Spiral and helical formation of passive and active polymers with stiffness heterogeneity in a spherical cavity.

Biomolecules usually adopt ubiquitous circular structures which are important for their functionality. Based on three-dimensional Langevin dynamics simulations, we investigate the conformational change of a polymer confined in a spherical cavity. Both passive and active polymers with either homogeneous or heterogeneous stiffness are analyzed in a comparative manner. For a homogeneous chain, continuous rigidity along the backbone promotes a flat spiral expanding along the cavity surface, while activity-induced softening results in a less-ordered spiral structure. Stiffness heterogeneity basically plays a destructive role in spiral formation. However, as the chain is endowed with activity, the heterogeneity effect depends on the stiffness of the front edge of the chain. As the head is rigid, the flat spiral largely holds, whereas such a structure easily loses as the head is flexible. More intriguingly, a short flexible head induces a distinct compact helix in the interior of the cavity. Under low friction conditions, the prominent inertial effect leads to the break-up of both spiral and helix. In the presence of crowding, the flat spiral close to the surface keeps its stability, while the compact helix inside tends to be dissolved. Our results decipher the significant effects of activity, rigidity, confinement and crowding on modulating polymer conformations, which provides a deeper insight about mechanisms for circular structure formation of biopolymers in crowded environments.