Novel phases and phase transitions in models of epithelial tissues - Pasupalak Anshuman Gadadhar (Nanyang Technological University, 2023)
In multicellular organisms, individual cells play a myriad of roles in maintaining life, both as single cells and as collectives in tissues and organs. While single cell properties and their functioning is mostly well documented and understood, their working as a collective is largely unknown. In this thesis, we focus on one such collective, epithelial tissues. Epithelial tissues are ubiquitous in animals, however differ in form and function. As such it is challenging to characterize them through the lens of conventional biochemistry. An alternative approach would be to coarse-grain these bio-processes and identify physical phenomena that arise, and model these tissues using simple computational models. Several physical properties have thus been identified that are deemed essential for regulation of epithelial mechanics, such as, cell density, cell-cell interactions, cell shapes, cell propulsion and external factors such as mechanical stress. It is well known that epithelial tissues perform essential processes like tissue development and repair via an Epithelial to Mesenchymal Transition (EMT), where epithelial tissues lose their rigidity and acquire migratory properties and show collective movement. We show in this thesis, considering a model of tissues incorporating the effects of cell shapes and cell propulsion, that the EMT transition is analogous to the melting transition in two dimensional systems, which occurs via an intermediate hexatic phase. We show that this transition follows the Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY) theory of two dimensional melting, where melting occurs due to emergence of topological defects. Cell tissues as a material, resemble to packings of foams, bubbles and emulsions, due to their inherent structural similarities. These materials are known to be deformable, being able to withstand large structural deformations before fracture. We consider different models that are able to capture the structural properties of these materials and show that, when subject to high strains, they display a previously unreported shear weakening regime, where the shear stress drops to infinitesimal values at large shear deformations. We show that the underlying cause of this shear weakening originates from the geometrical properties of the models and not their mechanical interactions. Finally, we develop a rigorous framework to model epithelial tissues, starting from single cell properties, incorporating the effects of cell density, shapes, propulsion and inter-cellular adhesion, to further our understanding of the interplay of all these parameters. In the limiting equilibrium case, we highlight the role of cell density and adhesion in our model, which agrees qualitatively to experimental studies on epithelial tissue mechanics.