In this article, we show, using a mathematical multiscale model, how cell adhesion may be regulated by interactions between E-cadherin and beta-catenin and how the control of cell adhesion may be related to cell migration, to the epithelial-mesenchymal transition and to invasion in populations of eukaryotic cells. E-cadherin mediates cell-cell adhesion and plays a critical role in the formation and maintenance of junctional contacts between cells. Loss of E-cadherin-mediated adhesion is a key feature of the epithelial-mesenchymal transition. beta-catenin is an intracellular protein associated with the actin cytoskeleton of a cell. E-cadherins bind to beta-catenin to form a complex which can interact both with neighboring cells to form bonds, and with the cytoskeleton of the cell. When cells detach from one another, beta-catenin is released into the cytoplasm, targeted for degradation, and downregulated. In this process there are multiple protein-complexes involved which interact with beta-catenin and E-cadherin. Within a mathematical individual-based multiscale model, we are able to explain experimentally observed patterns solely by a variation of cell-cell adhesive interactions. Implications for cell migration and cancer invasion are also discussed.

Transendothelial migration is a crucial process of the metastatic cascade in which a malignant cell attaches itself to the endothelial layer forming the inner wall of a blood or lymph vessel and creates a gap through which it enters into the bloodstream (or lymphatic system) and then is transported to distant parts of the body. In this process both biological pathways involving cell adhesion molecules such as VE-cadherin and N-cadherin, and the biophysical properties of the cells play an important role. In this paper, we present one of the first mathematical models considering the problem of cancer cell intravasation. We use an individual force-based multi-scale approach which accounts for intra- and inter-cellular protein pathways and for the physical properties of the cells, and a modelling framework which accounts for the biological shape of the vessel. Using our model, we study the influence of different protein pathways in the achievement of transendothelial migration and give quantitative simulation results comparable with real experiments.

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