Probing proteins in solution by (129)Xe NMR spectroscopy

The interaction of xenon with different proteins in aqueous solution is investigated by (129)Xe NMR spectroscopy. Chemical shifts are measured in horse metmyoglobin, hen egg white lysozyme, and horse cytochrome c solutions as a function of xenon concentration. In these systems, xenon is in fast exchange between all possible environments. The results suggest that nonspecific interactions exist between xenon and the protein exteriors and the data are analyzed in term of parameters which characterize the protein surfaces. The experimental data for horse metmyoglobin are interpreted using a model in which xenon forms a 1:1 complex with the protein and the chemical shift of the complexed xenon is reported (Locci et al., Keystone Symposia "Frontiers of NMR in Molecular Biology VI", Jan. 9--15, 1999, Breckenridge, CO, Abstract E216, p. 53; Locci et al., XeMAT 2000 "Optical Polarization and Xenon NMR of Materials", June 28--30, 2000, Sestri Levante, Italy, p. 46).     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

Changes in Porcine Muscle Water Characteristics during Growth—An in Vitro Low-Field NMR Relaxation Study

This study investigates the effects of developmental stage and muscle type on the mobility and distribution of water within skeletal muscles, using low-field ¹H-NMR transverse relaxation measurements in vitro on four different porcine muscles (M. longissimus dorsi, M. semitendinosus, M. biceps femoris, M. vastus intermedius) from a total of 48 pigs slaughtered at various weight classes between 25 kg and 150 kg. Principal component analysis (PCA) revealed effects of both slaughter weight and muscle type on the transverse relaxation decay. Independent of developmental stage and muscle type, distributed exponential analysis of the NMR T₂ relaxation data imparted the existence of three distinct water populations, T_2b, T₂₁, and T₂₂, with relaxation times of approximately 1–10, 45–120, and 200–500 ms, respectively. The most profound change during muscle growth was a shift toward faster relaxation in the intermediate time constant, T₂₁. It decreased by approx. 24% in all four muscle types during the period from 25 to 150 kg live weight. Determination of dry matter, fat, and protein content in the muscles showed that the changes in relaxation time of the intermediate time constant, T₂₁, during growth should be ascribed mainly to a change in protein content, as the protein content explained 77% of the variation in the T₂₁ time constant. Partial least squares (PLS) regression revealed validated correlations in the region of 0.58 to 0.77 between NMR transverse relaxation data and muscle development for all the four muscle types, which indicates that NMR relaxation measurements may be used in the prediction of muscle developmental stage.     

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.     

Unconditionally Stable Methods for Hamilton–Jacobi Equations

We present new numerical methods for constructing approximate solutions to the Cauchy problem for Hamilton–Jacobi equations of the form u_t+H(D_xu)=0. The methods are based on dimensional splitting and front tracking for solving the associated (non-strictly hyperbolic) system of conservation laws p_t+D_xH(p)=0, where p=D_xu. In particular, our methods depend heavily on a front tracking method for one-dimensional scalar conservation laws with discontinuous coefficients. The proposed methods are unconditionally stable in the sense that the time step is not limited by the space discretization and they can be viewed as “large-time-step” Godunov-type (or front tracking) methods. We present several numerical examples illustrating the main features of the proposed methods. We also compare our methods with several methods from the literature.     

Measurement of Small One-Bond Proton–Carbon Residual Dipolar Coupling Constants in Partially Oriented C Natural Abundance Oligosaccharide Samples: Analysis of Heteronuclear JCH-Modulated Spectra with the BIRD Inversion Pulse

Two 2D J-modulated HSQC-based experiments were designed for precise determination of small residual dipolar one-bond carbon–proton coupling constants in ¹³C natural abundance carbohydrates. Crucial to the precision of a few hundredths of Hz achieved by these methods was the use of long modulation intervals and BIRD pulses, which acted as semiselective inversion pulses. The BIRD pulses eliminated effective evolution of all but ¹J_CH couplings, resulting in signal modulation that can be described by simple modulation functions. A thorough analysis of such modulation functions for a typical four-spin carbohydrate spin system was performed for both experiments. The results showed that the evolution of the ¹H–¹H and long-range ¹H–¹³C couplings during the BIRD pulses did not necessitate the introduction of more complicated modulation functions. The effects of pulse imperfections were also inspected. While weakly coupled spin systems can be analyzed by simple fitting of cross peak intensities, in strongly coupled spin systems the evolution of the density matrix needs to be considered in order to analyse data accurately. However, if strong coupling effects are modest the errors in coupling constants determined by the “weak coupling” analysis are of similar magnitudes in oriented and isotropic samples and are partially cancelled during dipolar coupling calculation. Simple criteria have been established as to when the strong coupling treatment needs to be invoked.     

Coherent Raman and Infrared Studies of Sulfur Trioxide

High-resolution (0.001 cm⁻¹) coherent anti-Stokes Raman scattering (CARS) was used to observe the Q-branch structure of the IR-inactive ν₁ symmetric stretching mode of ³²S¹⁶O₃ and its various ¹⁸O isotopomers. The ν₁ spectrum of ³²S¹⁶O₃ reveals two intense Q-branches in the region 1065–1067 cm⁻¹, with surprisingly complex vibrational–rotational structure not resolved in earlier studies. Efforts to simulate this with a simple Fermi-resonance model involving ν₁ and 2ν₄ states do not reproduce the spectral detail, nor do they yield reasonable spectroscopic parameters. A more subtle combination of Fermi resonance and indirect Coriolis interactions with nearby states, 2ν₄(1=0, ±2), ν₂+ν₄(1=±1), 2ν₂(1=0), is suspected and a determination of the location of these coupled states by high-resolution infrared measurements is under way. At medium resolution (0.125 cm⁻¹), the infrared spectra reveal Q-branch features from which approximate band origins are estimated for the ν₂, ν₃, and ν₄ fundamental modes of ³²S¹⁸O₃, ³²S¹⁸O₂¹⁶O, and ³²S¹⁸O¹⁶O₂. These and literature data for ³²S¹⁶O₃ are used to calculate force constants for SO₃ and a comparison is made with similar values for SO₂ and SO. The frequencies and force constants are in excellent agreement with those obtained by Martin in a recent ab initio calculation.     

Transparent Boundary Conditions for Split-Step Padé Approximations of the One-Way Helmholtz Equation

In this paper, we generalize the nonlocal discrete transparent boundary condition introduced by F. Schmidt and P. Deuflhard (1995, Comput. Math. Appl.29, 53–76) and by F. Schmidt and D. Yevick (1997, J. Comput. Phys.134, 96–107) to propagation methods based on arbitrary Padé approximations of the two-dimensional one-way Helmholtz equation. Our approach leads to a recursive formula for the coefficients appearing in the nonlocal condition, which then yields an unconditionally stable propagation method.     

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.     

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.     

A General Deterministic Treatment of Derivatives in Particle Methods

A unified approach to approximating spatial derivatives in particle methods using integral operators is presented. The approach is an extension of particle strength exchange, originally developed for treating the Laplacian in advection–diffusion problems. Kernels of high order of accuracy are constructed that can be used to approximate derivatives of any degree. A new treatment for computing derivatives near the edge of particle coverage is introduced, using “one-sided” integrals that only look for information where it is available. The use of these integral approximations in wave propagation applications is considered and their error is analyzed in this context using Fourier methods. Finally, simple tests are performed to demonstrate the characteristics of the treatment, including an assessment of the effects of particle dispersion, and their results are discussed.     

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.     

Millimeter-Wave Spectroscopy, High-Resolution Infrared Spectrum, ab Initio Calculations, and Molecular Geometry of FPS

The transient thiophosphenous fluoride FPS was produced by pyrolysis of 2.5% F₂PSPF₂ in Ar at 1300–1800°C. High-resolution (≥0.004 cm⁻¹) Fourier transform infrared spectra of the a-type ν₁ and b-type ν₂ bands, centered respectively at 803.249 and 726.268 cm⁻¹, were measured and fitted to rotational and quartic centrifugal distortion parameters. The millimeter-wave spectrum, essentially b-type, was measured between 300 and 370 GHz in the ground state and in the ν₃ excited state for FP³²S and in the ground state for FP³⁴S. The frequencies were fitted to a Watson-type A-reduced Hamiltonian up to sextic distortion terms. High level ab initio calculations with large basis sets were performed on FPS and supported the first identification of its infrared and millimeter wave spectra. The calculated anharmonic force field provided precise ab initio rovibrational α constants which were combined with the experimental molecular parameters to determine an accurate equilibrium structure of the molecule: r_e(PS)=188.86 pm, r_e(PF)=158.70 pm, θ(FPS)=109.28°. The collision-controlled 1/e lifetime measured in a 10-Pa (1 : 20) F₂PSPF₂/Ar mixture was 2 s, more than two orders of magnitude larger than that of FPO under the same experimental conditions.     

H NMR Characterization of the Product from Single Solid-Phase Resin Beads Using Capillary NMR Flow Probes

A capillary NMR flow probe was designed to generate high-resolution ¹H NMR spectra at 600 MHz from the cleaved product of individual 160-μm Tentagel combinatorial chemistry beads. By injecting a dissolved sample sandwiched between an immiscible, perfluorinated organic liquid directly into the probe, NMR spectra of the product cleaved from single beads were acquired in just 1 h of spectrometer time without diffusional dilution. Sample handling efficiency on the single bead scale was comparable to that obtained with a bulk sample. Using the relative intensity of the DMSO-d₅H versus the analyte signals in a fully relaxed CPMG spectrum, the amount of product cleaved from a single bead was determined to be 540±170 pmol in one of the samples. Following the NMR data collection, the samples were examined with electrospray ionization mass spectrometry to provide additional structural information. By coupling with microliter-volume fluidic capabilities, the capillary flow probe described here will enable multidimensional characterization of single solid-phase resin products in an online manner.     

IR Spectrum of C8H2: Integrated Band Intensities and Some Observational Implications

Polyynes are of astrophysical interest since they appear to be involved in organic chemistry in very different mediums. In Titan's atmosphere, the lightest polyyne, C₄H₂, was detected by Voyager. Recently C₄H₂ and C₆H₂ have been discovered in a protoplanetary nebula, suggesting polyynes as a possible chemical pathway to PAH (polycyclic aromatic hydrocarbons). Moreover, several experimental simulations and modeling imply their production from the photochemistry of methane and their involvement in the formation of organic aerosols. After the study of C₄H₂ and C₆H₂ spectra in the UV and IR wavelength range, we report here the first spectrum of gaseous C₈H₂ in the range 400–4000 cm⁻¹ at room temperature and low resolution. The task was hardly achieved because of the high instability of this molecule with temperature and pressure. To avoid exothermic polymerization, the compound as mixed with a solvent. We have performed a separate spectroscopic study of the solvent to determine C₈H₂ partial pressure within the mixture. This allowed us to calculate C₈H₂ integrated band intensities. In the studied wavelength range, C₈H₂ presents three main bands similar to those of C₆H₂ in terms of vibrational type, position, and relative intensity. To study the possible identification of these polyynes by spatial observatories (Cassini–Huygens, ISO), we have also measured the C₆H₂ and C₈H₂ infrared spectra in the range 400–1500 cm⁻¹ at 0.35 cm⁻¹ resolution.     

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.     

Laser-polarized Xe NMR and MRI at Ultralow Magnetic Fields

Laser-polarized ¹²⁹Xe and a high-T_csuperconducting quantum interference device (SQUID) are used to obtain magnetic resonance images in porous materials at a magnetic field of 2.3 mT, corresponding to a Larmor frequency of 27 kHz. Image resolution of 1 mm is obtained with gradients of only 1 mT/m. The resolution of xenon chemical shifts in different physicochemical environments at ultralow fields is also demonstrated. Details of the circulating flow optical pumping apparatus and the SQUID spectrometer are presented.     

Moving Mesh Methods in Multiple Dimensions Based on Harmonic Maps

In practice, there are three types of adaptive methods using the finite element approach, namely the h-method, p-method, and r-method. In the h-method, the overall method contains two parts, a solution algorithm and a mesh selection algorithm. These two parts are independent of each other in the sense that the change of the PDEs will affect the first part only. However, in some of the existing versions of the r-method (also known as the moving mesh method), these two parts are strongly associated with each other and as a result any change of the PDEs will result in the rewriting of the whole code. In this work, we will propose a moving mesh method which also contains two parts, a solution algorithm and a mesh-redistribution algorithm. Our efforts are to keep the advantages of the r-method (e.g., keep the number of nodes unchanged) and of the h-method (e.g., the two parts in the code are independent). A framework for adaptive meshes based on the Hamilton–Schoen–Yau theory was proposed by Dvinsky. In this work, we will extend Dvinsky's method to provide an efficient solver for the mesh-redistribution algorithm. The key idea is to construct the harmonic map between the physical space and a parameter space by an iteration procedure. Each iteration step is to move the mesh closer to the harmonic map. This procedure is simple and easy to program and also enables us to keep the map harmonic even after long times of numerical integration. The numerical schemes are applied to a number of test problems in two dimensions. It is observed that the mesh-redistribution strategy based on the harmonic maps adapts the mesh extremely well to the solution without producing skew elements for multi-dimensional computations.     

New High-Resolution Semi-discrete Central Schemes for Hamilton–Jacobi Equations

We introduce a new high-resolution central scheme for multidimensional Hamilton–Jacobi equations. The scheme retains the simplicity of the non-oscillatory central schemes developed by C.-T. Lin and E. Tadmor (in press, SIAM J. Sci. Comput.), yet it enjoys a smaller amount of numerical viscosity, independent of 1/Δt. By letting Δt↓0 we obtain a new second-order central scheme in the particularly simple semi-discrete form, along the lines of the new semi-discrete central schemes recently introduced by the authors in the context of hyperbolic conservation laws. Fully discrete versions are obtained with appropriate Runge–Kutta solvers. The smaller amount of dissipation enables efficient integration of convection-diffusion equations, where the accumulated error is independent of a small time step dictated by the CFL limitation. The scheme is non-oscillatory thanks to the use of nonlinear limiters. Here we advocate the use of such limiters on second discrete derivatives, which is shown to yield an improved high resolution when compared to the usual limitation of first derivatives. Numerical experiments demonstrate the remarkable resolution obtained by the proposed new central scheme.     

Mass Flux Schemes and Connection to Shock Instability

We analyze numerical mass fluxes with an emphasis on their capability for accurately capturing shock and contact discontinuities. The study of mass flux is useful because it is the term common to all conservation equations and the numerical diffusivity introduced in it bears a direct consequence to the prediction of contact (stationary and moving) discontinuities, which are considered to be the limiting case of the boundary layer. We examine several prominent numerical flux schemes and analyze the structure of numerical diffusivity. This leads to a detailed investigation into the cause of certain catastrophic breakdowns by some numerical flux schemes. In particular, we identify the dissipative terms that are responsible for shock instabilities, such as the odd–even decoupling and the so-called “carbuncle phenomenon”. As a result, we propose a conjecture stating the connection of the pressure difference term to these multidimensional shock instabilities and hence a cure to those difficulties. The validity of this conjecture has been confirmed by examining a wide class of upwind schemes. The conjecture is useful to the flux function development, for it indicates whether the flux scheme under consideration will be afflicted with these kinds of failings. Thus, a class of shock-stable schemes can be identified. Interestingly, a shock-stable scheme's self-correcting capability is demonstrated with respect to carbuncle-contaminated profiles for flows at both low supersonic and high Mach numbers.