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Abstract

Biological cells constantly sense and adapt to the mechanical properties of their environment. While traditionally the cytoskeleton has been considered to be the prime determinant of cell mechanics, more recently it has been shown that the nucleus is also an essential element. In this thesis, we propose continuum models to investigate the effect of nuclear rigidity on whole-cell elasticity, the mechanosensitive accumulation of proteins in the nucleus as well as the formation of thick cytoskeletal filament bundles, so-called stress fibres. These aspects are modelled using a diffuse interface approach, the phase field method, coupled to standard elasticity theory and are numerically solved by a combination of spectral and matrix methods. First, we demonstrate the applicability of the approach to standard biological situations of single cells and cell monolayers without internal structures. We than extent it for single cells to include a nucleus and illustrate that nuclear mechanics has important implications on the mechanical response of cells for a selection of relevant situations. Combining this method with a reaction-diffusion system, we propose a model that shows that nuclear rigidity affects nuclear protein import. Lastly, we present a continuum model for the mechanosensitive formation of stress fibres by coupling a dynamic nematic order parameter tensor, as suggested by liquid crystal theory, to the elastic phase field method. This combined model can qualitatively capture prominent experimental observations. In conclusion, we developed a versatile continuum framework that can describe and quantify several important effects of mechanobiology.