[Paper Review] Two phase picture in driven polymer translocation

Takuya Saito, Takahiro Sakaue|arXiv (Cornell University)|May 17, 2012

Nanopore and Nanochannel Transport Studies3 citations

TL;DR

This paper revisits the two-phase model for driven polymer translocation, correcting a previous steady-state ansatz that violated mass conservation. By adopting an alternative ansatz consistent with iso-flux dynamics, the authors derive a modified scaling law for translocation time that matches the iso-flux model of Rowghanian and Grosberg, resolving incompatibility with physical constraints while reconciling with experimental trends through finite-size effects.

ABSTRACT

Two phase picture is a simple and effective methodology to capture the nonequilibrium dynamics of polymer associated with tension propagation. When applying it to the driven translocation process, there is a point to be noted, as briefly discussed in our recent article [Phys. Rev. E 85, 061803 (2012)]. In this article, we address this issue in detail and modify our previous prediction [Euro. Phys. J. E 34, 135 (2011)] by adopting an alternative steady-state ansatz. The modified scaling prediction turns out to be the same as that of the iso-flux model recently proposed by Rowghanian and Grosberg [J. Phys. Chem. B 115, 14127-14135 (2011)].

Motivation & Objective

• To resolve inconsistencies in the previous two-phase model for driven polymer translocation, particularly the violation of mass conservation due to an incompatible steady-state ansatz.
• To reformulate the dynamics using an alternative steady-state assumption that ensures consistency with the iso-flux condition.
• To derive a revised scaling prediction for the propagation and translocation time that aligns with recent iso-flux models.
• To clarify the physical validity of the two-phase formalism by analyzing self-consistency conditions for velocity gradients and relaxation times.
• To reconcile theoretical predictions with experimental observations, accounting for finite-size and pore-effect corrections.

Proposed method

• Reformulates the two-phase model by replacing the previous ansatz (V(t) = v_R(t)) with an alternative steady-state assumption that preserves mass conservation.
• Introduces a modified continuity equation (eq. 1) where the segment flux at the pore and moving domain boundary are balanced under the iso-flux condition.
• Applies dynamical equations of state (eqs. 2–4) relating force, extension, velocity, and segment density in the moving domain.
• Derives the tension-propagation law (eq. 7) using the new ansatz, with scaling exponents β = p_z(1−q) and γ = ν/(1+ν−νq).
• Analyzes self-consistency via relaxation time τ_relax ≃ R/V and shear rate ̇γ ≃ δv/R, showing that only the new ansatz satisfies δv ≤ V.
• Compares the new model with the iso-flux model of Rowghanian and Grosberg, confirming identical scaling predictions for translocation time.

Experimental results

Research questions

• RQ1 Why was the previous two-phase model’s steady-state ansatz incompatible with mass conservation in driven polymer translocation?
• RQ2 How does the alternative steady-state ansatz improve consistency with the iso-flux condition and physical constraints?
• RQ3 What is the resulting scaling law for the propagation time under the corrected ansatz, and how does it compare to existing models?
• RQ4 Why do numerical and experimental results still favor the earlier, inconsistent prediction despite its theoretical flaws?
• RQ5 To what extent do finite-size effects and pore-specific interactions explain the discrepancy between theory and experiment?

Key findings

• The corrected model replaces the previous ansatz V(t) = v_R(t) with a self-consistent steady-state assumption that satisfies the iso-flux condition j_R(t) ≃ j_0(t).
• The modified scaling prediction for propagation time is τ_p ≃ N_0^{1+ν} f^{-(p_z - p_ν)}, which matches the iso-flux model of Rowghanian and Grosberg.
• The self-consistency condition τ_relax · ̇γ ≤ 1 is satisfied only under the new ansatz, validating its physical plausibility.
• The previous ansatz leads to unphysical velocity gradients (δv_0 > V), violating the relaxation time condition and making it dynamically inconsistent.
• Finite-size effects and pore interactions may explain why earlier predictions, though theoretically flawed, still correlate with experiments.
• The model confirms that the unique driving mode in translocation is iso-flux dynamics, distinct from end-pulling mechanisms.