Cooperative effect of local active stresses on the macroscopic contractility of elastic fiber networks

The collective action of actively contractile units embedded in elastic biopolymer networks plays a crucial role in regulating the network's macroscopic mechanical response. Here, we investigate how the macroscopic boundary stress in model elastic fiber networks depends on the number and nature of embedded contractile units, each exerting an isotropic force dipole, as well as on the bending stiffness of fibers. We find that the macroscopic stress increases nonlinearly with the number of dipoles due to mutual stiffening of initially soft, bending-dominated networks. Using effective medium theory, we relate this enhanced contractility to an increase in the effective average network coordination number due to constraints imposed by the force dipoles. By comparing three distinct force dipole models that differ in their local structures, we demonstrate that the specific manner in which an active unit constrains the network strongly influences the onset and nature of the stiffening transition. Our results highlight that not only the quantity but also the local geometry of force-generating units critically determines the macroscopic mechanical behavior. This framework provides a physical basis for understanding how biological systems-such as molecular motors in the cytoskeleton, or adherent cells in the extracellular matrix-can modulate network-scale nonlinear elastic properties through local tuning of active force-generating units.