to internal dynamics: correlation of helical parameters from NOE-based NMR solution structures of d(GCGTACGC)(2) and d(CGCTAGCG)(2) with (13)C order parameters implies conformational coupling in dinucleotide units

The coupling between the conformational properties of double-stranded DNA and its internal dynamics has been examined. The solution structures of the isomeric DNA oligomers d(GCGTACGC)(2) (UM) and d(CGCTAGCG)(2) (CTSYM) were determined with (1)H NMR spectroscopy by utilizing distance restraints from total relaxation matrix analysis of NOESY cross-peak intensities in restrained molecular dynamics calculations. The root-mean-square deviation of the coordinates for the ensemble of structures was 0.13 A for UM and 0.49 A for CTSYM, with crystallographic equivalent R(c)=0.41 and 0.39 and sixth-root residual R(x)=0.11 and 0.10 for UM and CTSYM, respectively. Both UM and CTSYM are B-form with straight helical axes and show sequence-dependent variations in conformation. The internal dynamics of UM and CTSYM were previously determined by analysis of (13)C relaxation parameters in the context of the Lipari & Szabo model-free formalism. Helical parameters for the two DNA oligomers were examined for linear correlations with the order parameters (S(2)) of groups of (13)C spins in base-pairs and dinucleotide units of UM and CTSYM. Correlations were found for six interstrand base-pair parameters tip, y-displacement, inclination, buckle and stretch with various combinations of S(2) for atoms in Watson-Crick base-pairs and for two inter-base-pair parameters, rise and roll with various combinations of S(2) for atoms in dinucleotides. The correlations for the interstrand base-pair helical parameters indicate that the conformations of the deoxyribose residues of each strand are dynamically coupled. Also, the inter-base-pair separation has a profound effect on the local internal motions available to the DNA, supporting the idea that rise is a principal degree of freedom for DNA conformational variability. The correlations indicate collective atomic motions of spins that may represent specific motional modes in DNA, and that base sequence has a predictable effect on the relative order of groups of spins both in the bases and in the deoxyribose ring of the DNA backbone. These observations suggest that an important functional outcome of DNA base sequence is the modulation of both the conformation and dynamic behavior of the DNA backbone.     

Histidine side-chain dynamics and protonation monitored by 13C CPMG NMR relaxation dispersion

The use of ¹³C NMR relaxation dispersion experiments to monitor micro-millisecond fluctuations in the protonation states of histidine residues in proteins is investigated. To illustrate the approach, measurements on three specifically ¹³C labeled histidine residues in plastocyanin (PCu) from Anabaena variabilis (A.v.) are presented. Significant Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion is observed for ¹³C^ε1 nuclei in the histidine imidazole rings of A.v. PCu. The chemical shift changes obtained from the CPMG dispersion data are in good agreement with those obtained from the chemical shift titration experiments, and the CPMG derived exchange rates agree with those obtained previously from ¹⁵N backbone relaxation measurements. Compared to measurements of backbone nuclei, ¹³C^ε1 dispersion provides a more direct method to monitor interchanging protonation states or other kinds of conformational changes of histidine side chains or their environment. Advantages and shortcomings of using the ¹³C^ε1 dispersion experiments in combination with chemical shift titration experiments to obtain information on exchange dynamics of the histidine side chains are discussed.     

Accounting for conformational entropy in predicting binding free energies of protein-protein interactions

Protein-protein interactions are governed by the change in free energy upon binding, ΔG = ΔH - TΔS. These interactions are often marginally stable, so one must examine the balance between the change in enthalpy, ΔH, and the change in entropy, ΔS, when investigating known complexes, characterizing the effects of mutations, or designing optimized variants. To perform a large-scale study into the contribution of conformational entropy to binding free energy, we developed a technique called GOBLIN (Graphical mOdel for BiomoLecular INteractions) that performs physics-based free energy calculations for protein-protein complexes under both side-chain and backbone flexibility. Goblin uses a probabilistic graphical model that exploits conditional independencies in the Boltzmann distribution and employs variational inference techniques that approximate the free energy of binding in only a few minutes. We examined the role of conformational entropy on a benchmark set of more than 700 mutants in eight large, well-studied complexes. Our findings suggest that conformational entropy is important in protein-protein interactions--the root mean square error (RMSE) between calculated and experimentally measured ΔΔGs decreases by 12% when explicit entropic contributions were incorporated. GOBLIN models all atoms of the protein complex and detects changes to the binding entropy along the interface as well as positions distal to the binding interface. Our results also suggest that a variational approach to entropy calculations may be quantitatively more accurate than the knowledge-based approaches used by the well-known programs FOLDX and Rosetta--GOBLIN's RMSEs are 10 and 36% lower than these programs, respectively.