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Emergence of spatial patterns in a mathematical model for the co-culture dynamics of epithelial-like and mesenchymal-like cells

1. Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24,10129 Torino, Italy
2. School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, United Kingdom

Accumulating evidence indicates that the interaction between epithelial and mesenchymal cells plays a pivotal role in cancer development and metastasis formation. Here we propose an integro-differential model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. Our model takes into account the effects of chemotaxis, adhesive interactions between epithelial-like cells, proliferation and competition for nutrients. We present a sample of numerical results which display the emergence of spots, stripes and honeycomb patterns, depending on parameters and initial data. These simulations also suggest that epithelial-like and mesenchymal-like cells can segregate when there is little competition for nutrients. Furthermore, our computational results provide a possible explanation for how the concerted action between epithelial-cell adhesion and mesenchymal-cell spreading can precipitate the formation of ring-like structures, which resemble the fibrous capsules frequently observed in hepatic tumours.

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