Topological entanglement of interlocked knotted-unknotted polymer rings.

Topological entanglements in biopolymers could drive them to certain internal statics and dynamics with important implications for biological functions. In this study, by means of molecular dynamics simulations, we demonstrate that the minimal crossing pattern of a braid plays a major role in its structural and dynamical properties; the braid consists of a knotted ring and an interlocked entwined unknotted polymer ring. In particular, we show that depending on the bending rigidity of the chains, the conformational energy of the braid can be either lower or higher than the unlocked polymer rings. Additionally, we find that a non-identical crossing pattern in the braid could distinctly enforce concerted internal conformational fluctuations between the interlocked rings.