Constrained motion of self-propelling eccentric disks linked by a spring.

It has been supposed that the interplay of elasticity and activity plays a key role in triggering the non-equilibrium behaviors in biological systems. However, the experimental model system is missing to investigate the spatiotemporally dynamical phenomena. Here, a model system of an active chain, where active eccentric-disks are linked by a spring, is designed to study the interplay of activity, elasticity, and friction. Individual active chain exhibits longitudinal and transverse motions; however, it starts to self-rotate when pinning one end and self-beat when clamping one end. In addition, our eccentric-disk model can qualitatively reproduce such behaviors and explain the unusual self-rotation of the first disk around its geometric center. Furthermore, the structure and dynamics of long chains were studied via simulations without steric interactions. It was found that a hairpin conformation emerges in free motion, while in the constrained motions, the rotational and beating frequencies scale with the flexure number (the ratio of self-propelling force to bending rigidity), χ, as ∼(χ)4/3. Scaling analysis suggests that it results from the balance between activity and energy dissipation. Our findings show that topological constraints play a vital role in non-equilibrium synergy behaviors.