Macromolecular Phasing

© 2006 American Institute of Physics, S-0031-9228-0603-030-4 M molecular biophysics is built on the twin pillars of genetic engineering and macromolecular structure determination. And x-ray crystallography is foremost among the methods used to determine the atomic-scale structure of macromolecules—very large molecules with sizes typically ranging from 50 to 1000 Å. X-ray crystallography played a pivotal role in the science of the 20th century and has led directly to no fewer than eight Nobel prizes. In 1912 Max von Laue explained how the periodic lattice of a crystal scatters an incident beam of x rays in specific directions in space, and, with Walter Friedrich and Paul Knipping, he discovered the first x-ray diffraction pattern. Practical x-ray diffraction crystallography dates back to the father-and-son team of William and Lawrence Bragg, who determined the crystal structure of sodium chloride (NaCl) in 1914, little more than a year after von Laue and his colleagues reported their discovery. By analyzing the directions and the intensities of the Bragg reflections—that is, the scattered beams—one can, in principle, figure out the spatial arrangement of the atoms inside the crystal. In practice, the inversion from measured diffraction intensities to atomic structure is not as straightforward as one might think: The intensity relates to the amplitude of a scattered wave, but not to its phase relative to the other scattered waves. Without those phases, one simply does not know how to add all scattered waves together to retrieve the original structure, especially when that structure is a macromolecule such as a protein or virus. That difficulty is called the phase problem of x-ray crystallography, and its solution is often referred to as phasing a structure (see reference 1 and the article by Keith Nugent, David Paganin, and Tim Gureyev, PHYSICS TODAY, August 2001, page 27). The crystal structure may be expressed in terms of the electron density r(r) as a function of position r in the unit cell of the crystal; from that density one can infer the positions of the atoms. The electron density is related to the Bragg reflection amplitudes, or structure factors, FH, which are Fourier transforms of the density function: