Polymer translocation through a hole

Abstract

The average residence time τ of a polymer of length N passing through a narrow hole under a chemical potential gradient is calculated. In the proposed model, details of the hole parametrize the rate constant $k_0$ for transporting a monomer across the hole, independent of the chain length. We show that any asymmetry in the average conformations of the polymer across the hole is sufficient to generate the driving force for the polymer translocation. If chemical potential gradient is absent, ${\mathrm{\tau \sim N}}^2,$ with the proportionality constant depending on the size exponent of the polymer before and after the translocation. For translocation along the chemical potential gradient Δμ, τ is proportional to ${\mathrm{N(T/k}}_0\mathrm{\Delta \mu )}$ and $N^2{\mathrm{/k}}_0,$ respectively, for large and small $\mathrm{N\Delta \mu /T.}$ For translocation against the chemical potential gradient, $\mathrm{\tau \sim }\exp \mathrm{(N)}$ for long polymers.