Conformational Equilibria in Polypeptides. I. Determination of AccurateJHCCoupling Constants in Antamanide by 2D NMR Multiplet Simulation

High-precision heteronuclear three-bond coupling constants including³J(H^N, C′),³J(H^N, C^β),³J(H^α,C^γ), and³J(H^β, C′) are determined for the nonproline residues in uniformly¹³C-enrichedantamanide,cyclo-(-Val¹-Pro²-Pro³-Ala⁴-Phe⁵-Phe⁶-Pro⁷-Pro⁸-Phe⁹- Phe¹⁰-), using quantitative numerical 2D NMR spectrum evaluation based on the product-operator formalism. The experimental basis comprises two-dimensional¹H,¹³C-heteronuclear relayed E.COSY spectra [J. M. Schmidt, R. R. Ernst, S. Aimoto, and M. Kainosho,J. Biomol. NMR6,95 (1995)], the multiplet patterns of which are subjected to iterative least-squares 2D multiplet-simulation procedures. Accuracy and precision of the spectrum fit are assessed byFstatistics and analysis of variances (ANOVA) leading to confidence intervals for the optimized spin-system parameters. The long-range J coupling constants obtained and their standard deviations provide the experimental foundation for a later detailed analysis of φ and χ₁dihedral-angle equilibrium conformations contributing to the flexible peptide structure.     

Accurate Measurements of Multiple-Bond C–H Coupling Constants from Phase-Sensitive 2D INEPT Spectra

Measurements of multiple-bond ¹³C–¹H coupling constants are of great interest for the assignment of nonprotonated ¹³C resonances and the elucidation of molecular conformation in solution. Usually, the heteronuclear multiple-bond coupling constants were measured either by the J_CH splittings mostly in selective 2D spectra or in 3D spectra, which are time consuming, or by the cross peak intensity analysis in 2D quantitative heteronuclear J correlation spectra (1994, G. Zhu, A. Renwick, and A. Bax, J. Magn. Reson. A 110, 257; 1994, A. Bax, G. W. Vuister, S. Grzesiek, F. Delaglio, A. C. Wang, R. Tschudin, and G. Zhu, Methods Enzymol. 239, 79.), which suffer from the accuracy problem caused by the signal-to-noise ratio and the nonpure absorptive peak patterns. Concerted incrementation of the duration for developing proton antiphase magnetization with respect to carbon-13 and the evolution time for proton chemical shift in different steps in a modified INEPT pulse sequence provides a new method for accurate measurements of heteronuclear multiple-bond coupling constants in a single 2D experiment.     

The Electric Dipole and the Nuclear Quadrupole Moment of Methyl Bromide in the Ground Vibrational State

A set of high-resolution Stark measurements at millimeter-wave frequencies is reported for CH₃⁷⁹Br and CH₃⁸¹Br. These results are analyzed together with previous data available in the literature to find new sets of molecular (rotational, hyperfine, and dipole moments) constants for both isotopic species. A particular improvement is obtained in the evaluation of the dipole moments, whose values are μ(79) = 1.82171 (26) 0, μ(8l) = 1.82185 (26) D, and for the hyperfine-structure parameters, which are estimated by assuming the most recent model for centrifugal distortion (M. R. Aliev and J. T. Hougen, J. Mol. Spectrosc.106, 110-123 (1984)), obtaining eqQ⁷⁹₀ = 577.1088 (57) MHz, χ⁷⁹_J = −0.63 (16) kHz, χ⁷⁹_K = 12.6 (16) kHz and eqQ⁸¹₀ = 482.1030 (94) MHz, χ⁸¹_J = −0.57 (17) kHz, χ⁸¹_K = 9.3 (22) kHz.     

The accuracy of whole brain N-acetylaspartate quantification

A non-localizing pulse sequence to quantify the total amount of N-acetylaspartate (NAA) in the whole brain (WBNAA) was introduced recently [Magn. Reson. Med. 40, 684–689 (1998)]. However, it is known that regional magnetic field inhomogeneities, ΔB₀s, arising from susceptibility differences at tissue interfaces, shift and broaden local resonances to outside the integration window, leading to an underestimation of the true amount of NAA in the entire brain. To quantify the upper limit of this loss, the whole-head proton MR spectrum (¹H-MRS) of the water was integrated over the same frequency width as the NAA. The ratio of this area/total-water-line was 75 ± 5% in 5 volunteers. The procedure was repeated with the brain-only water peak, obtained by summing signals only from voxels within that organ from a three-dimensional chemical-shift-imaging (3D CSI) set. It indicated that <10% of the water signal loss occurred in the brain. Therefore, by analogy, WBNAA accounts for >90% of that metabolite.     

Spin Echo Analysis of Restricted Diffusion under Generalized Gradient Waveforms: Planar, Cylindrical, and Spherical Pores with Wall Relaxivity

A simple matrix formalism presented by Callaghan [J. Magn. Reson.129, 74–84 (1997)], and based on the multiple propagator approach of Caprihanet al.[J. Magn. Reson. A118, 94–102 (1996)], allows for the calculation of the echo attenuation,E(q), in spin echo diffusion experiments, for practically all gradient waveforms. We have extended the method to the treatment of restricted diffusion in parallel plate, cylindrical, and spherical geometries, including the effects of fluid–surface interactions. In particular, theq-space coherence curves are presented for the finite-width gradient pulse PGSE experiment and the results of the matrix calculations compare precisely with published computer simulations. It is shown that the use of long gradient pulses (δ a²/D) create the illusion of smaller pores if a narrow pulse approximation is assumed, while ignoring the presence of significant wall relaxation can lead to both an underestimation of the pore dimensions and a misidentification of the pore geometry.     

On Neglecting Chemical Exchange Effects When Correcting in VivoP MRS Data for Partial Saturation

This article replies to Spencer et al. (J. Magn. Reson.149, 251–257, 2001) concerning the degree to which chemical exchange affects partial saturation corrections using saturation factors. Considering the important case of in vivo³¹P NMR, we employ differential analysis to demonstrate a broad range of experimental conditions over which chemical exchange minimally affects saturation factors, and near-optimum signal-to-noise ratio is preserved. The analysis contradicts Spencer et al.'s broad claim that chemical exchange results in a strong dependence of saturation factors upon M₀'s and T₁ and exchange parameters. For Spencer et al.'s example of a dynamic ³¹P NMR experiment in which phosphocreatine varies 20-fold, we show that our strategy of measuring saturation factors at the start and end of the study reduces errors in saturation corrections to 2% for the high-energy phosphates.     

Iterative analysis of strong coupling effects in semiselective J spectroscopy

A computer program for the iterative analysis of semiselective J spectra (A. Bax, J. Magn. Reson.52, 330 (1983)) is described, and experimental and calculated f₁ cross sections through semiselective 2D J spectra for the three-spin system of fumaric acid monoethyl ester and the five-spin system of thiophene are compared.     

Suppression of artifacts induced by homonuclear decoupling in amino-acid-type edited methyl H–C correlation experiments

A detailed theoretical and experimental analysis of the artifacts induced by homonuclear band-selective decoupling during CT frequency labeling is presented. The effects are discussed in the context of an amino-acid-type editing filter implemented in ¹H–¹³C CT-HSQC experiments of methyl groups in proteins. It is shown that both Bloch–Siegert shifts and modulation sidebands are efficiently suppressed by using additional off-resonance decoupling as proposed by Zhang and Gorenstein [J. Magn. Reson. 132 (1998) 81], and appropriate adjustment of a set of pulse sequence parameters. The theoretical predictions are confirmed by experiments performed on ¹³C-labeled protein samples, yielding artifact-free amino-acid-type edited methyl spectra.     

Correlation inequalities and the Kosterlitz-Thouless transition for anisotropic rotators

I give a proof of the Kosterlitz-Thouless transition for sufficiently anisotropic (J _zJ _x ^–1 =J _zJ _y ^–1 <2q ^–(JKT)^–J) two-dimensionalN-component rotators (N 3). The method is based on Wells' inequality and is related to mean field Gaussian inequalities.     

Sensitivity- and Gradient-Enhanced Hetero (ω1) Half-Filtered TOCSY Experiment for Measuring Long-Range Heteronuclear Coupling Constants

An enhanced version of the X(ω₁) half-filtered TOCSY experiment for measurement of long-range heteronuclear coupling constants is proposed which yields high-quality spectra with substantially increased sensitivity and resolution. The modified method features gradient-enhanced X filtering sequences, broadband homonuclear decoupling duringt₁, optional¹J_XHscaling in theF₁domain, and gradient coherence selection in combination with the sensitivity-enhanced protocol for the TOCSY transfer. These modifications extend the applicability of the method—coupling constants can be measured accurately for natural abundance samples at low concentrations and for compounds yielding complex spectra. Computer-aided analysis of E.COSY-type multiplets is applied for the determination of heteronuclear long-range coupling constants.     

Selective Homonuclear Polarization Transfer in the Tilted Rotating Frame under Magic Angle Spinning in Solids

An application of the R2TR method (1995,Chem. Phys. Lett.232,424) to selective homonuclear polarization transfer under magic angle spinning is proposed. It is shown that, for a spinning speed fast enough to remove the maximum homonuclear dipolar coupling constant ω_Dinvolved, the flip-flop and flop-flop mechanisms are suitable for recoupling the spins with a chemical shift difference larger than ω_Dand a difference comparable to or smaller than ω_D, respectively. It is also shown that, for fast polarization transfer, the off-resonance frequencies should be much higher than the RF intensity in the flip-flop condition, while for the flop-flop condition, the off-resonance frequencies should be much lower than the RF intensity. Some one- and two-dimensional experiments are proposed by utilizing the capability of the R2TR method to abruptly switch on and off the recoupling condition, and are demonstrated for triply¹³C-enriched -alanine. The mixing time required for population transfer was found to be ca. 0.5 ms for the methine and methyl¹³C spins separated by 1.5 Å and ca. 5 ms for the methyl and the carboxyl carbons separated by 2.5 Å. The experimental results and theoretical simulations show that selective polarization transfer is achieved when the difference in the isotropic chemical shifts between the relevant pair of spins and a neighboring spin is more than 1000 Hz.     

The Multidimensional Filter Diagonalization Method: II. Application to 2D Projections of 2D, 3D, and 4D NMR Experiments

The theory of the multidimensional filter diagonalization method (FDM) described in the previous paper (V. A. Mandelshtam, 2000, J. Magn. Reson. 144, 343–356 (2000)) is applied to NMR time signals with up to four independent time variables. Direct projections of the multidimensional time signals produce new kinds of 2D spectra. The resolution obtained by FDM can be far superior to that obtained by conventional phase-sensitive FT processing, and correlation peaks in heteronuclear and homonuclear experiments can be condensed to sharp singlets, removing all spin–spin couplings. Examples of singlet-HSQC and singlet-TOCSY spectra show big gains in resolution. It is not necessary to have a finely digitized spectrum, in which the individual multiplet components are resolved, for the methods to work. Examples of FDM spectra, ranging from simple organic molecules and steroids to metalloproteins, are shown.     

Measurement of Magnitude and Sign of Heteronuclear Coupling Constants in Transition Metal Complexes

Sets of specifically tailored E.COSY-type correlation experiments and double-quantum/zero-quantum (DQ/ZQ) experiments are presented which enable the determination of sign and size of small heteronuclear coupling constants across the metal center of transition metal complexes. For the octahedrally coordinated complexes, [Ru(TPM)(H)(CO)(PPh₃)]⁺[BF₄]⁻(1) and [Ir(TPM)(H)(CO)(CO₂CH₃)]⁺[BF₄]⁻(2), 14 of 15 and 15 of 15 possible two-bond scalar coupling constants across the metal center were measured, respectively, using¹⁵N and¹⁵N/¹³C enriched samples (TPM = tris(1-pyrazolyl)methane)). The reduced coupling constants²K_X-M-Y= 4π²²J/(hγ_Xγ_Y) were found to be positive when the coupled nuclei X and Y weretranswith respect to the metal center, and negative when the coupled nuclei were incisposition. The validity of this sign rule was verified forJ_CC,J_NN,J_PN,J_PC,J_CN,J_HP,J_HC, andJ_HNcouplings. Idiosyncracies associated with 2D NMR spectra for the sign determination of coupling constants with¹⁵N which lead to corrections for the signs ofJ_HN,J_PN, andJ_CNcouplings reported previously are discussed.     

Comparative Studies of Phase-Cycling Schemes for Multiple π-Pulse Sequences

Recently, a new phase cycling scheme was introduced by this laboratory for use in biological solid-state NMR experiments involving multiple π-pulses with characteristics that suggested it may enhance the sensitivity of these kind of experiments (Y. Li and J. N. S. Evans, 1995,Chem. Phys. Lett.241,79 and Erratum, 1995,ibid.246,527; Y. Li and J. N. S. Evans, 1996,J. Magn. Reson. B111,296). The new sequence followed the supercycled concept proposed a decade ago for heteronuclear decoupling experiments. In this paper, more detailed experiments demonstrate that the claim of enhanced sensitivity was unfounded, and in fact the supercycle proposed differs little from the established XY-8 and XY-16 based supercycles.     

Recoupled Polarization-Transfer Methods for Solid-State H–C Heteronuclear Correlation in the Limit of Fast MAS

An in-depth account of the effects of homonuclear couplings and multiple heteronuclear couplings is given for a recently published technique for ¹H–¹³C dipolar correlation in solids under very fast MAS, where the heteronuclear dipolar coupling is recoupled by means of REDOR π-pulse trains. The method bears similarities to well-known solution-state NMR techniques, which form the framework of a heteronuclear multiple-quantum experiment. The so-called recoupled polarization-transfer (REPT) technique is versatile in that rotor-synchronized ¹H–¹³C shift correlation spectra can be recorded. In addition, weak heteronuclear dipolar coupling constants can be extracted by means of spinning sideband analysis in the indirect dimension of the experiment. These sidebands are generated by rotor encoding of the reconversion Hamiltonian. We present generalized variants of the initially described heteronuclear multiple-quantum correlation (HMQC) experiment, which are better suited for certain applications. Using these techniques, measurements on model compounds with ¹³C in natural abundance, as well as simulations, confirm the very weak effect of ¹H–¹H homonuclear couplings on the spectra recorded with spinning frequencies of 25–30 kHz. The effect of remote heteronuclear couplings on the spinning-sideband patterns of CH_n groups is discussed, and ¹³C spectral editing of rigid organic solids is shown to be practicable with these techniques.     

The Multidimensional Filter Diagonalization Method: I. Theory and Numerical Implementation

The theory and numerical aspects of the recently developed multidimensional version of the filter diagonalization method (FDM) are described in detail. FDM can construct various “ersatz” or “hybrid” spectra from multidimensional time signals. Spectral resolution is not limited by the time-frequency uncertainty principle in each separate frequency dimension, but rather by the total joint information content of the signal, i.e., N_total = N₁ × N₂ × × N_D, where some of the interferometric dimensions do not have to be represented by more than a few (e.g., two) time increments. It is shown that FDM can be used to compute various reduced-dimensionality projections of a high-dimensional spectrum directly, i.e., avoiding construction of the latter. A subsequent paper (J. Magn. Reson. 144, 357–366 (2000)) is concerned with applications of the method to 2D, 3D, and 4D NMR experiments.     

Accurate Measurement of Small Spin–Spin Couplings in Partially Aligned Molecules Using a Novel J-Mismatch Compensated Spin-State-Selection Filter

The accurate measurement of small spin–spin coupling constants in macromolecules dissolved in a liquid crystalline phase is important in the context of molecular structure investigation by modern liquid state NMR. A new spin-state-selection filter, DIPSAP, is presented with significantly reduced sensitivity to J-mismatch of the filter delays compared to previously proposed pulse sequences. DIPSAP presents an attractive new approach for the accurate measurement of small spin–spin coupling constants in molecules dissolved in anisotropic solution. Application to the measurement of ¹⁵N–¹³C′ and ¹H^N–¹³C′ coupling constants in the peptide planes of ¹³C, ¹⁵N labeled proteins demonstrates the high accuracy obtained by a DIPSAP-based experiment.     

Diborane : High resolution infrared rovibration studies of B2H6 and B2D6

Ground state rotation and quartic distortion constants were obtained for ¹¹B₂D₆ from the analysis of high resolution (0.05 cm⁻¹) Fourier transform infrared spectra. The bands studied comprised the ν₁₇, ν₁₈ type A, and ν₁₄, ν₉ + ν₁₅ type C bands of ¹¹B₂H₆ and the ν₁₆, ν₁₇, ν₁₈ type A, ν₈ type B, and ν₁₄ type C bands of ¹¹B₂D₆. In the case of ¹¹B₂H₆, the authors' ground state data were combined with those of Lafferty et al. obtained from a previous study (J. Mol. Spectrosc. 33, 345–367 (1970)) at comparable resolution of the ν₁₆ type A and ν₈ type B fundamentals. Information on the ground state rotational energy manifold of ¹¹B₂H₆ was accumulated up to J = 23, K_a = 18, and of ¹¹B₂D₆ up to J = 32, K_a = 22. This permitted rather precise determination of the distortion constants Δ_J⁰, Δ_JK⁰, Δ_K⁰, although δ_J⁰ and δ_K⁰ proved to be too small (< 10⁻⁷ cm⁻¹) and were constrained to values calculated from the force field. Sets of upper state parameters were determined for all vibrational levels studied. Although these appear to be essentially unperturbed globally, several localized perturbations were observed and identified.     

Semi-Constant-Time HMSQC (SCT-HMSQC-HA) for the Measurement of JHH Couplings in N-Labeled Proteins

A simple method for accurately measuring ³J_H^NH^α coupling constants in ¹⁵N-labeled proteins is described. This semi-constant-time HMSQC-HA experiment combines the rapidity and convenience of the recently introduced CT-HMQC-HA scheme (Postingl and Otting, J. Biomol. NMR 12, 319–324 (1998)) with the high resolution and robustness of the HSQC experiment. The proposed method is demonstrated for the 76-residue human ubiquitin and Saccharopolyspora erythraea calerythrin (176 residues). Our results imply that the SCT-HMSQC-HA experiment is suitable also for proteins with less favorable NMR properties due to its good resolution and sensitivity.