Protection of an unstable reaction intermediate examined with linear free energy relationships in tyrosyl-tRNA synthetase

Linear free energy relationships (LFERs) are powerful tools in the search to understand the relationship between molecular structure and activity. They frequently link the changes in the rate constants for a reaction to changes in the equilibrium constant caused by alterations in structure. In physical-organic chemistry, these have been interpreted to give information on the structure of the transition state. Similar phenomena have been observed for reactions catalyzed by a series of engineered mutants of tyrosyl-tRNA synthetase from Bacillus stearothermophilus. LFERs are applied in this study to probe how the enzyme minimizes its side reactions. A linear free energy relationship is shown between the binding of the unstable enzyme-tyrosyl adenylate complex and its rate constant of hydrolysis. However, mutations of a key residue, His48, show significant deviation from the relationship, implying a role for the side chain in protection of the complex from hydroxide attack. A second linear free energy relationship is shown linking the rate and equilibrium constants for tyrosyl adenylate binding to the enzyme. Four distinct classes of mutation are discussed in the context of this relationship. The data from all but one of these groups of mutations conform well to a linear free energy relationship between the dissociation rate and dissociation equilibrium constants for the enzyme-tyrosyl adenylate complex with slope beta = 1.01 +/- 0.08. The specificity of binding of tyrosyl adenylate is determined solely by its dissociation rate constant of the intermediate, and the mutations have relatively little effect on the enzyme-tyrosyl adenylate association rate.(ABSTRACT TRUNCATED AT 250 WORDS)     

Potential of mean force for protein-protein interaction studies.

Calculating protein-protein interaction energies is crucial for understanding protein-protein associations. On the basis of the methodology of mean-field potential, we have developed an empirical approach to estimate binding free energy for protein-protein interactions. This knowledge-based approach has been used to derive distance-dependent free energies of protein complexes from a nonredundant training set in the Protein Data Bank (PDB), with a careful treatment of homology. We calculate atom pair potentials for 16 pair interactions, which can reflect the importance of hydrophobic interactions and specific hydrogen-bonding interactions. The derived potentials for hydrogen-bonding interactions show a valley of favorable interactions at a distance of approximately 3 A, corresponding to that of an established hydrogen bond. For the test set of 28 protein complexes, the calculated energies have a correlation coefficient of 0.75 compared with experimental binding free energies. The performance of the method in ranking the binding energies of different protein-protein complexes shows that the energy estimation can be applied to value binding free energies for protein-protein associations.     

An energetic scale for equilibrium H/D fractionation factors illuminates hydrogen bond free energies in proteins

Equilibrium H/D fractionation factors have been extensively employed to qualitatively assess hydrogen bond strengths in protein structure, enzyme active sites, and DNA. It remains unclear how fractionation factors correlate with hydrogen bond free energies, however. Here we develop an empirical relationship between fractionation factors and free energy, allowing for the simple and quantitative measurement of hydrogen bond free energies. Applying our empirical relationship to prior fractionation factor studies in proteins, we find: [1] Within the folded state, backbone hydrogen bonds are only marginally stronger on average in α‐helices compared to β‐sheets by ～0.2 kcal/mol. [2] Charge‐stabilized hydrogen bonds are stronger than neutral hydrogen bonds by ～2 kcal/mol on average, and can be as strong as –7 kcal/mol. [3] Changes in a few hydrogen bonds during an enzyme catalytic cycle can stabilize an intermediate state by –4.2 kcal/mol. [4] Backbone hydrogen bonds can make a large overall contribution to the energetics of conformational changes, possibly playing an important role in directing conformational changes. [5] Backbone hydrogen bonding becomes more uniform overall upon ligand binding, which may facilitate participation of the entire protein structure in events at the active site. Our energetic scale provides a simple method for further exploration of hydrogen bond free energies.     

Cooperativity effects in linear formaldehyde oligomers using density functional theory calculations

This work reports hydrogen bonding interaction in linear formaldehyde oligomers using density functional theory method. Many-body analysis technique has been used to study the various interactions in these oligomers and to obtain % contributions from individual many-body energy terms to the binding energies of these oligomers. Co-operativity effects are studied using different indicators viz. hydrogen bond strength, inter- and intramolecular distances, dissociation energy, dipole co-operativity, energy per hydrogen bond, excess energy and non-additive energy. All these indicators show strong positive hydrogen bond co-operativity in linear formaldehyde oligomers. The dipole moment changes from 2.51 D in monomer to 20.92 D in formaldehyde heptamer.     

What determines the van der Waals coefficient beta in the LIE (linear interaction energy) method to estimate binding free energies using molecular dynamics simulations?

Recently a semiempirical method has been proposed by Aqvist et al. to calculate absolute and relative binding free energies. In this method, the absolute binding free energy of a ligand is estimated as deltaGbind = alpha + beta, where Vel(bound) and Vvdw(bound) are the electrostatic and van der Waals interaction energies between the ligand and the solvated protein from an molecular dynamics (MD) trajectory with ligand bound to protein and Vel(free) and Vel(free) and Vvdw(free) are the electrostatic and van der Waals interaction energies between the ligand and the water from an MD trajectory with the ligand in water. A set of values, alpha = 0.5 and beta = 0.16, was found to give results in good agreement with experimental data. Later, however, different optimal values of beta were found in studies of compounds binding to P450cam and avidin. The present work investigates how the optimal value of beta depends on the nature of binding sites for different protein-ligand interactions. By examining seven ligands interacting with five proteins, we have discovered a linear correlation between the value of beta and the weighted non-polar desolvation ratio (WNDR), with a correlation coefficient of 0.96. We have also examined the ability of this correlation to predict optimal values of beta for different ligands binding to a single protein. We studied twelve neutral compounds bound to avidin. In this case, the WNDR approach gave a better estimate of the absolute binding free energies than results obtained using the fixed value of beta found for biotin-avidin. In terms of reproducing the relative binding free energy to biotin, the fixed-beta value gave better results for compounds similar to biotin, but for compounds less similar to biotin, the WNDR approach led to better relative binding free energies.     

Stability of a model beta-sheet in water.

We have used molecular dynamics simulations to determine the stability in water of a model beta-sheet formed by two alanine dipeptide molecules with two intermolecular hydrogen bonds in the closely spaced antiparallel arrangement. In this paper we describe our computations of the binding free energy of the model sheet and a portion of the free energy surface as a function of a reaction co-ordinate for sheet formation. We used the free energy surface to identify stable conformations along the reaction co-ordinate. To determine whether or not the model sheet with two hydrogen bonds is more stable than a single amide hydrogen bond in water, we compared the results of the present calculations to results from our earlier study of linear hydrogen bond formation between two formamide molecules (the formamide "dimer"). The free energy surfaces for the sheet and formamide dimer each have two minima corresponding to locally stable hydrogen-bonded and solvent-separated configurations. The binding free energies of the model sheet and the formamide dimer are -5.5 and -0.34 kcal/mol, respectively. Thus, the model sheet with two hydrogen bonds is quite stable while the simple amide hydrogen bond is only marginally stable. To understand the relative stabilities of the model sheet and formamide dimer in terms of solute-solute and solute-water interactions, we decomposed the free energy differences between hydrogen-bonded and solvent-separated conformations into energetic and entropic contributions. The changes in the peptide-peptide energy and the entropy are roughly twice as large for the sheet as they are for the formamide dimer. The magnitude of the peptide-water energy difference for the sheet is less than twice (by about 3.5 kcal/mol) that for the formamide dimer, and this accounts for the stability of the sheet. The presence of the side-chains and/or blocking groups apparently prevents the amide groups in the sheet from being solvated as favorably in the separated arrangement as in the formamide dimer, where the amide groups are completely exposed to the solvent.     

Free energy simulations and MM-PBSA analyses on the affinity and specificity of steroid binding to antiestradiol antibody

Antiestradiol antibody 57-2 binds 17beta-estradiol (E2) with moderately high affinity (K(a) = 5 x 10(8) M(-1)). The structurally related natural estrogens estrone and estriol as well synthetic 17-deoxy-estradiol and 17alpha-estradiol are bound to the antibody with 3.7-4.9 kcal mol(-1) lower binding free energies than E2. Free energy perturbation (FEP) simulations and the molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) method were applied to investigate the factors responsible for the relatively low cross-reactivity of the antibody with these four steroids, differing from E2 by the substituents of the steroid D-ring. In addition, computational alanine scanning of the binding site residues was carried out with the MM-PBSA method. Both the FEP and MM-PBSA methods reproduced the experimental relative affinities of the five steroids in good agreement with experiment. On the basis of FEP simulations, the number of hydrogen bonds formed between the antibody and steroids, which varied from 0 to 3 in the steroids studied, determined directly the magnitude of the steroid-antibody interaction free energies. One hydrogen bond was calculated to contribute about 3 kcal mol(-1) to the interaction energy. Because the relative binding free energies of estrone (two antibody-steroid hydrogen bonds), estriol (three hydrogen bonds), 17-deoxy-estradiol (no hydrogen bonds), and 17alpha-estradiol (two hydrogen bonds) are close to each other and clearly lower than that of E2 (three hydrogen bonds), the water-steroid interactions lost upon binding to the antibody make an important contribution to the binding free energies. The MM-PBSA calculations showed that the binding of steroids to the antiestradiol antibody is driven by van der Waals interactions, whereas specificity is solely due to electrostatic interactions. In addition, binding of steroids to the antiestradiol antibody 57-2 was compared to the binding to the antiprogesterone antibody DB3 and antitestosterone antibody 3-C4F5, studied earlier with the MM-PBSA method.     

Use of binding energy in catalysis analyzed by mutagenesis of the tyrosyl-tRNA synthetase

The utilization of enzyme-substrate binding energy in catalysis has been investigated by experiments on mutant tyrosyl-tRNA synthetases that have been generated by site-directed mutagenesis. The mutants are poorer enzymes because they lack side chains that form hydrogen bonds with ATP and tyrosine during stages of the reaction. The hydrogen bonds are not directly involved in the chemical processes but are at some distance from the seat of reaction. The free energy profiles for the formation of enzyme-bound tyrosyl adenylate and the equilibria between the substrates and products were determined from a combination of pre-steady-state kinetics and equilibrium binding methods. By comparison of the profile of each mutant with wild-type enzyme, a picture is built up of how the course of reaction is affected by the influence of each side chain on the energies of the complexes of the enzyme with substrates, transition states, and intermediates (tyrosyl adenylate). As the activation reaction proceeds, the apparent binding energies of certain side chains with the tyrosine and nucleotide moieties increase, being weakest in the enzyme-substrate complex, stronger in the transition state, and strongest in the enzyme-intermediate complex. Most marked is the interaction of Cys-35 with the 3'-hydroxyl of the ribose. Removal of the side chain of Cys-35 leads to no change in the dissociation constant of ATP but causes a 10-fold lowering of the catalytic rate constant. It contributes no net apparent binding energy in the E X Tyr X ATP complex and stabilizes the transition state by 1.2 kcal/mol and the E X Tyr-AMP complex by 1.6 kcal/mol.(ABSTRACT TRUNCATED AT 250 WORDS)     

Linear free energy relationship for the anomeric effect: MP2, DFT and ab initio study of 2-substituted-1,4-dioxanes

The anomeric effect of 2-substituted 1,4-dioxane derivatives was calculated and compared with the values for substituted cyclohexane. The bond lengths, bond angles, torsion angles, and relative energies of axial and equatorial conformers of 2-substituted 1,4-dioxanes were calculated by the second-order Møller–Plesset (MP2), density functional theory (DFT/B3LYP), and Hartree–Fock (HF) methods using 6-31G^∗ basis set. The energy differences between the axial and equatorial conformers, endo and exo-anomeric effects, repulsive non-bond and H-bonding interactions were investigated. A linear free energy relationship (LFER) between calculated (MP2/6-31G^∗) anomeric effect and inductive substituent constants (σ_I) was obtained for 2-substituted-1,4-dioxanes (slope = 6.19 and r² = 0.967). The calculated energy differences indicate lower equatorial orientation for 2-substituted-1,4-dioxanes compared to the 2-substituted-tetrahydropyrans. The contribution of resonance, hyperconjugation, inductive, steric, hydrogen bonding, electrostatic interaction, and level of theory influences the anomeric effect.     

On the interpretation of the observed linear free energy relationship in phosphate hydrolysis: a thorough computational study of phosphate diester hydrolysis in solution

The hydrolysis of phosphate esters is crucially important to biological systems, being involved in, among other things, signaling, energy transduction, biosynthesis, and the regulation of protein function. Despite this, there are many questions that remain unanswered in this important field, particularly with regard to the preferred mechanism of hydrolysis of phosphate esters, which can proceed through any of multiple pathways that are either associative or dissociative in nature. Previous comparisons of calculated and observed linear free energy relationships (LFERs) for phosphate monoester dianions with different leaving groups showed that the TS character gradually changes from associative to dissociative with the increasing acidity of the leaving group, while reproducing the experimental LFER. Here, we have generated ab initio potential energy surfaces for the hydrolysis of phosphate diesters in solution, with a variety of leaving groups. Once again, the reaction changes from a compact concerted pathway to one that is more expansive in character when the acidity of the leaving group increases. When such systems are examined in solution, it is essential to take into consideration the contribution of solute to the overall activation entropy, which remains a major computational challenge. The popular method of calculating the entropy using a quasi-harmonic approximation appears to markedly overestimate the configurational entropy for systems with multiple occupied energy wells. We introduce an improved restraint release approach for evaluating configurational entropies and apply this approach to our systems. We demonstrate that when this factor is taken into account, it is possible to reproduce the experimental LFER for this system with reasonable accuracy.     

Thermodynamic cycle analysis and inhibitor design against beta-lactamase

Beta-lactamases are the most widespread resistance mechanism to beta-lactam antibiotics, such as the penicillins and cephalosporins. Transition-state analogues that bind to the enzymes with nanomolar affinities have been introduced in an effort to reverse the resistance conferred by these enzymes. To understand the origins of this affinity, and to guide design of future inhibitors, double-mutant thermodynamic cycle experiments were undertaken. An unexpected hydrogen bond between the nonconserved Asn289 and a key inhibitor carboxylate was observed in the X-ray crystal structure of a 1 nM inhibitor (compound 1) in complex with AmpC beta-lactamase. To investigate the energy of this hydrogen bond, the mutant enzyme N289A was made, as was an analogue of 1 that lacked the carboxylate (compound 2). The differential affinity of the four different protein and analogue complexes indicates that the carboxylate-amide hydrogen bond contributes 1.7 kcal/mol to overall binding affinity. Synthesis of an analogue of 1 where the carboxylate was replaced with an aldehyde led to an inhibitor that lost all this hydrogen bond energy, consistent with the importance of the ionic nature of this hydrogen bond. To investigate the structural bases of these energies, X-ray crystal structures of N289A/1 and N289A/2 were determined to 1.49 and 1.39 A, respectively. These structures suggest that no significant rearrangement occurs in the mutant versus the wild-type complexes with both compounds. The mutant enzymes L119A and L293A were made to investigate the interaction between a phenyl ring in 1 and these residues. Whereas deletion of the phenyl itself diminishes affinity by 5-fold, the double-mutant cycles suggest that this energy does not come through interaction with the leucines, despite the close contact in the structure. The energies of these interactions provide key information for the design of improved inhibitors against beta-lactamases. The high magnitude of the ion-dipole interaction between Asn289 and the carboxylate of 1 is consistent with the idea that ionic interactions can provide significant net affinity in inhibitor complexes.     

Observation of a short, strong hydrogen bond in the active site of hydroxynitrile lyase from Hevea brasiliensis explains a large pKa shift of the catalytic base induced by the reaction intermediate

The hydroxynitrile lyase from Hevea brasiliensis (HbHNL) uses a catalytic triad consisting of Ser(80)-His(235)-Asp(207) to enhance the basicity of Ser(80)-O gamma for abstracting a proton from the OH group of the substrate cyanohydrin. Following the observation of a relatively short distance between a carboxyl oxygen of Asp(207) and the N delta(1)(His(235)) in a 1.1 A crystal structure of HbHNL, we here show by (1)H and (15)N-NMR spectroscopy that a short, strong hydrogen bond (SSHB) is formed between the two residues upon binding of the competitive inhibitor thiocyanate to HbHNL: the proton resonance of H-N delta 1(His(235)) moves from 15.41 ppm in the free enzyme to 19.35 ppm in the complex, the largest downfield shift observed so far upon inhibitor binding. Simultaneously, the D/H fractionation factor decreases from 0.98 to 0.35. In the observable pH range, i.e. between pH 4 and 10, no significant changes in chemical shifts (and therefore hydrogen bond strength) were observed for free HbHNL. For the complex with thiocyanate, the 19.35 ppm signal returned to 15.41 ppm at approximately pH 8, which indicates a pK(a) near this value for the H-N epsilon(2)(His(235)). These NMR results were analyzed on the basis of finite difference Poisson-Boltzmann calculations, which yielded the relative free energies of four protonation states of the His(235)-Asp(207) pair in solution as well as in the protein environment with and without bound inhibitor. The calculations explain all the NMR features, i.e. they suggest why a short, strong hydrogen bond is formed upon inhibitor binding and why this short, strong hydrogen bond reverts back to a normal one at approximately pH 8. Importantly, the computations also yield a shift of the free energy of the anionic state relative to the zwitterionic reference state by about 10.6 kcal/mol, equivalent to a shift in the apparent pK(a) of His(235) from 2.5 to 10. This huge inhibitor-induced increase in basicity is a prerequisite for His(235) to act as general base in the HbHNL-catalyzed cyanohydrin reaction.     

Role of DNA conformation & energetic insights in Msx-1-DNA recognition as revealed by molecular dynamics studies on specific and nonspecific complexes

In most of homeodomain–DNA complexes, glutamine or lysine is present at 50th position and interacts with 5th and 6th nucleotide of core recognition region. Molecular dynamics simulations of Msx-1–DNA complex (Q50-TG) and its variant complexes, that is specific (Q50K-CC), nonspecific (Q50-CC) having mutation in DNA and (Q50K-TG) in protein, have been carried out. Analysis of protein–DNA interactions and structure of DNA in specific and nonspecific complexes show that amino acid residues use sequence-dependent shape of DNA to interact. The binding free energies of all four complexes were analysed to define role of amino acid residue at 50th position in terms of binding strength considering the variation in DNA on stability of protein–DNA complexes. The order of stability of protein–DNA complexes shows that specific complexes are more stable than nonspecific ones. Decomposition analysis shows that N-terminal amino acid residues have been found to contribute maximally in binding free energy of protein–DNA complexes. Among specific protein–DNA complexes, K50 contributes more as compared to Q50 towards binding free energy in respective complexes. The sequence dependence of local conformation of DNA enables Q50/Q50K to make hydrogen bond with nucleotide(s) of DNA. The changes in amino acid sequence of protein are accommodated and stabilized around TAAT core region of DNA having variation in nucleotides.     

Structure-activity relationships in engineered proteins: analysis of use of binding energy by linear free energy relationships

The activity of mutant enzymes can be analyzed quantitatively by structure-activity relationships in a manner analogous to Br?nsted or Hammett plots for simple organic reactions. The slopes of such plots, the beta values, indicate for the enzymatic reactions the fraction of the overall binding energy used in stabilizing particular complexes. In particular, information can be derived about the interactions between the enzyme and the transition state. The activities of many mutant tyrosyl-tRNA synthetases fit well simple linear free energy relationships. The formation of enzyme-bound tyrosyl adenylate (E.Tyr-AMP) from enzyme-bound tyrosine and ATP (E.Tyr-ATP) results in an increase in binding energy between the enzyme and the side chain of tyrosine and the ribose ring of ATP. Linear free energy plots of enzymes mutated in these positions give the fraction of the binding energy change that occurs on formation of the transition state for the chemical reaction and the various complexes. It is shown that groups that specifically stabilize the transition state of the reaction are characterized by beta values much greater than 1. This is found for residues that bind the gamma-phosphate of ATP (Thr-40 and His-45) and have previously been postulated to be involved in transition-state stabilization.(ABSTRACT TRUNCATED AT 250 WORDS)     

Insight into the binding modes and inhibition mechanisms of adamantyl-based 1,3-disubstituted urea inhibitors in the active site of the human soluble epoxide hydrolase

Soluble epoxide hydrolase (sEH) is a promising new target for treating hypertension and inflammation. Considerable efforts have been devoted to develop novel inhibitors. In this study, the binding modes and interaction mechanisms of a series of adamantyl-based 1,3-disubstituted urea inhibitors were investigated by molecular docking, molecular dynamics simulations, binding free energy calculations, and binding energy decomposition analysis. Based on binding affinity, the most favorable binding mode was determined for each inhibitor. The calculation results indicate that the total binding free energy (ΔG_TOT, the sum of enthalpy ΔG_MM-GB/SA, and entropy ?TΔS) presents a good correlation with the experimental inhibitory activity (IC₅₀, r²?=?.99). The van der Waals energy contributes most to the total binding free energy (ΔG_TOT). A detailed discussion on the interactions between inhibitors and those residues located in the active pocket is made based on hydrogen bond and binding modes analysis. According to binding energy decomposition, the residues Asp333 and Trp334 contribute the most to binding free energy in all systems. Furthermore, Hip523 plays a major role in determining this class of inhibitor-binding orientations. Combined with the results of hydrogen bond analysis and binding free energy, we believe that the conserved hydrogen bonds play a role only in anchoring the inhibitors to the exact site for binding and the number of hydrogen bonds may not directly relate to the binding free energy. The results we obtained will provide valuable information for the design of high potency sEH inhibitors.     

Artificial protein cavities as specific ligand-binding templates: characterization of an engineered heterocyclic cation-binding site that preserves the evolved specificity of the parent protein.

Cavity complementation has been observed in many proteins, where an appropriate small molecule binds to a cavity-forming mutant. Here, the binding of compounds to the W191G cavity mutant of cytochrome c peroxidase is characterized by X-ray crystallography and binding thermodynamics. Unlike cavities created by removal of hydrophobic side-chains, the W191G cavity does not bind neutral or hydrophobic compounds, but displays a strong specificity for heterocyclic cations, consistent with the role of the protein to stabilize a tryptophan radical at this site. Ligand dissociation constants for the protonated cationic state ranged from 6 microM for 2-amino-5-methylthiazole to 1 mM for neutral ligands, and binding was associated with a large enthalpy-entropy compensation. X-ray structures show that each of 18 compounds with binding behavior bind specifically within the artificial cavity and not elsewhere in the protein. The compounds make multiple hydrogen bonds to the cavity walls using a subset of the interactions seen between the protein and solvent in the absence of ligand. For all ligands, every atom that is capable of making a hydrogen bond does so with either protein or solvent. The most often seen interaction is to Asp235, and most compounds bind with a specific orientation that is defined by their ability to interact with this residue. Four of the ligands do not have conventional hydrogen bonding atoms, but were nevertheless observed to orient their most polar CH bond towards Asp235. Two of the larger ligands induce disorder in a surface loop between Pro190 and Asn195 that has been identified as a mobile gate to cavity access. Despite the predominance of hydrogen bonding and electrostatic interactions, the small variation in observed binding free energies were not correlated readily with the strength, type or number of hydrogen bonds or with calculated electrostatic energies alone. Thus, as with naturally occurring binding sites, affinities to W191G are likely to be due to a subtle balance of polar, non-polar, and solvation terms. These studies demonstrate how cavity complementation and judicious choice of site can be used to produce a protein template with an unusual ligand-binding specificity.     

Probing the electronic structures and properties of neutral and anionic ScSi n (0,−1) (n = 1–6) clusters using ccCA-TM and G4 theory

We apply molecular docking, molecular dynamics (MD) simulation, and binding free energy calculation to investigate and reveal the binding mechanism between five xanthine inhibitors and DPP-4. The electrostatic and van der Waals interactions of the five inhibitors with DPP-4 are analyzed and discussed. The computed binding free energies using MM-PBSA method are in qualitatively agreement with experimental inhibitory potency of five inhibitors. The hydrogen bonds of inhibitors with Ser630 and Asp663 can stabilize the inhibitors in binding sites. The van der Waals interactions, especially the key contacts with His740, Asn710, Trp629, and Tyr666 have larger contributions to the binding free energy and play important roles in distinguishing the variant bioactivity of five inhibitors.     

Temperature-dependence of protein hydrogen bond properties as studied by high-resolution NMR

The temperature-dependence of a large number of NMR parameters describing hydrogen bond properties in the protein ubiquitin was followed over a range from 5 to 65 degrees C. The parameters comprise hydrogen bond (H-bond) scalar couplings, h3JNC', chemical shifts, amide proton exchange rates, 15N relaxation parameters as well as covalent 1JNC' and 1JNH couplings. A global weakening of the h3JNC' coupling with increasing temperature is accompanied by a global upfield shift of the amide protons and a decrease of the sequential 1JNC' couplings. If interpreted as a linear increase of the N...O distance, the change in h3JNC' corresponds to an average linear thermal expansion coefficient for the NH-->O hydrogen bonds of 1.7 x 10(-4)/K, which is in good agreement with overall volume expansion coefficients observed for proteins. A residue-specific analysis reveals that not all hydrogen bonds are affected to the same extent by the thermal expansion. The end of beta-sheet beta1/beta5 at hydrogen bond E64-->Q2 appears as the most thermolabile, whereas the adjacent hydrogen bond I3-->L15 connecting beta-strands beta1 and beta2 is even stabilized slightly at higher temperatures. Additional evidence for the stabilization of the beta1/beta2 beta-hairpin at higher temperatures is found in reduced hydrogen exchange rates for strand end residue V17. This reduction corresponds to a stabilizing change in free energy of 9.7 kJ/mol for the beta1/beta2 hairpin. The result can be linked to the finding that the beta1/beta2 hairpin behaves as an autonomously folding unit in the A-state of ubiquitin under changed solvent conditions. For several amide groups the temperature-dependencies of the amide exchange rates and H-bond scalar couplings are uncorrelated. Therefore, amide exchange rates are not a sole function of the hydrogen bond "strength" as given by the electronic overlap of donors and acceptors, but are clearly dependent on other blocking mechanisms.     

An empirical approach to protein conformation stability and flexibility

Experimental measurements of disulfide bond stability at various stages of protein folding are considered in terms of the effective concentrations of the thiol groups relative to each other; values of up to 10⁷M are observed, so that intramolecular interactions within the interior of a protein are much more stable, and provide greater stability to the folded conformation, than those on the surface or in a flexible segment. Intramolecular interactions can have substantially lower free energies than intermolecular, for solely entropic reasons; this implies that polar interactions, such as hydrogen bonds and salt bridges, can provide net stabilization to a folded conformation, in spite of the unfolded protein having intermolecular interactions with the solvent. These considerations can account for the lower free energy and enthalpy of the folded state and are useful for considering protein flexibility.