Pulling a DNA molecule through a nanopore embedded in a charged membrane: tension propagation against 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 an anionic biopolymer pulled through a nanopore embedded in a cationic membrane. We show that for the realistic case of an anionic polyelectrolyte such as a single-stranded DNA, the translocation dynamics at low salt where screening is weak and at finite positive membrane charge, is governed by the attractive electrostatic interactions between the polymer coil on the {\it cis} side and the charged membrane. These interactions result in a non-monotonic polymer length and membrane charge dependence of the exponent $\alpha$ characterizing the translocation time $\tau \propto N_0^\alpha$ of the polymer with length $N_0$. Due to the same electrostatic polymer-membrane coupling, in the regime of long polymers $N_0\gtrsim500$, the translocation exponent exceeds its upper limit $\alpha=2$ previously observed for the same system without electrostatic interactions.