Analysis and processing of dark-field electron micrographs for three-dimensional reconstruction

Dark-field electron microscopy has the potential of providing high resolution images of biological molecules with a resolution of 5 A. The two dimensional information from dark-field electron micorgraphs may be used to generate a three dimensional structure of the molecule if the relative projection directions of the images are known. This thesis describes computational techniques aimed at recovering this three dimensional information from single images of molecules which adopt unknown orientations with respect to the imaging beam. Dark-field images contain large amounts of noise, primarily a result of structure in the carbon film used to support the specimen. The application of maximum entropy methods, in an attempt to enhance the quality of the original images by removing the noise, is described. It is seen that, to be useful, these methods require a number of other constraints. However, the additional constraints lead to significantly increased computational times which render the algorithm impractical. An algorithm is described that permits the a posteriori determination of the relative projection direction of a large number of molecules. The method uses the central section theorem to determine the relative orientations of the images. Quaternion mathematics is used to determine optimum alignments of images. A number of algorithm-specific parameters are developed to indicate the degree of success of the alignment procedure. Simulated images and dark-field electron micrographs of the Klenow Fragment of DNA Polymerase I are used to test the efficacy of the alignment algorithm. The simulations indicate, on the basis of signal-to-ratio as a measure of image quality, that the algorithm should be able to determine projection directions from dark-field micrographs of single molecules. However, application to electron micrographs provides low quality alignments. Reasons for the discrepancy between the simulations of experimental situations are discussed. Preliminary experiments indicate that visual selection of high quality images yields improved alignments. It is suggested that this improvement results from selection of particles that have retained their integrity during the imaging procedure. It is concluded that the alignment procedure will probably be successful when applied to higher quality dark-field electron micrographs.Ph.D