Solid-State NMR of Peptide Fibrils and Assemblies

A fibril does not tumble. The narrow lines of a solution spectrum exist because isotropic reorientation averages chemical shift anisotropy and dipolar couplings toward zero on the NMR timescale; in an insoluble peptide assembly that averaging is absent and those interactions survive at full strength, spreading every resonance over tens of kilohertz. The other structural route is closed too: intact amyloid fibrils are insoluble and do not form diffraction-quality three-dimensional crystals, and that combination is why atomic-resolution structures of them were unavailable until magic-angle spinning (MAS) NMR was brought to bear ^[1].

What spinning restores, and what it takes away

Rotating the sample about an axis inclined at 54.74° to the static field scales the anisotropic terms by (3cos²θ − 1)/2, which is zero at that angle. Spin fast relative to the anisotropy and what survives is the isotropic chemical shift — the same quantity a solution spectrum reports. That is geometry rather than a finding, and it is stated here without citation.

The resolution recovered is not marginal. Fibrils of Aβ(16–22), the seven-residue peptide N-acetyl-Lys-Leu-Val-Phe-Phe-Ala-Glu-NH₂, give ¹³C linewidths below 2 ppm in one- and two-dimensional spectra of selectively and uniformly labelled samples, for side-chain as well as backbone carbons, which demonstrates that the peptide occupies a well-ordered conformation in the fibril rather than a distribution of them ^[2]. Linewidth is therefore the first diagnostic you run. A broad spectrum from a fibril sample usually reports heterogeneity in the preparation, not a fault in the probe.

The cost is that MAS averages away the dipolar couplings that carry distance. Cross-polarisation from protons to ¹³C or ¹⁵N, and proton decoupling during acquisition, are standard on essentially every experiment and are practice rather than findings; they buy sensitivity and repetition rate, not structure. The structural content has to be deliberately put back.

Recoupling supplies the restraints

Recoupling sequences apply rotor-synchronised pulses that interfere with the spatial averaging so a chosen interaction survives while isotropic-shift resolution is kept. Finite-pulse radiofrequency-driven recoupling (fpRFDR) restores homonuclear ¹³C–¹³C couplings under fast MAS using a phase- and symmetry-cycled π-pulse train with one rotor-synchronous π pulse per rotation period, and its efficiency is not strongly dependent on chemical shift differences or resonance offsets, unlike earlier fast-MAS methods ^[3]. Its constant-time variant, CT-fpRFDR, varies the effective dipolar evolution by refocusing with a rotor-synchronised solid echo while holding the total recoupling period fixed, so relaxation does not contaminate the decay. On the model tripeptide [1-¹³C]Ala–[1-¹³C]Gly–Gly at 30.3 kHz spinning in a 17.6 T field, CT-fpRFDR returned a ¹³C–¹³C distance of 3.27 Å against 3.20 Å from X-ray diffraction ^[3]. That is the accuracy demonstrated on a crystalline tripeptide standard; it is not a figure you may carry over to a fibril.

Constant-time design is the recurring theme, because it removes relaxation and pulse imperfection from the observable. PITHIRDS-CT is built from symmetry properties of the recoupled dipole–dipole Hamiltonian under cyclic displacements in time relative to the MAS rotation period, and yields data relatively insensitive to radiofrequency pulse imperfections and to nuclear spin relaxation. ¹³C data on singly ¹³C-labelled amino acid powders and on amyloid fibrils establish its use for intermolecular distances, while ¹⁵N- and ¹³C-detected intramolecular ¹⁵N–¹⁵N measurements on peptides with α-helical and β-sheet structures establish its use for backbone ψ torsion angles in residues that are uniformly ¹⁵N- and ¹³C-labelled ^[4].

Heteronuclear distances come from rotational-echo double resonance (REDOR). In fibrils of TTR(105–115), an 11-residue transthyretin fragment, four backbone ¹³C–¹⁵N distances were determined by REDOR on two selectively ¹³C,¹⁵N-labelled samples, alongside complete sequence-specific backbone and side-chain assignments for residues 105–114 ^[5]. The later full structure of that peptide in the fibril rested on 76 self-consistent experimental measurements: 41 restraints on 19 backbone dihedral angles and 35 ¹³C–¹⁵N distances between 3 and 6 Å, obtained from 2D and 3D spectra on three fibril samples each uniformly ¹³C,¹⁵N-labelled in a consecutive stretch of four residues ^[1]. That is the honest scale of a peptide fibril structure: tens of restraints, several separately prepared samples.

Labelling decides what you can assign

A uniformly ¹³C,¹⁵N-labelled peptide gives every carbon at once, which is both the point and the problem: crowded spectra, and dipolar truncation in which strong one-bond couplings suppress the weak long-range transfers you actually want. Four labelling schemes buy a way out, and each answers a different question.

Segmental labelling, straightforward when the peptide is made by solid-phase synthesis from labelled amino acids, puts uniform label on a short consecutive run of residues and leaves the rest at natural abundance. Three such samples, each labelled across four consecutive residues, carried the TTR(105–115) structure ^[1]; in Aβ(16–22) fibrils, labelling Leu17 through Ala21 as a block reduced the 2D ¹³C/¹³C correlation spectrum to amino-acid-specific patterns from which most main-chain and side-chain carbons could be assigned ^[3].

Sparse, alternating labelling attacks truncation directly. Growing an expression host on [1,3-¹³C]glycerol or [2-¹³C]glycerol as carbon source produces biosynthetically site-directed labelling in which neighbouring carbons are largely not labelled together; proton-driven spin diffusion spectra of such samples of the micro-crystalline α-spectrin SH3 domain gave long-range distance correlations up to approximately 7 Å, and 286 inter-residue ¹³C–¹³C plus six ¹⁵N–¹⁵N restraints ^[6]. Note the two constraints on that result: it needs biosynthetic expression rather than chemical synthesis, and it was obtained on a folded protein domain in a micro-crystalline preparation, not on a fibril.

Isotopic dilution answers the question a distance restraint cannot answer by itself — whether a contact lies within one molecule or between neighbours. Mixing labelled peptide with unlabelled peptide before assembly thins intermolecular contacts while leaving intramolecular ones intact. In Aβ(1–40) fibrils this is what permitted side-chain contacts to be sorted into intramolecular and intermolecular classes, and quaternary contacts to be classified as internal, within a single molecular layer, or external, between layers ^[7].

Mixed labelling inverts the trick. Assembling fibrils from a mixture of [¹⁵N,¹²C]- and [¹⁴N,¹³C]-labelled molecules makes every observable ¹⁵N–¹³C cross-peak intermolecular by construction. Applied to fibrils of the 86-residue SH3 domain of PI3 kinase — a protein domain, not a peptide — this quantified interstrand distances directly, and recording the same spectra with dynamic nuclear polarisation at 100 K raised the number of detectable intermolecular ¹⁵N–¹³C constraints from 23 to 52, part of 111 intermolecular constraints in total; the authors attribute the gain both to signal enhancement and to the quenching at low temperature of dynamic processes that otherwise cost spectral intensity ^[8].

Chemical shifts as the cheapest restraints you have

Before any recoupling experiment, the assigned isotropic shifts already carry backbone conformation. Secondary chemical shifts — differences from liquid-state random-coil values — measured on immobilised polypeptides under MAS correlate with the backbone torsion angle ψ previously determined crystallographically, and the authors present that correlation explicitly as a qualitative basis for structure refinement rather than a substitute for measurement ^[9]. In fibrils, the same information is used quantitatively but with the same caution: analysis of the ¹⁵N, ¹³CO, ¹³C_α and ¹³C_β shifts of TTR(105–115) allowed quantitative predictions of the backbone torsion angles φ and ψ ^[5], and examination of the ¹³C shifts of Aβ(16–22) revealed β-strand conformation across the entire molecule ^[3].

Two consequences. Shift-derived torsion angles are empirical predictions calibrated on reference structures, so treat them as restraints to be tested against dipolar measurements rather than as measurements themselves. And because shifts respond to conformation site by site, they are the earliest detector of a mixed preparation: you can count species from a correlation spectrum long before you can characterise any of them.

Parallel in-register versus antiparallel

The supramolecular question — how neighbouring molecules stack along the fibril axis — is decided by intermolecular distances between chemically identical sites. In a parallel in-register β-sheet, residue i of one molecule sits directly beside residue i of its neighbour, one inter-strand hydrogen-bond spacing away; in an antiparallel or out-of-register sheet it does not. A peptide carrying a single ¹³C label therefore reports the arrangement without any assignment problem at all: strong homonuclear dipolar dephasing means those labelled sites are close on adjacent molecules, which is precisely the measurement constant-time homonuclear recoupling was designed to make robust ^[4].

That experiment settled several systems. Peptides carrying a single carbonyl ¹³C label at Gln15, Lys16, Leu17 or Val18 of Aβ(10–35) were assembled and their interpeptide distances measured by dipolar recoupling to a resolution of 0.2 Å, establishing that this core segment forms a parallel β-sheet in which identical residues on adjacent chains are aligned directly, in register ^[10]. For the full-length 40-residue peptide the result reversed a prior assumption rather than confirming it: an antiparallel organisation was often assumed and was invoked in the structural models then current, but multiple-quantum ¹³C NMR data indicated an in-register, parallel organisation ^[11].

Parallel in-register is not, however, a property of amyloid as such. Multiple-quantum ¹³C NMR together with ¹³C/¹⁵N REDOR on Aβ(16–22) fibrils indicate an antiparallel organisation of β-sheets in that seven-residue peptide, which is what led the authors to suggest that supramolecular organisation can depend on the peptide sequence ^[2]. Sequence is not the only lever. Fibrils formed by the Asp23-to-Asn variant of the 40-residue peptide can contain either parallel or antiparallel sheets; with a protocol that yields structurally pure antiparallel samples, those fibrils proved thermodynamically metastable with respect to conversion to parallel structures and propagated less efficiently than parallel fibrils in seeded growth, so they must nucleate more efficiently in order to be observable at all ^[12].

Read that before generalising from your own sample. A registry assignment is a statement about the fibrils in that rotor. It is not a statement about the peptide.

The preparation is part of the structure

Different fibril morphologies of the 40-residue peptide seen by electron microscopy have different underlying molecular structures; the predominant structure can be controlled by subtle variations in fibril growth conditions; and both morphology and molecular structure are self-propagating when fibrils grow from preformed seeds ^[13]. Seeding from a characterised stock is therefore the only reliable way to reproduce a structure between batches, and unseeded growth is a lottery weighted by conditions you may not be recording.

The differences between polymorphs are not cosmetic. A full model of a periodically twisted Aβ(1–40) morphology, twist period 120 ± 20 nm, has threefold symmetry about the growth axis, implied by mass-per-length data and by the observation of a single set of ¹³C signals; compared with a previously reported striated-ribbon morphology, the two differ in overall symmetry — twofold versus threefold — in the conformation of non-β-strand segments, and in certain quaternary contacts, while both contain in-register parallel β-sheets built from nearly the same β-strand segments ^[14]. Polymorphism lives in the turns and the interfaces, which is usually exactly where the structural conclusion is being drawn.

Coexistence inside one tube is worse than variation between tubes. GNNQQNY, a seven-residue segment of the yeast protein Sup35p, shows concentration-dependent polymorphism: monoclinic and orthorhombic crystals at low concentration and amyloid fibrils at higher concentration, with fibril samples that reproducibly contain three coexisting structural forms, seen as three distinct, self-consistent sets of correlated NMR signals whose chemical shifts differ from one another and from the crystals ^[15]. Even agitation counts: the quaternary-contact models for Aβ(1–40) apply specifically to fibrils grown with gentle agitation, and fibrils grown without agitation gave evidence of different internal quaternary contacts and were morphologically distinct ^[7].

The practical consequence is a methods section, not a caveat. Record and hold constant the peptide concentration, buffer, ionic strength, pH, temperature, agitation regime and seed source, and report them. A structure without that description is not reproducible, because the structure belongs to the preparation.

Quantities and time

Sensitivity sets the bill. Multidimensional MAS structure determination has typically required several isotopically labelled samples of 10–20 mg each; pushing magic-angle rotation to frequencies around 100 kHz narrows proton lines enough for efficient and sensitive proton detection, and on that basis a well-defined de novo structure of the model protein ubiquitin was obtained from two samples of roughly 500 µg each ^[16]. For a synthetic peptide, combine those figures with the restraint census above — several differently labelled samples per structure — and it is usually the synthesis, not the spectrometer, that sets the schedule.

Where sensitivity is still the limit, dynamic nuclear polarisation at low temperature is the standard lever, and its benefit is not purely a time saving: in the SH3-domain fibril above, the count of intermolecular ¹⁵N–¹³C constraints that could be detected at all more than doubled at 100 K ^[8]. Whether that transfers to a given peptide preparation depends on how ordered it remains at those temperatures, which the same experiments have to establish.

Where this sits beside solution NMR and cryo-EM

Against the solution NMR guide: same nuclei and the same shifts, incompatible samples. Solution restraints come from nuclear Overhauser effects in a molecule that reorients; MAS restraints come from dipolar couplings deliberately restored in one that does not. A peptide that is monomeric and soluble is a solution problem, and once it assembles its solution spectrum reports the residual monomer rather than the assembly — a limitation of the observable, stated here as reasoning rather than as a cited result.

Against the cryo-EM guide: the two methods now answer the same question, and they do not always answer it identically, partly because they are not always looking at the same polymorph. A monomorphic Aβ42 fibril preparation gave a MAS NMR structure derived from over 500 ¹³C–¹³C and ¹³C–¹⁵N distance and backbone-angle constraints, with a backbone RMSD over residues Q15–A42 of 0.71 ± 0.12 Å and an all-heavy-atom RMSD of 1.07 ± 0.08 Å, and with intermolecular ¹³C–¹⁵N constraints demonstrating that the fibrils are parallel in register ^[17]. A separately determined Aβ(1–42) polymorph placed residues 15–42 in a double-horseshoe cross-β entity with two molecules per fibril layer, while residues 1–14 were partially ordered and in a β-strand conformation but showed no unambiguous distance restraints to the remainder of the core ^[18]. A cryo-EM structure of an Aβ(1–42) fibril built from two intertwined protofilaments, at 4.0 Å resolution, resolved the backbone of all 42 residues and nearly all side chains, with the entire N-terminus forming part of the cross-β structure ^[19].

The defensible reading is not that one method missed the N-terminus. The preparations differ, and so may the polymorphs. What the comparison does license is narrower and more useful: MAS NMR delivers site-resolved backbone conformation and specific interatomic distances, including intermolecular ones that no image can supply directly, and it does so on whatever the rotor contains; cryo-EM delivers a density map from the particles that were selected and averaged. A segment with no restraints in an NMR structure and a segment with no density in a map are both statements about that specimen.

So what does a MAS NMR fibril structure entitle you to claim? For this preparation: these residues adopt these backbone torsion angles, these atoms lie within these distances, neighbouring molecules stack in this registry. What it does not entitle you to claim: that a differently grown sample of the same peptide shares the structure, that unrestrained segments are disordered rather than merely unmeasured, or that the spread of a deposited coordinate bundle measures motion rather than the precision of one restraint set under one protocol.