Untying of Complex Knots on Stretched Polymers in Elongational Fields

Knotting is a prevalent phenomenon which occurs in long polymer chains. We perform Brownian dynamics simulations and single-molecule DNA experiments to investigate knot untying in elongational fields that is induced by the knot being convected off the chain. The change in knot size as the knot moves off the chain and unties causes a change in the effective Weissenberg number, which in turn leads to a change in chain extension. Large-scale chain conformational changes are observed in both simulations and experiments for complex knots at low Weissenberg numbers (Wi). We investigate the knot untying time and untying-induced change in extension for a range of knot types and field strengths. Simulations predict a quadratic relationship between the change in extension due to knot untying and initial knot size for Wi ≥ 1.5. Due to the changes in chain extension as a knot unties, the untying process can be diffusion- or convection-driven.