Reconstruction of imperfectly ordered zinc-induced tubulin sheets using cross-correlation and real space averaging

Abstract

Large negatively-stained two-dimensional tubulin arrays induced by incubation with zinc were examined using electron microscopy. When Fourier methods are applied for the reconstruction, the resolution depends critically on the order of these arrays. The real space cross-correlation method as described in this paper, however, can be satisfactorily applied to disordered arrays. The method involves selection of a small area which is used as a reference to locate correlation peaks in other regions. In this way the locations of various unit cells are determined, often at points which deviate from the exact lattice. The unit cells at their determined locations are averaged, and the average is used as an improved reference in another search for correlation peaks. The process can be iterated to refine the reference and improve the correlation mapping. If necessary, poorly correlating unit cells can be ignored in the averaging, and rotational as well as translational corrections can be considered; but neither of these steps were found to be necessary in the studies on the zinc-induced tubulin sheets reported here. When both correlation and Fourier methods were compared for the same areas of selected sheets, the two methods gave comparable results for relatively well ordered regions, but the correlation images were superior for the more poorly ordered regions. In addition, even for the relatively well ordered regions the correlation images revealed some details that were lacking in the simple Fourier reconstructions but did appear in more extensive studies involving three-dimensional reconstruction. A direct comparison of the efficacy of real space and Fourier space reconstruction methods is presented using disordered model data.