Metastable Knots in Confined Semiflexible Chains

Abstract

We study the size distribution of spontaneous knots on semiflexible chains confined in square cross-section channels using Monte Carlo simulations. The most probable knot size, i.e. the metastable knot size, is found to vary nonmonotonically with the channel size. In the case of weak confinement, the metastable knot size is larger than the knot size in bulk because the segments within the knot feel less channel confinement than the segments outside the knot, and the channel pushes the segments into knot cores to reduce the overall free energy. Conversely, in the case of strong confinement, the metastable knot size is smaller than the one in bulk because the segments within the knot experience more channel confinement, and the channel expels segments from the knot core. We demonstrate that a simple theory can capture this nonmonotonic behavior and quantitatively explain the metastable knot size as a function of the channel size. These results may have implications for tuning the channel size to either generate or screen knots.