Effect of charge patterns along a solid-state nanopore on polyelectrolyte translocation

Homopolymer and heteropolymer translocation through patterned pores under fluctuating forces

We investigate the translocation of a semiflexible polymer through extended patterned pores using Langevin dynamics simulations, specifically focusing on the influence of a time-dependent driving force. Our findings reveal that, akin to its flexible counterpart, a rigid chain-like molecule translocates faster when subjected to an oscillating force than a constant force of equivalent average magnitude. The enhanced translocation is strongly correlated with the stiffness of the polymer and the stickiness of the pores. The arrangement of the pores plays a pivotal role in translocation dynamics, deeply influenced by the interplay between polymer stiffness and pore-polymer interactions. For heterogeneous polymers with periodically varying stiffness, the oscillating force introduces significant variations in the translocation time distributions based on segment sizes and orientations. On the basis of these insights, we propose a sequencing approach that harnesses distinct pore surface properties that are capable of accurately predicting sequences in heteropolymers with diverse bending rigidities.

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.

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.

Translocation, Rejection and Trapping of Polyampholytes

Polyampholytes (PA) are a special class of polymers comprising both positive and negative monomers along their sequence. Most proteins have positive and negative residues and are PAs. Proteins have a well-defined sequence while synthetic PAs have a random charge sequence. We investigated the translocation behavior of random polyampholyte chains through a pore under the action of an electric field by means of Monte Carlo simulations. The simulations incorporated a realistic translocation potential profile along an extended asymmetric pore and translocation was studied for both directions of engagement. The study was conducted from the perspective of statistics for disordered systems. The translocation behavior (translocation vs. rejection) was recorded for all 220 sequences comprised of N = 20 charged monomers. The results were compared with those for 107 random sequences of N = 40 to better demonstrate asymptotic laws. At early times, rejection was mainly controlled by the charge sequence of the head part, but late translocation/rejection was governed by the escape from a trapped state over an antagonistic barrier built up along the sequence. The probability distribution of translocation times from all successful attempts revealed a power-law tail. At finite times, there was a population of trapped sequences that relaxed very slowly (logarithmically) with time. If a subensemble of sequences with prescribed net charge was considered the power-law decay was steeper for a more favorable net charge. Our findings were rationalized by theoretical arguments developed for long chains. We also provided operational criteria for the translocation behavior of a sequence, explaining the selection by the translocation process. From the perspective of protein translocation, our findings can help rationalize the behavior of intrinsically disordered proteins (IDPs), which can be modeled as polyampholytes. Most IDP sequences have a strong net charge favoring translocation. Even for sequences with those large net charges, the translocation times remained very dispersed and the translocation was highly sequence-selective.

The translocation dynamics of the polymer through a conical pore: Non-stuck, weak-stuck, and strong-stuck modes

The external voltage-driven polymer translocation through a conical pore (with a large opening at the entry and a small tip at the exit) is studied by using the Langevin dynamics simulation in this paper. The entire translocation process is divided into an approaching stage and a threading stage. First, the approaching stage starts from the polymer entering the large opening and ends up at a terminal monomer reaching the pore tip. In this stage, the polymer will undergo the conformation adjustment to fit the narrowed cross-sectional area of the pore, leading to three approaching modes: the non-stuck mode with a terminal monomer arriving at the pore tip smoothly, the weak-stuck mode for the polymer stuck inside the pore for a short duration with minor conformational adjustments, and the strong-stuck mode with major conformational changes and a long duration. The approaching times (the duration of the approaching stage) of the three approaching modes show different behavior as a function of the pore apex angle. Second, the threading stage describes that the polymer threads through the pore tip with a linear fashion. In this stage, an increase in the apex angle causes the reduction of the threading time (the duration of the threading stage) due to the increase in the driving force with the apex angle at the tip. Moreover, we also find that with the increase in the apex angle or the polymer length, the polymer threading dynamics will change from the quasi-equilibrium state to the non-equilibrium state.

Pore shapes effects on polymer translocation

We translocated polymers through pores of different shapes and interaction patterns in three dimensions by Langevin molecular dynamics. There were four simple cylindrical pores of the same length but with different diameters. The results showed that even though decreasing the pore diameter would always decrease the translocation velocity, it was strongly dependent on the shape of the increased pore diameter. Although increasing the pore diameter made the translocation faster in simple cylindrical pores, it was complicated in different pore shapes, e.g. increasing the diameter in the middle decreased the translocation velocity. Investigating polymer shapes through the translocation process and comparing the shapes by the cumulative waiting time for different pore structures reveals the non-equilibrium properties of translocation. Moreover, polymer shape parameters such as gyration radius, polymer center of mass, and average aspect ratio help us to distinguish different pore shapes and/or different polymers.

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

A polyelectrolyte threading through a nanopore in a trivalent salt solution is investigated by means of molecular dynamics simulations under a reflective wall boundary. By varying the chain length N and the strength E of the driving electric field applied inside the pore, the translocation time is carefully calculated to get rid of the bouncing effect because of the boundary. The results are analyzed under the scaling form ⟨τ⟩ ∼ N ^α E ^-δ and four driving force regimes; namely, the unbiased, the weakly driven, the strongly driven trumpet, and the strongly driven isoflux regime, are distinguished. The exponents are calculated in each regime and compared with the cases in the monovalent and divalent salt solutions. Owing to strong condensation of counter ions, the changes of the exponents in the force regimes are found to be nontrivial. A large increase in translocation time can be, however, achieved as the driving field is weak. The variations of the chain size, the ion condensation, and the effective chain charge show that the process is proceeded in a quasi-equilibrium way in the unbiased regime and deviated to exhibit strong nonequilibrium characteristics as E increases. Several astonishing scaling behaviors of the waiting time function, the translocation velocity, and the diffusion properties are discovered in the study. The results provide deep insights into the phenomena of polyelectrolyte translocation in various salt solutions at different driving forces.

Polyelectrolyte Translocation through a Tortuous Nanopore

Although nanopores have shown tremendous promise for use in DNA sequencing, the rate of translocation through most pores studied previously is too rapid for the genetic information to be read accurately. In this study, dissipative particle dynamics simulations were employed to investigate the feasibility of using tortuous nanopores to control the rate of polyelectrolyte translocation. Unlike many previous studies, our simulation method incorporates the effects of hydrodynamic and electrostatic interactions and the spatial variation of electric field strength. The average translocation time, ⟨τ⟩, increases with the pore length and tortuosity but decreases as the pore width increases. For the longest pore investigated, the introduction of tortuosity results in ⟨τ⟩ increasing by as much as 187% as compared to a straight pore. The temporal variation of bond tension indicates that slower translocation in tortuous nanopores is caused by inhibition of tension propagation.

Conformational fluctuations of a DNA electrophoretically translocating through a nanopore under the action of a motor protein

Single-file single-molecule electrophoresis through a nanopore has emerged as one of the successful methods in DNA sequencing. In gaining sufficient accuracy in the readout of the sequence, it is essential to position every nucleotide of the sequence with great accuracy and precision at the interrogation point of the nanopore. A combination of a ratcheting enzyme and a threaded DNA across a protein pore under an electric field is experimentally shown to be a viable method for DNA sequencing within the single-molecule electrophoresis technique. Using coarse-grained models of the enzyme and the protein nanopore, and Langevin dynamics simulations, we have characterized the conformational fluctuations of the DNA inside the nanopore. We show that the conformational fluctuations of DNA are significant for slowly operating enzymes such as phi29 DNA polymerase. Our results imply that there is considerable uncertainty in precisely positioning a nucleotide at the interrogation point of the nanopore. The discrepancy between the results of coarse-grained simulations and the experimentally successful accurate sequencing suggests that additional features of the experiments, such as explicit treatment of electrolyte ions and hydrodynamics, must be incorporated in the simulations to accurately model experimental constructs.

Simulation study on the migration of diblock copolymers in periodically patterned slits

The forced migration of diblock copolymers (A_NAB_NB) in periodically patterned slits was investigated by using Langevin dynamics simulation. The lower surface of the slit consists of stripe α and stripe β distributed in alternating sequence, while the upper one is formed only by stripe β. The interaction between block A and stripe α is strongly attractive, while all other interactions are purely repulsive. Simulation results show that the migration of the diblock copolymer is remarkably dependent on the driving force and there is a transition region at moderate driving force. The transition driving force f_t, where the transition region occurs, decreases monotonously with increasing length of block B (N_B) but is independent of the polymer length and the periodic length of the slit, which is interpreted from the free energy landscape of diblock copolymer migration. The results also show that periodic slits could be used to separate diblock polymers with different N_B by tuning the external driving force.

Trapped and non-trapped polymer translocations through a spherical pore

The polymer translocation through a spherical pore is studied using the Langevin dynamics simulation. The translocation events are classified into two types: one is the trapped translocation in which the entire polymer is trapped in the pore and the other is the non-trapped translocation where the pore cannot hold the whole polymer. We find that the trapped translocation is favored at large spheres and small external voltages. However, the monomer-pore attraction would lead to the non-monotonic behavior of the trapped translocation possibility out of all translocation events. Moreover, both the trapped and non-trapped translocation times are dependent on the polymer length, pore size, external voltage, and the monomer-pore attraction. There exist two pathways for the polymer in the trapped translocation: an actively trapped pathway for the polymer trapped in the pore before the head monomer arrives at the pore exit, and a passively trapped pathway for the polymer trapped in the pore while the head monomer is struggling to move out of the pore. The studies of trapped pathways can provide a deep understanding of the polymer translocation behavior.

Simulation study on the translocation of polyelectrolyte through conical nanopores

Experiments have suggested that the conical nanopore may be a reasonable sensor for the biopolymer analysis as it can provide high-resolution current signal. In this paper, we use Langevin dynamics simulation to study the translocation of charged polymer (polyelectrolyte) through three different conical nanopores, a single-conical nanopore with large entry and small exit (pore I), a single-conical nanopore with small entry and large exit (pore II), and a double-conical nanopore with the tip (narrowest place) at the middle (pore III). Simulation shows that the detailed translocation behaviors are of pore structure dependence. Pore I might be the most reasonable one for the polyelectrolyte analysis, especially at strong monomer-pore attraction, since it can efficiently reduce the polyelectrolyte speed at the tip. The simulation results are interpreted by the free energy profiles of the polyelectrolyte translocation through different pores and the time of individual monomer passing through the tips.

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.

Single molecule electrophoresis of star polymers through nanopores: Simulations

We study the translocation of charged star polymers through a solid-state nanopore using coarse-grained Langevin dynamics simulations, in the context of using nanopores as high-throughput devices to characterize polymers based on their architecture. The translocation is driven by an externally applied electric field. Our key observation is that translocation kinetics is highly sensitive to the functionality (number of arms) of the star polymer. The mean translocation time is found to vary non-monotonically with polymer functionality, exhibiting a critical value for which translocation is the fastest. The origin of this effect lies in the competition between the higher driving force inside the nanopore and inter-arm electrostatic repulsion in entering the pore, as the functionality is increased. Our simulations also show that the value of the critical functionality can be tuned by varying nanopore dimensions. Moreover, for narrow nanopores, star polymers above a threshold functionality do not translocate at all. These observations suggest the use of nanopores as a high-throughput low-cost analytical tool to characterize and separate star polymers.

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.

Theoretical study on the polymer translocation into an attractive sphere

We report a non-sampling model, combining the blob method with the standard lattice-based approximation, to calculate the free energy for the polymer translocation into an attractive sphere (i.e., spherical confined trans side) through a small pore. The translocation time is then calculated by the Fokker-Planck equation based on the free energy profile. There is a competition between the confinement effect of the sphere and the polymer-sphere attraction. The translocation time is increased due to the confinement effect of the sphere, whereas it is reduced by the polymer-sphere attraction. The two effects offset each other at a special polymer-sphere attraction which is dependent on the sphere size, the polymer length, and the driving force. Moreover, the entire translocation process can be divided into an uncrowded stage where the polymer does not experience the confinement effect of the sphere and a crowded stage where the polymer is confined by the sphere. At the critical sphere radius, the durations of the two (uncrowded and crowded) stages are the same. The critical sphere radius R^* has a scaling relation with the polymer length N as R^* ∼ N^β. The calculation results show that the current model can effectively treat the translocation of a three-dimensional self-avoiding polymer into the spherical confined trans side.

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.

Role of non-equilibrium conformations on driven polymer translocation

One of the major theoretical methods in understanding polymer translocation through a nanopore is the Fokker-Planck formalism based on the assumption of quasi-equilibrium of polymer conformations. The criterion for applicability of the quasi-equilibrium approximation for polymer translocation is that the average translocation time per Kuhn segment, ⟨τ⟩/NK, is longer than the relaxation time τ0 of the polymer. Toward an understanding of conditions that would satisfy this criterion, we have performed coarse-grained three dimensional Langevin dynamics and multi-particle collision dynamics simulations. We have studied the role of initial conformations of a polyelectrolyte chain (which were artificially generated with a flow field) on the kinetics of its translocation across a nanopore under the action of an externally applied transmembrane voltage V (in the absence of the initial flow field). Stretched (out-of-equilibrium) polyelectrolyte chain conformations are deliberately and systematically generated and used as initial conformations in translocation simulations. Independent simulations are performed to study the relaxation behavior of these stretched chains, and a comparison is made between the relaxation time scale and the mean translocation time (⟨τ⟩). For such artificially stretched initial states, ⟨τ⟩/NK < τ0, demonstrating the inapplicability of the quasi-equilibrium approximation. Nevertheless, we observe a scaling of ⟨τ⟩ ∼ 1/V over the entire range of chain stretching studied, in agreement with the predictions of the Fokker-Planck model. On the other hand, for realistic situations where the initial artificially imposed flow field is absent, a comparison of experimental data reported in the literature with the theory of polyelectrolyte dynamics reveals that the Zimm relaxation time (τZimm) is shorter than the mean translocation time for several polymers including single stranded DNA (ssDNA), double stranded DNA (dsDNA), and synthetic polymers. Even when these data are rescaled assuming a constant effective velocity of translocation, it is found that for flexible (ssDNA and synthetic) polymers with NK Kuhn segments, the condition ⟨τ⟩/NK < τZimm is satisfied. We predict that for flexible polymers such as ssDNA, a crossover from quasi-equilibrium to non-equilibrium behavior would occur at NK ∼ O(1000).

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.

Topology-Sensitive Microfluidic Filter for Polymers of Varying Stiffness

The separation of polymers based on their size, rigidity, and topology is an essential but also highly challenging task for nanoscience and engineering. Using hybrid molecular dynamics simulations that correctly take into account hydrodynamics, we have designed microfluidic channels for separating linear from ring polymers in dilute solutions. We establish that the transport velocity of the polymers is independent of their topology and rigidity when the channel walls are smooth and repulsive. However, when the walls are decorated with attractive spots arranged on lines parallel to the flow, ring polymers exhibit an order of magnitude higher transport velocity compared to linear chains. The spots induce a homeotropic-like reorientation of ring polymers close to walls leading to a tank treading motion along them, whereas linear chains are immobilized upon adsorption. This mechanism becomes more enhanced with increasing polymer rigidity. The presented technique holds thus promise for reliably separating nanoparticles based on their topology.

Effects of Nanopore Charge Decorations on the Translocation Dynamics of DNA

We have investigated the dynamics of single-stranded DNA as it translocates through charge-mutated protein nanopores. Translocation of DNA is a crucial step in nanopore-based sequencing platforms, where control over translocation speed remains one of the main challenges. Taking advantage of the interactions between negatively charged DNA and positively charged amino acid residues, the translocation speed of DNA can be manipulated by deliberate charge decorations inside the nanopore. We employed coarse-grained Langevin dynamics simulations to monitor the step-by-step movement of DNA through different mutations of α-hemolysin protein nanopores. We found that although the average translocation time per nucleotide is longer, in agreement with experiments, the DNA nucleotides do not translocate with a uniform speed. Furthermore, the location and spacing of the charge decorations can alter the translocation dynamics significantly, trapping DNA in some cases. Our findings can give insights when designing charge patterns in nanopores.

Temperature dependence of the translocation time of polymer through repulsive nanopores

The forced translocation of a polymer chain through repulsive nanopores was studied by using Langevin dynamics simulations. The polymer is in the compact globule state at low temperature and in the random coil state at high temperature. Simulation results show that the mean translocation time 〈τ〉 is highly dependent on the temperature T and the minimal 〈τ〉 is located near the coil-globule transition temperature. Moreover, the scaling behaviors 〈τ〉 ∼ N^α and 〈τ〉 ∼ F^-δ are studied, with N the polymer length and F the driving force inside the nanopore. Universal values α = 1.4 and δ = 0.85 are observed for the polymer in the random coil state. While for the polymer in the compact globule state, α decreases from α = 2 at weak driving to 1.2 at strong driving for short N and δ increases with decreasing T in the low F region, but we find universal exponents α = 1.6 for long N and δ = 0.85 in the large F region. Results show that polymer's conformation plays a much more important role than the diffusion coefficient in controlling the translocation time of the polymer chain.

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.

Electrostatic Control of Polymer Translocation Speed through α‑Hemolysin Protein Pore

The electrostatic origins behind the speed of translocation of a uniformly charged flexible macromolecule through α-hemolysin (αHL) protein pores under a voltage are investigated using variations in pH and electrolyte concentration. We have measured durations of successful threading of poly(styrenesulfonate) through αHL at two different pH conditions, pH 4.5 and pH 7.5, under various salt concentration conditions. Salt concentrations in the donor (cis) and the recipient (trans) compartments influence the polymer translocation dynamics differently, depending on pH. At both pH 4.5 and pH 7.5, decreasing the cis salt concentration, c_s,cis , results in faster polymer translocations. On the other hand, a decrease in trans salt concentration, c_s,trans , retards the polymer transport process at pH 4.5, while at pH 7.5 the translocation time is observed to be independent of c_s,trans . We present a theoretical model to calculate the translocation times from the free energy of the polymer along the translocation process to describe our experimental results. We show that the charge density of the polymer inside the nanopore is significantly affected by c_s,cis , explaining the cis salt effect on the speed of polymer translocation. The trans salt effects are attributed to the electrostatic interaction between the polymer and the exit portion of the αHL pore, which is determined by the pH of the trans compartment. At low pH where the net charge of the end of the αHL is positive, the attractive electrostatic interaction in trans becomes stronger, as c_s,trans decreases, resulting in delays in translocation process.

Conformation Change, Tension Propagation and Drift-Diffusion Properties of Polyelectrolyte in Nanopore Translocation

Using Langevin dynamics simulations, conformational, mechanical and dynamical properties of charged polymers threading through a nanopore are investigated. The shape descriptors display different variation behaviors for the cis- and trans-side sub-chains, which reflects a strong cis-trans dynamical asymmetry, especially when the driving field is strong. The calculation of bond stretching shows how the bond tension propagates on the chain backbone, and the chain section straightened by the tension force is determined by the ratio of the direct to the contour distances of the monomer to the pore. With the study of the waiting time function, the threading process is divided into the tension-propagation stage and the tail-retraction stage. At the end, the drift velocity, diffusive property and probability density distribution are explored. Owing to the non-equilibrium nature, translocation is not a simple drift-diffusion process, but exhibits several intermediate behaviors, such as ballistic motion, normal diffusion and super diffusion, before ending with the last, negative-diffusion behavior.

Fingerprinting of Peptides with a Large Channel of Bacteriophage Phi29 DNA Packaging Motor

Nanopore technology has become a highly sensitive and powerful tool for single molecule sensing of chemicals and biopolymers. Protein pores have the advantages of size amenability, channel homogeneity, and fabrication reproducibility. But most well-studied protein pores for sensing are too small for passage of peptide analytes that are typically a few nanometers in dimension. The funnel-shaped channel of bacteriophage phi29 DNA packaging motor has previously been inserted into a lipid membrane to serve as a larger pore with a narrowest N-terminal constriction of 3.6 nm and a wider C-terminal end of 6 nm. Here, the utility of phi29 motor channel for fingerprinting of various peptides using single molecule electrophysiological assays is reported. The translocation of peptides is proved unequivocally by single molecule fluorescence imaging. Current blockage percentage and distinctive current signatures are used to distinguish peptides with high confidence. Each peptide generated one or two distinct current blockage peaks, serving as typical fingerprint for each peptide. The oligomeric states of peptides can also be studied in real time at single molecule level. The results demonstrate the potential for further development of phi29 motor channel for detection of disease-associated peptide biomarkers.

Translocation dynamics of knotted polymers under a constant or periodic external field

We perform Brownian dynamics simulations to examine how knots alter the dynamics of polymers moving through nanopores under an external field. In the first part of this paper, we study the situation when the field is constant. Here, knots halt translocation above a critical force with jamming occurring at smaller forces for twist topologies compared to non-twist topologies. Slightly below the jamming transition, the polymer's transit times exhibit large fluctuations. This phenomenon is an example of the knot's molecular individualism since the conformation of the knot plays a large role in the chain's subsequent dynamics. In the second part of the paper, we study the motion of the chain when one cycles the field on and off. If the off time is comparable to the knot's relaxation time, one can adjust the swelling of the knot at the pore and hence design strategies to ratchet the polymer in a controllable fashion. We examine how the off time affects the ratcheting dynamics. We also examine how this strategy alters the fluctuations in the polymer's transit time. We find that cycling the force field can reduce fluctuations near the knot's jamming transition, but can enhance the fluctuations at very high forces since knots get trapped in metastable states during the relaxation process. The latter effect appears to be more prominent for non-torus topologies than torus ones. We conclude by discussing the feasibility of this approach to control polymer motion in biotechnology applications such as sequencing.

Polyelectrolyte Threading through a Nanopore

Threading charged polymers through a nanopore, driven by electric fields E, is investigated by means of Langevin dynamics simulations. The mean translocation time 〈 τ 〉 is shown to follow a scaling law Nα, and the exponent α increases monotonically from 1.16 (4) to 1.40 (3) with E. The result is double-checked by the calculation of mean square displacement of translocation coordinate, which asserts a scaling behavior tβ (for t near τ) with β complying with the relation αβ = 2. At a fixed chain length N, 〈τ〉 displayed a reciprocal scaling behavior E-1 in the weak and also in the strong fields, connected by a transition E-1.64(5) in the intermediate fields. The variations of the radius of gyration of chain and the positions of chain end are monitored during a translocation process; far-from-equilibrium behaviors are observed when the driving field is strong. A strong field can strip off the condensed ions on the chain when it passes the pore. The total charges of condensed ions are hence decreased. The studies for the probability and density distributions reveal that the monomers in the trans-region are gathered near the wall and form a pancake-like density profile with a hump cloud over it in the strong fields, due to fast translocation.

Simulation on the translocation of homopolymers through sandwich-like compound channels

The forced translocation of homopolymers through αβα sandwich-like compound channels was investigated by Monte Carlo simulation. The interaction between polymer and part α is strongly attractive, whereas that between polymer and part β is purely repulsive. Simulation results show that the translocation is influenced obviously by the length of part β (Lβ) and the starting position of part β (Lα1). For small Lβ, the translocation is mainly governed by the escaping process, and polymer is trapped near the exit of the channel. However, the translocation time can be tuned by varying Lα1 and the fastest translocation can be achieved at relatively large Lα1. Whereas for large Lβ and small Lα1, the translocation is mainly controlled by the filling process. It is difficult for polymer to enter the channel, and polymer is trapped at the first αβ interface. Finally, the dynamics for the filling process and the escaping process are discussed from the view of free-energy landscape, respectively.

Suspended Solid-state Membranes on Glass Chips with Sub 1-pF Capacitance for Biomolecule Sensing Applications

Solid-state membranes are finding use in many applications in nanoelectronics and nanomedicine, from single molecule sensors to water filtration, and yet many of their electronics applications are limited by the relatively high current noise and low bandwidth stemming from the relatively high capacitance (>10 pF) of the membrane chips. To address this problem, we devised an integrated fabrication process to grow and define circular silicon nitride membranes on glass chips that successfully lower the chip capacitance to below 1 pF. We use these devices to demonstrate low-noise, high-bandwidth DNA translocation measurements. We also make use of this versatile, low-capacitance platform to suspend other thin, two-dimensional membrane such as graphene.

Observing Changes in the Structure and Oligomerization State of a Helical Protein Dimer Using Solid-State Nanopores

Protein analysis using solid-state nanopores is challenging due to limitations in bandwidth and signal-to-noise ratio. Recent improvements of those two aspects have made feasible the study of small peptides using solid-state nanopores, which have an advantage over biological counterparts in tunability of the pore diameter. Here, we report on the detection and characterization of peptides as small as 33 amino acids. Silicon nitride nanopores with thicknesses less than 10 nm are used to provide signal-to-noise (S/N) levels up to S/N ∼ 10 at 100 kHz. We demonstrate differentiation of monomer and dimer forms of the GCN4-p1 leucine zipper, a coiled-coil structure well studied in molecular biology, and compare with the unstructured 33-residue monomer. GCN4-p1 is sequence segment associated with homodimerization of the transcription factor General Control Nonderepressible 4 (GCN4), which is involved in the control of amino acid synthesis in yeast. The differentiation between two oligomeric forms demonstrates the capabilities of improved solid-state nanopore platforms to extract structural information involving short peptide structures.

Polymer translocation: the first two decades and the recent diversification

Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous-infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.