Bayesian Estimation of NMR Spectral Parameters Under Low Signal-to-Noise Conditions

The Bayesian statistical method of spectral estimation is applied to NMR free induction decay signals at various values of signal-to-noise ratio (SNR). The frequency and amplitude estimates from the Bayesian calculations are more accurate than those from the commonly used fast Fourier transformation (FFT) of the same data sets. Both real and synthetic data sets are examined with the Bayesian results being superior in all cases. In addition to the superior performance at low SNR the Bayesian derived amplitudes and frequency estimates were not as affected by signal decay as in Fourier Transformed spectra. Finally, the amplitudes obtained are equal to the FFT integrated intensities resulting in an apparent frequency domain signal-to-noise ratio (SNR) greater than the FFT SNR by a factor proportional to the FFT frequency domain linewidth. For typical high resolution spectra this improvement was approximately a factor of 2.5. Even greater improvement is obtained when rapidly decaying signals are analyzed. Bayesian computation time for the 6 line p-chloroanaline and chloroform spectrum was approximately 12 minutes on a modern computer work station.     

改进的贝叶斯压缩感知目标方位估计

针对基于高斯先验模型的贝叶斯压缩感知在目标方位(Direction Of Arrival,DOA)估计中可能出现明显随机伪峰的问题,改进了高斯先验模型,并在此基础上提出了一种贝叶斯压缩感知目标方位估计方法。通过波束输出噪声背景预估与二值指示变量标记,并引入基于信号先验方差的噪声方差估计方法,与变分贝叶斯推断相结合改进目标方位估计性能和优化迭代收敛过程。利用32元线阵对改进算法进行数值仿真处理和分析结果表明,该改进方法不仅可以准确估计目标信号的方位,而且可以显著地减少空间谱中伪峰的数量。实际海上实验数据处理结果表明,使用改进后的贝叶斯压缩感知方法进行DOA估计,可以显著地抑制空间谱中随机的伪峰,提高波束输出峰值背景比,具有更强的目标检测能力。     

Resolution enhancement in in vivo NMR spectroscopy: detection of intermolecular zero-quantum coherences

Intermolecular zero-quantum coherences are insensitive to magnetic field inhomogeneities. For this reason we have applied the HOMOGENIZED sequence [Vathyam et al., Science 272 (1996) 92] to phantoms containing metabolites at low concentrations, phantoms with air inclusions, an intact grape, and the head of a rat in vivo at 750 MHz. In the 1H-spectra, the water signal is efficiently suppressed and line broadening due to susceptibility gradients is effectively removed along the indirectly detected dimension. We have obtained a 1H-spectrum of a 2.5 mM solution of gamma-aminobutyric acid in 12 min scan time. In the phantom with air inclusions a reduction of line widths from 0.48 ppm in the direct dimension to 0.07 ppm in the indirect dimension was observed, while in a deshimmed grape the reduction was from 1.4 to 0.07 ppm. In a spectrum of the grape we were able to resolve glucose resonances at 0.3 ppm from the water in 6 min scan time. J-coupling information was partly retained. In the in vivo spectra of the rat brain five major metabolites were observed.     

Effects of zero-filling and apodization on spectral integrals in discrete Fourier-transform spectroscopy of noisy data

The influence of noise on the standard deviation of spectral integrals is examined. Calculations assuming discrete Fourier-transform data are compared with Monte-Carlo simulations. The effects of zero-filling and apodization are examined for free-induction-decay (FID) signals and for symmetric spin-echo signals in one and two dimensions, with particular attention to features not previously presented in the literature. Findings suggest that for mild apodization, the known sensitivity enhancement due to zero-filling in either the real or the imaginary part signal [E. Bartholdi, R.R. Ernst, Fourier spectroscopy and the causality principle, J. Magn. Reson., 11 (1973) 9-19] is maintained; however, for stronger apodization filters, this enhancement can be obliterated completely. It is shown that results obtained by analysis of one-dimensional signals can be readily applied to multi-dimensional data. Furthermore, zero-filling has a negligible effect for symmetric spin-echo signals with implications for signal averaging in magnetic resonance imaging and spectroscopic imaging.     

X-ray and high resolution selenium-77 solid state NMR spectroscopy as complementary probes to structural studies of organophosphorus diselenides

high resolution solid state NMR spectroscopy was employed to study structural properties of bis(diisopropoxyphosphorothioyl) diselenide 1 and bis(dineopentoxyphosphorothioyl) diselenide 2. The principal elements T_ii of effective dipolar/chemical shift tensor were calculated from spinning sideband intensities employing the WIN-MAS program. The values of anisotropy and asymmetry parameters reflect the distortion of the selenium environment. It was found that the T₃₃ component mostly contributes to changes in the isotropic chemical shifts. CP/MAS experiments were used to decide the assignment of space group by counting the number of crystallographically unique selenium centers in the unit cell. Crystals of diselenide 1 are triclinic, space group P with a=8.485(3) Å, b=8.508(1) Å, c=8.511(2) Å, =98.835(15)°, β=111.653(24)°, γ=93.524(21)°, V=559.5(3) ų, D_c=1.544(2) g/cm³ and Z=1. Refinement using 2222 reflections for 157 variables gives R=0.037. Crystals of diselenide 2 are triclinic, space group P1 with a=9.1418(8) Å, b=9.1465(8) Å, c=9.9200(9) Å, =74.751(8)°, β=74.629(7)°, γ=82.216(7)°, V=769.7(1) ų, D_c=1.365(2) g/cm³ and Z=1. Refinement using 3316 reflections for 297 variables gives R=0.0272.     

Double-quantum homonuclear NMR correlation spectroscopy of quadrupolar nuclei subjected to magic-angle spinning and high magnetic field

We present a new application of the symmetry-based dipolar recoupling scheme, for exciting directly double-quantum (2Q) coherences between the central transition of homonuclear half-integer quadrupolar nuclei. With respect to previously published 2Q-recoupling methods (M. Eden, D. Zhou, J. Yu, Chem. Phys. Lett. 431 (2006) 397), the sequence is used without π/2 bracketing pulses and with an original super-cycling. This leads to an improved efficiency (a factor of two for spin-5/2) and to a much higher robustness to radio-frequency field inhomogeneity and resonance offset. The 2Q-coherence excitation performances are demonstrated experimentally by ²⁷Al NMR experiments on the aluminophosphates berlinite, VPI5, AlPO₄-14, and AlPO₄-CJ3. The two-dimensional 2Q–1Q correlation experiments incorporating these recoupling sequences allow the observation of 2Q cross-peaks between central transitions, even at high magnetic field where the difference in offset between octahedral and tetrahedral ²⁷Al sites exceeds 10 kHz.     

Selective refocusing pulses in magic-angle spinning NMR: characterization and applications to multi-dimensional protein spectroscopy

Band-selective pulses are frequently used in multi-dimensional NMR in solution, but have been used relatively less often in solid-state NMR applications because of the complications imposed by magic-angle spinning. In this work, we examine the frequency profiles and the refocusing efficiency of several commonly employed selective general rotation pi pulses through experiments and numerical simulations. We demonstrate that highly efficient refocusing of transverse magnetization can be achieved, with experiments that agree well with numerical simulations. We also show that the rotational echo is shifted by a half rotor period if a selective pulse is applied over an integer number of rotor periods. Appropriately synchronizing indirect evolution periods with selective pulses ensures proper phasing of cross peaks in 2D spectra. The improved performance of selective pulses in multi-dimensional protein spectroscopy is demonstrated on the 56-residue beta1 immunoglobulin binding domain of protein G (GB1).     

Grand Canonical Ensembles of Sparse Networks and Bayesian Inference

Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes and are typically not exchangeable. Here we consider hierarchical models for exchangeable networks in the sparse limit, i.e., with the total number of links scaling linearly with the total number of nodes. The approach is grand canonical, i.e., the number of nodes of the network is not fixed a priori: it is finite but can be arbitrarily large. In this way the grand canonical network ensembles circumvent the difficulties in treating infinite sparse exchangeable networks which according to the Aldous-Hoover theorem must vanish. The approach can treat networks with given degree distribution or networks with given distribution of latent variables. When only a subgraph induced by a subset of nodes is known, this model allows a Bayesian estimation of the network size and the degree sequence (or the sequence of latent variables) of the entire network which can be used for network reconstruction.     

Spherical neutron polarimetry applied to spin-echo and time-of-flight spectroscopy

The changes in direction of the neutron spin that take place on scattering by a magnetic interaction vector are highly dependent on their relative directions. In some circumstances, without zero-field polarimeter, it is impossible to distinguish between a simple depolarisation and a rotation of the polarisation vector.Motivated by the investigation of chiral magnetic fluctuations, we have implemented the third-generation zero-field polarimeter Cryopad on the neutron spin-echo spectrometer SPAN at the Helmholtz Centre Berlin (HCB). We present the method and the limitations of this novel technique that is now available on IN15 at the ILL.The huge progress accomplished with ³He neutron spin filters/flippers are going to facilitate the exploitation of polarised beams at spallation sources. Zero-field polarimeters like Cryopad are used routinely at several steady-state sources but their design would be inefficient at a pulse source. We have investigated the possibility to implement a zero-field polarimeter on a time-of-flight spectrometer. We propose a design that would lead to a better efficiency and present the finite element calculations.     

Feasibility of arsenic and antimony NMR spectroscopy in solids: An investigation of some group 15 compounds

The feasibility of obtaining ⁷⁵As and ^121/123Sb NMR spectra for solids at high and moderate magnetic field strengths is explored. Arsenic-75 nuclear quadrupolar coupling constants and chemical shifts have been measured for arsenobetaine bromide and tetraphenylarsonium bromide. Similarly, ^121/123Sb NMR parameters have been measured for tetraphenylstibonium bromide and potassium hexahydroxoantimonate. The predicted pseudo-tetrahedral symmetry at arsenic and the known trigonal bipyramidal symmetry at antimony in their respective tetraphenyl-bromide “salts” are reflected in the measured ⁷⁵As and ¹²¹Sb nuclear quadrupole coupling constants, C_Q(⁷⁵As)=7.8 MHz and C_Q(¹²¹Sb)=159 MHz, respectively. Results of density functional theory quantum chemistry calculations for isolated molecules using ADF and first-principles calculations using CASTEP, a gauge-including projector augmented wave method to deal with the periodic nature of solids, are compared with experiment. Although the experiments can be time consuming, measurements of ⁷⁵As and ¹²¹Sb NMR spectra (at 154 and 215 MHz, respectively, i.e., at B₀=21.14 T) with linewidths in excess of 1 MHz are feasible using uniform broadband excitation shaped pulse techniques (e.g., WURST and WURST-QCPMG).     

Perspectives of solution NMR spectroscopy for structural and functional studies of integral membrane proteins

This article discusses future perspectives of solution NMR spectroscopy to study structures and functions of integral membrane proteins at atomic resolution, based on a review of recent progress in this area. Several selected examples of structure determinations, as well as functional studies of integral membrane proteins are highlighted. We expect NMR spectroscopy to make future key scientific contributions to understanding membrane protein function, in particular for large membrane protein systems with known three-dimensional structure. Such situations can benefit from the fact that functional NMR studies have substantially less limitations by molecular size than a full de novo structure determination. Therefore, the general potential for NMR spectroscopy to solve biologic key questions associated with integral membrane proteins is very promising.     

Studies on the structures and interactions of glutathione in aqueous solution by molecular dynamics simulations and NMR spectroscopy

All-atom molecular simulations and temperature-dependent NMR have been used to investigate the conformations and hydrogen bonds of glutathione (GSH) in aqueous solution. The simulations start from three different initial conformations. The properties are characterized by intramolecular distances, radius of gyration, root-mean-square deviation, and solvent-accessible surface. GSH is highly flexible in aqueous solutions in the simulations. Moreover, conformations can covert between “extended” and “folded” states. Interestingly, the two different hydrogen atoms in cysteine (H_N2) and glycin (H_N3) show different capabilities in forming NH?OW hydrogen bonds. The temperature-dependent NMR results of the different amide hydrogen atoms also show agreements with the MD simulations. Competing formation of GSH hydrogen-bonding interactions in aqueous solutions leads to hydrogen-bonding networks and the distribution of conformations. These changes will affect the activity of GSH under physiological conditions.     

Correction of baseline and lineshape distortions in fourier transform NMR spectroscopy by estimation of missing signals

Lineshape distortions and baseline undulations are the well-known undesirable effects of the linear phase correction, when applied to signals the initial part of which is corrupted, either duplicated or missing. While the former imperfection can be cured easily by proper time setting, the latter is more principal. It is shown, however, that some general prior knowledge of spectra enables the reconstruction of the missing part of the signal with high fidelity and the removal of most of the distortions appearing in the absorption-mode spectra. For this purpose a simple procedure is proposed yielding good results even after a single iteration step. Simplicity, negligible computational requirements, and its efficacy are the main advantages of this method.     

Time-domain terahertz and infrared spectroscopy of BaTiO3–PVDF nanocomposites

Several composites of BaTiO₃ nanoparticles obtained by mechanosynthesis embedded into a PVDF matrix were studied using time-domain THz and FTIR spectroscopies and microwave measurements with the split-post-resonator technique. No indication of the ferroelectric phase transition could be seen in the temperature dependence of the effective dielectric response, in agreement with expectations based on various effective medium models. The effective soft-mode frequency is strongly shifted up and smeared. No conclusion on the size effect of ferroelectricity can be drawn from the effective dielectric response.     

Stochastic analysis of recurrence plots with applications to the detection of deterministic signals

Recurrence plots have been widely used for a variety of purposes such as analyzing dynamical systems, denoising, as well as detection of deterministic signals embedded in noise. Though it has been postulated previously that recurrence plots contain time correlation information here we make the relationship between unthresholded recurrence plots and the covariance of a random process more precise. Computations using examples from harmonic processes, autoregressive models, and outputs from nonlinear systems are shown to illustrate this relationship. Finally, the use of recurrence plots for detection of deterministic signals in the presence of noise is investigated and compared to traditional signal detection methods based on the likelihood ratio test. Results using simulated data show that detectors based on certain statistics derived from recurrence plots are sub-optimal when compared to well-known detectors based on the likelihood ratio.     

Double-quantum NMR spectroscopy of P species submitted to very large CSAs

We introduce an original pulse sequence, , which is a block super-cycled sequence employing as basic element a π pulse sandwiched by ‘window’ intervals. This homonuclear dipolar recoupling method allows the efficient excitation of double-quantum coherences between spin-1/2 nuclei submitted to very large chemical shift anisotropy. We demonstrate that this technique can be employed in double-quantum ↔ single-quantum ³¹P homonuclear correlation experiment at high magnetic field (B₀  14 T) and high MAS frequencies (ν_R  30 kHz). The performances of are compared to those of the double-quantum recoupling methods, such as BABA and bracketed fp-RFDR, which were already employed at fast MAS rates. The sequence displays a higher robustness to CSA and offset than the other existing techniques.     

Solid-state photodimerization of 4-aryl-1,4-dihydropyridines studied by C CPMAS NMR spectroscopy

¹³C CPMAS NMR spectroscopy has been applied to monitor the solid-state reaction of two different photodimerizing 4-phenyl-1,4-dihydropyridines yielding a cage dimer in one case and an anti-dimer in the other case. The spectra of the reacting monomers exhibit a magnetical inequivalence of chemically equivalent CO and C2/4 carbon atoms caused by a rotation of the pseudoaxially oriented 4-phenyl substituent out off the plane through N1, C3, C8 which could be determined by X-ray crystal structure analyses of the centrosymmetrically arranged monomers. The ¹³C CPMAS NMR monitoring of the cage dimer formation proves that the reaction takes place in two steps via a syn-dimer for which a non-symmetrical structure was derived from the spectrum. The non-symmetrical structure was confirmed by X-ray crystal structure analysis of one structurally related derivative. A centrosymmetric structure for both the finally formed cage dimer and the anti-dimer of the other monitored photoreaction was proved by their spectra with one set of signals for each half of the dimers, respectively. Thus, conformational properties of the molecules as well as the symmetry of the products can be directly derived from the ¹³C CPMAS NMR spectra.     

Increasing the sensitivity of 2D high-resolution NMR methods applied to quadrupolar nuclei

Gan and Kwak recently proposed a soft-pulse added mixing (SPAM) idea in the classical two-pulse multiple-quantum magic-angle spinning scheme. In the SPAM method, a soft pi/2 pulse is added after the second hard-pulse (conversion pulse) and all coherence orders in between them are constructively used to obtain the signal. We, here, further extend this idea to distributed samples where the signal mainly results from echo pathways and that from anti-echo pathways dies out after a few t1 increments. We show that, with a combination of SPAM and collection of fewer anti-echoes, an enhancement of the signal to noise ratio by a factor of ca. 3 may be obtained over the z-filtered version. This may prove to be useful even for samples with long T2' relaxation times.