The nuclear lamina functions as a structural support system for the nucleus and must be broken down during mitosis. Not much is known about the process by which this breakdown is initiated. Prior studies have suggested that the nuclear envelope is depleted of lamin B1 at high curvatures, which destabilized the nuclear lamina and possibly plays a role in mitotic nuclear envelope breakdown. A statistical probability model has been proposed to describe this depletion based on the Gaussian curvature of the nuclear lamina. However, this model has only been tested on limited two-dimensional data. In this thesis, a quantitative image analysis pipeline is created and applied to test the relation between the absolute Gaussian curvature of the nuclear lamina and the density of lamin B1 in three-dimensional confocal images. To accomplish this, the nuclear lamina are segmented with unsharp-masking and steerable filters. The curvature of the nuclear lamina is computed using a grey-scale surface curvature estimation. Two different density states of the lamin B1 meshwork are found and a transition from high to low density is shown for increasing curvatures. These results support the previously proposed probability model for the depletion of lamin B1 at high curvatures and provides a deeper understanding of the structure of the nuclear lamina. Additionally, the image analysis pipeline established in this thesis provides helpful tools for effective segmentation and curvature estimation of the nuclear lamina and can be applied in future research.

Expansion microscopy (ExM) is a new approach to super-resolution that relies on the physical isotropic expansion of a sample in a swellable polymer network. We developed a novel ExM method termed Sevenfold Post-labelling Expansion Microscopy (SP-ExM) that enables sevenfold expansion in a single step of thick cerebellar mouse brain and human tumour and peritumoral cortex samples, while preserving proteins for bulk staining of the entire proteome. Using SP-ExM, we localized proteins with nanoscale precision in their ultrastructural context without any specialized procedures or equipment. As such, SP-ExM contributes to better understanding the ultrastructural layout of specific proteins in health and disease.

The principle of competitive exclusion states that, in equilibrium, the amount of coexisting species is limited by the amount of limiting resource types in an ecosystem. However, in phytoplankton communities the paradox of plankton appears, amounts of plankton species can coexist that far exceed this
upper limit. A resource competition model is formulated and it is shown that the paradox arises for several systems, which indicates that the bloom in biodiversity is a result of the resource competition and not of any external factors. A proof is given that the principle of competitive exclusion only holds in equilibrium solutions. Therefore, as long as a system does not intersect with an equilibrium solution the biodiversity is not restricted by the amount of limiting resource types. It is concluded that intersecting with an equilibrium solution is avoided when there are only unstable equilibrium solutions present in the system. When a plankton species allows an asymptotically stable equilibrium solution, with a region of convergence equal to the domain of the system, to appear it will be called dominant. It is proven that an asymptotically stable equilibrium solution always exists in a simplified system with less than three limiting resource types. Furthermore, an algorithm is constructed that determines all the new equilibrium solutions, and their respective stabilities, when a new plankton species is introduced to a system.
By applying this algorithm it can be determined whether a species is suitable for an ecosystem, when the goal is to maintain biodiversity. The resource competition model is expanded to include light as an additional resource for all plankton species. It is observed that the coexistence of the plankton species and the total biomass is limited
if there is too little light for the plankton species to consume, or if one plankton species becomes dominant due to it being significantly better at consuming light than the other species.
Additionally, the physical context of a flowing river is introduced, with dispersive and advective mass transfer and finite length. It is observed that while the spatial distribution of the plankton species along the river is strongly influenced by the spatial parameters, the biodiversity of the ecosystem is still primarily determined by the original parameters from the resource competition model, as long as the dispersive mass transfer is the dominant type of mass transfer not too large in comparison to the length of the river.