Proton-driven spin diffusion in rotating solids via reversible and irreversible quantum dynamics

Electronic Structures of Radical-Pair-Forming Cofactors in a Heliobacterial Reaction Center

Photosynthetic reaction centers (RCs) are membrane proteins converting photonic excitations into electric gradients. The heliobacterial RCs (HbRCs) are assumed to be the precursors of all known RCs, making them a compelling subject for investigating structural and functional relationships. A comprehensive picture of the electronic structure of the HbRCs is still missing. In this work, the combination of selective isotope labelling of 13C and 15N nuclei and the utilization of photo-CIDNP MAS NMR (photochemically induced dynamic nuclear polarization magic-angle spinning nuclear magnetic resonance) allows for highly enhanced signals from the radical-pair-forming cofactors. The remarkable magnetic-field dependence of the solid-state photo-CIDNP effect allows for observation of positive signals of the electron donor cofactor at 4.7 T, which is interpreted in terms of a dominant contribution of the differential relaxation (DR) mechanism. Conversely, at 9.4 T, the emissive signals mainly originate from the electron acceptor, due to the strong activation of the three-spin mixing (TSM) mechanism. Consequently, we have utilized two-dimensional homonuclear photo-CIDNP MAS NMR at both 4.7 T and 9.4 T. These findings from experimental investigations are corroborated by calculations based on density functional theory (DFT). This allows us to present a comprehensive investigation of the electronic structure of the cofactors involved in electron transfer (ET).

Barriers to resolution in 1H NMR of rotating solids

The role of 1H solid-state NMR in structure elucidation of solids is becoming more preponderant, particularly as faster magic-angle spinning rates (MAS) become available which improve 1H detected assignment strategies. However, current 1H spectral resolution is still relatively poor, with linewidths of typically a few hundred Hz, even at the fastest rates available today. Here we detail and assess the factors limiting proton linewidths and line shapes in MAS experiments with five different samples, exemplifying the different sources of broadening that affect the residual linewidth. We disentangle the different contributions through one- and two-dimensional experiments: by using dilution to identify the contribution of ABMS; by using extensive deuteration to identify the dipolar contributions; and by using variable MAS rates to determine the ratio between homogeneous and inhomogeneous components. We find that the overall widths and the nature of the different contributions to the linewidths can vary very considerably. While we find that faster spinning always yields narrower lines and longer coherence lifetimes, we also find that for some resonances the dipolar contribution is no longer dominant at 100 kHz MAS. When the inhomogeneous sources of broadening, such as ABMS and chemical shift disorder, are dominant, two-dimensional 1H-1H correlation experiments yield better resolution for assignment. Particularly the extraction of the antidiagonal of a 2D peak will remove any correlated inhomogeneous broadening, giving substantially narrower 1H linewidths.

Nuclear spin diffusion under fast magic-angle spinning in solid-state NMR

Solid-state nuclear spin diffusion is the coherent and reversible process through which spin order is transferred via dipolar couplings. With the recent increases in magic-angle spinning (MAS) frequencies and magnetic fields becoming routinely applied in solid-state nuclear magnetic resonance, understanding how the increased 1H resolution obtained affects spin diffusion is necessary for interpretation of several common experiments. To investigate the coherent contributions to spin diffusion with fast MAS, we have developed a low-order correlation in Liouville space model based on the work of Dumez et al. (J. Chem. Phys. 33, 224501, 2010). Specifically, we introduce a new method for basis set selection, which accounts for the resonance-offset dependence at fast MAS. Furthermore, we consider the necessity of including chemical shift, both isotropic and anisotropic, in the modeling of spin diffusion. Using this model, we explore how different experimental factors change the nature of spin diffusion. Then, we show case studies to exemplify the issues that arise in using spin diffusion techniques at fast spinning. We show that the efficiency of polarization transfer via spin diffusion occurring within a deuterated and 100% back-exchanged protein sample at 60 kHz MAS is almost entirely dependent on resonance offset. We additionally identify temperature-dependent magnetization transfer in beta-aspartyl L-alanine, which could be explained by the influence of an incoherent relaxation-based nuclear Overhauser effect.

Ultrafast Magic Angle Spinning Solid-State NMR Spectroscopy: Advances in Methodology and Applications

Solid-state NMR spectroscopy is one of the most commonly used techniques to study the atomic-resolution structure and dynamics of various chemical, biological, material, and pharmaceutical systems spanning multiple forms, including crystalline, liquid crystalline, fibrous, and amorphous states. Despite the unique advantages of solid-state NMR spectroscopy, its poor spectral resolution and sensitivity have severely limited the scope of this technique. Fortunately, the recent developments in probe technology that mechanically rotate the sample fast (100 kHz and above) to obtain "solution-like" NMR spectra of solids with higher resolution and sensitivity have opened numerous avenues for the development of novel NMR techniques and their applications to study a plethora of solids including globular and membrane-associated proteins, self-assembled protein aggregates such as amyloid fibers, RNA, viral assemblies, polymorphic pharmaceuticals, metal-organic framework, bone materials, and inorganic materials. While the ultrafast-MAS continues to be developed, the minute sample quantity and radio frequency requirements, shorter recycle delays enabling fast data acquisition, the feasibility of employing proton detection, enhancement in proton spectral resolution and polarization transfer efficiency, and high sensitivity per unit sample are some of the remarkable benefits of the ultrafast-MAS technology as demonstrated by the reported studies in the literature. Although the very low sample volume and very high RF power could be limitations for some of the systems, the advantages have spurred solid-state NMR investigation into increasingly complex biological and material systems. As ultrafast-MAS NMR techniques are increasingly used in multidisciplinary research areas, further development of instrumentation, probes, and advanced methods are pursued in parallel to overcome the limitations and challenges for widespread applications. This review article is focused on providing timely comprehensive coverage of the major developments on instrumentation, theory, techniques, applications, limitations, and future scope of ultrafast-MAS technology.

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.

Fast Magic‐Angle‐Spinning NMR Reveals the Evasive Hepatitis B Virus Capsid C‐Terminal Domain**

Experimentally determined protein structures often feature missing domains. One example is the C‐terminal domain (CTD) of the hepatitis B virus capsid protein, a functionally central part of this assembly, crucial in regulating nucleic‐acid interactions, cellular trafficking, nuclear import, particle assembly and maturation. However, its structure remained elusive to all current techniques, including NMR. Here we show that the recently developed proton‐detected fast magic‐angle‐spinning solid‐state NMR at >100 kHz MAS allows one to detect this domain and unveil its structural and dynamic behavior. We describe the experimental framework used and compare the domain's behavior in different capsid states. The developed approaches extend solid‐state NMR observations to residues characterized by large‐amplitude motion on the microsecond timescale, and shall allow one to shed light on other flexible protein domains still lacking their structural and dynamic characterization.

Solid-State NMR Dipolar and Chemical Shift Anisotropy Recoupling Techniques for Structural and Dynamical Studies in Biological Systems

With the development of NMR methodology and technology during the past decades, solid-state NMR (ssNMR) has become a particularly important tool for investigating structure and dynamics at atomic scale in biological systems, where the recoupling techniques play pivotal roles in modern high-resolution MAS NMR. In this review, following a brief introduction on the basic theory of recoupling in ssNMR, we highlight the recent advances in dipolar and chemical shift anisotropy recoupling methods, as well as their applications in structural determination and dynamical characterization at multiple time scales (i.e., fast-, intermediate-, and slow-motion). The performances of these prevalent recoupling techniques are compared and discussed in multiple aspects, together with the representative applications in biomolecules. Given the recent emerging advances in NMR technology, new challenges for recoupling methodology development and potential opportunities for biological systems are also discussed.

Theory and simulations of homonuclear three-spin systems in rotating solids

The homonuclear dipolar coupling is the internal spin interaction that contributes the most to the line shapes in magic-angle-spinning (MAS) ¹H NMR spectra of solids, and linewidths typically extend over several hundred Hertz, limiting the ¹H resolution. Understanding and reducing this contribution could provide rich structural information for organic solids. Here, we use average Hamiltonian theory to study two- and three-spin systems in the fast MAS regime. Specifically, we develop analytical expressions to third order in the case of two and three inequivalent spins (I = ½). The results show that the full third-order expression of the Hamiltonian, without secular approximations or truncation to second order, is the description that agrees the best, by far, with full numerical calculations. We determine the effect on the NMR spectrum of the different Hamiltonian terms, which are shown to produce both residual shifts and splittings in the three-spin systems. Both the shifts and splittings have a fairly complex dependence on the spinning rate with the eigenstates having a polynomial ω_r dependence. The effect on powder line shapes is also shown, and we find that the anisotropic residual shift does not have zero average so that the powder line shape is broadened and shifted from the isotropic position. This suggests that in ¹H MAS spectra, even at the fastest MAS rates attainable today, the positions observed are not exactly the isotropic shifts.

Recent progress in dipolar recoupling techniques under fast MAS in solid-state NMR spectroscopy

With the recent advances in NMR hardware and probe design technology, magic-angle spinning (MAS) rates over 100 ​kHz are accessible now, even on commercial solid NMR probes. Under such fast MAS conditions, excellent spectral resolution has been achieved by efficient suppression of anisotropic interactions, which also opens an avenue to the proton-detected NMR experiments in solids. Numerous methods have been developed to take full advantage of fast MAS during the last decades. Among them, dipolar recoupling techniques under fast MAS play vital roles in the determination of the molecular structure and dynamics, and are also key elements in multi-dimensional correlation NMR experiments. Herein, we review the dipolar recoupling techniques, especially those developed in the past two decades for fast-to-ultrafast MAS conditions. A major focus for our discussion is the ratio of RF field strength (in frequency) to MAS frequency, ν₁/ν_r, in different pulse sequences, which determines whether these dipolar recoupling techniques are suitable for NMR experiments under fast MAS conditions. Systematic comparisons are made among both heteronuclear and homonuclear dipolar recoupling schemes. In addition, the schemes developed specially for proton-detection NMR experiments under ultrafast MAS conditions are highlighted as well.

The origin of negative cross-peaks in proton-spin diffusion spectrum of fully protonated solids at fast MAS: Coherent or incoherent effect?

Spin-diffusion (SD) is amongst the first methods proposed to spatially transfer polarization between dipolar-coupled nuclear spins. Lab-frame SD has proved particularly useful in structural characterization of a large variety of molecules. During SD, the rate of magnetization transfer between the two nuclei depends on the square of the dipolar coupling and the zero-quantum lineshape of the two spins. The relative sign of the diagonal and cross-peaks is determined by the spin part of the dipolar Hamiltonian. Practically, SD experiments are used in two ways: (a) SD transfer amongst only the protons (known as proton spin-diffusion or PSD) and b) SD amongst rare nuclei, coupled to a strong proton bath, known as proton driven spin-diffusion (PDSD). It is well established that the diagonal and cross-peaks have the same sign during SD based polarization transfer. 2D PSD experiments recorded on Histidine.HCl.H₂O sample at fast magic angle spinning (MAS) show that some of the cross-peaks in the 2D spectrum are negative with respect to the diagonal peaks. Cross-relaxation due to stochastic motion is generally believed to give rise to such negative peaks. Herein, we use theoretical calculations, numerical simulations and experiments to show that the origin of the negative cross-peaks in PSD spectrum is due to coherent interactions. The origin of negative peaks can be specifically ascribed to a four spin, double-flip-double flop term, in the third-order Hamiltonian. These terms become the dominant terms at fast spinning when additional - conditions are satisfied.

Combining Molecular and Spin Dynamics Simulations with Solid-State NMR: A Case Study of Amphiphilic Lysine-Leucine Repeat Peptide Aggregates

Interpreting dynamics in solid-state molecular systems requires characterization of the potentially heterogeneous environmental contexts of molecules. In particular, the analysis of solid-state nuclear magnetic resonance (ssNMR) data to elucidate molecular dynamics (MD) involves modeling the restriction to overall tumbling by neighbors, as well as the concentrations of water and buffer. In this exploration of the factors that influence motion, we utilize atomistic MD trajectories of peptide aggregates with varying hydration to mimic an amorphous solid-state environment and predict ssNMR relaxation rates. We also account for spin diffusion in multiply spin-labeled (up to 19 nuclei) residues, with several models of dipolar-coupling networks. The framework serves as a general approach to determine essential spin couplings affecting relaxation, benchmark MD force fields, and reveal the hydration dependence of dynamics in a crowded environment. We demonstrate the methodology on a previously characterized amphiphilic 14-residue lysine-leucine repeat peptide, LKα14 (Ac-LKKLLKLLKKLLKL-c), which has an α-helical secondary structure and putatively forms leucine-burying tetramers in the solid state. We measure the R₁ relaxation rates of uniformly ¹³C-labeled and site-specific ²H-labeled leucines in the hydrophobic core of LKα14 at multiple hydration levels. Studies of 9 and 18 tetramer bundles reveal the following: (a) for the incoherent component of ¹³C relaxation, the nearest-neighbor spin interactions dominate, while the ¹H-¹H interactions have minimal impact; (b) the AMBER ff14SB dihedral barriers for the leucine C_γ-C_δ bond ("methyl rotation barriers") must be lowered by a factor of 0.7 to better match the ²H data; (c) proton-driven spin diffusion explains some of the discrepancy between experimental and simulated rates for the C_β and C_α nuclei; and (d) ¹³C relaxation rates are mostly underestimated in the MD simulations at all hydrations, and the discrepancies identify likely motions missing in the 50 ns MD trajectories.

Probing Membrane Protein Insertion into Lipid Bilayers by Solid-State NMR

Determination of the environment surrounding a protein is often key to understanding its function and can also be used to infer the structural properties of the protein. By using proton-detected solid-state NMR, we show that reduced spin diffusion within the protein under conditions of fast magic-angle spinning, high magnetic field, and sample deuteration allows the efficient measurement of site-specific exposure to mobile water and lipids. We demonstrate this site specificity on two membrane proteins, the human voltage dependent anion channel, and the alkane transporter AlkL from Pseudomonas putida. Transfer from lipids is observed selectively in the membrane spanning region, and an average lipid-protein transfer rate of 6 s^-1 was determined for residues protected from exchange. Transfer within the protein, as tracked in the ¹⁵ N-¹ H 2D plane, was estimated from initial rates and found to be in a similar range of about 8 to 15 s^-1 for several resolved residues, explaining the site specificity.

Fast simulations of multidimensional NMR spectra of proteins and peptides

To simulate full multidimensional nuclear magnetic resonance spectra of peptides and proteins in a reasonable time frame, a strategy for separating the time-consuming full-density matrix calculations from the chemical shift prediction and calculation of coupling patterns is presented. The simulation setup uses SIMulation Program for SOlid-state NMR (SIMPSON) to calculate total correlation spectroscopy transfer amplitudes and average distances as a source for nuclear Overhauser effect spectroscopy transfer amplitudes. Simulated ¹ H 1D, 2D total correlation spectroscopy, and 2D nuclear Overhauser effect spectroscopy nuclear magnetic resonance spectra of peptides with sequence Pro─Ala─Gly─Tyr─Asn and Asn─Phe─Gly─Ala─Ile─Leu and of ubiquitin are presented. In all cases, the simulations lasted from a few seconds to tens of seconds on a normal laptop computer.

Electron-driven spin diffusion supports crossing the diffusion barrier in MAS DNP

Dynamic nuclear polarization (DNP) can be applied to enhance the sensitivity of solid-state NMR experiments by several orders of magnitude due to microwave-driven transfer of spin polarization from unpaired electrons to nuclei. While the underlying quantum mechanical aspects are sufficiently well understood on a microscopic level, the exact description of the large-scale spin dynamics, usually involving hundreds to thousands of nuclear spins per electron, is still lacking consensus. Generally, it is assumed that nuclear hyperpolarization can only be observed on nuclei which do not experience strong influence of the unpaired electrons and thus being significantly removed from the paramagnetic polarizing agents. At the same time, sufficiently strong hyperfine interaction is required for DNP transfer. Therefore, efficient nuclear spin diffusion from the strongly-interacting nuclei to the NMR-observable bulk is considered to be essential for efficient nuclear hyperpolarization. Based on experimental results obtained on the endohedral fullerene N@C60 as a polarizing agent sparsely diluted in C60, we discuss the effect of the spin-diffusion barrier. We introduce electron-driven spin diffusion (EDSD) as a novel mechanism for nuclear polarization transfer in the proximity of an electron spin which is particularly relevant under magic-angle spinning (MAS) DNP conditions.

Quantitative Analysis of Solid-State Homonuclear Correlation Spectra of Antiparallel β-Sheet Alanine Tetramers

Poly-l-alanine (PLA) sequences are a key element in the structure of the crystalline domains of spider dragline silks, wild silkworm silks, antifreeze proteins, and amyloids. To date, no atomic-level structures of antiparallel (AP)-PLA longer than Ala₄ have been reported using the single-crystal X-ray diffraction analysis. In this work, dipolar-assisted rotational resonance solid-state NMR spectra were observed to determine the effective internuclear distances of ¹³C uniformly labeled alanine tetramer with antiparallel (AP) β-sheet structure whose atomic coordinates are determined from the X-ray crystallographic analysis. Initial build-up rates, R _{j, k}, were obtained from the build-up curves of the cross peaks by considering the internuclear distances arising in the master equation. Subsequently, experimentally obtained effective internuclear distances, r^eff_{j, k}(obs), were compared with the calculated r^eff_{j, k}(calc) values obtained from the X-ray crystallographic data. Fairly good correlation between r^eff_{j, k}(obs) and r^eff_{j, k}(calc) was obtained in the range of 1.0-6.0 Å, with the standard deviation of 0.244 Å, without considering the zero-quantum line-shape functions. It was further noted that the internuclear distances of intermolecular contributions provide details relating to the molecular packing in solid-state samples. Thus, the present data agree well with AP-β-sheet packing but do not agree with P-β-sheet packing.

Proton-Assisted Recoupling (PAR) in Peptides and Proteins

Proton-assisted recoupling (PAR) is examined by exploring optimal experimental conditions and magnetization transfer rates in a variety of biologically relevant nuclear spin-systems, including simple amino acids, model peptides, and two proteins-nanocrystalline protein G (GB1), and importantly amyloid beta 1-42 (M0Aβ1-42) fibrils. A selective PAR protocol, SUBPAR (setting up better proton assisted recoupling), is described to observe magnetization transfer in one-dimensional spectra, which minimizes experiment time (in comparison to two-dimensional experiments) and thereby enables an efficient assessment of optimal PAR conditions for a desired magnetization transfer. In the case of the peptide spin systems, experimental and simulated PAR data sets are compared on a semiquantitative level, thereby elucidating the interactions influencing PAR magnetization transfer and their manifestations in different spin transfer networks. Using the optimum Rabi frequencies determined by SUBPAR, PAR magnetization transfer trajectories (or buildup curves) were recorded and compared to simulated results for short peptides. PAR buildup curves were also recorded for M0Aβ1-42 and examined conjointly with a recent structural model. The majority of salient cross-peak intensities observed in the M0Aβ1-42 PAR spectra are well-modeled with a simple biexponential equation, although the fitting parameters do not show any strong correlation to internuclear distances. Nevertheless, these parameters provide a wealth of invaluable semiquantitative structural constraints for the M0Aβ1-42. The results presented here offer a complete protocol for recording PAR 13C-13C correlation spectra with high-efficiency and using the resulting information in protein structural studies.

Packing arrangement of 13C selectively labeled sequence model peptides of Samia cynthia ricini silk fibroin fibers studied by solid-state NMR

Samia cynthia ricini silk fibroin fiber was proposed to take anti-parallel β-sheet structure with staggered arrangement.

Accelerating proton spin diffusion in perdeuterated proteins at 100 kHz MAS

Fast magic-angle spinning (>60 kHz) has many advantages but makes spin-diffusion-type proton-proton long-range polarization transfer inefficient and highly dependent on chemical-shift offset. Using 100%-HN-[²H,¹³C,¹⁵N]-ubiquitin as a model substance, we quantify the influence of the chemical-shift difference on the spin diffusion between proton spins and compare two experiments which lead to an improved chemical-shift compensation of the transfer: rotating-frame spin diffusion and a new experiment, reverse amplitude-modulated MIRROR. Both approaches enable broadband spin diffusion, but the application of the first variant is limited due to fast spin relaxation in the rotating frame. The reverse MIRROR experiment, in contrast, is a promising candidate for the determination of structurally relevant distance restraints. The applied tailored rf-irradiation schemes allow full control over the range of recoupled chemical shifts and efficiently drive spin diffusion. Here, the relevant relaxation time is the larger longitudinal relaxation time, which leads to a higher signal-to-noise ratio in the spectra.

(14)N overtone NMR under MAS: signal enhancement using symmetry-based sequences and novel simulation strategies

Overtone ¹⁴N NMR spectroscopy is a promising route for the direct detection of ¹⁴N signals with good spectral resolution.

Overtone ¹⁴N NMR spectroscopy is a promising route for the direct detection of ¹⁴N signals with good spectral resolution. Its application is currently limited, however, by the absence of efficient polarization techniques for overtone signal enhancement and the lack of efficient numerical simulation techniques to aid in both the development of new methods and the analysis and interpretation of experimental data. In this paper we report a novel method for the transfer of polarization from ¹H to the ¹⁴N overtone using symmetry-based R-sequences that overcome many of the limitations of adiabatic approaches that have worked successfully on static samples. Refinement of these sequences and the analysis of the resulting spectra have been facilitated through the development of an efficient simulation strategy for ¹⁴N overtone NMR spectroscopy of spinning samples, using effective Hamiltonians on top of Floquet and Fokker–Planck equations.

Combined zero-quantum and spin-diffusion mixing for efficient homonuclear correlation spectroscopy under fast MAS: broadband recoupling and detection of long-range correlations

Fast magic angle spinning (MAS) NMR spectroscopy is emerging as an essential analytical and structural biology technique. Large resolution and sensitivity enhancements observed under fast MAS conditions enable structural and dynamics analysis of challenging systems, such as large macromolecular assemblies and isotopically dilute samples, using only a fraction of material required for conventional experiments. Homonuclear dipolar-based correlation spectroscopy constitutes a centerpiece in the MAS NMR methodological toolbox, and is used essentially in every biological and organic system for deriving resonance assignments and distance restraints information necessary for structural analysis. Under fast MAS conditions (rotation frequencies above 35-40 kHz), dipolar-based techniques that yield multi-bond correlations and non-trivial distance information are ineffective and suffer from low polarization transfer efficiency. To overcome this limitation, we have developed a family of experiments, CORD-RFDR. These experiments exploit the advantages of both zero-quantum RFDR and spin-diffusion based CORD methods, and exhibit highly efficient and broadband dipolar recoupling across the entire spectrum, for both short-range and long-range correlations. We have verified the performance of the CORD-RFDR sequences experimentally on a U-(13)C,(15)N-MLF tripeptide and by numerical simulations. We demonstrate applications of 2D CORD-RFDR correlation spectroscopy in dynein light chain LC8 and HIV-1 CA tubular assemblies. In the CORD-RFDR spectra of LC8 acquired at the MAS frequency of 40 kHz, many new intra- and inter-residue correlations are detected, which were not observed with conventional dipolar recoupling sequences. At a moderate MAS frequency of 14 kHz, the CORD-RFDR experiment exhibits excellent performance as well, as demonstrated in the HIV-1 CA tubular assemblies. Taken together, the results indicate that CORD-RFDR experiment is beneficial in a broad range of conditions, including both high and moderate MAS frequencies and magnetic fields.

Spectral editing through laser-flash excitation in two-dimensional photo-CIDNP MAS NMR experiments

In solid-state photochemically induced dynamic nuclear polarization (photo-CIDNP) MAS NMR experiments, strong signal enhancement is observed from molecules forming a spin-correlated radical pair in a rigid matrix. Two-dimensional (13)C-(13)C dipolar-assisted rotational resonance (DARR) photo-CIDNP MAS NMR experiments have been applied to obtain exact chemical shift assignments from those cofactors. Under continuous illumination, the signals are enhanced via three-spin mixing (TSM) and differential decay (DD) and their intensity corresponds to the electron spin density in pz orbitals. In multiple-(13)C labelled samples, spin diffusion leads to propagation of signal enhancement to all (13)C spins. Under steady-state conditions, direct signal assignment is possible due to the uniform signal intensity. The original intensities, however, are inaccessible and the information of the local electron spin density is lost. Upon laser-flash illumination, the signal is enhanced via the classical radical pair mechanism (RPM). The obtained intensities are related to isotropic hyperfine interactions aiso and both enhanced absorptive and emissive lines can be observed due to differences in the sign of the local isotropic hyperfine interaction. Exploiting the mechanism of the polarization, selectivity can be increased by the novel time-resolved two-dimensional dipolar-assisted rotational resonance (DARR) MAS NMR experiment which simplifies the signal assignment compared to complex spectra of the same RCs obtained by continuous illumination. Here we present two-dimensional time-resolved photo-CIDNP MAS NMR experiments providing both directly: signal assignment and spectral editing by sign and strength of aiso. Hence, this experiment provides a direct key to the electronic structure of the correlated radical pair.

The nuclear Overhauser effect from a quantitative perspective

The nuclear Overhauser enhancement or effect (NOE) is the most important measure in liquid-state NMR with macromolecules. Thus, the NOE is the subject of numerous reviews and books. Here, the NOE is revisited in light of our recently introduced measurements of exact nuclear Overhauser enhancements (eNOEs), which enabled the determination of multiple-state 3D protein structures. This review encompasses all relevant facets from the theoretical considerations to the use of eNOEs in multiple-state structure calculation. Important aspects include a detailed presentation of the relaxation theory relevant for the nuclear Overhauser effect, the estimation of the correction for spin diffusion, the experimental determination of the eNOEs, the conversion of eNOE rates into distances and validation of their quality, the distance-restraint classification and the protocols for calculation of structures and ensembles.

Higher order amyloid fibril structure by MAS NMR and DNP spectroscopy

Protein magic angle spinning (MAS) NMR spectroscopy has generated structural models of several amyloid fibril systems, thus providing valuable information regarding the forces and interactions that confer the extraordinary stability of the amyloid architecture. Despite these advances, however, obtaining atomic resolution information describing the higher levels of structural organization within the fibrils remains a significant challenge. Here, we detail MAS NMR experiments and sample labeling schemes designed specifically to probe such higher order amyloid structure, and we have applied them to the fibrils formed by an eleven-residue segment of the amyloidogenic protein transthyretin (TTR(105-115)). These experiments have allowed us to define unambiguously not only the arrangement of the peptide β-strands into β-sheets but also the β-sheet interfaces within each protofilament, and in addition to identify the nature of the protofilament-to-protofilament contacts that lead to the formation of the complete fibril. Our efforts have resulted in 111 quantitative distance and torsion angle restraints (10 per residue) that describe the various levels of structure organization. The experiments benefited extensively from the use of dynamic nuclear polarization (DNP), which in some cases allowed us to shorten the data acquisition time from days to hours and to improve significantly the signal-to-noise ratios of the spectra. The β-sheet interface and protofilament interactions identified here revealed local variations in the structure that result in multiple peaks for the exposed N- and C-termini of the peptide and in inhomogeneous line-broadening for the residues buried within the interior of the fibrils.

Membrane protein structure determination in membrana

The two principal components of biological membranes, the lipid bilayer and the proteins integrated within it, have coevolved for specific functions that mediate the interactions of cells with their environment. Molecular structures can provide very significant insights about protein function. In the case of membrane proteins, the physical and chemical properties of lipids and proteins are highly interdependent; therefore structure determination should include the membrane environment. Considering the membrane alongside the protein eliminates the possibility that crystal contacts or detergent molecules could distort protein structure, dynamics, and function and enables ligand binding studies to be performed in a natural setting. Solid-state NMR spectroscopy is compatible with three-dimensional structure determination of membrane proteins in phospholipid bilayer membranes under physiological conditions and has played an important role in elucidating the physical and chemical properties of biological membranes, providing key information about the structure and dynamics of the phospholipid components. Recently, developments in the recombinant expression of membrane proteins, sample preparation, pulse sequences for high-resolution spectroscopy, radio frequency probes, high-field magnets, and computational methods have enabled a number of membrane protein structures to be determined in lipid bilayer membranes. In this Account, we illustrate solid-state NMR methods with examples from two bacterial outer membrane proteins (OmpX and Ail) that form integral membrane β-barrels. The ability to measure orientation-dependent frequencies in the solid-state NMR spectra of membrane-embedded proteins provides the foundation for a powerful approach to structure determination based primarily on orientation restraints. Orientation restraints are particularly useful for NMR structural studies of membrane proteins because they provide information about both three-dimensional structure and the orientation of the protein within the membrane. When combined with dihedral angle restraints derived from analysis of isotropic chemical shifts, molecular fragment replacement, and de novo structure prediction, orientation restraints can yield high-quality three-dimensional structures with few or no distance restraints. Using complementary solid-state NMR methods based on oriented sample (OS) and magic angle spinning (MAS) approaches, one can resolve and assign multiple peaks through the use of (15)N/(13)C labeled samples and measure precise restraints to determine structures.

Gas vesicles across kingdoms: a comparative solid-state nuclear magnetic resonance study

The buoyancy organelles of aquatic microorganisms have to meet stringent specifications: allowing gases to equilibrate freely across the proteinaceous shell, preventing the condensation of water vapor inside the hollow cavity and resisting collapse under hydrostatic pressures that vary with column depth. These properties are provided by the 7- to 8-kDa gas vesicle protein A (GvpA), repeats of which form all but small, specialized portions of the shell. Magic angle spinning nuclear magnetic resonance is uniquely capable of providing high-resolution information on the fold and assembly of GvpA. Here we compare results for the gas vesicles of the haloarchaea Halobacterium salinarum with those obtained previously for the cyanobacterium Anabaena flos-aquae. The data suggest that the two organisms follow similar strategies for avoiding water condensation. On the other hand, in its relatively shallow habitat, H. salinarum is able to avoid collapse with a less costly GvpA fold than is adopted by A. flos-aquae.