Physical model for membrane protrusions during spreading

During cell spreading onto a substrate, the kinetics of the contact area is an observable quantity. This paper is concerned with a physical approach to modeling this process in the case of ameboid motility where the membrane detaches itself from the underlying cytoskeleton at the leading edge. The physical model we propose is based on previous reports which highlight that membrane tension regulates cell spreading. Using a phenomenological feedback loop to mimic stress-dependent biochemistry, we show that the actin polymerization rate can be coupled to the stress which builds up at the margin of the contact area between the cell and the substrate. In the limit of small variation of membrane tension, we show that the actin polymerization rate can be written in a closed form. Our analysis defines characteristic lengths which depend on elastic properties of the membrane-cytoskeleton complex, such as the membrane-cytoskeleton interaction, and on molecular parameters, the rate of actin polymerization. We discuss our model in the case of axi-symmetric and non-axi-symmetric spreading and we compute the characteristic time scales as a function of fundamental elastic constants such as the strength of membrane-cytoskeleton adherence.