Xrays, thanks to their short wave-lengths, can probe the shapes of proteins and biomolecules. But a single protein molecule can’t withstand a blast of high-energy photons for long enough to yield atom-scale structural information. To circumvent this limitation, structural biologists array countless copies of a protein in a crystal. Sharing the radiation dose, each molecule survives to contribute to the protein’s diffraction pattern.

Unfortunately, many proteins are expensive to produce in the large, pure quantities needed to make crystals. And many proteins defy crystallization altogether. Electron diffraction can coax structural information from small disordered samples, but so far not with atomic resolution and not from individual molecules. Other structural methods—neutron diffraction and nuclear magnetic resonance—demand samples that are large, crystalline, or both.

In 1990, the University of Washington’s John Sidles set himself the problem of locating the atoms in a single protein molecule. He sought a low-energy excitation whose origin...

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