Modeling the two-way feedback between contractility and matrix realignment reveals a nonlinear mode of cancer cell invasion

Significance The mechanical cross talk between intracellular and extracellular forces can promote the invasive potential of tumor cells in tumors. Using a quantitative model, we elucidate the two-way feedback loop between stress-dependent cell contractility and matrix fiber realignment and strain stiffening, which enables the cells to polarize and enhance their contractility to break free from the tumor and invade into the matrix. Our model predicts that intermediate matrix stiffness is optimal for invasion, and we find a positive correlation between cell elongation and alignment of fibers in the matrix. Importantly, our model can be used to explain how morphological and structural changes in the tumor microenvironment, such as elevated rigidity and fiber alignment prior to cell invasion, are prognostic of the malignant phenotype.