Invadopodia: the formation through the lens of ligand decay

Cancer is a major global health challenge, with metastasis identified as the leading cause of cancer-related deaths. A critical step in this process is the formation of invadopodia, actin-based membrane protrusions that enable cancer cells to degrade the extracellular matrix (ECM) and invade surrounding tissues. This research designs a two-dimensional mathematical model to examine the role of ligand decay in invadopodia formation. The model incorporated ligand-signal interactions with decay terms, while actin polymerisation is represented as plasma membrane velocity. Numerical algorithms were implemented using the level set method, second-order finite difference schemes, and the ghost fluid method to capture the movement of the free boundary membrane. Simulation results show that ligand concentration highest at the membrane interface due to receptor-ligand binding, with decay rates strongly influencing the extent and behavior of protrusion formation. These findings demonstrate that mathematical modeling provides an effective framework to capture the dynamics of invadopodia formation and offer new insights into the role of ligand decay in cancer cell invasion.