Numerical computation of signal stimulation from ligand-EGFR binding during invadopodia formation

Invadopodia are finger-like protrusions located at subcellular membrane which can lead to cancer cell invasion. The formation of invadopodia involves several steps such as actin polymerizations, degradation of extracellular matrix which produce ligand and signal stimulation that is occurred from the binding of ligand with epidermal growth factor receptor. In this paper, a mathematical model of signal transduction is investigated. Both signal and ligand are represented by Laplace equation with Dirichlet boundary condition for each region. The cell membrane is treated as free boundary surface to separate any activity that occurred in intracellular and extracellular regions. The motion of the interface is taken as gradient of interior signal and the cell membrane is set as zero level set function. The problem is solved numerically using finite difference scheme of upwind, interpolation and extrapolation methods. The results showed that the formation of invadopodia is formed when protrusions exist on the cell membrane