Signal transduction from ligand-receptor binding associated with the formation of invadopodia in an invasive cancer cell

Invadopodia are finger-like protrusions that are commonly spotted at the membrane of the invasive cancer cell. These structures are a major cause of death among cancer patients through metastasis process. Signal transduction stimulated upon contact between ligand and membrane receptors is identified as one of key factors in invadopodia formation. In this study, a time-dependent mathematical model of signal and ligand is investigated numerically. The moving boundary of plasma membrane is taken as a zero-level set function and is moved by the velocity that accounted as the difference of gradient between intra-cellular signal and extra-cellular ligand. The model is solved using a combination of ghost with linear extrapolation and finite difference methods. The results showed that the stimulation of signal from membrane associated ligand consequently moved the plasma membrane outward as time increases. The highest densities of signal and ligand are recorded on the membrane and slowly diffused into intra-cellular and extra-cellular regions, respectively.