On the distribution of DNA translocation times in solid-state nanopores: an analysis using Schrodinger's first-passage-time theory

In this short paper, a correction is made to the recently proposed solution of Li and Talaga to a 1D biased diffusion model for linear DNA translocation, and a new analysis will be given to their data. It was pointed out by us recently that this 1D linear translocation model is equivalent to the one that was considered by Schrodinger for the Ehrenhaft-Millikan measurements on electron charge. Here, we apply Schrodinger's first-passage-time distribution formula to the data set in Li and Talaga. It is found that Schrodinger's formula can be used to describe the time distribution of DNA translocation in solid-state nanopores. These fittings yield two useful parameters: the drift velocity of DNA translocation and the diffusion constant of DNA inside the nanopore. The results suggest two regimes of DNA translocation: (I) at low voltages, there are clear deviations from Smoluchowski's linear law of electrophoresis, which we attribute to the entropic barrier effects; (II) at high voltages, the translocation velocity is a linear function of the applied electric field. In regime II, the apparent diffusion constant exhibits a quadratic dependence on the applied electric field, suggesting a mechanism of Taylor-dispersion effect likely due the electro-osmotic flow field in the nanopore channel. This analysis yields a dispersion-free diffusion constant value of 11.2 nm(2) mu s(-1) for the segment of DNA inside the nanopore, which is in quantitative agreement with the Stokes-Einstein theory. The implication of Schrodinger's formula for DNA sequencing is discussed.