Adaptive nonequilibrium design of actin-based metamaterials: fundamental and practical limits of control

The adaptive and surprising emergent properties of biological materials self-assembled in far-from-equilibrium environments serve as an inspiration for efforts to design nanomaterials and their properties. In particular, controlling the conditions of self-assembly can modulate material properties, but there is no systematic understanding of either how to parameterize this control or how emph{controllable} a given material can be. Here, we demonstrate that branched actin networks can be encoded with extit{metamaterial} properties by dynamically controlling the applied force under which they grow, and that the protocols can be selected using multi-task reinforcement learning. These actin networks have tunable responses over a large dynamic range depending on the chosen external protocol, providing a pathway to encoding ``memory'' within these structures. Interestingly, we show that encoding memory requires dissipation and the rate of encoding is constrained by the flow of entropy -- both physical and information theoretical. Taken together, these results emphasize the utility and necessity of nonequilibrium control for designing self-assembled nanostructures.