Entropic Tug of War: Topological Constraints Spontaneously Rectify the Dynamics of a Polymer with Heterogeneous Fluctuations

Polymers with active segments constitute prospective future materials and are used as a model for some biological systems such as chromatin. The directions of the active forces are typically introduced with temporal or spatial correlations to establish directional motion of the chain and corresponding active dynamics. Instead, here we consider an active-passive copolymer, where the two segments differ only by the magnitude of their fluctuations and feature no artificial correlations. Here we show that although the model itself does not possess directional dynamics, if the chains are concentrated, directional persistent motion spontaneously arises as a consequence of the broken translational symmetry owing to the topological constraints. Using scaling arguments and simulations, we explain the phenomenon and describe the ensuing dynamics. Our work has thus far-reaching consequences for the mechanical properties of all dense active polymeric systems with heterogeneous fluctuations and in particular for chromatin conformation and dynamics that are crucial for biological functionality.