The SHELX approach to the experimental phasing of macromolecules

Experimental phasing of macromolecules Except in relatively rare cases where atomic resolution data permit the phase problem to be solved by ab initio direct methods, experimental phasing usually implies the presence of ’ ‘heavy ’ atoms. In order to locate the heavy atoms, we need their structure factors FA. The phases φA calculated for the heavy atom substructure enable us to estimate starting phases φT for the full macromolecular structure by: φT = φA + α After refining these phases we can use them and the native structure factors FT to calculate an electron density map of the macromolecule. As we will see, α, FA and FT can all be estimated from the experimental data. Data files used for shelxc/d/e shelxc reads the experimental data and writes three files in addition to some useful statistics that are output to the console (and can be displayed graphically by Thomas Schneider’s hkl2map). These files are: name.hkl – reflection indices, merged native intensity for density modification with shelxe and possibly later refinement with shelxl. name_fa.ins – instruction file for running shelxd. name_fa.hkl – reflection indices, FA and α. The analysis of MAD data Karle (1980) and Hendrickson, Smith & Sheriff (1985) showed by algebra that the measured intensities in a MAD experiment, assuming only one type of heavy atom, should be given by: |F±|2 = |FT|2 + a|FA|2 + b|FT||FA|cosα ± c|FT||FA|sinα where a = (f ” 2+f ’ 2)/f02, b = 2f’/f0, c = 2f”/f0 and α = φT – φA. We need to know f ’ and f ” for each wavelength. In a 2-wavelength MAD experiment, we have 4 equations for the 3 unknowns FA, FT and α, so with error-free data we should get a perfect map! For SIRAS, we have 2 equations for the derivative plus a native dataset. Given perfect isomorphism, the phase problem is solved. Unfortunately for SAD we only have 2 equations for the 3 unknowns. SAD phasing For a single wavelength SAD experiment, we only have equations for |F+|2 and |F–|2. Subtracting the second from the first, we obtain