Free Energy and Diffusivity in the Fokker–Planck Theory of Polymer Translocation

A robust theoretical framework describing polymer translocation through nanopores is important for developing novel applications of nanopore technology in single-molecule characterization of biological and synthetic polymers. In this work, we revisit the Fokker–Planck based theory of driven polymer translocation through a narrow nanopore. A bead–spring model of a uniformly charged polyelectrolyte chain translocating through a semi-implicit model of a nanopore embedded in a membrane are used to gain insights into the underlying free energy landscape and kinetics of translocation. The free energy landscape is predicted using metadynamics simulation, an enhanced sampling method. A direct comparison with the theoretical free energy formulation proposed in the literature allows us to introduce a modification related to the entropic contribution in the theory. Additional classical Langevin dynamics simulation runs are performed to obtain the translocation time distribution for polymers of lengths N driven by voltages V through nanopores of radii rp. In agreement with earlier reports, a scaling of the mean translocation time ⟨τLD⟩ ∼ Nα/V is observed, with α ∼ 1.40–1.48 depending on the nanopore size. Fitting the mean exit time ⟨τFP⟩ given by the Fokker–Planck theory to Langevin dynamics simulation results helps gain insights into the diffusivity kFP used in the theory. We report a peculiar variation of kFP with N in the range of N and rp studied, which significantly deviates from the Rouse prediction of kFP ∼ N–1 for the center-of-mass diffusivity of a polymer chain. Predictions from the modified theory agree with several experimentally observed scaling results in the literature. The theoretical framework can be utilized in developing nanopore technology for molecular characterization and selective separation of polymers.