A simple two pulse phase modulation (TPPM) scheme greatly reduces the residual linewidths arising from insufficient proton decoupling power in double resonance magic angle spinning (MAS) experiments. Optimization of pulse lengths and phases in the sequence produces substantial improvements in both the resolution and sensitivity of dilute spins (e.g., 13C) over a broad range of spinning speeds at high magnetic field. The theoretical complications introduced by large homo‐ and heteronuclear interactions among the spins, as well as the amplitude modulation imposed by MAS, are explored analytically and numerically. To our knowledge, this method is the first phase‐switched sequence to exhibit improvement over continuous‐wave (cw) decoupling in a strongly coupled homogeneous spin system undergoing sample spinning.

Heteronuclear decoupling in rotating solids

The NMR free induction decay from a spinning sample having inhomogeneous anisotropic interactions (chemical shifts, first order quadrupole couplings) takes the form of a train of rotational spin echoes. The Fourier transform of the echo envelope is a sharp spectrum from which the effects of anisotropy have been removed. The Fourier transform of the echo shape contains information concerning the anisotropies: This information can be extracted by a moment analysis. The effects of localized homonuclear spin–spin interactions are to convert the ’’isotropic’’ spectrum into a characteristic powder pattern. Second order quadrupole coupling produces a similar effect. It is shown in this case that the usual second‐order level shifts cannot be used to calculated this pattern, which must be described by a proper average Hamiltonian theory. Finally it is shown that rotational spin echoes provide a convenient means of studying very slow random molecular rotations (τc≲1 sec).

NMR in rotating solids

THE nuclear magnetic resonance spectrum of a solid rotated at high speed consists of a narrowed central line and a set of side-spectra spaced at integral multiples of the rotation rate of either side1,2. The interaction energy between each pair on nuclear magnets in the solid contains the angular factor (3 cos2θ – 1), where θ is the angle between the internuclear vector and the applied field. When the solid rotates about an axis making an angle α with the applied field, the angular factor may be expressed3 as the sum of its mean value ½ (3 cos2 α – 1) (3 cos2 γ – 1), where γ is the angle between the internuclear vector and the axis of rotation, and two time-dependent terms, (3/2) sin 2α sin 2γ cos ωr
t, and (3/2) sin2 α sin2 γ cos 2 ωr
t, where ωr is the angular frequency of rotation. The two time-dependent terms lead to the formation of the side-spectra. It should be noted that when α is 90°, as in our earlier experiments1,2, the first of these terms is absent, so that side-spectra occur in this case at even multiples of ωr only ; for general α, the side-spectra occur at odd and even multiples of ωr. The form of the mean value of the angular factor for each nuclear pair leads to the conclusion that the central spectrum should have the shape found for the static crystal when the applied field is directed along the axis of rotation, but reduced in width by the factor ½ (3 cos2 α – 1), and having a second moment4 reduced by a factor ¼ (3 cos2 α – 1)2. Thus, in particular, when α has the value cos−1 (1/√3) = 54° 44′, the dipolar broadening of the central line should be removed5. With a speed of rotation large compared with the static line-width, the side-spectra will be displaced far from the centre and will be weak, leaving only a sharp central line broadened by residual non-dipolar causes.

Removal of Dipolar Broadening of Nuclear Magnetic Resonance Spectra of Solids by Specimen Rotation

We present a new method of performing chemical shift correlation spectroscopy in solids with magic angle spinning (MAS). Its key feature is a longitudinal mixing period of π pulses that recouples the dipolar interaction. We discuss experimental results for triply‐13C‐labeled alanine and a theory combining MAS and π pulses.

Chemical shift correlation spectroscopy in rotating solids: Radio frequency‐driven dipolar recoupling and longitudinal exchange

The 140-residue protein α-synuclein (AS) is able to form amyloid fibrils and as such is the main component of protein inclusions involved in Parkinson's disease. We have investigated the structure and dynamics of full-length AS fibrils by high-resolution solid-state NMR spectroscopy. Homonuclear and heteronuclear 2D and 3D spectra of fibrils grown from uniformly 13C/15N-labeled AS and AS reverse-labeled for two of the most abundant amino acids, K and V, were analyzed. 13C and 15N signals exhibited linewidths of <0.7 ppm. Sequential assignments were obtained for 48 residues in the hydrophobic core region. We identified two different types of fibrils displaying chemical-shift differences of up to 13 ppm in the 15N dimension and up to 5 ppm for backbone and side-chain 13C chemical shifts. EM studies suggested that molecular structure is correlated with fibril morphology. Investigation of the secondary structure revealed that most amino acids of the core region belong to β-strands with similar torsion angles in both conformations. Selection of regions with different mobility indicated the existence of monomers in the sample and allowed the identification of mobile segments of the protein within the fibril in the presence of monomeric protein. At least 35 C-terminal residues were mobile and lacked a defined secondary structure, whereas the N terminus was rigid starting from residue 22. Our findings agree well with the overall picture obtained with other methods and provide insight into the amyloid fibril structure and dynamics with residue-specific resolution. 

EM
protein structure
amyloid
Parkinson's disease
protein aggregation

https://www.pnas.org/content/pnas/102/44/15871.full.pdf

Molecular-level secondary structure, polymorphism, and dynamics of full-length α-synuclein fibrils studied by solid-state NMR

HINDERED molecular rotation in solids reduces the width of their observed nuclear magnetic resonance spectra, with a consequent decrease in the measured second moments1. By contrast, on general theoretical grounds it has been shown2 that the second moments of dipolar-broadened spectra should remain invariant and should not be reduced by such motion. In a recent explanation3 of this apparent discrepancy the nuclear magnetic interaction was divided into two parts, namely, a steady mean interaction and a fluctuating part. The steady mean interaction is less than the interaction in a static crystal devoid of hindered rotation and generates an observed spectrum narrower than that of the static crystal. The fluctuating part of the interaction generates side-spectra set at integral multiples of the frequency of molecular rotation on either side of the central narrowed spectrum. Since the molecules do not rotate uniformly, but are re-oriented with an irregular motion, these side-spectra are dispersed over a band of frequencies with an intensity too weak to be observed. It was shown, however3, that when these weak side-spectra are included the second moment does indeed remain invariant even though the second moment of the central portion, which is all that is observed experimentally, becomes smaller.

/pdf/nuclear-magnetic-resonance-spectra-from-a-crystal-rotated-at-kjdsnlr7qp.pdf

Nuclear Magnetic Resonance Spectra from a Crystal rotated at High Speed

Nuclear cross-relaxation induced by specimen rotation

THE static dipolar interaction between the nuclei in a solid causes its nuclear magnetic resonance spectrum to be much broader than that of a liquid. In the liquid state the isotropic re-orientation and diffusion of the molecules average their nuclear dipolar interaction almost to zero, often revealing a fine structure originating from the different chemical shifts of the nuclei, and from their indirect spin–spin interactions. In solids this fine structure is obscured by the stronger dipolar interactions. As we have shown previously1–3, the dipolar broadening may nevertheless be removed in solids also, the necessary averaging being achieved by high-speed rotation about an axis inclined at an angle 54° 44′ to the direction of the applied field. When the rotation-rate is comparable with the static line-width, the narrowed central line is resolved from the satellite lines which appear on either side of it at integral multiples of the rotation frequency. Thus, for example, rotation of solid sodium chloride at a rate of 800 c./s. gives a resolved sodium-23 spectrum consisting of a central line and three pairs of satellites2. At a rotation-rate of 1,600 c./s. the central line and only one pair of weak well-resolved satellites are observed, while at 2,500 c./s. only the narrow central line is visible.

E. R. Andrew

Papers

Nuclear Magnetic Resonance Spectra from a Crystal rotated at High Speed

Removal of Dipolar Broadening of Nuclear Magnetic Resonance Spectra of Solids by Specimen Rotation

Nuclear cross-relaxation induced by specimen rotation

Fine Structure of the Nuclear Magnetic Resonance Spectra of Solids: Chemical Shift Structure of the Spectrum of Phosphorus Pentachloride