Poisson-Fokker-Planck model for biomolecules translocation through nanopore driven by electroosmotic flow

A non-continuous electroosmotic flow model (PFP model) is built based on Poisson equation, Fokker-Planck equation and Navier-Stokse equation, and used to predict the DNA molecule translocation through nanopore. PFP model discards the continuum assumption of ion translocation and considers ions as discrete particles. In addition, this model includes the contributions of Coulomb electrostatic potential between ions, Brownian motion of ions and viscous friction to ion transportation. No ionic diffusion coefficient and other phenomenological parameters are needed in the PFP model. It is worth noting that the PFP model can describe non-equilibrium electroosmotic transportation of ions in a channel of a size comparable with the mean free path of ion. A modified clustering method is proposed for the numerical solution of PFP model, and ion current translocation through nanopore with a radius of 1 nm is simulated using the modified clustering method. The external electric field, wall charge density of nanopore, surface charge density of DNA, as well as ion average number density, influence the electroosmotic velocity profile of electrolyte solution, the velocity of DNA translocation through nanopore and ion current blockade. Results show that the ion average number density of electrolyte and surface charge density of nanopore have a significant effect on the translocation velocity of DNA and the ion current blockade. The translocation velocity of DNA is proportional to the surface charge density of nanopore, and is inversely proportional to ion average number density of electrolyte solution. Thus, the translocation velocity of DNAs can be controlled to improve the accuracy of sequencing by adjusting the external electric field, ion average number density of electrolyte and surface charge density of nanopore. Ion current decreases when the ion average number density is larger than the critical value and increases when the ion average number density is lower than the critical value. Our numerical simulation shows that the translocation velocity of DNA given by the PFP model agrees with the experimental, results better than that given by PNP model or PB model.