Computing numerically the access resistance of a pore

Correlations in Charged Multipore Systems: Implications for Enhancing Selectivity and Permeability in Nanoporous Membranes

Nanoporous membranes have emerged as powerful tools for diverse applications, including gas separation and water desalination. Achieving high permeability for desired molecules alongside exceptional rejection of other species presents a significant design challenge. One potential strategy involves optimizing the chemistry and geometry of isolated nanopores to enhance permeability and selectivity while maximizing their density within a membrane. However, the impact of the pore proximity on membrane performance remains an open question. Through path sampling simulations of model graphitic membranes with multiple subnanometer pores, we reveal that nanoscale proximity between pores detrimentally affects water permeability and salt rejection. Specifically, counterion transport is decelerated, while co-ion transport is accelerated, due to direct interactions among water molecules, salt ions, and the dipoles within neighboring pores. Notably, the observed ionic transport time scales significantly deviate from established theories such as the access resistance model but are well explained using the simple phenomenological model that we develop in this work. We use this model to prescreen and optimize pore arrangements that elicit minimal correlations at a target pore density. These findings deepen our understanding of multipore systems, informing the rational design of nanoporous membranes for enhanced separation processes such as water desalination. They also shed light on the physiology of biological cells that employ ion channel proteins to modulate ion transport and reversal potentials.

Pressure-driven power generation and ion separation using a non-uniformly charged nanopore

Due to its versatile potential applications, nanofluidic devices have drawn much attention of researches in various fields. Among these, pressure-driven power generation is considered as a candidate for the next generation alternative green energy source, and pressure-driven ion separation (nanofiltration) for desalination. Aiming to achieve a better performance in these two representative cases, a cylindrical nanopore having different types of non-uniform surface charge profile is adopted, and its performance under various conditions assessed. We show that lower the surface charge density near the nanopore inlet region can suppress the effect of ion concentration polarization (ICP) and improve the selectivity, thereby enhancing appreciably its power generation performance. For a fixed averaged surface charge density, if the bulk salt concentration is low, the higher the surface charge density near the nanopore openings, the better its performance. The degree of ICP can be alleviated by applying a sufficiently large pressure difference. Although previous studies showed that salt rejection is influenced significantly by the profile of the electric field inside a nanopore, we find that the electric field at nanopore openings also plays a role. Through choosing appropriately the surface charge profile, it is possible to solve the trade-off between rejection and flow rate.

Electrodiffusion Phenomena in Neuroscience and the Nernst–Planck–Poisson Equations

This work is aimed to give an electrochemical insight into the ionic transport phenomena in the cellular environment of organized brain tissue. The Nernst–Planck–Poisson (NPP) model is presented, and its applications in the description of electrodiffusion phenomena relevant in nanoscale neurophysiology are reviewed. These phenomena include: the signal propagation in neurons, the liquid junction potential in extracellular space, electrochemical transport in ion channels, the electrical potential distortions invisible to patch-clamp technique, and calcium transport through mitochondrial membrane. The limitations, as well as the extensions of the NPP model that allow us to overcome these limitations, are also discussed.

Aerolysin, a Powerful Protein Sensor for Fundamental Studies and Development of Upcoming Applications

The nanopore electrical approach is a breakthrough in single molecular level detection of particles as small as ions, and complex as biomolecules. This technique can be used for molecule analysis and characterization as well as for the understanding of confined medium dynamics in chemical or biological reactions. Altogether, the information obtained from these kinds of experiments will allow us to address challenges in a variety of biological fields. The sensing, design, and manufacture of nanopores is crucial to realize these objectives. For some time now, aerolysin, a pore forming toxin, and its mutants have shown high potential in real time analytical chemistry, size discrimination of neutral polymers, oligosaccharides, oligonucleotides and peptides at monomeric resolution, sequence identification, chemical modification on DNA, potential biomarkers detection, and protein folding analysis. This review focuses on the results obtained with aerolysin nanopores on the fields of chemistry, biology, physics, and biotechnology. We discuss and compare as well the results obtained with other protein channel sensors.

Colloquium: Ionic phenomena in nanoscale pores through 2D materials

Ion transport through nanopores permeates through many areas of science and technology, from cell behavior to sensing and separation to catalysis and batteries. Two-dimensional materials, such as graphene, molybdenum disulfide (MoS2), and hexagonal boron nitride (hBN), are recent additions to these fields. Low-dimensional materials present new opportunities to develop filtration, sensing, and power technologies, encompassing ion exclusion membranes, DNA sequencing, single molecule detection, osmotic power generation, and beyond. Moreover, the physics of ionic transport through pores and constrictions within these materials is a distinct realm of competing many-particle interactions (e.g., solvation/dehydration, electrostatic blockade, hydrogen bond dynamics) and confinement. This opens up alternative routes to creating biomimetic pores and may even give analogues of quantum phenomena, such as quantized conductance, in the classical domain. These prospects make membranes of 2D materials - i.e., 2D membranes - fascinating. We will discuss the physics and applications of ionic transport through nanopores in 2D membranes.

Robust Sandwich-Structured Nanofluidic Diodes Modulating Ionic Transport for an Enhanced Electrochromic Performance

Biomimetic solid-state nanofluidic diodes have attracted extensive research interest due to the possible applications in various fields, such as biosensing, energy conversion, and nanofluidic circuits. However, contributions of exterior surface to the transmembrane ionic transport are often ignored, which can be a crucial factor for ion rectification behavior. Herein, a rational design of robust sandwich-structured nanofluidic diode is shown by creating opposite charges on the exterior surfaces of a nanoporous membrane using inorganic oxides with distinct isoelectric points. Potential-induced changes in ion concentration within the nanopores lead to a current rectification; the results are subsequently supported by a theoretical simulation. Except for providing surface charges, functional inorganic oxides used in this work are complementary electrochromic materials. Hence, the sandwich-structured nanofluidic diode is further developed into an electrochromic membrane exhibiting a visual color change in response to redox potentials. The results show that the surface-charge-governed ionic transport and the nanoporous structure facilitate the migration of Li+ ions, which in turn enhance the electrochromic performance. It is envisioned that this work will create new avenues to design and optimize nanofluidic diodes and electrochromic devices.

Golden aspect ratio for ion transport simulation in nanopores

Access resistance indicates how well current carriers from a bulk medium can converge to a pore or opening and is an important concept in nanofluidic devices and in cell physiology. In simplified scenarios, when the bulk dimensions are infinite in all directions, it depends only on the resistivity and pore radius. These conditions are not valid in all-atom molecular dynamics simulations of transport, due to the computational cost of large simulation cells, and can even break down in micro- and nanoscale systems due to strong confinement. Here, we examine a scaling theory for the access resistance that predicts a special simulation cell aspect ratio-the golden aspect ratio-where finite-size effects are eliminated. Using both continuum and all-atom simulations, we demonstrate that this golden aspect ratio exists and that it takes on a universal value in linear response and moderate concentrations. Outside of linear response, it gains an apparent dependence on characteristics of the transport scenario (concentration, voltages, etc.) for small simulation cells, but this dependence vanishes at larger length scales. These results will enable the use of all-atom molecular dynamics simulations to study contextual properties of access resistance-its dependence on protein and molecular-scale fluctuations, the presence of charges, and other functional groups-and yield the opportunity to quantitatively compare computed and measured resistances.

Do Bistable Steric Poisson-Nernst-Planck Models Describe Single-Channel Gating?

Experiments measuring currents through single protein channels show unstable currents, a phenomena called the gating of a single channel. Channels switch between an "open" state with a well-defined single amplitude of current and "closed" states with nearly zero current. The existing mean-field theory of ion channels focuses almost solely on the open state. The physical modeling of the dynamical features of ion channels is still in its infancy and does not describe the transitions between open and closed states nor the distribution of the duration times of open states. One hypothesis is that gating corresponds to noise-induced fast transitions between multiple steady (equilibrium) states of the underlying system. In this work, we aim to test this hypothesis. Particularly, our study focuses on the (high-order) steric Poisson-Nernst-Planck (PNP)-Cahn-Hilliard model since it has been successful in predicting permeability and selectivity of ionic channels in their open state and since it gives rise to multiple steady states. We show that this system gives rise to a gatinglike behavior, but that important features of this switching behavior are different from the defining features of gating in biological systems. Furthermore, we show that noise prohibits switching in the system of study. The above phenomena are expected to occur in other PNP-type models, strongly suggesting that one has to go beyond overdamped (gradient flow) Nernst-Planck type dynamics to explain the spontaneous gating of single channels.

Maxwell-Hall access resistance in graphene nanopores

The resistance due to the convergence from bulk to a constriction, for example, a nanopore, is a mainstay of transport phenomena. In classical electrical conduction, Maxwell, and later Hall for ionic conduction, predicted this access or convergence resistance to be independent of the bulk dimensions and inversely dependent on the pore radius, a, for a perfectly circular pore. More generally, though, this resistance is contextual, it depends on the presence of functional groups/charges and fluctuations, as well as the (effective) constriction geometry/dimensions. Addressing the context generically requires all-atom simulations, but this demands enormous resources due to the algebraically decaying nature of convergence. We develop a finite-size scaling analysis, reminiscent of the treatment of critical phenomena, that makes the convergence resistance accessible in such simulations. This analysis suggests that there is a "golden aspect ratio" for the simulation cell that yields the infinite system result with a finite system. We employ this approach to resolve the experimental and theoretical discrepancies in the radius-dependence of graphene nanopore resistance.

Ion Transport in Confined Geometries below the Nanoscale: Access Resistance Dominates Protein Channel Conductance in Diluted Solutions

Synthetic nanopores and mesoscopic protein channels have common traits like the importance of electrostatic interactions between the permeating ions and the nanochannel. Ion transport at the nanoscale occurs under confinement conditions so that the usual assumptions made in microfluidics are challenged, among others, by interfacial effects such as access resistance (AR). Here, we show that a sound interpretation of electrophysiological measurements in terms of channel ion selective properties requires the consideration of interfacial effects, up to the point that they dominate protein channel conductance in diluted solutions. We measure AR in a large ion channel, the bacterial porin OmpF, by means of single-channel conductance measurements in electrolyte solutions containing varying concentrations of high molecular weight PEG, sterically excluded from the pore. Comparison of experiments performed in charged and neutral planar membranes shows that lipid surface charges modify the ion distribution and determine the value of AR, indicating that lipid molecules are more than passive scaffolds even in the case of large transmembrane proteins. We also found that AR may reach up to 80% of the total channel conductance in diluted solutions, where electrophysiological recordings register essentially the AR of the system and depend marginally on the pore characteristics. These findings may have implications for several low aspect ratio biological channels that perform their physiological function in a low ionic strength and macromolecule crowded environment, just the two conditions enhancing the AR contribution.

Effect of endosomal acidification on small ion transport through the anthrax toxin PA63 channel

Tight regulation of pH is critical for the structure and function of cells and organelles. The pH environment changes dramatically along the endocytic pathway, an internalization transport process that is 'hijacked' by many intracellularly active bacterial exotoxins, including the anthrax toxin. Here, we investigate the role of pH on single-channel properties of the anthrax toxin protective antigen (PA₆₃ ). Using conductance and current noise analysis, blocker binding, ion selectivity, and poly(ethylene glycol) partitioning measurements, we show that the channel exists in two different open states ('maximum' and 'main') at pH ≥ 5.5, while only a maximum conductance state is detected at pH < 5.5. We describe two substantially distinct patterns of PA₆₃ conductance dependence on KCl concentration uncovered at pH 6.5 and 4.5.

Aberrantly Large Single-Channel Conductance of Polyhistidine Arm-Containing Protein Nanopores

There have been only a few studies reporting on the impact of polyhistidine affinity tags on the structure, function, and dynamics of proteins. Because of the relatively short size of the tags, they are often thought to have little or no effect on the conformation or activity of a protein. Here, using membrane protein design and single-molecule electrophysiology, we determined that the presence of a hexahistidine arm at the N-terminus of a truncated FhuA-based protein nanopore, leaving the C-terminus untagged, produces an unusual increase in the unitary conductance to ∼8 nS in 1 M KCl. To the best of our knowledge, this is the largest single-channel conductance ever recorded with a monomeric β-barrel outer membrane protein. The hexahistidine arm was captured by an anti-polyhistidine tag monoclonal antibody added to the side of the channel-forming protein addition, but not to the opposite side, documenting that this truncated FhuA-based protein nanopore inserts into a planar lipid bilayer with a preferred orientation. This finding is in agreement with the protein insertion in vivo, in which the large loops face the extracellular side of the membrane. The aberrantly large single-channel conductance, likely induced by a greater cross-sectional area of the pore lumen, along with the vectorial insertion into a lipid membrane, will have profound implications for further developments of engineered protein nanopores.

Geometrical Effect in 2D Nanopores

A long-standing problem in the application of solid-state nanopores is the lack of the precise control over the geometry of artificially formed pores compared to the well-defined geometry in their biological counterpart, that is, protein nanopores. To date, experimentally investigated solid-state nanopores have been shown to adopt an approximately circular shape. In this Letter, we investigate the geometrical effect of the nanopore shape on ionic blockage induced by DNA translocation using triangular h-BN nanopores and approximately circular molybdenum disulfide (MoS₂) nanopores. We observe a striking geometry-dependent ion scattering effect, which is further corroborated by a modified ionic blockage model. The well-acknowledged ionic blockage model is derived from uniform ion permeability through the 2D nanopore plane and hemisphere like access region in the nanopore vicinity. On the basis of our experimental results, we propose a modified ionic blockage model, which is highly related to the ionic profile caused by geometrical variations. Our findings shed light on the rational design of 2D nanopores and should be applicable to arbitrary nanopore shapes.

Validity of the Electrodiffusion Model for Calculating Conductance of Simple Ion Channels

We examine the validity and utility of the electrodiffusion (ED) equation, i.e., the generalized Nernst-Planck equation, to characterize, in combination with molecular dynamics, the electrophysiological behavior of simple ion channels. As models, we consider three systems-two naturally occurring channels formed by α-helical bundles of peptaibols, trichotoxin, and alamethicin, and a synthetic, hexameric channel, formed by a peptide that contains only leucine and serine. All these channels mediate transport of potassium and chloride ions. Starting with equilibrium properties, such as the potential of mean force experienced by an ion traversing the channel and diffusivity, obtained from molecular dynamics simulations, the ED equation can be used to determine the full current-voltage dependence with modest or no additional effort. The potential of mean force can be obtained not only from equilibrium simulations, but also, with comparable accuracy, from nonequilibrium simulations at a single voltage. The main assumptions underlying the ED equation appear to hold well for the channels and voltages studied here. To expand the utility of the ED equation, we examine what are the necessary and sufficient conditions for Ohmic and nonrectifying behavior and relate deviations from this behavior to the shape of the ionic potential of mean force.

DNA sequence-dependent ionic currents in ultra-small solid-state nanopores

Measurements of ionic currents through nanopores partially blocked by DNA have emerged as a powerful method for characterization of the DNA nucleotide sequence. Although the effect of the nucleotide sequence on the nanopore blockade current has been experimentally demonstrated, prediction and interpretation of such measurements remain a formidable challenge. Using atomic resolution computational approaches, here we show how the sequence, molecular conformation, and pore geometry affect the blockade ionic current in model solid-state nanopores. We demonstrate that the blockade current from a DNA molecule is determined by the chemical identities and conformations of at least three consecutive nucleotides. We find the blockade currents produced by the nucleotide triplets to vary considerably with their nucleotide sequences despite having nearly identical molecular conformations. Encouragingly, we find blockade current differences as large as 25% for single-base substitutions in ultra small (1.6 nm × 1.1 nm cross section; 2 nm length) solid-state nanopores. Despite the complex dependence of the blockade current on the sequence and conformation of the DNA triplets, we find that, under many conditions, the number of thymine bases is positively correlated with the current, whereas the number of purine bases and the presence of both purines and pyrimidines in the triplet are negatively correlated with the current. Based on these observations, we construct a simple theoretical model that relates the ion current to the base content of a solid-state nanopore. Furthermore, we show that compact conformations of DNA in narrow pores provide the greatest signal-to-noise ratio for single base detection, whereas reduction of the nanopore length increases the ionic current noise. Thus, the sequence dependence of the nanopore blockade current can be theoretically rationalized, although the predictions will likely need to be customized for each nanopore type.

The Effect of Hydrodynamic Slip on Membrane-Based Salinity-Gradient-Driven Energy Harvesting

The effect of hydrodynamic slip on salinity-gradient-driven power conversion by the process of reverse electrodialysis, in which the free energy of mixing of salt and fresh water across a nanoporous membrane is harnessed to drive an electric current in an external circuit, is investigated theoretically using a continuum fluid dynamics model. A general one-dimensional model is derived that decouples transport inside the membrane pores from the effects of electrical resistance at the pore ends, from which an analytical expression for the power conversion rate is obtained for a perfectly ion-selective membrane as a function of the slip length, surface charge density, membrane thickness, pore radius, and other membrane and electrolyte properties. The theoretical model agrees quantitatively with finite-element numerical calculations and predicts significant enhancements--up to several times--of salinity-gradient power conversion due to hydrodynamic slip for realistic systems.

Modelling the Bioelectronic Interface in Engineered Tethered Membranes: From Biosensing to Electroporation

This paper studies the construction and predictive models of three novel measurement platforms: (i) a Pore Formation Measurement Platform (PFMP) for detecting the presence of pore forming proteins and peptides, (ii) the Ion Channel Switch (ICS) biosensor for detecting the presence of analyte molecules in a fluid chamber, and (iii) an Electroporation Measurement Platform (EMP) that provides reliable measurements of the electroporation phenomenon. Common to all three measurement platforms is that they are comprised of an engineered tethered membrane that is formed via a rapid solvent exchange technique allowing the platform to have a lifetime of several months. The membrane is tethered to a gold electrode bioelectronic interface that includes an ionic reservoir separating the membrane and gold surface, allowing the membrane to mimic the physiological response of natural cell membranes. The electrical response of the PFMP, ICS, and EMP are predicted using continuum theories for electrodiffusive flow coupled with boundary conditions for modelling chemical reactions and electrical double layers present at the bioelectronic interface. Experimental measurements are used to validate the predictive accuracy of the dynamic models. These include using the PFMP for measuring the pore formation dynamics of the antimicrobial peptide PGLa and the protein toxin Staphylococcal α-Hemolysin; the ICS biosensor for measuring nano-molar concentrations of streptavidin, ferritin, thyroid stimulating hormone (TSH), and human chorionic gonadotropin (pregnancy hormone hCG); and the EMP for measuring electroporation of membranes with different tethering densities, and membrane compositions.

Numerically testing phenomenological models for conductance of a solid-state nanopore

The ionic conductance of a solid-state nanopore plays an important role in analyzing biomolecules transported through the pore. The phenomenological pore-conductance is assumed to be a sum of three contributions: bulk, surface (for a charged nanopore) and access ones. Despite being commonly used, phenomenological results were not rigorously derived in theory and their accuracies have not been tested yet. By carrying out numerical modeling on the nanopore conductance, I show that both the ion concentration and the surface charge can affect the accuracy. For a charged solid-state nanopore solvated in an intermediate-ion-concentration electrolyte (e.g. 50 mM), the phenomenological result can be substantially larger than the numerically calculated one. The criteria for properly applying phenomenological results are provided.

Interacting ions in biophysics: real is not ideal

Ions in water are important throughout biology, from molecules to organs. Classically, ions in water were treated as ideal noninteracting particles in a perfect gas. Excess free energy of each ion was zero. Mathematics was not available to deal consistently with flows, or interactions with other ions or boundaries. Nonclassical approaches are needed because ions in biological conditions flow and interact. The concentration gradient of one ion can drive the flow of another, even in a bulk solution. A variational multiscale approach is needed to deal with interactions and flow. The recently developed energetic variational approach to dissipative systems allows mathematically consistent treatment of the bio-ions Na(+), K(+), Ca(2+), and Cl(-) as they interact and flow. Interactions produce large excess free energy that dominate the properties of the high concentration of ions in and near protein active sites, ion channels, and nucleic acids: the number density of ions is often >10 M. Ions in such crowded quarters interact strongly with each other as well as with the surrounding protein. Nonideal behavior found in many experiments has classically been ascribed to allosteric interactions mediated by the protein and its conformation changes. The ion-ion interactions present in crowded solutions-independent of conformation changes of the protein-are likely to change the interpretation of many allosteric phenomena. Computation of all atoms is a popular alternative to the multiscale approach. Such computations involve formidable challenges. Biological systems exist on very different scales from atomic motion. Biological systems exist in ionic mixtures (like extracellular and intracellular solutions), and usually involve flow and trace concentrations of messenger ions (e.g., 10(-7) M Ca(2+)). Energetic variational methods can deal with these characteristic properties of biological systems as we await the maturation and calibration of all-atom simulations of ionic mixtures and divalents.

Probing Access Resistance of Solid-state Nanopores with a Scanning Probe Microscope Tip

An apparatus that integrates solid-state nanopore ionic current measurement with a Scanning Probe Microscope has been developed. When a micrometer-scale scanning probe tip is near a voltage biased nanometer-scale pore (10-100 nm), the tip partially blocks the flow of ions to the pore and increases the pore access resistance. The apparatus records the current blockage caused by the probe tip and the location of the tip simultaneously. By measuring the current blockage map near a nanopore as a function of the tip position in 3D space in salt solution, we estimate the relative pore resistance increase due to the tip, ΔR/R(0), as a function of the tip location, nanopore geometry, and salt concentration. The amplitude of ΔR/R(0) also depends on the ratio of the pore length to its radius as Ohm's law predicts. When the tip is very close to the pore surface, ~10 nm, our experiments show that ΔR/R(0) depends on salt concentration as predicted by the Poisson and Nernst-Planck equations. Furthermore, our measurements show that ΔR/R(0) goes to zero when the tip is about five times the pore diameter away from the center of the pore entrance. The results in this work not only demonstrate a way to probe the access resistance of nanopores experimentally, they also provide a way to locate the nanopore in salt solution, and open the door to future nanopore experiments for detecting single biomolecules attached to a probe tip.

Low resistance, large dimension entrance to the inner cavity of BK channels determined by changing side-chain volume

Large-conductance Ca²⁺- and voltage-activated K⁺ (BK) channels have the largest conductance (250–300 pS) of all K⁺-selective channels. Yet, the contributions of the various parts of the ion conduction pathway to the conductance are not known. Here, we examine the contribution of the entrance to the inner cavity to the large conductance. Residues at E321/E324 on each of the four α subunits encircle the entrance to the inner cavity. To determine if 321/324 is accessible from the inner conduction pathway, we measured single-channel current amplitudes before and after exposure and wash of thiol reagents to the intracellular side of E321C and E324C channels. MPA⁻ increased currents and MTSET⁺ decreased currents, with no difference between positions 321 and 324, indicating that side chains at 321/324 are accessible from the inner conduction pathway and have equivalent effects on conductance. For neutral amino acids, decreasing the size of the entrance to the inner cavity by substituting large side-chain amino acids at 321/324 decreased outward single-channel conductance, whereas increasing the size of the entrance with smaller side-chain substitutions had little effect. Reductions in outward conductance were negated by high [K⁺]_i. Substitutions had little effect on inward conductance. Fitting plots of conductance versus side-chain volume with a model consisting of one variable and one fixed resistor in series indicated an effective diameter and length of the entrance to the inner cavity for wild-type channels of 17.7 and 5.6 Å, respectively, with the resistance of the entrance ∼7% of the total resistance of the conduction pathway. The estimated dimensions are consistent with the structure of MthK, an archaeal homologue to BK channels. Our observations suggest that BK channels have a low resistance, large entrance to the inner cavity, with the entrance being as large as necessary to not limit current, but not much larger.

Unraveling single-stranded DNA in a solid-state nanopore

Solid-state nanopores are an emerging class of single-molecule sensors. Whereas most studies so far focused on double-stranded DNA (dsDNA) molecules, exploration of single-stranded DNA (ssDNA) is of great interest as well, for example to employ such a nanopore device to read out the sequence. Here, we study the translocation of long random-sequence ssDNA through nanopores. Using atomic force microscopy, we observe the ssDNA to hybridize into a random coil, forming blobs of around 100 nm in diameter for 7 kb ssDNA. These large entangled structures have to unravel, when they arrive at the pore entrance. Indeed, we observe strong blockade events with a translocation time that is exponentially dependent on voltage, tau approximately e(-V/V(0)). Interestingly, this is very different than for dsDNA, for which tau approximately 1/V. We report translocations of ssDNA but also of ssDNA-dsDNA constructs where we compare the conductance-blockade levels for ssDNA versus dsDNA as a function of voltage.

Functionalization of micro- and nano-apertures with chromate-selective solvent polymeric membrane

A new miniaturization approach to create micro- and nanoscale ion selective electrodes (ISEs) was demonstrated and the concept tested with an environmentally relevant chromate-selective membrane consisting of 7.7:62.2:31.1 wt % Aliquat336:2-NPOE:PVC. Apertures of 100 nM and 30 microM dimensions were made using MEMS fabrication techniques and functionalized through a macroscale application of solvent polymeric membrane. Performance studies for the microscale ISE showed a response slope of -58.6+/-5.6 mV decade(-1) and limit of detection (LOD) of 2.1 x 10(-5)+/-1.1 x 10(-5) M, versus -65.2+/-4.2 mV decade(-1) and 1.8 x 10(-5)+/-6 x 10(-6) M for the nanoscale ISE. This was consistent with control studies with carefully conditioned coated wire electrodes, which demonstrated a response slope of -61.7+/-2.4 mV decade(-1) and a LOD of 3.0 x 10(-6)+/-1 x 10(-6) M. Response times for the best micro- and nanoscale ISEs were in the 10-20 s timeframe. Electrical resistance measurements were in the GOmega range for the microscale ISEs and nanoscale ISEs. Appropriate ISE geometry was confirmed through AFM measurements and calculations based on electrical properties for micro- and nanoscale apertures. These micro- and nanoscale ISEs are expected to have significant impact in the field of microscale analytical processes.

Temperature dependence of proton permeation through a voltage-gated proton channel

Voltage-gated proton channels are found in many different types of cells, where they facilitate proton movement through the membrane. The mechanism of proton permeation through the channel is an issue of long-term interest, but it remains an open question. To address this issue, we examined the temperature dependence of proton permeation. Under whole cell recordings, rapid temperature changes within a few milliseconds were imposed. This method allowed for the measurement of current amplitudes immediately before and after a temperature jump, from which the ratios of these currents (Iratio) were determined. The use of Iratio for evaluating the temperature dependence minimized the contributions of factors other than permeation. Temperature jumps of various degrees (DeltaT, -15 to 15 degrees C) were applied over a wide temperature range (4-49 degrees C), and the Q10s for the proton currents were evaluated from the Iratios. Q10 exhibited a high temperature dependence, varying from 2.2 at 10 degrees C to 1.3 at 40 degrees C. This implies that processes with different temperature dependencies underlie the observed Q10. A novel resistivity pulse method revealed that the access resistance with its low temperature dependence predominated in high temperature ranges. The measured temperature dependence of Q10 was decomposed into Q10 of the channel and of the access resistances. Finally, the Q10 for proton permeation through the voltage-gated proton channel itself was calculated and found to vary from 2.8 at 5 degrees C to 2.2 at 45 degrees C, as expected for an activation enthalpy of 64 kJ/mol. The thermodynamic features for proton permeation through proton-selective channels were discussed for the underlying mechanism.

Exploring Multidimensional Free Energy Landscapes Using Time-Dependent Biases on Collective Variables

A new implementation of the adaptive biasing force (ABF) method is described. This implementation supports a wide range of collective variables and can be applied to the computation of multidimensional energy profiles. It is provided to the community as part of a code that implements several analogous methods, including metadynamics. ABF and metadynamics have not previously been tested side by side on identical systems. Here, numerical tests are carried out on processes including conformational changes in model peptides and translocation of a halide ion across a lipid membrane through a peptide nanotube. On the basis of these examples, we discuss similarities and differences between the ABF and metadynamics schemes. Both approaches provide enhanced sampling and free energy profiles in quantitative agreement with each other in different applications. The method of choice depends on the dimension of the reaction coordinate space, the height of the barriers, and the relaxation times of degrees of freedom in the orthogonal space, which are not explicitly described by the chosen collective variables.

Self-consistent analytic solution for the current and the access resistance in open ion channels

A self-consistent analytic approach is introduced for the estimation of the access resistance and the current through an open ion channel for an arbitrary number of species. For an ion current flowing radially inward from infinity to the channel mouth, the Poisson-Boltzmann-Nernst-Planck equations are solved analytically in the bulk with spherical symmetry in three dimensions, by linearization. Within the channel, the Poisson-Nernst-Planck equation is solved analytically in a one-dimensional approximation. An iterative procedure is used to match the two solutions together at the channel mouth in a self-consistent way. It is shown that the current-voltage characteristics obtained are in good quantitative agreement with experimental measurements.

Extracellular space attenuates the effect of gap junctional remodeling on wave propagation: a computational study

Ionic channels and gap junctions are remodeled in cells from the 5-day epicardial border zone (EBZ) of the healing canine infarct. The main objective of the study was to determine the effect of gap junctional conductance (Gj) remodeling and Cx43 redistribution to the lateral membrane on conduction velocity (theta) and anisotropic ratio, and how gap junctional remodeling is modulated by the extracellular space. We first implemented subcellular monodomain and two-domain computer models of normal epicardium (NZ) to understand how extracellular space modulates the relationship between Gj and theta in NZ. We found that the extracellular space flattens the Gj-theta relationship, thus theta becomes less sensitive to changes in Gj. We then investigated the functional consequences of Gj remodeling and Cx43 distribution in subcellular computer models of cells of the outer pathway (IZo) and central pathway (IZc) of reentrant circuits. In IZo cells, side-to-side (transverse) Gj is 10% the value in NZ cells. Such Gj remodeling causes a 45% decrease in transverse theta (theta(T)). Inclusion of an extracellular space reduces the decrease in theta(T) to 31%. In IZc cells, Cx43 redistribution along the lateral membrane results in a 29% increase in theta(T). That increase in theta(T) is a consequence of the decrease in access resistance to the Cx43 plaques that occur with the Cx43 redistribution. Extracellular space reduces the increase in theta(T) to 10%.

IN CONCLUSION

1), The extracellular space included in normal epicardial simulations flattens the Gj-theta relationship with theta becoming less sensitive to changes in Gj. 2), The extracellular space attenuates the effects of gap junction epicardial border zone remodeling (i.e., Gj reduction and Cx43 lateralization) on theta(T).

Pore structure and function of synthetic nanopores with fixed charges: tip shape and rectification properties

We present a complete theoretical study of the relationship between the structure (tip shape and dimensions) and function (selectivity and rectification) of asymmetric nanopores on the basis of previous experimental studies. The theoretical model uses a continuum approach based on the Nernst-Planck equations. According to our results, the nanopore transport properties, such as current-voltage (I-V) characteristics, conductance, rectification ratio, and selectivity, are dictated mainly by the shape of the pore tip (we have distinguished bullet-like, conical, trumpet-like, and hybrid shapes) and the concentration of pore surface charges. As a consequence, the nanopore performance in practical applications will depend not only on the base and tip openings but also on the pore shape. In particular, we show that the pore opening dimensions estimated from the pore conductance can be very different, depending on the pore shape assumed. The results obtained can also be of practical relevance for the design of nanopores, nanopipettes, and nanoelectrodes, where the electrical interactions between the charges attached to the nanostructure and the mobile charges confined in the reduced volume of the inside solution dictate the device performance in practical applications. Because single tracks are the elementary building blocks for nanoporous membranes, the understanding and control of their individual properties should also be crucial in protein separation, water desalination, and bio-molecule detection using arrays of identical nanopores.

Energetics of Ion Transport in a Peptide Nanotube

Ion channels constitute an important family of integral membrane proteins responsible for the regulation of ion transport across the cell membrane. Yet, the underlying energetics of the permeation events and how the latter are modulated by the environment, specifically near the mouth of the pore, remain only partially characterized. Here, a synthetic membrane channel formed by cyclic peptides of alternated d- and l-hydrophobic alpha-amino acids was considered. The free energy delineating the translocation of a sodium ion was measured along the conduction pathway by means of molecular dynamics simulations. The free-energy profiles that underly the permeation of the open-ended tubular structure are shown to not only depend on the characteristics of the latter but also inherently on the location of the mouth of the synthetic channel with respect to the membrane surface.