Abstract
The degradation of the extracellular matrix is driven by actin-based protrusions known as invadopodia, lead to the cancer cell invasion across the surrounding tissue barriers. Signal transduction through the binding between ligand and membrane associated receptor is important in order to establish the actin polymerization, and consequently push the membrane of migrating cells. In this study, we considered one-dimensional Stefan-like problem of the signal transduction and cell membrane is treated as a free boundary surface to separate any activity that happened on intra- and extra-cellular regions. The velocity concerning the movement of the free boundary is calculated by the decrease of signal gradient on the front. The problem is solved numerically using finite-difference scheme of fixed-domain method. Our results showed that both free boundary positions and signal distributions are increasing as time progresses.
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