Tug-of-War in a Double-Nanopore System

We simulate a tug-of-war (TOW) scenario for a model double-stranded DNA threading through a double nanopore (DNP) system. The DNA, simultaneously captured at both pores is subject to two equal and opposite forces $-\vec{f}_L= \vec{f}_R$ (TOW), where $\vec{f}_L$ and $\vec{f}_R$ are the forces applied to the left and the right pore respectively. Even though the net force on the DNA polymer $\Delta \vec{f}_{LR}=\vec{f}_L+ \vec{f}_R=0$, the mean first passage time (MFPT) $\langle \tau \rangle$ depends on the magnitude of the TOW forces $\left | f_L \right | = \left |f_R \right | = f_{LR}$. We qualitatively explain this dependence of $\langle \tau \rangle$ on $f_{LR}$ from the known results for the single-pore translocation of a triblock copolymer. We demonstrate that the time of flight (TOF) of a monomer with index $m$ ($\langle \tau_{LR}(m) \rangle$) from one pore to the other exhibits quasi-periodic structure commensurate with the distance between the pores $d_{LR}$. Finally, we study the case $\Delta \vec{f}_{LR}=\vec{f}_L+ \vec{f}_R \ne 0$, and qualitatively reproduce the experimental result of the dependence of the MFPT on $\Delta\vec{f}_{LR}$. For a moderate bias, the MFPT for the DNP system for a chain length $N$ follows the same scaling ansatz as that of for the single nanopore, $\langle \tau \rangle = \left( AN^{1+\nu} + \eta_{pore}N \right) \left(\Delta f_{LR}\right)^{-1}$, where $\eta_{pore}$ is the pore friction, which enables us to estimate $\langle \tau \rangle$ for a long chain. Our Brownian dynamics simulation studies provide fundamental insights and valuable information about the details of the translocation speed obtained from $\langle \tau_{LR}(m) \rangle$, and accuracy of the translation of the data obtained in the time-domain to units of genomic distances.