Dipolar Line Research Articles

Crystallinity and perfection in ethylene vitrimers probed by combined calorimetry, scattering, and time-domain NMR

The kinetics of crystallization and crystal-crystal transformations in ethylene vitrimers are studied by time-domain NMR. These vitrimers previously exhibited polymorphic transition of crystal structures, which are shown here to be distinguishable by NMR via their dipolar line widths based upon different proton densities and fast internal motions. The conditions under which the polymorphs are formed and interconvert are identified via time-resolved NMR experiments, with a focus on recrystallization after full and partial melting. DSC experiments are used to clarify an unexpected superheating effect, which challenges the determination of actual melting points. We further identify a strong memory effect in isothermal (re)crystallization. Implications of the dynamic nature of the vitrimers in relation to the kinetics of crystallization are discussed. We find that internal perfecting of crystals, enabled by the vitrimeric exchange process, can have a large effect on the DSC-detected melting enthalpy without change in overall crystallinity.

Residual dipolar line width in magic-angle spinning proton solid-state NMR.

Magic-angle spinning is routinely used to average anisotropic interactions in solid-state nuclear magnetic resonance (NMR). Due to the fact that the homonuclear dipolar Hamiltonian of a strongly coupled spin system does not commute with itself at different time points during the rotation, second-order and higher-order terms lead to a residual dipolar line broadening in the observed resonances. Additional truncation of the residual broadening due to isotropic chemical-shift differences can be observed. We analyze the residual line broadening in coupled proton spin systems based on theoretical calculations of effective Hamiltonians up to third order using Floquet theory and compare these results to numerically obtained effective Hamiltonians in small spin systems. We show that at spinning frequencies beyond 75 kHz, second-order terms dominate the residual line width, leading to a dependence of the second moment which we use to characterize the line width. However, chemical-shift truncation leads to a partial dependence of the line width which looks as if third-order effective Hamiltonian terms are contributing significantly. At slower spinning frequencies, cross terms between the chemical shift and the dipolar coupling can contribute in third-order effective Hamiltonians. We show that second-order contributions not only broaden the line, but also lead to a shift of the center of gravity of the line. Experimental data reveal such spinning-frequency-dependent line shifts in proton spectra in model substances that can be explained by line shifts induced by the second-order dipolar Hamiltonian.

Moisture-activated dynamics on crystallite surfaces in cellulose

The structural basis of the interdependence between moisture content and activation of cooperative dynamics in natural cellulose is explored using a solid state NMR experiment which is able to localize these motions to cellulose chains on the surface of the unitary crystallite. Making assumptions based on current knowledge of biosynthesis of cellulose and the dipolar line widths of H spectra in solids, it is shown that the sorption of moisture causes the activation of cooperative motion of cellulose chains on the surface of the cellulose crystallite in a manner which is related to the moisture content. An important implication for these results is that densification of cellulose and associated changes in the water sorption isotherm, is possible by structural relaxation on the nano, or unitary crystallite scale. The result is also discussed in term of the evolving and modern picture of cellulose.

Pole-zero analysis of scattering resonances of multilayered nanospheres

We demonstrate a general pole-zero method for the design of the scattering resonances of multilayered nanospheres, and we apply it to the relevant cases of strongly dispersive light scattering from metal-dielectric-metal and all-dielectric nanostructures. The pole-zero method is based on the full-wave iterative solution of the Mie scattering theory of multilayered spheres, which is valid beyond the conventional quasistatic limit. By investigating scattering resonances in the complex frequency plane, we show how to engineer anomalous Fano-like dipolar line shapes from complex pole-zero interactions controlled by the geometrical parameters of the structures. The pole-zero method is then applied to the design of the backscattering and forward-scattering efficiencies beyond the dipolar approximation. The engineering of scattering and absorption resonances with customized line shapes in metal-dielectric nanostructures provides unique opportunities for active devices including optical sensors, light emitters, and nonlinear elements.

Dipolar Biexcitons in Lateral Traps in Si/SiGe/Si Heterostructures

Si/Si1–xGex/Si heterostructures with large-scale (micrometer-size) lateral potential fluctuations at the upper SiGe/Si-cap heterointerface are grown. These potential fluctuations are caused by partial strain relaxation in the SiGe layer. Low-temperature photoluminescence (PL) spectra show that these fluctuations form lateral traps where photoexcited nonequilibrium charge carriers are accumulated and bind into dipolar excitons, which ultimately recombine. At temperatures below 6 K, a new narrow line with a width considerably less than that of the dipolar exciton PL line emerges in the spectra as the level of excitation increases. It is shown that this line is associated with the recombination of dipolar biexcitons in large-scale traps.

Characterization of Bifunctional Spin Labels for Investigating the Structural and Dynamic Properties of Membrane Proteins Using EPR Spectroscopy.

Site-directed spin labeling (SDSL) coupled with electron paramagnetic resonance (EPR) spectroscopy is a very powerful technique to study structural and dynamic properties of membrane proteins. The most widely used spin label is methanthiosulfonate (MTSL). However, the flexibility of this spin label introduces greater uncertainties in EPR measurements obtained for determining structures, side-chain dynamics, and backbone motion of membrane protein systems. Recently, a newer bifunctional spin label (BSL), 3,4-bis(methanethiosulfonylmethyl)-2,2,5,5-tetramethyl-2,5-dihydro-1H-pyrrol-1-yloxy, has been introduced to overcome the dynamic limitations associated with the MTSL spin label and has been invaluable in determining protein backbone dynamics and inter-residue distances due to its restricted internal motion and fewer size restrictions. While BSL has been successful in providing more accurate information about the structure and dynamics of several proteins, a detailed characterization of the spin label is still lacking. In this study, we characterized BSLs by performing CW-EPR spectral line shape analysis as a function of temperature on spin-labeled sites inside and outside of the membrane for the integral membrane protein KCNE1 in POPC/POPG lipid bilayers and POPC/POPG lipodisq nanoparticles. The experimental data revealed a powder pattern spectral line shape for all of the KCNE1-BSL samples at 296 K, suggesting the motion of BSLs approaches the rigid limit regime for these series of samples. BSLs were further utilized to report for the first time the distance measurement between two BSLs attached on an integral membrane protein KCNE1 in POPC/POPG lipid bilayers at room temperature using dipolar line broadening CW-EPR spectroscopy. The CW dipolar line broadening EPR data revealed a 15 ± 2 Å distance between doubly attached BSLs on KCNE1 (53/57-63/67) which is consistent with molecular dynamics modeling and the solution NMR structure of KCNE1 which yielded a distance of 17 Å. This study demonstrates the utility of investigating the structural and dynamic properties of membrane proteins in physiologically relevant membrane mimetics using BSLs.

Plasmon Length: A Universal Parameter to Describe Size Effects in Gold Nanoparticles.

Localized surface plasmon resonances are central to many sensing and signal transmission applications. Tuning of the plasmon energy and line width through particle size and shape is critical to the design of such devices. To gain quantitative information on the size dependence of plasmonic properties, mainly due to retardation effects, we correlated optical spectra and structures for 500 individual gold particles of five different shapes. We show that the effects of size on the dipolar plasmon frequency and line width are shape-independent when size is described by the plasmon length, the length over which the oscillations take place. This result suggests that edge effects are rather unimportant for dipolar modes in a large size range between 50 and 350 nm. Therefore, in describing the size-dependent plasmonic properties of nanoparticles, one should focus on the distance along which the oscillation occurs rather than its intrinsic shape.

Wide-Line Solid-State NMR Characterizations of Sodium Alanates

Pure NaAlH4, TiCl3-doped NaAlH4, and pure Na3AlH6 were characterized using 1H, 23Na, and 27Al solid-state NMR. The signal intensities and linewidths of 1H NMR spectra using several spin echo sequences and backprediction of a single pulse experiment were compared to find the optimal experiment to measure wide-line NMR spectra of the alanates. Second moment calculations using the Van Vleck equations compared with fits of the dipolar coupling line broadening confirm that NaAlH4 has a rigid crystal lattice. On the other hand, for Na3AlH6, a narrowing of the proton and aluminum lineshape was observed, indicating a fast rotational motion of AlH6 clusters at room temperature. A broadening of the 1H and 27Al linewidth was observed upon lowering the temperature. This process is successfully described using thermally activated rotational jumps of AlH6 clusters assuming a fast rotational motion around one single C4 axis and a slower rotation around the other two C4 axes with an activation barrier of Ea = 25 kJ/mol a...

Sphingomyelinase-Induced Domain Shape Relaxation Driven by Out-of-Equilibrium Changes of Composition

Sphingomyelinase (SMase)-induced ceramide (Cer)-enriched domains in a lipid monolayer are shown to result from an out-of-equilibrium situation. This is induced by a change of composition caused by the enzymatic production of Cer in a sphingomyelin (SM) monolayer that leads to a fast SM/Cer demixing into a liquid-condensed (LC), Cer-enriched and a liquid-expanded, SM-enriched phases. The morphological evolution and kinetic dependence of Cer-enriched domains is studied under continuous observation by epifluorescence microscopy. Domain shape annealing is observed from branched to rounded shapes after SMase activity quenching by EDTA, with a decay halftime of ∼10 min. An out-of-equilibrium fast domain growth is not the determinant factor for domain morphology. Domain shape rearrangement in nearly equilibrium conditions result from the counteraction of intradomain dipolar repulsion and line tension, according to McConnell's shape transition theory. Phase separation causes a transient compositional overshoot within the LC phase that implies an increased out-of-equilibrium enrichment of Cer into the LC domains. As a consequence, higher intradomain repulsion leads to transient branched structures that relax to rounded shapes by lowering the proportion of Cer in the domain to equilibrium values. The fast action of SMase can be taken as a compositional perturbation that brings about important consequences for the surface organization.

Dipole tensor-based atomic-resolution structure determination of a nanocrystalline protein by solid-state NMR

Magic-angle spinning (MAS) solid-state NMR (SSNMR) techniques have emerged in recent years for solving complete structures of uniformly labeled proteins lacking macroscopic order. Strategies used thus far have relied primarily on semiquantitative distance restraints, analogous to the nuclear Overhauser effect (NOE) routinely used in solution NMR. Here, we present a complementary approach for using relative orientations of molecular fragments, determined from dipolar line shapes. Whereas SSNMR distance restraints typically have an uncertainty of approximately 1 A, the tensor-based experiments report on relative vector (pseudobond) angles with precision of a few degrees. By using 3D techniques of this type, vector angle (VEAN) restraints were determined for the majority of the 56-residue B1 immunoglobulin binding domain of protein G [protein GB1 (a total of 47 HN-HN, 49 HN-HC, and 12 HA-HB restraints)]. By using distance restraints alone in the structure calculations, the overall backbone root-mean-square deviation (bbRMSD) was 1.01 +/- 0.13 A (1.52 +/- 0.12 A for all heavy atoms), which improved to 0.49 +/- 0.05 A (1.19 +/- 0.07 A) on the addition of empirical chemical shift [torsion angle likelihood obtained from shift and sequence similarity (TALOS)] restraints. VEAN restraints further improved the ensemble to 0.31 +/- 0.06 A bbRMSD (1.06 +/- 0.07 A); relative to the structure with distances alone, most of the improvement remained (bbRMSD 0.64 +/- 0.09 A; 1.29 +/- 0.07 A) when TALOS restraints were removed before refinement. These results represent significant progress toward atomic-resolution protein structure determination by SSNMR, capabilities that can be applied to a large range of membrane proteins and fibrils, which are often not amenable to solution NMR or x-ray crystallography.

Decomposition of a NMR signal comprising a single resonance in exchange with a Pake doublet: Application to the analysis of 1H NMR spectra of water molecules embedded in synthetic clays

Conventional 1H NMR spectra of water in clays generally consist of several broad overlapping resonances. However, when a type of water is partially oriented, it leads to a Pake doublet superposed to the resonances corresponding to different types of non-oriented water. With the help of a recent method based on nutation experiments, the proportions of the different kinds of water could be determined. Thus, we are able to determine interesting NMR parameters like dipolar couplings, exchange rate, and line broadening. These determinations are complemented by spin relaxation times and self-diffusion measurements which bring additional information about the dynamical behavior of water.

Transient behavior of surface plasmon polaritons scattered at a subwavelength groove

We present a numerical study and analytical model of the optical near field diffracted in the vicinity of subwavelength grooves milled in silver surfaces. The Green's tensor approach permits the computation of the phase and amplitude dependence of the diffracted wave as a function of the groove geometry. It is shown that the field diffracted along the interface by the groove is equivalent to replacing the groove by an oscillating dipolar line source. An analytic expression is derived from the Green's function formalism, which reproduces well the asymptotic surface plasmon polariton (SPP) wave as well as the transient surface wave in the near zone close to the groove. The agreement between this model and the full simulation is very good, showing that the transient ``near-zone'' regime does not depend on the precise shape of the groove. Finally, it is shown that a composite diffractive evanescent wave model that includes the asymptotic SPP can describe the wavelength evolution in this transient near zone. Such a semianalytical model may be useful for the design and optimization of more elaborate photonic circuits, whose behavior in a large part will be controlled by surface waves.

Spin Dynamics in Disordered Solids

Modern state of studies in spin dynamics of statically disordered media is presented. Next four fundamental problems are attended mainly: 1) delocalization of nuclear polarization in subsystem of impurity nuclei (it is exemplified in model nuclear spin system 8Li-6 Li in the LiF single crystal) 2) nuclear relaxation via paramagnetic impurities in crystals of arbitrary space dimension d 3) free induction decay and EPR line form function at d ≤ 3; and 4) form function of the hole, burned on the wing of the dipolar EPR line.

Dipole-dipole interactions of high-spin paramagnetic centers in disordered systems

Dipole-dipole interactions between distant paramagnetic centers (PCs) where at least one PC has spinS>1/2 are examined. The results provide a basis for the application of pulsed electron-electron double resonance method to the measurement of distances between PCs involving high-spin species. A projection operator technique based on spectral decomposition of the secular Hamiltonian is used to calculate electron paramagnetic resonance (EPR) line splitting caused by the dipole coupling. This allows calculation of operators projecting an arbitrary wave function onto high-spin PC eigenstates when the eigenvectors of the Hamiltonian are not known. The effective spin vectors — that is, the expectation values for vector spin operators in the PC eigenstates — are calculated. The dependence of these effective spin vectors on the external magnetic field is calculated. There is a qualitative difference between pairs having at least one integer spin (non-Kramers PC) and pairs of two half-integer (Kramers PC) spins. With the help of these effective spin vectors, the dipolar line shape of EPR lines is calculated. Analytical relations are obtained for PCs with spinS=1/2 and 1. The dependence of Pake patterns on variations of zero-field splitting, Zeeman energy, temperature and dipolar coupling are illustrated.

Backbone Conformational Constraints in a Microcrystalline U-15N-Labeled Protein by 3D Dipolar-Shift Solid-State NMR Spectroscopy

Structural studies of uniformly labeled proteins by magic-angle spinning NMR spectroscopy have rapidly matured in recent years. Site-specific chemical shifts of several proteins have been assigned and structures determined from 2D or 3D data sets containing internuclear distance information. Here we demonstrate the application of a complementary technique for constraining protein backbone geometry using a site-resolved 3D dipolar-shift pulse sequence. The dipolar line shapes report on the relative orientations of 1H-15N[i] to 1H-15N[i+1] dipole vectors, constraining the torsion angles phi[i] and psi[i]. In addition, from the same 3D data set, several 1H-15N[i] to1H-15N[i+2] line shapes are extracted to constrain the torsion angles phi[i], psi[i], phi[i+1], and psi[i+1]. We report results for the majority of sites in the 56-residue beta1 immunoglobulin binding domain of protein G (GB1), using 3D experiments at 600 MHz 1H frequency. Excellent agreement between the SSNMR results and a new 1.14 A crystal structure illustrate the general potential of this technique for high-resolution structural refinement of solid proteins.

Broadband-PISEMA solid-state NMR spectroscopy

The measurement of heteronuclear dipolar couplings using a 2D separated-local-field technique, Polarization Inversion Spin Exchange at the Magic Angle (PISEMA), is a unique way to determine the structure, dynamics and topology of molecules in solid-state. However, the resolution and sensitivity of PISEMA are highly dependent on the offset frequency of protons. To overcome this difficulty, in this study, a broadband-PISEMA pulse sequence is proposed. Experimental data from a single crystal and simulated results suggest that the new sequence compensates the offset effects. This is accomplished using a pair of 180° pulses that invert the spin-locked magnetization of I and S nuclei after certain number of SEMA cycles in the t 1 period. In addition, unlike PISEMA, BB-PISEMA provides offset-independent dipolar coupling line shapes even when low rf fields are applied.

A distance ruler for RNA using EPR and site-directed spin labeling.

As a basic model study for measuring distances in RNA molecules using continuous wave (CW) EPR spectroscopy, site-directed spin-labeled 10-mer RNA duplexes and HIV-1 TAR RNA motifs with various interspin distances were examined. The spin labels were attached to the 2'-NH2 positions of appropriately placed uridines in the duplexes, and interspin distances were measured from both molecular dynamics simulations (MD) and Fourier deconvolution methods (FD). The 10-mer duplexes have interspin distances ranging from 10 A to 30 A based on MD; however, dipolar line broadening of the CW EPR spectrum is only observed for the RNAs for predicted interspin distances of 10-21 A and not for distances over 25 A. The conformational changes in TAR (transactivating responsive region) RNA in the presence and in the absence of different divalent metal ions were monitored by measuring distances between two nucleotides in the bulge region. The predicted interspin distances obtained from the FD method and those from MD calculations match well for both the model RNA duplexes and the structural changes predicted for TAR RNA. These results demonstrate that distance measurement using EPR spectroscopy is a potentially powerful method to help predict the structures of RNA molecules.

C 13 – 1 H dipolar-driven C13–13C recoupling without C13 rf irradiation in nuclear magnetic resonance of rotating solids

Two recently proposed C13–13C recoupling methods under magic angle spinning (MAS), resonant interference recoupling (RIR), and C13–1H dipolar-assisted rotational resonance (DARR), are examined on a common theoretical foundation using the average Hamiltonian theory. In both methods, a rf field is applied on not C13 but H1 to recouple the C13–1H dipolar interactions, and spectral overlap necessary to conserve energy for C13–13C polarization transfer is achieved by the C13–1H dipolar line broadening. While DARR employs time-independent C13–1H interactions recoupled by suitable rf irradiation to H1 spins, RIR uses time-dependent C13–1H interactions modulated appropriately by H1 rf irradiation. There are two distinct cases where C13–1H line broadening realizes C13–13C spectral overlap. For a pair of a carbonyl or aromatic carbon and an aliphatic carbon, spectral overlap can be achieved between one of the spinning sidebands of the former C13 resonance and the C13–1H dipolar powder pattern of the latter. On the other hand for a pair of spins with a small chemical shift difference, the two center bands are overlapped with each other due to C13–1H dipolar broadening. For the former, we show that both RIR and DARR occur in the first order, while for the latter, DARR recoupling is appreciable for time-independent C13–1H interactions. We refer to the former DARR as the first-order DARR recoupling and the latter as the second-order DARR. Experimentally, we examined the following C13–1H recoupling methods for DARR: H1 CW irradiation fulfilling a rotary-resonance condition or a modulatory-resonance condition, and H1 π pulses applied synchronously to MAS. For RIR, the FSLG-m2m¯m sequence is applied to H1. Several one-dimensional DARR and RIR experiments were done for N-acetyl[1,2-13C, 15N] DL-valine, and [2,3-13C] L-alanine. It was found that the polarization transfer rate for RIR is larger than that for DARR except for fast spinning, while the rate for DARR is less sensitive to the spinning speed. Further, we showed that the efficiency of the second-order DARR recoupling is not significantly less than that of the first-order DARR. Among the C13–1H recoupling methods examined, CW irradiation at the n=1 rotary-resonance condition is superior for DARR because it gives a larger C13–1H dipolar broadening, leading to broadband recoupling. We showed that a broadband-recoupling experiment with the first and the second-order DARR by CW irradiation at the n=1 rotary-resonance condition is applicable to signal assignment as well as structural determination of a multiply/uniformly C13 labeled molecule as demonstrated by two-dimensional C13–13C DARR polarization-transfer experiments of uniformly C13, N15-labeled glycylisoleucine.

Nuclear magnetic resonance spin-spin relaxation of the crystals of bone, dental enamel, and synthetic hydroxyapatites.

Studies of the apatitic crystals of bone and enamel by a variety of spectroscopic techniques have established clearly that their chemical composition, short-range order, and physical chemical reactivity are distinctly different from those of pure hydroxyapatite. Moreover, these characteristics change with aging and maturation of the bone and enamel crystals. Phosphorus-31 solid state nuclear magnetic resonance (NMR) spin-spin relaxation studies were carried out on bovine bone and dental enamel crystals of different ages and the data were compared with those obtained from pure and carbonated hydroxyapatites. By measuring the 31P Hahn spin echo amplitude as a function of echo time, Van Vleck second moments (expansion coefficients describing the homonuclear dipolar line shape) were obtained and analyzed in terms of the number density of phosphorus nuclei. 31P magnetization prepared by a 90 degree pulse or by proton-phosphorus cross-polarization (CP) yielded different second moments and experienced different degrees of proton spin-spin coupling, suggesting that these two preparation methods sample different regions, possibly the interior and the surface, respectively, of bone mineral crystals. Distinct differences were found between the biological apatites and the synthetic hydroxyapatites and as a function of the age and maturity of the biological apatites. The data provide evidence that a significant fraction of the protonated phosphates (HPO4(-2)) are located on the surfaces of the biological crystals, and the concentration of unprotonated phosphates (PO4(-3)) within the apatitic lattice is elevated with respect to the surface. The total concentration of the surface HPO4(-2) groups is higher in the younger, less mature biological crystals.

A Two-Dimensional Magic-Angle Decoupling and Magic-Angle Turning Solid-State NMR Method: An Application to Study Chemical Shift Tensors from Peptides That Are Nonselectively Labeled with 15N Isotope

A two-dimensional solid-state NMR technique is presented that can be used to determine the 15N chemical shift and 1H−15N dipolar coupling tensors in powder samples of polypeptides containing 15N isotopes at multiple sites. By combining the magic-angle rf decoupling in one time period and the magic-angle turning pulse sequence in another time period of a 2D experiment, we obtain 2D spectra in which the convoluted chemical shift anisotropy (CSA) and dipolar coupling line shapes appear along one axis and the normal MAS spectrum appears along the other axis. The magnitudes of the principal elements of the 15N CSA tensors and their orientations in the molecular frame for n-acetyl-15N-l-Val-15N-l-Leu (NAVL) and n-acetyl-15N-d,l-Val (NAV) powder samples are determined using this method. The magnitudes of the 15N CSA tensors are 60.2 ± 1, 87.1 ± 1, and 230.1 ± 1 ppm for the Val residue in NAVL; 58.7 ± 1, 93.7 ± 1, and 232.8 ± 1 ppm for the Leu residue in NAVL; 59.6 ± 1, 80.5 ± 1, and 235.3 ± 1 ppm for site I in NAV; and 57.5 ± 2, 81.0 ± 2, and 227.0 ± 2 ppm for site II in NAV. The experimental results also suggest that the most-shielded axis, σ11N, and the σ22N axis of the 15N CSA tensor are significantly tilted away from the peptide plane and the normal to the peptide plane, respectively. The tilt angles (αN) are 34 ± 12° for Val and 36 ± 11° for Leu in NAVL, whereas it is 5 ± 22° in NAV. The angles (βN) between the least-shielded axis of the 15N CSA tensor, σ33N, in the peptide plane and the N−H bond are determined to be 20 ± 2° for Val and 18 ± 2° for Leu in NAVL and 21 ± 2° for NAV. The values are in good agreement with some of the recent solid-state NMR experimental studies on peptides. The values for the βN angle reported in this study are also in agreement with the solution NMR studies on water-soluble proteins.