Based on our formulation of the DNA electrophoresis near a pore [P. Rowghanian and A. Y. Grosberg, Phys. Rev. E 87, 042723 (2013)], we address the electrophoretic DNA capture into a nanopore as a steady-state process of particle absorption to a sink placed on top of an energy barrier. Reproducing the previously observed diffusion-limited and barrier-limited regimes as two different limits of the particle absorption process and matching the data, our model suggests a slower growth of the capture rate with the DNA length for very large DNA molecules than the previous model, motivating more experiments beyond the current range of electric field and DNA length. At moderately weak electric fields, our model predicts a different effect, stating that the DNA length dependence of the capture rate first disappears as the field is reduced and eventually reverses to a decreasing trend with $N$.
In a previous paper [S. Ghosal, Phys. Rev. E 74, 041901 (2006)] a hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through an axially symmetric slowly varying nanopore was presented in the limit of a vanishingly small Debye length. Here the case of a finite Debye layer thickness is considered while restricting the pore geometry to that of a cylinder of length much larger than the diameter. Further, the possibility of a uniform surface charge on the walls of the nanopore is taken into account. It is thereby shown that the calculated transit times are consistent …
The translocation of double-stranded DNA through a solid-state nanopore may either decrease or increase the ionic current depending on the ionic concentration of the surrounding solution. Below a certain crossover ionic concentration, the current change inverts from a current blockade to current enhancement. In this paper, we show that the crossover concentration for bundled DNA nanostructures composed of multiple connected DNA double-helices is lower than that of double-stranded DNA. Our measurements suggest that counterion mobility in the vicinity of DNA is reduced depending on the three-dim…
We consider voltage-driving DNA translocation through a nanopore in the present study. By assuming the DNA is coaxial with the cylindrical nanopore, a hydrodynamic model for determining effective force on a single DNA molecule in a nanopore was presented, in which density functional theory (DFT) combined with the continuum Navier-Stokes (NS) equations is utilized to investigate electro-osmotic flow and the viscous drag force acting on the DNA inside a nanopore. Surface charge on the walls of the nanopore is also taken into account in our model. The consistence between our calculation and the p…
Solid-state nanopores are single molecule sensors that measure changes in ionic current as charged polymers such as DNA pass through. Here, we present comprehensive experiments on the length, voltage and salt dependence of the frequency of double-stranded DNA translocations through conical quartz nanopores with mean opening diameter 15 nm. We observe an entropic barrier limited, length dependent translocation frequency at 4M LiCl salt concentration and a drift-dominated, length independent translocation frequency at 1M KCl salt concentration. These observations are described by a unifying conv…
The threading of a polymer chain through a small pore is a classic problem in polymer dynamics and underlies nanopore sensing technology. However important experimental aspects of the polymer motion in a solid-state nanopore, such as an accurate measurement of the velocity variation during translocation, have remained elusive. In this work we analysed the translocation through conical quartz nanopores of a 7 kbp DNA double-strand labelled with six markers equally spaced along its contour. These markers, constructed from DNA hairpins, give direct experimental access to the translocation dynamic…
Recent work has shown that the resistive force arising from viscous effects within the pore region could explain [Ghosal, S. Phys. Rev. E. vol. 71, 051904 (2006) and Phys. Rev. Lett. vol. 98, 238104 (2007)] observed translocation times in certain experiments involving voltage driven translocations of DNA through nanopores. The electrokinetic flow inside the pore and the accompanying viscous effects also play a crucial role in the interpretation of experiments where the DNA is immobilized inside a nanopore[U. Keyser, et al., Nature Physics vol. 2, 473 (2006)]. In this paper the viscous force is…
Graphene nanopore based sensor devices are exhibiting the great potential for the detection of DNA. To understand the fundamental aspects of DNA translocating through a graphene nanopore, in this work, molecular dynamics (MD) simulations and potential of mean force (PMF) calculations were carried out to investigate the layer impact of small graphene nanopore (2 nm-3 nm) to DNA translocation. It was observed that the ionic conductance was sensitive to graphene layer of open-nanopores, the probability for DNA translocation through graphene nanopore was related with the thickness of graphene nano…
Double-stranded DNA translocates through sufficiently large nanopores either in a linear, single-file fashion or in a folded hairpin conformation when captured somewhere along its length. We show that the folding state of DNA can be controlled by changing the electrolyte concentration, pH and PEG content of the measurement buffer. At 1 M LiCl or 0.35 M KCl in neutral pH, single-file translocations make up more than 90% of the total. We attribute the effect to the onset of electroosmotic flow from the pore at low ionic strength. Our hypothesis on the critical role of flows is supported by the p…
Motivated by DNA electrophoresis near a nanopore, we consider the flow field around an "elongated jet", a long thin source which injects momentum into a liquid. This solution qualitatively describes the electro-osmotic flow around a long rigid polymer, where due to electrohydrodynamic coupling, the solvent receives momentum from the electric field. Based on the qualitative behavior of the elongated jet solution, we develop a coarse-grained scheme which reproduces the known theoretical results regarding the electrophoretic behavior of a long rigid polymer and a polymer coil in a uniform field, …
In this short note, a correction is made to the recently proposed solution [1] to a 1D biased diffusion model for linear DNA translocation and a new analysis will be given to the data in [1]. It was pointed out [2] by us recently that this 1D linear translocation model is equivalent to the one that was considered by Schrodinger [3] for the Enrenhaft-Millikan measurements [4,5] on electron charge. Here we apply Schrodinger's first-passage-time distribution formula to the data set in [1]. It is found that Schrodinger's formula can be used to describe the time distribution of DNA translocation in…
Using theory and simulations, we carried out a first systematic characterization of DNA unzipping via nanopore translocation. Starting from partially unzipped states, we found three dynamical regimes depending on the applied force, f: (i) heterogeneous DNA retraction and rezipping (f < 17pN), (ii) normal (17pN < f < 60pN) and (iii) anomalous (f > 60pN) drift-diffusive behavior. We show that the normal drift-diffusion regime can be effectively modelled as a one-dimensional stochastic process in a tilted periodic potential. We use the theory of stochastic processes to recover the potential from …
Extracting the sequence information of DNA from the blocked ionic current is the crucial step of the ionic current-based nanopore sequencing approaches. The thinnest graphene nanopore, which contained only one layer of carbon atoms, potentially has ultra-high DNA sequencing sensitivity. However, the dynamical translocation information of DNA contained in the blocked ionic current has not been well understood to date. In this letter, an assessment to the sensitivity of ionic current-based graphene nanopore DNA sensing approach was carried out using molecular dynamics simulations. By filtering t…
The capture and translocation of biomolecules through nanometer-scale pores are processes with a potential large number of applications, and hence they have been intensively studied in the recent years. The aim of this paper is to review existing models of the capture process by a nanopore, together with some recent experimental data of short single- and double-stranded DNA captured by Cytolysin A (ClyA) nanopore. ClyA is a transmembrane protein of bacterial origin which has been recently engineered through site-specific mutations, to allow the translocation of double- and single-stranded DNA.…
We report translocation experiments on double-strand DNA through a silicon oxide nanopore. Samples containing DNA fragments with seven different lengths between 2000 to 96000 basepairs have been electrophoretically driven through a 10 nm pore. We find a power-law scaling of the translocation time versus length, with an exponent of 1.26 $\pm$ 0.07. This behavior is qualitatively different from the linear behavior observed in similar experiments performed with protein pores. We address the observed nonlinear scaling in a theoretical model that describes experiments where hydrodynamic drag on the…
The passage of DNA through a nanopore can be effectively decomposed into two distinct phases, docking and actual translocation. In experiments each phase is characterized by a distinct current signature which allows the discrimination of the two events. However, at low voltages a clear distinction of the two phases is lost. By using numerical simulations we clarify how the current signature associated to the docking events depends on the applied voltage. The simulations show that at small voltage the DNA globule enhances the pore conductance due to an enrichment of charge carriers. At high vol…
The translocation of a short DNA fragment through a nanopore is addressed when the perforated membrane contains an embedded electrode. Accurate numerical solutions of the coupled Poisson, Nernst-Planck, and Stokes equations for a realistic, fully three-dimensional setup as well as analytical approximations for a simplified model are worked out. By applying a suitable voltage to the membrane electrode, the DNA can be forced to preferably traverse the pore either along the pore axis or at a small but finite distance from the pore wall.
A tandem cell is proposed for DNA sequencing in which an exonuclease enzyme cleaves bases (mononucleotides) from a strand of DNA for identification inside a nanopore. It has two nanopores and three compartments with the structure [cis1, upstream nanopore (UNP), trans1=cis2, downstream nanopore (DNP), trans2]. The exonuclease is attached to the exit side of UNP in trans1/cis2. A cleaved base cannot regress into cis1 because of the remaining DNA strand in UNP. A profiled electric field over DNP with positive and negative components slows down base translocation through DNP. The proposed structur…
We present a new concept for the separation of DNA molecules by contour length that combines a nanofluidic ratchet, nanopore translocation and pulsed fields. Using Langevin Dynamics simulations, we show that it is possible to design pulsed field sequences to ratchet captured semiflexible molecules in such a way that only short chains successfully translocate, effectively transforming the nanopore process into a low pass molecular filter. We also show that asymmetric pulses can significantly enhance the device efficiency. The process itself can be performed with many pores in parallel, and it s…
In this paper we investigate the effects of graphene nanopore geometry on homopolymer ssDNA pulling process through nanopore using steered molecular dynamic (SMD) simulations. Different graphene nanopores are examined including axially symmetric and asymmetric monolayer graphene nanopores as well as five layer graphene polyhedral crystals (GPC). The pulling force profile, moving fashion of ssDNA, work done in irreversible DNA pulling and orientations of DNA bases near the nanopore are assessed. Simulation results demonstrate the strong effect of the pore shape as well as geometrical symmetry o…
A solid-state nanopore can electrophoretically capture a DNA molecule and pull it through in a folded configuration. The resulting ionic current signal indicates where along its length the DNA was captured. A statistical study using an 8 nm wide nanopore reveals a strong bias favoring the capture of molecules near their ends. A theoretical model shows that bias to be a consequence of configurational entropy, rather than a search by the polymer for an energetically favorable configuration. We also quantified the fluctuations and length-dependence of the speed of simultaneously translocating pol…
The determination of a patient's DNA sequence can, in principle, reveal an increased risk to fall ill with particular diseases [1,2] and help to design "personalized medicine" [3]. Moreover, statistical studies and comparison of genomes [4] of a large number of individuals are crucial for the analysis of mutations [5] and hereditary diseases, paving the way to preventive medicine [6]. DNA sequencing is, however, currently still a vastly time-consuming and very expensive task [4], consisting of pre-processing steps, the actual sequencing using the Sanger method, and post-processing in the form …
Longitudinal resolution and lateral sensitivity are decisive characteristics that determine the suitability of a nanopore sensor for sequencing a strand of DNA as well as other important polymers. Previous modeling of DNA induced ionic current blockades in single atom thick graphene nanopores has shown these nanopores to have sufficient longitudinal resolution to distinguish individual nucleobases along the length of a DNA molecule. Here we experimentally focus on the sensitivity to small changes in DNA diameter that can be discerned with graphene nanopores. We show that remarkably large sensi…
Flow-driven rotary motors drive functional processes in human society such as windmills and water wheels. Although examples of such rotary motors also feature prominently in cell biology, their synthetic construction at the nanoscale has thus far remained elusive. Here, we demonstrate flow-driven rotary motion of a self-organized DNA nanostructure that is docked onto a nanopore in a thin solid-state membrane. An elastic DNA bundle self assembles into a chiral conformation upon phoretic docking onto the solid-state nanopore, and subsequently displays a sustained unidirectional rotary motion of …
Recent experiments of translocation of double stranded DNA through nanopores [M. Wanunu \textit{et al.} Nature Nanotech. {\bf 5}, 160 (2010)] reveal that the DNA capture rate can be significantly influenced by a salt gradient across the pore. We show that osmotic flow combined with electrophoretic effects can quantitatively explain the experimental data on the salt-gradient dependence of the capture rate.
The detection of biomolecules at the single molecular level have important applications in the fields of biosensing and biomedical diagnosis. Solid state nanopore (SS-nanopore) is an effective tool to perform the single molecular detection, due to its unique properties of label-free and less sample consumption. The current SS-nanopore translocations of small biomolecules are driven by the electronic field force, thus easily influenced by the charges, shapes and sizes of the target molecules. Therefore, it remains a great challenge to control biomolecules to translocate through SS-nanopore, par…
A multiscale approach is used to simulate the translocation of DNA through a nanopore. Within this scheme, the interactions of the molecule with the surrounding fluid (solvent) are explicitly taken into account. By generating polymers of various initial configurations and lengths we map the probability distibutions of the passage times of the DNA through the nanopore. A scaling law behavior for the most probable of these times with respect to length is derived, and shown to exhibit an exponent that is in a good agreement with the experimental findings. The essential features of the DNA dynamic…
Nanopores -- nanosized holes that can transport ions and molecules -- are very promising devices for genomic screening, in particular DNA sequencing. Both solid-state and biological pores suffer from the drawback, however, that the channel constituting the pore is long, viz. 10-100 times the distance between two bases in a DNA molecule (0.5 nm for single-stranded DNA). Here, we demonstrate that it is possible to realize and use ultrathin nanopores fabricated in graphene monolayers for single-molecule DNA translocation. The pores are obtained by placing a graphene flake over a microsize hole in…
Several studies suggest strong correlation between different types of cancer and the relative concentration of short circulating RNA sequences (miRNA). Because of short length and low concentration, miRNA detection is not easy. Standard methods such as RT-PCR require both the standard PCR amplification step and a preliminary additional step of reverse transcription. In this paper, we investigate the use of DNA nanopores as a tool to detect short oligonucleotide sequences at the single molecule level. These nanostructures show two different conformations depending on the presence of DNA analogu…
DNA capture with high fidelity is an essential part of nanopore translocation. We report several important aspects of the capture process and subsequent translocation of a model DNA polymer through a solid-state nanopore in presence of an extended electric field using the Brownian dynamics simulation that enables us to record statistics of the conformations at every stage of the translocation process. By releasing the equilibrated DNAs from different equipotentials, we observe that the capture time distribution depends on the initial starting point and follows a Poisson process. The field grad…
Solid-state nanopores are promising tools for single molecule detection of both DNA and proteins. In this study, we investigate the patterns of ionic current blockades as DNA translocates into or out of the geometric confinement of such conically shaped pores. We studied how the geometry of a nanopore affects the detected ionic current signal of a translocating DNA molecule over a wide range of salt concentration. The blockade level in the ionic current depends on the translocation direction at a high salt concentration, and at lower salt concentrations we find a non-intuitive ionic current de…
Using first-principles quantum transport simulations, based on the nonequilibrium Green function formalism combined with density functional theory (NEGF+DFT), we examine changes in the total and local electronic currents within the plane of graphene nanoribbon with zigzag edges (ZGNR) hosting a nanopore which are induced by inserting a DNA nucleobase into the pore. We find a sizable change of the zero-bias conductance of two-terminal ZGNR + nanopore device after the nucleobase is placed into the most probable position (according to molecular dynamics trajectories) inside the nanopore of a smal…
The advent of solid state nanodevices allows for interrogating the physico-chemical properties of a polyelectrolyte chain by electrophoretically driving it through a nanopore. Salient dynamical aspects of the translocation process have been recently characterized by theoretical and computational studies of model polymer chains free from self-entanglement. However, sufficiently long equilibrated chains are necessarily knotted. The impact of such topological "defects" on the translocation process is largely unexplored, and is addressed in this study. By using Brownian dynamics simulations on a c…
We present a multiscale approach to the modeling of polymer dynamics in the presence of a fluid solvent. The approach combines Langevin Molecular Dynamics (MD) techniques with a mesoscopic Lattice-Boltzmann (LB) method for the solvent dynamics. A unique feature of the present approach is that hydrodynamic interactions between the solute macromolecule and the aqueous solvent are handled explicitly, and yet in a computationally tractable way due to the dual particle-field nature of the LB solver. The suitability of the present LB-MD multiscale approach is demonstrated for the problem of polymer …
We demonstrate simultaneous measurements of DNA translocation into glass nanopores using ionic current detection and fluorescent imaging. We verify the correspondence between the passage of a single DNA molecule through the nanopore and the accompanying characteristic ionic current blockage. By tracking the motion of individual DNA molecules in the nanocapillary perpendicular to the optical axis and using a model, we can extract an effective mobility constant for DNA in our geometry under high electric fields.
A hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through a nanopore is presented. It is assumed that the speed is determined by a balance of electrical and viscous forces arising from within the pore and that classical continuum electrostatics and hydrodynamics may be considered applicable. An explicit formula for the translocation speed as a function of the pore geometry and other physical parameters is obtained and is shown to be consistent with experimental measurements on DNA translocation through nanopores in silicon membranes. Experiments also show a we…
Methods for reducing and directly controlling the speed of DNA through a nanopore are needed to enhance sensing performance for direct strand sequencing and detection/mapping of sequence-specific features. We have created a method for reducing and controlling the speed of DNA that uses two independently controllable nanopores operated with an active control logic. The pores are positioned sufficiently close to permit co-capture of a single DNA by both pores. Once co-capture occurs, control logic turns on constant competing voltages at the pores leading to a `tug-of-war' whereby the molecule is…
Single-molecule based 3rd generation DNA sequencing technologies have been explored with tremendous effort, among which nanopore sequencing is considered as one of the most promising to achieve the goal of $1,000 genome project towards personalized medicine. Solid state nanopore is consented to be complementary to protein nanopore and subjected to extensive investigations in the past decade. However, the prevailing solid-state nanopore preparation still relies on focused ion or electron beams, which are expensive and time consuming. Here we demonstrate the fabrication of nanopores down to 19 n…
Both the translational diffusion coefficient $D$ and the electrophoretic mobility $μ$ of a short rod-like molecule (such as dsDNA) that is being pulled towards a nanopore by an electric field should depend on its orientation. Since a charged rod-like molecule tends to orient in the presence of an inhomogeneous electric field, $D$ and $μ$ will change as the molecule approaches the nanopore, and this will impact the capture process. We present a simplified study of this problem using theoretical arguments and Langevin Dynamics simulations. In particular, we introduce a new \textit{orientational …
We present in this paper an original approach to compute the electrophoretic mobility of rigid nucleo-protein complexes like nucleosomes. This model allows to address theoretically the influence of complex position along DNA, as well as wrapped length of DNA on the electrophoretic mobility of the complex. The predictions of the model are in qualitative agreement with experimental results on mononucleosomes assembled on short DNA fragments (<400bp). Influence of additional experimental parameters like gel concentration, ionic strength, effective charges is also discussed in the framework of the…
Gel electrophoresis allows to separate knotted DNA (nicked circular) of equal length according to the knot type. At low electric fields, complex knots being more compact, drift faster than simpler knots. Recent experiments have shown that the drift velocity dependence on the knot type is inverted when changing from low to high electric fields. We present a computer simulation on a lattice of a closed, knotted, charged DNA chain drifting in an external electric field in a topologically restricted medium. Using a simple Monte Carlo algorithm, the dependence of the electrophoretic migration of th…
Nanopore sequencing of DNA is a single-molecule technique that may achieve long reads, low cost, and high speed with minimal sample preparation and instrumentation. Here, we build on recent progress with respect to nanopore resolution and DNA control to interpret the procession of ion current levels observed during the translocation of DNA through the pore MspA. As approximately four nucleotides affect the ion current of each level, we measured the ion current corresponding to all 256 four-nucleotide combinations (quadromers). This quadromer map is highly predictive of ion current levels of pr…
We investigate the translocation of rods with different charge distributions using hybrid Langevin Dynamics and Lattice Boltzmann (LD-LB) simulations. Electrostatic interactions are added to the system using the $P^3M$ algorithm to model the electrohydrodynamic interactions (EHI). We first examine the free-solution electrophoretic properties of rods with various charge distributions. Our translocation simulation results suggest that the order parameter is asymmetric during the capture and escape processes despite the symmetric electric field lines, while the impacts of the charge distribution …
The last decade, nanopores have emerged as a new and interesting tool for the study of biological macromolecules like proteins and DNA. While biological pores, especially alpha-hemolysin, have been promising for the detection of DNA, their poor chemical stability limits their use. For this reason, researchers are trying to mimic their behaviour using more stable, solid-state nanopores. The most successful tools to fabricate such nanopores use high energy electron or ions beams to drill or reshape holes in very thin membranes. While the resolution of these methods can be very good, they require…
We propose using graphene electrodes with hydrogenated edges for solid-state nanopore-based DNA sequencing, and perform molecular dynamics simulations in conjunction with electronic transport calculations to explore the potential merits of this idea. The results of our investigation show that, compared to the unhydrogenated system, edge-hydrogenated graphene electrodes facilitate the temporary formation of H-bonds with suitable atomic sites in the translocating DNA molecule. As a consequence, the average conductivity is drastically raised by about 3 orders of magnitude while exhibiting signifi…
We consider elongated cylindrical particles, modeling e.g. DNA fragments or nano-rods, while translocating under the action of an externally applied voltage through a solid state nanopore. Particular emphasis is put on the concomitant potential energy landscape, encountered by the particle on its passage through the pore due to the complex interplay of various electrohydrodynamic effects beyond the realm of small Debye lengths. We find that the net potential energy difference across the membrane may be of opposite sign for short and long particles of equal diameters and charge densities (e.g. …
Translocation of DNA through a nanopore with embedded electrodes is at the centre of new rapid inexpensive sequencing methods which allow distinguishing the four nucleobases by their different electronic structure. However, the subnanometer separation between nucleotides in DNA requires ultra-sharp probes. Here, we propose a device architecture consisting of a nanopore formed in bilayer graphene, with the two layers acting as separate electrical contacts. The 0.34 nm interlayer distance of graphene is ideally suited for electrical coupling to a single nucleobase, avoiding the difficulty of fab…
Engineering the synthetic nanopores through lipid bilayer membrane to access the interior of a cell is a long persisting challenge in biotechnology. Here, we demonstrate the stability and dynamics of a tile-based 6-helix DNA nanotube (DNT) embedded in POPC lipid bilayer using the analysis of 0.2 microsecond long equilibrium MD simulation trajectories. We observe that the head groups of the lipid molecules close to the lumen cooperatively tilt towards the hydrophilic sugar-phosphate backbone of DNA and form a toroidal structure around the patch of DNT protruding in the membrane. Further, we exp…
We discuss multiscale simulations of long biopolymer translocation through wide nanopores that can accommodate multiple polymer strands. The simulations provide clear evidence of folding quantization, namely, the translocation proceeds through multi-folded configurations characterized by a well-defined integer number of folds. As a consequence, the translocation time acquires a dependence on the average folding number, which results in a deviation from the single-exponent power-law characterizing single-file translocation through narrow pores. The mechanism of folding quantization allows polym…
We investigate the impact of dielectric boundary forces on the translocation process of charged rigid DNA segments through solid neutral nanopores. We assess the electrostatic contribution to the translocation free energy barrier of a model DNA segment by evaluating the potential of mean force in absence and presence of polarization effects by means of coarse-grained molecular dynamics simulations. The effect of induced polarization charges has been taken into account by employing ICC*, a recently developed algorithm that can efficiently compute induced polarization charges induced on suitably…
Using Brownian dynamics simulations, we study the migration of long charged chains in an electrophoretic microchannel device consisting of an array of microscopic entropic traps with alternating deep regions and narrow constrictions. Such a device has been designed and fabricated recently by Han et al. for the separation of DNA molecules (Science, 2000). Our simulation reproduces the experimental observation that the mobility increases with the length of the DNA. A detailed data analysis allows to identify the reasons for this behavior. Two distinct mechanisms contribute to slowing down shorte…
We employ a multiscale approach to model the translocation of biopolymers through nanometer size pores. Our computational scheme combines microscopic Langevin molecular dynamics (MD) with a mesoscopic lattice Boltzmann (LB) method for the solvent dynamics, explicitly taking into account the interactions of the molecule with the surrounding fluid. Both dynamical and statistical aspects of the translocation process were investigated, by simulating polymers of various initial configurations and lengths. For a representative molecule size, we explore the effects of important parameters that enter …
We investigate the process of biopolymer translocation through a narrow pore using a multiscale approach which explicitly accounts for the hydrodynamic interactions of the molecule with the surrounding solvent. The simulations confirm that the coupling of the correlated molecular motion to hydrodynamics results in significant acceleration of the translocation process. Based on these results, we construct a phenomenological model which incorporates the statistical and dynamical features of the translocation process and predicts a power law dependence of the translocation time on the polymer len…
