Simulations of the untying of molecular friction knots between individual polymer strands

The dynamics of molecular knots is implicated in a broad range of phenomena, from DNA replication to relaxation of polymer melts. Motivated by the recent experiments, in which biopolymer knots have been observed and manipulated at a single-molecule level, we have used computer simulations to study the dynamics of "friction knots" joining individual polymer strands. A friction knot splicing two ropes becomes jammed when the ropes are pulled apart. In contrast, molecular friction knots eventually become undone by thermal motion. We show that depending on the knot type and on the polymer structure, a microscopic friction knot can be strong (the time τ the knot stays tied increases with the force F applied to separate the strands) or weak (τ decreases with increasing F). The strong knot behavior is a microscopic analog of macroscopic knot jamming. We further describe a simple model explaining these behaviors.