A theoretical and computational study of cavity formation in biological systems

In this thesis, I present my work on the emergence of self-organised structure within cellular systems, with a particular emphasis on the formation of fluid filled cavities. Self-organisation is a striking hallmark of living systems, and plays a particularly import role in developmental biology. To study such systems, I develop a novel hydrodynamic theory of cells in a background fluid of water and solutes. The solutes and water can move passively across the membrane of the cells. Furthermore, solutes can be actively transported in or out of the cell both isotropi- cally and along a polar axis. Within this theory I demonstrate the existence of two potential mechanisms for cavity formation: spinodal phase separation driven by cell-cell adhesions, and an instability driven by active pumping of solutes into defects in the polarity field. This theory is general in scope, i.e. it is a framework to describe a variety of behaviours of any system consisting of adhering cells that can polarise and actively pump fluid. I also present a study of a specific experimental system: mouse embryonic stem cell (mESC) aggregates. When grown from wild type cells, these aggregates form a spherical structure with cells polarised towards the centre. Fluid is pumped into the centre and a cavity opens. Such aggregates are the simplest example of mESC organoids that recapitulate key in vivo developmental processes in vitro. In order to quantify the growth of mESC aggregates, I develop an image segmentation and analysis pipeline. This pipeline allows me to extract meaningful, structured information from noisy 3D experimental time series data. In order to model the growth of mESC aggregates in silico, I develop a novel 2D model of polarised, deformable cells with continuous boundaries, called the Spline Model. Using the Spline Model as a prototype, I recapitulate key features of the experiments. Finally, I develop a 3D model of polarised, deformable cells. I demonstrate quantitative agreement between cell shapes produced by this model and in experiment. I study the dynamics of cell aggregates for the case where adhesion forces are coupled to apicobasal polarity, and make quantitative comparisons between these simulations and experiments. I find a positive correlation between the measured polarity of E- cadherin and predictions based on integration of extracellular matrix signalling. Furthermore, by coupling polarity to increased apical adhesion, I demonstrate the ability of extended cellular aggregates to undergo a transition to a compact state. When the coupling is removed, the transition no longer occurs. This behaviour is reminiscent of β1-KO cells, in which polarity alignment mechanisms are disrupted, that fail to form compact, organised aggregates