Rigidity homeostasis of actin networks via tension-sensitive crosslinker dynamics

The actin cortex is an actively remodeling biopolymer network that maintains rigidity below the Maxwellian isostatic coordination number and adapts to fluctuating external stresses. This rigidity homeostasis is achieved by prestresses and enzymatic activities that selectively modify the network's topology and geometry based on local mechanical properties. Here, we study how the dynamics of catch-bonding crosslinkers contribute to the rigidity homeostasis. Using a central-force spring network model, we show that force-inhibited node splitting, which mimics unbinding of catch bonds, results in rigid networks at lower coordination numbers than random splitting. Combined with the formation of new crosslinkers via node merging, we create models that achieve steady states with robust elastic moduli across a wide range of the external deformations. We study the topological and geometrical metrics of such networks and compare them to homeostatic networks generated from selective edge moves on tension- and bending-dominated networks, as well as static networks that maximize rigidity found via rational design. Our results establish crosslinker dynamics as a mechanism for physical learning and provide design rules for fabricated biomemetic polymers.