Analytic study of three-dimensional single cell migration with and without proteolytic enzymes

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.

Cell-ECM Interactions in Tumor Invasion

The cancer cells obtain their invasion potential not only by genetic mutations, but also by changing their cellular biophysical and biomechanical features and adapting to the surrounding microenvironments. The extracellular matrix, as a crucial component of the tumor microenvironment, provides the mechanical support for the tissue, mediates the cell-microenvironment interactions, and plays a key role in cancer cell invasion. The biomechanics of the extracellular matrix, particularly collagen, have been extensively studied in the biomechanics community. Cell migration has also enjoyed much attention from both the experimental and modeling efforts. However, the detailed mechanistic understanding of tumor cell-ECM interactions, especially during cancer invasion, has been unclear. This chapter reviews the recent advances in the studies of ECM biomechanics, cell migration, and cell-ECM interactions in the context of cancer invasion.