Riding the wave: Polymers in time-dependent nonequilibrium baths

Directed transport is a characteristic feature of numerous biological systems in response to signals such as nutrient and chemical gradients. These signals often depend on time owing to the high complexity of interactions in these systems. In this study, we focus on the steady-state behavior of polymeric systems responding to such time-dependent signals. We model them as ideal Rouse polymers submerged in a nonequilibrium bath, which is described by a spatially and temporally varying self-propulsion wave field. Through a coarse-graining analysis, we show that these polymers display rich emergent response to the temporal stimuli as a function of their length and topology. In particular, long polymers and structures with ring and star topologies ride the wave, displaying a positive drift in the direction of the wave, whereas shorter polymers and fully connected structures drift against the wave signal. We confirm these analytical predictions with robust numerical simulations, showing that the response of polymeric systems to temporal stimuli can be controlled by the topology or the length of the polymer.