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

Abstract

In this short note, a correction is made to the recently proposed solution [1] to a 1D biased diffusion model for linear DNA translocation and a new analysis will be given to the data in [1]. It was pointed out [2] by us recently that this 1D linear translocation model is equivalent to the one that was considered by Schrödinger [3] for the Enrenhaft-Millikan measurements [4,5] on electron charge. Here we apply Schrödinger’s first-passage-time distribution formula to the data set in [1]. 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: drift velocity of DNA translocation and 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 [6] 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 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 for the segment of DNA inside the nanopore which is in agreement with Stokes-Einstein theory quantitatively. The implication of Schrödinger’s formula for DNA sequencing is discussed.

Polymer translocation through nano-pores in vibrating thin membranes

“…The values of τ have been evaluated, together with the errors on the average , from successful translocation events for each state point. In all cases the probability distribution of the translocation times follows a first-time-passage diffusion-like distribution proposed by Ling and Ling43. We show a few examples of our data in Supplementary Fig.…”

Smooth DNA Transport through a Narrowed Pore Geometry

“…The dwell time distributions are asymmetric in shape, and are characterized by sharply increasing peaks at early times followed by broader decays at longer times. The distribution shapes were fit to first-passage time distributions obtained from the 1D Fokker-Planck equation (70,71):…”

“…71,72). Phenomenological estimates of b eff for each pore were based on I O and DI values measured during DNA translocation(73,74) (see the Supporting Material SM-4), whereas L C values were calculated fromFIGURE 1 Single-molecule DNA electrophoresis.…”

Synchronized Optical and Electronic Detection of Biomolecules Using a Low Noise Nanopore Platform

“…44 The length of unfolded 5 kbp DNA is 1.7 µm; the Ling distribution indicated a molecule length of 1.064 µm confirming that molecules were folded during translocation. The mean translocation time and drift velocity were 0.283 ms and 3.76 mm/s, which are in good agreement with literature.…”