Flexible-geometry conformational energy maps for the amino acid residue preceding a proline.

Previously calculated conformational energy maps suggest that the alpha-helical conformation for the residue preceding a proline is disfavored relative to the extended conformation by more than 7 kcal/mol. In known protein structures this conformation is observed, however, to occur for about 9% of all prolines. In addition, introduction or removal of prolines at theoretically unfavorable positions in proteins and peptides can have modest effects on stability and structure. To investigate the discrepancy between calculation and experiment, we have determined how the conformation of the proline affects the calculated energy. We have also explored the effect of bond length and bond angle relaxation on the conformational energy map. The conformational energy of the preceding residue is found to be unaffected by the conformation of the proline, but the effect of allowing covalent bond relaxation is dramatic. If bond lengths and angles, and dihedral angles within the pyrrolidine ring, are allowed to relax, a calculated energy difference between the alpha and beta conformations of 1.1 kcal/mol is obtained, in reasonable agreement with experiment. The detailed shape of the calculated energy surface is also in excellent agreement with the observed conformational distributions in known protein structures.     

On the role of the cis-proline residue in the active site of DsbA

In addition to the Cys-Xaa-Xaa-Cys motif at position 30-33, DsbA, the essential catalyst for disulfide bond formation in the bacterial periplasm shares with other oxidoreductases of the thioredoxin family a cis-proline in proximity of the active site residues. In the variant DsbA(P151A), this residue has been changed to an alanine, an almost isosteric residue which is not disposed to adopt the cis conformation. The substitution strongly destabilized the structure of DsbA, as determined by the decrease in the free energy of folding. The pKa of the thiol of Cys30 was only marginally decreased. Although in vivo the variant appeared to be correctly oxidized, it exhibited an activity less than half that of the wild-type enzyme with respect to the folding of alkaline phosphatase, used as a reporter of the disulfide bond formation in the periplasm. DsbA(P151A) crystallized in a different crystal form from the wild-type protein, in space group P2(1) with six molecules in the asymmetric unit. Its X-ray structure was determined to 2.8 A resolution. The most significant conformational changes occurred at the active site. The loop 149-152 adopted a new backbone conformation with Ala151 in a trans conformation. This rearrangement resulted in the loss of van der Waals interactions between this loop and the disulfide bond. His32 from the Cys-Xaa-Xaa-Cys sequence presented in four out of six molecules in the asymmetric unit a gauche conformation not observed in the wild-type protein. The X-ray structure and folding studies on DsbA(P151A) were consistent with the cis-proline playing a major role in the stabilization of the protein. A role for the positioning of the substrate is discussed. These important properties for the enzyme function might explain the conservation of this residue in DsbA and related proteins possessing the thioredoxin fold.     

Binding and release of cholesterol in the Osh4 protein of yeast

Sterols have been shown experimentally to bind to the Osh4 protein (a homolog of the oxysterol binding proteins) of Saccharomyces cerevisiae within a binding tunnel, which consists of antiparallel beta-sheets that resemble a beta-barrel and three alpha-helices of the N-terminus. This and other Osh proteins are essential for intracellular transport of sterols and ultimately cell life. Molecular dynamics (MD) simulations are used to study the binding of cholesterol to Osh4 at the atomic level. The structure of the protein is stable during the course of all MD simulations and has little deviation from the experimental crystal structure. The conformational stability of cholesterol within the binding tunnel is aided in part by direct or water-mediated interactions between the 3-hydroxyl (3-OH) group of cholesterol and Trp(46), Gln(96), Tyr(97), Asn(165), and/or Gln(181) as well as dispersive interactions with Phe(42), Leu(24), Leu(39), Ile(167), and Ile(203). These residues along with other nonpolar residues in the binding tunnel and lid contribute nearly 75% to the total binding energy. The strongest and most populated interaction is between Gln(96) and 3-OH with a cholesterol/Gln(96) interaction energy of -4.5 +/- 1.0 kcal/mol. Phe(42) has a similar level of attraction to cholesterol with -4.1 +/- 0.3 kcal/mol. A MD simulation without the N-terminus lid that covers the binding tunnel resulted in similar binding conformations and binding energies when compared with simulations with the full-length protein. Steered MD was used to determine details of the mechanism used by Osh4 to release cholesterol to the cytoplasm. Phe(42), Gln(96), Asn(165), Gln(181), Pro(211), and Ile(206) are found to direct the cholesterol as it exits the binding tunnel as well as Lys(109). The mechanism of sterol release is conceptualized as a molecular ladder with the rungs being amino acids or water-mediated amino acids that interact with 3-OH.     

Comparison of intramolecular and intermolecular reactions in protein folding

The intrinsic component of the standard free energy change for the formation of a disulfide bond in a protein molecule is compared to that for an analogous chemical reaction. The former reaction, which represents theintramolecular formation of a disulfide bond in a protein molecule from a cysteine group containing a mixed disulfide bond with glutathione, and a free cysteine residue, is a unimolecular reaction. In contrast, its chemical analogue is a bimolecular reaction, and corresponds to theintermolecular disulfide interchange between a mixed disulfide-bonded compound between a cysteine residue and glutathione, and a free cysteine molecule. The difference in the intrinsic free energy of the above two reactions is estimated by two different approaches. First, a theoretical estimate of the magnitude of the difference in free energy of the two reactions (for a standard state of 1 M) is obtained using a gas-phase statistical thermodynamic approach, which indicates that the intramolecular reaction is energetically favored over its intermolecular counterpart by as much as 15.6 kcal/mole. For comparison, an experimentally derived value is also obtained, using experimental data from a study by Konishi et al. of the regeneration of the protein ribonuclease A (RNase A) from its reduced form by reduced and oxidized glutathiones. The intrinsic component of the free energy change of the intramolecular reaction, as it occurs in the protein molecule, is obtained from such experimental data by accounting explicitly for the free energy change (assumed to be solely an entropy change) pertaining to the conformational changes (ring closure) that the protein molecule undergoes in the course of the reaction. On the basis of the value derived from such an experimental approach, the intramolecular reaction is also energetically more favorable as compared to its intermolecular analogue, but only by a difference of 2.3 kcal/mole (for a standard state of 1 M). The large apparent discrepancy between the two values estimated from the theoretical and experimental approaches is rationalized by the postulation of several additional factors not inherent in the gas-phase theoretical estimate, such as dehydration and intramolecular hydrogen-bonding effects, which can largely compensate for the otherwise favorable energetics of the intramolecular reaction.     

Combined use of molecular dynamics simulations and NMR to explore peptide bond isomerization and multiple intramolecular hydrogen-bonding possibilities in a cyclic pentapeptide, cyclo(Gly-Pro-D-Phe-Gly-Val).

The conformational behavior of a model cyclic pentapeptide--cyclo(Gly-L-Pro-D-Phe-Gly-L-Val)--has been explored through the combined use of in vacuo molecular dynamics simulations and a range of nmr experiments (preceding paper). The molecular dynamics analysis suggests that, despite the conformational constraints imposed by formation of the pentapeptide cycle, this pentapeptide undergoes conformational transitions between various hydrogen-bonded conformations, characterized by low energy barriers. An inverse gamma turn with Pro in position i + 1 and a gamma turn with D-Phe in position i + 1 are two alternatives occurring frequently. Like other DLDDL cyclic pentapeptides, cyclo(Gly-Pro-D-Phe-Gly-Val) is also stabilized by an inverse gamma-turn structure with the beta-branched Val residue in position i + 1, and this hydrogen bond is retained in the different conformational families. The gamma-turn around D-Phe3 and the inverse gamma turn around Val5 are consistent with the nmr observations. 3JNH-CH alpha coupling constants of the all-trans forms were calculated from one of the molecular dynamics trajectories and are comparable to nmr experimental data, suggesting that the conformational states visited during the simulation are representative of the conformational distribution in solution. In addition to the equilibrium among various hydrogen-bonded all-trans conformers, the observation in nmr spectra of two sets of resonances for all peptide protons indicated a slow conformational interconversion of the Gly-Pro peptide bond between trans and cis isomers. The activation energy between these two conformers was determined experimentally by magnetization transfer and was calculated by high temperature constrained molecular dynamics simulation. Both methods yield a free energy of activation of ca. 20 kcal/mol. Furthermore, the free energy of activation is dependent on the direction of rotation of the Gly-Pro peptide bond.     

Rotamer strain energy in protein helices - quantification of a major force opposing protein folding

It is widely believed that the dominant force opposing protein folding is the entropic cost of restricting internal rotations. The energetic changes from restricting side-chain torsional motion are more complex than simply a loss of conformational entropy, however. A second force opposing protein folding arises when a side-chain in the folded state is not in its lowest-energy rotamer, giving rotameric strain. chi strain energy results from a dihedral angle being shifted from the most stable conformation of a rotamer when a protein folds. We calculated the energy of a side-chain as a function of its dihedral angles in a poly(Ala) helix. Using these energy profiles, we quantify conformational entropy, rotameric strain energy and chi strain energy for all 17 amino acid residues with side-chains in alpha-helices. We can calculate these terms for any amino acid in a helix interior in a protein, as a function of its side-chain dihedral angles, and have implemented this algorithm on a web page. The mean change in rotameric strain energy on folding is 0.42 kcal mol-1 per residue and the mean chi strain energy is 0.64 kcal mol-1 per residue. Loss of conformational entropy opposes folding by a mean of 1.1 kcal mol-1 per residue, and the mean total force opposing restricting a side-chain into a helix is 2.2 kcal mol-1. Conformational entropy estimates alone therefore greatly underestimate the forces opposing protein folding. The introduction of strain when a protein folds should not be neglected when attempting to quantify the balance of forces affecting protein stability. Consideration of rotameric strain energy may help the use of rotamer libraries in protein design and rationalise the effects of mutations where side-chain conformations change.     

Energetics of a hydrogen bond (charged and neutral) and of a cation-pi interaction in apoflavodoxin.

Anabaena apoflavodoxin contains a single histidine residue (H34) that interacts with two aromatic residues (F7 and Y47). The histidine and phenylalanine rings are almost coplanar and they can establish a cation-pi interaction when the histidine is protonated. The histidine and tyrosine side-chains are engaged in a hydrogen bond, which is their only contact. We analyse the energetics of these interactions using p Ka-shift analysis, double-mutant cycle analysis at two pH values, and X-ray crystallography. The H/F interaction is very weak when the histidine is neutral, but it is strengthened by 0.5 kcal mol-1on histidine protonation. Supporting this fact, the histidine p Kain a F7L mutant is 0.4 pH units lower than in wild-type. The strength of the H/Y hydrogen bond is 0.7 kcal mol-1when the histidine is charged, and it becomes stronger (1.3 kcal mol-1) when the histidine is neutral. This is consistent with our observation that the (H34)Nepsilon2-OH(Y47) distance is slightly shorter in the apoflavodoxin structure at pH 9.0 than in the previously reported structure at pH 6.0. It is also consistent with a histidine p Kavalue 0.6 pH units higher in a Y47F mutant than in the wild-type protein. We suggest that the higher stability of the neutral hydrogen bond could be due to a higher desolvation penalty of the charged hydrogen bond that would offset its more favourable enthalpy of formation. The relationship between hydrogen bond strength and the contribution of hydrogen bonds to protein stability is discussed.     

Globular protein stability: aspects of interest in protein turnover

The conformational stability of globular proteins is remarkably low. Under physiological conditions, the native globular conformation is only from 5 to 15 kcal/mole more stable than unfolded conformations. In addition, small changes in the structure of a protein such as removing one terminal residue or cleaving a single peptide bond frequently lead to a substantial decrease in the stability. Likewise, single substitutions in the amino acid sequence can increase or decrease the stability by several kilocalories per mole. The low conformational stability of globular proteins and the sensitivity to small changes in structure suggest a possible role for conformational stability in the intracellular degradation of proteins. Several lines of evidence from in vivo studies of protein degradation are consistent with this idea.     

Folding of the twisted beta-sheet in bovine pancreatic trypsin inhibitor

The dominant role of local interactions has been demonstrated for the formation of the strongly twisted antiparallel beta-sheet structure consisting of residues 18-35 in bovine pancreatic trypsin inhibitor. Conformational energy minimization has indicated that this beta-sheet has a strong twist even in the absence of the rest of the protein molecule. The twist is maintained essentially unchanged when energy minimization is carried out by starting from the native conformation. By starting from a nontwisted beta-sheet conformation of residues 18-35, a strongly twisted structure (higher in energy than the native) is obtained. The high twist of the native-like beta-sheet is a consequence of its amino acid sequence, but it is enhanced strongly by interchain interactions that operate within the beta-sheet. The existence of the twisted beta-sheet structure does not require the presence of a disulfide bond between residue 14 and residue 38. It actually may facilitate the formation of this bond. Therefore, it is likely that the beta-sheet structure forms during an earlier stage of folding than the formation of this disulfide bond. This study provides an example of the manner in which conformational energy calculations can be used to provide information about the probable pathway of the folding of a protein.     

Atomistic and coarse-grained analysis of double spectrin repeat units: the molecular origins of flexibility

Spectrin is an ubiquitous protein in metazoan cells, and its flexibility is one of the keys to maintaining cellular structure and organization. Both alpha-spectrin and beta-spectrin polypeptides consist primarily of triple coiled-coil modular repeat units, and two important factors that determine spectrin flexibility are the bending flexibility between two consecutive repeat units and the conformational flexibility of individual repeat units. Atomistic molecular dynamics (MD) simulations are used here to study double spectrin repeat units (DSRUs) from the human erythrocyte beta-spectrin (HEbeta89) and the chicken brain alpha-spectrin (CBalpha1617). From the results of MD simulations, a highly conserved Trp residue in the A-helix of most repeat units that has been suggested to be important in conferring stability to the coiled-coil structures is found not to have a significant effect on the conformational flexibility of individual repeat units. Characterization of the bending flexibility for two consecutive repeats of spectrin via atomistic simulations and coarse-grained (CG) modeling indicate that the bending flexibility is governed by the interactions between the AB-loop of the first repeat unit, the BC-loop of the second repeat unit and the linker region. Specifically, interactions between residues in these regions can lead to a strong directionality in the bending behavior of two repeat units. The biological implications of these finding are discussed.     

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.     

Relationship between local and global stabilities of proteins: site-directed mutants and chemically-modified derivatives of cytochrome c.

The methionine 80 sulfur-heme iron bond of rat cytochrome c, whose stability is decreased by mutating the phylogenetically invariant residue proline 30 to alanine and increased when tyrosine 67 is changed to phenylalanine, recovers its wild-type characteristics when both substitutions are performed on the same molecule. Titrations with urea, analyzed according to the heteropolymer theory [Alonso, D. O. V., & Dill, K. A. (1991) Biochemistry 30, 5974-5985], indicate that both single mutations increase the solvent exposure of hydrophobic groups in the unfolded state, while in the double mutant this conformational perturbation disappears. Similar increases in solvent exposure of hydrophobic groups are observed when the sulfur-iron bond of the wild-type protein is broken by alkylation of the methionine sulfur, by high pH, or by binding the heme iron with cyanide. The compensatory effects of the two single mutations do not extend to the overall stability of the protein. The added loss of conformational stability due to the single mutations amounts to 7.3 kcal/mol out of the 9 kcal/mol representing the overall free energy of stabilization of the native conformation of the wild-type protein. The folded conformation of the doubly mutated protein is only 2 kcal/mol less stable than that of the wild type. These results indicate that the double mutant protein is able to retain the essential folding pattern of cytochrome c and the thermodynamic stability of the methionine sulfur-heme iron bond, in spite of structural differences that weaken the overall stability of the molecule.     

Increasing the conformational stability by replacement of heme axial ligand in c-type cytochrome

To investigate the role of the heme axial ligand in the conformational stability of c-type cytochrome, we constructed M58C and M58H mutants of the red alga Porphyra yezoensis cytochrome c(6) in which the sixth heme iron ligand (Met58) was replaced with Cys and His residues, respectively. The Gibbs free energy change for unfolding of the M58H mutant in water (DeltaG degrees (unf)=1.48 kcal/mol) was lower than that of the wild-type (2.43 kcal/mol), possibly due to the steric effects of the mutation on the apoprotein structure. On the other hand, the M58C mutant exhibited a DeltaG degrees (unf) of 5.45 kcal/mol, a significant increase by 3.02 kcal/mol compared with that of wild-type. This increase was possibly responsible for the sixth heme axial bond of M58C mutant being more stable than that of wild-type according to the heme-bound denaturation curve. Based on these observations, we propose that the sixth heme axial ligand is an important key to determine the conformational stability of c-type cytochromes, and the sixth Cys heme ligand will give stabilizing effects.     

D614G substitution at the hinge region enhances the stability of trimeric SARS-CoV-2 spike protein

Mutations in the spike protein of SARS-CoV-2 are the major causes for the modulation of ongoing COVID-19 infection. Currently, the D614G substitution in the spike protein has become dominant worldwide. It is associated with higher infectivity than the ancestral (D614)variant. We demonstrate using Gaussian network model-based normal mode analysis that the D614G substitution occurs at the hinge region that facilitates domain-domain motions between receptor binding domain and S2 region of the spike protein. Computer-aided mutagenesis and inter-residue energy calculations reveal that contacts involving D614 are energetically frustrated. However, contacts involving G614 are energetically favourable, implying the substitution strengthens residue contacts that are formed within as well as between protomers. We also find that the free energy difference (ΔΔG) between two variants is -2.6 kcal/mol for closed and -2.0 kcal/mol for 1-RBD up conformation. Thus, the thermodynamic stability has increased upon D614G substitution. Whereas the reverse mutation in spike protein structures having G614 substitution has resulted in the free energy differences of 6.6 kcal/mol and 6.3 kcal/mol for closed and 1-RBD up conformations, respectively, indicating that the overall thermodynamic stability has decreased. These results suggest that the D614G substitution modulates the flexibility of spike protein and confers enhanced thermodynamic stability irrespective of conformational states. This data concurs with the known information demonstrating increased availability of the functional form of spikeprotein trimer upon D614G substitution.     

Hydrogen bonding stabilizes globular proteins.

It is clear that intramolecular hydrogen bonds are essential to the structure and stability of globular proteins. It is not clear, however, whether they make a net favorable contribution to this stability. Experimental and theoretical studies are at odds over this important question. Measurements of the change in conformational stability, delta (delta G), for the mutation of a hydrogen bonded residue to one incapable of hydrogen bonding suggest a stabilization of 1.0 kcal/mol per hydrogen bond. If the delta (delta G) values are corrected for differences in side-chain hydrophobicity and conformational entropy, then the estimated stabilization becomes 2.2 kcal/mol per hydrogen bond. These and other experimental studies discussed here are consistent and compelling: hydrogen bonding stabilizes globular proteins.     

Theoretical study on isomerization and peptide bond cleavage at aspartic residue

Isomerization and peptide bond cleavage at aspartic residue (Asp) in peptide models have been reported. In this study, the mechanisms and energies concerning the isomerization and peptide bond cleavage at Asp residue were investigated by the density functional theory (DFT) at B3LYP/6-311++G(d,p). The integral equation formalism-polarizable continuum model (IEF-PCM) was utilized to calculate solvation effect by single-point calculation of the gas-phase B3LYP/6-311++G(d,p)-optimized structure. Mechanisms and energies of the dehydration in isomerization reaction of Asp residue were comparatively analyzed with the deamidation reaction of Asn residue. The results show that the succinimide intermediate was formed preferentially through the step-wise reaction via the tetrahedral intermediate. The cleavage at C-terminus is more preferential than those at N-terminus. In comparison to isomerization, peptide bond cleavage is ～20 kcal mol^?1 and lower in activation barrier than the isomerization. So, in this case, the isomerization of Asp is inhibited by the peptide bond cleavage.     

Restoration of structural stability and ligand binding after removal of the conserved disulfide bond in tear lipocalin

Disulfide bonds play diverse structural and functional roles in proteins. In tear lipocalin (TL), the conserved sole disulfide bond regulates stability and ligand binding. Probing protein structure often involves thiol selective labeling for which removal of the disulfide bonds may be necessary. Loss of the disulfide bond may destabilize the protein so strategies to retain the native state are needed. Several approaches were tested to regain the native conformational state in the disulfide-less protein. These included the addition of trimethylamine N-oxide (TMAO) and the substitution of the Cys residues of disulfide bond with residues that can either form a potential salt bridge or others that can create a hydrophobic interaction. TMAO stabilized the protein relaxed by removal of the disulfide bond. In the disulfide-less mutants of TL, 1.0 M TMAO increased the free energy change (ΔG⁰) significantly from 2.1 to 3.8 kcal/mol. Moderate recovery was observed for the ligand binding tested with NBD-cholesterol. Because the disulfide bond of TL is solvent exposed, the substitution of the disulfide bond with a potential salt bridge or hydrophobic interaction did not stabilize the protein. This approach should work for buried disulfide bonds. However, for proteins with solvent exposed disulfide bonds, the use of TMAO may be an excellent strategy to restore the native conformational states in disulfide-less analogs of the proteins.