Entropy in biological binding processes: estimation of translational entropy loss

Thermodynamics of Folding and Binding in an Affibody:Affibody Complex

Affibody binding proteins are selected from phage-displayed libraries of variants of the 58 residue Z domain. Z(Taq) is an affibody originally selected as a binder to Taq DNA polymerase. The anti-Z(Taq) affibody was selected as a binder to Z(Taq) and the Z(Taq):anti-Z(Taq) complex is formed with a dissociation constant K(d)=0.1 microM. We have determined the structure of the Z(Taq):anti-Z(Taq) complex as well as the free state structures of Z(Taq) and anti-Z(Taq) using NMR. Here we complement the structural data with thermodynamic studies of Z(Taq) and anti-Z(Taq) folding and complex formation. Both affibody proteins show cooperative two-state thermal denaturation at melting temperatures T(M) approximately 56 degrees C. Z(Taq):anti-Z(Taq) complex formation at 25 degrees C in 50 mM NaCl and 20 mM phosphate buffer (pH 6.4) is enthalpy driven with DeltaH degrees (bind) = -9.0 (+/-0.1) kcal mol(-1)(.) The heat capacity change DeltaC(P) degrees (,bind)=-0.43 (+/-0.01) kcal mol(-1) K(-1) is in accordance with the predominantly non-polar character of the binding surface, as judged from calculations based on changes in accessible surface areas. A further dissection of the small binding entropy at 25 degrees C (-TDeltaS degrees (bind) = -0.6 (+/-0.1) kcal mol(-1)) suggests that a favourable desolvation of non-polar surface is almost completely balanced by unfavourable conformational entropy changes and loss of rotational and translational entropy. Such effects can therefore be limiting for strong binding also when interacting protein components are stable and homogeneously folded. The combined structure and thermodynamics data suggest that protein properties are not likely to be a serious limitation for the development of engineered binding proteins based on the Z domain.

Unusual Entropy-Driven Affinity of Chromobacterium violaceum Lectin CV-IIL toward Fucose and Mannose,

The purple pigmented bacterium Chromobacterium violaceum is a dominant component of tropical soil microbiota that can cause rare but fatal septicaemia in humans. Its sequenced genome provides insight into the abundant potential of this organism for biotechnological and pharmaceutical applications and allowed an ORF encoding a protein that is 60% identical to the fucose binding lectin (PA-IIL) from Pseudomonas aeruginosa and the mannose binding lectin (RS-IIL) from Ralstonia solanacearum to be identified. The lectin, CV-IIL, has recently been purified from C. violaceum [Zinger-Yosovich, K., Sudakevitz, D., Imberty, A., Garber, N. C., and Gilboa-Garber, N. (2006) Microbiology 152, 457-463] and has been confirmed to be a tetramer with subunit size of 11.86 kDa and a binding preference for fucose. We describe here the cloning of CV-IIL and its expression as a recombinant protein. A complete structure-function characterization has been made in an effort to analyze the specificity and affinity of CV-IIL for fucose and mannose. Crystal structures of CV-IIL complexes with monosaccharides have yielded the molecular basis of the specificity. Each monomer contains two close calcium cations that mediate the binding of the monosaccharides, which occurs in different orientations for fucose and mannose. The thermodynamics of binding has been analyzed by titration microcalorimetry, giving dissociation constants of 1.7 and 19 microM for alpha-methyl fucoside and alpha-methyl mannoside, respectively. Further analysis demonstrated a strongly favorable entropy term that is unusual in carbohydrate binding. A comparison with both PA-IIL and RS-IIL, which have binding preferences for fucose and mannose, respectively, yielded insights into the monosaccharide specificity of this important class of soluble bacterial lectins.

The ubiquitin domain superfold: structure-based sequence alignments and characterization of binding epitopes

Ubiquitin-like domains are present, apart from ubiquitin-like proteins themselves, in many multidomain proteins involved in different signal transduction processes. The sequence conservation for all ubiquitin superfold family members is rather poor, even between subfamily members, leading to mistakes in sequence alignments using conventional sequence alignment methods. However, a correct alignment is essential, especially for in silico methods that predict binding partners on the basis of sequence and structure. In this study, using 3D-structural information we have generated and manually corrected sequence alignments for proteins of the five ubiquitin superfold subfamilies. On the basis of this alignment, we suggest domains for which structural information will be useful to allow homology modelling. In addition, we have analysed the energetic and electrostatic properties of ubiquitin-like domains in complex with various functional binding proteins using the protein design algorithm FoldX. On the basis of an in silico alanine-scanning mutagenesis, we provide a detailed binding epitope mapping of the hotspots of the ubiquitin domain fold, involved in the interaction with different domains and proteins. Finally, we provide a consensus fingerprint sequence that identifies all sequences described to belong to the ubiquitin superfold family. It is possible that the method that we describe may be applied to other domain families sharing a similar fold but having low levels of sequence homology.

Recognizing and Defining True Ras Binding Domains II: In Silico Prediction Based on Homology Modelling and Energy Calculations

Considering the large number of putative Ras effector proteins, it is highly desirable to develop computational methods to be able to identify true Ras binding molecules. Based on a limited sequence homology among members of the Ras association (RA) and Ras binding (RB) sub-domain families of the ubiquitin super-family, we have built structural homology models of Ras proteins in complex with different RA and RB domains, using the FOLD-X software. A critical step in our approach is to use different templates of Ras complexes, in order to account for the structural variation among the RA and RB domains. The homology models are validated by predicting the effect of mutating hot spot residues in the interface, and residues important for the specificity of interaction with different Ras proteins. The FOLD-X calculated energies of the best-modelled complexes are in good agreement with previously published experimental data and with new data reported here. Based on these results, we can establish energy thresholds above, or below which, we can predict with 96% confidence that a RA/RB domain will or will not interact with Ras. This study shows the importance of in depth structural analysis, high quality force-fields and modelling for correct prediction. Our work opens the possibility of genome-wide prediction for this protein family and for others, where there is enough structural information.

Lectins: tools for the molecular understanding of the glycocode

Recent progress in glycobiology has revealed that cell surface oligosaccharides play an essential role in recognition events. More precisely, these saccharides may be complexed by lectins, carbohydrate-binding proteins other than enzymes and antibodies, able to recognise sugars in a highly specific manner. The ubiquity of lectin-carbohydrate interactions opens enormous potential for their exploitation in medicine. Therefore, extraordinary effort is made into the identification of new lectins as well as into the achievement of a deep understanding of their functions and of the precise mechanism of their association with specific ligands. In this review, a summary of the main features of lectins, particularly those found in legumes, will be presented with a focus on the mechanism of carbohydrate-binding. An overview of lectin-carbohydrate interactions will also be given, together with an insight into their energetics. In addition, therapeutic applications of lectins will be discussed.

Energetics of Structural Transitions of the Addiction Antitoxin MazE

The Escherichia coli mazEF addiction module plays a crucial role in the cell death program that is triggered under various stress conditions. It codes for the toxin MazF and the antitoxin MazE, which interferes with the lethal action of the toxin. To better understand the role of various conformations of MazE in bacterial life, its order-disorder transitions were monitored by differential scanning calorimetry, spectropolarimetry, and fluorimetry. The changes in spectral and thermodynamic properties accompanying MazE dimer denaturation can be described in terms of a compensating reversible process of the partial folding of the unstructured C-terminal half (high mean net charge, low mean hydrophobicity) and monomerization coupled with the partial unfolding of the structured N-terminal half (low mean net charge, high mean hydrophobicity). At pH<or=4.5 and T<50 degrees C, the unstructured polypeptide chains of the MazE dimer fold into (pre)molten globule-like conformations that thermally stabilize the dimeric form of the protein. The simulation based on the thermodynamic and structural information on various addiction modules suggests that both the conformational adaptability of the dimeric antitoxin form (binding to the toxins and DNA) and the reversible transformation to the more flexible monomeric form are essential for the regulation of bacterial cell life and death.

Energetic diversity of DNA minor-groove recognition by small molecules displayed through some model ligand-DNA systems

Energetics of interactions occurring in the model ligand-DNA systems constituted from distamycin A (DST), netropsin (NET) and the oligomeric duplexes d(GCAAGTTGCGATATACG)d(CGTATATCGCAACTTGC)=D#1 and d(GCAAGTTGCGAAAAACG)d(CGTTTTTCGCAACTTGC)=D#2 was studied by spectropolarimetry, UV-absorption spectroscopy and isothermal titration calorimetry. Model analysis of the measured signals was applied to describe individual and competitive binding in terms of populations of various species in the solution. Our results reveal several unprecedented ligand-DNA binding features. DST binds to the neighboring 5'-AAGTT-3' and 5'-ATATA-3' sites of D#1 statistically in a 2:1 binding mode. By contrast, its association to D#2 appears to be a 2:1 binding event only at the DST/D#2 molar ratios between 0 and 2 while its further binding to D#2 may be considered as a step-by-step binding to the unoccupied 5'-AAAAA-3' sites resulting first in DST3D#2 and finally in DST4D#2 complex formation. Competition between DST and NET binding shows that for the most part DST displaces NET from its complexes with D#1 and D#2. In contrast to the obligatory 1:1 binding of DST to the ligand-free 5'-AAAAA-3' sites observed at DST/5'-AAAAA-3' <1 the displacement of NET bound to the 5'-AAAAA-3' sites by added DST occurs even at the smallest additions of DST in a 2:1 manner. NET can also displace DST molecules but only those bound monomerically to the 5'-AAAAA-3' sites of DST3D#2. Actually, only half of these molecules can be displaced due to the simultaneous rebinding of the displaced DST to the unreacted 5'-AAAAA-3' sites in DST3D#2. Binding of DST and NET to D#1 and D#2 is an enthalpy driven process accompanied by large unfavorable (DST), small (NET) or large favorable (NET binding to 5'-AAAAA-3') entropy contributions and negative deltaCP degrees that are reasonably close to deltaCP degrees predicted from the calculated changes in solvent-accessible surface areas that accompany complex formation. Although various modes of DST and NET binding within D#1 and D#2 are characterized by significant energetic differences they seem to be governed by the same driving forces; the hydrophobic transfer of ligand from the solution into the duplex binding site and the accompanying specific non-covalent ligand-DNA and ligand-ligand interactions occurring within the DNA minor groove.

Quantification of helix-helix binding affinities in micelles and lipid bilayers

A theoretical approach for estimating association free energies of alpha-helices in nonpolar media has been developed. The parameters of energy functions have been derived from DeltaDeltaG values of mutants in water-soluble proteins and partitioning of organic solutes between water and nonpolar solvents. The proposed approach was verified successfully against three sets of published data: (1) dissociation constants of alpha-helical oligomers formed by 27 hydrophobic peptides; (2) stabilities of 22 bacteriorhodopsin mutants, and (3) protein-ligand binding affinities in aqueous solution. It has been found that coalescence of helices is driven exclusively by van der Waals interactions and H-bonds, whereas the principal destabilizing contributions are represented by side-chain conformational entropy and transfer energy of atoms from a detergent or lipid to the protein interior. Electrostatic interactions of alpha-helices were relatively weak but important for reproducing the experimental data. Immobilization free energy, which originates from restricting rotational and translational rigid-body movements of molecules during their association, was found to be less than 1 kcal/mole. The energetics of amino acid substitutions in bacteriorhodopsin was complicated by specific binding of lipid and water molecules to cavities created in certain mutants.

A detailed thermodynamic analysis of ras/effector complex interfaces

Many cellular functions are based on the interaction and crosstalk of various signaling proteins. Among these, members of the Ras family of small GTP-binding proteins are important for communicating signals into different pathways. In order to answer the question of how binding affinity and specificity is achieved, we analyzed binding energetics on the molecular level, with reference to the available structural data. The interaction of two members of the Ras subfamily with two different effector proteins, namely Raf and RalGDS, were investigated using isothermal titration calorimetry and a fluorescence-based method. Experiments with alanine mutants, located in the complex interfaces, yielded an energy map for the contact areas of the Ras/effector complexes, which could be differentiated into enthalpy and entropy contributions. In addition, by using double mutant cycle analysis, we probed the energetic contribution of selected pairs of amino acid residues. The resulting energy landscapes of the Ras/effector interface areas show a highly different topology when comparing the two effectors, Raf and RalGDS, demonstrating the specificity of the respective interactions. Particularly, we observe a high degree of compensating effects between enthalpy and entropy; differences between these components are much greater than the overall free energy differences. This is observed also when using the software FOLD-X to predict the effect of point mutations on the crystal structures of the different complexes. Prediction of the free energy changes shows a very good correlation with the experimentally observed energies. Furthermore, in line with experimental data, energy decomposition indicates that many different components of large magnitude counteract each other to produce a smaller change in overall free energy, illustrating the importance of long-range electrostatic forces in complex formation.

Compensatory energetic mechanisms mediating the assembly of signaling complexes between interleukin-2 and its alpha, beta, and gamma(c) receptors

Interleukin-2 is a key immuno-regulatory cytokine whose actions are mediated by three different cell surface receptors: the alpha, beta and the "common gamma" (gamma(c)) chains. We have undertaken a complete thermodynamic characterization of the stepwise assembly cycle for multiple possible combinations of the receptor-ligand, and receptor-receptor interactions that are necessary for formation of the high-affinity IL-2/alphabetagamma(c) signaling complex. We find an entropically favorable high affinity interaction between IL-2 and its alpha receptor, a moderately entropically favorable low affinity interaction between IL-2 and its beta receptor, and no interaction between IL-2 and the shared receptor, gamma(c). Formation of the stable intermediate trimolecular complexes of IL-2 with alpha and beta receptors, as well as IL-2 with beta and gamma(c) receptors proceeds through enthalpy-entropy compensation mechanisms. Surprisingly, we see a moderate affinity interaction between the unliganded receptor alpha and beta chains, suggesting that a preformed alphabeta complex may serve as the initial interaction complex for IL-2. Reconstitution of the IL-2/Ralphabetagamma(c) high-affinity quaternary signaling complex shows it to be assembled through cooperative energetics to form a 1:1:1:1 assembly. Collectively, the favorable entropy of the bimolecular interactions appears to be offset by the loss in rigid body entropy of the receptor components in the higher-order complexes, but overcome by the formation of increasingly enthalpically favorable composite interfaces. This enthalpic mechanism utilized by gamma(c) contrasts with the favorable entropic mechanism utilized by gp130 for degenerate cytokine interaction. In conclusion, we find that several energetically redundant pathways exist for formation of IL-2 receptor signaling complexes, suggesting a more complex equilibrium on the cell surface than has been previously appreciated.

Thermodynamics of Binding to SH3 Domains: The Energetic Impact of Polyproline II (PII) Helix Formation

Although numerous biophysical studies have focused on elucidating the structural and thermodynamic determinants that govern the free energy of binding between various SH3 domains and their putative recognition sequences, a quantitative accounting of the energetics of this interaction has proven enigmatic. Specifically, the binding results in a large and negative change on the standard enthalpy and entropy functions, a result which is inconsistent with the positive values for these quantities that is expected from the hydrophobic nature of the binding pocket. Here, the binding of the C-terminal SH3 domain of Sem-5 to its putative recognition peptide on the Sos (Son of Sevenless) protein is investigated using isothermal titration calorimetry under a variety of temperature and pH conditions. In addition, the energy associated with folding the Sos peptide into the binding competent polyproline II conformation is quantitatively evaluated. These results provide a rationale for the observed discrepancy between the experimental and predicted behavior and indicate that the determinants of binding in this system cannot be ascertained from a static structural representation of the binding process.

Transition state stabilization by general acid catalysis, water expulsion, and enzyme reorganization in Medicago savita chalcone isomerase

In aqueous solution, Medicago savita chalcone isomerase (CHI) enhances the reaction rate for the unimolecular rearrangement of chalcone (CHN) into flavanone by seven orders of magnitude. Conformations of CHN and their relative free energies in water and CHI were investigated by the thermodynamic perturbation method. In water, CHN adopts two conformations (I and II) with conformation I being higher in energy than conformation II by 3 kcal/mol. Only I can give rise to a near attack conformer (NAC) where the nucleophile O2' and the electrophile C9 are placed in proximity. In CHI, I binds less tightly than II by approximately 2 kcal/mol, resulting in the free energy for NAC formation being approximately 2 kcal/mol higher in the enzyme than in water. This unfavorable feature in the ground state of the CHI reaction requires the predominant catalytic advantage to be taken in the step of NAC --> transition state (TS). From the molecular dynamics simulations of apo-CHI, CHI complexed with CHN (CHI.CHN) and CHI.TS, we found: (i) Lys-97-general-acid catalysis of the O2'(-) nucleophilic addition; (ii) expulsion of three water molecules in the process of TS formation; (iii) release of enzyme structural distortion on TS formation. In the conclusion, CHI's remarkable efficiency of stabilizing the TS and its relatively poor ability in organizing the ground state is compared with chorismate mutase whose catalytic prowess, when compared with water, originates predominantly from the enhanced NAC population at the active site.

Challenges in enzyme mechanism and energetics

Since the discovery of enzymes as biological catalysts, study of their enormous catalytic power and exquisite specificity has been central to biochemistry. Nevertheless, there is no universally accepted comprehensive description. Rather, numerous proposals have been presented over the past half century. The difficulty in developing a comprehensive description for the catalytic power of enzymes derives from the highly cooperative nature of their energetics, which renders impossible a simple division of mechanistic features and an absolute partitioning of catalytic contributions into independent and energetically additive components. Site-directed mutagenesis has emerged as an enormously powerful approach to probe enzymatic catalysis, illuminating many basic features of enzyme function and behavior. The emphasis of site-directed mutagenesis on the role of individual residues has also, inadvertently, limited experimental and conceptual attention to the fundamentally cooperative nature of enzyme function and energetics. The first part of this review highlights the structural and functional interconnectivity central to enzymatic catalysis. In the second part we ask: What are the features of enzymes that distinguish them from simple chemical catalysts? The answers are presented in conceptual models that, while simplified, help illustrate the vast amount known about how enzymes achieve catalysis. In the last section, we highlight the molecular and energetic questions that remain for future investigation and describe experimental approaches that will be necessary to answer these questions. The promise of advancing and integrating cutting edge conceptual, experimental, and computational tools brings mechanistic enzymology to a new era, one poised for novel fundamental insights into biological catalysis.

Loss of translational entropy in molecular associations

Molecular associations in solution are opposed by the loss of entropy (DeltaS) that results from the restriction of motion of each component in the complex. Theoretical estimates of DeltaS are essential for rationalizing binding affinities, as well as for calculating entropic contribution to enzyme catalysis. Recently a statistical-mechanical framework has been proposed for estimating efficiently the translational entropy loss (DeltaS(trsl)), while taking explicitly into account the complex intermolecular interactions between the solute and the solvent. This framework relates the translational entropy of a solute in solution to its "free volume," defined as the volume accessible to the center of mass of the solute in the presence of the solvent and calculated by using an extension of the cell model (CM) for condensed phases. The translational entropy of pure water, estimated with the CM algorithm, shows good agreement with the experimental information. The free volume of various solutes in water, calculated within the CM by using molecular dynamics simulations with explicit solvent, displays a strong correlation with the solutes' polar and total surface areas. This correlation is used to propose a parameterization that can be used to calculate routinely the translational entropy of a solute in water. We also applied the CM formalism to calculate the free volume and translational entropy loss (DeltaS(trsl)) on binding of benzene to a cavity in a mutant T4-lysozyme. Our results agree with previously published estimates of the binding of benzene to this mutant T4-lysozyme. These and other considerations suggest that the cell model is a simple yet efficient theoretical framework to evaluate the translational entropy loss on molecular association in solution.

Thermodynamics of aminoglycoside-rRNA recognition

2-Deoxystreptamine (2-DOS) aminoglycosides are a family of structurally related broad-spectrum antibiotics that are used widely in the treatment of infections caused by aerobic Gram-negative bacilli. Their antibiotic activities are ascribed to their abilities to bind a highly conserved A site in the 16 S rRNA of the 30 S ribosomal subunit and interfere with protein synthesis. The abilities of the 2-DOS aminoglycosides to recognize a specific subdomain of a large RNA molecule make these compounds archetypical models for RNA-targeting drugs. This article presents a series of calorimetric, spectroscopic, osmotic stress, and computational studies designed to evaluate the thermodynamics (DeltaG, DeltaH, DeltaS, DeltaCp) of aminoglycoside-rRNA interactions, as well as the hydration changes that accompany these interactions. In conjunction with the current structural database, the results of these studies provide important insights into the molecular forces that dictate and control the rRNA binding affinities and specificities of the aminoglycosides. Significantly, identification of these molecular driving forces [which include binding-linked drug protonation reactions, polyelectrolyte contributions from counterion release, conformational changes, hydration effects, and molecular interactions (e.g., hydrogen bonds and van der Waals interactions)], as well as the relative magnitudes of their contributions to the binding free energy, could not be achieved by consideration of structural data alone, highlighting the importance of acquiring both thermodynamic and structural information for developing a complete understanding of the drug-RNA binding process. The results presented here begin to establish a database that can be used to predict, over a range of conditions, the relative affinity of a given aminoglycoside or aminoglycoside mimetic for a targeted RNA site vs binding to potential competing secondary sites. This type of predictive capability is essential for establishment of a rational design approach to the development of new RNA-targeted drugs.

Insight into the structure and function of the transferrin receptor from Neisseria meningitidis using microcalorimetric techniques

The transferrin receptor of Neisseria meningitidis is composed of the transmembrane protein TbpA and the outer membrane protein TbpB. Both receptor proteins have the capacity to independently bind their ligand human transferrin (htf). To elucidate the specific role of these proteins in receptor function, isothermal titration calorimetry was used to study the interaction between purified TbpA, TbpB or the entire receptor (TbpA + TbpB) with holo- and apo-htf. The entire receptor was shown to contain a single high affinity htf-binding site on TbpA and approximately two lower affinity binding sites on TbpB. The binding sites appear to be independent. Purified TbpA was shown to have strong ligand preference for apo-htf, whereas TbpA in the receptor complex with TbpB preferentially binds the holo form of htf. The orientation of the ligand specificity of TbpA toward holo-htf is proposed to be the physiological function of TbpB. Furthermore, the thermodynamic mode of htf binding by TbpB of isotypes I and II was shown to be different. A protocol for the generation of active, histidine-tagged TbpB as well as its individual N- and C-terminal domains is presented. Both domains are shown to strongly interact with each other, and isothermal titration calorimetry and circular dichroism experiments provide clear evidence for this interaction causing conformational changes. The N-terminal domain of TbpB was shown to be the site of htf binding, whereas the C-terminal domain is not involved in binding. Furthermore, the interactions between TbpA and the different domains of TbpB have been demonstrated.

Recognition of the intrinsically flexible addiction antidote MazE by a dromedary single domain antibody fragment. Structure, thermodynamics of binding, stability, and influence on interactions with DNA

The Escherichia coli mazEF operon defines a chromosomal addiction module that programs cell death under various stress conditions. It encodes the toxic and long-lived MazF and the labile antidote MazE. The denaturation of MazE is a two-state reversible dimer-monomer transition. At lower concentrations the denatured state is significantly populated. This leads to a new aspect of the regulation of MazE concentration, which may decide about the life and death of the cell. Interactions of MazE with a dromedary antibody domain, cAbMaz1 (previously used as a crystallization aid), as well as with promoter DNA were studied using microcalorimetric and spectroscopic techniques. Unique features of cAbMaz1 enable a specific enthalpy-driven recognition of MazE and, thus, a significant stabilization of its dimeric native conformation. The MazE dimer and the MazE dimer-cAbMaz1 complex show very similar binding characteristics with promoter DNA, i.e. three binding sites with apparent affinities in micromolar range and highly exothermic binding accompanied by large negative entropy contributions. A working model for the MazE-DNA assembly is proposed on the basis of the structural and binding data. Both binding and stability studies lead to a picture of MazE solution structure that is significantly more unfolded than the structure observed in a crystal of the MazE-cAbMaz1 complex.

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.

Converging free energy estimates: MM-PB(GB)SA studies on the protein-protein complex Ras-Raf

Estimating protein-protein interaction energies is a very challenging task for current simulation protocols. Here, absolute binding free energies are reported for the complex H-Ras/C-Raf1 using the MM-PB(GB)SA approach, testing the internal consistency and model dependence of the results. Averaging gas-phase energies (MM), solvation free energies as determined by Generalized Born models (GB/SA), and entropic contributions calculated by normal mode analysis for snapshots obtained from 10 ns explicit-solvent molecular dynamics in general results in an overestimation of the binding affinity when a solvent-accessible surface area-dependent model is used to estimate the nonpolar solvation contribution. Applying the sum of a cavity solvation free energy and explicitly modeled solute-solvent van der Waals interaction energies instead provides less negative estimates for the nonpolar solvation contribution. When the polar contribution to the solvation free energy is determined by solving the Poisson-Boltzmann equation (PB) instead, the calculated binding affinity strongly depends on the atomic radii set chosen. For three GB models investigated, different absolute deviations from PB energies were found for the unbound proteins and the complex. As an alternative to normal-mode calculations, quasiharmonic analyses have been performed to estimate entropic contributions due to changes of solute flexibility upon binding. However, such entropy estimates do not converge after 10 ns of simulation time, indicating that sampling issues may limit the applicability of this approach. Finally, binding free energies estimated from snapshots of the unbound proteins extracted from the complex trajectory result in an underestimate of binding affinity. This points to the need to exercise caution in applying the computationally cheaper "one-trajectory-alternative" to systems where there may be significant changes in flexibility and structure due to binding. The best estimate for the binding free energy of Ras-Raf obtained in this study of -8.3 kcal mol(-1) is in good agreement with the experimental result of -9.6 kcal mol(-1), however, further probing the transferability of the applied protocol that led to this result is necessary.

The consequences of translational and rotational entropy lost by small molecules on binding to proteins

When a small molecule binds to a protein, it loses a significant amount of rigid body translational and rotational entropy. Estimates of the associated energy barrier vary widely in the literature yet accurate estimates are important in the interpretation of results from fragment-based drug discovery techniques. This paper describes an analysis that allows the estimation of the rigid body entropy barrier from the increase in binding affinities that results when two fragments of known affinity and known binding mode are joined together. The paper reviews the relatively rare number of examples where good quality data is available. From the analysis of this data, we estimate that the barrier to binding, due to the loss of rigid-body entropy, is 15-20 kJ/mol, i.e. around 3 orders of magnitude in affinity at 298 K. This large barrier explains why it is comparatively rare to observe multiple fragments binding to non-overlapping adjacent sites in enzymes. The barrier is also consistent with medicinal chemistry experience where small changes in the critical binding regions of ligands are often poorly tolerated by enzymes.

Contributions to the binding free energy of ligands to avidin and streptavidin

The free energy of binding of a ligand to a macromolecule is here formally decomposed into the (effective) energy of interaction, reorganization energy of the ligand and the macromolecule, conformational entropy change of the ligand and the macromolecule, and translational and rotational entropy loss of the ligand. Molecular dynamics simulations with implicit solvation are used to evaluate these contributions in the binding of biotin, biotin analogs, and two peptides to avidin and streptavidin. We find that the largest contribution opposing binding is the protein reorganization energy, which is calculated to be from 10 to 30 kcal/mol for the ligands considered here. The ligand reorganization energy is also significant for flexible ligands. The translational/rotational entropy is 4.5-6 kcal/mol at 1 M standard state and room temperature. The calculated binding free energies are in the correct range, but the large statistical uncertainty in the protein reorganization energy precludes precise predictions. For some complexes, the simulations show multiple binding modes, different from the one observed in the crystal structure. This finding is probably due to deficiencies in the force field but may also reflect considerable ligand flexibility.

A view at the millennium: the efficiency of enzymatic catalysis

Binding TS in preference to S and increasing TDeltaS++by freezing out motions in E X S and E X TS have been accepted as the driving forces in enzymatic catalysis; however, the smaller value of DeltaG++ for a one-substrate enzymatic reaction, as compared to its nonenzymatic counterpart, is generally the result of a smaller value of DeltaH++. Ground-state conformers (E X NACs) are formed in enzymatic reactions that structurally resemble E X TS. E X NACs are in thermal equilibrium with all other E X S conformers and are turnstiles through which substrate molecules must pass to arrive at the lowest-energy TS. TS in E X TS may or may not be bound tighter than NAC in E X NAC.

Hierarchy of simulation models in predicting structure and energetics of the Src SH2 domain binding to tyrosyl phosphopeptides

Structure and energetics of the Src Src Homology 2 (SH2) domain binding with the recognition phosphopeptide pYEEI and its mutants are studied by a hierarchical computational approach. The proposed structure prediction strategy includes equilibrium sampling of the peptide conformational space by simulated tempering dynamics with the simplified, knowledge-based energy function, followed by structural clustering of the resulting conformations and binding free energy evaluation of a single representative from each cluster, a cluster center. This protocol is robust in rapid screening of low-energy conformations and recovers the crystal structure of the pYEEI peptide. Thermodynamics of the peptide-SH2 domain binding is analyzed by computing the average energy contributions over conformations from the clusters, structurally similar to the predicted peptide bound structure. Using this approach, the binding thermodynamics for a panel of studied peptides is predicted in a better agreement with the experiment than previously suggested models. However, the overall correlation between computed and experimental binding affinity remains rather modest. The results of this study show that small differences in binding free energies between the Ala and Gly mutants of the pYEEI peptide are considerably more difficult to predict than the structure of the bound peptides, indicating that accurate computational prediction of binding affinities still remains a major methodological and technical challenge.

Standard state and thermodynamic self-consistency

It is pointed out that even though the standard state for solutions is a fictitious state, it nonetheless should be thermodynamically self-consistent. Using a volumetric constraint, it is shown that the biochemical standard state concentration of 1M is too high for macromolecules like proteins and nucleic acids that it violates volumetric self-consistency. Also, at 1 M standard state, the mole fraction of these macromolecular solutes is not the commonly held value of 1/55.5, but rather a meaningless negative number. Thus, the ideal mixing entropy (also called cratic entropy) cannot be meaningfully calculated for macromolecules at such a standard state. The relevance of this conclusion to the interpretation of standard bimolecular binding entropy is discussed.

Cross-reactive binding of cyclic peptides to an anti-TGFalpha antibody Fab fragment: an X-ray structural and thermodynamic analysis

The monoclonal antibody tAb2 binds the N-terminal sequence of transforming growth factor alpha, VVSHFND. With the help of combinatorial peptide libraries it is possible to find homologous peptides that bind tAb2 with an affinity similar to that of the epitope. The conformational flexibility of short peptides can be constrained by cyclization in order to improve their affinity to the antibody and their stability towards proteolysis. Two cyclic peptides which are cross-reactive binders for tAb2 were selected earlier using combinatorial peptide libraries. One is cyclized by an amide bond between the N-alpha group and the side-chain of the last residue (cyclo-SHFNEYE), and the other by a disulfide bridge (cyclo-CSHFNDYC). The complex structures of tAb2 with the linear epitope peptide VVSHFND and with cyclo-SHFNEYE were determined by X-ray diffraction. Both peptides show a similar conformation and binding pattern in the complex. The linear peptide SHFNEYE does not bind tAb2, but cyclo-SHFNEYE is stabilized in a loop conformation suitable for binding. Hence the cyclization counteracts the exchange of aspartate in the epitope sequence to glutamate. Isothermal titration calorimetry was used to characterize the binding energetics of tAb2 with the two cyclic peptides and the epitope peptide. The binding reactions are enthalpically driven with an unfavorable entropic contribution under all measured conditions. The association reactions are characterized by negative DeltaC(p) changes and by the uptake of one proton per binding site. A putative candidate for proton uptake during binding is the histidine residue in each of the peptides. Hydrogen bonds and the putative formation of an electrostatic pair between the protonated histidine and a carboxy group may contribute markedly to the favorable enthalpy of complex formation. Implications to cyclization of peptides for stabilization are discussed.

Contribution of translational and rotational motions to molecular association in aqueous solution

Much uncertainty and controversy exist regarding the estimation of the enthalpy, entropy, and free energy of overall translational and rotational motions of solute molecules in aqueous solutions, quantities that are crucial to the understanding of molecular association/recognition processes and structure-based drug design. A critique of the literature on this topic is given that leads to a classification of the various views. The major stumbling block to experimentally determining the translational/rotational enthalpy and entropy is the elimination of vibrational perturbations from the measured effects. A solution to this problem, based on a combination of energy equi-partition and enthalpy-entropy compensation, is proposed and subjected to verification. This method is then applied to analyze experimental data on the dissociation/unfolding of dimeric proteins. For one translational/rotational unit at 1 M standard state in aqueous solution, the results for enthalpy (H degrees (tr)), entropy (S degrees (tr)), and free energy (G degrees (tr)) are H (degrees) (tr) = 4.5 +/- 1.5RT, S (degrees) (tr) = 5 +/- 4R, and G (degrees) (tr) = 0 +/- 5RT. Therefore, the overall translational and rotational motions make negligible contribution to binding affinity (free energy) in aqueous solutions at 1 M standard state.

Thermodynamics of trimer-of-hairpins formation by the SIV gp41 envelope protein

The gp41 envelope protein mediates the entry of primate immunodeficiency viruses into target cells by promoting the fusion of viral and cellular membranes. The structure of the gp41 ectodomain core represents a trimer of identical helical hairpins in which a central trimeric coiled-coil made up of three amino-terminal helices is wrapped in an outer layer of three antiparallel carboxyl-terminal helices. Triggering formation of this fusion-active gp41 conformation appears to cause close membrane apposition and thus overcome the activation energy barrier for lipid bilayer fusion. We present a detailed description of the folding thermodynamics of the simian immunodeficiency virus (SIV) gp41 core by using a recombinant trimeric N34(L6)C28 model. Differential scanning calorimetry and spectroscopic experiments on denaturant-induced and thermal unfolding indicate that the free energy of association of three 68 residue N34(L6)C28 peptides to a trimer-of-hairpins is 76 kJ mol(-1) at pH 7.0 and 25 degrees C in physiological buffer. The associated enthalpy change, Delta H(unf), is 177 kJ mol(-1), while the entropy of unfolding, Delta S(unf), is 0.32 kJ K(-1) mol(-1). The temperature of maximal stability is close to 20 degrees C. The unfolding heat capacity increment is approximately 9 kJ K(-1) mol(-1) (approximately 45 J K(-1) mol residue(-1)), which is lower than expected for unfolding of the trimer to an extended and fully hydrated polypeptide chain. Replacement by isoleucine of the polar residues Thr582 or Thr586 buried in the N-terminal trimeric coiled-coil interface leads to very strong stabilization of the trimer-of-hairpins, 30-35 kJ mol(-1). Single-point mutations in the central coiled-coil thus strongly stabilize the gp41 core structure. These thermodynamic characteristics may be important for the refolding of the gp41 envelope protein into its fusion-active conformation during membrane fusion.

Interaction of a designed interleukin-10 epitope mimic with an antibody studied by isothermal titration microcalorimetry

The mechanism of recognition of proteins and peptides by antibodies and the factors determining binding affinity and specificity are mediated by essentially the same features. However, additional effects of the usually unfolded and flexible solution structure of peptide ligands have to be considered. In an earlier study we designed and optimized six peptides (pepI to pepVI) mimicking the discontinuous binding site of interleukin-10 for the anti-interleukin-10 monoclonal antibody (mab) CB/RS/1. Three of them were selected for analysis of their solution conformation by circular dichroism measurements. The peptides differ in the content of alpha-helices and in the inducibility of helical secondary structures by trifluoroethanol. These properties, however, do not correlate with the binding affinity. PepVI, a 32-mer cyclic epitope mimic, has the highest affinity to mab CB/RS/1 identified to date. CD difference spectroscopy suggests an increase of the alpha-helix content of pepVI with complex formation. Binding of pepVI to mab CB/RS/1 is characterized by a large negative, favorable binding enthalpy and a smaller unfavorable loss of entropy (DeltaH degrees = -16.4 kcal x mol(-1), TDeltaS degrees = -6.9 kcal x mol(-1)) resulting in DeltaG degrees = -9.5 kcal x mol(-1) at 25 degrees C as determined by isothermal titration calorimetry. Binding of pepVI is enthalpically driven over the entire temperature range studied (10-35 degrees C). Complex formation is not accompanied by proton uptake or release. A negative heat capacity change DeltaC(p) of -0.354 kcal x mol(-1) x K(-1) was determined from the temperature dependence of DeltaH degrees. The selection of protein mimics with the observed thermodynamic properties is promoted by the applied identification and iterative optimization procedure.

Calculation of entropy changes in biological processes: folding, binding, and oligomerization

Changes in configurational entropy represent one of the major contributions to the thermodynamics of folding, binding, and oligomerization. Methods have been developed to estimate changes in the entropy of the backbone and side chains, and for the loss of translational entropy. These methods have been used in combination with empirical methods that provide estimates of the changes in entropy of solvation as well as estimates of the changes of enthalpy. The results of such calculations are in excellent agreement with experimentally observed values.

Mapping the energy surface for the folding reaction of the coiled-coil peptide GCN4-p1

The energy surface for the folding/unfolding reactions of the homodimeric coiled-coil peptide M2V GCN4-p1, a 33-residue segment comprising the leucine zipper domain of the transcriptional activator GCN4, was mapped by equilibrium and kinetic methods. Circular dichroism (CD) spectroscopy was used to monitor the urea-induced unfolding reaction at a series of temperatures and temperature-induced unfolding at a series of urea concentrations. A global analysis of the urea- and temperature-induced equilibrium unfolding data provides strong support for a two-state mechanism. The absence of a detectable population of intermediate states is also consistent with differential scanning calorimetry and thermal CD melts as a function of peptide concentration. Furthermore, a global analysis of stopped-flow CD kinetic data is consistent with a kinetic two-state mechanism as well. The urea dependence of the apparent folding and unfolding rate constants at a series of temperatures reveals that the activation enthalpy and entropy for unfolding in the absence of denaturant are both significantly greater than those for the refolding reaction. Although the unfolding barrier is dominated by the activation enthalpy, the activation entropy dominates the refolding barrier. The relative magnitudes of the urea dependence of the unfolding and refolding rate constants indicate that 55-65% of the surface area is buried in the transition state. The activation parameters imply a partially organized transition state and are consistent with a previous model in which the pair of C-terminal heptad repeats are docked in a coiled-coil-like motif [Zitzewitz et al. (2000) J. Mol. Biol. 296, 1105-1116].

Is counterion delocalization responsible for collapse in RNA folding?

Although energetic and phylogenetic methods have been very successful for prediction of nucleic acid secondary structures, arrangement of these secondary structure elements into tertiary structure has remained a difficult problem. Here we explore the packing arrangements of DNA, RNA, and DNA/RNA hybrid molecules in crystals. In the conventional view, the highly charged double helix will be pushed toward isolation by favorable solvation effects; interactions with other like-charged stacks would be strongly disfavored. Contrary to this expectation, we find that most of the cases analyzed ( approximately 80%) exhibit specific, preferential packing between elements of secondary structure, which falls into three categories: (i) interlocking of major grooves of two helices, (ii) side-by-side parallel packing of helices, and (iii) placement of the ribose-phosphate backbone ridge of one helix into the major groove of another. The preponderance of parallel packing motifs is especially surprising. This category is expected to be maximally disfavored by charge repulsion. Instead, it comprises in excess of 50% of all packing interactions in crystals of A-form RNA and has also been observed in crystal structures of large RNA molecules. To explain this puzzle, we introduce a novel model for RNA folding. A simple calculation suggests that the entropy gained by a cloud of condensed cations surrounding the helices more than offsets the Coulombic repulsion of parallel arrangements. We propose that these condensed counterions are responsible for entropy-driven RNA collapse, analogous to the role of the hydrophobic effect in protein folding.

Reversible denaturation of oligomeric human chaperonin 10: denatured state depends on chemical denaturant

Chaperonins cpn60/cpn10 (GroEL/GroES in Escherichia coli) assist folding of nonnative polypeptides. Folding of the chaperonins themselves is distinct in that it entails assembly of a sevenfold symmetrical structure. We have characterized denaturation and renaturation of the recombinant human chaperonin 10 (cpn10), which forms a heptamer. Denaturation induced by chemical denaturants urea and guanidine hydrochloride (GuHCl) as well as by heat was monitored by tyrosine fluorescence, far-ultraviolet circular dichroism, and cross-linking; all denaturation reactions were reversible. GuHCl-induced denaturation was found to be cpn10 concentration dependent, in accord with a native heptamer to denatured monomer transition. In contrast, urea-induced denaturation was not cpn10 concentration dependent, suggesting that under these conditions cpn10 heptamers denature without dissociation. There were no indications of equilibrium intermediates, such as folded monomers, in either denaturant. The different cpn10 denatured states observed in high [GuHCl] and high [urea] were supported by cross-linking experiments. Thermal denaturation revealed that monomer and heptamer reactions display the same enthalpy change (per monomer), whereas the entropy-increase is significantly larger for the heptamer. A thermodynamic cycle for oligomeric cpn10, combining chemical denaturation with the dissociation constant in absence of denaturant, shows that dissociated monomers are only marginally stable (3 kJ/mol). The thermodynamics for co-chaperonin stability appears conserved; therefore, instability of the monomer could be necessary to specify the native heptameric structure.

Analysis of the interactions of human ribonuclease inhibitor with angiogenin and ribonuclease A by mutagenesis: importance of inhibitor residues inside versus outside the C-terminal "hot spot"

Ribonuclease inhibitor (RI) binds diverse mammalian RNases with extraordinary avidity. Here, we have investigated the structural basis for this tight binding and broad specificity by mutational analysis of the complexes of RI with angiogenin (Ang) and RNase A (K(D)=0.5 fM and 43 fM, respectively). Both crystal structures are known; the interfaces are large, and the ligands dock similarly, although few of the specific interactions formed are analogous. Our previous mutagenesis studies focused primarily on one contact region, containing RI 434-438 and the enzymatic active site. Many single-residue replacements produced extensive losses of binding energy (2.3-5.9 kcal/mol), suggesting that this region constitutes a "hot spot" in both cases. We have now explored the roles of most of the remaining RI residues that interact with Ang and/or RNase A. One major cluster in each complex lies in a Trp-rich area of RI, containing Trp261, Trp263, Trp318, and Trp375. Although the energy losses from individual replacements in this portion of the Ang complex were small-to-moderate (0-1.5 kcal/mol), the changes from multiple substitutions were much greater than additive, and the binding energy provided by this region is estimated to be approximately 6 kcal/mol (30 % of total). Effects of replacing combinations of hot spot components had also been found to be superadditive, and this negative cooperativity is now shown to extend to the neighboring contact residue RI Ser460. The overall contribution of the hot spot, taking superadditivity into account, is then approximately 14-15 kcal/mol. The hot spot and Trp-rich regions, although spatially well separated, are themselves functionally linked. No other parts of the RI-Ang interface appear to be energetically important. Binding of RNase A is more sensitive to substitutions throughout the interface, with free energy losses>/=1 kcal/mol produced by nearly all replacements examined, so that the sum of losses greatly exceeds the binding energy of the complex. This discrepancy can be explained, in part, by positive cooperativity, as evident from the subadditive effects observed when combinations of residues in either the hot spot or Trp-rich region are replaced. These findings suggest that the binding energy may be more widely distributed in the RNase A complex than in the Ang complex.

Association entropy in adsorption processes

The association of two species to form a bound complex, e.g., the binding of a ligand to a protein or the adsorption of a peptide on a lipid membrane, involves an entropy loss, reflecting the conversion of free translational and rotational degrees of freedom into bound motions. Previous theoretical estimates of the standard entropy change in bimolecular binding processes, DeltaS(o), have been derived from the root-mean-square fluctuations in protein crystals, suggesting DeltaS(o) approximately -50 e.u., i.e., TDeltaS degrees approximately -25 kT = -15 kcal/mol. In this work we focus on adsorption, rather than binding processes. We first present a simple statistical-thermodynamic scheme for calculating the adsorption entropy, including its resolution into translational and rotational contributions, using the known distance-orientation dependent binding (adsorption) potential. We then utilize this scheme to calculate the free energy of interaction and entropy of pentalysine adsorption onto a lipid membrane, obtaining TDeltaS(o) approximately -1.7 kT approximately -1.3 kcal/mol. Most of this entropy change is due to the conversion of one free translation into a bound motion, the rest arising from the confinement of two rotational degrees of freedom. The smaller entropy loss in adsorption compared to binding processes arises partly because a smaller number of degrees of freedom become restricted, but mainly due to the fact that the binding potential is much "softer."

Energetics of drug-DNA interactions

Understanding the thermodynamics of drug binding to DNA is of both practical and fundamental interest. The practical interest lies in the contribution that thermodynamics can make to the rational design process for the development of new DNA targeted drugs. Thermodynamics offer key insights into the molecular forces that drive complex formation that cannot be obtained by structural or computational studies alone. The fundamental interest in these interactions lies in what they can reveal about the general problems of parsing and predicting ligand binding free energies. For these problems, drug-DNA interactions offer several distinct advantages, among them being that the structures of many drug-DNA complexes are known at high resolution and that such structures reveal that in many cases the drug acts as a rigid body, with little conformational change upon binding. Complete thermodynamic profiles (delta G, delta H, delta S, delta Cp) for numerous drug-DNA interactions have been obtained, with the help of high-sensitivity microcalorimetry. The purpose of this article is to offer a perspective on the interpretation of these thermodynamics parameters, and in particular how they might be correlated with known structural features. Obligatory conformational changes in the DNA to accommodate intercalators and the loss of translational and rotational freedom upon complex formation both present unfavorable free energy barriers for binding. Such barriers must be overcome by favorable free energy contributions from the hydrophobic transfer of ligand from solution into the binding site, polyelectrolyte contributions from coupled ion release, and molecular interactions (hydrogen and ionic bonds, van der Waals interactions) that form within the binding site. Theoretical and semiempirical tools that allow estimates of these contributions to be made will be discussed, and their use in dissecting experimental data illustrated. This process, even at the current level of approximation, can shed considerable light on the drug-DNA binding process.

Fast prediction and visualization of protein binding pockets with PASS

PASS (Putative Active Sites with Spheres) is a simple computational tool that uses geometry to characterize regions of buried volume in proteins and to identify positions likely to represent binding sites based upon the size, shape, and burial extent of these volumes. Its utility as a predictive tool for binding site identification is tested by predicting known binding sites of proteins in the PDB using both complexed macromolecules and their corresponding apoprotein structures. The results indicate that PASS can serve as a front-end to fast docking. The main utility of PASS lies in the fact that it can analyze a moderate-size protein (approximately 30 kDa) in under 20 s, which makes it suitable for interactive molecular modeling, protein database analysis, and aggressive virtual screening efforts. As a modeling tool, PASS (i) rapidly identifies favorable regions of the protein surface, (ii) simplifies visualization of residues modulating binding in these regions, and (iii) provides a means of directly visualizing buried volume, which is often inferred indirectly from curvature in a surface representation. PASS produces output in the form of standard PDB files, which are suitable for any modeling package, and provides script files to simplify visualization in Cerius2, InsightII, MOE, Quanta, RasMol, and Sybyl. PASS is freely available to all.

Structure-based thermodynamic analysis of the dissociation of protein phosphatase-1 catalytic subunit and microcystin-LR docked complexes

The relationship between the structure of a free ligand in solution and the structure of its bound form in a complex is of great importance to the understanding of the energetics and mechanism of molecular recognition and complex formation. In this study, we use a structure-based thermodynamic approach to study the dissociation of the complex between the toxin microcystin-LR (MLR) and the catalytic domain of protein phosphatase-1 (PP-1c) for which the crystal structure of the complex is known. We have calculated the thermodynamic parameters (enthalpy, entropy, heat capacity, and free energy) for the dissociation of the complex from its X-ray structure and found the calculated dissociation constant (4.0 x 10(-11)) to be in excellent agreement with the reported inhibitory constant (3.9 x 10(-11)). We have also calculated the thermodynamic parameters for the dissociation of 47 PP-1c:MLR complexes generated by docking an ensemble of NMR solution structures of MLR onto the crystal structure of PP-1c. In general, we observe that the lower the root-mean-square deviation (RMSD) of the docked complex (compared to the X-ray complex) the closer its free energy of dissociation (deltaGd(o)) is to that calculated from the X-ray complex. On the other hand, we note a significant scatter between the deltaGd(o) and the RMSD of the docked complexes. We have identified a group of seven docked complexes with deltaGd(o) values very close to the one calculated from the X-ray complex but with significantly dissimilar structures. The analysis of the corresponding enthalpy and entropy of dissociation shows a compensation effect suggesting that MLR molecules with significant structural variability can bind PP-1c and that substantial conformational flexibility in the PP-1c:MLR complex may exist in solution.

The energetics of HMG box interactions with DNA: thermodynamics of the DNA binding of the HMG box from mouse sox-5

The energetics of the Sox-5 HMG box interaction with DNA duplexes, containing the recognition sequence AACAAT, were studied by fluorescence spectroscopy, isothermal titration calorimetry (ITC) and differential scanning calorimetry (DSC). Fluorescence titration showed that the association constant of this HMG box with the duplexes is of the order 4x10(7) M(-1), increasing somewhat with temperature rise, i.e. the Gibbs energy is -40 kJ mol(-1) at 5 degrees C, decreasing to -48 kJ mol(-1) at 32 degrees C. ITC measurements of the enthalpy of association over this temperature range showed an endothermic effect below 17 degrees C and an exothermic effect above, suggesting a heat capacity change on binding of about -4 kJ K(-1) mol(-1), a value twice larger than expected from structural considerations. A straightforward interpretation of ITC data in heat capacity terms assumes, however, that the heat capacities of all participants in the association reaction do not change over the considered temperature range. Our previous studies showed that over the temperature range of the ITC experiments the HMG box of Sox-5 starts to unfold, absorbing heat and the heat capacities of the DNA duplexes also increase significantly. These heat capacity effects differ from that of the DNA/Sox-5 complex. Correcting the ITC measured binding enthalpies for the heat capacity changes of the components and complex yielded the net enthalpies which exhibit a temperature dependence of about -2 kJ K(-1) mol(-1), in good agreement with that predicted on the basis of dehydration of the protein-DNA interface. Using the derived heat capacity change and the enthalpy and Gibbs energy of association measured at 5 degrees C, the net enthalpy and entropy of association of the fully folded HMG box with the target DNA duplexes was determined over a broad temperature range. These functions were compared with those for other known cases of sequence specific DNA/protein association. It appears that the enthalpy and entropy of association of minor groove binding proteins are more positive than for proteins binding in the major groove. The observed thermodynamic characteristics of protein binding to the A+T-rich minor groove of DNA might result from dehydration of both polar and non-polar groups at the interface and release of counterions. The expected entropy of dehydration was calculated and found to be too large to be compensated by the negative entropy of reduction of translational/rotational freedom. This implies that DNA/HMG box association proceeds with significant decrease of conformational entropy, i.e. reduction in conformational mobility.

Analysis of the binding of hydroxamic acid and carboxylic acid inhibitors to the stromelysin-1 (matrix metalloproteinase-3) catalytic domain by isothermal titration calorimetry

Matrix metalloproteinases (MMPs) are implicated in diseases such as arthritis and cancer. Among these enzymes, stromelysin-1 can also activate the proenzymes of other MMPs, making it an attractive target for pharmaceutical design. Isothermal titration calorimetry (ITC) was used to analyze the binding of three inhibitors to the stromelysin catalytic domain (SCD). One inhibitor (Galardin) uses a hydroxamic acid group (pK(a) congruent with 8.7) to bind the active site zinc; the others (PD180557 and PD166793) use a carboxylic acid group (pK(a) congruent with 4.7). Binding affinity increased dramatically as the pH was decreased over the range 5.5-7.5. Experiments carried out at pH 6.7 in several different buffers revealed that approximately one and two protons are transferred to the enzyme-inhibitor complexes for the hydroxamic and carboxylic acid inhibitors, respectively. This suggests that both classes of inhibitors bind in the protonated state, and that one amino acid residue of the enzyme also becomes protonated upon binding. Similar experiments carried out with the H224N mutant gave strong evidence that this residue is histidine 224. DeltaG, DeltaH, DeltaS, and DeltaC(p) were determined for the three inhibitors at pH 6.7, and DeltaC(p) was used to obtain estimates of the solvational, translational, and conformational components of the entropy term. The results suggest that: (1) a polar group at the P1 position can contribute a large favorable enthalpy, (2) a hydrophobic group at P2' can contribute a favorable entropy of desolvation, and (3) P1' substituents of certain sizes may trigger an entropically unfavorable conformational change in the enzyme upon binding. These findings illustrate the value of complete thermodynamic profiles generated by ITC in discovering binding interactions that might go undetected when relying on binding affinities alone.

Predicting binding energetics from structure: looking beyond DeltaG degrees

Structure-based design of pharmaceuticals requires the ability to predict ligand affinity based on knowledge of structure. The primary term of interest is the binding affinity constant, K, or the free energy of binding, DeltaG degrees. It is common to attempt to predict DeltaG degrees based on empirically derived terms which represent common contributions such as the hydrophobic effect, hydrogen bonding, and conformational entropy. Although these approaches have met with some success, when they fail it is difficult to know which parameter(s) need refinement. Confidence in these approaches is also limited by the fact that DeltaG degrees typically is made up of compensating enthalpic and entropic terms, DeltaH degrees and DeltaS degrees, so that accurate prediction of a DeltaG degrees value may be fortuitous and may not indicate a reasonable understanding of the underlying relationship between structure and affinity. This is further complicated by the fact that both DeltaH degrees and DeltaS degrees are strongly temperature dependent through the heat capacity change, DeltaCp. In order to avoid these difficulties, we attempt to use structural data to predict DeltaH degrees, DeltaS degrees, and DeltaCp from which DeltaG degrees can be calculated as a function of temperature. The predictions are then compared to experimentally determined values. These calculations have been applied to several systems by ourselves and others. Systems include the binding of angiotensin II to an antibody, the dimerization of interleukin-8, and the binding of inhibitors to aspartic and serine proteases. Overall the calculations are very successful, and suggest that our understanding of the contributions of the hydrophobic effect, hydrogen bonding, and conformational entropy are quite good. Several of these systems show a strong dependence of the binding energetics on pH, indicative of changes in proton affinity of ionizable groups upon binding. It is critical to account for these protonation contributions to the binding energetics in order to assess the reliability of any computational prediction of energetics from structure. Methods have been developed for determining the energetics of proton binding using isothermal titration calorimetry. The availability of these methods provides a means of understanding how protein structure can modify the pKa's of ionizable groups. This information will further add to our understanding of structural energetic relationships and our ability accurately to predict binding affinities.

Structural bases of lectin-carbohydrate affinities: comparison with protein-folding energetics

We have made a comparative structure based analysis of the thermodynamics of lectin-carbohydrate (L-C) binding and protein folding. Examination of the total change in accessible surface area in those processes revealed a much larger decrease in free energy per unit of area buried in the case of L-C associations. According to our analysis, this larger stabilization of L-C interactions arises from a more favorable enthalpy of burying a unit of polar surface area, and from higher proportions of polar areas. Hydrogen bonds present at 14 L-C interfaces were identified, and their overall characteristics were compared to those reported before for hydrogen bonds in protein structures. Three major factors might explain why polar-polar interactions are stronger in L-C binding than in protein folding: (1) higher surface density of hydrogen bonds; (2) better hydrogen-bonding geometry; (3) larger proportion of hydrogen bonds involving charged groups. Theoretically, the binding entropy can be partitioned into three main contributions: entropy changes due to surface desolvation, entropy losses arising from freezing rotatable bonds, and entropic effects that result from restricting translation and overall rotation motions. These contributions were estimated from structural information and added up to give calculated binding entropies. Good correlation between experimental and calculated values was observed when solvation effects were treated according to a parametrization developed by other authors from protein folding studies. Finally, our structural parametrization gave calculated free energies that deviate from experimental values by 1.1 kcal/mol on the average; this amounts to an uncertainty of one order of magnitude in the binding constant.