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 -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.
Highlights
DNA is the key transmitter of the biological information carrying our genetic heritage
This scale separation allows to bypass the details of the pore electrohydrodynamics that can be absorbed into the effective force f driving the polymer and the effective pore friction ηp on it, enabling coarse-grained modeling of effects associated with non-equilibrium polymer conformations
In the remaining part of the article, we focus on the regime of long coarse-grained polymers and review the iso-flux tension propagation theory able to account for the conformational polymer fluctuations during translocation
Summary
DNA is the key transmitter of the biological information carrying our genetic heritage. In the case of polymers longer than the translocated pores whose characteristic size Lm ∼10–100 nm is comparable with the DNA persistence length, polymer fluctuations are substantial but the electrohydrodynamic forces can be assumed to act locally on DNA, i.e., exclusively on the polymer portion confined to the pore This scale separation allows to bypass the details of the pore electrohydrodynamics that can be absorbed into the effective force f driving the polymer and the effective pore friction ηp on it, enabling coarse-grained modeling of effects associated with non-equilibrium polymer conformations. The basic idea in this theory is to focus on the dynamics of a single degree of freedom, the translocation coordinate s(t), and include all the many-body effects arising from the (non-equilibrium) chain conformations on the cis side of the membrane into a time-dependent friction ηcis (t) This leads to a Brownian dynamics type of equation for s(t) which makes the problem both analytically and numerically tractable, and allows exact analytic results for the scaling of the translocation time as a function of the chain length. Our main results and prospects are discussed in the Summary and Conclusions section
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