Mathematical modeling of invadopodia formation.

In invasive cancer cells, specialized sub-cellular membrane structures which carry out a pivotal process in cancer invasion, termed invadopodia, are observed. Invadopodia appear irregularly within the cytoplasm and their general shape is small punctuated finger-like protrusions with dimension up to several μm long. They may exist and persist on a timescale between several tens of minutes to one hour. The formation of invadopodia requires the integration of several processes that include actin reorganization, extracellular matrix (ECM) degradation, signaling processes through receptors such as the epidermal growth factor receptor (EGFR) and matrix metalloproteinase (MMP) synthesis and delivery to the location of the invading front. In this paper, we consider a mathematical model investigating the coupling of these fundamental processes, and we investigate how invadopodia appear in this model. We investigate the spatio-temporal dynamics of the model in two spatial dimensions by using numerical computational simulations. We show that in a special parameter region of the model, random fluctuations of ECM degradation and a positive feedback loop regarding the up-regulation of MMPs allow us to reproduce finger-like protrusions which have similar size and lifetime as invadopodia. This study provides a new insight into how invadopodia appear in cancer cells and why space and time scales exist for invadopodia. Copyright Â