Effective driving force applied on DNA inside a solid-state nanopore

Bo Lu, David P. Hoogerheide, Qing Zhao, and Dapeng Yu

Phys. Rev. E 86, 011921 – Published 23 July 2012

Abstract

A detailed understanding of the origin of the electrophoretic force on DNA molecules in a solid-state nanopore is important for the development of nanopore-based sequencing technologies. Because of the discrepancies between recent attempts to predict this force and both direct and indirect experimental measurements, this topic has been the focus of much recent discussion. We show that the force is predictable to very good accuracy if all of the experimental conditions are accounted for properly. To resolve this issue, we compare the calculation efficiency and accuracy of numerical solutions of Poisson-Boltzmann and Poisson-Nernst-Planck descriptions of electrolyte behavior in the nanopore in the presence of DNA molecules. Two geometries—axially symmetric and cross-sectional—are compared and shown to be compatible. Numerical solutions are carried out on a sufficiently fine mesh to evaluate the viscous drag force acting on DNA inside a silicon nitride nanopore. By assuming the DNA is immobilized in the axial center of the nanopore, the calculation result of this viscous drag force is found to be rather larger than the experimental result. Because the viscous drag force decreases if DNA is closer to the surface of the nanopore, however, the relevant effective driving force is the average over all possible positions of the DNA in the nanopore. When this positional uncertainty is taken into account, the effective driving force acting on DNA inside the nanopore is found to agree very well with the experimental results.

Received 20 March 2012

DOI:https://doi.org/10.1103/PhysRevE.86.011921

Authors & Affiliations

Bo Lu¹, David P. Hoogerheide², Qing Zhao^1,*, and Dapeng Yu^1,†

¹State Key Laboratory for Mesoscopic Physics and Electron Microscopy Laboratory, School of Physics, Peking University, Beijing 100871, People's Republic of China
²Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

^*zhaoqing@pku.edu.cn
^†yudp@pku.edu.cn

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Issue

Vol. 86, Iss. 1 — July 2012

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Images

Figure 1
Schematic depiction of (a) the axially symmetric model and (b) the cross-section model. The inset to (a) magnifies the nanopore region and shows the hourglass geometry of a nanopore. The DNA molecule is a cylinder of one Kuhn length (100 nm) with a 2.2 nm diameter.Reuse & Permissions
Figure 2
Convergence of the effective driving force at fine mesh sizes for various salt concentrations and calculation models. The mesh size is specified at the DNA surface and in the SiN hourglass shape region and is varied from $10^{- 9} m$ to $5 \times 10^{- 12} m$ . The surface charge is $-$ 60 mC/m $^{2}$ and the driving voltage is 100 mV. The dashed line is the Debye length for 1 M KCl. The markers on the curves are the calculation points. The curves of the PB and PNP models at 1 M are indistinguishable on this scale.Reuse & Permissions
Figure 3
Effect of the surface charge and DNA charge at 1 M KCl, 100 mV driving force, and a nanopore surface charge density of $-$ 60 mC/m $^{2}$ . (a) Velocity field inside the nanopore. (b) Counter-ion ( $c$ +, red solid line) and co-ion ( $c$ $-$ , blue dashed line) distributions as a function of position from the DNA surface to the nanopore surface. (c) Electro-osmotic flow velocity profile as a function of position from the DNA surface to the nanopore surface. The vertical dashed lines in (b) and (c) correspond to the Debye length of 1 M KCl.Reuse & Permissions
Figure 4
(a) Effect of surface charge density (PNP and PB distribution) on the effective driving force under 100 mV bias. (b) Effect of nanopore diameter on the effective driving force at various electrolyte concentrations with a surface charge density of $-$ 30 mC/m $^{2}$ and 100 mV bias. The markers on the curves are the calculation points.Reuse & Permissions
Figure 5
The velocity field in a 10-nm-diam nanopore with the DNA molecule at various radial positions: (a) in the center, (b) 1 nm, (c) 2 nm, and (d) 3 nm from the center.Reuse & Permissions
Figure 6
Variation of the effective driving force and probability function $ρ (r)$ with DNA off-center displacement in a nanopore of radius 5 nm. Since DNA itself has a 1.1 nm diameter, we considered the displacement of DNA off the center from 0 to 3.9 nm. The top curves with triangular markers are the force profile (solid) and probability function (dashed) in 100 mM KCl; the bottom curves with circle markers are the force profile in 1 M KCl (solid) and the probability function (dashed). The arrows on each curve point toward the axis for that curve. Note that for both electrolyte concentrations, the DNA molecule is excluded by screened electrostatic repulsion from a region approximately three Debye lengths from the pore wall.Reuse & Permissions

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