Translocation dynamics of knotted polymers under a constant or periodic external field

We perform Brownian dynamics simulations to examine how knots alter the dynamics of polymers moving through nanopores under an external field. In the first part of this paper, we study the situation when the field is constant. Here, knots halt translocation above a critical force with jamming occurring at smaller forces for twist topologies compared to non-twist topologies. Slightly below the jamming transition, the polymer's transit times exhibit large fluctuations. This phenomenon is an example of the knot's molecular individualism since the conformation of the knot plays a large role in the chain's subsequent dynamics. In the second part of the paper, we study the motion of the chain when one cycles the field on and off. If the off time is comparable to the knot's relaxation time, one can adjust the swelling of the knot at the pore and hence design strategies to ratchet the polymer in a controllable fashion. We examine how the off time affects the ratcheting dynamics. We also examine how this strategy alters the fluctuations in the polymer's transit time. We find that cycling the force field can reduce fluctuations near the knot's jamming transition, but can enhance the fluctuations at very high forces since knots get trapped in metastable states during the relaxation process. The latter effect appears to be more prominent for non-torus topologies than torus ones. We conclude by discussing the feasibility of this approach to control polymer motion in biotechnology applications such as sequencing.