Distribution Of Translocation Times Research Articles

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 sequences comprised of N = 20 charged monomers. The results were compared with those for 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.

Localized potential well vs binding site: Mapping solute dynamics in a membrane channel onto one-dimensional description.

In the one-dimensional description, the interaction of a solute molecule with the channel wall is characterized by the potential of mean force U(x), where the x-coordinate is measured along the channel axis. When the molecule can reversibly bind to certain amino acid(s) of the protein forming the channel, this results in a localized well in the potential U(x). Alternatively, this binding can be modeled by introducing a discrete localized site, in addition to the continuum of states along x. Although both models may predict identical equilibrium distributions of the coordinate x, there is a fundamental difference between the two: in the first model, the molecule passing through the channel unavoidably visits the potential well, while in the latter, it may traverse the channel without being trapped at the discrete site. Here, we show that when the two models are parameterized to have the same thermodynamic properties, they automatically yield identical translocation probabilities and mean translocation times, yet they predict qualitatively different shapes of the translocation time distribution. Specifically, the potential well model yields a narrower distribution than the model with a discrete site, a difference that can be quantified by the distribution's coefficient of variation. This coefficient turns out to be always smaller than unity in the potential well model, whereas it may exceed unity when a discrete trapping site is present. Analysis of the translocation time distribution beyond its mean thus offers a way to differentiate between distinct translocation mechanisms.

Non-stationary analysis of molecule capture and translocation in nanopore arrays.

Analytical formulas for the ON- and OFF-time distributions as well as for the autocorrelation function were derived for the case of single molecule translocation through nanopore arrays. The obtained time-dependent expressions describe very well experimentally recorded statistics of DNA translocations through an array of solid state nanopores, which allows us to extract molecule and system related physical parameters from the experimental traces. The necessity of non-stationary analysis as opposite to the steady-state approximation has been vindicated for the molecule capture process, where different time-dependent regimes were identified. A long tail in the distribution of translocation times has been rationalized invoking Markov jumps, where a possible sequential ordering of events was elucidated through autocorrelation function analysis.

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.

Highly driven polymer translocation from a cylindrical cavity with a finite length.

We present a computer simulation study of polymer translocation in a situation where the chain is initially confined to a closed cylindrical cavity in order to reduce the impact of conformational diversity on the translocation times. In particular, we investigate how the coefficient of variation of the distribution of translocation times can be minimized by optimizing both the volume and the aspect ratio of the cavity. Interestingly, this type of confinement sometimes increases the number and impact of hairpin conformations such that the fluctuations in the translocation process do not follow a power law in time (for instance, these fluctuations can even vary non-monotonically with time). We develop a tension-propagation model for a polymer compressed into such a confining volume and find that its predictions are in good agreement with our simulation results in the experimentally relevant strongly driven limit. Both the theoretical calculations and the simulation data yield a minimum in the coefficient of variation of the distribution of translocation times for a cylindrical cavity with an aspect ratio that makes it similar to a hemisphere. This provides guidance for the design of new devices based on the preconfinement of the target polymer into cavities.

The Semiflexible Polymer Translocation into Laterally Unbounded Region between Two Parallel Flat Membranes.

Using the dynamic Monte Carlo method, we investigate dynamics of semiflexible polymer translocation through a nanopore into laterally unbounded region between two parallel flat membranes with separation R in presence of an electric field inside the pore. The average translocation time τ initially decreases rapidly with increase of R in the range of R < 10 and then almost keeps constant for R ≥ 10, and the decline range increases with increase of dimensionless bending stiffness κ. We mainly study the effect of chain length N, κ and electric field strength E on the translocation process for R = 5. The translocation dynamics is significantly altered in comparison to an unconfined environment. We find τ ~ Nα, where the exponent α increases with increase of E for small κ. α initially increases slowly with increase of E and then keeps constant for moderate κ. α decreases with increase of E for large κ. However, α decreases with increase of κ under various E. In addition, we find τ ~ κβ. β decreases with increase of N under various E. These behaviors are interpreted in terms of the probability distribution of translocation time and the waiting time of an individual monomer segment passing through the pore during translocation.

Driven diffusion against electrostatic or effective energy barrier across α-hemolysin

We analyze the translocation of a charged particle across an α-Hemolysin (αHL) pore in the framework of a driven diffusion over an extended energy barrier generated by the electrical charges of the αHL. A one-dimensional electrostatic potential is extracted from the full 3D solution of the Poisson's equation. We characterize the particle transport under the action of a constant forcing by studying the statistics of the translocation time. We derive an analytical expression of translocation time average that compares well with the results from Brownian dynamic simulations of driven particles over the electrostatic potential. Moreover, we show that the translocation time distributions can be perfectly described by a simple theory which replaces the true barrier by an equivalent structureless square barrier. Remarkably, our approach maintains its accuracy also for low-applied voltage regimes where the usual inverse-Gaussian approximation fails. Finally, we discuss how the comparison between the simulated time distributions and their theoretical prediction results to be greatly simplified when using the notion of the empirical Laplace transform technique.

Interfacing solid-state nanopores with gel media to slow DNA translocations.

We demonstrate the ability to slow DNA translocations through solid-state nanopores by interfacing the trans side of the membrane with gel media. In this work, we focus on two reptation regimes: when the DNA molecule is flexible on the length scale of a gel pore, and when the DNA behaves as persistent segments in tight gel pores. The first regime is investigated using agarose gels, which produce a very wide distribution of translocation times for 5 kbp dsDNA fragments, spanning over three orders of magnitude. The second regime is attained with polyacrylamide gels, which can maintain a tight spread and produce a shift in the distribution of the translocation times by an order of magnitude for 100 bp dsDNA fragments, if intermolecular crowding on the trans side is avoided. While previous approaches have proven successful at slowing DNA passage, they have generally been detrimental to the S/N, capture rate, or experimental simplicity. These results establish that by controlling the regime of DNA movement exiting a nanopore interfaced with a gel medium, it is possible to address the issue of rapid biomolecule translocations through nanopores-presently one of the largest hurdles facing nanopore-based analysis-without affecting the signal quality or capture efficiency.

Polymer translocation into and out of an ellipsoidal cavity.

Monte Carlo simulations are used to study the translocation of a polymer into and out of an ellipsoidal cavity through a narrow pore. We measure the polymer free energy F as a function of a translocation coordinate, s, defined to be the number of bonds that have entered the cavity. To study polymer insertion, we consider the case of a driving force acting on monomers inside the pore, as well as monomer attraction to the cavity wall. We examine the changes to F(s) upon variation in the shape anisometry and volume of the cavity, the polymer length, and the strength of the interactions driving the insertion. For athermal systems, the free energy functions are analyzed using a scaling approach, where we treat the confined portion of the polymer to be in the semi-dilute regime. The free energy functions are used with the Fokker-Planck (FP) equation to calculate mean translocation times, as well as translocation time distributions. We find that both polymer ejection and insertion are faster for ellipsoidal cavities than for spherical cavities. The results are in qualitative agreement with those of a Langevin dynamics study in the case of ejection but not for insertion. The discrepancy is likely due to out-of-equilibrium conformational behaviour that is not accounted for in the FP approach.

Translocation of a polymer through a nanopore starting from a confining nanotube.

In this manuscript, Langevin Dynamics simulations and Tension-Propagation theory are used to investigate the forced translocation of a polymer from a confining tube through a nanopore situated at one of the tube's ends. The diameter of the tube allows for a control over the polymer conformations: decreasing the tube diameter reduces the number of conformations available to the polymer chain both before and during translocation. As the tube diameter is decreased, the translocation time is observed to increase. Interestingly, while the width of the distribution of translocation times is reduced if the chain starts in a tube, it reaches a maximum for weakly confining tubes. A Tension-Propagation approach is developed for the tube-nanopore setup in the strongly driven limit. Good agreement between the simulations and the theory allows for an exploration of the underlying physical mechanisms, including the calculation of an effective pore friction and the assessing of the impact of monomer crowding on the trans side.

Determination of Molecular Weights in Polyelectrolyte Mixtures Using Polymer Translocation through a Protein Nanopore.

We introduce a single molecular analysis technique for the evaluation of molecular weight distributions of polyelectrolyte solutions by measuring translocation times of sodium polystyrenesulfonate (NaPSS) chains in a mixture passing through an α-hemolysin protein nanopore. The ionic current through an α-hemolysin nanopore is partially blocked transiently when the pore is occupied by a polymer chain with an average residence time proportional to the molecular weight of the polymer chain. We have measured the translocation times for an equimolar mixture of four different molecular weight NaPSS standards and observed distinct translocation time distribution peaks, each of which corresponding to the different components in the mixture. Size exclusion chromatography analyses were performed on the equimolar and equiweight NaPSS mixtures of the same components and compared with the translocation time measurements. The experimental results demonstrate that measuring translocation times can be a competitive technique for estimating the broad molecular weight distributions of polyelectrolytes.

Evaluating the applicability of the Fokker-Planck equation in polymer translocation: a Brownian dynamics study.

Brownian dynamics (BD) simulations are used to study the translocation dynamics of a coarse-grained polymer through a cylindrical nanopore. We consider the case of short polymers, with a polymer length, N, in the range N = 21-61. The rate of translocation is controlled by a tunable friction coefficient, γ0p, for monomers inside the nanopore. In the case of unforced translocation, the mean translocation time scales with polymer length as <τ1> ∼ (N - Np)(α), where Np is the average number of monomers in the nanopore. The exponent approaches the value α = 2 when the pore friction is sufficiently high, in accord with the prediction for the case of the quasi-static regime where pore friction dominates. In the case of forced translocation, the polymer chain is stretched and compressed on the cis and trans sides, respectively, for low γ0p. However, the chain approaches conformational quasi-equilibrium for sufficiently large γ0p. In this limit the observed scaling of <τ1> with driving force and chain length supports the Fokker-Planck (FP) prediction that <τ> ∝ N/fd for sufficiently strong driving force. Monte Carlo simulations are used to calculate translocation free energy functions for the system. The free energies are used with the FP equation to calculate translocation time distributions. At sufficiently high γ0p, the predicted distributions are in excellent agreement with those calculated from the BD simulations. Thus, the FP equation provides a valid description of translocation dynamics for sufficiently high pore friction for the range of polymer lengths considered here. Increasing N will require a corresponding increase in pore friction to maintain the validity of the FP approach. Outside the regime of low N and high pore friction, the polymer is out of equilibrium, and the FP approach is not valid.

High-Bandwidth Protein Analysis Using Solid-State Nanopores

High-bandwidth measurements of the ion current through hafnium oxide and silicon nitride nanopores allow the analysis of sub-30 kD protein molecules with unprecedented time resolution and detection efficiency. Measured capture rates suggest that at moderate transmembrane bias values, a substantial fraction of protein translocation events are detected. Our dwell-time resolution of 2.5 μs enables translocation time distributions to be fit to a first-passage time distribution derived from a 1D diffusion-drift model. The fits yield drift velocities that scale linearly with voltage, consistent with an electrophoretic process. Further, protein diffusion constants (D) are lower than the bulk diffusion constants (D0) by a factor of ∼50, and are voltage-independent in the regime tested. We reason that deviations of D from D0 are a result of confinement-driven pore/protein interactions, previously observed in porous systems. A straightforward Kramers model for this inhibited diffusion points to 9- to 12-kJ/mol interactions of the proteins with the nanopore. Reduction of μ and D are found to be material-dependent. Comparison of current-blockage levels of each protein yields volumetric information for the two proteins that is in good agreement with dynamic light scattering measurements. Finally, detection of a protein-protein complex is achieved.

Translocation Kinetics of DNA through Nanopores Interfaced with Agarose Gel

Nanopores have recently emerged as an exciting tool for the study of single biological molecules. Essential to many nanopore-based applications, including DNA sequencing, is the ability to control the motion of charged biomolecules through the pore. While previous studies have primarily focused on increasing the average translocation times by changing the salt concentration, counter ion type, etc., velocity fluctuations during passage of identical DNA molecules remains a limitation for many applications.Here, the aim is to reduce the spread in the distribution of translocation times by controlling the initial conformation of DNA molecules captured by a solid-state nanopore. The nanopores are fabricated on a silicon nitride membrane with agarose gel on the trans side, essentially covering the membrane in a matrix of agarose fiber bundles. The DNA injected into the solution on the cis side passes through the nanopore and becomes trapped within the pores of the agarose. Once in the gel, the geometry of the DNA is limited and each molecule is forced to adopt a similar conformation. We compare the translocation kinetics under both voltage polarities, either driving DNA from the solution to the gel or vice versa. Furthermore, the distribution of translocation times is studied as a function of the agarose pore size, which is tuneable (300nm - 1μm), and dsDNA fragment lengths, allowing us to probe various conformational states. This investigation of the translocation kinetics of DNA through solid-state nanopores when captured from a gel matrix will lead to a better understanding of electrophoretic motion of dsDNA molecules through nanoconfined geometries and may provide a path to not only control the distribution of translocation times, but also reduce the passage speed.

Polymer translocation dynamics in the quasi-static limit

Monte Carlo (MC) simulations are used to study the dynamics of polymer translocation through a nanopore in the limit where the translocation rate is sufficiently slow that the polymer maintains a state of conformational quasi-equilibrium. The system is modeled as a flexible hard-sphere chain that translocates through a cylindrical hole in a hard flat wall. In some calculations, the nanopore is connected at one end to a spherical cavity. Translocation times are measured directly using MC dynamics simulations. For sufficiently narrow pores, translocation is sufficiently slow that the mean translocation time scales with polymer length N according to <τ> ∝ (N - N(p))(2), where N(p) is the average number of monomers in the nanopore; this scaling is an indication of a quasi-static regime in which polymer-nanopore friction dominates. We use a multiple-histogram method to calculate the variation of the free energy with Q, a coordinate used to quantify the degree of translocation. The free energy functions are used with the Fokker-Planck formalism to calculate translocation time distributions in the quasi-static regime. These calculations also require a friction coefficient, characterized by a quantity N(eff), the effective number of monomers whose dynamics are affected by the confinement of the nanopore. This was determined by fixing the mean of the theoretical distribution to that of the distribution obtained from MC dynamics simulations. The theoretical distributions are in excellent quantitative agreement with the distributions obtained directly by the MC dynamics simulations for physically meaningful values of N(eff). The free energy functions for narrow-pore systems exhibit oscillations with an amplitude that is sensitive to the nanopore length. Generally, larger oscillation amplitudes correspond to longer translocation times.

On the Lubensky-Nelson Model of Polymer Translocation through Nanopores

We revisit the one-dimensional stochastic model of an earlier study by D. K. Lubensky and D. R. Nelson for the electrically driven translocation of polynucleotides through α-hemolysin pores. We show that the model correctly describes two further important properties of the experimentally observed translocation time distributions, namely their spread (width) and their exponential decay. The resulting overall agreement between theoretical and experimental translocation time distributions is thus very good.

Dynamics of polymer translocation into a circular nanocontainer through a nanopore

Using Langevin dynamics simulations, we investigate the dynamics of polymer translocation into a circular nanocontainer through a nanopore under a driving force F. We observe that the translocation probability initially increases and then saturates with increasing F, independent of φ, which is the average density of the whole chain in the nanocontainer. The translocation time distribution undergoes a transition from a Gaussian distribution to an asymmetric distribution with increasing φ. Moreover, we find a nonuniversal scaling exponent of the translocation time as chain length, depending on φ and F. These results are interpreted by the conformation of the translocated chain in the nanocontainer and the time of an individual segment passing through the pore during translocation.

The distribution of DNA translocation times in solid-state nanopores

This paper systematically investigates the effects of solution viscosity, applied voltageand DNA chain length on the distribution of DNA translocation times through8 ± 2 nm diameter silicon nitride nanopores. Linear dsDNA translocation events were selectedbased on the magnitude of current blockage and accumulated into scatter plotsof current blockage and event duration (translocation time). The translocationtime distribution was fitted to the solution of a Smoluchowski-type equation for1D biased diffusion to a sink. The DNA drifting speed under bias and diffusionconstant were extracted from the fits as functions of solution viscosity, appliedvoltage and DNA chain length. Combined with the Einstein–Smoluchowski relation,this model allowed evaluation of the viscous drag force on DNA molecules. Thismodel also allowed estimation of the uncertainty in determining the DNA chainlength due to the influence of friction on the spread of translocation times in ananopore measurement. The data analysis suggests that the simple 1D biaseddiffusion model fits the experimental data well for a wide range of conditions. Somedeviations from predicted behavior were observed and show where additionalphenomena are likely to contribute to the distribution of DNA translocation times.

Translocation of compact polymer chains through a nanopore

We perform dynamical Monte Carlo simulation to study the forced translocation of compact polymer chains in three-dimensional lattices. The chains are driven through a nanopore connecting two infinite channels by an external field. The scaling properties of average translocation time τ and translocation time distribution (TTD) are studied. The effects of contact energy (ɛC), electric field strength (E), and nanopore width (L) on the scaling exponent (α) of average translocation time τ∼Nα and the TTD are investigated. For the scaling behavior of τ∼Nα, we have found that there is no crossover behavior with weak field strength when the nanopore width is one lattice spacing, which is less than average bond length, while crossover behaviors are observed for larger nanopore widths. The scaling exponent α also depends on contact energy ɛC and electric field strength E. For the TTD, it shifts from the Gaussian to a right-skew distribution with the electric field E increasing for short chains; while for long chains, multi-peak distributions are observed. As a primary and simple model, compact polymer chains are extensively used to capture the structure and thermodynamic properties of proteins, therefore we can investigate the protein translocation by simulating compact chain translocation, and this study will be useful for exploring the complex translocation behaviors of proteins.

Translocation of closed polymers through a nanopore under an applied external field

The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics simulations. The power-law scaling of the translocation time τ with the chain length N and the distribution of translocation time are investigated separately. For closed circular polymers, a crossover scaling of translocation time with chain length is found to be τ ≃ Nα, with the exponent α varying from α = 0.71 for relatively short chains to α = 1.29 for longer chains under driving force F = 5. The scaling behaviour for longer chains is in good agreement with experimental results, in which the exponent α = 1.27 for the translocation of double-strand DNA. The distribution of translocation time D(τ) is close to a Gaussian function for duration time τ < τp and follows a falling exponential function for duration time τ > τp. For closed knotted polymers, the scaling exponent α is 1.27 for small field force (F = 5) and 1.38 for large field force (F = 10). The distribution of translocation time D(τ) remarkably features two peaks appearing in the case of large driving force. The interesting result of multiple peaks can conduce to the understanding of the influence of the number of strands of polymers in the pore at the same time on translocation dynamic process and scaling property.