Nanopore Conductance Research Articles

Investigating the expansion behavior of silicon nitride nanopores

Nanopores are a single-molecule detection platform that has attracted more and more researchers’ attention, but so far there is still a lack of systematic research on their stability. In this study, we investigated the mechanism behind the expansion behavior of solid-state nanopores and its effect on the electrical properties of nanopores. Through the analysis of electron energy loss spectroscopy, it was found that the expansion process of nanopores is accompanied by the loss of silicon elements. Three nanopore expansion models can well explain the differential impact of silicon element loss in different regions on the electrical properties of nanopores. Molecular dynamics simulations analyzed the differences in nanopore conductivity and expansion rate corresponding to different expansion models from the perspective of single-atom loss. Finally, we demonstrated that chemical modification can isolate direct contact between the nanopore wall and the solution, thereby greatly delaying the expansion behavior of solid-state nanopores.

Improved Conductance Blockage Modeling of Cylindrical Nanopores, from 2D to Thick Membranes.

The ionic current blockage from a nanopore sensor is a fundamental metric for characterizing its dimensions and identifying molecules translocating through it. Yet, most analytical models predicting the conductance of a nanopore in both open and obstructed states remain inaccurate. Here, using an oblate spheroidal coordinate framework to study the electrical response of nanopore access regions, we reveal that the widely used model from Kowalczyk et al. significantly overestimates access region contributions when blocked by a cylindrical object, like DNA. To address this, we present an improved analytical model for the obstructed access resistance, which we establish as highly accurate through finite-element simulations, especially for ultrathin membranes and long narrow channels. Equipped with an improved nanopore conductance model, this work provides tools for more accurate calculation of the pore size and for the expected blockade from DNA, of high practical value for many biosensing applications.

Differentiating Single Multiple Nanopore Through Conductance Distribution Analysis

AbstractSolid‐state nanopore sensors, a type of resistive pulse sensing, achieve optimal signal‐to‐noise performance with a single nanopore. However, the processes involved in solid‐state nanopore fabrication and subsequent measurements frequently lead to the formation of multiple nanopores, posing a challenge for precise detection. To address this issue, here, a novel and expedient technique to verify the presence of a single nanopore on a chip is developed. The methodology includes measuring the nanopore's conductance in solutions of various salt conditions, followed by a comparison of these results against a theoretical conductance model. This comparison is instrumental in distinguishing between single and multiple nanopores. Additionally, the study delves into various factors that influence the conductance curve, such as deviations in pore shape from the standard circle and inconsistencies in pore diameter. This approach significantly enhances the practical application of low‐cost nanopore preparation techniques, particularly in scenarios like controlled breakdown nanopore fabrication, where the formation of multiple nanopores is a common concern.

Nanoscale electrohydrodynamic ion transport: Influences of channel geometry and polarization-induced surface charges.

Electrohydrodynamic ion transport has been studied in nanotubes, nanoslits, and nanopores to mimic the advanced functionalities of biological ion channels. However, probing how the intricate interplay between the electrical and mechanical interactions affects ion conduction in asymmetric nanoconduits presents further obstacles. Here, ion transport across a conical nanopore embedded in a polarizable membrane under an electric field and pressure is analyzed by numerically solving a continuum model based on the Poisson, Nernst-Planck, and Navier-Stokes equations. We report an anomalous ionic current depletion, of up to 75%, and an unexpected rise in current rectification when pressure is exerted along the external electric field. Membrane polarization is revealed as the prerequisite to obtain this previously undetected electrohydrodynamic coupling. The electric field induces large surface charges at the pore tip due to its conical shape, creating nonuniform electrical double layers (EDL) with a massive accumulation of electrolyte ions near the orifice. Once applied, the pressure distorts the quasiequilibrium distribution of the EDL ions to influence the nanopore conductivity. Our fundamental approach to inspect the effect of pressure on the channel EDL (and thus ionic conductance) in contrast to its effect on the current arising from the hydrodynamic streaming of ions further explains the pressure-sensitive ion transport in different nanochannels and physical regimes manifested in past experiments, including the hitherto inexplicit mechanism behind the mechanically activated ion transport in carbon nanotubes. This enhances our broad understanding of nanoscale electrohydrodynamic ion transport, yielding a platform to build nanofluidic devices and ionic circuits with more robust and tunable responses to electrical and mechanical stimuli.

Ion concentration polarization causes a nearly pore-length-independent conductance of nanopores.

There has been a great amount of interest in nanopores as the basis for sensors and templates for preparation of biomimetic channels as well as model systems to understand transport properties at the nanoscale. The presence of surface charges on the pore walls has been shown to induce ion selectivity as well as enhance ionic conductance compared to uncharged pores. Here, using three-dimensional continuum modeling, we examine the role of the length of charged nanopores as well as applied voltage for controlling ion selectivity and ionic conductance of single nanopores and small nanopore arrays. First, we present conditions where the ion current and ion selectivity of nanopores with homogeneous surface charges remain unchanged, even if the pore length decreases by a factor of 6. This length-independent conductance is explained through the effect of ion concentration polarization (ICP), which modifies local ionic concentrations, not only at the pore entrances but also in the pore in a voltage-dependent manner. We describe how voltage controls the ion selectivity of nanopores with different lengths and present the conditions when charged nanopores conduct less current than uncharged pores of the same geometrical characteristics. The manuscript provides different measures of the extent of the depletion zone induced by ICP in single pores and nanopore arrays, including systems with ionic diodes. The modeling shown here will help design selective nanopores for a variety of applications where single nanopores and nanopore arrays are used.

Probing nanopore surface chemistry through real-time measurements of nanopore conductance response to pH changes.

We developed a flow cell apparatus and method for streamlined, real-time measurements of nanopore conductance (G) in response to pH changes. By time-resolving the measurements of interfacial kinetics, we were able to probe nanopore surface coating presence and properties more thoroughly than in our previous work. Nanopores have emerged as a prominent tool for single-molecule sensing, characterization, and sequencing of DNA, proteins, and carbohydrates. Nanopore surface chemistry affects analyte passage, signal characteristics, and sensor lifetime through a range of electrostatic, electrokinetic, and chemical phenomena, and optimizing nanopore surface chemistry has become increasingly important. Our work makes nanopore surface chemistry characterizations more accessible as a complement to routine single-pH conductance measurements used to infer nanopore size. We detail the design and operation of the apparatus and discuss the trends in G and capacitance. Characteristic G vs pH curves matching those obtained in previous work could be obtained with the addition of time-resolved interfacial kinetic information. We characterized native and chemically functionalized (carboxylated) silicon nitride (SiNx) nanopores, illustrating how the method can inform of thin film compositions, interfacial kinetics, and nanoscale chemical phenomena.

Cation pumping against a concentration gradient in conical nanopores characterized by load capacitors

We study the cation transport against an external concentration gradient (cation pumping) that occurs in conical nanopores when zero-average oscillatory and white noise potentials are externally applied. This pumping, based on the electrically asymmetric nanostructure, is characterized here by a load capacitor arrangement. In the case of white noise signals, the conical nanopore acts as an electrical valve that allows extraction of order from chaos. No molecular carriers, specific ion pumps, and competitive ion-binding phenomena are required. The nanopore conductance on/off states mimic those of the voltage-gated ion channels in the cell membrane. These channels allow modulating membrane potentials and ionic concentration gradients along oscillatory pulses in circadian rhythms and the cell cycle. We show that the combination of asymmetric nanostructures with load capacitors can be useful for the understanding of nanofluidic processes based on bioelectrochemical gradients.

Electrical conductance of conical nanopores: Symmetric and asymmetric salts and their mixtures.

We have studied experimentally the electrical conductance-voltage curves of negatively and positively charged conical nanopores bathed in ionic solutions with monovalent, divalent, and trivalent cations at electrochemically and biologically relevant ionic concentrations. To better understand the interaction between the pore surface charge and the mobile ions, both single salts and salt mixtures have been considered. We have paid attention to the effects on the conductance of the cation valency, the pore charge asymmetry, and the pore charge inversion phenomena due to trivalent ions, both in single salts and salt mixtures. In addition, we have described how small concentrations of multivalent ions can tune the nanopore conductance due to monovalent majority ions, together with the effect of these charges on the additivity of ionic conductance and fluoride-induced negative differential conductance phenomena. This compilation and discussion of previously presented experimental data offers significant insights on the interaction between fixed and mobile charges confined in nanoscale volumes and should be useful in establishing and checking new models for describing ionic transport in the vicinity of charged surfaces.

Electrical Conductance of Charged Nanopores.

A nanopore’s response to an electrical potential drop is characterized by its electrical conductance, . For the last two decades, it has been thought that at low electrolyte concentrations, , the conductance is concentration-independent such that . It has been recently demonstrated that surface charge regulation changes the dependency to , whereby the slope typically takes the values α = 1/3 or 1/2. However, experiments have observed slopes of 2/3 and 1 suggesting that additional mechanisms, such as convection and slip-lengths, appear. Here, we elucidate the interplay between three mechanisms: surface charge regulation, convection, and slip lengths. We show that the inclusion of convection does not change the slope, and when the effects of hydrodynamic slip are included, the slope is doubled. We show that when all effects are accounted for, α can take any value between 0 and 1 where the exact value of the slope depends on the material properties. This result is of utmost importance in designing any electro-kinetically driven nanofluidic system characterized by its conductance.

Enhanced electroosmotic flow, conductance and ion selectivity of a viscoplastic fluid in a hydrophobic cylindrical pore

We have studied the electroosmotic flow (EOF) of a non-Newtonian viscoplastic fluid, modeled as a Herschel-Bulkley (H-B) fluid, through a single hydrophobic nanopore in a uniformly charged solid hydrophobic membrane separating two identical reservoirs. An interfacial slip velocity develops when the viscoplastic fluid is strained over a hydrophobic surface. It is well established in the context of Newtonian fluid that the interfacial slip at the charged surface augments the EOF. For the viscoplastic fluid, the EOF depends on the fluid behavioral index and the yield stress. We have illustrated the impact of the interfacial slip on the EOF, conductance and ion selectivity of the cylindrical nanopore at different yield stresses for both the shear thinning and the shear thickening cases of the H-B fluid. The slip velocity, characterized by the slip length, enhances the average flow and conductance of the pore and this impact is pronounced for the shear thinning case. The unyielded zone, which develops along the central line of the pore, contracts as the slip length is increased. The ion concentration polarization enhances for the shear thinning fluid, however, the slip length creates a marginal increment. The counterion selectivity of the pore is found to be significant for the Newtonian case as compared to the non-Newtonian fluid and the velocity slip enhances the ion selectivity further. We have determined an analytic solution for the EOF of a power-law fluid in a long hydrophobic tube. Our computed solution for the case of a long tube effectively coincides with this analytic solution. An increment in the pore length reduces its conductance but enhances the ion selectivity. The increment of the average EOF for the hydrophobic pore as compared to the no-slip case grows as the pore length is increased.

Ion Transport in pH-Regulated Double-Barreled Nanopores.

Single-molecule detection and characterization with nanopores is a powerful technique that does not require labeling. Multinanopore systems, especially double nanopores, have attracted wide attention and have been applied in many fields. However, theoretical studies of electrokinetic ion transport in nanopores mainly focus on single nanopores. In this paper, for the first time, a theoretical study of pH-regulated double-barreled nanopores is conducted using three-dimensional Poisson-Nernst-Planck equations and Navier-Stokes equations. Four ionic species and the surface chemistry on the walls of the nanopores are included. The results demonstrate that the properties of the bulk salt solution significantly affect nanopore conductivity and ion transport phenomena in nanopores. There are two ion-enriched zones and two ion-depleted zones in double-barreled nanopores. Due to the symmetry of the double-barreled nanopore structure and surface charge density, there is no ionic rectification effect in double-barreled nanopores. The ion selectivity is similar to that of conventional single pH-regulated nanopores.

Photoswitchable Binary Nanopore Conductance and Selective Electronic Detection of Single Biomolecules under Wavelength and Voltage Polarity Control.

We fabricated photoregulated thin-film nanopores by covalently linking azobenzene photoswitches to silicon nitride pores with ∼10 nm diameters. The photoresponsive coatings could be repeatedly optically switched with deterministic ∼6 nm changes to the effective nanopore diameter and of ∼3× to the nanopore ionic conductance. The sensitivity to anionic DNA and a neutral complex carbohydrate biopolymer (maltodextrin) could be photoswitched "on" and "off" with an analyte selectivity set by applied voltage polarity. Photocontrol of nanopore state and mass transport characteristics is important for their use as ionic circuit elements (e.g., resistors and binary bits) and as chemically tuned filters. It expands single-molecule sensing capabilities in personalized medicine, genomics, glycomics, and, augmented by voltage polarity selectivity, especially in multiplexed biopolymer information storage schemes. We demonstrate repeatedly photocontrolled stable nanopore size, polarity, conductance, and sensing selectivity, by illumination wavelength and voltage polarity, with broad utility including single-molecule sensing of biologically and technologically important polymers.

Effects of surface-charge regulation, convection, and slip lengths on the electrical conductance of charged nanopores

The nanofluidic paradigm that low-concentration conductance is concentration-independent has recently come under scrutiny. Recent works have shown that the conductance depends on the concentration and that the slope, $\ensuremath{\alpha}$, ranges between 0 and $1/2$. However, experiments have also measured slopes of $2/3$ and 1. In this work an analytical solution for the conductance is derived that accounts for surface charge regulation (SCR), advection (ADV), and slip-lengths (SL). This parameter free model demonstrates that $\ensuremath{\alpha}$ is determined by SCR, ADV, SL, and ranges between 0 and 1. Consequently our results imply that all three phenomena are essential in the design of nanofluidic systems.

Ionic Conductivity of Nanopores with Electrically Conductive Surface: Comparison Between 1D and 2D Models

AbstractNanoporous membranes with high ionic conductivity are advantageous in such electrochemical processes as (reverse) electrodialysis, capacitive deionization, and hydrogen energy conversion. In membranes with electrically conductive surface, the conductivity can be regulated by varying the surface potential. This work is devoted to the theoretical study of switchable ionic conductivity. The transport of ions is described by the 2D space charge model and 1D uniform potential model taking into account the Stern layer. The conductivity decreases with lowering the Stern layer permittivity due to enhanced screening of electronic surface charge. The growth of surface potential leads to the conductivity enhancement due to accumulation of more counter‐ions inside the nanopore. For nanopores with constant surface charge density, the ionic conductivity follows the bulk electrolyte conductivity at high ion concentrations, and becomes independent of concentration when the latter is low. In contrast, the nanopores with constant surface potential demonstrate a linear decrease of conductivity with lowering the logarithm of ion concentration. The deviation between 1D and 2D models becomes noticeable at higher values of Stern layer permittivity, pore radius, electrolyte concentration, and surface potential. The proposed models are verified by comparison with experimental data on pure water conductivity in charged porous matrix.

Influence of Electrolyte Concentration on Single-Molecule Sensing of Perfluorocarboxylic Acids.

Perfluorocarboxylic acids (PFCAs) are an emerging class of persistent organic pollutants. During the fabrication process, it is unavoidable to form PFCA homologs or isomers which exhibit distinct occurrence, bioaccumulation, and toxicity. The precision measurement of PFCAs is therefore of significant importance. However, the existing characterization techniques, such as LC-MS/MS, cannot fully meet the requirement of isomer-specific analysis, largely due to the lack of authentic standards. Single-molecule sensors (SMSs) based on nanopore electrochemistry may be a feasible solution for PFCAs determination, thanks to their ultra-high spatiotemporal resolutions. Hence, as a first step, this work was to elucidate the influence of electrolyte concentration on the four most critical indicators of nanopore measurements, and furthermore, performance of nanopore SMSs. More specifically, three of the most representative short-chain PFCAs, perfluoropentanoic acid (PFPeA), perfluorohexanoic acid (PFHxA) and perfluoroheptanoic acid (PFHpA), were adopted as the target analytes, aerolysin nanopore was employed as the sensing interface, and 2, 3 and 4 M KCl solutions were used as electrolytes. It was found that, when the concentration of KCl solution increased from 2 to 4 M, the conductance of aerolysin nanopore increased almost linearly at a rate of 0.5 nS per molar KCl within the whole voltage range, the current blockade of PFPeA at −50 mV increased from 61.74 to 66.57% owing to the enhanced steric exclusion effect, the maximum dwell time was more than doubled from 14.5 to 31.5 ms, and the barrier limited capture rate increased by 8.3 times from 0.46 to 3.85 Hz. As a result, when using 4 M KCl as the electrolyte, over 90% of the PFPeA, PFHxA and PFHpA were accurately identified from a mixed sample, and the calculated limit of detection of PFPeA reached 320 nM, more than 24 times lower than in 2 M KCl. It was thus clear that tuning the electrolyte concentration was a simple but very effective approach to improve the performance of nanopore SMSs for PFCAs determination.

Modelling the Ionic Conductivity of Nanopores with Electrically Conductive Surface

The ionic conductivity of nanopores with electrically conductive surface is investigated theoretically. The generalization of two-dimensional (2D) Space–charge model to calculating the ion transport under the applied potential gradient in a nanopore with constant surface potential is proposed for the first time. The results are compared with one-dimensional (1D) Uniform potential model, which is derived from the Space–charge model by assuming the independence of potential, ion concentrations, and pressure on the radial coordinate. We have found that the increase of surface potential magnitude leads to the enhancement of conductivity due to the increase of counter–ion concentration inside the nanopore. It is shown that the 1D and 2D models provide close results when the pore radius is smaller than the Debye length. Otherwise, the 1D model essentially overestimates the ionic conductivity. According to the 2D model, the ionic conductivity decreases with increasing the nanopore radius, while the 1D model predicts the opposite trend, which is not physically correct

Insertion state of modular protein nanopores into a membrane

In the past decade, significant progress has been made in the development of new protein nanopores. Despite these advancements, there is a pressing need for the creation of nanopores equipped with relatively large functional groups for the sampling of biomolecular events on their extramembranous side. Here, we designed, produced, and analyzed protein nanopores encompassing a robust truncation of a monomeric β-barrel membrane protein. An exogenous stably folded protein was anchored within the aqueous phase via a flexible peptide tether of varying length. We have extensively examined the pore-forming properties of these modular protein nanopores using protein engineering and single-molecule electrophysiology. This study revealed distinctions in the nanopore conductance and current fluctuations that arose from tethering the exogenous protein to either the N terminus or the C terminus. Remarkably, these nanopores insert into a planar lipid membrane with one specific conductance among a set of three substate conductance values. Moreover, we demonstrate that the occurrence probabilities of these insertion substates depend on the length of the peptide tether, the orientation of the exogenous protein with respect to the nanopore opening, and the molecular mass of tethered protein. In addition, the three conductance values remain unaltered by major changes in the composition of modular nanopores. The outcomes of this work serve as a platform for further developments in areas of protein engineering of transmembrane pores and biosensor technology.

Electrokinetic behavior of a pH-regulated dielectric cylindrical nanopore

A continuum model is adopted to describe the electrokinetic behavior of a pH-regulated cylindrical nanopore, the surface of which has charge-regulated carboxyl groups. We focus on the influences of the permittivity of the nanopore material, nanopore size, salt concentration, and solution pH on this behavior, and the underlying mechanisms. The influence of the nanopore permittivity becomes significant when a nanopore is shorter than ca. 50 nm. It is interesting to observe that if it is longer than ca. 100 nm, the nanopore conductance decreases with increasing permittivity. If it is sufficiently short, the conductance increases with increasing permittivity. If the nanopore length takes a medium level, the conductance is insensitive to the variation in the permittivity. For a short nanopore (~20 nm), the conductivity increases with increasing permittivity. However, if pH is sufficiently high, it becomes insensitive to permittivity. Although the larger the permittivity the greater the conductivity, in general, this effect becomes insignificant when the bulk salt concentration is sufficiently high, implying that the effect of membrane polarization is important only if the bulk salt concentration is sufficiently low.

Current Blockades of Proteins inside Nanopores for Real-Time Metabolome Analysis.

Biological nanopores are emerging as powerful and low-cost sensors for real-time analysis of biological samples. Proteins can be incorporated inside the nanopore, and ligand binding to the protein adaptor yields changes in nanopore conductance. In order to understand the origin of these conductance changes and develop sensors for detecting metabolites, we tested the signal originating from 13 different protein adaptors. We found that the quality of the protein signal depended on both the size and charge of the protein. The engineering of a dipole within the surface of the adaptor reduced the current noise by slowing the protein dynamics within the nanopore. Further, the charge of the ligand and the induced conformational changes of the adaptor defined the conductance changes upon metabolite binding, suggesting that the protein resides in an electrokinetic minimum within the nanopore, the position of which is altered by the ligand. These results represent an important step toward understanding the dynamics of the electrophoretic trapping of proteins inside nanopores and will allow developing next-generation sensors for metabolome analysis.

Surface charge regulation of functionalized conical nanopore conductance by divalent cations and anions

The surface charge regulation in nanoscale volumes is a subject of wide interest to biological and chemical soft matter systems. Also, electrolyte mixtures with monovalent and divalent ions are commonplace in practical applications with micro and nanoporous ion-exchange membranes. We have studied experimentally and theoretically the conductance of conical nanopores functionalized with negative and positive surface charges that are bathed by electrolyte mixtures of the monovalent ions K+ and Cl− and the divalent ions Mg2+, Ba2+, Ca2+, and SO42−. Small concentrations of these ions can modulate the nanopore selectivity and conductance because of their interaction with the charged groups on the pore surface. We have also given a qualitative description of the surface charge regulation using a simplified model for multivalent ion mixtures.