Title: Rigidity Homeostasis of the Actin Cortex via Tension-Sensitive Filament and
Crosslinker Dynamics

Abstract:The actin cortex is a biopolymer network that maintains mechanical rigidity despite constant structural changes through assembly and disassembly of filaments and crosslinkers. The biological advantage of this energy-intensive remodeling, as well as the microscopic mechanisms underlying rigidity homeostasis, remains unclear. To address these questions, we have developed two independent elastic network models that achieve rigidity homeostasis while undergoing complete architectural turnover, capturing filament and crosslinkers dynamics, respectively. We find that both models require the following minimal ingredients: (1) preferential disassembly of edges or nodes that are under small tension or force, (2) a small fraction of random disassembly, and (3) energy injection upon assembly. The trajectories toward steady states are analyzed with graph-theoretical metrics to reveal the relationship between rigidity and network topology. Remarkably, we find that the edges in our networks undergo diffusion, whereas the elastic moduli and structural correlations remain statistically invariant, analogous to the representational drift found in learning systems in which the architecture self-adjust via local rules. We hypothesize that the cortex functions as a tunable matter, where remodeling dynamics enables the cell to balance robustness and flexibility in fluctuating mechanical environments, creating survival advantages that justify the energy consumption. Our models provide platforms to design and study bio-inspired tunable metamaterials.