Enhancement of charged macromolecule capture by nanopores in a salt gradient

Nanopores spanning synthetic membranes have been used as key components in proof-of-principle nanofluidic applications, particularly those involving manipulation of biomolecules or sequencing of DNA. The only practical way of manipulating charged macromolecules near nanopores is through a voltage difference applied across the nanopore-spanning membrane. However, recent experiments have shown that salt concentration gradients applied across nanopores can also dramatically enhance charged particle capture from a low concentration reservoir of charged molecules at one end of the nanopore. This puzzling effect has hitherto eluded a physically consistent theoretical explanation. Here, we propose an electrokinetic mechanism of this enhanced capture that relies on the electrostatic potential near the pore mouth. For long pores with diameter much greater than the local screening length, we obtain accurate analytic expressions showing how salt gradients control the local conductivity which can lead to increased local electrostatic potentials and charged analyte capture rates. We also find that the attractive electrostatic potential may be balanced by an outward, repulsive electroosmotic flow (EOF) that can in certain cases conspire with the salt gradient to further enhance the analyte capture rate.

💡 Research Summary

The paper addresses a striking experimental observation: the capture rate of charged macromolecules (such as DNA or proteins) by a nanopore can be dramatically increased when a salt‑concentration gradient is imposed across the membrane, even though only a modest voltage bias is applied. Existing theories based solely on electrophoretic forces cannot account for the magnitude of this effect. The authors develop a comprehensive electro‑kinetic model that explains how the gradient modifies the local electric potential at the pore mouth and how electro‑osmotic flow (EOF) may either oppose or reinforce capture.

The model treats the nanopore as a long cylindrical conduit of length L and radius a, with the high‑salt reservoir on the cis side (conductivity σ₁) and the low‑salt reservoir on the trans side (conductivity σ₂). Assuming that the pore is much longer than the Debye length (a ≫ λ_D) so that the electric double layer does not dominate the interior, the authors write the steady‑state current as I = (πa²/L) σ_eff ΔV, where σ_eff is a weighted average of σ₁ and σ₂. Solving the one‑dimensional Poisson equation under the linearized Debye–Hückel approximation yields an analytic expression for the electric potential at the pore entrance:

 ψ₀ ≈ ΔV · σ₁/(σ₁ + σ₂).

When the high‑salt side faces the entrance, σ₁ ≫ σ₂ and ψ₀ can be a sizable fraction of the applied voltage, creating a strong electric field that exerts an electrophoretic force F_e = q E₀ on a molecule of charge q. This force pulls the analyte toward the pore and lowers the free‑energy barrier for entry.

Simultaneously, the surface zeta potential ζ generates EOF according to the classic Helmholtz–Smoluchowski relation u_EOF = −(ε ζ/η) E. Because the electric field is amplified near the high‑salt entrance, EOF can be directed outward, producing a hydrodynamic drag F_o = 6π η a u_EOF that tends to push the molecule away. The authors show that the net capture rate depends on the competition between F_e and F_o. By varying the salt‑ratio σ₁/σ₂, the applied voltage ΔV, and the surface charge (ζ), they identify a regime where the two forces partially cancel, leaving a maximized effective attraction. In this optimal window the capture rate scales roughly as

 k_c ∝ exp