Brownian Dynamics Simulations of Knotted Polymers Moving through Pores Under a Constant or Periodic External Field

Nanopore sequencing is a technique where DNA moves through a pore and base-pair information is read along the chain as a time-varying electric signal. Currently, one hurdle facing this technique is that DNA passes too quickly through the pore, rendering the signal to be noisy. One relatively unexplored idea is to use entanglements like knots to retard the motion of the chain. If the external field is constant, we find that knots jam at the pore’s entrance above a critical tension and halt the polymer’s motion. This by itself may not be surprising, but one can use this information to design strategies to control the polymer’s speed. For example, if one cycles the external field on and off at the relaxation time scale of the knot, one can control the swelling of the knot at the pore’s entrance and ratchet the polymer through the pore. We discuss how knot topology and cycle time affects the polymer’s dynamics, and we further discuss what force regimes lead to large fluctuations in the polymer’s transit times. 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 study here encompasses a rich variety of physics – some phenomena we observe include slip-stick motion, caging, and molecular individualism.