Numerical computation of ligand and signal associated to invadopodia formation

Invadopodia are protrusions that are commonly spotted at the plasma membrane of the invasive cancer cells. In forming invadopodia, several molecular interactions are involved such as the ligand, extracellular matrix (ECM), matrix metalloproteinases (MMPs), actin, and signal which are interrelated. In this paper, the mathematical model of ligand and signal transduction is taken in the heat equation with the MMPs is set as function g. Besides, the actin regulation moved the interface and thus computed as the signal gradient. The mathematical model is solved using the combination of methods finite difference, ghost fluid with linear extrapolation, and level set. Apart from that, the convergence results are also given to determine the effectiveness of the above-mentioned methods. Results showed that the stimulation of signal transduction from the ligand and membrane-associated receptor binding consequently moved the plasma membrane. Also, the methods used gave a good agreement in the convergence results