Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. III. Probable and average conformations of enkephalin

The program SMAPPS (Statistical-Mechanical Algorithm for Predicting Protein Structure) was originally designed to determine the probable and average backbone (?, ψ) conformations of a polypeptide by the application of equilibrium statistical mechanics in conjunction with an adaptive importance sampling Monte Carlo procedure. In the present paper, the algorithm has been extended to include the variation of all side-chain (χ) and peptide-bond (ω) dihedral angles of a polypeptide during the Monte Carlo search of the conformational space. To test the effectiveness of the generalized algorithm, SMAPPS was used to calculate the probable and average conformations of Met-enkephalin for which all dihedral angles of the pentapeptide were allowed to vary. The total conformational energy for each randomly generated structure of Met-enkephalin was obtained by summing over the interaction energies of all pairs of nonbonded atoms of the whole molecule. The interaction energies were computed by the program ECEPP /2 (Empirical Conformational Energy Program for Peptides). Solvent effects were not included in the computation. The results of the Monte Carlo calculation of the structure of Met-enkephalin indicate that the thermodynamically preferred conformation of the pentapeptide contains a γ-turn involving the three residues Gly²-Gly³-Phe⁴. The γ-turn conformation, however, does not correspond to the structure of lowest conformational energy. Rather, the global minimum-energy conformation, recently determined by a new optimization technique developed in this laboratory, contains a type II′ β-bend that is formed by the interaction of the four residues Gly²-Gly³-Phe⁴-Met⁵. A similar minimum-energy conformation is found by the SMAPPS procedure. The thermodynamically preferred γ-turn structure has a conformational energy of 4.93 kcal/mole higher than the β-bend structure of lowest energy but, because of the inclusion of entropy in the SMAPPS procedure, it is estimated to be ～ 9 kcal/mole lower in free energy. The calculation of the average conformation of Met-enkephalin was repeated until a total of ten independent average conformations were established. As far as the phenylalanine residue of the pentapeptide is concerned, the results of the ten independent average conformations were all found to lie in the region of conformational space corresponding to the γ-turn. These results further support the conclusion that the γturn conformation is thermodynamically favored.     

Conformational energy and circular dichroism computed for cyclo-(pro-gly)3

An analytic cyclization procedure has allowed the complete specification of c-(Pro-Gly)₃ conformation by three dihedral angles. Utilizing this simplification, the intramolecular potential energy of c-(Pro-Gly)₃ has been computed over all of conformational space. Conformers with all peptide bonds trans have the lowest total potential energy. Circular dichroism spectra calculated for the low-energy regions provide the basis for the interpretation of experimental CD spectra.     

Conformational studies of linear β-D-1,4′-mannan and galactan

The nonbonded interaction energy of disaccharides, mannobiose and galactobiose and polysaccharides mannan and galactan have been computed as a function of dihedral angles (?,ψ). The conformation (40°, ?20°) has been preferred for the mannan chain from nonbonded interaction energy considerations. The O₅…O₃′ type of intramolecular hydrogen bond has been found to be possible in the above conformation. Comparison of the allowed region of mannan with those of cellulose and xylan indicates that the monomer unit, in mannan chain has slightly higher freedom of rotation than that of cellulose and less than that of xylan. As in cellulose and mannan, the freedom of rotation of the monomer units in β-1,4′ galactan is highly restricted. Unlike mannan (which prefers an extended conformation) the β-1,4′ galactan prefers a helical conformation similar to amylose. Just as in amylose the O₂…O₃′ type hydrogen bond between contiguous residues is also possible in β-1,4′ galactan.     

Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. II. Average backbone structure of enkephalin

The average conformation of Met-enkephalin was determined by using an adaptive, importance-sampling Monte Carlo algorithm (SMAPPS—Statistical Mechanical Algorithm for Predicting Protein Structure). In the calculation, only the backbone dihedral angles (? and ψ) were allowed to vary; i.e., all side-chain (χ) and peptide-bond (ω) dihedral angles were kept fixed at the values corresponding to a low-energy structure of the pentapeptide. The total conformational energy for each randomly generated structure of the polypeptide was obtained by summing over the interaction energies of all pairs of nonbonded atoms of the whole molecule. The interaction energies were computed by the program ECEPP/2 (Empirical Conformational Energy Program for Peptides). Solvent effects were not included in the computation. The calculation was repeated until a total of 10 independent average conformations were established. The regions of conformational space occupied by the average structures were compared with the regions of low conditional free energy obtained by SMAPPS in the first paper of this series. Such a comparison provides an analysis of the capacity of SMAPPS to adjust the Monte Carlo search to regions of highest probability. The results demonstrate that the ability of SMAPPS to focus the Monte Carlo search is excellent. Finally, the 10 independent average conformations and the mean of the 10 average structures were utilized as the initial conformations for a direct energy minimization of the pentapeptide. Of the 11 final energy-minimized structures, three of the conformations were found to be equivalent to the conformation of lowest energy determined previously. In addition, all but two of the remaining energy-minimized structures were found to correspond to one of the two other conformations of high probability obtained in the first paper of this series. These results indicate that a set of independent average conformations can provide a rational, unbiased choice for the initial conformation, to be used in a direct energy minimization of a polypeptide. The final energy-minimized structures consequently constitute a set of low-energy conformations, which include the global energy minimum.     

Monte Carlo simulations of a protein molecule with and without hydration energy calculated by the hydration-shell model

Monte Carlo simulations of a small protein, carmbin, were carried out with and without hydration energy. The methodology presented here is characterized, as compared with the other similar simulations of proteins in solution, by two points: (1) protein conformations are treated in fixed geometry so that dihedral angles are independent variables rather than cartesian coordinates of atoms; and (2) instead of treating water molecules explicitly in the calculation, hydration energy is incorporated in the conformational energy function in the form of g _i A _i, whereA _i is the accessible surface area of an atomic groupi in a given conformation, andg _i is the free energy of hydration per unit surface area of the atomic group (i.e., hydration-shell model). Reality of this model was tested by carrying out Monte Carlo simulations for the two kinds of starting conformations, native and unfolded ones, and in the two kinds of systems,in vacuo and solution. In the simulations starting from the native conformation, the differences between the mean propertiesin vacuo and solution simulations are not very large, but their fluctuations around the mean conformation during the simulation are relatively smaller in solution thanin vacuo. On the other hand, in the simulations starting from the unfolded conformation, the molecule fluctuates much more largely in solution thanin vacuo, and the effects of taking into account the hydration energy are pronounced very much. The results suggest that the method presented in this paper is useful for the simulations of proteins in solution.     

Conformational transitions and geometry differences between low-energy conformers of N-acetyl-N′-methyl alanineamide: An ab initio study at the 4-21G level with gradient relaxed geometries

Energy pathways between the α_R, β′, C, and β-regions of the conformational energy surface of N-acetyl-N′-methylalanyl amide were obtained by SCF ab initio calculations on the 4-21G level, with gradient geometry optimization at each point. The calculations indicate that no barrier exists at this computational level between α_R and β′. The variation of geometry (bond distances and bond angles) with conformation is analyzed in detail, and the most important geometrical parameters that should be treated as variables in both empirical energy calculations and in the fitting of polypeptide chains in proteins by x-ray methods are identified. In addition to the ?,ψ correlation discussed previously for the helical state, a correlation of these dihedral angles in the β-region is described.     

Molecular structure of the cis-syn photodimer of d(TpT) (cyanoethyl ester)

The three-dimensional structure was determined by x-ray crystallography for d(T[p](CE)T), a uv photoproduct of the cyanoethyl (CE) derivative of d(TpT), having the cis-syn cyclobutane (CB) geometry and the S-configuration at the chiral phosphorus atom. The crystals of C₂₃H₃₀N₅O₁₂P · 2H₂O belong to the orthorhombic space group P2₁2₁2₁ (Z = 4), with cell dimensions a = 11.596 Å, b = 14.834 Å, and c = 15.946 Å, containing two water molecules per asymmetric unit. The CB ring is puckered with a dihedral angle of 151°. The two pyrimidine bases are rotated by –29° from the position of direct overlap of their corresponding atoms. This represents a major distortion of DNA, since in DNA adjacent thymines are rotated by +36°. The pyrimidine rings are puckered with Cremer–Pople parameters for T[p] and in parentheses [p]T: Q: 0.24 Å (0.31 Å); θ: 123° (120°); ?: 141° (86°). These represent half-chairs designated as ⁶H₁ (T[p]) and ₆H⁵ ([p]T). The CB and pyrimidine ring conformations are interrelated, and we postulate that they execute a coupled interconversion in solution. The T[p] segment has the syn glycosyl conformation, a ²T₃ sugar pucker, and gauche^? conformation at C4′-C5′; the [p]T segment is anti, ³T₄, trans. The C5′-O5′ torsion of the [p]T unit is –124.5°, and the C3′-O3′ torsion of the T[p] unit is –152.9°. Bond angles and bond lengths involving the phosphorus atom are similar to those of other phosphotriesters. The P-O3′ and P-05′ torsion angles are –138.1° and 58.6°, respectively. Several intermolecular (but no intramolecular) hydrogen bonds are found in the crystal.     

X-Ray and stereochemical studies on xylan diacetate

By means of x-ray fiber diffraction, it has been found that xylan diacetate crystallizes with two chains or four residues in a monoclinic cell (space group P2₁): a = 7.64, b = 12.44, c (fiber axis) = 10.31 Å, and γ = 85°. Pairs of residues are related by a twofold screw axis in the c direction. Based on the observed fiber repeat and chain symmetry, the probable conformation of a pair of xylose diacetate residues joined via a β-1,4′ linkage has been obtained by energy minimization methods. The conformations corresponding to a threefold screw axis and a twofold screw axis along the chain have been compared and the reason why xylan diacetate assumes a twofold screw axis seems to be due to intermolecular packing effects rather than intramolecular non-bonded interactions.     

Molecular Structure,Conformation and Interactions of Antitumor Antibiotic Cyanonaphthridinomycin,a Covalent Binder of DNA

Abstract

X-ray, NMR and molecular modeling studies on cyanonaphthridinomycin (C₂₂ H₂₆N₄O₅), a DNA binding antibiotic, have been carried out to study the structure, conformation and interactions with DNA. The crystals belong to the space group P₂₁ with the cell dimensions of a = 5.934(1), b = 20.684(4), c = 16.866(3)A γ = 90.9° and Z = 4(two molecules/asymmetric unit). The structure was solved by direct methods and difference Fourier methods and refined to an R value of 0.087 for 4061 reflections. The conformation of the molecule is compared with that of naphthridinomycin. There are differences in the orientation of the methoxyl group and the saturated oxazole ring. 1 and 2D NMR studies have been carried out and the dihedral angles obtained from coupling constants have been compared with those obtained from the crystal structure. Molecular mechanics studies were carried out to obtain the energy minimized structure and its comparison with X-ray and NMR results. Molecular modelling studies were performed to propose models for drug-DNA interactions. Both partial intercalation and groove-binding models have been proposed.     

A conformational analysis of mono and dialkyl ethers of 2,2′-dihydroxy-1,1′-binaphthalene by circular dichroism spectroscopy and cholesteric induction in nematic liquid crystals

The coupling of the analysis of the absorption and circular dichroism (CD) spectra with that of the cholesteric mesophases induced in nematic liquid crystals indicated some interesting conformational features of bridged and nonbridged mono- and dialkylethers of optically active 2,2′-dihydroxy-1,1′-binaphthalene. Bridged derivatives are characterized by relatively small dihedral angles. Simple monoalkyl ethers are characterized by larger dihedral angles but they all assume an s-cis conformation, owing to the existence of intramolecular hydrogen bonds. Nonbridged dialkylethers prefer even larger dihedral angles and, depending on the bulkiness of the alkyl groups, the s-trans conformation can be found. Interestingly, the conformation of dialkylethers is strongly dependent on the structure of the liquid crystal solvent, because the intramolecular hydrogen bond is not possible there. © 1995 Wiley-Liss, Inc.     

Fluctuations of an alpha-helix.

Fluctuations in backbone dihedral angles in the α-helical conformation of homopolypeptides are studied based on an assumption that the conformational energy function of a polypeptide consisting of n amino-acid residues can be approximated by a 2n-dimensional parabola around the minimum point in the range of fluctuations. A formula is derived that relates 〈Δθ_iΔθ_j〉, the mean value of the product of deviations of dihedral angles ?_i and ψ_i (collectively designated by θ_i) from their energy minimum values, with a matrix inverse to the second derivative matrix F ,_n of the conformational energy function at the minimum point. A method of calculating the inverse matrix F _n^?1 explicitly is given. The method is applied to calculating 〈Δθ_iΔθ_j〉 for the α-helices of poly(L -alanine) and polyglycine. The autocorrelations 〈(Δ?_i)²〉 and 〈(Δψ_i)²〉 at 300°K are found to be about 66 deg² and 49 deg², respectively, for poly(L -alanine), and 84 deg² and 116 deg², respectively, for polyglycine. The length of correlations of fluctuations along the chain is found for both polypeptides to be about eight residues long.     

Theoretical drug design: 6-azauridine-5'-phosphate--its X-ray crystal structure, potential energy maps, and mechanism of inhibition of orotidine-5'-phosphate decarboxylase.

The cytostatic drug 6-azauridine is converted in vivo to 6-azauridine-5′-phosphate (z⁶Urd-5′-P), which blocks the enzyme orotidine-5′-phosphate decarboxylase (Ord-5′-Pdecase) and therefore inhibits the de novo production of uridine-5′-phosphate (Urd-5′-P). In order to relate the structure and function of z⁶Urd-5′-P, it was crystallized as trihydrate, space group P2₁2₁2₁ with a = 20.615 Å, b = 6.265 Å, c = 11.881 Å, and the structure established by Patterson methods. Atomic parameters were refined by full-matrix least-squares methods to R = 0.066 using 1638 counter measured x-ray data. The ribose of z⁶Urd-5′-P is in a twisted C(2′)-exo, C(3′)endo conformation, the heterocycle is in extreme anti position with angle N(6)-N(1)-C(1′)-O(4′) at 86.3°, and the orientation about the C(4′)-C(5′) bond is gauche, trans in contrast to gauche, gauche found for all the other 5′-ribonucleotides. Conformational energy calculations show that z⁶Urd-5′-P may adopt an extreme anti conformation not allowed to Urd-5′-P, and they also predict the same unusual trans, gauche conformation about the C(4′)-C(5′) bond in orotidine-5′-phosphate (Ord-5′-P) and in z⁶Urd-5′-P, which renders the distances O(2)…O(5′) in z⁶Urd-5′-P and O(7)…O(5′) in Ord-5′-P comparable. On this basis the function of z⁶Urd-5′-P as an Ord-5′-Pdecase inhibitor can be explained as being due to its structural similarity with the substrate Ord-5′-P and further clarifies the inhibitory action of 5′-nucleotides bearing the heterocycles oxipurinol, xanthine, or allopurinol [J. A. Fyfe, R. L. Miller, and T. A. Krenitsky, J. Biol. Chem. 248 , 3801 (1973)]. With this in mind, new inhibitors for Ord-5′-Pdecase may be designed.     

Crystal and molecular structure of V-anhydrous amylose

The conformation and crystalline packing of V-anhydrous amylose has been investigated by a combination of linked atom model building and X-ray diffraction analysis. The unit cell, the P2₁2₁2₁ space group, the left-handed sixfold helical conformation with all O(6) in gt rotational positions, and the intrahelical O(2)---O(3) and O(2)---O(6) hydrogen bonds are substantially in agreement with previous studies. A new model for packing of the chains in the unit cell and the presence of crystallographic water is proposed. Packing appears to be stabilized by corner-to-center chain O(2)---O(2) hydrogen bonds. The nature of the transition from the amylose–DMSO complex to V_a-amylose was considered and it is shown that the transition involves translation of the amylose chains parallel to the a and b unit cell axes with only slight changes in the orientation of the helix. No significant conformational changes result from the transition.     

The conformation of tetrafluorinated methyl galactoside anomers: crystallographic and NMR studies

The first single-crystal X-ray diffraction study of tetrafluorinated monosaccharide derivatives is presented. Both α- and β-methyl 2,3-dideoxy-2,2,3,3-tetrafluoro-d-galactopyranoside anomers adopt the ⁴C₁ conformation. The values for the C1–O1 and C1–O5 bond lengths and the O5–C1–O1–CH₃ dihedral angles are in line with what can be expected from the anomeric and exo-anomeric effects. The chair conformations are slightly distorted, presumably due to repulsion between 1,3-diaxial C–O and C–F bonds. The asymmetric unit of both compounds contains up to three independent molecules, which differ in the conformation of the hydroxymethyl group (including in one case a ‘forbidden’ gg rotamer). The molecular packing of the β-anomer shows a clear segregation between fluorinated and hydrophilic domains, while for the α-anomer the regions of fluorine segregation are broken by interleafing of OMe groups. There is one close OH?F contact, which is likely to arise from the crystal packing. NMR studies show that the two anomers also adopt a ⁴C₁ conformation in solution (D₂O, CDCl₃).     

Semiempirical energy calculations on model compounds of polypeptides. Crystal structures of DL-acetylleucine N-methylamide and DL-acetyl-amino-n-butyric acid N-methylamide

The sum E of the packing and conformation energies of the crystals of DL -acetylleucine N-methylamide (ALNMA) and DL -acetyl-α-amino-n-butyric acid N-methylamide (ABAMA) is calculated as a function of the crystallographic parameters and the conformational angles. The intermolecular energy is assumed to be the pairwise sum of nonbonded and electrostatic atomic interactions, while both these terms and intrinsic terms describing barriers of internal rotation contribute to the intramolecular energy. For ALNMA E is minimized with respect to 18 parameters: the minimum found when starting from the experimental structure agrees with this within 0.07 Å and 3°, except for one angle which deviates by 6° the average deviations of the atomic coordinates are \documentclass{article}\pagestyle{empty}\begin{document}$ |\overline {\Delta x|} = 0.02,|\overline {\Delta y|} = 0.07,|\overline {\Delta z|} = 0.08 $\end{document} Å. Another minimum with about the same energy shows slightly worse agreement. A comparison between different sets of nonbonded functions is made. The prediction of conformation and intermolecular packing of ABAMA is attempted on the basis of the knowledge of the unit cell and the space group. In agreement with available experimental data it is found that only one-di-mensional arrays of molecules linked by pairs of hydrogen bonds are compatible with the unit cell. The more stable of two possible conformations of the main chain agrees approximately with the experimental conformation. The calculation is not conclusive with regard to the side-chain conformation and the packing of non-hydrogen-bonded molecules.     

A stereochemical model for phospholipids. II: Conformational analysis and molecular packing of phosphatidylethanolamine (PE)

A partition energy method procedure was applied to select the energetically favoured conformations of phosphatidylethanolamine (PE) as polar constituents of phospholipid molecules. The result indicated a large degree of freedom for the two torsion angles of the ester bond of the phosphate and a gauche, gauche star conformation for the ethane bond.A packing process of the molecule was carried out through a potential energy calculation by considering the conformers selected above, using previously published procedure and conventions. All the arrangements which possess the best packing energy values were characterised by an orientation of the PN dipolar segment parallel to the lattice plain. Rotation of the internal torsion angles and rotation in the eulerian space of the molecule produced differences in the charged groups that interact. An additional minimum was present in the energy packing process of those conformers which have the first torsion angle of the phosphate in a trans conformation. This minimum, which corresponds to an orientation of the molecule orthogonal to the lattice plane, requires a complete neutralisation of the point charges on the system.The results of the calculation underline the importance of changes in the behaviour of the polar group of the phospholipids in the packing process.     

Conformation of histidine model peptides. III. Chiroptical properties of cyclo-L-alanyl-L-histidine and cyclo-L-histidinyl-L-histidine

The chiroptical properties of the cyclic dipeptides cyclo-L -alanyl-L -histidine and cyclo-L -histidinyl-L -histidine have been investigated as a function of molecular conformation. The rotatory strengths of the n-π* transitions of the peptide chromophores and the lowest energy π-π* transitions of the imidazole chromophores have been calculated as a function of the angle of fold of the cyclic dipeptide group and the dihedral angles χ¹ and χ² of the amino acid side chains. The results of this investigation are consistent with the preferred position of the dihedral angle χ¹ occurring near 60° in the free base form of cyclo-L -alanyl-L -histidine, and near 180° when the imidazole side chain is protonated. Furthermore, in the case of the free base form of the imidazole group, it is possible that the tautomeric isomer in which N^ε is protonated may be more prevalent than the isomer in which N^δ is protonated.     

Spatial configurations of polynucleotide chains. 3. Polydeoxyribonucleotides

The virtual bond scheme set forth in preceding papers for treating the average properties of polyriboadenylic acid (poly rA) is here applied to the calculation of the unperturbed mean-square end-to-end distance of polydeoxyriboadenylic acid (poly dA). The modifications in structure and in charge distribution resulting from the replacement of the hydroxyl group at C_2′ in the ribose residue by hydrogen in deoxyribose produce only minor modifications in the conformational energies associated with the poly dA chain as compared to those found for poly rA. The main difference is manifested in the energy associated with rotations about the C_3′–O_3′ bond of the deoxyribose residue in the C_2′-endo conformation; accessible rotations are confined to the range between 0° and 30° relative to the trans conformation, whereas in the ribose unit the accessible regions comprise two ranges centered at approximately 35° and 85°. The characteristic ratio 〈r²〉0/nl² calculated on the basis of the conformational energy estimates is ≈9 for the poly dA chain with all deoxyribose residues in the C_3′-endo conformation and ≈21 with all residues in the C_2′-endo form. Satisfactory agreement is achieved between the theoretical values and experimental results on apurinic acid by treating the poly dA chain as a random copolymer of C_3′-endo and C_2′-endo conformational isomers present in a ratio of ～1 to 9.     

Solvent effects on the conformational preferences of model peptoids. MP2 study

The influence of aqueous environment on the main‐chain conformation (ω₀, ?, and ψ dihedral angles) of two model peptoids: N‐acetyl‐N‐methylglycine N’‐methylamide (Ac‐N(Me)‐Gly‐NHMe) ( 1 ) and N‐acetyl‐N‐methylglycine N’,N’‐dimethylamide (Ac‐N(Me)‐Gly‐NMe₂) ( 2 ) was investigated by MP2/6‐311++G(d,p) method. The Ramachandran maps of both studied molecules with cis and trans configuration of the N‐terminal amide bond in the gas phase and in water environment were obtained and all energy minima localized. The polarizable continuum model was applied to estimate the solvation effect on conformation. Energy minima of the Ac‐N(Me)‐Gly‐NHMe and Ac‐N(Me)‐Gly‐NMe₂ have been analyzed in terms of the possible hydrogen bonds and C = O dipole attraction. To validate the theoretical results obtained, conformations of the similar structures gathered in the Cambridge Crystallographic Data Centre were analyzed. Obtained results indicate that aqueous environment in model peptoids 1 and 2 favors the conformation F (? and ψ = ?70º, 180º), and additionally significantly increases the percentage of structures with cis configuration of N‐terminal amide bond in studied compounds. Copyright © 2014 European Peptide Society and John Wiley & Sons, Ltd.     

The optical properties of tyrosine-containing cyclic dipeptides

The chiroptical properties of the cyclic dipeptides cyclo (L -alanyl-L -tyrosine) and cyclo(L -tyrosyl-L -tyrosine) have been investigated as a function of molecular conformation. Theoretical optical calculations and conformational energy calculations have been carried out as a function of the side-chain dihedral angles χ¹ and χ², and as a function of the angle of fold of the cyclic dipeptide backbone. The results of these theoretical calculations have been compared with experimental circular dichroism (CD) data. Theoretical predictions are in very good agreement with experiment for c(L -Tyr-L -Tyr). Agreement was not quite as good for c(L -Ala-L -Tyr), although the signs of all of the Cotton effects were apparently predicted correctly except for that associated with the lowest energy tyrosine absorption band.