Distinct connectivity states in actomyosin networks described using the Flory-Stockmayer theory.*

Actomyosin networks are active systems with a central role in mechanical interactions between the cell and its environment. Actomyosin networks are formed by actin filaments, myosin motors, and actin-binding proteins (ABPs) such as α-actinin and Arp2/3. ABPs allow the transformation of small independent movements of myosin motors into large-scale motions in the actomyosin networks by connecting actin filaments together. The influence of the connectivity of actomyosin networks on the structure, rheology and mechanics of the network has been previously studied experimentally and using coarse-grained molecular simulations.
In this work we model the actomyosin networks using the Flory-Stockmayer theory to describe the conditions under which connectivity percolation occurs. We also compare our model to a mechanochemical coarse-grained model of actomyosin networks. We find that the connectivity of the network is modulated by Arp2/3 in a non-monotonic way. Finally, we relate the connectivity percolation to the rigidity percolation and propose different connectivity states that give rise to distinct behaviors of the actomyosin network.