Influence of concentration polarization on DNA translocation through a nanopore

Concentration polarization can be induced by the unique ion-perm selectivity of small nanopores, leading to a salt concentration gradient across nanopores. This concentration gradient can create diffusio-osmosis and induce an electric field, affecting ionic currents on DNA that translocates through a nanopore. Here this influence is theoretically investigated by solving the continuum Poisson-Nernst-Planck model for different salt concentrations, DNA surface charge densities, and pore properties. By implementing the perturbation method, we can explicitly compute the contribution of concentration polarization to the ionic current. The induced electric field by concentration polarization is opposite to the imposed electric field and decreases the migration current, and the induced diffusio-osmosis can decrease the convection current as well. Our studies suggest that the importance of the concentration polarization can be determined by the parameter $\lambda /G$ where $\lambda$ is the double-layer thickness and $G$ is the gap size. When $\lambda /G$ is larger than a critical value, the influence of concentration polarization becomes more prominent. This conclusion is supported by the studies on the dependence of the ionic current on salt concentration and pore properties, showing that the difference between two models with and without accounting for concentration polarization is larger for low salts and small pores, which correspond to larger $\lambda /G$.

Figure 1

Schematics of concentration polarization due to the DNA translocation inside the nanopore.

Figure 2

Schematics of the computational model.

Figure 3

The relative ionic current change $\mathrm{\Delta }I/I_b$ as a function of salt concentration when $q_m=0$ and $q=-0.08\mathrm{C}/{\mathrm{m}}^2$. The lines and symbols correspond, respectively, to theoretical predictions and experimental data [25].[25]

Figure 4

The distributions of the local salt concentration $C^{\left(1\right)}=\frac{C_{+}^{\left(1\right)}+C_{-}^{\left(1\right)}}{2}$ when the DNA is inside the nanopore for $50\mathrm{mM}$ (a) and $1\mathrm{M}$ (b). The simulation parameters are the same as in Fig. 3.

Figure 5

(a) The relative migration current $I_m/I_b$; (b) the relative convection current $I_c/I_b$ as a function of salt concentration. The lines correspond, respectively, to theoretical predictions of the models with (solid lines) and without (dashed lines) considering concentration polarization.

Figure 6

The relative ionic current change $\mathrm{\Delta }I/I_b$ as a function of $\lambda /G$. The solid and the dashed lines correspond, respectively, to the predictions with concentration polarization and without concentration polarization.

Figure 7

The relative ionic current change $\mathrm{\Delta }I/I_b$ as a function of $\lambda /G$ by varying $d$ when the salt concentration is $30\mathrm{mM}$. The solid and the dashed lines correspond, respectively, to the predictions with concentration polarization and without concentration polarization. The inset shows $\mathrm{\Delta }I/I_b$ as a function of the pore diameter $d$.

Figure 8

The relative ionic current change $\mathrm{\Delta }I/I_b$ as a function of $\lambda /G$ by varying salt concentration for different DNA charge densities: (a) $q=-0.04\mathrm{C}/{\mathrm{m}}^2$ and (b) $q=-0.15\mathrm{C}/{\mathrm{m}}^2$. The solid and the dashed lines correspond, respectively, to the predictions with concentration polarization and without concentration polarization.

Figure 9

The relative ionic current change $\mathrm{\Delta }I/I_b$ as a function of salt concentration. The lines and symbols correspond, respectively, to theoretical predictions and experimental data [25]. The solid line and the dashed line correspond, respectively, to $q_m=0$ and $q_m=-0.08\mathrm{C}/{\mathrm{m}}^2$.

Figure 10

The relative ionic current change $\mathrm{\Delta }I/I_b$ as a function of the nanopore thickness when the salt concentration is $30\mathrm{mM}, d=10\mathrm{nm}, q=-0.08\mathrm{C}/{\mathrm{m}}^2$, and $q_m=0$. The solid and the dashed lines correspond, respectively, to the predictions with concentration polarization and without concentration polarization.