ThreeDimensional Variance of Weighted BackProjection Reconstruction
Abstract
This dissertation addresses the statistical aspects of 3D reconstruction in studying biological macromolecules from electron microscopy. The primary concentration is on the development and application of a 3D variance estimation algorithm in the weighted backprojection reconstruction from a random conical tilt series. The purpose of the studies is to detect 3D particle conformational changes, to assess the structural differences of two related reconstructions and to address the significance of local features in a reconstruction. Other topics include the 3D spectral signaltonoise ratio (SSNR) estimation algorithm, the estimation of 3D signaltonoise ratio (SNR) and 3D resolution, and the statistics of quantum and photographic noises combined. Using the "two steps" strategy: defining the 3 D variance from a "gedankenexperiment" and estimating it by comparing neighbor projections, a 3D variance estimate (of each reconstruction voxel) is established, which maximally exploits the noise information hidden in the projections. Then the statistical properties of the 3D variance estimate, the contributions of different projection noise sources, the effect of filtration, projection inhomogeneity and number of projections, and the statistical assessments from using 3D variance is systematically analyzed. A practical application protocol of 3D variance is subsequently proposed. In the two applications to four projection classes of the 50S ribosomal subunit depleted of L7/L12 proteins and to a hemocyaninFab complex, the 3D locations of structurally flexible regions of the particles are demonstrated from the 3D variance maps; the structural differences between the classes are assessed by using the statistical ttest; and the 3D antibody binding site is revealed. Also, the concept of resolution is readdressed, various 3D resolution measures are compared, and a 3D SSNR estimation algorithm is developed. Then, the 3D SNR and 3D SSNR of a weighted backprojection reconstruction are expressed as functions of projection sampling geometry, object size and shape, number of projections, and spectral projection signal and noise levels. Finally, the probability density function of the combination of quantum and photographic noises is derived and its possible application for characterizing the emulsion noise is discussed.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1992
 Bibcode:
 1992PhDT.......140L
 Keywords:

 THREE DIMENSIONAL VARIANCE;
 MACROMOLECULES;
 Biophysics: General; Physics: General