Conformational behavior of α,α-dialkylated peptides

The preferred conformations of N-acetyl-N′-methyl amides of some dialkylglycines have been determined by empirical conformational-energy calculations; minimum-energy conformations were located by minimizing the energy with respect to all the dihedral angles of the molecules. The conformational space of these compounds is sterically restricted, and low-energy conformations are found only in the regions of fully extended and helical structures. Increasing the bulkiness of the substituents on the C^α, the fully extended conformation becomes gradually more stable than the helical structure preferred in the cases of dimethylglycine. This trend is, however, strongly dependent on the bond angles between the substituents on the C^α atom: In particular, helical structures are favored by standard values (111°) of the N-C^α-C′ angle, while fully extended conformations are favored by smaller values of the same angle, as experimentally observed, for instance, in the case of α,α-di-n-propylglycine.     

Conformational dependence of vicinal 13C′NCαH coupling constants in peptides: A dirac vector model investigation

Theoretical calculations of the heteronuclear vicinal coupling constant ³J(¹³C′NC^αH) in peptides have been carried out using the Dirac vector model. The results showed an angular dependence for this coupling constant, which can be expressed in the form ³J(¹³C′NC^αH) = A cos² θ + B cos θ + C, where A, B, and C are constants and θ is related to the torsional angle ? of the peptide backbone. The results of the present calculations are in very good agreement with those obtained using finite perturbation theory at the INDO level of approximation.     

Conformational dependence of the vicinal proton coupling constant for the Cα?Cβ bond in peptides

We use the nmr data concerning the C^αH? C^βH fragment in eight peptides with rigid side chains to parametrize a Karplus correlation between the vicinal proton J_αβ coupling constant and the dihedral angle θ. When considering molecules containing the fragment C^αH^α? C^βH^βH^β′, the three-dimensional structure of the model peptides does not need to be known with accurate precision, since each set of J_αβ and J_αβ′ coupling constants is then related to the coefficients of the Karplus equation. A good correlation is observed with the Karplus equation, which is in substantial agreement with the J_αβ coupling constants reported for rigid as well as rotating C^α? C^β bonds in peptides.     

NMR study of the structure of short-chain peptides in solution.

The electron-mediated spin–spin coupling constant J between the amide NH and the α-CH protons in the dipeptide fragment C^α? CO(NH? C^αH)R? C′ONH? C^α is dependent on the dihedral angle of rotation (Φ) around the N? C bond. Measurement of J in a series of zwitterionic dipeptides H₃N⁺? CHR₁? CONH? CHR₂? CO₂^? (which is conformationally similar to the dipeptide fragment) in TFA solution shows that J is independent of R₁, but dependent on the steric bulk of R₂. The data are interpreted in terms of a model that assumes that what we measure is an average value of J? a thermal average over all the possible rotamers. The groups R₁ and R₂ are, in most cases, sterically kept apart by the trans and planar amide bonds, and hence the independence of J of R₁. This model is consistent with the theoretical calculations done on the dipeptide fragment. The effect of the structural characteristics of the side chains (e.g., the effect of lengthening and branching the side chains) on the J values in dipeptides is discussed in the light of the existing results of theoretical calculations. Study of 〈J〉 values in tripeptides (C₆H₅CH₂OCONH? CHR₁? CONH? CHR₂? CO₂CH₃, essentially three linked peptide units) shows that electrostatic interaction between the two amide bonds modifies the potential energy surface and the 〈J〉 value of a dipeptide subunit in the tripeptides. Also in some cases, direct steric interaction between the two side chains in the two adjacent dipeptide subunits in the tripeptide affects the potential energy surfaces of the individual dipeptide subunits and hence the 〈J〉 values. The influence of the structural characteristics of the side chains of individual amino acids on structure formation at or beyond the dipeptide level is discussed at various points. The J(NH? ^αCH) values of CH₃CONH? CHR? CONH₂ and CH₃CONH? CHR? CO₂CH₃ with the same R are quite different for R = valine, leucine, phenylalanine, methionine, but equal for R = glycine. This, coupled with the fact that one of the carboxamide NH resonances has a chemical shift different from its counterpart in simple amides like CH₃CONH₂ and the other carboxamide NH has the same chemical shift as its counterpart in CH₃CONH₂, suggest the presence of a hydrogen bond in dipeptide CH₃CONH? CHR? CONH₂ with carboxamide NH as the donor. Theoretical evidence for two seven-membered hydrogen-bonded rings with the carboxamide NH as donor and the acetyl oxygen as acceptor is summarized. Our data cannot suggest the number of such hydrogen-bonded rings, nor can they conclude the relative proportion of these rings in a particular dipeptide. A discussion of the difficulty of interpretation is presented and the data are discussed under certain simplifying assumptions.     

Conversion from a virtual-bond chain to a complete polypeptide backbone chain

A method for generating a complete polypeptide backbone structure from a set of C^α coordinates is presented. Initial trial values of ? and ψ for a selected residue are chosen (essentially from an identification of the conformational region of the virtual-bond backbone, e.g., and α-helical region), and values of ? and ψ for the remaining residues (both towards the N- and C-terminus) are then computed, subject to the constraint that the chain have the same virtual-bond angles and virtual-bond dihedral angles as the given set of C^α coordinates. The conversion from C^α coordinates to full backbone dihedral angles (?,ψ) involves the solution of a set of algebraic equations relating the virtual-bond angles and virtual-bond dihedral angles to standard peptide geometry and backbone dihedral angles. The procedure has been tested successfully on C^α coordinates taken from standard-geometry full-atom structures of bovine pancreatic trypsin inhibitor (BPTI). Some difficulty was encountered with error-sensitive residues, but on the whole the backbone generation was successful. Application of the method to C^α coordinates for BPTI derived from simplified model calculations (involving nonstandard geometry) showed that such coordinates may be inconsistent with the requirement that ?_Pro be near ?75°. In such a case, i.e., for residues for which the algebraic method failed, a leastsquares minimizer was then used in conjunction with the algebraic method; the mean-square deviation of the calculated C^α coordinates from the given ones was minimized by varying the backbone dihedral angles. Thus, these inconsistencies were circumvented and a full backbone structure whose C^α coordinates had an rms deviation of 0.26 Å from the given set of C^α coordinates was obtained.     

Flexibility of the pyrrolidine ring in proline peptides

A survey of over 50 crystal structures indicates that both imino acid and peptide derivatives of proline populate ring conformers consistent with the torsional potentials about single bonds. In both cases, lower barriers for rotation about C? N bonds relative to those about C? C bonds favor smaller values for dihedral angles about the former bonds. In peptides a minimum in the torsional potential about C? N bonds occurs at zero dihedral angle, further favoring small angles. The pyrrolidine-ring dihedral angles of the proline compounds in the solid state obey a cyclopentane-type pseudorotation function. Thus the puckering of the five-membered ring can be quantitatively described by two parameters. Consistent with small dihedral angles about C? N bonds, C^β and/or C^γ are puckered out of the mean plane of the ring in nearly all of the nonstrained compounds. Utilizing the consistent force-field method of Lifson and coworkers [see A. Warshel, M. Levitt, and S. Lifson (1970) J. Mol. Spectrosc. 33 , 84] the intramolecular energy of five proline peptides was minimized with respect to all internal coordinates. In addition, the energy surface near minima was explored by constraining a particular dihedral angle and reminimizing the energy with respect to all remaining variables. In linear peptides two types of pyrrolidine-ring conformers have identical predicted energies. In the cyclic dipeptide cyclo (Pro-Gly) one of the ring conformers is favored by about 3 kcal/mol, while the cyclic tripeptide cyclo(Pro-Gly-Gly) favors the other conformer by a comparable margin. In agreement with observations in the solid state and in solution, C^β and/or C^γ are puckered in the predicted conformers. A correlation between proline Φ and the details of the puckered conformation was predicted and found to match precisely conformers observed in crystals. For the diamides N-acetyl-L -proline-N′-methyl-amide and N-acetyl-L -proline-N′,N′-dimethylamide (AcProMe₂A) 30% and 60% cis acetyl peptide bonds were predicted in good agreement with observations in nonpolar solvents for the respective compounds. The conformational distributions with respect to proline Ψ are also in accord with experimental observations. For AcProMe₂A, a model for a -Pro-Pro-sequence in a peptide chain, this study is the first to predict stable conformers for proline Ψ either ca. ?50° or 140° for both cis and trans peptides.     

Conformational dependence of <Superscript>13</Superscript>C shielding and coupling constants for methionine methyl groups

Methionine residues fulfill a broad range of roles in protein function related to conformational plasticity, ligand binding, and sensing/mediating the effects of oxidative stress. A high degree of internal mobility, intrinsic detection sensitivity of the methyl group, and low copy number have made methionine labeling a popular approach for NMR investigation of selectively labeled protein macromolecules. However, selective labeling approaches are subject to more limited information content. In order to optimize the information available from such studies, we have performed DFT calculations on model systems to evaluate the conformational dependence of ³ J _CSCC, ³ J _CSCH, and the isotropic shielding, σ_iso. Results have been compared with experimental data reported in the literature, as well as data obtained on [methyl-¹³C]methionine and on model compounds. These studies indicate that relative to oxygen, the presence of the sulfur atom in the coupling pathway results in a significantly smaller coupling constant, ³ J _CSCC/³ J _COCC ~ 0.7. It is further demonstrated that the ³ J _CSCH coupling constant depends primarily on the subtended CSCH dihedral angle, and secondarily on the CSCC dihedral angle. Comparison of theoretical shielding calculations with the experimental shift range of the methyl group for methionine residues in proteins supports the conclusion that the intra-residue conformationally-dependent shift perturbation is the dominant determinant of δ¹³Cε. Analysis of calmodulin data based on these calculations indicates that several residues adopt non-standard rotamers characterized by very large ~100° χ³ values. The utility of the δ¹³Cε as a basis for estimating the gauche/trans ratio for χ³ is evaluated, and physical and technical factors that limit the accuracy of both the NMR and crystallographic analyses are discussed.     

Calculations of binding affinity between C8-substituted GTP analogs and the bacterial cell-division protein FtsZ

The FtsZ protein is a self-polymerizing GTPase that plays a central role in bacterial cell division. Several C8-substituted GTP analogs are known to inhibit the polymerization of FtsZ by competing for the same binding site as its endogenous activating ligand GTP. Free energy calculations of the relative binding affinities to FtsZ for a set of five C8-substituted GTP analogs were performed. The calculated values agree well with the available experimental data, and the main contribution to the free energy differences is determined to be the conformational restriction of the ligands. The dihedral angle distributions around the glycosidic bond of these compounds in water are known to vary considerably depending on the physicochemical properties of the substituent at C8. However, within the FtsZ protein, this substitution has a negligible influence on the dihedral angle distributions, which fall within the narrow range of −140° to −90° for all investigated compounds. The corresponding ensemble average of the coupling constants ³ J(C4,H1′) is calculated to be 2.95 ± 0.1 Hz. The contribution of the conformational selection of the GTP analogs upon binding was quantified from the corresponding populations. The obtained restraining free energy values follow the same trend as the relative binding affinities to FtsZ, indicating their dominant contribution.     

The nonplanar peptide unit. IV. Geometry and nonplanar distortions of the cis-peptide unit

Semiempirical quantum chemical calculations were carried out using the CNDO/2 and the INDO methods on the model compound cis-N-methylacetamide in order to get an insight into the problem of possible nonplanar distortions of the cis-peptide unit. In addition, the crystal structure data of cyclic peptides containing cis-peptide units were analyzed. These studies have indicated that the dihedral angles θ_N and Δ_ω are correlated approximately by the relation Δ_ω = ?θ_N, whereas θ_C is small and is uncorrelated with Δ_ω, as was found in the case of the trans-peptide unit. Both theory and crystal data suggest that out-of-plane distortions at the nitrogen atom of the peptide unit were quite likely to occur and should be included in the conformational calculations. The average geometry for the planar cis-peptide unit has also been obtained from the observed examples.     

Association studies of N-acetyl-amino acid N,N-dimethylamides in carbon tetrachloride

The self-association of N-acetylglycine N,N-dimethylamide, N-acetyl-L -valine N,N-dimethylamide, and N-acetyl-L -phenylalanine N,N-dimethylamide in carbon tetrachloride was investigated by using ir and ¹H-nmr methods. It was concluded from ir measurements that the associated species is the dimer formed as a result of the simultaneous formation of two intermolecular hydrogen bonds. This is supported by the results of ¹H-nmr measurements. Thermodynamic quantities for the association were determined from the temperature and concentration dependence of the NH proton chemical shifts of the sample solutions. Compared with the Gly derivative, L -Val and L -Phe derivatives have larger values of ?ΔH for association, which shows good correlation with Δv_NH values, the difference between the maxima of the monomer and dimer bands, obtained from ir spectra. This is due to the less stable monomer conformation and to the stronger intermolecular hydrogen bonding of the dimers in L -Val and L -Phe derivatives. The line shapes of both methyl proton resonances of L -Val residue and methylene proton resonances of L -Phe residue were found to vary with concentration and temperature of the sample solutions. These data indicate that the rotation about the C^α—C^β bond is restricted by the steric hindrance present in the associated dimers. All these experimental results can be related to the fact that L -Val and L -Phe derivatives have a warped framework because of the bulky side chains, whereas the Gly derivative has a planar framework.     

Conformational analysis of thyrotropin releasing factor by proton magnetic resonance spectroscopy

The proton magnetic resonance spectrum of thyrotropin releasing factor (TRF) in solution in deuterium oxide and deuterated dimethylsulfoxide (DMSO–d₆) has been analyzed. Two forms differing in cis–trans isomerism about the His-Pro peptide bond are observed. From the temperature dependence of chemical shift of the amide protons, it is concluded that TRF in DMSO–d₆ does not contain intramolecular hydrogen bonds. Measurement of NH? C_αH coupling constant provides an estimate of the histidine dihedral angle ?. Structural information about the histidine side-chain is deduced from C_αH? C_βH coupling constants and from the nonequivalence of the two prolyl δ-protons. In DMSO–d₆, there is evidence for a tautomeric equilibrium corresponding to an exchange of imidazole proton between the two nitrogen atoms N-δ and N-ε. In water, the N-εH tautomer is found to be the predominant tautomeric form of the imidazole ring. These results in combination with energy calculation, vibrational analysis, and carbon nmr studies allow the determination of the conformationof TRF.     

Structural versatility of peptides from Cα,α-dialkylated glycines. I. A conformational energy computation and x-ray diffraction study of homo-peptides from Cα,α-diethylglycine

Conformational energy computations on a derivative and a homo-dipeptide of C^α,α-diethylglycine were performed. In both cases the N- and C-terminal groups are blocked as acetamido and methylamido moieties, respectively. It was found that the C^α,α-diethylglycine residues are conformationally restricted and that the minimum energy conformation corresponds to the fully extended C₅ structure when the N? C^α? C′ bond angle is smaller than 108° (as experimentally observed). The results of the theoretical analysis are in agreement with the crystal-state structural propensity of the complete series of N-trifluoroacetylated homo-peptides of this C^α,α-dialkylated residue from monomer to pentamer, determined by x-ray diffraction and also described in this work. Interestingly, for the first time, a crystallographically planar peptide backbone was observed (in the protected tripeptide). A comparison with peptides of C^α,α-dimethylglycine, C^α-methyl, C^α-ethylglycine, and C^α,α-di-n-propylglycine indicates that the fully extended conformation becomes more stable than the helical structures when both amino acid side-chain C^β atoms are substituted.     

Asymmetric Karplus curves for the protein side-chain <Superscript>3</Superscript><Emphasis Type="Italic">J</Emphasis> couplings

The standard Karplus equation for calculating ³ J coupling constants from any given dihedral angle requires three empirical coefficients be determined that relate to the magnitudes of three modes of the angle dependency of ³ J. Considering cosine modes only (bimodal, unimodal and baseline component), Karplus curves are generally symmetric with respect to the sign of the angle argument. Typically, their primary and secondary maxima differ in amplitude, whereas the two minima are of equal depth. However, chiral molecular topologies, such as those surrounding the main-chain and side-chain torsions in amino-acid residues, preclude, as regards substituent positioning, exact mirror-image conformations from being formed—for any given torsion-angle value. It is therefore unlikely that ³ J couplings assume identical values for the corresponding positive and negative dihedral angles. This suggests that a better empirical fit of the torsion-angle dependency of ³ J could be obtained when removing the constraint of symmetrically identical coupling constants. A sine term added to the Karplus equation allows independent modelling of both curve minima typically located near dihedral-angle values of +90° and −90°. Revisiting an extensive ³ J coupling dataset previously recorded to determine the side-chain torsions χ₁ in the protein flavodoxin, the asymmetric Karplus model accomplishes a more accurate fit to the experimental data. Asymmetries revealed in the angle dependencies exceed the experimental precision in determining ³ J. Accounting for these effects helps improve molecular models. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Quantitative two-dimensional nmr study of dermenkephalin,a highly potent and selective δ-opioid peptide

Dermenkephalin, H-Tyr-(D ) Met-Phe-His-Leu-Met-Asp-NH₂, a highly potent and selective δ-opioid peptide isolated from frog skin, was studied in DMSO-d₆ solution by two-dimensional nmr spectroscopy, including the determination of NH temperature coefficients, the evaluation of ³J coupling constants from phase-sensitive correlated spectroscopy (COSY) and the volumes of nuclear Overhauser effect (NOE) correlations. The two-dimensional NOE spectroscopy (NOESY) spectrum of dermenkephalin revealed sequential, medium-, and long-range effects. To put this information on a quantitative basis, special attention was devoted to J cross-peak suppression, quantification of the NOE volumes and analysis of the overlaps, normalization of the NOEs against diagonal peaks and H_ββ′ geminal interactions. Although most of the dihedral angles deduced from the ³J_Nα coupling constants together with several N_iα_i and α_iN_{i + 1} NOEs pointed to a partially extended peptide backbone, several N_i N_{i + 1} NOEs and β_i N_{i + 1} interactions argued in favor of a folded structure. Moreover, several long-range correlations of strong intensities were found that supported a close spatial proximity between the side chains of D -Met² and Met⁶, Tyr¹ and His⁴, Tyr¹ and Asp⁷, and His⁴ and the C-terminal amide group. In Phe, the g^? rotamer in the side chain is deduced from the ³J_αβ coupling constants and αβ and Nβ NOE correlations. Whereas the amide proton dependency was not indicative of stable hydrogen bonds, the nonuniform values of the temperature coefficient may reflect an equilibrium mixture of folded and extended conformers. The overall data should provide realistic starting models for energy minimization and modelization studies. © 1993 John Wiley & Sons, Inc.     

Structural versatility of peptides from Cα,α-dialkylated glycines. II. An IR absorption and 1H-nmr study of homo-oligopeptides from Cα,α-diethylglycine

The conformational preferences of the N-trifluoroacetylated homo-peptides of C^α,α-diethylglycine from monomer to pentamer in chloroform solution were determined by using ir absorption and ¹H-nmr. Intramolecular hydrogen bonding was found to be the dominant factor for all NH groups. The likely absence of a conformational transition upon increasing main-chain length, and the remarkable stability to dilution, heating, and addition of perturbing agents, are additional relevant findings of this study. These results are in agreement with those of the fully extended, C₅-conformation-forming homo-peptides from the higher homolog C^α,α-di-n-propylglycine, but contrast dramatically to those of the homo-peptides from the lower homolog C^α,α-dimethylglycine, which have been shown to adopt the 3₁₀-helical structure.     

A dihedral angle-vicinal proton coupling constant correlation for the α–β bond of amino acid residues

A coupling constant-dihedral angle correlation for the H? Cα? Cβ? H system of amino acid residues in peptides has been derived from a set of model compounds covering the full range of dihedral angles. The expression obtained, J = 11.0 cos₂ θ ?1.4 cos θ + 1.6 sin₂θ, is close to those already used in pmr studies of peptide conformation, and provides a firmer foundation for them. A factor limiting the precision of this and other “Karplus relations” is illustrated.     

Analyse conformationnelle de la N-méthylamide de l'acide L-pyroglutamique par diffusion Rayleigh depolarisée,spectroscopie de vibration et calcul de l'energie conformationnelle

Conformational analysis of N-methylamide of pyroglutamic acid has been performed by theoretical energy calculations and experimental physical techniques, namely, laser Raman spectroscopy and depolarized Rayleigh scattering. The two theoretically predicted conformations are evidenced in crystalline state (ψ₁ = +169°) and in aqueous solution (ψ₁ ? ?20°). This study confirms the interest of a careful vibrational analysis of peptides and N-deuterated derivatives for providing an estimate of the dihedral angle ψ. The relationship between amide III frequency and ψ values is emphasized.     

Assignment of secondary structure from Cα coordinates

A multiple regression analysis has established a nonlinear relationship between the backbone dihedral angles and the C^α coordinates obtained from the x-ray crystal structures of 14 proteins. The regression equations have been applied to predict specific dihedral angles of each residue in the backbone of 24 proteins. Overall this method (Nonlinear Regression Distance Torsion) predicts values of ϕ and ψ within a ±45° window of those found in the x-ray structure with an accuracy of 94 and 91% and within a ±30° window of 88 and 81%. Two methods for the assignment of motif from C^α coordinates are reported. For the first method, motif is assigned from the dihedral angles predicted using the regression equations. By the second method, motif of the ith residue is assigned from the distance C^α_i-1 to C^α_i+2 (v₆) and torsional angle C^α_i-1, C^α_i, C^α_i+1, C^α_i+2 (v₁₃). For the 24 proteins, 23.7% of the residues by the former method and 19.6% by the latter method are assigned differently than in the Protein Data Bank. © 1997 John Wiley & Sons, Inc.     

Computer simulation of the cyclodextrin–phenylalanine complex

The results of the molecular dynamics simulations of the complexes of α-cyclodextrin-l-phenylalanine and β-cyclodextrine- L- phenylalanine in vacuo and in aqueous solution are presented. The trajectories of the insertion angle, rotation of the aromatic ring of the phenylalanine inside the macrocycle and the dihedral angle χ² (Cα–Cβ–Cγ–C_D2) describing the relative movement of the aromatic ring with respect to the polar region give detailed information of the dynamics of the complexes. It is found that the complex with α-cyclodextrin in water is not stable, in agreement with experimental data, while in all other situations studied the complex is stable within the computational limits. Comparing the different cases and the experimental evidence it comes out that a simulation of the complexes without an explicit treatment of the solvent gives unreliable results.     

Chiroptical properties of S-proline conformational isomers

The chiroptical properties of S-proline conformational isomers are examined on a theoretical model in which electronic wave functions are obtained from semiempirical molecular orbital calculations. The CNDO/S molecular orbital model is used to perform SCF-MO calculations on ground state electronic structure and excited states are constructed in the virtual orbital-configuration interaction approximation. Electronic rotatory strengths and dipole strengths are calculated directly from the complete (but approximate) molecular electronic wave functions. Zwitterionic, cationic, and anionic S-proline structures are studied twotypes of conformational variables are represented in the calculations: (1) pyrrolidine ring conformation; and (2) rotation about the C^α-COO^? bond. Rotatory strengths are found to be somewhat sensitive to rotational isomerism about the C^α-COO^? bond, but are found to be rather insensitive to conformational changes within the pyrrolidine ring. The CD spectrum of zwitterionic S-proline down to ～160 nm appears to be well accounted for by the theoretically calculated results if conformational preferences with respect to rotation about the C^α-COO^? bond can be assumed to exist in solution media. Furthermore, spectra-structure correlations are offered for the anionic and cationic forms of S-proline in solution.