The electron density function can be expressed as

r (x,y,z)= 2 / Vc å å å ½ F(hkl) ½ cos [ 2p (hx + kx + lz) - f (hkl)]

The process of x-ray diffraction corresponds to a Fourier analysis which breaks down the object r (x,y,z) into its constituent terms. The phase information, f (hkl), is lost. The Fourier synthesis given above corresponds to a summation of the terms to reconstruct the object. This cannot be achieved without the phase information. Practicioners of structure determination from x-ray crystallographic data employ a number of techniques to attempt to reconstuct the phase information. For small molecules direct methods exist which can often be utilized to obtain the desired electron density map. For large molecules, such as proteins, the experimental data set may contain around 50,000 reflections. For such structures laboratory intensive techniques requiring the crystallographer to soak-in a heavy atom into the original crystal are utilized. The synthesis of heavy atom derivatives and the collection and interpretation of their data is a labor intensive process which can consume from one to two years of effort to solve the structure. The heavy atom techniques employed typically produce a final electron density map for the crystal structure under investigate with the phase information accurate to within 30° . The challenge is then to devise a way to directly compute the missing phase information accurate to with at least 30° . Approaches for attacking this problem utilizing massively parallel computers is discussed.

Publications related to this topic

The Phase Problem in Protein Crystallography: Potential Approaches Utilizing Massively Parallel Computers, E. J. Meehan and J. Michael Meehan, in Teraflop Computing and New Grand Challenge Applications, pg 227-233, ed. Rajiv Kalia and Priya Vashishta (eds.), Nova Science Publishers, Inc. 1995, ISBN 1-56072-247-9.