Dielectric trapping of biopolymers translocating through insulating membranes

Sensitive sequencing of biopolymers by nanopore-based translocation techniques requires extension of the time spent by the molecule in the pore. We develop an electrostatic theory of polymer translocation to show that the translocation time can be extended via the dielectric trapping of the polymer. In dilute salt conditions, the dielectric contrast between the low permittivity membrane and large permittivity solvent gives rise to attractive interactions between the cis and trans portions of the polymer. This self-attraction acts as a dielectric trap that can enhance the translocation time by orders of magnitude. We also find that electrostatic interactions result in the piecewise scaling of the translocation time $\tau$ with the polymer length $L$. In the short polymer regime $L\lesssim10$ nm where the external drift force dominates electrostatic polymer interactions, the translocation is characterized by the drift behavior $\tau\sim L^2$. In the intermediate length regime $10\;{\rm nm}\lesssim L\lesssim\kappa_{\rm b}^{-1}$ where $\kappa_{\rm b}$ is the Debye-H\"{u}ckel screening parameter, the dielectric trap takes over the drift force. As a result, increasing polymer length leads to quasi-exponential growth of the translocation time. Finally, in the regime of long polymers $L\gtrsim\kappa_{\rm b}^{-1}$ where salt screening leads to the saturation of the dielectric trap, the translocation time grows linearly as $\tau\sim L$. This strong departure from the drift behavior highlights the essential role played by electrostatic interactions in polymer translocation.