Inverse problems are problems where we want to estimate the values of certain parameters of a system given observations of the system. Such problems occur in several areas of science and... Show moreInverse problems are problems where we want to estimate the values of certain parameters of a system given observations of the system. Such problems occur in several areas of science and engineering. Inverse problems are often ill-posed, which means that the observations of the system do not uniquely define the parameters we seek to estimate, or that the solution is highly sensitive to small changes in the observation. In order to solve such problems, therefore, we need to make use of additional knowledge about the system at hand. One such prior information is given by the notion of sparsity. Sparsity refers to the knowledge that the solution to the inverse problem can be expressed as a combination of a few terms. The sparsity of a solution can be controlled explicitly or implicitly. An explicit way to induce sparsity is to minimize the number of non-zero terms in the solution. Implicit use of sparsity can be made, for e.g., by making adjustments to the algorithm used to arrive at the solution.In this thesis we studied various inverse problems that arise in different application areas, such as tomographic imaging and equation learning for biology, and showed how ideas of sparsity can be used in each case to design effective algorithms to solve such problems. Show less
Cryo-focused ion beam (FIB)-milling of biological samples can be used to generate thin electron-transparent slices from cells grown or deposited on EM grids. These so called cryo-lamellae allow... Show moreCryo-focused ion beam (FIB)-milling of biological samples can be used to generate thin electron-transparent slices from cells grown or deposited on EM grids. These so called cryo-lamellae allow high-resolution structural studies of the natural cellular environment by in situ cryo-electron tomography. However, the cryo-lamella workflow is a low-throughput technique and can easily be hindered by technical issues like the bending of the lamellae during the final cryo-FIB-milling steps. The severity of lamella bending seems to correlate with crinkling of the EM grid support film at cryogenic temperatures, which could generate tensions that may be transferred onto the thin lamella, leading to its bending and breakage. To protect the lamellae from such forces, we milled "micro-expansion joints" alongside the lamellae, creating gaps in the support that can act as physical buffers to safely absorb material motion. We demonstrate that the presence of micro-expansion joints drastically decreases bending of lamellae milled from eukaryotic cells grown and frozen on EM grids. Furthermore, we show that this adaptation does not create additional instabilities that could impede subsequent parts of the cryolamella workflow, as we obtained high-quality Volta phase plate tomograms revealing macromolecules in their natural structural context. The minimal additional effort required to implement micro-expansion joints in the cryo-FIB-milling workflow makes them a straightforward solution against cryo-lamella bending to increase the throughput of in situ structural biology studies. Show less
Correlative light and electron microscopy (CLEM) refers to the observation of the same structures or ultrastructures with both light microscopy (LM) and electron microscopy (EM). LM provides an... Show moreCorrelative light and electron microscopy (CLEM) refers to the observation of the same structures or ultrastructures with both light microscopy (LM) and electron microscopy (EM). LM provides an overview of the studied material, and enables the quick localization of structures that are fluorescently labeled, while EM allows high resolution imaging of structures. The thesis describes several technical developments that allow CLEM. In the first chapters, methods are described for room temperature CLEM. This includes tissue labeling with fluorescent dyes in ultrathin resin sections, and fluorescence imaging before further preparation for EM and electron tomography. The methods are applied to tissue biopsies, and to the study of regulated exocytosis of Weibel-Palade bodies. In the following chapters, CLEM developments are extended with CLEM of vitreous samples, i.e. cryo-CLEM. Vitrification allows easy maintenance of fluorescent probes, and it allows correlation with cryo-EM, a technique that preserves biological structures to atomic resolution. The thesis describes the design of a microscope stage for cryo-fluorescence microscopy. Following cryo-FM, samples are studied directly by cryo-EM and cryo-electron tomography. The technique is used to study mitochondrial ultrastructure, and the role of actin in the exocytosis of pancreatic zymogen granules. Show less
