Active interfacial degradation/deposition of an elastic matrix by a fluid inclusion: Theory and pattern formation

During collective invasion in 3D, cohesive cellular tissues migrate within a fibrous extracellular matrix (ECM). This process requires significant remodeling of the ECM by cells, notably proteolysis at the cell–ECM interface by specialized molecules. Motivated by this problem, we develop a theoretical framework to study the dynamics of a fluid inclusion (modeling the cellular tissue) embedded in an elastic matrix (the ECM), which undergoes surface degradation/deposition. To account for the active nature of this process, we develop a continuum theory based on irreversible thermodynamics, leading to a kinetic relation for the degradation front that locally resembles the force–velocity relation of a molecular motor. We further study the effect of mechanotransduction on the stability of the cell–ECM interface, finding a variety of self-organized dynamical patterns of collective invasion. Our work identifies ECM proteolysis as an active process possibly driving the self-organization of cellular tissues.