MUSIC and Aromatic Residues: Amino Acid Type-Selective H–N Correlations, III

Amino acid type-selective experiments can help to remove ambiguities in automated assignment procedures for ¹⁵N/¹³C-labeled proteins. Here we present five triple-resonance experiments that yield amino acid type-selective ¹H–¹⁵N correlations for aromatic amino acids. Four of the novel experiments are based on the MUSIC coherence transfer scheme that replaces the initial INEPT transfer and is selective for CH₂. The MUSIC sequence is combined with selective excitation pulses to create experiments for Trp (W-HSQC) as well as Phe, Tyr, and His (FYH-HSQC). In addition, an experiment selective for Trp H¹–N¹ is presented. The new experiments are recorded as two-dimensional experiments and their performance is demonstrated with the application to a protein domain of 115 amino acids.     

A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows

We propose a new model and a solution method for two-phase compressible flows. The model involves six equations obtained from conservation principles applied to each phase, completed by a seventh equation for the evolution of the volume fraction. This equation is necessary to close the overall system. The model is valid for fluid mixtures, as well as for pure fluids. The system of partial differential equations is hyperbolic. Hyperbolicity is obtained because each phase is considered to be compressible. Two difficulties arise for the solution: one of the equations is written in non-conservative form; non-conservative terms exist in the momentum and energy equations. We propose robust and accurate discretisation of these terms. The method solves the same system at each mesh point with the same algorithm. It allows the simulation of interface problems between pure fluids as well as multiphase mixtures. Several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible. The method provides reliable results, is able to compute strong shock waves, and deals with complex equations of state.     

Modeling Three-Dimensional Multiphase Flow Using a Level Contour Reconstruction Method for Front Tracking without Connectivity

Three-dimensional multiphase flow and flow with phase change are simulated using a simplified method of tracking and reconstructing the phase interface. The new level contour reconstruction technique presented here enables front tracking methods to naturally, automatically, and robustly model the merging and breakup of interfaces in three-dimensional flows. The method is designed so that the phase surface is treated as a collection of physically linked but not logically connected surface elements. Eliminating the need to bookkeep logical connections between neighboring surface elements greatly simplifies the Lagrangian tracking of interfaces, particularly for 3D flows exhibiting topology change. The motivation for this new method is the modeling of complex three-dimensional boiling flows where repeated merging and breakup are inherent features of the interface dynamics. Results of 3D film boiling simulations with multiple interacting bubbles are presented. The capabilities of the new interface reconstruction method are also tested in a variety of two-phase flows without phase change. Three-dimensional simulations of bubble merging and droplet collision, coalescence, and breakup demonstrate the new method's ability to easily handle topology change by film rupture or filamentary breakup. Validation tests are conducted for drop oscillation and bubble rise. The susceptibility of the numerical method to parasitic currents is also thoroughly assessed.     

A new method for variable temperature gradient shimming

Sample convection can severely attenuate the signals observed in pulsed field gradient spin--echo experiments such as those used for gradient shimming. A new class of pulse sequences is proposed, in which a double spin--echo refocuses the phase errors caused by sample convection, enabling gradient shimming to be performed reliably over a wide range of temperatures.     

Positive Numerical Integration Methods for Chemical Kinetic Systems

Chemical kinetics conserves mass and renders nonnegative solutions; a good numerical simulation would ideally produce mass-balanced, positive concentration vectors. Many time-stepping methods are mass conservative; however, unconditional positivity restricts the order of a traditional method to one. The projection method presented in this paper ensures mass conservation and positivity. First, a numerical approximation is computed with one step of a mass-preserving traditional scheme. If there are negative components, the nearest vector in the reaction simplex is found by solving a quadratic optimization problem; this vector is shown to better approximate the true solution. A simpler version involves just one projection step and stabilizes the reaction simplex. This technique works best when the underlying time-stepping scheme favors positivity. Projected methods are more accurate than clipping and allow larger time steps for kinetic systems which are unstable outside the positive quadrant.     

Linewidth-Resolved N HSQC, a Simple 3D Method to Measure N Relaxation Times from T1 and T2 Linewidths

A three-dimensional approach for measuring ¹⁵N relaxation times is described. Instead of selecting particular values for the relaxation period, in the proposed method the relaxation period is incremented periodically in order to create a 3D spectrum. This additional frequency domain of the transformed spectrum contains the relaxation time information in the T₁ and T₂ linewidths, and thus the longitudinal and transverse ¹⁵N relaxation times can be measured without determination of 2D cross peak volumes/intensities and subsequent curve fitting procedures.     

NMR spectral quantitation by principal component analysis. III. A generalized procedure for determination of lineshape variations

We present a general procedure for automatic quantitation of a series of spectral peaks based on principal component analysis (PCA). PCA has been previously used for spectral quantitation of a single resonant peak of constant shape but variable amplitude. Here we extend this procedure to estimate all of the peak parameters: amplitude, position (frequency), phase and linewidth. The procedure consists of a series of iterative steps in which the estimates of position and phase from one stage of iteration are used to correct the spectra prior to the next stage. The process is convergent to a stable result, typically in less than 5 iterations. If desired, remaining linewidth variations can then be corrected. Correction of (typically) unwanted variations of these types is important not only for direct peak quantitation, but also as a preprocessing step for spectral data prior to application of pattern recognition/classification techniques. The procedure is demonstrated on simulated data and on a set of 992 (31)P NMR in vivo spectra taken from a kinetic study of rat muscle energetics. The proposed procedure is robust, makes very limited assumptions about the lineshape, and performs well with data of low signal-to-noise ratio.     

A two-dimensional artifact from asynchronous decoupling

Many heteronuclear NMR experiments employ decoupling to collapse the heteronuclear multiplet, using decoupling schemes with a periodic phase modulation like WALTZ, MLEV, or GARP. Because of the periodic nature of these schemes, cycling sidebands are generated, whose intensity can be strongly reduced by decoupling asynchronously. We show that the most common implementation of asynchronous decoupling on modern spectrometers is such that the cycling sidebands are subjected to a periodic modulation. For multidimensional experiments, this results in ridges that can seriously compromise the quality of the spectrum. Based on our model, the artifact in a 2D [(1)H]-(15)N NOE equilibrium experiment is simulated and it is shown that the artifact can be prevented by using synchronous decoupling.     

GAMMA simulations of stray field responses: slice thickness and pulse calibration

A stray field (STRAFI) module has been added to the GAMMA magnetic resonance simulation platform in order to facilitate computational investigations of NMR experiments in large static field gradients that are on the order of 50 T/m. The package has been used to examine system response during echo trains generated by the application of shaped pulses. The associated echo amplitude maxima and effective slice thickness are presented. A new accurate method for STRAFI pulse calibration based on relative echo amplitudes is proposed.     

Improved narrowband dipolar recoupling for homonuclear distance measurements in rotating solids

Recovery of the magnetic dipolar interaction between nuclei bearing the same gyromagnetic ratio in rotating solids can be promoted by synchronous rf irradiation. Determination of the dipolar interaction strength can serve as a tool for structural elucidation in polycrystalline powders. Spinning frequency dependent narrow-band (nb) RFDR and SEDRA experiments are utilized as simple techniques for the determination of dipolar interactions between the nuclei in coupled homonuclear spin pairs. The magnetization exchange and coherence dephasing due to a fixed number of rotor-synchronously applied pi-pulses is monitored at spinning frequencies in the vicinity of the rotational resonance (R(2)) conditions. The powder nbRFDR and nbSEDRA decay curves of spin magnetizations and coherences, respectively, as a function of the spinning frequency can be measured and analyzed using simple rate equations providing a quantitative measure of the dipolar coupling. The effects of the phenomenological relaxation parameters in these rate equations are discussed and an improved methodology is suggested for analyzing nbRFDR data for small dipolar couplings. The distance between the labeled nuclei in the 1,3-(13)C(2)-hydroxybutyric acid molecule is rederived using existing nbRFDR results and the new simulation procedure. A nbSEDRA experiment has been performed successfully on a powder sample of singly labeled 1-(13)C-L-leucine measuring the dipolar interaction between the labeled carboxyl carbon and the natural abundant beta-carbon. Both narrowband techniques are employed for the determination of the nuclear distances between the side-chain carbons of leucine and its carbonyl carbon in a tripeptide Leu-Gly-Phe that is singly (13)C-labeled at the leucine carbonyl carbon position.     

Implementation Aspects of 3D Lattice-BGK: Boundaries, Accuracy, and a New Fast Relaxation Method

In many realistic fluid-dynamical simulations the specification of the boundary conditions, the error sources, and the number of time steps to reach a steady state are important practical considerations. In this paper we study these issues in the case of the lattice-BGK model. The objective is to present a comprehensive overview of some pitfalls and shortcomings of the lattice-BGK method and to introduce some new ideas useful in practical simulations. We begin with an evaluation of the widely used bounce-back boundary condition in staircase geometries by simulating flow in an inclined tube. It is shown that the bounce-back scheme is first-order accurate in space when the location of the non-slip wall is assumed to be at the boundary nodes. Moreover, for a specific inclination angle of 45 degrees, the scheme is found to be second-order accurate when the location of the non-slip velocity is fitted halfway between the last fluid nodes and the first solid nodes. The error as a function of the relaxation parameter is in that case qualitatively similar to that of flat walls. Next, a comparison of simulations of fluid flow by means of pressure boundaries and by means of body force is presented. A good agreement between these two boundary conditions has been found in the creeping-flow regime. For higher Reynolds numbers differences have been found that are probably caused by problems associated with the pressure boundaries. Furthermore, two widely used 3D models, namelyD₃Q₁₅andD₃Q₁₉, are analysed. It is shown that theD₃Q₁₅model may induce artificial checkerboard invariants due to the connectivity of the lattice. Finally, a new iterative method, which significantly reduces the saturation time, is presented and validated on different benchmark problems.     

Separating Structure and Dynamics in CSA/DD Cross-Correlated Relaxation: A Case Study on Trehalose and Ubiquitin

We present two new sensitivity enhanced gradient NMR experiments for measuring interference effects between chemical shift anisotropy (CSA) and dipolar coupling interactions in a scalar coupled two-spin system in both the laboratory and rotating frames. We apply these methods for quantitative measurement of longitudinal and transverse cross-correlation rates involving interference of ¹³C CSA and ¹³C–¹H dipolar coupling in a disaccharide, α,α- -trehalose, at natural abundance of ¹³C as well as interference of amide ¹⁵N CSA and ¹⁵N–¹H dipolar coupling in uniformly ¹⁵N-labeled ubiquitin. We demonstrate that the standard heteronuclear T₁, T₂, and steady-state NOE autocorrelation experiments augmented by cross-correlation measurements provide sufficient experimental data to quantitatively separate the structural and dynamic contributions to these relaxation rates when the simplifying assumptions of isotropic overall tumbling and an axially symmetric chemical shift tensor are valid.     

Phase-Accuracy Comparisons and Improved Far-Field Estimates for 3-D Edge Elements on Tetrahedral Meshes

Edge-element methods have proved very effective for 3-D electromagnetic computations and are widely used on unstructured meshes. However, the accuracy of standard edge elements can be criticised because of their low order. This paper analyses discrete dispersion relations together with numerical propagation accuracy to determine the effect of tetrahedral shape on the phase accuracy of standard 3-D edge-element approximations in comparison to other methods. Scattering computations for the sphere obtained with edge elements are compared with results obtained with vertex elements, and a new formulation of the far-field integral approximations for use with edge elements is shown to give improved cross sections over conventional formulations.     

Non-CPMG Fast Spin Echo with full signal

The standard Fast Spin Echo sequence used in MR imaging relies on the CPMG condition. A consequence of this condition is that only one component of the transverse magnetization can be measured. To counter this, some phase modulation schemes (XY, MLEV.) for the pulse train have been proposed, but they are useful only over a very restricted range, close to pi, of the refocusing pulse rotation angle. Some other solutions not relying on phase modulation have also been suggested, but they destroy one half the available signal. Revisiting the phase modulation approach, J. Murdoch ("Second SMR Scientific Meeting," p. 1145, 1994) suggested that a quadratic phase modulation could generate a train of classical echoes. We show here that indeed a quadratic phase modulation has a very suitable property: after an adequate change of frame, the dynamic of the system composed of all the protons situated in one pixel can be seen as stationary. If the parameter of the quadratic phase modulation is well chosen, it is then possible to put the dynamic system in a combination of two suitable states and obtain a signal identical to the signal of a classical spin echo, at least for nutation of the refocusing pulse higher than, approximately, two radians.     

Tailored HCCH-TOCSY experiment for resonance assignment in the proximity of a paramagnetic center

The presence of a paramagnetic center may disturb both coherent and incoherent communication between nuclear spins that are affected, to some extent, by the hyperfine interaction. This is a limiting factor to an extensive use of paramagnetic probes in NMR spectroscopy to enhance partial alignment and to exploit cross correlation effects and pseudocontact shifts. We propose here an HCCH-TOCSY experiment tailored to identify spin systems involving resonances that are partly or completely affected by hyperfine interaction. The efficiency of polarization transfer steps when fast relaxing nuclei are involved is discussed. The sequence is tested for the protein Calbindin D(9k), in which one of the two native Ca2+ ions is replaced by the paramagnetic Ce3+ ion as well as for the oxidized form of cytochrome b(562).     

A rotational approach to localized SPAMM 1-1 tagging

Magnetic resonance tagging usually relies on controlling the phase dispersion of the transverse magnetization component. Phase dispersion is, however, affected by the inherent phase of selective excitation pulses, thus limiting their combination with tagging sequences to the application of refocusable pulses, as in the localized spatial modulation of magnetization (L-SPAMM) technique. In this study, we examine the effect of selective excitation pulses on a L-SPAMM 1-1 sequence, showing that in the case of two identical pulses the phase component is canceled out, and thus preemphasis and refocus gradients are not needed, allowing us to take advantage of a constant gradient throughout the tagging sequence, and also that one might choose nonrefocusable maximum and minimum phase pulses.     

Analytical Planar Mixing Transfer Functions for Two Coupled Spin-1 Nuclei

Analytical coherence transfer functions are presented for spin systems consisting of two spins 1 under planar mixing conditions. Compared to isotropic mixing experiments, larger transfer amplitudes are found and differences in the multiplet patterns are discussed.     

2D(13)C-(13)C MAS NMR correlation spectroscopy with mixing by true (1)H spin diffusion reveals long-range intermolecular distance restraints in ultra high magnetic field

An improved 2D (13)C-(13)C CP(3) MAS NMR correlation experiment with mixing by true (1)H spin diffusion is presented. With CP(3), correlations can be detected over a much longer range than with direct (1)H-(13)C or (13)C-(13)C dipolar recoupling. The experiment employs a (1)H spin diffusion mixing period tau(m) sandwiched between two cross-polarization periods. An optimized CP(3) sequence for measuring polarization transfer on a length scale between 0.3 and 1.0 nm using short mixing times of 0.1 ms < tau(m) < 1 ms is presented. For such a short tau(m), cross talk from residual transverse magnetization of the donating nuclear species after a CP can be suppressed by extended phase cycling. The utility of the experiment for genuine structure determination is demonstrated using a self-aggregated Chl a/H(2)O sample. The number of intramolecular cross-peaks increases for longer mixing times and this obscures the intermolecular transfer events. Hence, the experiment will be useful for short mixing times only. For a short tau(m) = 0.1 ms, intermolecular correlations are detected between the ends of phytyl tails and ring carbons of neighboring Chl a molecules in the aggregate. In this way the model for the structure, with stacks of Chl a that are arranged back to back with interdigitating phytyl chains stretched between two bilayers, is validated.     

An Efficient Algorithm for Truncating Spatial Domain in Modeling Light Scattering by Finite-Difference Technique

The finite-difference time domain technique is one of the most robust and accurate numerical methods for the solution of light scattering by small particles with arbitrary composition and geometry. In practice, this method requires that the spatial domain for the computation of near-field be truncated. An absorbing boundary condition must be imposed in conjunction with this truncation. The performance of this boundary condition is essential to the stability of numerical computations and the reliability of results. In the present study, a new boundary condition, referred to as the mixed T algorithm, has been developed, which is a generalization of the transmitting boundary condition originally developed by Liao and co-workers. The present algorithm does not require spatial interpolation for wave values at interior grid points. In addition, it produces two minima of spurious reflections at small and large incident angles, allowing efficient absorption of the scattered waves at the boundary for large incident angles. When the third-order mixed T algorithm is used, the reflection coefficient of the boundary is less than 1% for incident angles from 0° to about 70°. We find that the numerical instability associated with the transmitting boundary condition is caused by the location-dependent amplitude of outgoing waves in the vicinity of the boundary. For this reason, the mixed T algorithm is stabilized by consistently introducing diffusive coefficients into the boundary equation. When the stabilized algorithm is applied, the near-field within the truncated domain can be computed by using single-precision arithmetic without overflows for more than 10⁵steps in the time-marching iteration. Finally, the new absorbing boundary condition is validated by carrying out numerical experiments involving the propagation of a TM wave excited by a sinusoidal point source, simultaneous simulation of the wave propagation in small and large domains, and the scattering of a TM wave by an infinite circular cylinder.     

Signal enhancement in 5QMAS spectra of spin-5/2 quadrupolar nuclei

5QMAS experiments on spin-5/2 systems display a low sensitivity compared with their 3QMAS counterparts. Nevertheless, the superior resolution of 5QMAS over 3QMAS makes these experiments a favorable choice for many materials. We report an enhancement scheme for the 5QMAS experiment, using an improved five-quantum excitation pulse scheme combined with a FAM-II conversion pulse. The results are verified experimentally on a polycrystalline sample of gamma-(27)Al(2)O(3), showing an enhancement factor of 2.4 over the simple two-pulse (CW) 5QMAS scheme. Numerical computations of the efficiency parameter epsilon support these results.