14N chemical shifts and quadrupole coupling constants of inorganic nitrates

The isotropic chemical shift and the nuclear quadrupole coupling constant for (14)N were obtained for 14 inorganic nitrates by solid-state MAS NMR measurements at two different field strengths, 9.4 and 11.7 T. The compounds studied were polycrystalline powders of AgNO(3), Al(NO(3))(3), Ba(NO(3))(2), Ca(NO(3))(2), CsNO(3), KNO(3), LiNO(3), Mg(NO(3))(2), NaNO(3), Pb(NO(3))(2), RbNO(3), Sr(NO(3))(2), Th(NO(3))(4)center dot4H(2)O, and UO(2)(NO(3))(2)center dot3H(2)O. Even though the spectra show broadening due to (14)N quadrupole interactions, linewidths of a few hundred hertz and a good signal-to-noise ratio were achieved. From the position of the central peaks at the two fields, the chemical shifts and the nuclear quadrupole coupling constants were calculated. The chemical shifts for all compounds studied range from 282 to 342 ppm with respect to NH(4)Cl. The nuclear quadrupole coupling constants range from 429 kHz for AgNO(3) to 993 kHz for LiNO(3). These data are compared with those available in the literature.     

Dipolar and J encoded DQ MAS spectra under rotational resonance

A two-dimensional (2D) double-quantum (DQ) experiment under rotational resonance (R(2)) conditions is introduced for evaluating dipolar couplings in rotating solids. The contributions from the R(2)-recoupled dipolar interaction and the J coupling can be conveniently separated in the resulting 2D R(2)-DQ spectrum, so that the unknown dipolar coupling can readily be extracted, provided that the values of the involved J coupling constants are known. Since the measured parameters are integral intensity ratios between suitably chosen absorption peaks in the 2D spectrum, the proposed method is characterized by a reduced sensitivity to relaxation parameters. The effect of rotor-modulated terms, including chemical shift anisotropy, is efficiently averaged out by synchronizing the excitation/reconversion time with the rotor period. All of these features are demonstrated theoretically by the example of two model systems, namely, isolated spin-pairs and a three-spin system. The results of the theoretical models are applied to both (13)C and (1)H nuclei to extract dipolar couplings in uniformly (13)C labeled L-alanine and a crosslinked natural rubber.     

Investigating magnetically aligned phospholipid bilayers with EPR spectroscopy at 94 GHz

In this paper, we report our initial results on studying magnetically aligned phospholipid bilayers (bicelles) at high magnetic fields (approximately 3.4 T) with electron paramagnetic resonance (EPR) spectroscopy at 95 GHz (W-band). In order to characterize this system for W-band EPR studies, we have utilized the nitroxide spin probe 3beta-doxyl-5alpha-cholestane to demonstrate the effects of macroscopic bilayer alignment. At W-band due to the increase in magnetic field strength (when compared to X-band studies at 9.5 GHz) (S. M. Garber et al., J. Am. Chem. Soc. 121, 3240-3241 (1999)), we were able to examine magnetically aligned phospholipid bilayers at two orientations with the bilayer normal oriented either perpendicular or parallel (upon addition of YbCl3) with respect to the direction of the static magnetic field. Additionally, at a magnetic field of 3.4 T (g=2 resonance at W-band), we were able to study the parallel alignment with a lower concentration of Yb3+, thereby eliminating the possible unwanted effects associated with lanthanide-protein interactions and paramagnetic shifts and/or line broadening induced by the lanthanide ions. The development of this new spin label alignment technique will open up a whole new area of investigation for phospholipid bilayer systems and membrane protein EPR studies at high magnetic fields.     

Probe--sample coupling in the magnetic resonance force microscope

The magnetic resonance force microscope (MRFM) provides a route to achieving scanned probe magnetic resonance imaging with extremely high spatial resolution. Achieving this capability will require understanding the force exerted on a microscopic magnetic probe by a spatially extended sample over which the probe is scanned. Here we present a detailed analysis of this interaction between probe and sample. We focus on understanding the situation where the micromagnet mounted on the mechanical resonator generates a very inhomogeneous magnetic field and is scanned over a sample with at least one spatial dimension much larger than that of the micromagnet. This situation differs quite significantly from the conditions under which most MRFM experiments have been carried out where the sample is mounted on the mechanical resonator and placed in a rather weak magnetic field gradient. In addition to the concept of a sensitive slice (the spatial region where the magnetic resonance condition is met) it is valuable to map the forces exerted on the probe by spins at various locations; this leads to the concept of the force slice (the region in which spins exert force on the resonator). Results of this analysis, obtained both analytically and numerically, will be qualitatively compared with an initial experimental finding from an EPR-MRFM experiment carried out on DPPH at 4 K.     

An Efficient NMR Experiment for Analyzing Sugar-Puckering in Unlabeled DNA: Application to the 26-kDa Dead Ringer–DNA Complex

We present a new NMR experiment for estimating the type and degree of sugar-puckering in high-molecular-weight unlabeled DNA molecules. The experiment consists of a NOESY sequence preceded by a constant-time scalar coupling period. Two subexperiments are compared, each differing in the amount of time the (3)J(H3'H2') and (3)J(H3'H2") couplings are active on the H3' magnetization. The resultant data are easy to analyze, since a comparison of the signal intensities of any resolved NOE cross peak originating from H3' atoms of the duplex can be used to estimate the sum of the (3)J(H3'H2') and (3)J(H3'H2") couplings and thus the puckering type of the deoxyribose ring. Isotope filters to eliminate signals of the (13)C-labeled component in the F1-dimension are implemented, facilitating analyses of high-molecular-weight protein-DNA complexes containing (13)C-labeled protein and unlabeled DNA. The utility of the experiment is demonstrated on the 26-kDa Dead Ringer protein-DNA complex and reveals that the DNA uniformly adopts the S-type configuration when bound to protein.     

Numerical simulation of one- and two-dimensional ESEEM experiments

Numerical simulation has become an indispensable tool for the interpretation of pulse EPR experiments. In this work it is shown how automatic orientation selection, grouping of operator factors, and direct selection and elimination of coherences can be used to improve the efficiency of time-domain simulations of one- and two-dimensional electron spin echo envelope modulation (ESEEM) spectra. The program allows for the computation of magnetic interactions of any symmetry and can be used to simulate spin systems with an arbitrary number of nuclei with any spin quantum number. Experimental restrictions due to finite microwave pulse lengths are addressed and the enhancement of forbidden coherences by microwave pulse matching is illustrated. A comparison of simulated and experimental HYSCORE (hyperfine sublevel correlation) spectra of ordered and disordered systems with varying complexity shows good qualitative agreement.     

Particle Transport through Scattering Regions with Clear Layers and Inclusions

This paper introduces generalized diffusion models for the transport of particles in scattering media with nonscattering inclusions. Classical diffusion is known as a good approximation of transport only in scattering media. Based on asymptotic expansions and the coupling of transport and diffusion models, generalized diffusion equations with nonlocal interface conditions are proposed which offer a computationally cheap, yet accurate, alternative to solving the full phase-space transport equations. The paper shows which computational model should be used depending on the size and shape of the nonscattering inclusions in the simplified setting of two space dimensions. An important application is the treatment of clear layers in near-infrared (NIR) spectroscopy, an imaging technique based on the propagation of NIR photons in human tissues.     

Sequential HNCACB and CBCANH protein NMR pulse sequences

The pulse sequences HNCACB and CBCANH correlating side chain C(beta) resonances with amide resonances in the protein backbone do not distinguish between inter- and intraresidue correlations. The new pulse sequences sequential HNCACB and sequential CBCANH make this distinction by suppressing coherence transfer between 13C(alpha) and 15N via the one-bond J(NC(alpha)) coupling so that only the sequential correlations are observed in the spectrum. The experimental results of applying sequential HNCACB in a clean-TROSY-adapted implementation to the protein Chymotrypsin Inhibitor 2 at 800 MHz are presented.     

Dynamics of Spin I=3/2 under Spin-Locking Conditions in an Ordered Environment

We have derived approximate analytic solutions to the master equation describing the evolution of the spin I=3/2 density operator in the presence of a radio-frequency (RF) field and both static and fluctuating quadrupolar interactions. Spectra resulting from Fourier transformation of the evolutions of the on-resonance spin-locked magnetization into the various coherences display two satellite pairs and, in some cases, a central line. The central line is generally trimodal, consisting of a narrow component related to a slowly relaxing mode and two broad components pertaining to two faster relaxing modes. The rates of the fast modes are sensitive to slow molecular motion. Neither the amplitude nor the width of the narrow component is affected by the magnitude of the static coupling, whereas the corresponding features of the broad components depend in a rather complicated manner on the spin-lock field strength and static quadrupolar interaction. Under certain experimental conditions, the dependencies of the amplitudes on the dynamics are seen to vanish and the relaxation rates reduce to relatively simple expressions. One of the promising emerging features is the fact that the evolutions into the selectively detected quadrupolar spin polarization order and the rank-two double-quantum coherence do not exhibit a slowly relaxing mode and are particularly sensitive to slow molecular motion. Furthermore, these coherences can only be excited in the presence of a static coupling and this makes it possible to discern nuclei in anisotropic from those in isotropic environment. The feasibility of the spin-lock pulse sequences with limited RF power and a nonvanishing average electric field gradient has been demonstrated through experiments on sodium in a dense lyotropic DNA liquid crystal.     

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.     

Through-Bond Correlation of Sugar and Base Protons in Unlabeled Nucleic Acids

This work presents two methods for through-bond correlation between sugar and base protons in view of model-independent assignment in unlabeled or slightly enriched nucleic acids. Each method uses a combination of multiple-bond and one-bond heteronuclear J-couplings to the aromatic carbon C6 for pyrimidines ((3)J(H1',C6) and (1)J(H6,C6)) or C8 for purines ((3)J(H1',C8) and (1)J(H8,C8)). The techniques are demonstrated in the duplex [d(CGCGAATTCGCG)](2) and the dimeric G-quadruplex [d(GGGTTCAGG)](2) at natural abundance.     

A General-Purpose Finite-Volume Advection Scheme for Continuous and Discontinuous Fields on Unstructured Grids

We present a new general-purpose advection scheme for unstructured meshes based on the use of a variation of the interface-tracking flux formulation recently put forward by O. Ubbink and R. I. Issa (J. Comput. Phys.153, 26 (1999)), in combination with an extended version of the flux-limited advection scheme of J. Thuburn (J. Comput. Phys.123, 74 (1996)), for continuous fields. Thus, along with a high-order mode for continuous fields, the new scheme presented here includes optional integrated interface-tracking modes for discontinuous fields. In all modes, the method is conservative, monotonic, and compatible. It is also highly shape preserving. The scheme works on unstructured meshes composed of any kind of connectivity element, including triangular and quadrilateral elements in two dimensions and tetrahedral and hexahedral elements in three dimensions. The scheme is finite-volume based and is applicable to control-volume finite-element and edge-based node-centered computations. An explicit–implicit extension to the continuous-field scheme is provided only to allow for computations in which the local Courant number exceeds unity. The transition from the explicit mode to the implicit mode is performed locally and in a continuous fashion, providing a smooth hybrid explicit–implicit calculation. Results for a variety of test problems utilizing the continuous and discontinuous advection schemes are presented.     

Physics-Based Preconditioning and the Newton–Krylov Method for Non-equilibrium Radiation Diffusion

An algorithm is presented for the solution of the time dependent reaction-diffusion systems which arise in non-equilibrium radiation diffusion applications. This system of nonlinear equations is solved by coupling three numerical methods, Jacobian-free Newton–Krylov, operator splitting, and multigrid linear solvers. An inexact Newton's method is used to solve the system of nonlinear equations. Since building the Jacobian matrix for problems of interest can be challenging, we employ a Jacobian–free implementation of Newton's method, where the action of the Jacobian matrix on a vector is approximated by a first order Taylor series expansion. Preconditioned generalized minimal residual (PGMRES) is the Krylov method used to solve the linear systems that come from the iterations of Newton's method. The preconditioner in this solution method is constructed using a physics-based divide and conquer approach, often referred to as operator splitting. This solution procedure inverts the scalar elliptic systems that make up the preconditioner using simple multigrid methods. The preconditioner also addresses the strong coupling between equations with local 2×2 block solves. The intra-cell coupling is applied after the inter-cell coupling has already been addressed by the elliptic solves. Results are presented using this solution procedure that demonstrate its efficiency while incurring minimal memory requirements.     

Solution of Time-Dependent Diffusion Equations with Variable Coefficients Using Multiwavelets

A new numerical algorithm is developed for the solution of time-dependent differential equations of diffusion type. It allows for an accurate and efficient treatment of multidimensional problems with variable coefficients, nonlinearities, and general boundary conditions. For space discretization we use the multiwavelet bases introduced by Alpert (1993,SIAM J. Math. Anal.24, 246–262), and then applied to the representation of differential operators and functions of operators presented by Alpert, Beylkin, and Vozovoi (Representation of operators in the multiwavelet basis, in preparation). An important advantage of multiwavelet basis functions is the fact that they are supported only on non-overlapping subdomains. Thus multiwavelet bases are attractive for solving problems in finite (non periodic) domains. Boundary conditions are imposed with a penalty technique of Hesthaven and Gottlieb (1996,SIAM J. Sci. Comput., 579–612) which can be used to impose rather general boundary conditions. The penalty approach was extended to a procedure for ensuring the continuity of the solution and its first derivative across interior boundaries between neighboring subdomains while time stepping the solution of a time dependent problem. This penalty procedure on the interfaces allows for a simplification and sparsification of the representation of differential operators by discarding the elements responsible for interactions between neighboring subdomains. Consequently the matrices representing the differential operators (on the finest scale) have block-diagonal structure. For a fixed order of multiwavelets (i.e., a fixed number of vanishing moments) the computational complexity of the present algorithm is proportional to the number of subdomains. The time discretization method of Beylkin, Keiser, and Vozovoi (1998, PAM Report 347) is used in view of its favorable stability properties. Numerical results are presented for evolution equations with variable coefficients in one and two dimensions.     

Multifrequency Probe for Pulsed EPR and ENDOR Spectroscopy

The design, construction, and performance of a multifrequency pulsed EPR and ENDOR probe for use at cryogenic temperatures are described. Interchangeable resonators based on a folded strip line design allow variation of the resonance frequency over a range of 5-11 GHz. Variable coupling to the resonator is achieved capacitively via a simple mechanical adjustment which is thermally and mechanically stable. The entire assembly is robust and easily fabricated. Common methods of analyzing the resonator parameters such as the Q-factor and coupling coefficient are discussed quantitatively. Probe performance data and multifrequency pulsed ENDOR spectra are presented.     

Design and implementation of a protection system for NMR spectrometers

We have implemented a scheme, SPECMON, for monitoring various parameters of a spectrometer, such as nitrogen pressure and sample temperature, and taking corrective action. The scheme is based on considerations of protection management which are of general application. Evaluation of the spectrometer state is incorporated in macros of the application software (VNMR) and is therefore very flexible. In contrast, corrective action is limited to the single one which is deemed fully safe: complete shutdown of the spectrometer and logging. Shutdown is implemented by a minor hardware modification of the spectrometer: the introduction of a second input to a relay already present for protection of the spectrometer power supply. Monitoring is handled by the host computer, and the shutdown command is transmitted via control lines of its series port, independent of the standard connection between the host computer and the NMR system console. The monitoring system (software and hardware) is unobtrusive in normal conditions, and it can be tested without affecting the operation of the spectrometer.     

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.     

An Extension of Alias Sampling Method for Parametrized Probability Distributions

An extension of the alias sampling technique for distribution functions depending on a number of parameters was developed. It takes advantage of modern computer architectures with large amounts of cheap memory, by using discrete representations of probability distribution functions. The sampling is done by fast interpolation techniques involving only elementary logical and arithmetical operations, allowing one to keep a higher degree of accuracy as the grids spacing is controlled by the user. By this method it is possible to obtain the value of interest by direct interpolation between the sampled values obtained with the same set of random numbers for the grid values of the parameters adjacent to the values of interest. Sampling tests carried for the case of Molière electron multi-scatter angle distribution show that this method can be successfully used in Monte Carlo codes for sampling complex probability distributions.     

A subspace time-domain algorithm for automated NMR spectral normalization

Recently, two methods have been proposed for quantitatively comparing NMR spectra of control and treated samples, in order to examine the possible occurring variations in cell metabolism and/or structure in response to numerous physical, chemical, and biological agents. These methods are the maximum superposition normalization algorithm (MaSNAl) and the minimum rank normalization algorithm (MiRaNAl). In this paper a new subspace-based time-domain normalization algorithm, denoted by SuTdNAl (subspace time-domain normalization algorithm), is presented. By the determination of the intersection of the column spaces of two Hankel matrices, the common signal poles and further on the components having proportionally varying amplitudes are detected. The method has the advantage that it is computationally less intensive than the MaSNAl and the MiRaNAl. Furthermore, no approximate estimate of the normalization factor is required. The algorithm was tested by Monte Carlo simulations on a set of simulation signals. It was shown that the SuTdNAl has a statistical performance similar to that of the MiRaNAl, which itself is an improvement over the MaSNAl. Furthermore, two samples of known contents are compared with the MiRaNAl, the SuTdNAl, and an older method using a standard. Finally, the SuTdNAl is tested on a realistic simulation example derived from an in vitro measurement on cells.     

The Three Dimensional Non-conforming Finite Element Solution of the Chapman–Ferraro Problem

We demonstrate the feasibility of using a non-conforming, piecewise harmonic finite element method on an unstructured grid in solving a magnetospheric physics problem. We use this approach to construct a global discrete model of the magnetic field of the magnetosphere that includes the effects of shielding currents at the outer boundary (the magnetopause). As in the approach of F. R. Toffolettoet al.(1994,Geophys. Res. Lett.21, 7) the internal magnetospheric field model is that of R. V. Hilmer and G.-H. Voigt (1995,J. Geophys. Res.) while the magnetopause shape is based on an empirically determined approximation (1997, J. Shueet al.,J. Geophys. Res.102, 9497). The results is a magnetic field model whose field lines are completely confined within the magnetosphere. The presented numerical results indicate that the discrete non-conforming finite element model is well-suited for magnetospheric field modeling.