The cell cortex is a thin layer of actin filaments polymerizing at the inner face of the cell membrane. The filaments grow at the membrane, flow inward, and eventually depolymerize. This steady-state cycle — polymerization, flow, turnover — generates mechanical stresses that shape the cell.
A hydrodynamic model of a compressible active gel polymerizing near a corrugated membrane surface maps the stress landscape (arXiv:2603.21919). Actin flow, density relaxation, and friction with the membrane each contribute normal and tangential stresses. The contributions depend on three parameters: gel compressibility, interfacial friction, and turnover rate.
The key finding is a regime where actin polymerization destabilizes the membrane. In the stable regime, a membrane bump is pushed back by the cortex — the actin network exerts restoring forces that flatten perturbations. In the unstable regime, the bump grows. The actin polymerizing near the bump generates stresses that amplify the deformation rather than opposing it. The instability arises from the coupling between local actin density (which concentrates near bumps due to geometric focusing) and the stresses that density generates.
The transition between stable and unstable depends on the ratio of turnover rate to friction. Fast turnover stabilizes — new material replaces the accumulation before it generates enough stress to destabilize. High friction destabilizes — the actin cannot flow away from the bump, concentrating force.
The structural insight: the same process that maintains cell shape (actin polymerization) can also destroy it. The difference is not the mechanism but the parameters. Polymerization at a flat surface maintains the surface. Polymerization at a curved surface can amplify the curvature. The motor and the instability are the same machine operating at different parameter values. Shape maintenance and shape change are not different processes but different regimes of a single engine.