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Pulling a DNA molecule through a nanopore embedded in an anionic membrane: tension propagation coupled to electrostatics

We consider the influence of electrostatic forces on driven translocation dynamics of a flexible polyelectrolyte being pulled through a nanopore by an external force on the head monomer. To this end, we augment the iso-flux tension propagation (IFTP) theory with electrostatics for a negatively charged biopolymer pulled through a nanopore embedded in a similarly charged anionic membrane. We show that for the realistic case such as a single-stranded DNA, the translocation dynamics at low salt where screening is weak and at finite negative membrane charge is unexpectedly accelerated despite the large repulsive electrostatic interactions between the polymer coil on the {\it cis} side and the charged membrane. This is due to the rapid release of the electrostatic potential energy of the coil during translocation, leading to an effectively attractive force that assists end-driven translocation. The speedup results in non-monotonic polymer length and membrane charge dependence of the exponent $α$ characterizing the translocation time $τ\propto N_0^α$ of the polymer with length $N_0$. In the regime of long polymers $N_0\gtrsim500$, the translocation exponent exceeds its upper limit $α=2$ previously observed for the same system without electrostatic interactions.