The overarching goal of this thesis is to set the foundations, but also make the first essential steps towards establishing a comprehensive, mesoscopic, hydrodynamic theory of epithelial tissues. The stage is set by an exhaustive study of topological defects in passive p-atic liquid crystals, singularities in the orientation field, that allow us to bridge our continuum theory with the discrete epithelial cellular network. After questioning the very existence of active liquid crystals, we confirm they form a new, distinct universality class of orientationally ordered systems, of which tissues are a typical case.
We then proceed to identify the precise nature of their orientational order. Although complex and long debated, we show that tissues exhibit only 6-fold (hexatic) and 2-fold (nematic) orientational order, at small and large scales respectively. Before concluding, we establish a predictive, quantitative duality between topological defect dynamics and cell...
Show moreThe overarching goal of this thesis is to set the foundations, but also make the first essential steps towards establishing a comprehensive, mesoscopic, hydrodynamic theory of epithelial tissues. The stage is set by an exhaustive study of topological defects in passive p-atic liquid crystals, singularities in the orientation field, that allow us to bridge our continuum theory with the discrete epithelial cellular network. After questioning the very existence of active liquid crystals, we confirm they form a new, distinct universality class of orientationally ordered systems, of which tissues are a typical case.
We then proceed to identify the precise nature of their orientational order. Although complex and long debated, we show that tissues exhibit only 6-fold (hexatic) and 2-fold (nematic) orientational order, at small and large scales respectively. Before concluding, we establish a predictive, quantitative duality between topological defect dynamics and cell intercalation. Cell intercalation is the origin of collective cell migration, an essential mechanism of epithelial tissues, necessary for functions such as morphogenesis, wound healing, and even cancer progression.
Our results are supported by a combination of experiments, analytics, and numerical simulations. The analytic and computational toolkit we utilize comprises concepts, mathematics, and models from hydrodynamics, theory of elasticity, statistical physics, and topology. Finally, we close with some thoughts on the emergence in living systems, revolving around our central theme of epithelial tissues.
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