Polymer escape through a three dimensional Double-Nanopore System

We study escape dynamics of a double-stranded DNA (dsDNA) through an idealized double nanopore (DNP) geometry subject to two equal and opposite forces (tug-of-war) using Brownian dynamics (BD) simulation. In addition to the geometrical restrictions imposed on the cocaptured dsDNA segment in between the pores, the presence of tug-of-war forces at each pore results in a variation of the local chain stiffness for the segment of the chain in between the pores which increases the overall stiffness of the chain. We use BD simulation results to understand how the intrinsic chain stiffness and the TOW forces affect the escape dynamics by monitoring the local chain persistence length $\ell_p$, the residence time of the individual monomers $W(m)$ in the nanopores, and the chain length dependence of the escape time $\langle \tau \rangle$ and its distribution. Finally, we generalize the scaling theory for the unbiased single nanopore translocation for a fully flexible chain for the escape of a semi-flexible chain through a DNP in presence of TOW forces. We establish that the stiffness dependent part of the escape time is approximately independent of the translocation mechanism so that $\langle \tau \rangle \sim \ell_p^{2/D+2}$, and therefore the generalized escape time for a semi-flexible chain can be written as $\langle \tau \rangle = AN^\alpha\ell_p^{2/D+2}$. We use BD simulation results to compare the predictions of the scaling theory. Our numerical studies supplemented by scaling analysis provide fundamental insights to design new experiments where a dsDNA moves slowly through a series of graphene nanopores.