Protein folding, the spontaneous transformation of a linear chain of amino acids into a functional three-dimensional shape, is critical to life as we know it. Protein misfolding, by contrast, can lead to disease. Many of our most feared diseases, including Alzheimer’s and Parkinson’s, are associated with a particular misfolding phenomenon, in which many copies of a misfolded protein assemble into long, tough, unbranched strands called amyloid fibrils. Curiously, the amino-acid sequences of amyloid-forming proteins don’t seem to have much in common, and even proteins not associated with any disease have been coaxed into forming amyloid fibrils in the lab.

The fibrils’ molecular structure has long been a mystery. They don’t dissolve or form regular crystals, so they can’t be analyzed by solution-based nuclear magnetic resonance (NMR) or x-ray crystallography. But some features of the structure are known. As early as 1968, it was observed that a key amyloid structural motif...

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