Multiscale modelling of active hydrogel elasticity driven by living polymers: softening by bacterial motor protein FtsZ

We present a neo-Hookean elasticity theory for hybrid mechano-active hydrogels, integrating motor proteins into polymer meshes to create composite materials with active softening due to modulable chain overlaps. Focusing on polyacrylamide (PA) hydrogels embedded with FtsZ, a bacterial cytokinetic protein powered by GTP, we develop a multiscale model using microscopic Flory theory of rubbery meshes through mesoscopic De Gennes' scaling concepts for meshwork dynamics and phenomenological Landau's formalism for second-order phase transitions. Our theoretical multiscale model explains the active softening observed in hybrid FtsZ-PA hydrogels by incorporating modulable meshwork dynamics, such as overlapping functionality and reptation dynamics, into an active mean-field of unbinding interactions. The novel FtsZ-based metamaterial and companion multiscale theory offer insights for designing, predicting, and controlling complex active hydrogels, with potential applications in technology and biomedicine.