Mechanosensitive Remodeling Sustains Rigidity Homeostasis and Elastic Memory in Actin Cortex Models

The actin cortex is a dynamic biopolymer network that, despite constant architectural changes through the assembly and disassembly of filaments and crosslinkers, sustains a rigid homeostatic state, i.e., a steady state of positive elastic moduli, and exhibits an elastic memory that far outlasts the structural turnover time scale. We still lack simple models that maintain collective rigidity and elastic memory at long times compared to the turnover time. To address this, we develop two complementary elastic network models in which rigidity homeostasis and long-lived elastic memory with complete turnover emerge as a result of mechanosensitive dynamics of filaments (edges) and crosslinkers (nodes), respectively. Both models require the following minimal ingredients: (1) preferential disassembly of edges or nodes under small tension or force, (2) a small but nonzero rate of random disassembly, and (3) energy injection upon assembly. Our models are robust to variations in random disassembly rates, can recover from drastic structural disruption, and exhibit diffusion of nodes and edges in steady state, displaying representational drift similar to that found in neuronal activities and physical learning circuits. We propose that the cortex is an example of "tunable matter," i.e., its mechanosensitive remodeling dynamics tune properties of its edges and nodes so that the cortex as a whole can maintain robust but flexible rigidity in fluctuating mechanical environments.