A simplified multidimensional search used for crystal structure solution of pCpGpCpGpCpG with two duplexes pre asymmetric unit.

Abstract

A simplified multidimensional search was applied to determine the structure of deoxyhexamer CGCGCG in the crystal form belonging to the space group C222(1) (a = 45.6 A, b = 37.3 A, c = 70.3 A). This crystal form contains two Z-DNA duplexes per asymmetric unit in a similar orientation. The search consists of several main steps. As a first step, the analysis of packing modes is carried out and constraints for the position of duplexes in asymmetric unit are formulated. In order to choose true packing mode duplexes are represented as cylinders of a constant density and global search is carried out. Only reflections belonging to the plane in reciprocal space perpendicular to DNA axis were used in the calculations. An analytical representation of diffraction from a hollow cylinder is given which allows further refinement of corresponding parameters. During the global search the value of a linear correlation coefficient is estimated for each solution to pick up the best one. At the second step the "more local" search is carried out. The DNA model of a certain conformation (in our case Z-DNA) is taken and several parameters are being varied. These are: a) rotations of the independent duplexes around their axes (only two rotational parameters for two duplexes in our example) and b) a few positional parameters for which there is no corresponding constraint in the packing mode tested. In our case we had to vary only x1 and y2, where subindex corresponds to molecule number. The last stage concerned is quite similar to the multidimensional search realised in program ULTIMA. The only difference that the number of variable parameters is less in our search. This number for the case under consideration was 4 instead of 12 that would be necessary in a conventional multidimensional search.