Dynamics of end-pulled polymer translocation through a nanopore

Polymer Translocation and Nanopore Sequencing: A Review of Advances and Challenges

Various biological processes involve the translocation of macromolecules across nanopores; these pores are basically protein channels embedded in membranes. Understanding the mechanism of translocation is crucial to a range of technological applications, including DNA sequencing, single molecule detection, and controlled drug delivery. In this spirit, numerous efforts have been made to develop polymer translocation-based sequencing devices, these efforts include findings and insights from theoretical modeling, simulations, and experimental studies. As much as the past and ongoing studies have added to the knowledge, the practical realization of low-cost, high-throughput sequencing devices, however, has still not been realized. There are challenges, the foremost of which is controlling the speed of translocation at the single monomer level, which remain to be addressed in order to use polymer translocation-based methods for sensing applications. In this article, we review the recent studies aimed at developing control over the dynamics of polymer translocation through nanopores.

Coupling Effects of Electrostatic Interactions and Salt Concentration Gradient in Polymer Translocation through a Nanopore: A Coarse-Grained Molecular Dynamics Simulations Study

We study the influence of polymer pore interactions and focus on the role played by the concentration gradient of salt in the translocation of polyelectrolytes (PE) through nanopores explicitly using coarse-grained Langevin dynamics simulations. The mean translocation time is calculated by varying the applied voltage, the pH, and the salt concentration gradient. Changing the pH can alter the electrostatic interaction between the protein pore and the polyelectrolyte chain. The polymer pore interaction is weakened by the increase in the strength of the externally applied electric field that drives translocation. Additionally, the screening effect of the salt can reduce the strong charge-charge repulsion between the PE beads which can make translocation faster. The simulation results show there can be antagonistic or synergistic coupling between the salt concentration-induced screening effect and the drift force originating from the salt concentration gradient thereby affecting the translocation time. Our simulation results are explained qualitatively with free energy calculations.

Pulling a folded polymer through a nanopore

We investigate the translocation dynamics of a folded linear polymer which is pulled through a nanopore by an external force. To this end, we generalize the iso-flux tension propagation theory for end-pulled polymer translocation to include the case of two segments of the folded polymer traversing simultaneously trough the pore. Our theory is extensively benchmarked with corresponding molecular dynamics (MD) simulations. The translocation process for a folded polymer can be divided into two main stages. In the first stage, both branches are traversing the pore and their dynamics is coupled. If the branches are not of equal length, there is a second stage where translocation of the shorter branch has been completed. Using the assumption of equal monomer flux of both branches confirmed by MD simulations, we analytically derive the equations of motion for both branches and characterize the translocation dynamics in detail from the average waiting time and its scaling form.

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

We consider the influence of electrostatic forces on driven translocation dynamics of a flexible polyelectrolyte being pulled through a nanopore by an external force on the head monomer. To this end, we augment the iso-flux tension propagation theory with electrostatics for a negatively charged biopolymer pulled through a nanopore embedded in a similarly charged anionic membrane. We show that in the realistic case of a single-stranded DNA molecule, dilute salt conditions characterized by weak charge screening, and a negatively charged membrane, the translocation dynamics is unexpectedly accelerated despite the presence of large repulsive electrostatic interactions between the polymer coil on thecisside and the charged membrane. This is due to the rapid release of the electrostatic potential energy of the coil during translocation, leading to an effectively attractive force that assists end-driven translocation. The speedup results in non-monotonic polymer length and membrane charge dependence of the exponentαcharacterizing the translocation timeτ∝N0αof the polymer with lengthN0. In the regime of long polymersN0 ≳   500, the translocation exponent exceeds its upper limitα= 2 previously observed for the same system without electrostatic interactions.

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

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.

Translocation of Charged Polymers through a Nanopore in Monovalent and Divalent Salt Solutions: A Scaling Study Exploring over the Entire Driving Force Regimes

Langevin dynamics simulations are performed to study polyelectrolytes driven through a nanopore in monovalent and divalent salt solutions. The driving electric field E is applied inside the pore, and the strength is varied to cover the four characteristic force regimes depicted by a rederived scaling theory, namely the unbiased (UB) regime, the weakly-driven (WD) regime, the strongly-driven trumpet (SD(T)) regime and the strongly-driven isoflux (SD(I)) regime. By changing the chain length N, the mean translocation time is studied under the scaling form 〈 τ 〉 ∼ N α E - δ . The exponents α and δ are calculated in each force regime for the two studied salt cases. Both of them are found to vary with E and N and, hence, are not universal in the parameter's space. We further investigate the diffusion behavior of translocation. The subdiffusion exponent γ p is extracted. The three essential exponents ν s , q, z p are then obtained from the simulations. Together with γ p , the validness of the scaling theory is verified. Through a comparison with experiments, the location of a usual experimental condition on the scaling plot is pinpointed.

Reducing the variance in the translocation times by prestretching the polymer

Langevin dynamics simulations of polymer translocation are performed where the polymer is stretched via two opposing forces applied on the first and last monomer before and during translocation. In this setup, polymer translocation is achieved by imposing a bias between the two pulling forces such that there is net displacement towards the trans side. Under the influence of stretching forces, the elongated polymer ensemble contains less variations in conformations compared to an unstretched ensemble. Simulations demonstrate that this reduced spread in initial conformations yields a reduced variation in translocation times relative to the mean translocation time. This effect is explored for different ratios of the amplitude of thermal fluctuations to driving forces to control for the relative influence of the thermal path sampled by the polymer. Since the variance in translocation times is due to contributions coming from sampling both thermal noise and initial conformations, our simulations offer independent control over the two main sources of noise and allow us to shed light on how they both contribute to translocation dynamics. Simulation parameter space corresponding to experimentally relevant conditions is highlighted and shown to correspond to a significant decrease in the spread of translocation times, thus indicating that stretching DNA prior to translocation could assist nanopore-based sequencing and sizing applications.

Theory of pore-driven and end-pulled polymer translocation dynamics through a nanopore: an overview

We review recent progress on the theory of dynamics of polymer translocation through a nanopore based on the iso-flux tension propagation (IFTP) theory. We investigate both pore-driven translocation of flexible and a semi-flexible polymers, and the end-pulled case of flexible chains by means of the IFTP theory and extensive molecular dynamics (MD) simulations. The validity of the IFTP theory can be quantified by the waiting time distributions of the monomers which reveal the details of the dynamics of the translocation process. The IFTP theory allows a parameter-free description of the translocation process and can be used to derive exact analytic scaling forms in the appropriate limits, including the influence due to the pore friction that appears as a finite-size correction to asymptotic scaling. We show that in the case of pore-driven semi-flexible and end-pulled polymer chains the IFTP theory must be augmented with an explicit trans side friction term for a quantitative description of the translocation process.

Protein sequencing via nanopore based devices: a nanofluidics perspective

Proteins perform a huge number of central functions in living organisms, thus all the new techniques allowing their precise, fast and accurate characterization at single-molecule level certainly represent a burst in proteomics with important biomedical impact. In this review, we describe the recent progresses in the developing of nanopore based devices for protein sequencing. We start with a critical analysis of the main technical requirements for nanopore protein sequencing, summarizing some ideas and methodologies that have recently appeared in the literature. In the last sections, we focus on the physical modelling of the transport phenomena occurring in nanopore based devices. The multiscale nature of the problem is discussed and, in this respect, some of the main possible computational approaches are illustrated.

Polymer translocation under a pulling force: Scaling arguments and threshold forces

DNA translocation through nanopores is one of the most promising strategies for next-generation sequencing technologies. Most experimental and numerical works have focused on polymer translocation biased by electrophoresis, where a pulling force acts on the polymer within the nanopore. An alternative strategy, however, is emerging, which uses optical or magnetic tweezers. In this case, the pulling force is exerted directly at one end of the polymer, which strongly modifies the translocation process. In this paper, we report numerical simulations of both linear and structured (mimicking DNA) polymer models, simple enough to allow for a statistical treatment of the pore structure effects on the translocation time probability distributions. Based on extremely extended computer simulation data, we (i) propose scaling arguments for an extension of the predicted translocation times τ∼N^{2}F^{-1} over the moderate forces range and (ii) analyze the effect of pore size and polymer structuration on translocation times τ.