1. Introduction 2

2. Sources of structural information in solid-state NMR data 5

2.1 General remarks 5

2.2 Chemical shifts, linewidths, and magic-angle spinning 6

2.3 Dipole–dipole couplings and dipolar recoupling 8

2.4 Tensor correlation techniques 12

2.5 Solid-state NMR of aligned samples 14

2.6 Indirect sources of structural information 15

2.7 Sample preparation for solid-state NMR 15

3. Levels of structure in amyloid fibrils 18

4. Molecular structure of β-amyloid fibrils 25

4.1 Self-propagating, molecular-level polymorphism in Aβ1–40 fibrils 25

4.2 Structural model for Aβ1-40 fibrils 28

4.3 Staggering of β-strands in Aβ1-40 fibrils 32

4.4 Structure of Aβ1-42 fibrils 34

4.5 Structure of fibrils formed by short β-amyloid fragments 34

4.6 Structures of non-fibrillar aggregates 35

5. Molecular structure of other amyloid fibrils 36

5.1 Ure2p10–39 and full-length Ure2p fibrils 36

5.2 TTR105–115 fibrils 38

5.3 HET-s fibrils 38

5.4 Amylin fibrils 39

5.5 PrP fibrils 39

5.6 ccβ fibrils 40

5.7 α-synuclein fibrils 40

5.8 Calcitonin fibrils 41

6. Data relevant to various proposals regarding amyloid structure 41

6.1 β-helical models for amyloid fibrils 41

6.2 Amyloid fibrils as water-filled nanotubes 42

6.3 Domain swapping in amyloid fibrils 42

6.4 The parallel superpleated β-structure model 43

6.5 α-sheet structures in amyloid fibrils 43

7. Conclusions 44

8. Acknowledgments 46

9. References 46

Solid-state nuclear magnetic resonance (NMR) measurements have made major contributions to our understanding of the molecular structures of amyloid fibrils, including fibrils formed by the β-amyloid peptide associated with Alzheimer's disease, by proteins associated with fungal prions, and by a variety of other polypeptides. Because solid-state NMR techniques can be used to determine interatomic distances (both intramolecular and intermolecular), place constraints on backbone and side-chain torsion angles, and identify tertiary and quaternary contacts, full molecular models for amyloid fibrils can be developed from solid-state NMR data, especially when supplemented by lower-resolution structural constraints from electron microscopy and other sources. In addition, solid-state NMR data can be used as experimental tests of various proposals and hypotheses regarding the mechanisms of amyloid formation, the nature of intermediate structures, and the common structural features within amyloid fibrils. This review introduces the basic experimental and conceptual principles behind solid-state NMR methods that are applicable to amyloid fibrils, reviews the information about amyloid structures that has been obtained to date with these methods, and discusses how solid-state NMR data provide insights into the molecular interactions that stabilize amyloid structures, the generic propensity of polypeptide chains to form amyloid fibrils, and a number of related issues that are of current interest in the amyloid field.