A NEW FIGURE OF MERIT FOR PROTEIN PHASE SETS DISCRIMINATION

Anatoly Mishnev

21 Aizkraukles St., LV 1006, Riga, Latvia, E-mail: mishnevs@osi.lanet.lv

Keywords: direct methods, protein phasing, phase discrimination, autocorrelation function

The success of multisolution direct methods (DM) when applied to protein structures is hardly dependent on a suitable figure of merit (FOM) able to reliably identify the correct solution. In recent years it has been shown that conventional FOMs are not effective in picking out the best solutions from a large number of phase sets. Here we describe a new ACFFOM based on the general properties of the autocorrelation function (ACF) for a single unit cell and its relation to the Patterson function. It has been shown that the ACF is dependent on the phases of the structure factors (SF) [1]. When phase estimates are available from DM the ACF can be calculated for each phase set and compared with the Patterson function. For intramolecular vectors correct phases will produce the ACF nearly coincident with the Patterson. This approach has a similarity with molecular replacement method where the "known" structure is replaced by the electron density calculated using DM phases. To distinguish between good and bad phase sets we consider the values of the ACF A(u) at Patterson maxima. It is supposed that ACF for a good phase set should have maxima at the same positions as Patterson function. These considerations lead to the following FOM

ACFFOM = Si A2(ui) ,

where the sum is over the grid points corresponding to P(u) maxima and which assumes the highest value for the true phases..

The procedure of ACFFOM calculation is as follows:

  1. Calculate Patterson function and locate the maxima,
  2. Use the current phase set to calculate the electron density map,
  3. Define the molecule envelope and set the density in the solvent region to zero,
  4. Put modified in this way density into the eight times larger unit cell and complete it with the zero values of the density,
  5. By FFT find the SF of a new enlarged unit cell,
  6. Square the moduli of the SF and set all phases to zeros,
  7. Use FFT to calculate A(u) as described in [1],
  8. Compute ACFFOM.

The SAYTAN program [2] was used to derive 200 sets of phases for a small 300 non-hydrogen atoms protein APP [3]. Three of the phase sets had unweighted mean phase errors in the range of 38 - 42o. The ACFFOM was successfully applied to discriminate these good solutions.

  1. A.F. Mishnev, Acta Cryst. A52, (1996) 629-633
  2. T. Debaerdemaeker, C. Tate & M.M. Woolfson, Acta Cryst. A44 (1988) 353-357
  3. I. Glover, J. Haneef, J. Pitts, S. Wood, T. Moss, J. Tickle & T. Blundell Biopolymers 22 (1983) 293-304