Complex Morphologies of Biomolecular Condensates and Lipid Vesicles: A Continuum Modelling Approach

The morphology of biomolecular condensates and lipid vesicles is central to the spatial organisation and function of the cell. Despite extensive experimental observations, a theoretical understanding of the biophysical principles that govern these morphologies remains limited. This thesis addresses this gap using continuum modelling to study four distinct biophysical systems, linking physical mechanisms to cellular functions. First, we investigate HIV capsid translocation through the condensate-filled nuclear pore complex, revealing how symmetry-breaking in the system facilitates efficient capsid transport. Second, we analyse vesicle–condensate capillary bridges, finding two novel morphologies in simulation and experiment. These findings highlight a potential role in membrane contact site formation, arising from the increased stability of membrane–membrane contact morphologies, as measured by their spring constant. Third, we examine vesicle–vesicle wrapping mediated by an adhesive depletion interaction, identifying two distinct regimes of complete wrapping: geometry-limited and adhesion-limited. We compare simulation results with experiments on giant unilamellar vesicles quantitatively by comparing the peak membrane curvature and the wrapping fraction. Fourth, we simulate vesicles under non-spherical confinement, showing that specific geometries can break vesicle symmetry and induce highly curved membrane shapes resembling those observed in confined cellular compartments. By elucidating the physical mechanisms that control these systems, we demonstrate how continuum modelling provides a useful framework for understanding the behaviour of diverse subcellular assemblies. The results offer quantitative predictions for experimental studies and suggest new directions for investigating how physical interactions shape the structure and function of cellular components.