Size-dependent transition from steady contraction to waves in actomyosin networks with turnover

Actomyosin networks play essential roles in many cellular processes, including intracellular transport, cell division and cell motility, and exhibit many spatiotemporal patterns. Despite extensive research, how the interplay between network mechanics, turnover and geometry leads to these different patterns is not well understood. We focus on the size-dependent behaviour of contracting actomyosin networks in the presence of turnover, using a reconstituted system based on cell extracts encapsulated in water-in-oil droplets. We show that the system can self-organize into different global contraction patterns, exhibiting persistent contractile flows in smaller droplets and periodic contractions in the form of waves or spirals in larger droplets. The transition between continuous and periodic contraction occurs at a characteristic length scale that is inversely dependent on the network contraction rate. These dynamics are captured by a theoretical model that considers the coexistence of different local density-dependent mechanical states with distinct rheological properties. The model shows how large-scale contractile behaviours emerge from the interplay between network percolation, which is essential for long-range force transmission, and rearrangements due to advection and turnover. Our findings thus demonstrate how varied contraction patterns can arise from the same microscopic constituents, without invoking specific biochemical regulation, merely by changing the system geometry.