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Multi-Phase-Field Models for Biological Systems: From cells to vessels

Authors: Maurício Moreira-Soares

Supervisors: Rui Travasso

PhD thesis, Universidade de Coimbra (2020)

Abstract: Active cell migration is one of the most fundamental abilities required for the sustainability of complex life forms: since it is essential in diverse processes from morphogenesis to leukocyte chemotaxis in immune response. The movement of a cell is the result of intricate mechanisms, that involve the coordination between mechanical forces, biochemical regulatory pathways and environmental cues. In this thesis we explore cell migration at different scales with a multi-phase-field approach. We start by focusing on epithelial cancer cells that have to employ mechanical strategies in order to migrate through the tissue’s basement membrane and infiltrate the bloodstream during the invasion stage of metastasis. In this work we explore how mechanical interactions such as spatial restriction and adhesion affect migration of a self-propelled droplet in dense fibrous media. Our results indicate that adhesiveness is critical for cell migration, by modulating cell morphology in crowded environments and by enhancing cell velocity. Next we proceed to study endothelial cells migration on fibronectin surfaces. We determine the dependence of cell shape on the adhesive patterns and propose a mathematical model for the intracellular mechanisms for cell adhesion and locomotion. In addition we present an active gel model for migration driven by actomyosin contractility. This set of models contains the building blocks for coupling cell migration with the intracellular biochemistry. We then explore multicellular migration in the context of angiogenesis - the growth of new blood vessels from a pre-existing vasculature. We demonstrate that the increased production of angiogenic factors by hypoxic cells is able to promote vessel anastomoses, the process by which two or more vessels merge. The simulations also verify that the morphology of these networks has an increased resilience toward variations in the endothelial cells’ proliferation and chemotactic response. We demonstrate that multi-phase-field models are extremely versatile and can be easily tailored to describe different biological systems at different scales. The minimalistic approaches we propose are able to produce results that are comparable with experimental data and give new insights to guide experimentalists.