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UBC Theses and Dissertations

The multi-levelled organization of cell migration : from individual cells to tissues Knutsdottir, Hildur


Cell migration is a complex interplay of biochemical and biophysical mechanisms. I investigate the link between individual and collective cell behaviour using mathematical and computational modelling. Specifically, I study: (1) cell-cell interactions in a discrete framework with a spatial sensing range, (2) migration of a cluster of cells during zebrafish (Danio rerio) development, and (3) collective migration of cancer cells and their interactions with the extracellular-matrix (ECM). My 1D model (1), is approximated by a continuum equation and investigated using asymptotic approximations, steady-state analysis, and linear stability analysis. Analysis and computations characterize regimes corresponding to cell clustering, and provide a link between micro and macro-scale parameters. Results suggest that drift (i.e. due to chemotaxis), can disrupt the formation of cellular aggregates. In (2), I investigate spontaneous polarization of a cell-cluster (the posterior lateral line primordium, PLLP) in zebrafish development. I use a cell-based computational framework (hybrid discrete cell model, HyDiCell3D) coupled with differential equation model to track the segregation and migration of the PLLP. My model includes mutual inhibition between the diffusible growth factors Wnt and FGF. I find that a non-uniform degradation of an extracellular chemokine (CXCL12a) and chemotaxis is essential for long-range cohesive migration. Results compare favourably with data from the Chitnis lab (NIH). I continue using HyDiCell3D in (3) to elucidate mechanisms that facilitate cancer invasion. I focus on: wound healing in a cell-sheet (2D epithelium), and cell-clusters (3D spheroids) embedded in ECM with internal signalling mediated by podocalyxin, a trans-membrane molecule. Experimental data from the Roskelley lab (UBC) motivates the model derivation. I use the models to investigate the role of cell-cell and cell-ECM adhesion in collective migration as well as the emergence of a distinct phenotype (leader-cells) that guide the migration. ECM induced disruption in the localization of podocalyxin on the cell membrane is captured in the model along with morphological changes of spheroids. The model predicts that cell polarity and cell division axis influence the invasive potential. Lastly, I developed quantitative methods for image analysis and automated tracking of cells in a densely packed environment to compare modelling results and biological data.

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