Maximum likelihood reconstruction of three-dimensional objects with helical symmetry from two-dimensional projections of unknown orientation and application to electron microscope images of viruses.

摘要

A wide variety of biological objects have helical symmetry, including viruses such as Tobacco Mosaic Virus. An important method for studying such objects is cryo electron microscopy (cryo EM) which provides 2-D projection images of the 3-D distribution of electron scattering intensity of the object. A critical problem is that cryo EM images have low SNR due to the sensitivity of the object to the electron beam, which motivates using low beam currents, and variations in the thickness of the ice surrounding the object in the cryo EM specimen. A second critical problem is that the orientation of the projections is unknown and, because of the low SNR, difficult to determine from the individual images. In this thesis, a statistical model and maximum likelihood estimator are proposed for 3-D signal reconstruction of a helical object from cryo EM images. While a helical object is often represented by a Fourier-Bessel series, which includes the periodicity and helical symmetry constraints, the modeling approach described in this thesis represents a helical object as a helical array of identical subobjects where each subobject is the so-called motif of the helical object. Using this motif-focused model, maximum likelihood 3-D reconstructions are computed by a variety of generalized expectation maximization algorithms for simultaneously determining the parameters of the helical symmetry and the 3-D electron scattering intensity of the motif. Numerical examples of the 3-D reconstructions computed by distributed-memory parallel software are provided based on synthetic and experimental images.