Actin-rich protrusions: leading to cancer cell invasion through mathematical formulation

Metastasis accounts for most cancer-related deaths, with invadopodia formation playing a central role in tumor cell invasion. Invadopodia are actin-rich protrusions that degrade the extracellular matrix (ECM), enabling cancer cells to penetrate and spread. This research presents a simplified mathematical model to investigate the effect of signal decay on invadopodia dynamics using the level set method. The model incorporates ligand diffusion and intracellular signaling with a decay term to capture essential biological behavior while remaining computationally efficient. The plasma membrane is represented as a moving interface driven by jump velocity, defined by the gradients of ligand and signal variables. Numerical discretisation techniques are applied to simulate signal distribution, ligand interaction, and interface deformation. The findings suggest that signal decay significantly influences membrane protrusion behavior, where reduced signaling activity leads to shrinking of the interface while stronger gradients sustain invadopodia growth. This approach provides both visual and quantitative insights into cancer cell invasion mechanisms, demonstrating the potential of mathematical modeling as a tool to support future therapeutic strategies targeting metastasis.