Poisson-Fokker-Planck model for biomolecules translocation through nanopore driven by electroosmotic flow

A non-continuous electroosmotic flow model (PFP model) is built based on Poisson equation, Fokker-Planck equation and Navier-Stokse equation, and used to predict the DNA molecule translocation through nanopore. PFP model discards the continuum assumption of ion translocation and considers ions as discrete particles. In addition, this model includes the contributions of Coulomb electrostatic potential between ions, Brownian motion of ions and viscous friction to ion transportation. No ionic diffusion coefficient and other phenomenological parameters are needed in the PFP model. It is worth noting that the PFP model can describe non-equilibrium electroosmotic transportation of ions in a channel of a size comparable with the mean free path of ion. A modified clustering method is proposed for the numerical solution of PFP model, and ion current translocation through nanopore with a radius of 1 nm is simulated using the modified clustering method. The external electric field, wall charge density of nanopore, surface charge density of DNA, as well as ion average number density, influence the electroosmotic velocity profile of electrolyte solution, the velocity of DNA translocation through nanopore and ion current blockade. Results show that the ion average number density of electrolyte and surface charge density of nanopore have a significant effect on the translocation velocity of DNA and the ion current blockade. The translocation velocity of DNA is proportional to the surface charge density of nanopore, and is inversely proportional to ion average number density of electrolyte solution. Thus, the translocation velocity of DNAs can be controlled to improve the accuracy of sequencing by adjusting the external electric field, ion average number density of electrolyte and surface charge density of nanopore. Ion current decreases when the ion average number density is larger than the critical value and increases when the ion average number density is lower than the critical value. Our numerical simulation shows that the translocation velocity of DNA given by the PFP model agrees with the experimental, results better than that given by PNP model or PB model.     

Controlling ionic current through a nanopore by tuning pH: a local equilibrium Monte Carlo study

ABSTRACT

The purpose of this work is to create a model of a nanofluidic transistor which is able to mimic the effects of pH on nanopore conductance. The pH of the electrolyte is an experimentally controllable parameter through which the charge pattern can be tuned: pH affects the ratio of the protonated/deprotonated forms of the functional groups anchored to the surface of the nanopore (for example, amino and carboxyl groups). Thus, the behaviour of the bipolar transistor changes as it becomes ion selective in acidic/basic environments. We relate the surface charge to pH and perform particle simulations (Local Equilibrium Monte Carlo) with different nanopore geometries (cylindrical and double conical). The simulations form a self consistent system with the Nernst–Planck equation with which we compute ionic flux. We discuss the mechanism behind pH-control of ionic current: formation of depletion zones.     

离子浓度及表面结构对岩石孔隙内水流动特性的影响

酸性环境引发的岩石孔隙表面溶解增加了孔隙内水溶液的盐离子浓度,破坏了孔隙的表面结构.本文采用分子动力学模拟的方法研究了纳米级岩石孔隙内水溶液的流动特性,分析了盐离子浓度和孔隙表面结构对水流速度分布的影响及原因.研究结果表明:纳米级岩石孔隙内的水溶液流动符合泊肃叶流动特性,流速呈"抛物线"分布;随盐离子浓度增加,水溶液内部氢键网络变得更为致密,水黏度随其呈线性增长;水溶液中离子浓度越大,孔隙表面对水流动的阻力越大,最大流速越小,速度分布的"抛物线"曲率半径越大;岩石孔隙表面结构的破坏改变了流动表面的粗糙程度,增加了孔隙表面对H2O分子的吸引力.随表面结构破坏程度的增大,水溶液在近壁区域的密度增大,流速降低;当表面破坏程度达到50%时,水溶液在近壁区域出现了明显的负边界滑移现象.     

Effect of salt concentration on the electrophoretic speed of a polyelectrolyte through a nanopore

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 with recent measurements in silicon nanopores.     

Density functional theory study on ion adsorption and electroosmotic flow in a membrane with charged cylindrical pores†

ABSTRACT

Ion adsorption and electroosmotic flow induced by an external electric field have a variety of practical applications, especially for membrane technology. In this work, a partially perturbative density functional theory (DFT) based on the modified fundamental measure theory was applied to investigate the ion density distributions and partitions in a charged cylindrical pore. Different types of electrolyte solutions, including both charge symmetric and asymmetric, were examined using the proposed theory with various pore diameters, bulk densities, ion valencies and surface charge densities. The ion concentration profiles calculated with the theory exhibit good agreements with the results of the Monte Carlo simulations, while the results of the Poisson–Boltzmann equation deviate greatly especially for the high valence electrolytes in narrow cylindrical pores. Some interesting phenomena discovered in both experiments and simulations, such as the reverse distribution of the ions and charge inversion, can be well reproduced with the DFT. Based on the ion concentration distributions obtained from the DFT, the transient velocity profiles of the electroosmotic flow in the charged cylindrical nanopores were calculated with the Navier–Stokes (NS) equation. The characteristics of the electroosmotic flow were discussed under the different bulk electrolyte concentrations and thickness of the electric double layer inside the nanopore. The enhancement of the velocity near the pore wall, which cannot be described by the traditional theory, was well characterised by the DFT combined with the NS equation.     

Salt permeation and exclusion in hydroxylated and functionalized silica pores

We use combined ab initio molecular dynamics (AIMD), grand canonical Monte Carlo, and molecular dynamics techniques to study the effect of pore surface chemistry and confinement on the permeation of salt into silica nanopore arrays filled with water. AIMD shows that 11.6 A diameter hydroxylated silica pores are relatively stable in water, whereas amine groups on functionalized pore surfaces abstract silanol protons, turning into NH3+. Free energy calculations using an ab initio parametrized force field show that the hydroxylated pores strongly attract Na+ and repel Cl- ions. Pores lined with NH3+ have the reverse surface charge polarity. Finally, studies of ions in carbon nanotubes suggest that hydration of Cl- is more strongly frustrated by pure confinement effects than Na+.     

Wigner crystal in snaked nanochannels

We study the properties of a Wigner crystal in snaked nanochannels and show that they are characterized by a conducting sliding phase at low charge densities and an insulating pinned phase above a critical charge density. The transition between these phases has a devil’s staircase structure typical for the Aubry transition in dynamical maps and the Frenkel-Kontorova model. We discuss the implications of this phenomenon for charge density waves in quasi-one-dimensional organic conductors and for supercapacitors in nanopore materials.     

Probing nanotube-nanopore interactions

We demonstrate a new nanoscale system consisting of a nanotube threaded through a nanopore in aqueous solution. Its electrical and mechanical properties are sensitive to experimentally controllable conformational changes on sub-Angstrom length scales. Ionic current transport through a nanopore is significantly suppressed by the threading nanotube and the mechanical interactions between the nanotube and pore are accounted for by a folding geometry. The experiments provide first measurements of the longitudinal resolution and metrology of a solid-state nanopore "microscope." This new nanostructure provides a means to study molecule-nanotube interactions in conducting ionic solutions as well as geometrical and surface properties of nanopores and nanotubes.     

Charge inversion at minute electrolyte concentrations

Anionic dimyristoylphosphatidic acid monolayers spread on LaCl3 solutions reveal strong cation adsorption and a sharp transition to surface overcharging at unexpectedly low bulk salt concentrations. We determine the surface accumulation of La3+ with anomalous x-ray reflectivity and find that La3+ compensates the lipid surface charge by forming a Stern layer with approximately 1 La3+ ion per 3 lipids below a critical bulk concentration, ct approximately 500 nM. Above ct, the surface concentration of La3+ increases to a saturation level with approximately 1 La3+ per lipid, thus implying that the total electric charge of the La3+ exceeds the surface charge. This overcharge is observed at approximately 4 orders of magnitude lower concentration than predicted in ion-ion correlation theories. We suggest that transverse electrostatic correlations between mobile ions and surface charges (interfacial Bjerrum pairing) may contribute to the charge inversion.     

Pink noise of ionic conductance through single artificial nanopores revisited

We report voltage-clamp measurements through single conical nanopore obtained by chemical etching of a single ion track in polyimide film. Special attention is paid to the pink noise of the ionic current (i.e., 1/f noise) measured with different filling liquids. The relative pink-noise amplitude is almost independent of concentration and pH for KCl solutions, but varies strongly using ionic liquids. In particular, we show that depending on the ionic liquid, the transport of charge carriers is strongly facilitated (low noise and higher conductivity than in the bulk) or jammed. These results show that the origin of the pink noise can be ascribed neither to fluctuations of the pore geometry nor to the pore wall charges, but rather to a cooperative effect on ions motion in confined geometry.     

Molecular understanding of osmosis in semipermeable membranes

We investigate single-file osmosis of water through a semipermeable membrane with an uncharged, a positively and a negatively charged nanopore. Molecular dynamics simulations indicate that the osmotic flux through a negatively charged pore (J_) is higher compared to the osmotic flux in a positively charged pore (J+) followed by the osmotic flux in the uncharged pore (J(0)), i.e., J_ > J+ > J(0). The molecular mechanisms governing osmosis, steady state osmosis, and the observed osmotic flux dependence on the nanopore charge are explained by computing all the molecular interactions involved and identifying the molecular interactions that play an important role during and after osmosis. This study helps in a fundamental understanding of osmosis and in the design of advanced nanoporous membranes for various applications of osmosis.     

Nanoscale volcanoes: accretion of matter at ion-sculpted nanopores

We demonstrate the formation of nanoscale volcano-like structures induced by ion-beam irradiation of nanoscale pores in freestanding silicon nitride membranes. Accreted matter is delivered to the volcanoes from micrometer distances along the surface. Volcano formation accompanies nanopore shrinking and depends on geometrical factors and the presence of a conducting layer on the membrane's back surface. We argue that surface electric fields play an important role in accounting for the experimental observations.     

Concentration polarization in translocation of DNA through nanopores and nanochannels

In this Letter we provide a theory to show that high-field electrokinetic translocation of DNA through nanopores or nanochannels causes large transient variations of the ionic concentrations in front and at the back of the DNA due to concentration polarization (CP). The CP causes strong local conductivity variations, which can successfully explain the nontrivial current transients and ionic distributions observed in molecular dynamics simulations of nanopore DNA translocations as well as the transient current dips and spikes measured for translocating hairpin DNA. Most importantly, as the future of sequencing of DNA by nanopore translocation will be based on time-varying electrical conductance, CP, must be considered in experimental design and interpretation--currently these studies are mostly based on the incomplete pore conductance models that ignore CP and transients in the electrical conductance.     

Mechanical properties of sorbents depending on nanopore sizes

The effect of the nanopore size on the mechanical properties of a porous carbon material with the density of 1.4 g/сm³ is discussed. The atomistic models of porous carbon materials depending on the nanopore size are constructed. The numerical experiments are implemented with using the molecular mechanical method based on the Brenner potential. The Young’s moduli are evaluated for porous carbon structures at certain nanopore dimensions and are found to decrease with the enlarging nanopores.     

Three-dimensional tomography of the beryllium fermi surface: surface charge redistribution

The discontinuity in the lattice periodic potential at surfaces often leads to the creation of new electronic surface states. We developed a photoemission based Fermi surface tomography whose surface sensitivity allowed us to quantify the charge redistribution on the Be(0001) surface. The volume enclosed by the bulklike Fermi surface is significantly reduced at the surface, consistent with the charge transfer to the two surface states as estimated from the area within their two-dimensional Fermi contours. This result represents the first quantification of the charge redistribution on a natural surface termination.     

基于AFM的固液界面表面电荷密度测量方法

固液界面的表面电荷会影响微纳流体系统的流体阻力,因此如何测量固液界面的表面电荷密度以及分析表面电荷的产生机理对于研究表面电荷对流体阻力的影响具有较大的意义。提出了一种基于接触式AFM的固液界面表面电荷密度测量方法。基于该方法测量了浸在去离子水和0.01 mol/L的NaCl溶液中的高硼硅玻璃和二氧化硅样本的表面电荷密度,并研究了溶液pH值对表面电荷的影响。研究结果表明高硼硅玻璃和二氧化硅由于表面硅烷基的电离带负电。溶液pH值和离子浓度的增加都会增加浸在去离子水和0.01 mol/L的NaCl溶液中高硼硅玻璃和二氧化硅的表面电荷密度的绝对值。     

Electrostatic properties of mercaptoundecanoic-acid-coated-gold surfaces interacting with TiO2 surfaces

We studied electrostatic properties of the MUA-coated-gold surface and the TiO₂ surface for design of gold–TiO₂ distribution, which may be controlled with electrostatic interactions. The forces between the surfaces were measured as a function of the salt concentration and pH value using the AFM. By applying the DLVO theory to the forces, the potential and charge density of the surfaces were quantitatively acquired for each salt concentration and each pH value. The potential and charge density dependences on the salt concentrations and the pH values were explained with the law of mass action and the ionizable groups on the surface.     

Non-monotonic swelling of a macroion due to correlation-induced charge inversion

It is known that a large, charged body immersed in a solution of multivalent counterions may undergo charge inversion as the counterions adsorb to its surface. We use the theory of charge inversion to examine the case of a deformable, porous macroion which may adsorb multivalent ions into its bulk to form a three-dimensional strongly-correlated liquid. This adsorption may lead to non-monotonic changes in the size of the macroion as multivalent ions are added to the solution. The macroion first shrinks as its bare charge is screened and then reswells as the adsorbed ions invert the sign of the net charge. We derive a value for the outward pressure experienced by such a macroion as a function of the ion concentration in solution. We find that for small deviations in the concentration of multivalent ions away from the neutral point (where the net charge of the body is zero), the swollen size grows parabolically with the logarithm of the ratio of multivalent ion concentration to the concentration at the neutral point.     

Driven translocation dynamics of polynucleotides through a nanopore: off-lattice Monte-Carlo simulations

The driven translocation dynamics of a polynucleotide chain through a nanopore is studied using off-lattice Monte-Carlo simulations, which plays an important role in the nanopore sequencing of polynucleotides. We report a detailed study on the dependence of translocation dynamics on the chain length and the local geometry near the nanopore. In particular, we find that the length dependence of the infection time of the chain could exhibit very different behaviors for different geometries.     

Stick-slip transition at the nanometer scale

We report the first observation of a stick-slip transition of surfactant solution flow through nanopores. From the experimental data, we were able to determine both the slip length and the critical wall shear stress from which slip occurs. Whereas the latter is found to increase linearly with the concentration, the former remains constant and approximately equal to 20 nm over the studied range of concentrations. We model slip to occur in the surfactant bilayer adsorbed at the nanopore wall. The stick-slip transition is then related to a reorganization of the surfactant bilayer from an entangled structure into independent layers flowing past one another, as evidenced by independent surface plasmon resonance experiments. We conclude from our analysis that surfactant solutions are always slipping in larger tubes. However, the larger the tube diameter, the smaller the relative slip contribution to the total flow.