(A) Mass conservation is related to cell boundary movement. There is a velocity field, v(x, t ), within the shaded region representing the material in consideration. The boundary of the material can move from mass fluxes at the boundary J1,2. Cells build actin filaments from actin monomers; therefore the actin network can extend and retracting according monomer fluxes. (B) For a moving cell with a flat and broad lamellipodium, there is a polymerizing actin network at the leading edge. Mass flux of actin monomers (G-actin) increases F-actin network mass and drives membrane protrusion.