Softer when Thicker: a Conserved Scaling Law Governs Actin Cortex Mechanics
Scaling laws are powerful tools in material science to relate geometric and mechanical properties of materials. The actin cortex, a dynamic network beneath the plasma membrane, is essential for cellular morphogenesis, force generation, and tissue organization. Despite its critical role, the mechanical properties of the cortex itself remain poorly understood. Using the magnetic pincher, a new technique we recently developed, we directly measure the thickness (h) and elastic modulus (E) of the actin cortex in live cells, uncovering a universal scaling (E ~ h-2) across multiple cell types. Drawing an analogy to cellular solids, common in nature and material science, we identified an origin for this scaling: the volume fraction of actin filaments varies concomitantly with the cortex thickness, due to a conservation of filamentous actin quantity. Thus thinner cortices exhibit higher actin density and stiffness, while thicker cortices are sparser and softer. The relationship holds under diverse perturbations targeting myosin contractility, actin nucleation, and turnover, but is lost upon actin disassembly, highlighting its dependence on the intact actin network. Our results establish that cells, across cell types, function within a rather limited range of quantity of cortical actin filaments and primarily modulate cortex thickness to tune mechanical properties, with profound implications for cell shape regulation, tissue mechanics, and the interpretation of indentation-based mechanical measurements.