The Dynamics of Tight Knots on Tensioned, Single Polymer Chains

In the limit of very long chains, coiled polymers almost always self-entangle and form knots. Here we perform Brownian dynamics simulations to study the motion of knotted polymers under high tension. In this regime, we find that knots exhibit glass-like dynamics. For example, instead of continuously moving along contour, the knot can occasionally get trapped in long-lived, metastable states. This caging behavior is highly dependent on the friction between self-entanglements, and we characterize how this arrested motion depends on the structure along the polymeric backbone. In short, we find that knot jamming arises from a ‘rough’ energy landscape along the polymer backbone due to short-range (excluded volume) interactions between polymer segments. When the potential wells in this landscape have a depth of several kT, the polymer reptates through the knot in slow, discrete hops. In the second part of the talk, we briefly discuss how this glass-like dynamics could lead to peculiar behaviors in knot relaxation. For example, we find that certain topologies swell normally when the chain’s tension is released, but other topologies remain trapped in a tight conformation for long periods of time before relaxing. We discuss how the backbone ‘roughness’ alters this relaxation process and conclude by mentioning how knot jamming and relaxation could be important in various applications such as nanopore sequencing.