Lamellipodia in Stationary and Fluctuating States

We review recent mathematical models describing the diffusive transport, reaction, and turnover of actin and regulators at the leading edge of motile cells. These models are motivated by experimental results using cells with flat, steady lamellipodia studied by Single Molecule Speckle microscopy. The same cells can also be made to exhibit protruding and retracting lamellipodia, which demonstrate how changes in actin polymerization lead to changes in the rate of protrusion. The second part of this chapter provides a description of these fluctuations as an excitable actin system pushing against the cell membrane by polymerization.