(342c) Mobility of Knots in Tensioned Polymer Chains

In the limit of very long chains, coiled polymers almost always self-entangle and form knots.  In this study, we characterize the motion of these knots while the chain is under tension, as this problem gives insight into the physics of jamming as entangled DNA passes through pores.  We perform Brownian dynamics simulations to examine two regimes:  the moderate tension regime (Fl_p/kT ~ O(1) ) and the tightly jammed regime (Fl_p/kT >> 1), where F is the tension on the polymer, l_p is the persistence length, and kT is the temperature.  In the moderate tension regime, the knot diffuses smoothly along the chain in a manner akin to reptation.  Its mobility is a non-monotonic function of tension due to two competing effects:  as the tension increases, the drag on the knot decreases due to decreasing knot size, but its motion becomes hindered due to fewer entropic configurations.  In the strong tension regime, the knot makes discrete hops and its mobility decreases exponentially in a manner similar to a strong glass.  We develop a coarse-grained 1D model to describe the essential physics behind these transitions, and determine how other interactions such as electrostatics change this motion.  We conclude our talk by describing how this information can guide us in developing better strategies for polymer manipulation in biotechnology applications such as next-generation sequencing.