Active regeneration unites high- and low-temperature features in cooperative self-assembly

Cytoskeletal filaments are capable of self-assembly in the absence of externally supplied chemical energy, but the rapid turnover rates essential for their biological function require a constant flux of adenosine triphosphate (ATP) or guanosine triphosphate (GTP) hydrolysis. The same is true for two-dimensional protein assemblies employed in the formation of vesicles from cellular membranes, which rely on ATP-hydrolyzing enzymes to rapidly disassemble upon completion of the process. Recent observations suggest that the nucleolus, p granules, and other three-dimensional membraneless organelles may also demand dissipation of chemical energy to maintain their fluidity. Cooperative binding plays a crucial role in the dynamics of these higher-dimensional structures, but is absent from classic models of one-dimensional cytoskeletal assembly. In this paper, we present a thermodynamically consistent model of active regeneration with cooperative assembly, and compute the maximum turnover rate and minimum disassembly time as a function of the chemical driving force and the binding energy. We find that these driven structures resemble different equilibrium states above and below the nucleation barrier. In particular, we show that the maximal acceleration under large binding energies unites infinite-temperature local fluctuations with low-temperature nucleation kinetics.