Ion current rectification, limiting and overlimiting conductances in nanopores.

Liesbeth Van Oeffelen,Gustaaf Borghs,Daniel Charlier,Liesbet Lagae,Willem Van Roy,Hosni Idrissi

doi:10.1371/journal.pone.0124171

Liesbeth Van Oeffelen, Gustaaf Borghs + Show 4 more

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https://doi.org/10.1371/journal.pone.0124171

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Abstract

Previous reports on Poisson-Nernst-Planck (PNP) simulations of solid-state nanopores have focused on steady state behaviour under simplified boundary conditions. These are Neumann boundary conditions for the voltage at the pore walls, and in some cases also Donnan equilibrium boundary conditions for concentrations and voltages at both entrances of the nanopore. In this paper, we report time-dependent and steady state PNP simulations under less restrictive boundary conditions, including Neumann boundary conditions applied throughout the membrane relatively far away from the nanopore. We simulated ion currents through cylindrical and conical nanopores with several surface charge configurations, studying the spatial and temporal dependence of the currents contributed by each ion species. This revealed that, due to slow co-diffusion of oppositely charged ions, steady state is generally not reached in simulations or in practice. Furthermore, it is shown that ion concentration polarization is responsible for the observed limiting conductances and ion current rectification in nanopores with asymmetric surface charges or shapes. Hence, after more than a decade of collective research attempting to understand the nature of ion current rectification in solid-state nanopores, a relatively intuitive model is retrieved. Moreover, we measured and simulated current-voltage characteristics of rectifying silicon nitride nanopores presenting overlimiting conductances. The similarity between measurement and simulation shows that overlimiting conductances can result from the increased conductance of the electric double-layer at the membrane surface at the depletion side due to voltage-induced polarization charges. The MATLAB source code of the simulation software is available via the website http://micr.vub.ac.be.

Highlights

The voltage in a nanopore or nanochannel has previously been modeled using Neumann boundary conditions at the pore or channel walls [1,2,3,4,5,6,7], i.e., by setting the normal component of the electric field V? equal to the surface charge density σS divided by the permittivity of the PLOS ONE | DOI:10.1371/journal.pone.0124171 May 15, 2015Ion Current Rectification, Limiting and Overlimiting Conductances doi:10.1371/journal.pone.0124171.g001 fluid inside the pore or channel: V? = σS/
We study time-dependent and steady state simulations of a cylindrical nanopore in an uncharged membrane, the effects of surface charges occurring in different configurations, and those of a conical shape
We noticed that steady state could not be reached, even after 0.2 μs, which corresponds to 20 RC time constants

Summary

Introduction

The voltage in a nanopore or nanochannel has previously been modeled using Neumann boundary conditions at the pore or channel walls [1,2,3,4,5,6,7], i.e., by setting the normal component of the electric field V? One thereby implicitly assumes that the normal component of the electric field inside the membrane equals zero This is a restrictive boundary condition as ions outside the pore at the membrane can be co-responsible for screening the surface charges within the pore, resulting in equipotential lines not perpendicular to the surface within the membrane. Donnan equilibrium boundary conditions are often used to set the concentrations and voltages at both entrances of the nanopore [1, 2, 4, 8, 9]. This may form a restrictive boundary condition as the equilibrium approximation is only valid at relatively low bias voltages

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