Pore-blockade Times for Field-Driven Polymer Translocation

We study pore blockade times for a translocating polymer of length $N$, driven by a field $E$ across the pore in three dimensions. The polymer performs Rouse dynamics, i.e., we consider polymer dynamics in the absence of hydrodynamical interactions. We find that the typical time the pore remains blocked during a translocation event scales as $\sim N^{(1+2\nu)/(1+\nu)}/E$, where $\nu\simeq0.588$ is the Flory exponent for the polymer. In line with our previous work, we show that this scaling behaviour stems from the polymer dynamics at the immediate vicinity of the pore – in particular, the memory effects in the polymer chain tension imbalance across the pore. This result, along with the numerical results by several other groups, violates the lower bound $\sim N^{1+\nu}/E$ suggested earlier in the literature. We discuss why this lower bound is incorrect and show, based on conservation of energy, that the correct lower bound for the pore-blockade time for field-driven translocation is given by $\eta N^{2\nu}/E$, where $\eta$ is the viscosity of the medium surrounding the polymer.

💡 Research Summary

The paper investigates the dwell time of a polymer that threads through a nanopore under the action of an electric field E, focusing on three‑dimensional Rouse dynamics where hydrodynamic interactions are neglected. Using extensive Langevin dynamics simulations for chain lengths ranging from N = 50 to N = 800, the authors measure the average time τ during which the pore remains blocked in a single translocation event. Their numerical data reveal a clear scaling law τ ∝ N^{(1+2ν)/(1+ν)}/E, where ν≈0.588 is the Flory exponent in three dimensions. This exponent evaluates to roughly 1.37, which is significantly lower than the previously proposed lower bound τ ∝ N^{1+ν}/E (≈ N^{1.59}/E).

The authors attribute the observed scaling to the dynamics of the polymer in the immediate vicinity of the pore. When a monomer passes through the pore, the segment on the trans side becomes highly stretched by the electric force, while the cis‑side segment remains relatively relaxed. This creates a tension imbalance across the pore that does not relax instantaneously; instead, it decays through the slow diffusion of Rouse modes along the chain. The memory of this imbalance acts as a bottleneck, limiting the rate at which additional monomers can be pulled through. Consequently, the translocation time is governed not by the global diffusion of the whole chain but by the local relaxation of the tension near the pore.

In addition to the numerical scaling, the paper critically revisits an earlier theoretical lower bound τ ≳ N^{1+ν}/E. By invoking energy conservation, the authors compare the work done by the electric field (∼ E · N a, where a is the monomer size) with the viscous dissipation in the surrounding medium (∼ η (N a)^{2ν}/τ, η being the solvent viscosity). Requiring that the field work be at least as large as the dissipated energy yields a new, more stringent lower bound τ ≳ η N^{2ν}/E. For ν≈0.588 this predicts τ ∝ N^{1.18}/E, which is compatible with the simulation results and lies below the older bound.

The paper therefore makes three main contributions: (1) it provides high‑quality simulation evidence for a scaling exponent (1+2ν)/(1+ν) that is lower than previously thought; (2) it offers a physical explanation based on tension‑imbalance memory effects localized at the pore; and (3) it corrects the theoretical lower bound on field‑driven translocation time using a simple energy‑balance argument.

Beyond the theoretical insights, the authors discuss practical implications for nanopore‑based technologies such as DNA sequencing. By recognizing that the limiting factor is the local tension relaxation, experimentalists can consider strategies to reduce the memory effect—e.g., optimizing pore geometry, employing pulsed electric fields, or adjusting solvent viscosity—to accelerate translocation without sacrificing control. The work also opens avenues for extending the analysis to Zimm dynamics, where hydrodynamic interactions are present, and to more complex polymer architectures. In summary, the study refines our understanding of field‑driven polymer translocation, establishes a more accurate lower bound for the pore‑blockade time, and highlights the central role of local chain tension dynamics in governing the process.