Continuum model of actin-myosin flow

The front part of a cell is divided to two regions called lamellum and lamellipodium (lamellipodial). This part plays an essential role for cell migration. Indeed, there are many protein filaments called actin in lamellum and lamellipodium, which induce the cell motion with polymerization in the leading edge of the cell. The actin filaments adhere to the extracellular matrix (ECM) by means of focal adhesions and they have contact by myosin motor proteins. The myosin motor proteins cause actin retrograde and anterograde flow exerted contractile stress on them. The focal adhesions exert frictional stress on the actin filaments. In this work, we developed a two-dimensional continuum model of the fan-shaped lamellipodial to obtain the actin retrograde flow. In addition, the actin filaments are assumed as a highly viscous Newtonian fluid. We also investigated the effects of the myosin distribution and cell speed on the actin flow.