Mechanical stress induced by the polymerisation of an active gel near a surface

Actin flow in the cortical cytoskeleton underneath the cell membrane generates mechanical stresses that shape the cell surface. We study this mechanism using an hydrodynamic model of a compressible active gel polymerising at the membrane and undergoing turnover. We determine how actin flow, density relaxation and friction of actin with the membrane generate stress on a corrugated membrane at the linear order in deformation. Analytical solutions in limiting regimes, combined with finite element methods in the general case, provide a map of normal and tangential stresses as functions of compressibility, interfacial friction and actin turnover, and determine the conditions under which actin polymerisation can render the membrane linearly unstable. The non-linear regime is also briefly discussed.