Theoretical Modeling of Polymer Translocation: From the Electrohydrodynamics of Short Polymers to the Fluctuating Long Polymers

Abstract

The theoretical formulation of driven polymer translocation through nanopores is complicated by the combination of the pore electrohydrodynamics and the nonequilibrium polymer dynamics originating from the conformational polymer fluctuations. In this review, we discuss the modeling of polymer translocation in the distinct regimes of short and long polymers where these two effects decouple. For the case of short polymers where polymer fluctuations are negligible, we present a stiff polymer model including the details of the electrohydrodynamic forces on the translocating molecule. We first show that the electrohydrodynamic theory can accurately characterize the hydrostatic pressure dependence of the polymer translocation velocity and time in pressure-voltage-driven polymer trapping experiments. Then, we discuss the electrostatic correlation mechanisms responsible for the experimentally observed DNA mobility inversion by added multivalent cations in solid-state pores, and the rapid growth of polymer capture rates by added monovalent salt in α -Hemolysin pores. In the opposite regime of long polymers where polymer fluctuations prevail, we review the iso-flux tension propagation (IFTP) theory, which can characterize the translocation dynamics at the level of single segments. The IFTP theory is valid for a variety of polymer translocation and pulling scenarios. We discuss the predictions of the theory for fully flexible and rodlike pore-driven and end-pulled translocation scenarios, where exact analytic results can be derived for the scaling of the translocation time with chain length and driving force.

Scaling Theory of a Polymer Ejecting from a Cavity into a Semi-Space

“…Simulations have been largely invested in the study of polymer ejection and translocation [ 27 , 28 , 29 ]. It was found that the ejection process evolves faster for an orderly packed DNA spool than a disordered or knotted DNA chain [ 30 , 31 ].…”

Translocation of a Polyelectrolyte through a Nanopore in the Presence of Trivalent Counterions: A Comparison with the Cases in Monovalent and Divalent Salt Solutions

“… 76 In this situation, tension propagation theories have been used to characterize the translocation dynamics and scaling behavior at different levels of driving forces. 47 , 70 , 76 However, these theories were developed under the framework of neutral polymers. It is thus important to know the limitation of the tension propagation theories.…”

Pulling a DNA molecule through a nanopore embedded in an anionic membrane: tension propagation coupled to electrostatics

“…This requires taking into account both the presence of counterions in the solution and the dielectric properties of the membrane through which the polyelectrolyte is translocating. Recently there has been an intense effort to model polyeletrolyte translocation including the details of the pore electrohydrodynamics and/or electrostatic polymer-membrane interactions, however, with the price of neglecting conformational polymer fluctuations [5,39,41]. This simplified modeling has allowed to characterize the electrohydrodynamic mechanism of experimentally observed DNA mobility reversal by charge inversion [42] and pressure-voltage traps [43], and also enabled to identify strategies for faster polymer capture and slower translocation required for accurate biosequencing.…”