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

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.