LAUSR

Knotting is a prevalent phenomenon which occurs at the macroscale (e.g., in headphone cords) and at the microscale (e.g., in DNA and proteins). For a confined polymer, the knotting probability can rapidly approach 100% as the degree of confinement increases, while the mechanism of knot formation in a confined space is unclear. In this work, we use computer simulation to generate equilibrium conformations of a polymer confined in a sphere or a tube and then calculate the knotting probability, pknot, and the knot complexity that is quantified by the minimal crossing number, Ncross. Surprisingly, we find a universal correlation between pknot and ⟨Ncross⟩. Further analysis reveals that the universal correlation is caused by the fact that the distribution of knot types, i.e., the knot spectrum, of a confined polymer follows a universal behavior, only depending on the total knotting probability, regardless of the polymer length, bending stiffness, and degree of confinement. Such universal behavior reveals a pos...