On the distribution of DNA translocation times in solid-state nanopores: an analysis using Schrödinger'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 Schrödinger for the Ehrenhaft­Millikan measurements on electron charge. Here, we apply Schrödinger's first-passage-time distribution formula to the data set in Li and Talaga. It is found that Schrödinger'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 nm2 µs-1 for the segment of DNA inside the nanopore, which is in quantitative agreement with the Stokes­Einstein theory. The implication of Schrödinger's formula for DNA sequencing is discussed.