Molecular orbital calculations on the conformation of polypeptides and proteins. II. Conformational energy maps and stereochemical rotational states of aromatic residues

Our previous quantum-mechanical calculations, by an all-valence-electrons method (PCILO) taking into account simultaneously the σ and π electrons of the system, on the conformation energy maps of the glycyl and alanyl residues are extended to the evaluation of these maps and of the stereochemical rotational states of the aromatic residues, phenylalanyl, tyrosyl, histidyl, and tryptophanyl in dipeptides. Calculations on model compounds are used for the predetermination of the side-chain rotational angles χ₁ and χ₂ which are then used as selected parameters for the evaluation of the conformational energy maps as function of the backbone rotational angles Φ and ψ. The theory predicts that the most stable conformation for these aromatic residues should occur in the same region, around Φ = 200, ψ = 140°, in which it was predicted to occur for the glycyl and alanyl residues and which was completely overlooked by most of the previous “empirical” computations. Recent experimental work by a group of Russian authors using NMR and infrared techniques seems to confirm the theoretical result for the alanyl and phenylalanyl residues. The paper indicates also the secondary local minima which appear for the different residues. The theoretically allowed general conformational area for the four aromatic residues, within the reasonable value of 5 kcal/mole above the deepest minimum, is somewhat larger than the similar area allowed by the “hard sphere” empirical calculations. Practically all available representative experimental points from the study of small molecules and of the proteins lysozyme and myoglobin fall within the allowed area, the agreement being better with the results of the quantum mechanical calculations than with those of the “hard sphere” approximation. The values of the side-chain rotational angles χ₁ and χ₂ and of their allowed combinations agree less satisfactorily with experiment, the experimentally observed combinations being more varied than the theoretically allowed ones. These last ones having, however, been predetermined on studies with model compounds, this situation is not astonishing. It is proposed to refine these results by a minimization with respect to the four parameters Φ, ψ, χ₁, and χ₂ involved.     

The solution structure of gomesin, an antimicrobial cysteine-rich peptide from the spider.

Gomesin is the first peptide isolated from spider exhibiting antimicrobial activities. This highly cationic peptide is composed of 18 amino-acid residues including four cysteines forming two disulfide linkages. The solution structure of gomesin has been determined using proton two-dimensional NMR (2D-NMR) and restrained molecular dynamics calculations. The global fold of gomesin consists in a well-resolved two-stranded antiparallel betasheet connected by a noncanonical betaturn. A comparison between the structures of gomesin and protegrin-1 from porcine and androctonin from scorpion outlines several common features in the distribution of hydrophobic and hydrophilic residues. The N- and C-termini, the betaturn and one face of the betasheet are hydrophilic, but the hydrophobicity of the other face depends on the peptide. The similarities suggest that the molecules interact with membranes in an analogous manner. The importance of the intramolecular disulfide bridges in the biological activity of gomesin is being investigated.     

Molecular orbital calculations on the conformation of polypeptides and proteins. V. Conformational energy maps and stereochemical rotational states of aliphatic residues

The quantum-mechanical calculations by the PCILO method on the conformation of amino acid residues of proteins have been extended to the valyl, leucyl, and isoleucyl residues. In distinction to the earlier “empirical” computations, the quantum-mechanical results indicate very similar energy contours for the stable conformations of the three residues. Their general outline is also similar to that of the alanyl residue, although reduced by about 25%. Contrary to the “empirical” computations, the present results predict that the region corresponding to the α-helix should be one of great stability for the three residues and in particular for the valyl residue. The quantum-mechanical results are in excellent agreement with the experimental conformations of the aliphatic residues in lysozyme and myoglobin. Their prediction as to the ready availability of the valyl residue in the α-helical conformation agrees moreover with Ptitsyn's statistical evaluation of the participation of this residue in the inner turns of the helical regions in six globular proteins. The maximum conformational space allowed for the aliphatic residues is somewhat smaller than that allowed for the aromatic ones, while the minimum conformational space (region of stability common to all the residues) is similar in both groups.     

Conformation and hydrogen ion titration of proteins: a continuum electrostatic model with conformational flexibility.

A new method for including local conformational flexibility in calculations of the hydrogen ion titration of proteins using macroscopic electrostatic models is presented. Intrinsic pKa values and electrostatic interactions between titrating sites are calculated from an ensemble of conformers in which the positions of titrating side chains are systematically varied. The method is applied to the Asp, Glu, and Tyr residues of hen lysozyme. The effects of different minimization and/or sampling protocols for both single-conformer and multi-conformer calculations are studied. For single-conformer calculations it is found that the results are sensitive to the choice of all-hydrogen versus polar-hydrogen-only atomic models and to the minimization protocol chosen. The best overall agreement of single-conformer calculations with experiment is obtained with an all-hydrogen model and either a two-step minimization process or minimization using a high dielectric constant. Multi-conformational calculations give significantly improved agreement with experiment, slightly smaller shifts between model compound pKa values and calculated intrinsic pKa values, and reduced sensitivity of the intrinsic pKa calculations to the initial details of the structure compared to single-conformer calculations. The extent of these improvements depends on the type of minimization used during the generation of conformers, with more extensive minimization giving greater improvements. The ordering of the titrations of the active-site residues, Glu-35 and Asp-52, is particularly sensitive to the minimization and sampling protocols used. The balance of strong site-site interactions in the active site suggests a need for including site-site conformational correlations.     

Refinement of the thrombin-bound structure of a hirudin peptide by a restrained electrostatically driven Monte Carlo method.

Energy refinement of the structure of a linear peptide, hirudin56-65, bound to thrombin was carried out using a conformational search method in combination with restrained minimization. Five conformations originated from nmr data and distance geometry calculations having a similar global folding pattern but quite different backbone conformations were used as the starting structures. As a result of this approach, a series of low-energy conformations compatible with a set of upper and lower bounds of interproton distances determined from transferred nuclear Overhauser effects were found. A comparison among the lowest energy conformations of each run showed that the combination of energy refinement plus distance constraints led to a very well-defined structure for both the backbone and the side chains of the last 7 residues of the polypeptide. Furthermore, the low-energy conformations generated with this technique contain a segment of 3(10)-helix involving the last 5 residues at the COOH terminal end.     

Model for the differential stabilities of rhinovirus and poliovirus to mild acidic pH, based on electrostatics calculations.

Previous calculations of electrostatic interactions in the rhinovirus capsid have identified a subset of histidine residues, paired with lysine or arginine, that may be involved in pH-induced conformational changes related to viral uncoating. Further calculations with the finite difference method, accounting for the dielectric environment of the ionizable groups, suggest that charge burial in the crystal conformation will prevent protonation of these histidine residues in the pentamer-pentamer interface. Calculations with a modelled pentamer-pentamer interface in which three beta-strands are removed recover mildly acidic pKa values for the histidines. These results are discussed in the context of the structural interactions of these three beta-strands, which form a beta-sheet extension from the rest of the capsid, and with regard to the conformation of the homologous beta-sheet extension in poliovirus, which also possesses homologous histidine-lysine/arginine pairs. A model is developed in which the structural stability of the beta-sheet extension is related to the difference in acid stability of rhinovirus and poliovirus. It is suggested that, for poliovirus prior to cell receptor binding, the beta-sheet extension is stable at pH 3, the pentamer-pentamer interface histidines remain buried, and the virus is acid-stable. Cell receptor binding of poliovirus destabilizes the beta-sheet extension and the acid lability that is proposed to result could be involved in viral uncoating. For rhinovirus it is suggested that the observed conformational change in the absence of cell receptor binding involves a further acidic pH-activated process or conformational fluctuations that rearrange the beta-sheet extension and expose the pentamer-pentamer interface histidine residues to the acidic medium. Sequence analysis and electrostatics calculations reveal an aspartic acid in the beta-sheet extension that may have different pKa values in rhinovirus and poliovirus.     

Computer simulation of the conformational properties of retro-inverso peptides. II. Ab initio study, spatial electron distribution, and population analysis of N-formylglycine methylamide, N-formyl N'-acetyldiaminomethane, and N-methylmalonamide

Ab initio minimal and split-valence basis set calculations have been performed on compounds that are involved in retro–inverso modifications, i.e., gem-diaminoalkyl and malonyl structures. These calculations are compared with empirical force field calculations and the minor differences discussed. All calculations agree that the preferred helical conformation of the isolated gem-diaminoalkyl and malonyl derivatives of residues found in the retro-inverso modified peptides is 5–8 kcal/mol lower than the C conformation preferred by the isolated peptide residues. Population analysis and contour plots of the charge distribution are used to help explain the differences between the model compounds.     

The native state conformational ensemble of the SH3 domain from alpha-spectrin.

The folding/unfolding equilibrium of the alpha-spectrin SH3 domain has been measured by NMR-detected hydrogen/deuterium exchange and by differential scanning calorimetry. Protection factors against exchange have been obtained under native conditions for more than half of the residues in the domain. Most protected residues are located at the beta-strands, the short 3(10) helix, and part of the long RT loop, whereas the loops connecting secondary structure elements show no measurable protection. Apparent stability constants per residue and their corresponding Gibbs energies have been calculated from the exchange experiments. The most stable region of the SH3 domain is defined by the central portions of the beta-strands. The peptide binding region, on the other hand, is composed of a highly stable region (residues 53-57) and a highly unstable region, the loop between residues 34-41 (n-Src loop). All residues in the domain have apparent Gibbs energies lower than the global unfolding Gibbs energy measured by differential scanning calorimetry, indicating that under our experimental conditions the amide exchange of all residues in the SH3 domain occurs primarily via local unfolding reactions. A structure-based thermodynamic analysis has allowed us to predict correctly the thermodynamics of the global unfolding of the domain and to define the ensemble of conformational states that quantitatively accounts for the observed pattern of hydrogen exchange protection. These results demonstrate that under native conditions the SH3 domain needs to be considered as an ensemble of conformations and that the hydrogen exchange data obtained under those conditions cannot be interpreted by a two-state equilibrium. The observation that specific regions of a protein are able to undergo independent local folding/unfolding reactions indicates that under native conditions the scale of cooperative interactions is regional rather than global.     

Structural reorganization triggered by charging of Lys residues in the hydrophobic interior of a protein

Structural consequences of ionization of residues buried in the hydrophobic interior of proteins were examined systematically in 25 proteins with internal Lys residues. Crystal structures showed that the ionizable groups are buried. NMR spectroscopy showed that in 2 of 25 cases studied, the ionization of an internal Lys unfolded the protein globally. In five cases, the internal charge triggered localized changes in structure and dynamics, and in three cases, it promoted partial or local unfolding. Remarkably, in 15 proteins, the ionization of the internal Lys had no detectable structural consequences. Highly stable proteins appear to be inherently capable of withstanding the presence of charge in their hydrophobic interior, without the need for specialized structural adaptations. The extent of structural reorganization paralleled loosely with global thermodynamic stability, suggesting that structure-based pK(a) calculations for buried residues could be improved by calculation of thermodynamic stability and by enhanced conformational sampling.     

Prediction of functionally important residues based solely on the computed energetics of protein structure

Catalytic and other functionally important residues in proteins can often be mutated to yield more stable proteins. Many of these residues are charged residues that are located in electrostatically unfavorable environments. Here it is demonstrated that because continuum electrostatics methods can identify these destabilizing residues, the same methods can also be used to identify functionally important residues in otherwise uncharacterized proteins. To establish this point, detailed calculations are performed on six proteins for which good structural and mutational data are available from experiments. In all cases it is shown that functionally important residues known to be destabilizing experimentally are among the most destabilizing residues found in the calculations. A larger scale analysis performed on 216 different proteins demonstrates the existence of a general relationship between the calculated electrostatic energy of a charged residue and its degree of evolutionary conservation. This relationship becomes obscured when electrostatic energies are calculated using Coulomb's law instead of the more complete continuum electrostatics method. Finally, in a first predictive application of the method, calculations are performed on three proteins whose structures have recently been reported by a structural genomics consortium.     

Incorporating protein conformational flexibility into the calculation of pH-dependent protein properties.

A method for combining calculations of residue pKa's with changes in the position of polar hydrogens has been developed. The Boltzmann distributions of proton positions in hydroxyls and neutral titratable residues are found in the same Monte Carlo sampling procedure that determines the amino acid ionization states at each pH. Electrostatic, Lennard-Jones potentials, and torsion angle energies are considered at each proton position. Many acidic and basic residues are found to have significant electrostatic interactions with either a water- or hydroxyl-containing side chain. Protonation state changes are coupled to reorientation of the neighboring hydroxyl dipoles, resulting in smaller free energy differences between neutral and ionized residues than when the protein is held rigid. Multiconformation pH titration gives better agreement with the experimental pKa's for triclinic hen egg lysozyme than conventional rigid protein calculations. The hydroxyl motion significantly increases the protein dielectric response, making it sensitive to the composition of the local protein structure. More than one conformer per residue is often found at a given pH, providing information about the distribution of low-energy lysozyme structures.     

Changes in the electron density of the cofactor NADPH on binding to E. coli dihydrofolate reductase.

Quantum-mechanical electron density calculations reveal that a significant polarization is induced in the cofactor NADPH (reduced nicotinamide adenine dinucleotide phosphate) on binding to the enzyme dihydrofolate reductase. The calculations indicate that electron density corresponding to approximately 0.7 electron charges is shifted within the molecule, extending over more than 20 A. Further calculations on proposed enzyme mutants show that the polarization of NADPH on binding to DHFR is, in large part, induced by a motif of three positively charged residues. This motif was also identified to be directly responsible for the positive electrostatic potential surrounding the cofactor binding site in the enzyme. The possibility of this long-range polarization of NADPH was originally proposed based on a previous study of ligand binding to DHFR where a conserved structural motif of three positively charged residues was found to play a major role in polarizing the substrate folate over its entire length of 18 A.     

Distance calculation of residues neighbouring to lysozyme antigenic sites. Site-neighbouring residues whose evolutionary substitution can modify the characteristics and binding energy of the sites.

By using the antigenic structure of lysozyme determined in this laboratory and the X-ray co-ordinates we have calculated the closest-atom distances between each of the residues in the three antigenic sites and all the other amino acids of the lysozyme molecule. These calculations enabled us to identify the nearest neighbours to each of the site residues. Thus the immediate environment of each site residue is described. For the three antigenic sites there is a total of 71 neighbouring residues. The effects of evolutionary amino acid substitutions in site-neighbouring residues on the binding capacity of protein binding sites in general and on protein antigenic sites in particular are discussed. These, together with the direct replacements in site residues, will acount for the major effects. However, the limitations of this treatment are stressed. The smaller effects on antigenic sites of replacements at once-removed and even at more distant locations, which, when they become cumulative, could be considerable, are brought to attention, together with any influences of conformational readjustments that can take place as a result of evolutionary amino acid replacements.     

Influence of lysine content and pH on the stability of alanine-based copolypeptides

To account for the relative contributions of lysine and alanine residues to the stability of alpha-helices of copolymers of these two residues, conformational energy calculations were carried out for several hexadecapeptides at several pHs. All the calculations considered explicitly the coupling between the conformation of the molecule and the ionization equilibria as a function of pH. The total free energy function used in these calculations included terms that account for the solvation free energy and free energy of ionization. These terms were evaluated by means of a fast multigrid boundary element method. Reasonable agreement with experimental values was obtained for the helix contents and vicinal coupling constants ((3)J(HNalpha)). The helix contents were found to depend strongly on the lysine content, in agreement with recent experimental results of Williams et al. (Journal of the American Chemical Society, 1998, Vol. 120, pp. 11033-11043) In the lowest energy conformation computed for a hexadecapeptide containing 3 lysine residues at pH 6, the lysine side chains are preferentially hydrated; this decreases the hydration of the backbone CO and NH groups, thereby forcing the latter to form hydrogen bonds with each other in the helical conformation. The lowest energy conformation computed for a hexadecapeptide containing 6 lysine residues at pH 6 shows a close proximity between the NH3(+) groups of the lysine side chains, a feature that was previously observed in calculations of short alanine-based oligopeptides. The calculation on a blocked 16-mer of alanine shows a 7% helix content based on the Boltzmann averaged vicinal coupling constants computed from the dihedral angles phi, consistent with previous experimental evidence on triblock copolymers containing a central block of alanines, and with earlier theoretical calculations.     

Ab initio self-consistent x-ray absorption fine structure analysis for metalloproteins

X-ray absorption fine structure is a powerful tool for probing the structures of metals in proteins in both crystalline and noncrystalline environments. Until recently, a fundamental problem in biological XAFS has been that ad hoc assumptions must be made concerning the vibrational properties of the amino acid residues that are coordinated to the metal to fit the data. Here, an automatic procedure for accurate structural determination of active sites of metalloproteins is presented. It is based on direct multiple-scattering simulation of experimental X-ray absorption fine structure spectra combining electron multiple scattering calculations with density functional theory calculations of vibrational modes of amino acid residues and the genetic algorithm differential evolution to determine a global minimum in the space of fitting parameters. Structure determination of the metalloprotein active site is obtained through a self-consistent iterative procedure with only minimal initial information.     

Solution structure of Fe(II) cytochrome c551 from Pseudomonas aeruginosa as determined by two-dimensional 1H NMR.

The solution structure of Fe(II) cytochrome c551 from Pseudomonas aeruginosa based on 2D 1H NMR data is reported. Two sets of structure calculations were completed with a combination of simulated annealing and distance geometry calculations: one set of 20 structures included the heme-peptide covalent linkages, and one set of 10 structures excluded them. The main-chain atoms were well constrained within the two structural ensembles (1.30 and 1.35 A average RMSD, respectively) except for two regions spanning residues 30-40 and 60-70. The results were essentially the same when global fold comparisons were made between the ensembles with an average RMSD of 1.33 A. In total, 556 constraints were used, including 479 NOEs, 53 volume constraints, and 24 other distances. This report represents the first solution structure determination of a heme protein by 2D 1H NMR and should provide a basis for the application of these techniques to other proteins containing large prosthetic groups or cofactors.     

Ion channels in icosahedral virus: a comparative analysis of the structures and binding sites at their fivefold axes.

An analysis of the crystallographically determined structures of the icosahedral protein coats of Tomato Bushy Stunt Virus, Southern Bean Mosaic Virus, Satellite Tobacco Necrosis Virus, Human Rhinovirus 14 and Mengovirus around their fivefold axes is presented. Accessibilities surfaces, electrostatic energy profile calculations, ion-protein interaction energy calculations, free energy perturbation methods and comparisons with structures of chelating agents are used in this study. It is concluded that the structures built around the viral fivefold axes would be adequate for ion binding and transport. Relative ion preferences are derived for the binding sites, using free energy perturbation methods, which are consistent with the experimental data when available. In the cases where crystallographic studies determined the existence of ions on the fivefold axes, our results indicate that they would correspond to ions in crystallization or purification buffers. The environment of the fivefold axes are rich in polar residues in all icosahedral viral structures whose atomic coordinates are available, including some that are not being analyzed in detail in this work. The fivefold channel-like structures have most of the basic properties expected for real ion channels including a funnel at the entrance, a polar internal environment with frequent alternation of acidic and basic residues, ion binding sites, the capability to induce ion dehydration and ion transit from the external viral surface to the binding sites.     

Effect of trifluoroethanol on protein secondary structure: an NMR and CD study using a synthetic actin peptide.

The structure of a synthetic peptide comprising the 28 amino-terminal residues of actin has been examined by 1H-NMR and CD spectroscopy. The peptide is largely unstructured and flexible in solution but becomes increasingly structured at higher trifluoroethanol (TFE) concentrations. As judged by CD with the use of two additional peptides (actin 1-20 and actin 18-28), TFE induces formation of up to 48% helical content within residues 1-20, while residues 21-28 exhibit no helical propensity. Similar results were obtained by using NMR-derived distance information in restrained molecular dynamics calculations. The calculated structure of actin 1-28 peptide in 80% TFE is well defined for the first 23 residues with a backbone root mean square deviation of 0.5 A. Two helices are formed from residues 4-13 and 16-20, and a beta-turn is formed from residues 13-16. The N-terminal residues 1-3 exhibit increased flexibility and a helix-like conformation while the C-terminal residues 21-28 show no regular secondary structure. These results are compared with the predicted secondary structure and the structure of the corresponding sequence in the crystal structure of actin [Kabsch et al. (1990) Nature 347, 37-44]. The significance of the TFE-induced peptide structure is discussed.     

The solution structure of a DNA hairpin containing a loop of three thymidines determined by nuclear magnetic resonance and molecular mechanics.

We have determined by two-dimensional nuclear magnetic resonance studies and molecular mechanics calculations the three-dimensional solution structure of a 21 residue oligonucleotide capable of forming a hairpin structure with a loop of three thymidine residues. This structure is in equilibrium with a duplex form. At 33 degrees C, low ionic strength and in the presence of MgCl2 the hairpin form dominates in solution. Six Watson-Crick base pairs are formed topped by the loop structure. The residues 1-3 and 18-21 are not complementary and form dangling ends. Distance constraints have been derived from nuclear Overhauser enhancement measurements. These, together with molecular mechanics calculations, have been used to determine the structure. We do not observe stacking of thymidine residues either over the 3' or the 5' end of the stem.     

Improving macromolecular electrostatics calculations.

Electrostatic interactions play a key role in many aspects of protein engineering. Consequently, much effort has been put into the design of software for calculating electrostatic fields around macromolecules. We show that optimization of hydrogen bonding networks can improve both the results of pK(a) calculations and the results of electrostatic calculations performed by commonly used programs such as DelPhi. Further optimization can often be achieved by flipping the side chains of asparagine, histidine and glutamine around their chi2, chi2 and chi3 torsion angles, respectively, when this improves the local hydrogen bonding network. These optimizations are applied to some well characterized proteins: BPTI, hen egg white lysozyme and superoxide dismutase. A search for flipped residues in the PDB revealed that significant improvements in electrostatic calculations in or near the active site of enzymes can be expected for about one quarter of all enzymes in the PDB.