Actin-myosin force generation and symmetry breaking in the model contractile fiber

Myosin-powered force generation in nonmuscle cells underlies many cell biological processes and is based on contraction of random actin arrays. One of the most prominent examples of such arrays is a contractile fiber - A one-dimensional actin-myosin fiber with focal adhesions at its ends. We explore an active gel model widely used in theoretical biophysics with effective viscous dashpots at the ends of the actin-myosin gel strip as a model for such a fiber. Scaling analysis reveals that three length scales characterize the behavior of the model, which consists of two PDEs describing force balance and myosin transport in the fiber. We use singular perturbation analysis and numerical simulations to investigate how the myosin distribution, actin flow, and contractile force generated by the fiber depend on model parameters and fiber length. The model predicts that the contractile force either increases, with or without saturation, with fiber length, or reaches a maximum at certain length and then decreases in longer fibers, depending on parameters. The model also predicts a nontrivial symmetry-breaking mechanism: In long fibers with strong focal adhesions at the ends, the myosin distribution is not uniform but peak-like, and this peak can aggregate to one of the fiber's ends. We discuss the model's implication for mechanobiology of nonmuscle cells.