Stochastic Liouville equation simulation of multidimensional vibrational line shapes of trialanine

The line shapes detected in coherent femtosecond vibrational spectroscopies contain direct signatures of peptide conformational fluctuations through their effect on vibrational frequencies and intermode couplings. These effects are simulated in trialanine using a Green's function solution of a stochastic Liouville equation constructed for four collective bath coordinates (two Ramachandran angles affecting the mode couplings and two diagonal energies). We find that fluctuations of the Ramachandran angles which hardly affect the linear absorption can be effectively probed by two-dimensional spectra. The signal generated at k(1)+k(2)-k(3) is particularly sensitive to such fluctuations.     

Comparison of some dispersion-corrected and traditional functionals as applied to peptides and conformations of cyclohexane derivatives

We compare the energetic and structural properties of fully optimized α-helical and antiparallel β-sheet polyalanines and the energetic differences between axial and equatorial conformations of three cyclohexane derivatives (methyl, fluoro, and chloro) as calculated using several functionals designed to treat dispersion (B97-D, ωB97x-D, M06, M06L, and M06-2X) with other traditional functionals not specifically parametrized to treat dispersion (B3LYP, X3LYP, and PBE1PBE) and with experimental results. Those functionals developed to treat dispersion significantly overestimate interaction enthalpies of folding for the α-helix and predict unreasonable structures that contain Ramachandran φ and ψ and C = O[ellipsis (horizontal)]N H-bonding angles that are out of the bounds of databases compiled the β-sheets. These structures are consistent with overestimation of the interaction energies. For the cyclohexanes, these functionals overestimate the stabilities of the axial conformation, especially when used with smaller basis sets. Their performance improves when the basis set is improved from D95?? to aug-cc-pVTZ (which would not be possible with systems as large as the peptides).     

A non-Karplus effect: evidence from phosphorus heterocycles and DFT calculations of the dependence of vicinal phosphorus-hydrogen NMR coupling constants on lone-pair conformation

In contrast to literature reports of a Karplus-type curve that correlates (3)J(PH) with phosphorus-hydrogen dihedral angle, a recently reported glycine-derived 1,3,2-oxazaphospholidine (7c) has two hydrogen atoms on the ring with identical PNCH dihedral angles but measured coupling constants of ～6 and 1.5 Hz. DFT calculations were in accord with these values and suggested that the smaller coupling constant is negative. Experimental evidence of the opposite signs of these coupling constants was obtained by analysis of the ABX NMR spectrum of the new glycine-derived N-p-toluenesulfonyl phosphorus heterocycle 6c. DFT calculations on 6c and on Me(2)NPCl(2) and t-BuPCl(2) were also in accord with NMR data and allowed confirmation of unusual features including a lone pair effect on (3)J(PH), the negative coupling constant, temperature-dependent chemical shifts due to rotation about the sulfonamide S-N bond, and vicinal phosphorus-hydrogen coupling constants over 40 Hz. Calculation of phosphorus-hydrogen coupling constants both as a function of PYCH dihedral angle θ (Y = O, N, C) and lone pair-PYC dihedral angle ω shows similar θ,ω surfaces for (3)J(PH) with a range of (3)J(PH) from -4.4 to +51 Hz and demonstrates the large non-Karplus effect of lone-pair conformation on vicinal phosphorus-hydrogen coupling constants.     

Conformation and orientation of tetraalanine in a lyotropic liquid crystal studied by nuclear magnetic resonance

The (1)H NMR spectra of two isotopomers of tetraalanine deuterated on the two external methyl groups and on the two internal ones, respectively, were recorded in the lyotropic solvent cesium pentadecafluorooctanoate (CsPFO)/water. Eight dipolar couplings could be estimated from the spectra. The set of dipolar couplings was fitted assuming that one rigid conformer is present. Of the four major conformers considered, selected on the basis of theoretical calculations, the one characterized by the two couples of internal dihedral angles in the Ramachandran region of PPII resulted to be the only one to fit the set of couplings within experimental error. The data indicate that the molecule is oriented with the long molecular axis tilted with respect to the surface of the micelles formed by CsPFO.     

Insights into the mobility of methyl-bearing side chains in proteins from (3)J(CC) and (3)J(CN) couplings

Side-chain dynamics in proteins can be characterized by the NMR measurement of (13)C and (2)H relaxation rates. Evaluation of the corresponding spectral densities limits the slowest motions that can be studied quantitatively to the time scale on which the overall molecular tumbling takes place. A different measure for the degree of side-chain order about the C(alpha)-C(beta) bond (chi(1) angle) can be derived from (3)J(C)(')(-)(C)(gamma) and (3)J(N)(-)(C)(gamma) couplings. These couplings can be measured at high accuracy, in particular for Thr, Ile, and Val residues. In conjunction with the known backbone structures of ubiquitin and the third IgG-binding domain of protein G, and an extensive set of (13)C-(1)H side-chain dipolar coupling measurements in oriented media, these (3)J couplings were used to parametrize empirical Karplus relationships for (3)J(C)(')(-)(C)(gamma) and (3)J(N)(-)(C)(gamma). These Karplus curves agree well with results from DFT calculations, including an unusual phase shift, which causes the maximum (3)J(CC) and (3)J(CN) couplings to occur for dihedral angles slightly smaller than 180 degrees, particularly noticeable in Thr residues. The new Karplus curves permit determination of rotamer populations for the chi(1) torsion angles. Similar rotamer populations can be derived from side-chain dipolar couplings. Conversion of these rotamer populations into generalized order parameters, S(J)(2) and S(D)(2), provides a view of side-chain dynamics that is complementary to that obtained from (13)C and (2)H relaxation. On average, results agree well with literature values for (2)H-relaxation-derived S(rel)(2) values in ubiquitin and HIV protease, but also identify a fraction of residues for which S(J,D)(2) < S(rel)(2). This indicates that some of the rotameric averaging occurs on a time scale too slow to be observable in traditional relaxation measurements.     

DFT studies of the conformational/structural dependencies of geminal 1H,1H scalar coupling 2J(H,H') in substituted methanes

A study is presented of the structural dependencies for scalar, interproton J-coupling across two bonds in a series of substituted methanes. The coupled perturbed, density functional theory method with a B3PW91 functional and aug-cc-pVTZ-J basis sets is used to examine coupling between geminal protons (2)J(H,H') in methane and a series of substituted compounds CH(3)X (X = CH3, CH(2)CH(3), CH=CH2, CH=O, and NH2) as functions of the dihedral angle phi measured about the C1-X2 bonds. All four contributions are obtained but all conformational effects are dominated by the Fermi contact term. Simple linear combination of atomic orbitals (LCAO)-molecular orbital (MO) sum-over-states methods are used to examine the relationships of the coupling constants with dihedral angles as well as internal H-C-H and H-C1-X2 angles. This study explores some novel aspects of geminal H-H coupling including an analysis of the asymmetry in the conformational dependencies arising from non-next-nearest neighbor interactions. For each of the substituted methanes, explicit trigonometric/exponential expressions are given and these accurately reproduce the (2)J(H,H') structural dependencies with standard deviations usually less than 0.03 Hz. The molecular structures for representative bicyclic molecules were fully optimized, and DFT results for (2)J(H,H') reproduce all the trends in the experimental data. A discussion is given on the applicability of the equations for H--H coupling in the substituted methanes to coupling in the bicyclic molecules.     

The conformation of tetraalanine in water determined by polarized Raman, FT-IR, and VCD spectroscopy

The present article reports the conformation of cationic tetraalanine in aqueous solution. The determination of the dihedral angles of the two central amino acid residues was achieved by analyzing the amide I' band profile in the respective polarized visible Raman, Fourier transform-IR, and vibrational circular dichroism (VCD) spectra by means of a novel algorithm which utilizes the excitonic coupling between the amide I modes of nearest neighbor and second nearest peptide groups. It is an extension of a recently developed theory (Schweitzer-Stenner, R. Biophys. J., 2002, 83, 523-532). UV electronic circular dichroism (ECD) spectra of the peptides were used to validate the results of the structure analysis. The analyses yielded the dihedral angles (phi(12), psi(12)) = (-70 degrees, 155 degrees ) and (phi(23), psi(23)) = (-80 degrees, 145 degrees ). The obtained values are very close to the Ramachandran coordinates of the polyproline II helix (PPII). The data suggest that this is the conformation predominantly adopted by the peptide at room temperature. This notion was corroborated by the corresponding electronic circular dichroism spectrum. Tetraalanine exhibits a higher propensity for PPII than trialanine for which a 50:50 mixture of polyproline II and an extended beta-strand-like conformation was obtained from recent spectroscopic studies (Eker et al., J. Am. Chem. Soc. 2002, 124, 14330-14341). The temperature dependence of the CD spectra rule out that any cooperativity is involved in the strand if PPII transition. This led to the conclusion that solvent-peptide interactions give rise to the observed PPII stability. Our result can be utilized to understand why the denaturation of helix-forming peptides generally yields a PPII rather than a heterogeneous random conformation.     

A graphical tool for the prediction of vicinal proton-proton 3J(HH) coupling constants

The easy to use and free available graphical tool MestRe-J, developed for Win-32 platforms, calculates the vicinal proton-proton coupling constants 3J(HH) from the torsion angle phi between the coupled protons for the two kinds of generalized Karplus equations developed by Altona's group as well as for equations from other authors. Besides the classical Haasnoot-de Leeuw-Altona equations, including individual substituent effects that depend on their relative Huggins's electronegativities Deltachi, the program incorporates the more recent and precise Díez-Altona-Donders equations. The substituent effects in these equations, that include effects of interactions between substituents, depend on substituent parameters lambda optimized from the 3J(HH) couplings to methyl groups. Weighted time-averaged couplings can be calculated. The equations for 3J(HH) can be solved to provide the torsion angles phi.     

29Si-13C spin-spin couplings over an Si-O-Csp3 link

(29)Si-(13)C spin-spin couplings over one, two, and three bonds as well as other NMR parameters [delta((29)Si), delta((13)C), delta((1)H), (1)J((13)C-(1)H), and (2)J((29)Si-C-(1)H)] were calculated and measured for a series of trimethylsilylated alcohols of the types Me(3)Si-O-(CH(2))(n)CH(3) and Me(3)Si-O-CH(3-n)R(n)(n = 0-3; R = Me, Ph, or Vi). The signs of the coupling constants determined for selected compounds can likely be extended to all such compounds, as supported by theoretical calculations. Similar to couplings between other pairs of nuclei, the 2-bond and 3-bond (29)Si-O-(13)C couplings are of opposite signs ((2)J > 0 and (3)J < 0), and their relative magnitudes depend on the extent of branching at the alpha-carbon.     

RPA MNDO analysis of the dihedral angle dependence of vicinal J(SnSn) and J(SnC) NMR coupling constants

Vicinal J(SnCCSn) and J(SnCCC) spin-spin coupling constants are calculated within the RPA MNDO method for different dihedral angles, θ, determined by the intervening bonds, in model compounds. For both types of couplings, calculated values closely follow Karplus-like dependences. Results are discussed in terms of experimental values, and the effects of substituents attached to the coupled atoms are briefly analyzed for the θ = 0 ° and θ = 180 ° conformations. These last values were also calculated using the RPA AM1 method. Results indicate that the RPA MNDO and RPA AM1 approaches show interesting potential for studying the structural dependences of ³J(SnSn) and ³J(SnC) couplings in tin-containing compounds.     

Structural dependencies of h3JNC' scalar coupling in protein H-bond chains

The H-bond ((h3)J(NC')) and peptide bond ((1)J(NC')) scalar couplings establish connectivity of the electronic structure in the H-bond chains of proteins. The correlated changes of (h3)J(NC') and (1)J(NC') couplings extend over several peptide groups in the chains. Consequently, the electronic structure of the H-bond chains can affect (h3)J(NC') in a manner that is independent of the local H-bond geometry. By taking this into account, and by using a more complete set of H-bond geometry parameters, we have predicted (h3)J(NC') couplings in the H-bond chains with deviations commensurate to the standard deviations of the experimentally determined values. We have created a comprehensive database of (h3)J(NC') and (1)J(NC') couplings by measuring the coupling constants in ubiquitin (alphabeta-fold) intestinal fatty acid binding protein (beta-barrel) and carp parvalbumin (alpha-helical).     

N-Acetylated amino sugars: the dependence of NMR 3J(HNH2)-couplings on conformation, dynamics and solvent

N-Acetylated amino sugars are essential components of living organisms, but their dynamic conformational properties are poorly understood due to a lack of suitable experimental methodologies. Nuclear magnetic resonance (NMR) is ideally suited to these conformational studies, but accurate equations relating the conformation of key substituents (e.g., the acetamido group) to NMR observables are unavailable. To address this, density functional theory (DFT) methods have been used to calculate vicinal coupling constants in N-acetylated amino sugars and derive empirical Karplus equations for (3)J(H(N)H(2)) of N-acetyl-D-glucosamine (GlcNAc) and N-acetyl-D-galactosamine (GalNAc). The fitted Karplus parameters were found to be similar to those previously derived for peptide amide groups, but are consistently larger in magnitude. Local intramolecular interactions had a small effect on the calculated J-couplings and comparison with experimental data suggested that DFT slightly overestimated them. An implicit solvation model consistently lowered the magnitude of the calculated values, improving the agreement with the experimental data. However, an explicit solvent model, while having a small effect, worsened the agreement with experimental data. The largest contributor to experimentally-determined (3)J(H(N)H(2))-couplings is proposed to be librations of the amide group, which are well approximated by a Gaussian distribution about a mean dihedral angle. Exemplifying the usefulness of our derived Karplus equations, the libration of the amide group could be estimated in amino sugars from experimental data. The dynamical spread of the acetamido group in free alpha-GlcNAc, beta-GlcNAc and alpha-GalNAc was estimated to be 32 degrees , 42 degrees and 20 degrees , with corresponding mean dihedral angles of 160 degrees , 180 degrees and 146 degrees , respectively.     

抗癌药物冬凌草甲素的分子构型研究

本文用同核化学位移相关谱和二维J分解谱归属了冬凌草甲素的^1H谱, 测定了所有的质子标量偶合常数, 根据一系列的Karplus公式计算了二面角, 用自编WUPH计算程序, 计算出冬凌草甲素的分子构型。     

A systematic study of minima in alanine dipeptide

The alanine dipeptide is a standard system to model dihedral angles in proteins. It is shown that obtaining the Ramachandran plot accurately is a hard problem because of many local minima; depending on the details of geometry optimizations, different Ramachandran plots can be obtained. To locate all energy minima, starting from geometries from MD simulations, 250,000 geometry optimizations were performed at the level of RHF/6-31G*, followed by re-optimizations of the located 827 minima at the level of MP2/6–311++G**, yielding 30 unique minima, most of which were not previously reported in literature. Both in vacuo and solvated structures are discussed. The minima are systematically categorized based on four backbone dihedral angles. The Gibbs energies are evaluated and the structural factors determining the relative stabilities of conformers are discussed. © 2018 Wiley Periodicals, Inc.     

Indirect NMR spin-spin coupling constants 3J(P,C) and 2J(P,H) across the P-O...H-C link can be used for structure determination of nucleic acids

Calculated indirect NMR spin-spin coupling constants (3)J(P,C) and (2)J(P,H) were correlated with the local structure of the P-O...H-C linkage between the nucleic acid (NA) backbone phosphate and the H-C group(s) of a nucleic acid base. The calculations were carried out for selected nucleotides from the large ribosomal subunit (Ban et al. Science 2000, 289, 905) with the aim of identifying NMR parameters suitable for detection of certain noncanonical RNA structures. As calculations in the model system, dimethyl-phosphate-guanine, suggest, the calculated indirect spin-spin couplings across the linkage are sensitive to the mutual orientation and distance between the phosphate and nucleic acid base. A short distance between the nucleic acid base and phosphate group and the angles C...P-O and P...C-H smaller than 50 degrees are prerequisites for a measurable spin-spin interaction of either coupling (|J| > 1 Hz). A less favorable arrangement of the P-O...H-C motif, e.g., in nucleotides of the canonical A-RNA, results in an effective dumping of both spin-spin interactions and insignificant values of the NMR coupling constants. The present work indicates that quantum chemical calculations of the indirect spin-spin couplings across the P-O...H-C motif can help detect some rare but important backbone topologies, as seen for example in the reverse kink-turn. Measuring of (3)J(P,C) and (2)J(P,H) couplings can therefore provide critical constraints on the NA base and phosphate geometry and help to determine the structure of NAs.     

Dihedral psi angle dependence of the amide III vibration: a uniquely sensitive UV resonance Raman secondary structural probe.

UV resonance Raman studies of peptide and protein secondary structure demonstrate an extraordinary sensitivity of the amide III (Am III) vibration and the C(alpha)H bending vibration to the amide backbone conformation. We demonstrate that this sensitivity results from a Ramachandran dihedral psi angle dependent coupling of the amide N-H motion to (C)C(alpha)H motion, which results in a psi dependent mixing of the Am III and the (C)C(alpha)H bending motions. The vibrations are intimately mixed at psi approximately 120 degrees, which is associated with both the beta-sheet conformation and random coil conformations. In contrast, these motions are essentially unmixed for the alpha-helix conformation where psi approximately -60 degrees. Theoretical calculations demonstrate a sinusoidal dependence of this mixing on the psi angle and a linear dependence on the distance separating the N-H and (C)C(alpha)H hydrogens. Our results explain the Am III frequency dependence on conformation as well as the resonance Raman enhancement mechanism for the (C)C(alpha)H bending UV Raman band. These results may in the future help us extract amide psi angles from measured UV resonance Raman spectra.     

Self-consistent Karplus parametrization of 3J couplings depending on the polypeptide side-chain torsion chi1.

Recently proposed self-consistent 3J coupling analysis (Schmidt, J. M.; Blümel, M.; L?hr, F.; Rüterjans, H. J. Biomol. NMR 1999, 14, 1-12) has been carried out to calibrate Karplus parameters constituting the empirical dependence of 3J coupling constants on the chi1 dihedral angle in amino acid side chains. The procedure involves simultaneous least-squares optimization of six sets of three Karplus coefficients related to all six 3J coupling types accessible in 15N,13C-labeled proteins. A simple concept of fundamental and incremental component couplings is proposed to account for substituent effects, eventually yielding amino acid topology-specific Karplus parameters. The method is exemplified with recombinant Desulfovibrio vulgaris flavodoxin (147 amino acids, 16 kDa) with reference to a total of 749 experimental 3JHalpha,Hbeta, 3JN',Hbeta, 3JC',Hbeta, 3JHalpha,Cgamma, 3JN',Cgamma, and 3JC',Cgamma coupling constants. Unlike other parametrizations, the present method does not make reference to X-ray coordinates, so that the Karplus coefficients obtained are not influenced by differences between solution and crystal states. Cross validation using X-ray torsion angles demonstrates the improvement relative to previous parametrizations. The Karplus coefficients derived are applicable to other proteins, too. Parameter refinement also yields a series of chi1 torsion angles, providing valuable constraints for protein structure determination, as well as optional parameters of local angular mobility in the contexts of Gaussian random fluctuation or a three-site jump model. The procedure permits automatic stereospecific assignments of Hbeta and Cgamma chemical shifts. The majority of the flavodoxin side-chain conformations agrees with high-resolution X-ray structures of the protein. Marked deviations between NMR and X-ray datasets are attributed to different rotameric states due to crystal-packing effects and to conformational equilibria between multiple chi1 rotamers.     

Dicondensed indolinobenzospiropyrans as precursors of thermo- and photochromic spiropyrans. Part II: Assignment of (1)H and (13)C NMR spectra

The (1)H and (13)C NMR spectra of dicondensed indolinobenzospiropyrans as precursors of thermo- and photochromic spiropyrans, DC1-DC5, were completely assigned. Especially, the (1)H assignment and coupling characteristics of the diastereotopic protons at the carbon-3 position of the benzopyran rings were achieved by conducting (1)H-(1)H COSY and nOe experiments. The dihedral angles (theta(1), theta(2) and theta(3)) calculated from the experimental values of the vicinal coupling constants ((3)J) of DC5 are in good agreement with the observed values in the solid state. All of the carbons in the DC dye molecules were investigated through a combination of heteronuclear 2D-shift correlation spectroscopy (HETCOR) and DEPT135.     

Protein Backbone 1H(N)-13Calpha and 15N-13Calpha residual dipolar and J couplings: new constraints for NMR structure determination

A simple, sensitivity-enhanced experiment was devised for accurate measurement of backbone 15N-13Calpha and 1HN-13Calpha couplings in proteins. The measured residual dipolar couplings 2DHCA, 1DNCA, 3DHCA, and 2DNCA for protein GB1 display very good agreement with the refined NMR structure (PDB code: 3GB1). A Karplus-type relationship between the one-bond 1JNCA couplings and the backbone dihedral psi angles holds, and on the basis of the two-bond 2JNCA couplings a secondary structure index can be established.