  Polymer topology, which plays a principal role in the rheology of polymeric
fluids, and non-equilibrium materials, which exhibit time-varying rheological
properties, are topics of intense investigation. Here, we push composites of
circular DNA and dextran out-of-equilibrium via enzymatic digestion of DNA
rings to linear fragments. Our time-resolved rheology measurements reveal
discrete state-switching, with composites undergoing abrupt transitions between
dissipative and elastic-like states. The gating time and lifetime of the
elastic-like states, and the magnitude and sharpness of the transitions, are
surprisingly decorrelated from digestion rates and non-monotonically depend on
the DNA fraction. We model our results using sigmoidal two-state functions to
show that bulk state-switching can arise from continuous molecular-level
activity due to the necessity for cooperative percolation of entanglements to
support macroscopic stresses. Our platform, coupling the tunability of
topological composites with the power of enzymatic reactions, may be leveraged
for diverse material applications from wound-healing to self-repairing
infrastructure.
