A MULTISOLUTION METHOD OF PHASE DETERMINATION BY COMBINED MAXIMIZATION OF ENTROPY AND LIKELIHOOD .5. THE USE OF LIKELIHOOD AS A DISCRIMINATOR OF PHASE SETS PRODUCED BY THE SAYTAN PROGRAM FOR A SMALL PROTEIN

The use of a likelihood criterion associated with maximum-entropy (ME) extrapolation for selecting phase sets as part of a new multisolution phasing strategy, already applied to solving small crystal structures from single-crystal data [Gilmore, Bricogne & Bannister (1990). Acta Cryst. A46, 297-308] and X-ray powder diffraction data [Gilmore, Henderson & Bricogne (1991). Acta Cryst. A47, 830-841], has been tested on the small protein avian pancreatic polypeptide (APP) with 301 non-H atoms in the asymmetric unit in space group C2. A collection of 50 phase sets for APP were provided by Woolfson & Yao. They had been generated from random starting phases by the SAYTAN procedure [Woolfson & Yao (1990). Acta Cryst. A46, 409-413] using data to a resolution of 0.98 angstrom. Six of these had an unweighted mean absolute phase error, <\DELTA-phi\>, of less than 50-degrees, the remainder having phase errors of 60-degrees or more. However, none of the conventional figures of merit were able to identify these preferred sets. Each phase set was subjected to our standard procedure of entropy maximization and of evaluation of the log-likelihood gain resulting from the associated ME extrapolation. With only a small subset of data (to 2 angstrom resolution), the likelihood criterion identified unambiguously the phase sets with <\DELTA-phi\> less than 50-degrees. In contrast, conventional figures of merit showed no such ability. We conclude that, although SAYTAN is at present much more efficient than our program (MICE) at generating large trial phase sets, the latter is clearly superior in discerning the best of these phase sets. We therefore expect that our current efforts to make MICE run faster should result in better prospects of ab initio phasing for small macromolecules.