Phase modulated Lee–Goldburg magic angle spinning proton nuclear magnetic resonance experiments in the solid state: A bimodal Floquet theoretical treatment

Continuous Floquet theory in solid-state NMR

This article presents the application of continuous Floquet theory in solid-state nuclear magnetic resonance (NMR). Continuous Floquet theory extends the traditional Floquet theory to non-continuous Hamiltonians, enabling the description of observable effects not fully captured by the traditional Floquet theory due to its requirement for a periodic Hamiltonian. We present closed-form expressions for computing first- and second-order effective Hamiltonians, streamlining integration with the traditional Floquet theory and facilitating application in NMR experiments featuring multiple modulation frequencies. Subsequently, we show examples of the practical application of continuous Floquet theory by investigating several solid-state NMR experiments. These examples illustrate the importance of the duration of the pulse scheme regarding the width of the resonance conditions and the near-resonance behavior.

Solid-State NMR Double-Quantum Dipolar Recoupling Enhanced by Additional Phase Modulation

Additional phase modulation (APM) is proposed to generally enhance the theoretical efficiency of homonuclear double-quantum (DQ) recoupling in solid-state NMR. APM applies an additional phase list to DQ recoupling in steps of an entire block. The sine-based phase list can enhance the theoretical efficiency by 15-30 %, from 0.52 to 0.68 (non-γ-encoded recoupling) or from 0.73 to 0.84 (γ-encoded recoupling), with doubled recoupling time. The genetic-algorithm (GA) optimized APM can adiabatically enhance the efficiency to ∼1.0 at longer times. The concept of APM has been tested on SPR-51 , BaBa, and SPR-31 , which represent γ-encoded recoupling, non-γ-encoded recoupling, and another kind beyond the former two, respectively. Simulations reveal that enhancements from APM are due to the activation of more crystallites in the powder. Experiments on 2,3-13 C labeled alanine are used to validate the APM recoupling. This new concept shall shed light on developing more efficient homonuclear recoupling methods.

A continuous approach to Floquet theory for pulse-sequence optimization in solid-state NMR

We present a framework that uses a continuous frequency space to describe and design solid-state nuclear magnetic resonance (NMR) experiments. The approach is similar to the well-established Floquet treatment for NMR, but it is not restricted to periodic Hamiltonians and allows the design of experiments in a reverse fashion. The framework is based on perturbation theory on a continuous Fourier space, which leads to effective, i.e., time-independent, Hamiltonians. It allows the back-calculation of the pulse scheme from the desired effective Hamiltonian as a function of spin-system parameters. We show as an example how to back-calculate the rf irradiation in the MIRROR experiment from the desired chemical-shift offset behavior of the sequence.

Light- and pH-dependent structural changes in cyanobacteriochrome AnPixJg2

Cyanobacteriochromes (CBCRs) are phytochrome-related photosensory proteins that play an essential role in regulating phototaxis, chromatic acclimation, and cell aggregation in cyanobacteria. Here, we apply solid-state NMR spectroscopy to the red/green GAF2 domain of the CBCR AnPixJ assembled in vitro with a uniformly ¹³C- and ¹⁵N-labeled bilin chromophore, tracking changes in electronic structure, geometry, and structural heterogeneity of the chromophore as well as intimate contacts between the chromophore and protein residues in the photocycle. Our data confirm that the bilin ring D is strongly twisted with respect to the B-C plane in both dark and photoproduct states. We also identify a greater structural heterogeneity of the bilin chromophore in the photoproduct than in the dark state. In addition, the binding pocket is more hydrated in the photoproduct. Observation of interfacial ¹H contacts of the photoproduct chromophore, together with quantum mechanics/molecular mechanics (QM/MM)-based structural models for this photoproduct, clearly suggests the presence of a biprotonated (cationic) imidazolium side-chain for a conserved histidine residue (322) at a distance of ~2.7 Å, generalizing the recent theoretical findings that explicitly link the structural heterogeneity of the dark-state chromophore to the protonation of this specific residue. Moreover, we examine pH effects on this in vitro assembled holoprotein, showing a substantially altered electronic structure and protonation of the photoproduct chromophore even with a small pH drop from 7.8 to 7.2. Our studies provide further information regarding the light- and pH-induced changes of the chromophore and the rearrangements of the hydrogen-bonding and electrostatic interaction network around it. Possible correlations between structural heterogeneity of the chromophore, protonation of the histidine residue nearby, and hydration of the pocket in both photostates are discussed.

Floquet theory in magnetic resonance: Formalism and applications

Floquet theory is an elegant mathematical formalism originally developed to solve time-dependent differential equations. Besides other fields, it has found applications in optical spectroscopy and nuclear magnetic resonance (NMR). This review attempts to give a perspective of the Floquet formalism as applied in NMR and shows how it allows one to solve various problems with a focus on solid-state NMR. We include both matrix- and operator-based approaches. We discuss different problems where the Hamiltonian changes with time in a periodic way. Such situations occur, for example, in solid-state NMR experiments where the time dependence of the Hamiltonian originates either from magic-angle spinning or from the application of amplitude- or phase-modulated radiofrequency fields, or from both. Specific cases include multiple-quantum and multiple-frequency excitation schemes. In all these cases, Floquet analysis allows one to define an effective Hamiltonian and, moreover, to treat cases that cannot be described by the more popularly used and simpler-looking average Hamiltonian theory based on the Magnus expansion. An important example is given by spin dynamics originating from multiple-quantum phenomena (level crossings). We show that the Floquet formalism is a very general approach for solving diverse problems in spectroscopy.

Mechanistic Insights into the Structural Stability of Collagen-Containing Biomaterials Such as Bones and Cartilage

Structural stability of various collagen-containing biomaterials such as bones and cartilage is still a mystery. Despite the spectroscopic development of several decades, the detailed mechanism of collagen interaction with citrate in bones and glycosaminoglycans (GAGs) in the cartilage extracellular matrix (ECM) in its native state is unobservable. We present a significant advancement to probe the collagen interactions with citrate and GAGs in the ECM of native bones and cartilage along with specific/non-specific interactions inside the collagen assembly at the nanoscopic level through natural-abundance dynamic nuclear polarization-based solid-state nuclear magnetic resonance spectroscopy. The detected molecular-level interactions between citrate-collagen and GAG-collagen inside the native bone and cartilage matrices and other backbone and side-chain interactions in the collagen assembly are responsible for the structural stability and other biomechanical properties of these important classes of biomaterials.

Mechanistic investigation of enzymatic degradation of polyethylene terephthalate by nuclear magnetic resonance

The biocatalytic degradation of polyethylene terephthalate (PET) by thermophilic microbial enzymes has recently emerged as an option for a future eco-friendly recycling process for plastic waste, as it occurs under mild conditions and requires no harmful additives. In this chapter, we present a brief overview of solution and solid-state nuclear magnetic resonance (NMR) spectroscopic methods for the characterization of composition and chemical microstructure of PET and also associated chain dynamics over multiple time scales. Such detailed information provides an understanding of the enzymatic PET degradation mechanism by polyester hydrolases at the molecular level.

UV Pretreatment Impairs the Enzymatic Degradation of Polyethylene Terephthalate

The biocatalytic degradation of polyethylene terephthalate (PET) emerged recently as a promising alternative plastic recycling method. However, limited activity of previously known enzymes against post-consumer PET materials still prevents the application on an industrial scale. In this study, the influence of ultraviolet (UV) irradiation as a potential pretreatment method for the enzymatic degradation of PET was investigated. Attenuated total reflection Fourier transform infrared (ATR-FTIR) and ¹H solution nuclear magnetic resonance (NMR) analysis indicated a shortening of the polymer chains of UV-treated PET due to intra-chain scissions. The degradation of UV-treated PET films by a polyester hydrolase resulted in significantly lower weight losses compared to the untreated sample. We also examined site-specific and segmental chain dynamics over a time scale of sub-microseconds to seconds using centerband-only detection of exchange, rotating-frame spin-lattice relaxation (T_1ρ), and dipolar chemical shift correlation experiments which revealed an overall increase in the chain rigidity of the UV-treated sample. The observed dynamic changes are most likely associated with the increased crystallinity of the surface, where a decreased accessibility for the enzyme-catalyzed hydrolysis was found. Moreover, our NMR study provided further knowledge on how polymer chain conformation and dynamics of PET can mechanistically influence the enzymatic degradation.

Origin of the residual line width under frequency-switched Lee-Goldburg decoupling in MAS solid-state NMR

Homonuclear decoupling sequences in solid-state nuclear magnetic resonance (NMR) under magic-angle spinning (MAS) show experimentally significantly larger residual line width than expected from Floquet theory to second order. We present an in-depth theoretical and experimental analysis of the origin of the residual line width under decoupling based on frequency-switched Lee-Goldburg (FSLG) sequences. We analyze the effect of experimental pulse-shape errors (e.g., pulse transients and B 1 -field inhomogeneities) and use a Floquet-theory-based description of higher-order error terms that arise from the interference between the MAS rotation and the pulse sequence. It is shown that the magnitude of the third-order auto term of a single homo- or heteronuclear coupled spin pair is important and leads to significant line broadening under FSLG decoupling. Furthermore, we show the dependence of these third-order error terms on the angle of the effective field with the B 0 field. An analysis of second-order cross terms is presented that shows that the influence of three-spin terms is small since they are averaged by the pulse sequence. The importance of the inhomogeneity of the radio-frequency (rf) field is discussed and shown to be the main source of residual line broadening while pulse transients do not seem to play an important role. Experimentally, the influence of the combination of these error terms is shown by using restricted samples and pulse-transient compensation. The results show that all terms are additive but the major contribution to the residual line width comes from the rf-field inhomogeneity for the standard implementation of FSLG sequences, which is significant even for samples with a restricted volume.

MAS NMR on a Red/Far-Red Photochromic Cyanobacteriochrome All2699 from Nostoc

Unlike canonical phytochromes, the GAF domain of cyanobacteriochromes (CBCRs) can bind bilins autonomously and is sufficient for functional photocycles. Despite the astonishing spectral diversity of CBCRs, the GAF1 domain of the three-GAF-domain photoreceptor all2699 from the cyanobacterium Nostoc 7120 is the only CBCR-GAF known that converts from a red-absorbing (Pr) dark state to a far-red-absorbing (Pfr) photoproduct, analogous to the more conservative phytochromes. Here we report a solid-state NMR spectroscopic study of all2699g1 in its Pr state. Conclusive NMR evidence unveils a particular stereochemical heterogeneity at the tetrahedral C3¹ atom, whereas the crystal structure shows exclusively the R-stereochemistry at this chiral center. Additional NMR experiments were performed on a construct comprising the GAF1 and GAF2 domains of all2699, showing a greater precision in the chromophore-protein interactions in the GAF1-2 construct. A 3D Pr structural model of the all2699g1-2 construct predicts a tongue-like region extending from the GAF2 domain (akin to canonical phytochromes) in the direction of the chromophore, shielding it from the solvent. In addition, this stabilizing element allows exclusively the R-stereochemistry for the chromophore-protein linkage. Site-directed mutagenesis performed on three conserved motifs in the hairpin-like tip confirms the interaction of the tongue region with the GAF1-bound chromophore.

Assignment of NMR resonances of protons covalently bound to photochemically active cofactors in photosynthetic reaction centers by 13C-1H photo-CIDNP MAS-J-HMQC experiment

Modified versions of through-bond heteronuclear correlation (HETCOR) experiments are presented to take advantage of the light-induced hyperpolarization that occurs on ¹³C nuclei due to the solid-state photochemically induced dynamic nuclear polarization (photo-CIDNP) effect. Such ¹³C-¹H photo-CIDNP MAS-J-HMQC and photo-CIDNP MAS-J-HSQC experiments are applied to acquire the 2D ¹³C-¹H correlation spectra of selectively ¹³C-labeled photochemically active cofactors in the frozen quinone-blocked photosynthetic reaction center (RC) of the purple bacterium Rhodobacter (R.) sphaeroides wild-type (WT). Resulting spectra contain no correlation peaks arising from the protein backbone, which greatly simplifies the assignment of aliphatic region. Based on the photo-CIDNP MAS-J-HMQC NMR experiment, we obtained assignment of selective ¹H NMR resonances of the cofactors involved in the electron transfer process in the RC and compared them with values theoretically predicted by density functional theory (DFT) calculation as well as with the chemical shifts obtained from monomeric cofactors in the solution. We also compared proton chemical shifts obtained by photo-CIDNP MAS-J-HMQC experiment under continuous illumination with the ones obtained in dark by classical cross-polarization (CP) HETCOR. We expect that the proposed approach will become a method of choice for obtaining ¹H chemical shift maps of the active cofactors in photosynthetic RCs and will aid the interpretation of heteronuclear spin-torch experiments.

13C → 1H transfer of light-induced hyperpolarization allows for selective detection of protons in frozen photosynthetic reaction center

In the present study, we exploit the light-induced hyperpolarization occurring on ¹³C nuclei due to the solid-state photochemically induced dynamic nuclear polarization (photo-CIDNP) effect to boost the NMR signal intensity of selected protons via inverse cross-polarization. Such hyperpolarization transfer is implemented into ¹H-detected two-dimensional ¹³C-¹H correlation magic-angle-spinning (MAS) NMR experiment to study protons in frozen photosynthetic reaction centers (RCs). As a first trial, the performance of such an experiment is tested on selectively ¹³C labeled RCs from the purple bacteria of Rhodobacter sphaeroides. We observed response from the protons belonging to the photochemically active cofactors in their native protein environment. Such an approach is a potential heteronuclear spin-torch experiment which could be complementary to the classical heteronuclear correlation (HETCOR) experiments for mapping proton chemical shifts of photosynthetic cofactors and to understand the role of the proton pool around the electron donors in the electron transfer process occurring during photosynthesis.

1H line width dependence on MAS speed in solid state NMR - Comparison of experiment and simulation

Recent developments in magic angle spinning (MAS) technology permit spinning frequencies of ≥100 kHz. We examine the effect of such fast MAS rates upon nuclear magnetic resonance proton line widths in the multi-spin system of β-Asp-Ala crystal. We perform powder pattern simulations employing Fokker-Plank approach with periodic boundary conditions and ¹H-chemical shift tensors calculated using the bond polarization theory. The theoretical predictions mirror well the experimental results. Both approaches demonstrate that homogeneous broadening has a linear-quadratic dependency on the inverse of the MAS spinning frequency and that, at the faster end of the spinning frequencies, the residual spectral line broadening becomes dominated by chemical shift distributions and susceptibility effects even for crystalline systems.

Five decades of homonuclear dipolar decoupling in solid-state NMR: Status and outlook

It has been slightly more than fifty years since the first homonuclear spin decoupling scheme, Lee-Goldburg decoupling, was proposed for removing homonuclear dipolar interactions in solid-state nuclear magnetic resonance. A family of such schemes has made observation of high-resolution NMR spectra of abundant spins possible in various applications in solid state. This review outlines the strategies used in this field and the future prospects of homonuclear spin decoupling in solid-state NMR.

Site-Specific Internal Motions in GB1 Protein Microcrystals Revealed by 3D ²H-¹³C-¹³C Solid-State NMR Spectroscopy

(2)H quadrupolar line shapes deliver rich information about protein dynamics. A newly designed 3D (2)H-(13)C-(13)C solid-state NMR magic angle spinning (MAS) experiment is presented and demonstrated on the microcrystalline β1 immunoglobulin binding domain of protein G (GB1). The implementation of (2)H-(13)C adiabatic rotor-echo-short-pulse-irradiation cross-polarization (RESPIRATION CP) ensures the accuracy of the extracted line shapes and provides enhanced sensitivity relative to conventional CP methods. The 3D (2)H-(13)C-(13)C spectrum reveals (2)H line shapes for 140 resolved aliphatic deuterium sites. Motional-averaged (2)H quadrupolar parameters obtained from the line-shape fitting identify side-chain motions. Restricted side-chain dynamics are observed for a number of polar residues including K13, D22, E27, K31, D36, N37, D46, D47, K50, and E56, which we attribute to the effects of salt bridges and hydrogen bonds. In contrast, we observe significantly enhanced side-chain flexibility for Q2, K4, K10, E15, E19, N35, N40, and E42, due to solvent exposure and low packing density. T11, T16, and T17 side chains exhibit motions with larger amplitudes than other Thr residues due to solvent interactions. The side chains of L5, V54, and V29 are highly rigid because they are packed in the core of the protein. High correlations were demonstrated between GB1 side-chain dynamics and its biological function. Large-amplitude side-chain motions are observed for regions contacting and interacting with immunoglobulin G (IgG). In contrast, rigid side chains are primarily found for residues in the structural core of the protein that are absent from protein binding and interactions.

Confined Polymerization in Highly Ordered Mesoporous Organosilicas

Hybrid mesoporous organosilica exhibiting crystal-like order in the walls provided an ideal channel reaction vessel for the confined polymerization of acrylonitrile (PAN). The resulting high-molecular-mass PAN fills the channels at high yield and forms an ordered nanostructure of polymer nanobundles enclosed into the hybrid matrix. The in situ thermal transformation of PAN into rigid polyconjugated and, eventually, into condensed polyaromatic carbon nanofibers, retains the periodic architecture. Simultaneously, the matrix evolves showing the fusion of the p-phenylene rings and the cleavage of carbonsilicon bonds: this gives rise to graphitic-carbon/silica nanocomposites containing hyper-oxydrylated silica nanophases. Interestingly, the 3D hexagonal mesostructure survives in the carbonaceous material. The exploitation of porous materials of high capacity and a hybrid nature, for polymerization in the confined state, followed by high temperature treatments, allowed us to achieve unique and precisely fabricated nanostructures, thus paving the way for the construction of fine-tuned electronic and light-harvesting materials.

Minimizing the effects of RF inhomogeneity and phase transients allows resolution of two peaks in the (1)H CRAMPS NMR spectrum of adamantane

One of the limiting factors to achieving highly resolved (1)H NMR spectra with (1)H homonuclear decoupling sequences is imperfections in the applied radiofrequency (RF) pulses, most notably phase transients and RF inhomogeneity. Through a series of simulations and solid-state NMR experiments, it is demonstrated that the combined effects of phase transients and RF inhomogeneity can be minimized by a combination of (i) restricting the sample to small volume of the rotor, (ii) by employing a super-cycled version of the DUMBO decoupling sequence, and (iii) by carefully adjusting the probe tuning such that the asymmetric component of phase transients is minimized. Under these optimal conditions, it was possible to clearly resolve two signals in the (1)H CRAMPS NMR spectrum of adamantane arising from the CH and CH2 protons in the molecule. It is proposed that adamantane could be a very useful setup sample for (1)H CRAMPS NMR as the two peaks are only resolved when the effects of RF inhomogeneity and phase transients are minimized.

A double-component Anderson-Weiss approach for describing NMR signals of mobile SIn units: application to constant-time DIPSHIFT experiments

A composed Gaussian local field is proposed to describe the effect of molecular motions on NMR signals of SIn units (e.g., CHn or NHn), based upon the well-know Anderson-Weiss (AW) approximation. The approach is exemplified on constant-time recoupled dipolar chemical-shift correlation (tC-recDIPSHIFT) experiments, providing an analytical formula that can be used as a fitting function in studies of intermediate-regime motions. By comparison of analytical tC-recDIPSHIFT curves and dynamic spin dynamics simulations, we show that for heteronuclear spin pairs (SI system), the AW treatment assuming the usual Gaussian local field is accurate. However, the approximation fails for the case of SIn spin systems for motional rates higher than a few kHz. Based on earlier work of Terao et al., who proposed a decomposition of CHn dipolar powder patterns into to 2(n) spin-pair-type patterns, we propose an AW approach based upon a double-Gaussian local field. We derive an analytical formula for tC-recDIPSHIFT signals, and demonstrate its accuracy by comparison with simulations of several motional geometries and rates, and with experimental results for a model sample. The approach is not limited to the tC-recDIPSHIFT experiment and should be of general use in dipolar-coupling based experiments probing (partially) mobile SIn molecular moieties.

Improving the resolution in proton-detected through-space heteronuclear multiple quantum correlation NMR spectroscopy

Connectivities and proximities between protons and low-gamma nuclei can be probed in solid-state NMR spectroscopy using two-dimensional (2D) proton-detected heteronuclear correlation, through Heteronuclear Multiple Quantum Correlation (HMQC) pulse sequence. The indirect detection via protons dramatically enhances the sensitivity. However, the spectra are often broadened along the indirect F1 dimension by the decay of heteronuclear multiple-quantum coherences under the strong (1)H-(1)H dipolar couplings. This work presents a systematic comparison of the performances of various decoupling schemes during the indirect t1 evolution period of dipolar-mediated HMQC (D-HMQC) experiment. We demonstrate that (1)H-(1)H dipolar decoupling sequences during t1, such as symmetry-based schemes, phase-modulated Lee-Goldburg (PMLG) and Decoupling Using Mind-Boggling Optimization (DUMBO), provide better resolution than continuous wave (1)H irradiation. We also report that high resolution requires the preservation of (1)H isotropic chemical shifts during the decoupling sequences. When observing indirectly broad spectra presenting numerous spinning sidebands, the D-HMQC sequence must be fully rotor-synchronized owing to the rotor-synchronized indirect sampling and dipolar recoupling sequence employed. In this case, we propose a solution to reduce artefact sidebands caused by the modulation of window delays before and after the decoupling application during the t1 period. Moreover, we show that (1)H-(1)H dipolar decoupling sequence using Smooth Amplitude Modulation (SAM) minimizes the t1-noise. The performances of the various decoupling schemes are assessed via numerical simulations and compared to 2D (1)H-{(13)C} D-HMQC experiments on [U-(13)C]-L-histidine⋅HCl⋅H2O at various magnetic fields and Magic Angle spinning (MAS) frequencies. Great resolution and sensitivity enhancements resulting from decoupling during t1 period enable the detection of heteronuclear correlation between aliphatic protons and ammonium (14)N sites in L-histidine⋅HCl⋅H2O.

Sensitivity and resolution enhancement of oriented solid-state NMR: application to membrane proteins

Oriented solid-state NMR (O-ssNMR) spectroscopy is a major technique for the high-resolution analysis of the structure and topology of transmembrane proteins in native-like environments. Unlike magic angle spinning (MAS) techniques, O-ssNMR spectroscopy requires membrane protein preparations that are uniformly oriented (mechanically or magnetically) so that anisotropic NMR parameters, such as dipolar and chemical shift interactions, can be measured to determine structure and orientation of membrane proteins in lipid bilayers. Traditional sample preparations involving mechanically aligned lipids often result in short relaxation times which broaden the (15)N resonances and encumber the manipulation of nuclear spin coherences. The introduction of lipid bicelles as membrane mimicking systems has changed this scenario, and the more favorable relaxation properties of membrane protein (15)N and (13)C resonances make it possible to develop new, more elaborate pulse sequences for higher spectral resolution and sensitivity. Here, we describe our recent progress in the optimization of O-ssNMR pulse sequences. We explain the theory behind these experiments, demonstrate their application to small and medium size proteins, and describe the technical details for setting up these new experiments on the new generation of NMR spectrometers.

A Floquet description of phase alternated sequences for efficient homonuclear recoupling in solid perdeuterated systems

A Floquet description of a phase alternated homonuclear recoupling scheme for perdeuterated systems is presented. As a result, we demonstrate improvements in the recoupling efficiency of the DOuble Nucleus Enhanced Recoupling [DONER; J. Am. Chem. Soc. 131 (2009) 17054] technique by utilizing Phase Alternated Recoupling Irradiation Schemes [PARIS; Chem. Phys. Lett. 469 (2009) 342]. The effect of proton and deuterium radio frequency irradiation during recoupling has been systematically studied and theoretical observations have been verified experimentally using a deuterated model compound, L-Alanine, at 10 and 20 kHz magic angle spinning frequency. Experimental results are well in agreement with theoretical observations, thereby significantly increasing the recoupling efficiency of conventional DONER in perdeuterated systems.

Progress in spin dynamics solid-state nuclear magnetic resonance with the application of Floquet-Magnus expansion to chemical shift anisotropy

The purpose of this article is to present an historical overview of theoretical approaches used for describing spin dynamics under static or rotating experiments in solid state nuclear magnetic resonance. The article gives a brief historical overview for major theories in nuclear magnetic resonance and the promising theories. We present the first application of Floquet-Magnus expansion to chemical shift anisotropy when irradiated by BABA pulse sequence.

Understanding cross-polarization (CP) NMR experiments through dipolar truncation

A theoretical model based on the phenomenon of dipolar truncation is proposed to explain the nuances of polarization transfer from abundant to less-abundant nuclei in cross-polarization (CP) NMR experiments. Specifically, the transfer of polarization from protons to carbons (in solids) in strongly coupled systems is described in terms of effective Hamiltonians based on dipolar truncation. Through suitable model spin systems, the important role of dipolar truncation in the propagation of spin polarization in CP experiments is outlined. We believe that the analytic theory presented herein provides a convenient framework for modeling polarization transfer in strongly coupled systems.

Detailed analysis of the TIMES and TIMES0 high-resolution MAS methods for high-resolution proton NMR

We analyze and compare the specifications of TIMES and TIMES(0) proton high-resolution NMR methods for solid-state samples. This comparison is performed in terms of resolution versus magic-angle spinning (MAS) spinning speed, ν(R), rf-field amplitude, ν(1), and tilt-angle for the effective rf-field, θ(p). The chemical-shift and homo-nuclear dipolar scaling factors are calculated for both methods. For all MAS speeds, the best resolution is always observed with rf-field of ν(1)≈120-130 kHz. At slow MAS speed (ν(R)≤10 kHz), the best resolution is observed for a tilt-angle of θ(P)≈90°. At moderate spinning speed (15≤ν(R)≤35 kHz), θ(P)≈55° gives the best resolution. At higher MAS speed (ν(R)≥60 kHz), with TIMES and TIMES(0) the best resolution is obtained for θ(P)≤40°; but we then recommend TIMES(0), owing to its simpler set-up. We also show that in addition to the usual high rf-field regime (ν(1)≈120-130 kHz), another low rf-regime (ν(1)≈40-50 kHz) exists at MAS speed higher than ν(R)≥60 kHz, which also gives a good (1)H resolution. This low rf-regime should be useful for multi-dimensional analyses of bio-molecules with (1)H detection under high-resolution, in order to limit the heating of the sample.

Exploring Chromophore-Binding Pocket: High-Resolution Solid-State H-C Interfacial Correlation NMR Spectra with Windowed PMLG Scheme

High-resolution two-dimensional (2D) (1)H-(13)C heteronuclear correlation spectra are recorded for selective observation of interfacial 3-5.5 Å contacts of the uniformly (13)C-labeled phycocyanobilin (PCB) chromophore with its unlabeled binding pocket. The experiment is based on a medium- and long-distance heteronuclear correlation (MELODI-HETCOR) method. For improving (1)H spectral resolution, a windowed phase-modulated Lee-Goldburg (wPMLG) decoupling scheme is applied during the t(1) evolution period. Our approach allows for identification of chromophore-protein interactions, in particular for elucidation of the hydrogen-bonding networks and charge distributions within the chromophore-binding pocket. The resulting pulse sequence is tested on the cyanobacterial (Cph1) phytochrome sensory module (residues 1-514, Cph1Δ2) containing uniformly (13)C- and (15)N-labeled PCB chromophore (u-[(13)C,(15)N]-PCB-Cph1Δ2) at 17.6 T.

Practical choice of ¹H-¹H decoupling schemes in through-bond ¹H-{X} HMQC experiments at ultra-fast MAS

Three (1)H-(1)H homonuclear dipolar decoupling schemes for (1)H indirect detection measurements at very fast MAS are compared. The sequences require the following conditions: (i) being operable at very fast MAS, (ii) a long T(2)(') value, (iii) a large scaling factor, (iv) a small number of adjustable parameters, (v) an acquisition window, (vi) a low rf-power requirement, and (vii) a z-rotation feature. To satisfy these conditions a modified sequence named TIlted Magic-Echo Sandwich with zero degree sandwich pulse (TIMES(0)) is introduced. The basic elements of TIMES(0) consist of one sampling window and two phase-ramped irradiations, which realize alternating positive and negative 360° rotations of (1)H magnetization around an effective field tilted with an angle θ from the B(0) axis. The TIMES(0) sequence benefits from very large chemical shift scaling factors at ultra-fast MAS that reach κ(cs)=0.90 for θ=25° at ν(r)=80kHz MAS and only four adjustable parameters, resulting in easy setup. Long κ(cs)T(2)(') values, where T(2)(') is a irreversible proton transverse relaxation time, greatly enhance the sensitivity in (1)H-{(13)C} through-bond J-HMQC (Heteronuclear Multiple-Quantum Coherence) measurements with (1)H-(1)H decoupling during magnetization transfer periods. Although similar sensitivity can be obtained with through-space D-HMQC sequences, in which (13)C-(1)H dipolar interactions are recoupled, J-HMQC experiments incorporating (1)H-(1)H decoupling benefit from lower t(1)-noise, more uniform excitation of both CH, CH(2) and CH(3) moieties, and easier identification of through-bond connectivities.

1H Homonuclear dipolar decoupling using symmetry-based pulse sequences at ultra fast magic-angle spinning frequencies

We demonstrate here the application of symmetry-based pulse sequences for homonuclear dipolar decoupling in solid-state NMR at magic-angle spinning (MAS) frequencies up to 65 kHz using moderate radiofrequency (RF) amplitudes. Theoretical arguments favouring the requirement of low RF amplitudes at high MAS frequencies are given for these sequences. A comparison with wPMLGmmxx¯ is given at 65 kHz of MAS frequency to emphasise that the symmetry-based pulse sequences have a lower RF amplitude requirement at high MAS frequencies.

Molecular level characterization of the inorganic-bioorganic interface by solid state NMR: alanine on a silica surface, a case study

The molecular interface between bioorganics and inorganics plays a key role in diverse scientific and technological research areas including nanoelectronics, biomimetics, biomineralization, and medical applications such as drug delivery systems and implant coatings. However, the physical/chemical basis of recognition of inorganic surfaces by biomolecules remains unclear. The molecular level elucidation of specific interfacial interactions and the structural and dynamical state of the surface bound molecules is of prime scientific importance. In this study, we demonstrate the ability of solid state NMR methods to accomplish these goals. L-[1-(13)C,(15)N]Alanine loaded onto SBA-15 mesoporous silica with a high surface area served as a model system. The interacting alanine moiety was identified as the -NH(3)(+) functional group by (15)N{(1)H}SLF NMR. (29)Si{(15)N} and (15)N{(29)Si}REDOR NMR revealed intermolecular interactions between the alanine -NH(3)(+) and three to four surface Si species, predominantly Q(3), with similar internuclear N...Si distances of 4.0-4.2 A. Distinct dynamic states of the adsorbed biomolecules were identified by (15)N{(13)C}REDOR NMR, indicating both bound and free alanine populations, depending on hydration level and temperature. In the bound populations, the -NH(3)(+) group is surface anchored while the free carboxylate end undergoes librations, implying the carboxylate has small or no contributions to surface binding. When surface water clusters grow bigger with increased hydration, the libration amplitude of the carboxyl end amplifies, until onset of dissolution occurs. Our measurements provide the first direct, comprehensive, molecular-level identification of the bioorganic-inorganic interface, showing binding functional groups, geometric constraints, stoichiometry, and dynamics, both for the adsorbed amino acid and the silica surface.

1H homonuclear dipolar decoupling using rotor-synchronised pulse sequences: towards pure absorption phase spectra

We demonstrate a pulse sequence using symmetry-based rotor-synchronised RN(n)(nu) sequences for homonuclear dipolar decoupling that achieves pure absorption phase high-resolution (1)H spectra in solid-state NMR. This sequence is compared with the phase-modulated Lee-Goldburg scheme. Experimental results are shown for samples of glycine and L-histidine.HCl.H(2)O for magic-angle-spinning frequencies in the range of 14-30 kHz and at two different magnetic fields.

Operator-based Floquet theory in solid-state NMR

This article reviews the application of operator-based Floquet theory in solid-state NMR. Basic expressions for calculating effective Hamiltonians based on van Vleck perturbation theory are reviewed for problems with a single frequency or multiple incommensurate frequencies. Such a treatment allows calculation of effective Hamiltonians for resonant and non-resonant problems. Examples from literature are given for single-mode to triple-mode Floquet problems, covering a wide range of applications in solid-state NMR under magic-angle spinning and radio-frequency irradiation of a single nucleus or multiple nuclei.

Line-narrowing in proton-detected nitrogen-14 NMR

In solids spinning at the magic angle, the indirect detection of single-quantum (SQ) and double-quantum (DQ) (14)N spectra (I=1) via spy nuclei S=1/2 such as protons can be achieved in the manner of heteronuclear single- or multiple-quantum correlation (HSQC or HMQC) spectroscopy. The HMQC method relies on the excitation of two-spin coherences of the type T(11)(I)T(11)(S) and T(21)(I)T(11)(S) at the beginning of the evolution interval t(1). The spectra obtained by Fourier transformation from t(1) to omega(1) may be broadened by the homogenous decay of the transverse terms of the spy nuclei S. This broadening is mostly due to homonuclear dipolar S-S' interactions between the proton spy nuclei. In this work we have investigated the possibility of inserting rotor-synchronized symmetry-based C or R sequences and decoupling schemes such as Phase-Modulated Lee-Goldburg (PMLG) sequences in the evolution period. These schemes reduce the homonuclear proton-proton interactions and lead to an enhancement of the resolution of both SQ and DQ proton-detected (14)N HMQC spectra. In addition, we have investigated the combination of HSQC with symmetry-based sequences and PMLG and shown that the highest resolution in the (14)N dimension is achieved by using HSQC in combination with symmetry-based sequences of the R-type. We show improvements in resolution in samples of l-alanine and the tripeptide ala-ala-gly (AAG). In particular, for l-alanine the width of the (14)N SQ peak is reduced from 2 to 1.2 kHz, in agreement with simulations. We report accurate measurements of quadrupolar coupling constants and asymmetry parameters for amide (14)N in AAG peptide bonds.

Directly and indirectly detected through-bond heteronuclear correlation solid-state NMR spectroscopy under fast MAS

Two-dimensional through-bond (1)H{(13)C} solid-state NMR experiments utilizing fast magic angle spinning (MAS) and homonuclear multipulse (1)H decoupling are presented. Remarkable efficiency of polarization transfer can be achieved at MAS rates exceeding 40 kHz, which is instrumental in these measurements. Schemes utilizing direct and indirect detection of heteronuclei are compared in terms of resolution and sensitivity. A simple procedure for optimization of (1)H homonuclear decoupling sequences under these conditions is proposed. The capabilities of these techniques were confirmed on two naturally abundant solids, tripeptide N-formyl-L-methionyl-L-leucyl-L-phenylalanine (f-MLF-OH) and brown coal.