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| MATHEMATICAL ANALYSIS | home > about hwi > what does hwi do? > structural biology > mathematical analysis | ||||
When an X-ray
beam strikes a crystal, the incident radiation is scattered in many directions
to form a distinctive diffraction pattern that is characteristic of the
atomic arrangement within the crystal. The intensities of the scattered
X-rays can be measured when they strike a photographic film or electronic
recorder. However, X-rays, like light or sound, are wavelike in nature,
and their intensities vary with time. In order to work backwards from
the diffraction pattern to the molecular structure, it is necessary to
know not only the intensity, but also the relative timing or phase when
each wave hits the recording device. Inability to measure the phase angles
experimentally gives rise to the so-called phase problem of X-ray crystallography.Dr. Herbert Hauptman and his collaborator, Dr. Jerome Karle of the Naval Research Laboratory, were awarded the 1985 Nobel Prize in Chemistry for developing techniques that permit crystallographers to solve the phase problem and to reconstruct mathematically the three-dimensional structures of the molecules responsible for a given diffraction pattern provided that these molecules contain fewer than 100 atoms. In recent years, continued research at HWI by Dr. Hauptman and his colleagues has resulted in a new robust procedure, known as Shake-and-Bake, that has been successfully applied to small proteins containing as many as 2000 atoms. Even larger proteins can be tackled by Shake-and-Bake if crystallography is coupled with molecular biology by first introducing selenium atoms into the protein molecule in place of the naturally occurring sulfur atoms in the amino acid methionine. Selenium scatters X-rays in special ways that allow the selenium substructure to be visualized first and then used as a bootstrap to find the complete molecule. Protein molecules containing several thousand atoms, and as many as 160 selenium sites, have been handled in this fashion. The Shake-and-Bake algorithm has been implemented in a computer program, known as SnB, that is distributed via the Internet and has been downloaded by hundreds of crystallographers throughout the world. Many of these scientists have used SnB to investigate protein structures such as the enzyme pictured at the left. |
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| Previous Step: X-ray Diffraction Next Step: Structure Interpretation | |||||
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