Advected percolation in the actomyosin cortex drives amoeboid cell motility

Spontaneous locomotion is a common feature of most metazoan cells, generally attributed to the fundamental properties of the actomyosin network. This force-producing machinery has been studied down to the most minute molecular details, especially in lamellipodium-driven migration. Nevertheless, how actomyosin networks work inside contraction-driven amoeboid cells still lacks unifying principles. Here, using stable motile blebs as a model amoeboid motile system, we image the dynamics of the actin cortex at the single filament level and reveal the co-existence of three phases of the actin network with distinct rheological properties. Physical modelling shows that these three phases organize spontaneously due to a rigidity percolation transition combined with an active advection of the percolated network. This spontaneous spatial organization of the mechanical properties of the actin network, which we propose to call advected percolation, constitutes a minimal and generic locomotion mechanism. It explains, down to the single actin filament level and up to the scale of the entire cell, how amoeboid cells can propel efficiently through complex 3D environments, a feature shared by immune and cancer cells.