  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 ATP or 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
1-dimensional cytoskeletal assembly. In this Letter, we present a
thermodynamically consistent model of actively 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.
