Abstract
Electron cryomicroscopy (cryo-EM) is a form of transmission electron microscopy, aimed at reconstructing the 3D structure of a macromolecular complex from a large set of 2D projection images, as they exhibit a very low signal-to-noise ratio (SNR). In the single-particle reconstruction (SPR) problem, several randomly oriented copies of the protein are available, each representing a certain viewing direction of the structure. This implies two main computational problems: (1) to determine the angular relationship between the individual projection images, i.e. determine the protein pose in each view, and (2) to solve the ill-posed tomographic reconstruction problem. Related to both problems one needs to handle the significant computation time complexity, without compromising accuracy. Then, the ultimate goal of cryo-EM is to estimate the most reliable 3D structure at the highest resolution achievable from the noisy, randomly oriented projection images.
Many statistical approaches to SPR have been proposed in the past. Typically, due to the computation time complexity, they rely on approximated maximum likelihood (ML) or maximum a posteriori (MAP) estimate of the structure. All methods presented in this thesis attempt to solve a specific part of the reconstruction problem in a statistically sound manner.
Firstly, we propose two methods for solving the problems (1) and (2). They can ultimately be extended and combined into a statistically sound solution to the full SPR problem. We use Bayesian statistical inversion to optimally cope with the high amount of noise, as well as to incorporate prior information to obtain more reliable estimates. For the first problem, we investigate the statistical recovery of the geometry between a set of projection images. In more detail, we show the equivalence between a MAP approach for estimating the protein structure. The resulting method is statistically optimal under the assumption of the uniform prior in the space of rotations. The marginal posterior is constructed by integrating over the view orientations and maximised by the expectation-maximisation (EM) algorithm. We use Monte Carlo integration to reduce the computational complexity.
Secondly, a statistical approach is presented for removing vesicle membrane structures from the projection images, for the purpose of improving the 3D reconstruction quality of the membrane proteins. The vesicle structures are learned and removed with a novel 2D statistical model of the vesicle structure, based on higher-order singular value decomposition (HOSVD). The vesicle structures are removed by projecting the micrographs onto the orthogonal complement of the estimated vesicle subspace. The method is applied to real membrane proteins reconstituted into vesicle membranes. The resulting 3D structure is the first reconstruction of the demonstrated protein by SPR. The subspace method is general and has potential for integration into the SPR algorithm for an even more reliable result.
Many statistical approaches to SPR have been proposed in the past. Typically, due to the computation time complexity, they rely on approximated maximum likelihood (ML) or maximum a posteriori (MAP) estimate of the structure. All methods presented in this thesis attempt to solve a specific part of the reconstruction problem in a statistically sound manner.
Firstly, we propose two methods for solving the problems (1) and (2). They can ultimately be extended and combined into a statistically sound solution to the full SPR problem. We use Bayesian statistical inversion to optimally cope with the high amount of noise, as well as to incorporate prior information to obtain more reliable estimates. For the first problem, we investigate the statistical recovery of the geometry between a set of projection images. In more detail, we show the equivalence between a MAP approach for estimating the protein structure. The resulting method is statistically optimal under the assumption of the uniform prior in the space of rotations. The marginal posterior is constructed by integrating over the view orientations and maximised by the expectation-maximisation (EM) algorithm. We use Monte Carlo integration to reduce the computational complexity.
Secondly, a statistical approach is presented for removing vesicle membrane structures from the projection images, for the purpose of improving the 3D reconstruction quality of the membrane proteins. The vesicle structures are learned and removed with a novel 2D statistical model of the vesicle structure, based on higher-order singular value decomposition (HOSVD). The vesicle structures are removed by projecting the micrographs onto the orthogonal complement of the estimated vesicle subspace. The method is applied to real membrane proteins reconstituted into vesicle membranes. The resulting 3D structure is the first reconstruction of the demonstrated protein by SPR. The subspace method is general and has potential for integration into the SPR algorithm for an even more reliable result.
| Originalsprog | Engelsk |
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| Forlag | Department of Computer Science, Faculty of Science, University of Copenhagen |
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| Status | Udgivet - 2015 |