Polymer-pore Interactions Research Articles

Influence of nanopore coating patterns on the translocation dynamics of polyelectrolytes.

Polyelectrolytes can electrophoretically be driven through nanopores in order to be detected. The respective translocation events are often very fast and the process needs to be controlled to promote efficient detection. To this end, we attempt to control the translocation dynamics by coating the inner surface of a nanopore. For this, different charge distributions are chosen that result in substantial variations of the pore-polymer interactions. In addition and in view of the existing detection modalities, experimental settings, and nanopore materials, different types of sensors inside the nanopore have been considered to probe the translocation process and its temporal spread. The respective transport of polyelectrolytes through the coated nanopores is modeled through a multi-physics computational scheme that incorporates a mesoscopic/electrokinetic description for the solvent and particle-based scheme for the polymer. This investigation could underline the interplay between sensing modality, nanopore material, and detection accuracy. The electro-osmotic flow and electrophoretic motion in a pore are analyzed together with the polymeric temporal and spatial fluctuations unraveling their correlations and pathways to optimize the translocation speed and dynamics. Accordingly, this work sketches pathways in order to tune the pore-polymer interactions in order to control the translocation dynamics and, in the long run, errors in their measurements.

Experimental investigation of the forces dictating polymer translocation through solid-state nanopores.

After realizing direct long-read DNA and RNA sequencing, nanopores show also potential for decoding information on other polymers, including proteins and nanostructured DNA. Understanding the process by which these biopolymers are captured and traverse nanopores however remains a challenging task due to the complex nature of the non-equilibrium translocation dynamics which occur on multiple timescales and are dictated mainly by forces over which full experimental control is challenging. This unfortunately also makes verification of theoretical ideas difficult. In this work, we present solid-state nanopore data of DNA fragments for a wide range of experimental conditions in hopes of showcasing the various underlying forces and processes during capture and translocation. Namely, we specifically attempt to establish the absolute and relative magnitude of electrophoretic forces, and frictional contributions originating from hydrodynamic interactions both inside and outside nanopores. This is achieved by studying the dependence of translocation times on nanopore size (3-20 nm diameter) and DNA length (500-45,000 bp), and by measuring the time-dependent translocation velocity of DNA nanostructures, which consists of a linear DNA polymer with three helix-bundle (3HB) sub-structures patterned along its contour. The velocity profile of the patterned nanostructure is measured under different applied voltages (0.1-1 V), in different salt concentrations (0.5-4 M LiCl), and in different pore geometry. The data allow us to corroborate the predictions of tension propagation and consolidate previously published observations regarding measurements of electrophoretic pulling force and pore-polymer interactions in nanopore systems. In addition to bridging nanopore experiment and theory, these results can be used to inform and design several biosensing and digital storage applications.

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.

Polyimide Hybrid Nanocomposites with Controlled Polymer Filling and Polymer-Matrix Interaction.

Polyimide hybrid nanocomposites with the polyimide confined at molecular length scales exhibit enhanced fracture resistance with excellent thermal-oxidative stability at low density. Previously, polyimide nanocomposites were fabricated by infiltration of a polyimide precursor into a nanoporous matrix followed by sequential thermally induced imidization and cross-linking of the polyimide under nanometer-scale confinement. However, byproducts formed during imidization became volatile at the cross-linking temperature, limiting the polymer fill level and degrading the nanocomposite fracture resistance. This is solved in the present work with an easier approach where the nanoporous matrix is filled with shorter preimidized polyimide chains that are cross-linked while in the pores to eliminate the need for confined imidization reactions, which produces better results compared to the previous study. In addition, we selected a preimidized polyimide that has a higher chain mobility and a stronger interaction with the matrix pore surface. Consequently, the toughness achieved with un-cross-linked preimidized polyimide chains in this work is equivalent to that achieved with the cross-linking of the previously used polyimide chains and is doubled when preimidized polyimide chains are cross-linked. The increased chain mobility enables more efficient polymer filling and higher polymer fill levels. The higher polymer-pore surface interaction increases the energy dissipation during polyimide molecular bridging, increasing the nanocomposite fracture resistance. The combination of the higher polymer fill and the stronger polymer-surface interaction is shown to provide significant improvements to the nanocomposite fracture resistance and is validated with a molecular bridging model.

Translocation through a narrow pore under a pulling force

We employ a three-dimensional molecular dynamics to simulate a driven polymer translocation through a nanopore by applying an external force, for four pore diameters and two external forces. To see the polymer and pore interaction effects on translocation time, we studied nine interaction energies. Moreover, to better understand the simulation results, we investigate polymer center of mass, shape factor and the monomer spatial distribution through the translocation process. Our results reveal that increasing the polymer-pore interaction energy is accompanied by an increase in the translocation time and decrease in the process rate. Furthermore, for pores with greater diameter, the translocation becomes faster. The shape analysis of the polymer indicates that the polymer shape is highly sensitive to the interaction energy. In great interactions, the monomers come close to the pore from both sides. As a result, the translocation becomes fast at first and slows down at last. Overall, it can be concluded that the external force does not play a major role in the shape and distribution of translocated monomers. However, the interaction energy between monomer and nanopore has a major effect especially on the distribution of translocated monomers on the trans side.

Translocation Dynamics of an Asymmetrically Charged Polymer through a Pore under the Influence of Different pH Conditions.

We study the translocation of a polymer with oppositely charged segments at both ends of the chain passing through a pore under the effect of an external electric field in the presence of a pH gradient using Langevin dynamics simulations. As observed in experiments, the electrostatic interactions between the pore and the polymer are tuned by altering the pH gradient. Our simulation studies show that with the change in charge distribution on the polymer and the pore that can mimic different pH conditions, the external driving force and the polymer-pore electrostatic interactions play a significant role in the translocation process. The external electric forces are dominant during the entry stage, and the entry time decreases with increase in the charge asymmetry of the pore-trapped polymer. During the exit stage, the electrostatic interactions as well as the external electric field act in concert in determining the exit time through the pore. Our simulation results can capture many features observed in experiments. Our results are explained qualitatively by calculating the free-energy change of the polymer chain during the translocation process.

Enhanced polymer capture speed and extended translocation time in pressure-solvation traps.

The efficiency of nanopore-based biosequencing techniques requires fast anionic polymer capture by like-charged pores followed by a prolonged translocation process. We show that this condition can be achieved by setting a pressure-solvation trap. Polyvalent cation addition to the KCl solution triggers the like-charge polymer-pore attraction. The attraction speeds-up the pressure-driven polymer capture but also traps the molecule at the pore exit, reducing the polymer capture time and extending the polymer escape time by several orders of magnitude. By direct comparison with translocation experiments [D. P. Hoogerheide et al., ACS Nano 8, 7384 (2014)1936-085110.1021/nn5025829], we characterize as well the electrohydrodynamics of polymers transport in pressure-voltage traps. We derive scaling laws that can accurately reproduce the pressure dependence of the experimentally measured polymer translocation velocity and time. We also find that during polymer capture, the electrostatic barrier on the translocating molecule slows down the liquid flow. This prediction identifies the streaming current measurement as a potential way to probe electrostatic polymer-pore interactions.

Sequencing of semiflexible polymers of varying bending rigidity using patterned pores.

We study the translocation of a semiflexible polymer through extended pores with patterned stickiness, using Langevin dynamics simulations. We find that the consequence of pore patterning on the translocation time dynamics is dramatic and depends strongly on the interplay of polymer stiffness and pore-polymer interactions. For heterogeneous polymers with periodically varying stiffness along their lengths, we find that variation of the block size of the sequences and the orientation results in large variations in the translocation time distributions. We show how this fact may be utilized to develop an effective sequencing strategy. This strategy involving multiple pores with patterned surface energetics can predict heteropolymer sequences having different bending rigidity to a high degree of accuracy.

Influence of the Location of Attractive Polymer-Pore Interactions on Translocation Dynamics.

We probe the influence of polymer-pore interactions on the translocation dynamics using Langevin dynamics simulations. We investigate the effect of the strength and location of the polymer-pore interaction using nanopores that are partially charged either at the entry or the exit or on both sides of the pore. We study the change in the translocation time as a function of the strength of the polymer-pore interaction for a given chain length and under the effect of an externally applied field. Under a moderate driving force and a chain length longer than the length of the pore, the translocation time shows a nonmonotonic increase with an increase in the attractive interaction. Also, an interaction on the cis side of the pore can increase the translocation probability. In the presence of an external field and a strong attractive force, the translocation time for shorter chains is independent of the polymer-pore interaction at the entry side of the pore, whereas an interaction on the trans side dominates the translocation process. Our simulation results are rationalized by a qualitative analysis of the free energy landscape for polymer translocation.

Multivalent cation induced attraction of anionic polymers by like-charged pores.

The efficiency of nanopore-based polymer sensing devices depends on the fast capture of anionic polyelectrolytes by negatively charged pores. This requires the cancellation of the electrostatic barrier associated with repulsive polymer-pore interactions. We develop a correlation-corrected theory to show that the barrier experienced by the polymer can be efficiently overcome by the addition of multivalent cations into the electrolyte solution. Cation adsorption into the pore enhances the screening ability of the pore medium with respect to the bulk reservoir which translates into an attractive force on the polymer. Beyond a critical multivalent cation concentration, this correlation-induced attraction overcomes the electrostatic barrier and triggers the adsorption of the polymer by the like-charged pore. It is shown that like-charge polymer-pore attraction is suppressed by monovalent salt but enhanced by the membrane charge strength and the pore confinement. Our predictions may provide enhanced control over polymer motion in translocation experiments.

Controlling polymer capture and translocation by electrostatic polymer-pore interactions.

Polymer translocation experiments typically involve anionic polyelectrolytes such as DNA molecules driven through negatively charged nanopores. Quantitative modeling of polymer capture to the nanopore followed by translocation therefore necessitates the consideration of the electrostatic barrier resulting from like-charge polymer-pore interactions. To this end, in this work we couple mean-field level electrohydrodynamic equations with the Smoluchowski formalism to characterize the interplay between the electrostatic barrier, the electrophoretic drift, and the electro-osmotic liquid flow. In particular, we find that due to distinct ion density regimes where the salt screening of the drift and barrier effects occurs, there exists a characteristic salt concentration maximizing the probability of barrier-limited polymer capture into the pore. We also show that in the barrier-dominated regime, the polymer translocation time τ increases exponentially with the membrane charge and decays exponentially fast with the pore radius and the salt concentration. These results suggest that the alteration of these parameters in the barrier-driven regime can be an efficient way to control the duration of the translocation process and facilitate more accurate measurements of the ionic current signal in the pore.

Tuning Polymer-Protein Interaction with Salt

Biological nanopores are known to interact with synthetic and biological polymers, enabling their use in label-free single-molecule analytical tasks such as sequencing and/or mass discrimination. The latter, called nanopore-based single molecule mass spectrometry (Np-SMMS) has, to date, only been shown for one synthetic polymer, poly(ethyleneglycol) (PEG). It is based on the fact that binding of PEG inside the pore gives rise to blocks of ionic current, with the degree of block being detectably different for PEG molecules differing in size by only one monomer1,2.In order to extend the range of application of Np-SMMS, and to obtain information on the mechanism underying mass sensitivity of polymer-induced pore block, we have begun to test the interaction of other neutral polymers with biological nanoores. Here, we report on poly(dimethylacrylamide) (PDMA), a water-soluble neutral polymer. Under conditions used for Np-SMMS of PEG with alpha-hemolysine (4M KCl, +40 mV), we obtained current blocks with polydisperse PDMA (Mn 1500 g/mol by MALDI) that were low in frequency (<0.1 Hz/ µM) short (tau <100 µs) and noisy, resulting in little mass resolution compared to PEG. We reasoned that we might take advantage of a specific salt effect of fluoride anion reported for the aHL pore3 in order to increase blocking frequency and dwell time. Using electrolyte solutions consiting of 4M K+ as cation and various proportions of Cl- and F- as anions (1:1, 2:1, 3:1, 4:1) we were able to obtain longer events (tau up to 400 µs) and higher frequencies (up to 0.15 Hz/µM), allowing significantly better mass resolution for PDMA than in 4 M KCl. However, the large noise component in the blocked current levels for PDMA as opposed to PEG remained, still compromising the peak-to-valley ratio of histograms. These findings suggest that the specific salt effect of F- on polymer-protein interaction is independent of the polymer and may be useful in tuning polymer pore interaction for a range of analytes.(1) Robertson et al. Single-Molecule Mass Spectrometry in Solution Using a Solitary Nanopore. Proc. Natl. Acad. Sci. U S A 2007, 104, 8207-8211.(2) Baaken et al. High-Resolution Size-Discrimination of Single Nonionic Synthetic Polymers with a Highly Charged Biological Nanopore. ACS Nano 2015, 9, 6443-6449.(3) Rodrigues et al. Hofmeister Effect in Confined Spaces: Halogen Ions and Single Molecule Detection. Biophys. J. 2011, 100, 2929-2935.

Stochastic resonance during a polymer translocation process.

We have studied the occurrence of stochastic resonance when a flexible polymer chain undergoes a single-file translocation through a nano-pore separating two spherical cavities, under a time-periodic external driving force. The translocation of the chain is controlled by a free energy barrier determined by chain length, pore length, pore-polymer interaction, and confinement inside the donor and receiver cavities. The external driving force is characterized by a frequency and amplitude. By combining the Fokker-Planck formalism for polymer translocation and a two-state model for stochastic resonance, we have derived analytical formulas for criteria for emergence of stochastic resonance during polymer translocation. We show that no stochastic resonance is possible if the free energy barrier for polymer translocation is purely entropic in nature. The polymer chain exhibits stochastic resonance only in the presence of an energy threshold in terms of polymer-pore interactions. Once stochastic resonance is feasible, the chain entropy controls the optimal synchronization conditions significantly.

Polymer capture by α-hemolysin pore upon salt concentration gradient

We have measured the rate of capture of single molecules of sodium poly(styrene sulfonate) by α-hemolysin protein pore by varying applied voltage, pH, and the salt concentration asymmetry across the pore. We show that electrostatic interaction between the polyelectrolyte and the protein pore significantly affects the polymer capture rate in addition to the enhancement of drift arising from electrolyte concentration gradient. At higher pH values where the electrostatic interaction between the polymer and the α-hemolysin pore is repulsive, an antagonistic coupling with the drift induced by salt concentration gradient emerges. This antagonistic coupling results in a nonmonotonic dependence of the polymer capture rate on the salt concentration in the donor compartment. The coupling between the pore-polymer interaction and drift can be weakened by increasing the strength of the electric field that drives the polymer translocation. In contrast, at lower pH values where the polymer-pore interaction is attractive, a synergy with the additional drift from salt concentration asymmetry arises and the capture rate depends monotonically on the donor salt concentration. For higher pH, we identify two regimes for the enhancement of capture rate by salt concentration gradient: (a) drift-dominated regime, where the capture rate is roughly quadratic in the ratio of salt concentration in the receiver compartment to that in the donor compartment, and (b) antagonistic coupling regime at higher values of this ratio with a linear relation for the polymer capture rate.

Study on the polymer translocation induced blockade ionic current inside a nanopore by Langevin dynamics simulation

The blockade ionic current inside a nanopore due to polymer translocation is studied using a three-dimensional Langevin dynamics method. The blockade current IB is dependent on the polymer length N, polymer configuration, polymer–pore interaction, and charge of the polymer. The behavior of IB can be explained using four factors: (1) the volume vacancy fraction fV inside the pore; (2) the conformation of the polymer; (3) the location of the polymer inside the pore; and (4) the total charge Ztot inside the pore. We find that IB increases with fV but decreases with increasing |Ztot|. The influence of the polymer’s conformation is complex, dependent on the size of polymer RG and the cross-sectional size of the pore s. A compact conformation can decrease IB when RG > s but increase IB when RG < s. For the latter case, the conformation of the polymer is too small to block the pore, thus providing a broad passage for the ions. At the same fV, monomers will locate close to the surface with a large polymer–pore attraction, which also provides a large IB.

Polymer translocation in solid-state nanopores: Dependence on hydrodynamic interactions and polymer configuration

We present a Brownian dynamics investigation of 3-D Rouse and Zimm polymer translocation through solid-state nanopores. We obtain different scaling exponents α for both polymers using two initial configurations: minimum energy, and ‘steady-state’. For forced translocation, Rouse polymers (no hydrodynamic interactions), shows a large dependence of α on initial configuration and voltage. Higher voltages result in crowding at the nanopore exit and reduced α. When the radius of gyration is in equilibrium at the beginning and end of translocation, α=1+υ where υ is the Flory exponent. For Zimm polymers (including hydrodynamic interactions), crowding is reduced and α=2υ. Increased pore diameter does not affect α at moderate voltages that reduce diffusion effects. For unforced translocation using narrow pores, both polymers give α=1+2υ. Due to increased polymer–pore interactions in the narrow pore, hydrodynamic drag effects are reduced, resulting in identical scaling.

Influence of pore friction on the universal aspects of driven polymer translocation

We derive a scaling ansatz for the mean first passage time (MFPT) τ of a driven polymer chain through a nanopore as a function of the chain length N, the external bias f, and the effective pore-polymer friction η, and demonstrate that the pore-polymer interaction, which we introduce as a correction term to asymptotic scaling, is responsible for the dominant finite-size effect. This ansatz provides a simple procedure to extract the asymptotic τ in the large-N limit from a finite chain length data (obtained either from experiment or simulation) by eliminating the correction-to-scaling term. We validate the ansatz applying it on a large set of data for τ obtained using Brownian dynamics (BD) and Brownian dynamics tension propagation (BDTP) simulation results (Ikonen T. et al., Phys. Rev. E, 85 (2012) 051803; J. Chem. Phys., 137 (2013) 085101) for a variety of combination for N, f, and η. As an important practical application we demonstrate how the rescaling procedure can be used to quantitatively estimate the magnitude of the pore-polymer interaction from simulations or experimental data. Finally, we extend the BDTP theory to incorporate Zimm dynamics and find that the asymptotic results for τ (or the translocation exponent) remains unaltered with the inclusion of the hydrodynamics interactions (HI), although the convergence is slower than what we observe for Rouse dynamics. Using the rescaling ansatz we find that these new findings are in good agreement with the existing experimental results as well as with lattice Boltzmann results for driven polymer translocation (PT) for small N.

Translocation dynamics of a short polymer driven by an oscillating force

We study the translocation dynamics of a short polymer moving in a noisy environment and driven by an oscillating force. The dynamics is numerically investigated by solving a Langevin equation in a two-dimensional domain. We consider a phenomenological cubic potential with a metastable state to model the polymer-pore interaction and the entropic free energy barrier characterizing the translocation process. The mean first translocation time of the center of inertia of polymers shows a nonmonotonic behavior, with a minimum, as a function of the number of the monomers. The dependence of the mean translocation time on the polymer chain length shows a monotonically increasing behavior for high values of the number of monomers. Moreover, the translocation time shows a minimum as a function of the frequency of the oscillating forcing field for all the polymer lengths investigated. This finding represents the evidence of the resonant activation phenomenon in the dynamics of polymer translocation, whose occurrence is maintained for different values of the noise intensity.

Separating different polymers using an interacting nanopore: A Monte Carlo study

Translocation of a multi-polymer system containing two kinds of polymers, polymer A and polymer B, through an interacting nanopore is studied using dynamic Monte Carlo method. Polymer A and polymer B have different polymer-pore interactions. The probability of one kind of polymer first translocating through a nanopore is dependent on the polymer-pore interactions and the magnitude of driving force for monomers inside the nanopore. At weak driving, there are separation regions where one kind of polymer translocates through the pore always before another kind of polymer. A phase diagram containing separation regions and mixed region is presented. At last, the first-in first-out rule for the polymer translocation is investigated.

204 Polymer translocation

The translocation of a single macromolecule through a protein pore or a solid-state nanopore involves three major stages: (1) approach of the macromolecule towards the pore, (2) capture/recognition of the macromolecule at the pore entrance, and (3) threading through the pore (see the Figure) (Muthukumar, 2011). All of these stages are controlled by conformational entropy of the macromolecule, charge decoration, and the geometry of the pore, hydrodynamics, and electrostatic interactions. Chief among the contributing factors are the entropic barrier presented by the pore to the penetration of the macromolecule, pore–polymer interactions, electro-osmotic flow, and the drift-diffusion of the macromolecule in electrolyte solutions. A unifying theory of these contributing factors will be described in the context of a few illustrative experimental data on DNA translocation and protein translocation through protein pores and solid-state nanopores. Future challenges to specific biological systems will be briefly discussed.