The Phase Problem & the Direct Method

Shake-and-Bake addresses a problem that has held up progress in molecular biology for decades. X-ray crystallography, the primary tool (and until recent years the only tool) for determining the structure of molecules, works by passing an x-ray beam through a crystallized molecule. The pattern of the diffracted xrays, recorded as an array of spots on a photographic plate, depends on the arrangement of atoms in the molecule.

The problem is that the diffraction pattern registers only the intensity of the waves. To work back to the molecular structure, it's necessary to also know the relative timing when each wave hits, called "phase data" -- the position of the wave crests and troughs relative to each other. Without the phase data, it often takes years of painstaking trial-and-error work relying on informed intuition to hit on the right structure.

Hauptman and Jerome Karle won a Nobel prize in 1985 for their work in the late 1940s and early 1950s on "the direct method" -- a mathematical approach that makes it possible to glean phase data from the diffraction intensities. The key insight behind the direct method derives from the "atomicity" of molecules -- i.e., atoms are small, discrete points relative to the spaces between them -- which limits the possible relationships between phase and intensity to a range of probabilities.

The direct method has made it relatively routine to determine structure for molecules of 100 or fewer atoms. As molecular size increases, however, the probability relationships become weaker, and the direct method breaks down for molecules larger than about 150 non-hydrogen atoms. Another method, based on inserting heavy metal atoms into the crystal structure, has worked reasonably well for very large molecules -- more than about 600 atoms. But for molecules in-between, ranging from about 200 to 500 atoms, structure determination remains a hit-and-miss proposition that takes months or years if it succeeds at all.

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