DNA translocation through polyelectrolyte-modified nanopores: An analytical approximation.

An analytical model for the electrophoretic speed of DNA translocating through nanopore functionalized with polyelectrolyte (PE) brush is developed for the first time. The electrophoretic speed depends on DNA surface potential, applied electric field, viscosity, and permittivity of solution along with velocity and electrostatic potential at liquid-polyelectrolyte layer (PEL) interface where the interface seemed to behave similar to that of a solid-state nanopore wall. Under the limit of Debye-Hückel linearization, the electrostatic potential at liquid-PEL interface and at DNA surface have been calculated. Velocity at liquid-PEL interface has been estimated by assuming a linear variation of hydrodynamic frictional force within the PEL. It is observed that velocity and electrostatic potential at liquid-PEL interface strongly depend on PE charge density and softness parameter. Present analytical results show excellent agreement with exact numerical results (i.e., without any approximation) at a higher salt concentration where Debye-Hückel linearization is applicable.