The nonequilibrium dynamics of a temporally responsive, single-molecule automaton

Molecules with multiple meta-stable configurations on rough energy landscapes could demonstrate complex hysteresis responses to various temporally changing environments. We argue that such nonequilibrium hysteresis responses could allow a molecule to recognize, memorize, and respond specifically to temporal patterns of a changing environment. Moreover, such molecules could be steered into far-from-equilibrium configurations if the environment is programmed to change according to specific protocols.  We demonstrate both behaviors in a simple solvable model of a linear polymer chain with a temporally controlled end-to-end distance λ(t). A polymer consisting of N foldable segments is modeled by a novel dual-rate master equation over the 2^N possible configurations. With an asymmetric energy landscape for folding/unfolding, we designed a polymer that can function as a molecular timer and temporal pattern recorder. Moreover, we discovered that the evolution of the dominant configuration of the molecule acts like an automaton, which allows us to design driving protocols to steer the molecule into nonequilibrium distributions dominated by any desired configuration.