Untying Knotted DNA with Elongational Flows

We present Brownian dynamics simulations of initially knotted double-stranded DNA molecules untying in elongational flows. We show that the motions of the knots are governed by a diffusion-convection equation by deriving scalings that collapse the simulation data. When being convected, all knots displace nonaffinely, and their rates of translation along the chain are topologically dictated. We discover that torus knots "corkscrew" when driven by flow, whereas nontorus knots do not. We show that a simple mechanism can explain a coupling between this rotation and the translation of a knot, explaining observed differences in knot translation rates. These types of knots are encountered in nanoscale manipulation of DNA, occur in biology at multiple length scales (DNA to umbilical cords), and are ubiquitous in daily life (e.g., hair). These results may have a broad impact on manipulations of such knots via flows, with applications to genomic sequencing and polymer processing.