Electrophoretic Capture and Passage of a Polyelectrolyte Molecule through a Nanopore

Capture and passage of a long polyelectrolyte molecule such as DNA through a very narrow pore drilled in a membrane is considered. An external voltage is applied to a dilute electrolyte solution of polymeric molecules which is separated by a dielectric membrane into a cis and trans side. The external voltage creates an electric field which due to the narrowness of the pore, is the strongest inside the pore. Passage of the polymers through the pore from the cis to the trans side of the membrane is facilitated mostly by the force exerted inside the pore by this strong field, and involves a significant deformation of the naturally coiled polymeric molecule. The passage is thus controlled by the propagation of entropic tension along the coil as it locally uncoils and moves towards the pore. The polymer is in particular highly stretched when it enters the very narrow pore; the resulting loss and regain of entropy due to this stretch is the dominant dissipative mechanism during the passage. Before the passage begins, the molecule is drawn towards the pore by the electric field outside the pore. The electrophoretic force exerted on the molecule in the non-uniform electric field near the pore is characterized by the localization of the electroosmotic flow around the polymer. The entropically unfavorable capture of the polymer into the pore is facilitated by this electrophoretic force, which is formulated in terms of a Kramers process of overcoming a barrier.