Electrostatics of polymer translocation through membrane nanopores in electrolyte solutions

Abstract

The transport of polymers across membranes in electrolyte solutions happens in most biological systems and is necessary for cells to function. Moreover, the poly-mer translocation process has proven to be very important in experiments and applications as well, providing a rich source of information about the polymer’s size and composition [1], [2], making the polymer translocation procedure a po-tential sequencing method that is efficient, cheap, and quick [3], [4]. However, no consensus on the theoretical understanding of the translocation mechanism has been reached yet [3], leaving it a major challenge for theoretical modelling due to its steric, hydrodynamic, and electrostatic interactions [2], [5]. Here, we calculate the electrostatic energy cost of the translocating polymer in both the approach and translocation phases and investigate the dependence of the poly-mer’s grand potential on different model tunable parameters. In the case of neu-tral membranes, low permittivity carbon-based membranes repel the approaching polymer with energy magnitude between ∼ 11 kBT and ∼ 27 kBT , while high permittivity engineered membranes attract the approaching polymer with almost the same energy magnitude. This behavior can be attributed to polymer image-charge interactions, which become amplified with low permittivity membranes. In strong salt solutions, the membrane exhibits a repulsive barrier that turns to a metastable well in dilute solutions. In pure solvents, the metastable well becomes a deep, stable well that traps the polymer in the pore for some time, where the translocation phase is mainly governed by the attractive trans-cis side interac-tion. For weakly charged membranes, the membrane charge attraction wins over the image-charge repulsion, leading to an attractive minimum at zt ≈ −1 nm followed by a repulsive barrier at lt = L/2 while for stronger membrane charges, the attractive well turns to a metastable point followed by an attractive, stable well. These results suggest that, in translocation experiments, DNA motion can be controlled by tuning the system parameters, such as the solution concentration or the membrane charge.