Calculation of the minimum energy conformation of biomolecules using a global optimization technique I. Methodology and application to a model molecular fragment (Normal pentane)

The conformational energy of a molecule is minimized with respect to interatomic distances using Bremermann's method of unconstrained global optimization (1970). The optimal set of distances is then used for calculating the preferred conformation of the molecule. A simultaneous optimization of all the dihedral angles is achieved. The classical potential function is used in this study. An illustration of the method is given by applying it to normal pentane, which is a commonly occurring fragment of biomolecules. Results show that, for the standard geometry (bond lengths and bond angles), the all-trans) conformation is the preferred one. However, fluctuations of the geometry within the limits of the vibrational spectra can lead to preferred conformations that are not necessarily all-trans.     

Equilibrium transitions between side‐chain conformations in leucine and isoleucine

Despite recent improvements in computational methods for protein design, we still lack a quantitative, predictive understanding of the intrinsic probabilities for amino acids to adopt particular side‐chain conformations. Surprisingly, this question has remained unsettled for many years, in part because of inconsistent results from different experimental approaches. To explicitly determine the relative populations of different side‐chain dihedral angles, we performed all‐atom hard‐sphere Langevin Dynamics simulations of leucine (Leu) and isoleucine (Ile) dipeptide mimetics with stereo‐chemical constraints and repulsive‐only steric interactions between non‐bonded atoms. We determine the relative populations of the different χ₁ and χ₂ dihedral angle combinations as a function of the backbone dihedral angles ? and ψ. We also propose, and test, a mechanism for inter‐conversion between the different side‐chain conformations. Specifically, we discover that some of the transitions between side‐chain dihedral angle combinations are very frequent, whereas others are orders of magnitude less frequent, because they require rare coordinated motions to avoid steric clashes. For example, to transition between different values of χ₂, the Leu side‐chain bond angles κ₁ and κ₂ must increase, whereas to transition in χ₁, the Ile bond angles λ₁ and λ₂ must increase. These results emphasize the importance of computational approaches in stimulating further experimental studies of the conformations of side‐chains in proteins. Moreover, our studies emphasize the power of simple steric models to inform our understanding of protein structure, dynamics, and design. Proteins 2015; 83:1488–1499. © 2015 Wiley Periodicals, Inc.     

Variation of the NH-C alpha-H coupling constant with dihedral angle in the NMR spectra of peptides

Proton magnetic resonance data and conformational calculations of a series of model compounds containing a NH-C^αH group substituted as in peptides have been used to generate a proton–proton coupling constant–dihedral angle relation for the peptide unit. For those substances used in which the dihedral angle about the N-C^α bond is not fixed, the angle distribution was calculated from conformational theory. Using eight examples in which the number of theoretical assumptions were least, the best values of the coefficients A, B, and C in the expression J(θ) = Acos²θ + B cosθ + Csin²θ were found by a least-squares procedure to be 7.9, ?1.55, and 1.35, respectively. This relation gives reasonable values for the dihedral angles ? in cyclic oligopeptide structures for which the availability of both NMR data and other structural information allow comparison. When applied to N-acetylamino acid N-methylamides having side chains extending beyond C^β, however, agreement with the calculated conformational distribution was found for Leu, Met, and Trp, but observed values of J were larger than expected for Val, He, Phe, and Tyr, These disagreements are considered to be the result of interactions not yet taken into account in the usual conformational calculations.     

Agreement between Single Crystal X-Ray and Molecular Mechanical Sugar Ring Conformations

Abstract

We have calculated the deoxyribose sugar energy for a wide range of puckering parameters, (q, W), using different force fields. The intra-ring bond lengths, bond angles, and dihedral angles are calculated for every energy minimized structure and compared with 224 sugar ring structures available from DNA single crystal x-ray data. A modified Weiner's force field yields an excellent agreement with x-ray data.

The calculated energy surface shows a variable amplitude repuckering path, with an average distortion of 0.42 Å. Most of the experimental values of (q, W) fall within 1.0 Kcal/mol from the calculated minimum.     

Are Long-Range Structural Correlations Behind the Aggregration Phenomena of Polyglutamine Diseases?

We have characterized the conformational ensembles of polyglutamine peptides of various lengths (ranging from to ), both with and without the presence of a C-terminal polyproline hexapeptide. For this, we used state-of-the-art molecular dynamics simulations combined with a novel statistical analysis to characterize the various properties of the backbone dihedral angles and secondary structural motifs of the glutamine residues. For (i.e., just above the pathological length for Huntington''s disease), the equilibrium conformations of the monomer consist primarily of disordered, compact structures with non-negligible -helical and turn content. We also observed a relatively small population of extended structures suitable for forming aggregates including - and -strands, and - and -hairpins. Most importantly, for we find that there exists a long-range correlation (ranging for at least residues) among the backbone dihedral angles of the Q residues. For polyglutamine peptides below the pathological length, the population of the extended strands and hairpins is considerably smaller, and the correlations are short-range (at most residues apart). Adding a C-terminal hexaproline to suppresses both the population of these rare motifs and the long-range correlation of the dihedral angles. We argue that the long-range correlation of the polyglutamine homopeptide, along with the presence of these rare motifs, could be responsible for its aggregation phenomena.     

DFT study on crystalline 1,1-diamino-2,2-dintroethylene under high pressures

DFT calculations have been performed to study the structural, electronic, absorption, and thermodynamic properties of crystalline 1,1-diamino-2,2-dintroethylene (α-FOX-7) in the pressure range of 0–40 GPa. A comprehensive analysis of the variation trends of the lattice constants, bond lengths, bond angles, and twist angles under compression shows that six structural transformations occur in α-FOX-7 at 2, 5, 11, 19, 29, and 35 GPa, respectively. The C1-N1 and C1-N2 bond lengths decrease much faster than any other bonds under compression, indicating that the C-NO₂ cleavage is possible to trigger the decomposition of α-FOX-7. The intra-molecular H-bonding interaction weakens at 2 and 5 GPa, which may be caused by the structural transformations, but it then strengthens with the increasing pressure up to 40 GPa. The inter-molecular H-bonding interaction strengthens with the increasing pressure. The band gap of α-FOX-7 increases at 11 GPa suddenly and decreases obviously at 19, 29, and 35 GPa, which are caused by the structural transformations. α-FOX-7 has relatively high optical activity at high pressure. All the structural transformations are endothermic and not spontaneous at room temperature.     

New Insights into the Interdependence between Amino Acid Stereochemistry and Protein Structure

To successfully design new proteins and understand the effects of mutations in natural proteins, we must understand the geometric and physicochemical principles underlying protein structure. The side chains of amino acids in peptides and proteins adopt specific dihedral angle combinations; however, we still do not have a fundamental quantitative understanding of why some side-chain dihedral angle combinations are highly populated and others are not. Here we employ a hard-sphere plus stereochemical constraint model of dipeptide mimetics to enumerate the side-chain dihedral angles of leucine (Leu) and isoleucine (Ile), and identify those conformations that are sterically allowed versus those that are not as a function of the backbone dihedral angles ϕ and ψ. We compare our results with the observed distributions of side-chain dihedral angles in proteins of known structure. With the hard-sphere plus stereochemical constraint model, we obtain agreement between the model predictions and the observed side-chain dihedral angle distributions for Leu and Ile. These results quantify the extent to which local, geometrical constraints determine protein side-chain conformations.     

Vibrational approach to the dynamics of an α-helix

The dynamics of a finite α-helix have been studied in the harmonic approximation by a vibrational analysis of the atomic motions about their equilibrium positions. The system were represented by an empirical potential energy function, and all degrees of freedom (bond lengths, bond angles, and torsional angles) were allowed to vary. The complete results were compared with a more restrictive model in which the peptide dihedral angle was kept rigid; also, a model potential excluding hydrogen bonds was examined. Thermal fluctuations in the backbone dihedral angles ? and ψ are 12° to 15°. The fluctuations of adjacent dihedral angles are highly correlated, and the correlation pattern is affected by the flexibility of the peptide dihedral angle. Time-dependent autocorrelations in the motion of ? and ψ appear to decay due to dephasing in less than 1 psec, while the motions of the carbonyl oxygen and amide hydrogens out of the peptide plane are more harmonic. Length fluctuations have been evaluated and exhibit a strong end effect; the calculated elastic modulus is in agreement with other values. Rigid and adiabatic total energy surfaces corresponding to dihedral angle rotations in the middle of the helix have been obtained and compared with the quadratic approximation to those surfaces. The magnitudes and correlations between the fluctuations obtained by averaging over the adiabatic energy surface most closely resemble the vibrational results. Of particular interest is the fact that hydrogen bonds play a relatively small role in the local dihedral angle fluctuations, though the hydrogen bonds are important in the energy of overall length changes.     

X-ray structure of a mono(1-methylthyminato) complex of cisplatin,chloro-(1-methylthyminato-N3)-cis-diammineplatinum(II) monohydrate

The crystal structure of chloro-(1-methyltyminato- N3)-cis-diammineplatinum(II) monohydrate, cis- (NH₃)₂Pt(C₆H₇N₂O₂)Cl·H₂O, is reported. The compound crystallizes in space group P$\text{1}$ with a = 6.911(2) Å, b = 8.598(3) Å, c = 11.464(4) Å, α = 100.13(3)°, β = 120.03(3)°, γ = 93.16(3)°, Z = 2. The structure was refined to R = 0.048 and R_w = 0.057. The compound contains the deprotonated 1-methylthymine ligand coordinated to Pt through N3 (1.973(10) Å). This distance represents the shortest Pt-N3(pyrimidine-2.4-dione) bond reported so far. The two PtNH₃ bond lengths differ significantly: PtNH₃ (trans to Cl) is longer (2.052(10) Å) than PtNH₃ (trans to N3 of 1-MeT) (2.002(11) Å). The PtCl distance (2.326(3) Å) is normal, as is the large dihedral angle between the Pt coordination plane and the nucleobase (76.5°).     

Dihedral angle and secondary structure database of short amino acid fragments

Dihedral angles of amino acids are of considerable importance in protein tertiary structure prediction as they define the backbone of a protein and hence almost define the protein's entire conformation. Most ab initio protein structure prediction methods predict the secondary structure of a protein before predicting the tertiary structure because three-dimensional fold consists of repeating units of secondary structures. Hence, both dihedral angles and secondary structures are important in tertiary structure prediction of proteins. Here we describe a database called DASSD (Dihedral Angle and Secondary Structure Database of Short Amino acid Fragments) that contains dihedral angle values and secondary structure details of short amino acid fragments of lengths 1, 3 and 5. Information stored in this database was extracted from a set of 5,227 non-redundant high resolution (less than 2-angstroms) protein structures. In total, DASSD stores details for about 733,000 fragments. This database finds application in the development of ab initio protein structure prediction methods using fragment libraries and fragment assembly techniques. It is also useful in protein secondary structure prediction.

Availability     

Molecular structures of electron-transfer active complexes [Re(XQ)(CO)3(NN)] (XQ=N-Me-4,4-bipyridinium or N-Ph-4,4-bipyridinium; NN=bpy, 4,4-Me2-2,2-bpy or N,N-bis-isopropyl-1,4-diazabutadiene) in the solid state and solution: an X-ray and NOESY NMR study

Crystal and molecular structures of a series of complexes [Re(XQ⁺)(CO)₃(NN)]²⁺ (XQ=N-methyl-4,4^′-bipyridinium (MQ⁺) and N-phenyl-4,4^′-bipyridinium (PQ⁺) and NN=bpy, 4,4^′-dimethyl-bpy (dmb) or N,N^′-bis-isopropyl-1,4-diazabutadiene (ⁱPr-DAB)) in the solid state have been determined by X-ray diffraction. Aromatic rings within the XQ⁺ ligand were found to be highly staggered. The dihedral angles between the pyridine and pyridinium rings were found in the range 39°-45° for MQ⁺ and 28°-46° for PQ⁺. The exceptionally low dihedral angle of 8° in [Re(MQ⁺)(CO)₃(dmb)]²⁺ is due to crystal-packing effects. The pyridinium and phenyl rings of the PQ⁺ ligand are even more staggered, with dihedral angles in the range 40°-55°. The pyridine ring of the XQ⁺ ligand is oriented relative to the equatorial ligands in such a way that it bisects the angles between the equatorial Re-N and Re-C bonds in all complexes, except for [Re(PQ⁺)(CO)₃(ⁱPr-DAB)](PF₆)₂, where it bisects the DAB ligand. Structures of the complexes [Re(XQ⁺)(CO)₃(NN)]²⁺ (NN=bpy, dmb) were also studied in solution using NOESY NMR. It was found that the orientation of the XQ⁺ ligand relative to the equatorial ligands is the same as in the solid state. The XQ⁺ ligands become even more staggered on going to the solution where pyridine-pyridinium dihedral angles range from 42° to 45°. A value of ∼69° was found for the pyridinium-phenyl dihedral angle in PQ⁺ complexes. The structural data obtained are related to electron-transfer activity of XQ⁺ complexes. It follows that any ground- or excited-state electron transfer reactions or optical charge transfer excitation have to be coupled with a major reorganization of the XQ⁺ ligand, namely twisting of its aromatic rings and shortening of the interring C-C bond. This conclusion has important implications for estimates of Marcus inner reorganization energy and electron transfer dynamics.     

Inhibiton of human placental 17 beta-hydroxysteroid dehydrogenase by steroids and nonsteroidal alcohols: aspects of inhibitor structure and binding specificity

Inhibition of human placental 17β-hydroxysteroid dehydrogenase by C₁₈ and C₁₉ steroids and nonsteroidal alcohols was assayed at pH 9.0 with 17β-estradiol 3-methyl ether and NAD⁺ as reactants. The nonstaroidal alcohols tested were poor inhibitors. Cyclopentanol and cyclohexanol had K_i values greater than 5 mm. Nonaromatic C₁₈ and C₁₉ steroids with oxygen functions at both positions 3 and 17 gave no detectable inhibition or had K_i, values greater than or equal to 160 μm. 3μ-Hydroxy-5,16-androstadiene, 5-androsten-3β-ol, 1,3,5(10)-estratrien-3-ol, and 1,3,5(10),16-estratetraen-3-ol, steroids lacking a C(17) oxygen function, had K_i values of 1.8, 6.0, 0.04, and 0.17 μm, respectively, demonstrating that both C₁₈ and C₁₉ steroids can bind at the steroid site. Binding specificity is narrowed and binding affinity for nonaromatic steroids weakened by oxygen functions at C(17) or both C(3) and C(17). The structural implications of the specificity data for steroid recognition and complex formation and in vivo control of enzyme activity are discussed.     

Geometry of experimentally observed RNA residues in tRNA and dinucleoside monophosphates: the effect of small variations in the backbone angles.

The polymerization of various experimentally observed conformers of RNA from tRNA and some dinucleoside monophosphates have been examined with a program that computes the basic helix parameters directly from the six backbone torsion angles ω′, ?′, ψ′, ψ, ?, ω to give n (= 360/θ), the number of residues per turn; h, the rise per residue; and r, the radius of the phosphate atoms from the helix axis. The single-stranded regions of tRNA that have A-form residues have a notably lower value of n than the double-stranded regions. The G-U “wobble” base pair is shown to be an energetically strained left-handed form. The A-form dinucleoside monophosphates also have a low value of n. A model of UpAl polymerized as a fourfold left-handed helix with the bases on the outside and phosphates on the inside is investigated for its sharp 90° turn angle characteristics. UpA2 cannot be polymerized due to a low values of h (1.31 Å) and r (2.72 Å), which cause steric hindering. An eightfold model of poly(rA) is discussed as are the nonhelical residues of tRNA. Finally, the effects of small changes in dihedral angles and bond lengths and angles on the helical parameters are investigated and discussed by way of explaining this behavior.     

An NMR study of the conformational mobility of steroid estrogen 7α-methyl-8α analogues

All the signals in the ¹H and ¹³C NMR spectra of some analogues of 7α-methyl-8α-and 6-oxa-8α-steroid estrogens were completely assigned. Considering the values of nuclear Overhauser effect and vicinal coupling constants, these steroids were shown to exhibit a fast, on the NMR time scale, conformational equilibrium arising due to the inversion of ring B. The conformer populations were obtained from a comparison of the experimental and theoretical values of the dihedral angles and the interproton distances. This conformational equilibrium was shown to depend on the nature of atom in position 6: for the 7α-methyl-6-oxa-8α analogues of the steroid estrogens, the population of the conformer with the pseudoaxial orientation of the 7α-methyl group was observed to be decreased compared with the 7α-methyl-8α analogue.     

Simulation of conformational possibilities of DNA via calculation of nonbonded interactions of complementary dinucleoside phosphate complexes

Using classical potential functions, we carried out potential-energy calculations on the complementary deoxydinucleoside phosphate complexes dApdA:dUpdU, dUpdA:dUpdA, and dApdU:dApdU. All dihedral and bond angles, except those of the nitrogen bases, were varied. The resulting minimum-energy conformations of the complexes are close to DNA A- and B-family conformations, with a typical arrangement of the nitrogen bases. The dihedral and bond angles of one of the molecules forming the complex can thereby differ by several degrees from those of the other molecule. For different base sequences, some dihedral and bond angles may vary over a range of several degrees without appreciably changing the total energy of the complex. Some low-energy conformations of the complexes corresponding to other regions of the conformational space are also found. The biological consequences of possible changes in dihedral and bond angles, occurring on interaction with other molecules, are discussed.     

Interaction of metal ions with humic-like models. Part 6. Molecular structure,spectral and thermal properties of diaquabis(2,6-dimethoxybenzoato)dioxouranium(VI) monohydrate

The crystal and molecular structure of [UO₂(DMB)₂(H₂O)₂]·H₂O (DMB = 2,6-dimethoxybenzoate), complex I, has been detcrmined by X-ray diffraction and refined to a final R value of 0.0411. The compound belongs to the space group P2₁/a with cell constants a = 12.649(4), b = 14.418(5), c = 13.460(4) Å and Z = 4. As in the analogous complex [UO₂(DHB)₂(H₂O)₂]·8H₂O (DHB = 2,6- dihydroxybenzoate), compound II, the uranyl ion is bound to two bidentate carboxylate groups and two water molecules, but the point-symmetry is lower because the carboxylates, and the water molecules, are in vicinal positions. The lack of hydrogen- bonds between carboxylate groups and ortho-methoxy substituents and, possibly, steric factors account for the rotation of the phenyl rings with respect to the equatorial plane of the metal, the dihedral angle between the ‘best planes’ being about 77°. Detectable changes in the bond distances and angles within the carboxylate groups are produced by the non-planarity of the ligand. Spectroscopic and thermal properties of complexes I and II are also compared.     

Agreement between single crystal X-ray and molecular mechanical sugar ring conformations

We have calculated the deoxyribose sugar energy for a wide range of puckering parameters, (q, W), using different force fields. The intra-ring bond lengths, bond angles, and dihedral angles are calculated for every energy minimized structure and compared with 224 sugar ring structures available from DNA single crystal x-ray data. A modified Weiner's force field yields an excellent agreement with x-ray data. The calculated energy surface shows a variable amplitude repuckering path, with an average distortion of 0.42 A. Most of the experimental values of (q, W) fall within 1.0 Kcal/mol from the calculated minimum.     

Reference ranges for urinary concentrations and ratios of endogenous steroids, which can be used as markers for steroid misuse, in a Caucasian population of athletes

The detection of misuse with naturally occuring steroids is a great challenge for doping control laboratories. Intake of natural anabolic steroids alters the steroid profile. Thus, screening for exogenous use of these steroids can be established by monitoring a range of endogenous steroids, which constitute the steroid profile, and evaluate their concentrations and ratios against reference ranges. Elevated values of the steroid profile constitute an atypical finding after which a confirmatory IRMS procedure is needed to unequivocally establish the exogenous origin of a natural steroid. However, the large inter-individual differences in urinary steroid concentrations and the recent availability of a whole range of natural steroids (e.g. dehydroepiandrosterone and androstenedione) which each exert a different effect on the monitored parameters in doping control complicate the interpretation of the current steroid profile.The screening of an extended steroid profile can provide additional parameters to support the atypical findings and can give specific information upon the steroids which have been administered.The natural concentrations of 29 endogenous steroids and 11 ratios in a predominantly Caucasian population of athletes were determined. The upper reference values at 97.5%, 99% and 99.9% levels were assessed for male (n = 2027) and female (n = 1004) populations. Monitoring minor metabolites and evaluation of concentration ratios with respect to their natural abundances could improve the interpretation of the steroid profile in doping analysis.     

Geometry of the five-membered ring mathematical demonstration of the pseudorotation formulae

The geometrical relations between the 15 typical parameters (bond lengths and angles, torsion angles) of a five-membered ring are derived for any ring then for a regular one. It is demonstrated that for the case of the 20 symmetrical C ₂ and C _sconformations, only geometrical considerations are needed to obtain the pseudorotation formulae for the torsion angles. However, the puckering intensity as well as the bond angle values cannot be expressed from geometrical constraints alone but would require energetical considerations.