VERY LOW RESOLUTION AB-INITIO PHASING. PROBLEMS AND ADVANCES

V.Y.Lunin¹, N.L.Lunina¹, T.E.Petrova¹, A.G.Urzhumtsev², A.D.Podjarny³

¹Institute of Mathematical Problems of Biology, RAS, 142292 Pushchino, Moscow Region, Russia,
²LCM³B, Université Henri Poincaré, Nancy 1, Faculté des Sciences, 54506 Vandoeuvre-lès-Nancy, France,
³IGBMC, BP 163, parc d'Innovation, 67404 Illkirch, c.u. de Strasbourg, France

Keywords: ab-initio phasing, very low resolution, macromolecules

Different approaches to very low-resolution (VLR) ab-initio phasing (e.g. electron density histogram based phases search [1], Few-Atoms-Models (FAM) method [2,3], molecular replacement with the use of envelope models [4,5]) show the same essential features. The criteria used for the search of the solution may reach their best values at false solutions. Furthermore, the attempts to refine some solution may result in very good criteria values without any improvement of phases. Nevertheless the true solution is usually near one of the several 'flat' optimums of the search criterion (but not necessarily the global one). The suggested way to overcome these difficulties is first to select all 'admissible' variants of the solution, then to separate them into a small number of compact clusters and finally to calculate centroid phases for every cluster. As the result a small number of alternative solutions is usually obtained and the problem is to decide which of them is the closest to the true solution.

As a possible way of choice of the best solution, a generalised maximum likelihood approach was suggested [3]. For every cluster, the centroid phases produce an envelope and the corresponding prior probability distribution for atomic coordinates. The generalised likelihood is defined as the probability to obtain structure factor magnitudes close to the experimental ones when generating atoms randomly within the tested envelope, in the contrast to the definition of the usual likelihood where these values are equal. A simple Monte-Carlo type procedure may be used to calculate generalised likelihood values for alternative envelopes and to select the best one.

Another criterion which can be applied to choose the best cluster is the globurality. It is based on the assumption that a well-phased synthesis reveals (at the lowest possible cut-off level) a number of globular connected regions equal to the number of molecules in the unit cell.

The molecular envelope found can then be refined further by the FAM-method or used as a target synthesis in the solution of the molecular replacement problem.

The procedures developed were successfully applied to VLR experimental diffraction data of T50S ribosomal particle crystals (space group P4₁2₁2/P4₃2₁2, a=b=498, c=198 Å) [6]. Two of the views of the 40 Å resolution FAM-phased Fourier synthesis are shown below.

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