| 90% of the cancer-inflicted mortality comes from the acquired metastatic ability. Metastatic cancer cells can physically travel through the extracellular matrix (ECM) by regulating enzymatic proteolysis. By colocalizing enzymes such as Matrix Metalloproteases (MMPs) at the invasion site, cancer cells actively degrade the ECM structures to promote the invasion efficiency. In this theoretical study, we propose a mechano-chemically coupled model to study this multiphysical phenomenon. We use the regular perturbation method to derive an analytical expression for the deformation field induced by cell-exert stresses on a nonlinear, inhomogeneous material. We then propose a chemical model that reflects the dynamics of the system, which includes the enzyme kinetics and enzyme diffusion. The mechanical and chemical models are coupled under the considerations that, (1) material stiffness is related to the concentration of the denaturized substrate constituent; (2) catalytic reaction is accelerated by the mechanical strain energy, as found in the recent single molecule assays. Using this model, we study a synthetic stress field that is consistent with the experimental observations. It is found that by coupling force to the degradation process, the dynamics of the system is significantly altered. We perform a parametrized study on mechanical forces, colocalized enzyme concentration, and the enzyme release pattern to study its individual effects on the invasion. Qualitatively, the study reveals the importance of each parameters on affecting the invasion efficiency from a rigorous physical and mathematical point of views. |
