THE GOLDMAN CONSTANT FIELD ASSUMPTION - SIGNIFICANCE AND APPLICABILITY CONDITIONS

Ionic transport phenomena in simple, porous membranes can be approximately represented by the Nernst-Planck flux equations and Poisson's equation. In order to solve this set of equations for each particular case, the Goldman constant field assumption is one of the most widely used. In the present paper the significance and the applicability conditions of the above hypothesis is critically examined. and the particular situations where it is exact are shown. These conditions are later verified by solving numerically the electrodiffusion equations. The analysis carried out shows that some of the earlier studies based on asymptotic expansions and numerical solutions should be partially revised.

Information Processing Schemes Based on Monolayer Protected Metallic Nanoclusters

Nanostructures are potentially useful as building blocks to complement future electronics because of their high versatility and packing densities. The fabrication and characterization of particular nanostructures and the use of new theoretical tools to describe their properties are receiving much attention. However, the integration of these individual systems into general schemes that could perform simple tasks is also necessary because modern electronics operation relies on the concerted action of many basic units. We review here new conceptual schemes that can allow information processing with ligand or monolayer protected metallic nanoclusters (MPCs) on the basis of the experimentally de…

Optical Gating of Photosensitive Synthetic Ion Channels

4-oxo-4-(pyren-4-ylmethoxy) butanoic acid is used as a photolabile protecting group to show the optical gating of nanofluidic devices based on synthetic ion channels. The inner surface of the channels is decorated with monolayers of photolabile hydrophobic molecules that can be removed by irradiation, which leads to the generation of hydrophilic groups. This process can be exploited in the UV-light-triggered permselective transport of ionic species in aqueous solution through the channels. The optical gating of a single conical nanochannel and multichannel polymeric membranes is characterised experimentally and theoretically by means of current-voltage and selective permeation measurements,…

Ionic circuitry with nanofluidic diodes

Ionic circuits composed of nanopores functionalized with polyelectrolyte chains can operate in aqueous solutions, thus allowing the control of electrical signals and information processing in physiological environments. We demonstrate experimentally and theoretically that different orientations of single-pore membranes with the same and opposite surface charges can operate reliably in series, parallel, and mixed series-parallel arrangements of two, three, and four nanofluidic diodes using schemes similar to those of solid-state electronics. We consider also different experimental procedures to externally tune the fixed charges of the molecular chains functionalized on the pore surface, show…

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…

Fabrication of Single Cylindrical Au-Coated Nanopores with Non-Homogeneous Fixed Charge Distribution Exhibiting High Current Rectifications

We have designed and characterized a cylindrical nanopore that exhibits high electrochemical current rectification ratios at low and intermediate electrolyte concentrations. For this purpose, the track-etched single cylindrical nanopore in polymer membrane is coated with a gold (Au) layer via electroless plating technique. Then, a non-homogeneous fixed charge distribution inside the Au-coated nanopore is obtained by incorporating thiol-terminated uncharged poly(N-isopropylacrylamide) (PNIPAM) chains in series to poly(4-vinyl pyridine) (PVP) chains, which are positively charged at acidic pH values. The functionalization reaction is checked by measuring the current–voltage (I–V) curves prior …

Bioelectrical Signals and Ion Channels in the Modeling of Multicellular Patterns and Cancer Biophysics

AbstractBioelectrical signals and ion channels are central to spatial patterns in cell ensembles, a problem of fundamental interest in positional information and cancer processes. We propose a model for electrically connected cells based on simple biological concepts: i) the membrane potential of a single cell characterizes its electrical state; ii) the long-range electrical coupling of the multicellular ensemble is realized by a network of gap junction channels between neighboring cells; and iii) the spatial distribution of an external biochemical agent can modify the conductances of the ion channels in a cell membrane and the multicellular electrical state. We focus on electrical effects …

The interplay between cooperativity and diversity in model threshold ensembles

The interplay between cooperativity and diversity is crucial for biological ensembles because single molecule experiments show a significant degree of heterogeneity and also for artificial nanostructures because of the high individual variability characteristic of nanoscale units. We study the cross-effects between cooperativity and diversity in model threshold ensembles composed of individually different units that show a cooperative behaviour. The units are modelled as statistical distributions of parameters (the individual threshold potentials here) characterized by central and width distribution values. The simulations show that the interplay between cooperativity and diversity results …

Electric field enhanced water dissociation at the bipolar membrane junction from ac impedance spectra measurements

Abstract Preliminary experimental results of the ac impedance spectra of a bipolar ion-exchange membrane are reported and interpreted on the basis of a previous theoretical model based on the Nernst–Planck/Poisson equations. It is shown that the experiments can provide valuable electrochemical information about the bipolar junction structure and the electric-field enhanced water dissociation phenomenon that occurs at this junction, although the high number of unknown parameters involved makes it difficult to obtain accurate values for the parameters characteristic of this phenomenon.

Label-free histamine detection with nanofluidic diodes through metal ion displacement mechanism

[EN] We design and characterize a nanofluidic device for the label-free specific detection of histamine neurotransmitter based on a metal ion displacement mechanism. The sensor consists of an asymmetric polymer nanopore fabricated via ion track-etching technique. The nanopore sensor surface having metal-nitrilotriacetic (NTA-Ni2+) chelates is obtained by covalent coupling of native carboxylic acid groups with N-alpha,N-alpha-bis(carboxymethyl)-L-lysine (BCML), followed by exposure to Ni2+ ion solution. The BCML immobilization and subsequent Ni2+ ion complexation with NTA moieties change the surface charge concentration, which has a significant impact on the current-voltage (I-V) curve after…

Protein transport through gold-coated, charged nanopores: Effects of applied voltage

The flux of bovine serum albumin and bovine hemoglobin through charged nanopores inside polymeric membranes is analysed as a function of the applied voltage to the nanopore surface, the solution ionic strength and pH. The electrostatic interaction of the protein with the nanopore surface gives low transport rates except at the protein isoelectric point and the minimum of the effective, voltage-induced nanopore charge. This electrostatic sieving effect allows for the separation of proteins with similar molecular weights.

Label-Free Pyrophosphate Recognition with Functionalized Asymmetric Nanopores

[EN] The label¿free detection of pyrophosphate (PPi) anions with a nanofluidic sensing device based on asymmetric nanopores is demonstrated. The pore surface is functionalized with zinc complexes based on two di(2¿picolyl)amine [bis(DPA)] moieties using carbodiimide coupling chemistry. The complexation of zinc (Zn2+) ion is achieved by exposing the modified pore to a solution of zinc chloride to form bis(Zn2+¿DPA) complexes. The chemical functionalization is demonstrated by recording the changes in the observed current¿voltage (I¿V) curves before and after pore modification. The bis(Zn2+¿DPA) complexes on the pore walls serve as recognition sites for pyrophosphate anion. The experimental re…

Associative Memory Based on Double-Gating of Molecularly Linked Nanosystem Arrays:  A Theoretical Scheme

We discuss theoretically the properties of an associative memory (a system that can retrieve a stored pattern that is similar to the input pattern) based on the ideal conductive properties of a molecularly linked nanosystem array. Two schemes are considered for the memory based on the gate potential modulation of the drain-source current through the array. In the first scheme, the basic units of the electric circuit are nanosystems (e.g., nanoparticles) arranged in a series array. Each nanosystem is assumed to have two states of conductances, GM and Gm (GM ≫ Gm), that can be tuned externally by the gate and backgate potentials. The bit sequence associated with a given pattern is stored as t…

Counterion transport numbers of poly(acrylic acid)-grafted porous ion-exchange membranes as determined from current step measurements

Abstract The effect of an electric current on the concentration polarization of the external bathing solutions and the permselectivity of poly(acrylic acid)-grafted porous ion-exchange membranes has been studied. The experimental approach is based on the transient behavior of the total electric potential drop through the membrane cell when a current step is imposed from external nonpolarizable electrodes. When this voltage drop is recorded as a function of time, a transition time characteristic of each membrane system is obtained. From this time, the counterion transport number for the salt solution (KClH2O) in the membrane can be obtained. The theoretical modeling is based on the time-dep…

Generalization of a finite-difference numerical method for the steady-state and transient solutions of the nernst—planck flux equations

Abstract A generalization of the numerical method of Brumleve and Buck for the solution of Nernst—Planck equations when convective flux and electric current are involved has been developed. The simulation procedure was applied to a specific case: transport of strong electrolytes in a wide-pore membrane with simultaneous diffusion, convection and electric current. Good agreement was found between experimental data and computed results.

IONIC TRANSPORT ACROSS POROUS CHARGED MEMBRANES AND THE GOLDMAN CONSTANT FIELD ASSUMPTION

Starting from a simple theoretical model based on Nernst-Planck flux equations and the Donnan equilibrium relationship, the ionic transport across a porous, charged membrane is analysed and conditions are given which make exact the so-called “constant field assumption”. The validity of the reported results is later verified in the case of a well-known problem: the ionic transport across a cation-exchange membrane under bi-ionic conditions.

Bipolar membranes under forward and reverse bias conditions. Theory vs. experiment

Abstract Bipolar membranes are layered structures composed of one cation-and one anion-exchange membrane joined together in series. The current—voltage curves of two recently developed bipolar membranes have been analysed theoretically and experimentally under both forward and reverse bias conditions. The experimental trends observed are high conductivity under forward bias conditions and high impedance first, and then electric field enhanced (EFE) water dissociation for high enough applied voltages, under reverse bias conditions. The forward bias measurements can contribute to a better knowledge of some of the transport parameters entering also in the reverse biased membrane. Comparison of…

Charging a Capacitor from an External Fluctuating Potential using a Single Conical Nanopore

We explore the electrical rectification of large amplitude fluctuating signals by an asymmetric nanostructure operating in aqueous solution. We show experimentally and theoretically that a load capacitor can be charged to voltages close to 1 V within a few minutes by converting zero time-average potentials of amplitudes in the range 0.5–3 V into average net currents using a single conical nanopore. This process suggests that significant energy conversion and storage from an electrically fluctuating environment is feasible with a nanoscale pore immersed in a liquid electrolyte solution, a system characteristic of bioelectronics interfaces, electrochemical cells, and nanoporous membranes.

Cell Systems Bioelectricity: How Different Intercellular Gap Junctions Could Regionalize a Multicellular Aggregate

Simple Summary Electric potential patterns across tissues are instructive for development, regeneration, and tumorigenesis because they can influence transcription, migration, and differentiation through biochemical and biomechanical downstream processes. Determining the origins of the spatial domains of distinct potential, which in turn decide anatomical features such as limbs, eyes, brain, and heart, is critical to a mature understanding of how bioelectric signaling drives morphogenesis. We studied theoretically how connexin proteins with different voltage-gated gap junction conductances can maintain multicellular regions at distinct membrane potentials. We analyzed a minimal model that i…

Size‐Based Cationic Molecular Sieving through Solid‐State Nanochannels

Advanced materials interfaces 8(6), 2001766 (2021). doi:10.1002/admi.202001766

Biomolecular conjugation inside synthetic polymer nanopores via glycoprotein-lectin interactions

We demonstrate the supramolecular bioconjugation of concanavalin A (Con A) protein with glycoenzyme horseradish peroxidase (HRP) inside single nanopores, fabricated in heavy ion tracked polymer membranes. Firstly, the HRP-enzyme was covalently immobilized on the inner wall of the pores using carbodiimide coupling chemistry. The immobilized HRP-enzyme molecules bear sugar (mannose) groups available for the binding of Con A protein. Secondly, the bioconjugation of Con A on the pore wall was achieved through its biospecific interactions with the mannose residues of the HRP enzyme. The immobilization of biomolecules inside the nanopore leads to the reduction of the available area for ionic tran…

Ion transport and selectivity in nanopores with spatially inhomogeneous fixed charge distributions

Polymeric nanopores with fixed charges show ionic selectivity when immersed in aqueous electrolyte solutions. The understanding of the electrical interaction between these charges and the mobile ions confined in the inside nanopore solution is the key issue in the design of potential applications. The authors have theoretically described the effects that spatially inhomogeneous fixed charge distributions exert on the ionic transport and selectivity properties of the nanopore. A comprehensive set of one-dimensional distributions including the skin, core, cluster, and asymmetric cases are analyzed on the basis of the Nernst-Planck equations. Current-voltage curves, nanopore potentials, and tr…

Electrical Pumping of Potassium Ions Against an External Concentration Gradient in a Biological Ion Channel

We show experimentally and theoretically that significant currents can be obtained with a biological ion channel, the OmpF porin of Escherichia coli, using zero-average potentials as driving forces. The channel rectifying properties can be used to pump potassium ions against an external concentration gradient under asymmetric pH conditions. The results are discussed in terms of the ionic selectivity and rectification ratio of the channel. The physical concepts involved may be applied to separation processes with synthetic nanopores and to bioelectrical phenomena. (C) 2013 AIP Publishing LLC.

Modeling of surface vs. bulk ionic conductivity in fixed charge membranes

A two-region model for describing the conductivity of porous fixed charge membranes is proposed. In the surface region, the conductivity is due to the mobile positive ions (counterions) around the negative fixed charges. In the pore center region, the conductive properties resemble those of the external electrolyte solution because the fixed charges are assumed to be effectively neutralized by the counterions in the surface region. Activation energies and surface diffusion coefficients are estimated by assuming that the counterion jump from a fixed charge group is the rate limiting process for surface transport. The barrier energy for this jump is calculated using a simple electrostatic mod…

Calcium binding and ionic conduction in single conical nanopores with polyacid chains: model and experiments.

Calcium binding to fixed charge groups confined over nanoscale regions is relevant to ion equilibrium and transport in the ionic channels of the cell membranes and artificial nanopores. We present an experimental and theoretical description of the dissociation equilibrium and transport in a single conical nanopore functionalized with pH-sensitive carboxylic acid groups and phosphonic acid chains. Different phenomena are simultaneously present in this basic problem of physical and biophysical chemistry: (i) the divalent nature of the phosphonic acid groups fixed to the pore walls and the influence of the pH and calcium on the reversible dissociation equilibrium of these groups; (ii) the asym…

Effects of pH on ion transport in weak amphoteric membranes

Abstract We have studied theoretically the effect of pH on the ion transport through amphoteric polymer membranes composed of weak polyelectrolytes where the charged groups are randomly distributed along the axial direction of the membrane. This system serves as a simplified model for the pH controlled ion transport and drug delivery through membranes of biological interest. The theoretical approach employed is based on the Nernst-Planck equations. The complete system of electrical charges formed by: (i) the pH dependent, amphoretic membrane fixed charge, and (ii) the four mobile charges (the salt ions and the hydrogen and hydroxide ions) have been taken into account without any additional …

Voltage-controlled current loops with nanofluidic diodes electrically coupled to solid state capacitors

[EN] We describe experimentally and theoretically voltage-controlled current loops obtained with nanofluidic diodes immersed in aqueous salt solutions. The coupling of these soft matter diodes with conventional electronic elements such as capacitors permits simple equivalent circuits which show electrical properties reminiscent of a resistor with memory. Different conductance levels can be reproducibly achieved under a wide range of experimental conditions (input voltage amplitudes and frequencies, load capacitances, electrolyte concentrations, and single pore and multipore membranes) by electrically coupling two types of passive components: the nanopores (ionics) and the capacitors (electr…

Ionic conduction through single-pore and multipore polymer membranes in aprotic organic electrolytes

Abstract We experimentally characterize the ionic conduction of single and multipore nanoporous membranes in aprotic organic electrolytes. To this end, soft-etched (SE) membranes with pore diameters in the nanometer range and track-etched (TE) membranes with pore diameters in the tens of nanometers range are investigated. In aqueous conditions, the membrane ionic conduction rates follow the same trend of the bulk solution conductivities. However, the ionic transport through the narrow SE-nanopores dramatically decreases in aprotic electrolytes due to the formation of solvated metal cations and their adsorption on the pore surface. The current-voltage recordings of single conical nanopores i…

Donnan equilibrium of ionic drugs in pH-dependent fixed charge membranes: theoretical modeling.

Abstract We have studied theoretically the partition equilibrium of a cationic drug between an electrolyte solution and a membrane with pH-dependent fixed charges using an extended Donnan formalism. The aqueous solution within the fixed charge membrane is assumed to be in equilibrium with an external aqueous solution containing six ionic species: the cationic drug (DH + ), the salt cations (Na + and Ca 2+ ), the salt anion (Cl − ), and the hydrogen and hydroxide ions. In addition to these mobile species, the membrane solution may also contain four fixed species attached to the membrane chains: strongly acid sulfonic groups (SO 3 − ), weakly acid carboxylic groups in dissociated (COO − ) a…

Donnan phenomena in membranes with charge due to ion adsorption. Effects of the interaction between adsorbed charged groups

A physical model for the modified Donnan phenomenon associated with ion adsorption on localized membrane sites is presented. This model accounts for the dependence of the concentration of adsorbed ions on electrolyte concentration and pH as it is influenced by the electrostatic interaction between adsorbed ions. The equilibrium thermodynamic concepts employed are based on the Donnan formalism for the ion equilibria between membrane and solution, and the Bragg–Williams approximation for an adsorption isotherm that incorported interaction between adsorbed ions. Our results include the concentration of charged groups in the membrane, the pH of the membrane phase solution, and the Donnan potent…

Model for ion transport in bipolar membranes.

A simple theory for multi-ionic transport, nonequilibrium water dissociation, and space-charge effects in bipolar membranes is developed on the basis of some of the concepts used in the solid-state n-p junction. Ion transport is described in terms of the Nernst-Planck flux equation and nonequilibrium water dissociation is accounted for by the Onsager theory of the second Wien effect. The model is expected to be of interest for biological and synthetic membranes, and can explain a number of observed effects.

Concatenated logic functions using nanofluidic diodes with all-electrical inputs and outputs

[EN] Nanopore-based logical schemes in ionic solutions typically involve single gates and chemical inputs. The design of computer-like functions requires the consecutive concatenation of several gates and the use of electrical potentials and currents to facilitate the downstream transfer of electrochemical information. We have demonstrated the robust operation of concatenated logic functions using biomimetic nanofluidic diodes based on single pore membranes. To this end, we have implemented first the logic functions AND and OR with combinations of single nanopores using all-electrical input and output signals. The concatenation of these gates allows the output of the OR gate to act as one o…

Biologically inspired information processing and synchronization in ensembles of non-identical threshold-potential nanostructures.

Nanotechnology produces basic structures that show a significant variability in their individual physical properties. This experimental fact may constitute a serious limitation for most applications requiring nominally identical building blocks. On the other hand, biological diversity is found in most natural systems. We show that reliable information processing can be achieved with heterogeneous groups of non-identical nanostructures by using some conceptual schemes characteristic of biological networks (diversity, frequency-based signal processing, rate and rank order coding, and synchronization). To this end, we simulate the integrated response of an ensemble of single-electron transisto…

Membrane potential bistability in nonexcitable cells as described by inward and outward voltage-gated ion channels.

The membrane potential of nonexcitable cells, defined as the electrical potential difference between the cell cytoplasm and the extracellular environment when the current is zero, is controlled by the individual electrical conductance of different ion channels. In particular, inward- and outward-rectifying voltage-gated channels are crucial for cell hyperpolarization/depolarization processes, being amenable to direct physical study. High (in absolute value) negative membrane potentials are characteristic of terminally differentiated cells, while low membrane potentials are found in relatively depolarized, more plastic cells (e.g., stem, embryonic, and cancer cells). We study theoretically t…

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

Abstract 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 grou…

Morphology changes induced by intercellular gap junction blocking: A reaction-diffusion mechanism.

Complex anatomical form is regulated in part by endogenous physiological communication between cells; however, the dynamics by which gap junctional (GJ) states across tissues regulate morphology are still poorly understood. We employed a biophysical modeling approach combining different signaling molecules (morphogens) to qualitatively describe the anteroposterior and lateral morphology changes in model multicellular systems due to intercellular GJ blockade. The model is based on two assumptions for blocking-induced patterning: (i) the local concentrations of two small antagonistic morphogens diffusing through the GJs along the axial direction, together with that of an independent, uncouple…

Sub-threshold signal processing in arrays of non-identical nanostructures

Weak input signals are routinely processed by molecular-scaled biological networks composed of non-identical units that operate correctly in a noisy environment. In order to show that artificial nanostructures can mimic this behavior, we explore theoretically noise-assisted signal processing in arrays of metallic nanoparticles functionalized with organic ligands that act as tunneling junctions connecting the nanoparticle to the external electrodes. The electronic transfer through the nanostructure is based on the Coulomb blockade and tunneling effects. Because of the fabrication uncertainties, these nanostructures are expected to show a high variability in their physical characteristics and…

Bioelectrical coupling in multicellular domains regulated by gap junctions: A conceptual approach.

We review the basic concepts involved in bioelectrically-coupled multicellular domains, focusing on the role of membrane potentials (Vmem). In the first model, single-cell Vmem is modulated by two generic polarizing and depolarizing ion channels, while intercellular coupling is implemented via voltage-gated gap junctions. Biochemical and bioelectrical signals are integrated via a feedback loop between Vmem and the transcription and translation of a protein forming an ion channel. The effective rate constants depend on the single-cell Vmem because these potentials modulate the local concentrations of signaling molecules and ions. This electrochemically-based idealization of the complex bioph…

Cesium-Induced Ionic Conduction through a Single Nanofluidic Pore Modified with Calixcrown Moieties

[EN] We demonstrate experimentally and theoretically a nanofluidic device for the selective recognition of the cesium ion by exploiting host¿guest interactions inside confined geometry. For this purpose, a host molecule, i.e., the amine-terminated p-tert-butylcalix[4]arene-crown (tBuC[4]C¿NH2), is successfully synthesized and functionalized on the surface of a single conical nanopore fabricated in a poly(ethylene terephthalate) (PET) membrane through carbodiimide coupling chemistry. On exposure to the cesium cation, the t-BuC[4]C¿Cs+ complex is formed through host¿guest interaction, leading to the generation of positive fixed charges on the pore surface. The asymmetrical distribution of the…

Estimation of pKa shifts in weak polyacids using a simple molecular model: effects of strong polybases, hydrogen bonding and divalent counterion binding

Abstract The pKa values of ionizable groups in macromolecules can be significantly different than those of the isolated groups in solution. We have estimated theoretically the changes in the dissociation constant of a weak acid (a) in the vicinity of another ionizable group (b) on the basis of the theoretical approach by Hill (J. Am. Chem. Soc. 78 (1956) 3330) for matching pairs of interacting sites on two large molecules. Three cases are considered for group b: the strong base, the same weak acid as group a with hydrogen bonding between them, and the same weak acid as group a with divalent counterion binding. The pKa shifts are evaluated in each case as a function of the interaction energy…

Nonlinear conductance and heterogeneity of voltage-gated ion channels allow defining electrical surface domains in cell membranes

Abstract The membrane potential of a cell measured by typical electrophysiological methods is only an average magnitude and experimental techniques allowing a more detailed mapping of the cell surface have shown the existence of spatial domains with locally different electric potentials and currents. Electrical potentials in non-neural cells are regulated by the nonlinear conductance of membrane ion channels. Voltage-gated potassium channels participate in cell hyperpolarization/depolarization processes and control the electrical signals over the cell surface, constituting good candidates to study basic biological questions on a more simplified scale than the complex cell membrane. These ch…

Individual Variability and Average Reliability in Parallel Networks of Heterogeneous Biological and Artificial Nanostructures

We simulate the collective electrical response of heterogeneous ensembles of biological and artificial nanostructures whose individual threshold potentials show a significant variability. This problem is of current interest because nanotechnology is bound to produce nanostructures with a significant experimental variability in their individual physical properties. This diversity is also present in biological systems that are however able to process information efficiently. The nanostructures considered are the ion channels of biological membranes, nanowire field-effect transistors, and metallic nanoparticle-based single electron transistors. These systems are simulated with canonical models…

Energy transduction and signal averaging of fluctuating electric fields by a single protein ion channel

[EN] We demonstrate the electrical rectification and signal averaging of fluctuating signals using a biological nanostructure in aqueous solution: a single protein ion channel inserted in the lipid bilayer characteristic of cell membranes. The conversion of oscillating, zero time-average potentials into directional currents permits charging of a load capacitor to significant steady-state voltages within a few minutes in the case of the outer membrane porin F (OmpF) protein, a bacterial channel of Escherichia coli. The experiments and simulations show signal averaging effects at a more fundamental level than the traditional cell and tissue scales, which are characterized by ensembles of many…

Ion Pairing in the Analysis of Voltammetric Data at the ITIES: RbTPB and RbTPBCl in 1,2-dichloroethane

The association of rubidium-tetraphenylborate (RbTPB) and rubidium-tetrakis(-chlorophenyl)borate (RbTPBCl) ion pairs in the organic solvent 1,2-dichloroethane (DCE) have been obtained from condutivity and voltammetric data. Conductivity measurements given K RbTPBCl =43 100 M -1 and yield a lower bound for K RbTPB (K RbTPB > 70000 M -1 ). The latter association constant is at variance with the previously accepted value. A method for analysing voltammetric data which allows for the determination of the association constants is presented. The positive polarization limit where the transfer of Rb + takes place is shifted by ca. 200 mV when changing the anion of the organic base electrolyte from …

A redox-sensitive nanofluidic diode based on nicotinamide-modified asymmetric nanopores

[EN] We demonstrate a redox-sensitive nanofluidic diode whose ion rectification is modulated by the oxidation and reduction of chemical moieties incorporated on its surface. To achieve this goal, we have first synthesized the chemical compounds 1-(4-aminobutyl)-3-carbamoylpyridin-1-ium (Nic-BuNH2) and 3-carbamoyl-1-(2,4-dinitrophenyl)pyridinium (Nic-DNP). Then, the surface of track-etched single asymmetric nanopores is decorated with the redox-sensitive Nic-BuNH2 and Nic-DNP molecules using carbodiimide coupling chemistry and Zincke reaction, respectively. The success of the modification reactions is monitored through the changes in the current¿voltage (I¿V) curves prior to and after pore f…

Reliable signal processing using parallel arrays of non-identical nanostructures and stochastic resonance

In the stochastic resonance (SR) phenomena, the response of a non-linear system to a weak periodic input signal is optimised by the presence of a particular level of noise which enhances signal detection. We explore, theoretically, the influence of thermal noise in arrays of metal nanoparticles functionalised with organic ligands acting as tunnelling junctions, with emphasis on the interplay between the SR phenomena and the nanostructure variability. In this system, the transference of a reduced number of electrons may suffice to implement a variety of electronic functions. However, because nanostructures are expected to show a significant variability in their physical characteristics, it i…

Ion size effects on the current efficiency of narrow charged pores

Abstract The effects of ion size on the current efficiency (CE) of charged membranes with narrow pores are studied theoretically. The CE is a measure of the membrane permselectivity defined as the ratio between the counterion flux and the sum of the counterion and coion fluxes when an electric potential difference is applied between the two solutions bathing the membrane. It is studied here as a function of two relevant experimental parameters: the ratio between the ionic radius and the pore radius, and the ratio between the external salt concentration and the membrane fixed charge concentration. The ratio of the CE values corresponding to the point and finite size ions is also calculated a…

Device variability and circuit redundancy in signal processing based on nanoswitches

Signal processing based on molecular switches whose conductance can be tuned by an external stimulus between two (on and off) states has been proposed recently (Cervera et al 2008 J. Appl. Phys. 104 084317). The basic building block is a metal nanoparticle linked to two electrodes by an organic ligand and a nanoswitch. The net charge delivered by this nanostructure exhibits a sharp resonance when the alternating potential applied between the electrodes has the same frequency as the periodic variation between the on and off conductance states induced on the nanoswitch. This resonance can be used to process an external signal by selectively extracting the weight of the different harmonics. Ho…

Ion conduction in the KcsA potassium channel analyzed with a minimal kinetic model.

We use a model by Nelson to study the current-voltage and conductance-concentration curves of bacterial potassium channel KcsA without assuming rapid ion translocation. Ion association to the channel filter is rate controlling at low concentrations, but dissociation and transport in the filter can limit conduction at high concentration for ions other than ${\mathrm{K}}^{+}$. The absolute values of the effective rate constants are tentative but the relative changes in these constants needed to qualitatively explain the experiments should be of significance.

Hybrid Circuits with Nanofluidic Diodes and Load Capacitors

[EN] The chemical and physical input signals characteristic of micro- and nanofluidic devices operating in ionic solutions should eventually be translated into output electric currents and potentials that are monitored with solid-state components. This crucial step requires the design of hybrid circuits showing robust electrical coupling between ionic solutions and electronic elements. We study experimentally and theoretically the connectivity of the nanofluidic diodes in single-pore and multipore membranes with conventional capacitor systems for the cases of constant, periodic, and white-noise input potentials. The experiments demonstrate the reliable operation of these hybrid circuits ove…

Impact of Surface Charge Directionality on Membrane Potential in Multi-ionic Systems

The membrane potential (Vmem), defined as the electric potential difference across a membrane flanked by two different salt solutions, is central to electrochemical energy harvesting and conversion. Also, Vmem and the ionic concentrations that establish it are important to biophysical chemistry because they regulate crucial cell processes. We study experimentally and theoretically the salt dependence of Vmem in single conical nanopores for the case of multi-ionic systems of different ionic charge numbers. The major advances of this work are (i) to measure Vmem using a series of ions (Na+, K+, Ca2+, Cl-, and SO42-) that are of interest to both energy conversion and cell biochemistry, (ii) to…

Carbohydrate-Mediated Biomolecular Recognition and Gating of Synthetic Ion Channels

Nanochannel-based biosensing devices have been proposed for selective detection of protein analyte molecules. However, the design and miniaturization of reusable channel-based biosensors is still a challenge in nanoscience and biotechnology. We present here a reusable nanofluidic biosensor based on reversible lectin-carbohydrate interactions. The nanochannels are fabricated in heavy ion tracked polymer membranes. The channel walls are functionalized with p-aminophenyl alpha-D-mannopyranoside (APMP) monolayers through carbodiimide coupling chemistry. The chemical (mannopyranoside) groups on the inner channel walls serve as binding sites and interact with specific protein molecules. The bindi…

Intercellular Connectivity and Multicellular Bioelectric Oscillations in Nonexcitable Cells: A Biophysical Model

Bioelectricity is emerging as a crucial mechanism for signal transmission and processing from the single-cell level to multicellular domains. We explore theoretically the oscillatory dynamics that result from the coupling between the genetic and bioelectric descriptions of nonexcitable cells in multicellular ensembles, connecting the genetic prepatterns defined over the ensemble with the resulting spatio-temporal map of cell potentials. These prepatterns assume the existence of a small patch in the ensemble with locally low values of the genetic rate constants that produce a specific ion channel protein whose conductance promotes the cell-polarized state (inward-rectifying channel). In this…

Optimizing Energy Transduction of Fluctuating Signals with Nanofluidic Diodes and Load Capacitors

[EN] The design and experimental implementation of hybrid circuits is considered allowing charge transfer and energy conversion between nanofluidic diodes in aqueous ionic solutions and conventional electronic elements such as capacitors. The fundamental concepts involved are reviewed for the case of fluctuating zero-average external potentials acting on single pore and multipore membranes. This problem is relevant to electrochemical energy conversion and storage, the stimulus-response characteristics of nanosensors and actuators, and the estimation of the accumulative effects caused by external signals on biological ion channels. Half-wave and full-wave voltage doublers and quadruplers can…

The interplay between genetic and bioelectrical signaling permits a spatial regionalisation of membrane potentials in model multicellular ensembles

AbstractThe single cell-centred approach emphasises ion channels as specific proteins that determine individual properties, disregarding their contribution to multicellular outcomes. We simulate the interplay between genetic and bioelectrical signals in non-excitable cells from the local single-cell level to the long range multicellular ensemble. The single-cell genetic regulation is based on mean-field kinetic equations involving the mRNA and protein concentrations. The transcription rate factor is assumed to depend on the absolute value of the cell potential, which is dictated by the voltage-gated cell ion channels and the intercellular gap junctions. The interplay between genetic and ele…

Bioelectrical model of head-tail patterning based on cell ion channels and intercellular gap junctions

Robust control of anterior-posterior axial patterning during regeneration is mediated by bioelectric signaling. However, a number of systems-level properties of bioelectrochemical circuits, including stochastic outcomes such as seen in permanently de-stabilized "cryptic" flatworms, are not completely understood. We present a bioelectrical model for head-tail patterning that combines single-cell characteristics such as membrane ion channels with multicellular community effects via voltage-gated gap junctions. It complements the biochemically-focused models by describing the effects of intercellular electrochemical coupling, cutting plane, and gap junction blocking of the multicellular ensemb…

Single cigar-shaped nanopores functionalized with amphoteric amino acid chains: experimental and theoretical characterization.

We present an experimental and theoretical characterization of single cigar-shaped nanopores with pH-responsive carboxylic acid and lysine chains functionalized on the pore surface. The nanopore characterization includes (i) optical images of the nanostructure obtained by FESEM; (ii) different chemical procedures for the nanopore preparation (etching time and functionalizations; pH and electrolyte concentration of the external solution) allowing externally tunable nanopore responses monitored by the current-voltage (I-V) curves; and (iii) transport simulations obtained with a multilayer nanopore model. We show that a single, approximately symmetric nanopore can be operated as a reconfigurab…

Noise assisted image processing by ensembles of R-SETs

AbstractWe study how noise can assist the processing of an image in a resistance-single electron transistor (R-SET) model. The image is an 8-bit black and white picture. Every grey level is codified linearly into a sub-threshold input potential applied for a prescribed time window to an ensemble of R-SETs that transforms it into a spiking frequency. The addition of a background white noise potential of high amplitude permits the ensemble to process the image by means of the stochastic resonance phenomenon. Aside from the positive aspects, we analyse the negative impact of using noise and how we can minimize it using redundancy and a longer measuring time. The results are compared with the c…

Modified Donnan phenomena in polyaniline with poly(vinyl sulphonate) chains

We develop a physical model, based on the modified Donnan phenomena ideas introduced previously by the authors, to describe the acid doping of the conducting polymer polyaniline. The theory is motivated by the experimental work of Asturias et al. [Ber. Bunsenges. Phys. Chem. 95, 1381 (1991)]. Good agreement between theory and experiment is found.

Ionic transport characteristics of negatively and positively charged conical nanopores in 1:1, 2:1, 3:1, 2:2, 1:2, and 1:3 electrolytes

We study experimentally the current (I)-voltage (V) curves of 1:1, 2:1, 3:1, 2:2, 1:2, and 1:3 electrolytes in positively and negatively charged conically-shaped pores of nanoscale dimensions. The positive charges are poly(allylamine hydrochloride) chains functionalized on the pore surface by electrostatic interactions while the negative charges are carboxylic acid groups. Under physiological conditions, these fixed-charge groups are ionized and strongly interact with the different monovalent, divalent, and trivalent ions in the pore solution. The current rectification of the I-V curves and the membrane potentials provide fundamental information on the interaction of the pore charge groups …

Electrical Coupling in Ensembles of Nonexcitable Cells: Modeling the Spatial Map of Single Cell Potentials

We analyze the coupling of model nonexcitable (non-neural) cells assuming that the cell membrane potential is the basic individual property. We obtain this potential on the basis of the inward and outward rectifying voltage-gated channels characteristic of cell membranes. We concentrate on the electrical coupling of a cell ensemble rather than on the biochemical and mechanical characteristics of the individual cells, obtain the map of single cell potentials using simple assumptions, and suggest procedures to collectively modify this spatial map. The response of the cell ensemble to an external perturbation and the consequences of cell isolation, heterogeneity, and ensemble size are also ana…

Lithium Ion Recognition with Nanofluidic Diodes through Host-Guest Complexation in Confined Geometries

[EN] The lithium ion recognition is receiving significant attention because of its application in pharmaceuticals, lubricants and, especially, in energy technology. We present a nanofluidic device for specific lithium ion recognition via host guest complexation in a confined environment. A lithium-selective receptor molecule, the aminoethyl-benzo-12-crown-4 (BC12C4-NH2), is designed and functionalized on single conical nanopores in polyethylene terephthalate (PET) membranes. The native carboxylic acid groups on the pore walls are covalently linked with the crown ether moieties and the process is monitored from the changes in the current voltage (I-V) curves. The B12-crown-4 moieties are kno…

Tetraalkylammonium Cations Conduction through a Single Nanofluidic Diode: Experimental and Theoretical Studies

[EN] We describe experimentally and theoretically the concentration-dependent conduction of tetraalkylammonium (TAA+) cations through a nanofluidic diode fabricated in a polymer membrane via asymmetric track-etching techniques. This single-pore membrane exhibits current rectification characteristics because of the ionized carboxylate groups on the pore surface. We use aqueous solutions of potassium (K+ ), ammonium (A+ ), tetramethylammonium (TMA+ ), tetraethylammonium (TEA+ ), and tetrabutylammonium (TBA+ ) ions with concentrations ranging from 50 to 500 mM under acidic (pH 3.5) and physiological (pH 6.5) conditions. Compared with the K+ and A+ ions, the TMA+ , TEA+ , and TBA+ ions show rel…

Nanopore charge inversion and current-voltage curves in mixtures of asymmetric electrolytes

[EN] We consider the screening of the negative charges (carboxylic acid groups) fixed on the surface of a conical-shaped track-etched nanopore by divalent magnesium (Mg2+) and trivalent lanthanum (La3+). The experimental current (I)-voltage (V) curves and current rectification ratios allow discussing fundamental questions about the overcompensation of spatially-fixed charges by multivalent ions over nanoscale volumes. The effects of charge inversion or reversal on nanopore transport are discussed in mixtures of asymmetric electrolytes (LaCl3 and MgCl2 with KCl). In particular, pore charge inversion is demonstrated for La3+ as well as for mixtures of this trivalent ion at low concentrations …

Logic gates using nanofluidic diodes based on conical nanopores functionalized with polyprotic acid chains.

Single-track conical nanopores functionalized with polyprotic acid chains have pH-sensitive fixed charge groups and show three levels of conductance that allow integrating several functions on a single nanofluidic diode. Nanometer-scaled pores have previously been employed in separation and sensing but not in logic devices, despite the fact that biological ion channels with pH-dependent fixed charges are known to be responsible for information processing in biophysical structures. As a preliminary application, we propose a logic gate scheme where binary and multivalued logical functions are implemented.

Metallic Nanoparticles Linked to Molecular Switches as Signal Processing Devices

We explore theoretically the use of nanoscale switches whose conductance can be varied between two states by an external stimulus to implement signal processing devices. The building block is formed by a metallic nanoparticle linked to two electrodes by an organic ligand and a molecular switch. The system implementation exploits the sharp current resonance of the system that occurs when the frequencies of the applied potential and the induced variation on the switch conductance coincide.

Cooperative Effects Enhance Electric-Field-Induced Conductance Switching in Molecular Monolayers

The anchoring of molecules with functional groups at surfaces permits information processing based on two stable molecular states that can be tuned externally by light irradiation and external fields. By using a molecular model that incorporates the essential characteristics of the problem, we show that the local interactions between adjacent molecules in a densely packed monolayer can stabilize domains with the same molecular state because of cooperative processes, enhancing significantly the switching properties between the molecular states. The case of electric-field-induced conductance switching is exploited in two possible applications: the design of a logic gates system and the operat…

Converting external potential fluctuations into nonzero time-average electric currents using a single nanopore

The possibility of taking advantage of a fluctuating environment for energy and information transduction is a significant challenge in biological and artificial nanostructures. We demonstrate here directional electrical transduction from fluctuating external signals using a single nanopore of conical shape immersed in an ionic aqueous solution. To this end, we characterize experimentally the average output currents obtained by the electrical rectification of zero time-average input potentials. The transformation of external potential fluctuations into nonzero time-average responses using a single nanopore in liquid state is of fundamental significance for biology and nanophysics. This energ…

Validity of the electroneutrality and goldman constant-field assumptions in describing the diffusion potential for ternary electrolyte systems in simple, porous membranes

Abstract Three numerical algorithms capable of simulating transport processes through simple, porous membranes in the steady state have been employed in order to study the change in the diffusion potential with the membrane thickness and the ionic concentrations for the ternary systems NaClHClH20 and CaCI2NaC1H 2 O. The first simulation procedure uses Poisson's equation, the two others replace this equation by the electroneutrality and Goldman constant-field approximations respectively. From the results presented here, conditions for the applicability of the electroneutrality and constantfield assumption to ternary electrolyte systems are given.

Current‐voltage curves of bipolar membranes

Bipolar membranes consist of a layered ion‐exchange structure composed of a cation selective membrane joined to an anion selective membrane. They are analogous to semiconductor p‐n devices as both of them present current‐voltage curves exhibiting similar rectification properties. In this article, we present some current‐voltage curves obtained for different bipolar membranes at several temperatures. The results can be interpreted in terms of a simple model for ion transport and field‐enhanced water dissociation previously developed. The mechanism responsible for water splitting is assumed to be a catalytic proton transfer reaction between the charged groups and the water at the membrane int…

Deviations from equilibrium at the interface of a charged membrane

The local equilibrium assumption commonly employed for the transport through the interface of a charged membrane has been analysed from a simplified electric double layer model. This layer is characterized on the basis of a surface potential arising from a non-zero surface charge density placed on the membrane surface. The dependence of deviations from local equilibrium on the characteristic parameters of the problem is shown. Connection with the classical treatment by Donnan is discussed. Although the complexity of the problem calls for a number of simplifications, the results obtained appears to be significative. Thus, the analysis carried out displays not only that deviations from equili…

Polarity and bioelectrical patterning in a linear chain of non-excitable cells

Abstract Polarity in multicellular systems is influenced by bioelectrical signals because electric potentials can act as spatio-temporal patterns for other biochemical processes that eventually emerge as long-lasting biological outcomes. We study the role of the electric potential in establishing head-tail polarity for the case of a chain of non-excitable cells. This biophysical model incorporates both single-cell (membrane ion channels) and multicellular (intercellular gap junctions) characteristics. The results are presented in the form of a bioelectrical phase space that complements traditional biochemical approaches and provides qualitative insights for the case of anterior/posterior po…

Simple molecular model for the binding of antibiotic molecules to bacterial ion channels

A molecular model aimed at explaining recent experimental data by Nestorovich et al. [Proc. Natl. Acad. Sci. USA 99, 9789 (2002)] on the interaction of ampicillin molecules with the constriction zone in a channel of the general bacterial porin, OmpF (outer membrane protein F), is presented. The model extends T. L. Hill’s theory for intermolecular interactions in a pair of binding sites [J. Am. Chem. Soc. 78, 3330 (1956)] by incorporating two binding ions and two pairs of interacting sites. The results provide new physical insights on the role of the complementary pattern of the charge distributions in the ampicillin molecule and the narrowest part of the channel pore. Charge matching of int…

Conductive and Capacitive Properties of the Bipolar Membrane Junction Studied by AC Impedance Spectroscopy

The complete ac impedance spectrum of four bipolar membranes is analyzed both theoretically and experimentally taking into account both ionic transport and water dissociation together with the structural aspects of the bipolar junction. A theoretical model based on the Nernst-Planck and Poisson equations for the conductive and capacitive properties of the junction provides a qualitative description of the bipolar membranes for a broad range of electric currents and temperatures. Special attention is paid to the characteristics of the bipolar junction structure and the contact region between the two ion-exchange layers. It is observed that the effective area of this region increases with the…

Ionic Transport through Chemically Functionalized Hydrogen Peroxide-Sensitive Asymmetric Nanopores

We describe the fabrication of a chemical-sensitive nanofluidic device based on asymmetric nanopores whose transport characteristics can be modulated upon exposure to hydrogen peroxide (H2O2). We show experimentally and theoretically that the current-voltage curves provide a suitable method to monitor the H2O2-mediated change in pore surface characteristics from the electronic readouts. We demonstrate also that the single pore characteristics can be scaled to the case of a multipore membrane whose electric outputs can be readily controlled. Because H2O2 is an agent significant for medical diagnostics, the results should be useful for sensing nanofluidic devices.

pH and supporting electrolyte concentration effects on the passive transport of cationic and anionic drugs through fixed charge membranes

Abstract The effects of pH and supporting electrolyte concentration on the passive transport of an ionized (cationic or anionic) drug through a thick fixed charge membrane have been theoretically studied. This system constitutes a simplified model for the pH controlled ion transport and drug delivery through membranes of biological and pharmaceutical interest. Calculations were carried out for different values of the membrane fixed charge, supporting electrolyte and drug concentrations covering a broad range of the conditions usually found in experiments. The theoretical approach employed is based on the Nernst–Planck flux equations, and all of the species present in the system (the neutral…

Phospholipid monolayers at water∣oil interfaces: theoretical modelling of surface pressure–molecular area isotherms

Abstract The phospholipid adsorption and surface pressure–molecular area isotherms at interfaces are interpreted theoretically from two-dimensional (2D) lattice and real gas models that incorporate a minimum number of adjustable parameters. The first model is based on the lattice statistics of binary solutions and the molecular parameters introduced are the energy changes involved in the mixing process of the phospholipid and organic solvent molecules and the effective phospholipid head area. The surface pressure is interpreted in terms of the difference between the two liquid surface tensions. The second model makes use of (i) a non-localised adsorption model with a square-well potential e…

Electrical network of nanofluidic diodes in electrolyte solutions: Connectivity and coupling to electronic elements

[EN] We consider a nanopore network with simple connectivity, demonstrating a two-dimensional circuit (full-wave rectifier) with ensembles of conical pores acting as nanofluidic diodes. When the bridge nanopore network is fed with an input potential signal of fluctuating polarity, a fixed output polarity is obtained. The full-wave rectification characteristics are demonstrated with square, sinusoidal, and white noise input waveforms. The charging of a load capacitor located between the two legs of the bridge demonstrates that the nanofluidic network is effectively coupled to this electronic element. These results can be relevant for energy transduction and storage procedures with nanopores …

Activity coefficients and Donnan coion exclusion in charged membranes with weak-acid fixed charge groups

Abstract We have studied theoretically the effects that the dissociation equilibrium of weak-acid fixed charge groups (e.g. carboxyl groups) exerts on the mean activity coefficients in charged membranes using a Donnan formalism. The model calculations indicate that unless carbon dioxide is excluded from the external aqueous solution, the pH of the membrane solution can be low enough to affect significantly the effective fixed charge concentration and the coion exclusion when the membrane fixed charge concentration is high compared with the external solution salt concentration. Although this problem was already pointed out in previous studies, the possibility that the pH and salt concentrati…

Blocking of an ion channel by a highly charged drug: Modeling the effects of applied voltage, electrolyte concentration, and drug concentration

We present a simple physical model to estimate the blocked pore probability of an ion channel that can be blocked by a highly charged drug in solution. The model is inspired by recent experimental work on the blocking of the ${\mathrm{PA}}_{63}$ channel, involved in the anthrax toxin infection, by a highly charged drug [Karginov et al. PNAS 102, 15075 (2005)]. The drug binding to the pore is highly specific but the strong dependence of blocking on the applied voltage and electrolyte concentration suggests that long range electrostatic interactions are important. Since basic electrostatic concepts rather than detailed molecular models are considered, the microscopic details of the channel bl…

Protein diffusion through charged nanopores with different radii at low ionic strength

[EN] The diffusion of two similar molecular weight proteins, bovine serum albumin (BSA) and bovine haemoglobin (BHb), through nanoporous charged membranes with a wide range of pore radii is studied at low ionic strength. The effects of the solution pH and the membrane pore diameter on the pore permeability allow quantifying the electrostatic interaction between the chargedpore and the protein. Because of the large screening Debye length, both surface and bulk diffusion occur simultaneously. By increasing the pore diameter, the permeability tends to the bulk self-diffusion coefficient for each protein. By decreasing the pore diameter, the charges on the pore surface electrostatically hinder …

Effects of a macroscopic fixed charge inhomogeneity on some membrane transport properties

Abstract The effects that a macroscopic fixed charge inhomogeneity exerts on some membrane transport properties have been theoretically analyzed. To this end, we introduce two particular inhomogeneous fixed charge distributions on the basis of previous experimental work, and the transport equations are assumed to be the Nernst-Planck equations. It is found that a macroscopic redistribution of a constant quantity of fixed charge groups can modify the observed transport properties, the two inhomogeneous membranes here considered exhibiting permselectivities different from those of otherwise identical homogeneous membranes. Although the main emphasis of the study is on the basic aspects of tra…

Bioelectrical Coupling of Single-Cell States in Multicellular Systems.

The spatiotemporal distributions of signaling ions and molecules that modulate biochemical pathways in nonexcitable cells are influenced by multicellular electric potentials. These potentials act as distributed controllers encoding instructive spatial patterns in development and regeneration. We review experimental facts and discuss recent bioelectrical models that provide new physical insights and complement biochemical approaches. Single-cell states are modulated at the multicellular level because of the coupling between neighboring cells, thus allowing memories and multicellular patterns. The model is based on (i) two generic voltage-gated ion channels that promote the polarized and depo…

Effects of water dielectric saturation on the space–charge junction of a fixed-charge bipolar membrane

Abstract The dielectric saturation at the space–charge junction of a fixed-charge bipolar membrane is studied using the theoretical approach by Booth for the water dielectric constant and the Poisson equation for the electrical double layer at the junction. The numerical solution gives the electric field and dielectric constant profiles through the junction as well as the junction thickness as a function of the voltage drop. The water dielectric constant decreases substantially for the large electric fields that may occur at the narrow bipolar junction.

How does a transition zone affect the electric field enhanced water dissociation in bipolar membranes?

The changes in the electric field in the space charge regions and the corresponding effect on the water dissociation rate when a transition zone exists between the layers of a bipolar membrane are theoretically studied. A quasi-equilibrium approach based on the Poisson-Boltzmann equation for the space charge interfacial regions is used. The transition zone acts to decrease significantly the water dissociation rate. However, for realistic values of the thickness δ of the transition zone and provided that the ohmic drop over δ be small, this decrease in the dissociation rate is not very dependent on δ. The results obtained give theoretical support to some recent experimental findings.

Current rectification by nanoparticle blocking in single cylindrical nanopores.

Blocking of a charged pore by an oppositely charged nanoparticle can support rectifying properties in a cylindrical nanopore, as opposed to the usual case of a fixed asymmetry in the pore geometry and charge distribution. We present here experimental data and model calculations to confirm this fundamental effect. The nanostructure imaging and the effects of nanoparticle concentration, pore radius, and salt concentration on the electrical conductance–voltage (G–V) curves are discussed. Logic responses based on chemical and electrical inputs/outputs could also be implemented with a single pore acting as an effective nanofluidic diode. To better show the generality of the results, different ch…

Asymmetric nanopore rectification for ion pumping, electrical power generation, and information processing applications

Single-track, asymmetric nanopores can currently be functionalised with a spatially inhomogeneous distribution of fixed charges and a variety of pore tip shapes. Optimising the asymmetric nanopore characteristics is crucial for practical applications in nanofluidics. We have addressed here this question for three cases based on different input/output chemical and electrical signals: (i) ion pumping up a concentration gradient by means of a periodic, time-dependent bias potential, (ii) information processing with a single nanopore acting as the nanofluidic diode of a logic gate, and (iii) electrical energy harvesting using a nanopore that separates two solutions of different salt concentrati…

Convection, diffusion and reaction in a surface-based biosensor: Modeling of cooperativity and binding site competition on the surface and in the hydrogel

We study theoretically the transport and kinetic processes underlying the operation of a biosensor (particularly the surface plasmon sensor "Biacore") used to study the surface binding kinetics of biomolecules in solution to immobilized receptors. Unlike previous studies, we concentrate mainly on the modeling of system-specific phenomena rather than on the influence of mass transport limitations on the intrinsic kinetic rate constants determined from binding data. In the first problem, the case of two-site binding where each receptor unit on the surface can accommodate two analyte molecules on two different sites is considered. One analyte molecule always binds first to a specific site. Sub…

Logic Functions with Stimuli-Responsive Single Nanopores

[EN] We present the concept of logic functions based on a single stimuli-responsive nanopore and analyze its potential for electrochemical transducers and actuators. The responsive molecules at the surface of the polymeric nanopore immersed in an electrolyte solution are sensitive to thermal, chemical, electrical, and optical stimuli, which are the input signals required to externally tune the conductance of the nanopore (the logical output). A single nanostructure can be operated as a resistor or as a diode with a broad range of rectifying properties, allowing for logical information-processing schemes that are useful pH and temperature sensors, electro-optical detectors, and electrochemic…

Weakly coupled map lattice models for multicellular patterning and collective normalization of abnormal single-cell states

We present a weakly coupled map lattice model for patterning that explores the effects exerted by weakening the local dynamic rules on model biological and artificial networks composed of two-state building blocks (cells). To this end, we use two cellular automata models based on: (i) a smooth majority rule (model I) and (ii) a set of rules similar to those of Conway's Game of Life (model II). The normal and abnormal cell states evolve according with local rules that are modulated by a parameter $\kappa$. This parameter quantifies the effective weakening of the prescribed rules due to the limited coupling of each cell to its neighborhood and can be experimentally controlled by appropriate e…

Energy conversion from external fluctuating signals based on asymmetric nanopores

Electrical transduction from fluctuating external signals is central to energy conversion based on nanoscale electrochemical devices and bioelectronics interfaces. We demonstrate theoretically and experimentally a significant energy transduction from white noise signals using the electrical rectification of asymmetric nanopores in polymeric membranes immersed in aqueous electrolyte solutions. Load capacitor voltages of the order of 1 V are obtained within times of the order of 1 min by means of nanofluidic diodes which convert zero time-average potentials of amplitudes of the order of 1 V into average net currents. We consider single-nanopore and multipore membranes to show that the convers…

Community effects allow bioelectrical reprogramming of cell membrane potentials in multicellular aggregates: Model simulations.

Bioelectrical patterns are established by spatiotemporal correlations of cell membrane potentials at the multicellular level, being crucial to development, regeneration, and tumorigenesis. We have conducted multicellular simulations on bioelectrical community effects and intercellular coupling in multicellular aggregates. The simulations aim at establishing under which conditions a local heterogeneity consisting of a small patch of cells can be stabilized against a large aggregate of surrounding identical cells which are in a different bioelectrical state. In this way, instructive bioelectrical information can be persistently encoded in spatiotemporal patterns of separated domains with diff…

Double layer potential and degree of dissociation in charged lipid monolayers

Abstract One of the contributions to the surface potential in charged phospholipid monolayers at air–water interfaces is the double layer potential. In this note several misconceptions found in the literature concerning the relationship between the double layer potential and the degree of dissociation of the lipid polar headgroups are critically analyzed. The deviations of the double layer potential measurements from the Gouy–Chapman theory observed by several authors are explained by taking into account the dependence of the degree of dissociation with concentration, area per lipid molecule and pH.

Fabrication of soft-etched nanoporous polyimide membranes for ionic conduction and discrimination

Abstract Ionic selectivity in nanopores is usually based either on steric or charge exclusion mechanisms. By simultaneously incorporating both mechanisms into a functionalized membrane, an improved control over selectivity can be achieved. We describe the fabrication and experimental characterization of alkali metal cation-selective nanopores in heavy ion-tracked polyimide (PI) membranes using the soft-etching (SE) technique. The latent ion tracks in the PI membrane are selectively dissolved by an organic solvent to form tiny pores without affecting the bulk material. The ionic transport properties of SE-PI membranes are characterized using different electrolyte solutions containing alkali …

Passive Transport of Ionic Drugs through Membranes with pH-Dependent Fixed Charges

We have studied both theoretically and experimentally the passive transport of ionic drugs through membranes with pH-dependent fixed charge. The system considered constitutes a simplified model for pH-controlled drug delivery through membranes of biochemical and pharmaceutical interest. The theoretical approach employed is based on the Nernst-Planck flux equations and all of the species present in the system (the neutral or ionic drug and the hydrogen and hydroxide ions) have been taken into account together with a Langmuir-type isotherm for the adsorption of the ionic drug onto the membrane surface. The membrane permeabilities of cationic, anionic, and neutral drugs through porous membrane…

Multipore membranes with nanofluidic diodes allowing multifunctional rectification and logical responses

[EN] We have arranged two multipore membranes with conical nanopores in a three-compartment electrochemical cell. The membranes act as tunable nanofluidic diodes whose functionality is entirely based on the pH-reversed ion current rectification and does not require specific surface functionalizations. This electrochemical arrangement can display different electrical behaviors (quasi-linear ohmic response and inward/outward rectifications) as a function of the electrolyte concentration in the external solutions and the applied voltage at the pore tips. The multifunctional response permits to implement different logical responses including NOR and INHIBIT functions.

Electric field-assisted proton transfer and water dissociation at the junction of a fixed-charge bipolar membrane

Abstract Electric field-enhanced (EFE) water dissociation can occur at the interfacial space charge junction of both biological and synthetic fixed-charge bipolar membranes. This dissociation has so far been analysed on an electrochemical basis using modified second Wien effect and absolute rate theories. We propose a statistical thermodynamics model to describe the cooperative orientation of the water molecules by the electric field at the bipolar junction. The approach is simple and retains some of the essential aspects of the phenomenon. In particular, the EFE water dissociation can now be rationalised on the basis of a field-assisted proton transfer mechanism involving the membrane fixe…

Modeling of the Salt Permeability in Fixed Charge Multilayer Membranes

A Simple Model for Ac Impedance Spectra in Bipolar Membranes

A new model accounting for the ac impedance spectra of synthetic ion-exchange bipolar membranes is presented. The theoretical approach is based on the Nernst−Planck and Poisson equations and applies some of the concepts used in the semiconductor pn junctions to the case of a bipolar membrane. The results presented are the current−voltage curves and the impedance spectra at electric currents above the limiting current. It is shown that the model is able to identify the main contributions to the bipolar membrane impedance and gives valuable information about the bipolar junction structure and its influence on the characteristic parameters involved in the field-enhanced water dissociation phen…

Multivalued and Reversible Logic Gates Implemented with Metallic Nanoparticles and Organic Ligands

Modeling Information Processing Using Nonidentical Coulomb Blockade Nanostructures

In recent years, molecular-protected metallic nanoparticles (NPs) have attracted a great deal of attention. Because of their reduced size, they behave like tiny capacitors so that there is an energy penalty when adding an electron to the NP which suppresses the electric current at a potential lower than a threshold value. This phenomenon is known as Coulomb blockade (CB) and allows the transport of electrons to be modulated through an external gate provided that the energy penalty is higher than the thermal energy. Together with the possibility of tailoring their properties, molecular protected NPs are potential candidates as future components of high density, low consumption electronics. H…

Divalent Cations Reduce the pH Sensitivity of OmpF Channel Inducing the PKA Shift of Key Acidic Residues

In contrast to the highly-selective channels of neurophysiology employing mostly the exclusion mechanism, different factors account for the selectivity of large channels. Elucidation of these factors is essential for understanding the permeation mechanisms in ion channels and their regulation in vivo. The interaction between divalent cations and a protein channel, the bacterial porin OmpF, has been investigated paying attention to the channel selectivity and its dependence on the solution pH. Unlike the experiments performed in salts of monovalent cations, the channel is now practically insensitive to pH, being anion selective all over the pH range considered. Electrostatic calculations bas…

Temperature effects on counterion binding to spherical polyelectrolytes: the charge-discharge transition of lignosulfonate

Abstract The effect of temperature on the effective charge numbers and diffusion coefficients of polyelectrolytes has not nobee dealth with in many studies. The present study concerns the temperature behavior of lignosulfonate. Lignosulfonate is a polydisperse polyelectrolyte whose molecules are compact spheres in aqueous solutions. One of its most remarkable properties is that is loses its charge in 0.1 M NaCl aqueous solution at about 40°C. In order to explain this charge-discharge transition, a theory for ion binding to spherical polyelectrolytes based on the relative population of two hydration states of the charged groups is presented. The water molecules adjacent to the charged groups…

Electrical fluctuations in monolayer-protected metal nanoclusters

Abstract Monolayer-protected clusters (MPCs) are formed by a neutral or charged metallic core surrounded by an organic ligand monolayer. We estimate the electric potential fluctuations of a MPC in an electrolyte solution by using the equilibrium fluctuation–dissipation theorem and the non-linear Poisson–Boltzmann equation extended to account for ion penetration in the monolayer. Significant fluctuations are predicted because the MPC capacitance is small (approximately 1 aF). We study also the non-equilibrium case of a MPC sandwiched between two electrodes and estimate the current noise considering the nanocluster as a single electron transistor and using a theoretical approach based on the …

Designing voltage multipliers with nanofluidic diodes immersed in aqueous salt solutions.

[EN] Membranes with nanofluidic diodes allow the selective control of molecules in physiological salt solutions at ambient temperature. The electrical coupling of the membranes with conventional electronic elements such as capacitors suggests opportunities for the external monitoring of sensors and actuators. We demonstrate experimentally and theoretically the voltage multiplier functionality of simple electrical networks composed of membranes with conical nanopores coupled to load capacitors. The robust operation of half and full wave voltage multipliers is achieved in a broad range of experimental conditions (single pore and multipore membranes, electrolyte concentrations, voltage amplitu…

Ion selectivity and water dissociation in polymer bipolar membranes studied by membrane potential and current–voltage measurements

Abstract A polymer bipolar ion-exchange membrane consists of a layered structure involving one cation and one anion ion-exchange layer joined together in series. In this study, the ionic selectivity and water dissociation rate of six commercial bipolar membranes was evaluated from the measurements of the membrane potential in a concentration cell and the current–voltage curve in a four-point measuring cell. Bipolar membrane technology requires polymer membranes presenting high ion selectivities and water dissociation rates, and in this paper we have addressed the basic physico-chemical phenomena involved, both theoretically and experimentally. We have shown that the effects of the bipolar j…

Model calculations of ion transport against its concentration gradient when the driving force is a pH difference across a charged membrane

Model calculations of the steady-state ion transport against its external concentration gradient when the driving force of this transport is a pH difference across a charged membrane are presented. We have solved numerically the exact Nernst-Planck equations without any additional simplifying approximation, such as the Goldman constant field assumption within the membrane. The validity of this assumption for a broad range of pH values, and salt and membrane fixed charge concentrations was analyzed critically. The membrane characteristics studied are the ionic fluxes and the membrane potential. Special attention is paid to the physical mechanism which leads to the ion transport against the c…

Thermodynamics of electrokinetic processes—I. Formulations

Abstract The phenomenological equations of electrokinetic processes are studied according to five different formulations. Transformation matrices with Haase's formulation are given. A study of the measurable character of fluxes, forces and phenomenological coefficients in those formulations is also made. The extrinsic character, if so, of the formulations is examined and a general definition of formulations established only for binary solutions is given. Finally, a review of the literature is included, aiming to clarify the possible misunderstandings arising from the application of these five formulations.

Signal processing and frequency-dependent associative memory based on nanoswitches

A signal processing concept based on nanoscale switches whose conductance can be tuned by an external stimulus between two (ON and OFF) states is proposed and analyzed theoretically. The building block of the system is formed by a metal nanoparticle linked to two electrodes by an organic ligand and a molecular switch. When we apply an alternating potential to the system of the same frequency as the periodic variation between the ON and OFF states induced on the switch, the net charge delivered by the system exhibits a sharp resonance. This resonance can be used to process an external signal by selectively extracting the weight of the different harmonics. In addition, a frequency-dependent a…

Synthetic nanopores with fixed charges: An electrodiffusion model for ionic transport

Synthetic nanopores with fixed charges exhibit ionic equilibrium and transport properties that resemble those displayed by biological ion channels. We present an electrodiffusion model based on the Nernst-Planck flux equations, which allows for a qualitative description of the steady state ionic transport through a nanopore when the membrane fixed charges and all mobile carriers (including the water ions) are properly taken into account. In particular, we study the current-voltage curve, the electrical conductance, the reversal potential (a measure of the nanopore ionic selectivity), as well as the flux inhibition by protons and divalent cations in the nanopore. The model clearly shows how …

Negative differential resistance and threshold-switching in conical nanopores with KF solutions

Negative differential resistance (NDR) phenomena are under-explored in nanostructures operating in the liquid state. We characterize experimentally the NDR and threshold switching phenomena observed when conical nanopores are immersed in two identical KF solutions at low concentration. Sharp current drops in the nA range are obtained for applied voltages exceeding thresholds close to 1 V and a wide frequency window, which suggests that the threshold switching can be used to amplify small electrical perturbations because a small change in voltage typically results in a large change in current. While we have not given a detailed physical mechanism here, a phenomenological model is also includ…

Modulation of current-time traces by two-pore arrangements of polyimide nanofluidic diodes

Liquid state arrangements of two polymeric membranes with single conical nanopores constitute nanofluidic diodes that allow a rich electrical functionality based on the modulation of individual conductances in aqueous electrolyte solutions. In particular, the prescribed sequences of current-time traces can be obtained by preprogramed switching between series and parallel pore connection arrangements. Hybrid nanopore-solid-state circuits are also possible. The basic applied physics of the nanofluidic diode arrangements can be understood from simple circuit theory concepts and should be of widespread interest to sensing and actuating procedures, controlled release dispensers, and energy conve…

Logic gates scheme based on Coulomb blockade in metallic nanoclusters with organic ligands

We propose a logic gates scheme based on the electron transfer through metallic nanoclusters linked to organic ligands and discuss theoretically the characteristics needed for practical implementation. As a proof-of-the-concept, we demonstrate the OR, AND and NOT gates and study the performance in terms of temperature, applied voltage, and noise.

Modeling of Amino Acid Electrodiffusion through Fixed Charge Membranes

Abstract We study theoretically the electrodiffusion of amino acids through fixed charge membranes, calculating the ionic fractions of the amino acid in the membrane as well as its total flux as a function of the relevant experimental parameters (amino acid concentration, salt concentration, and pH of the external solution; membrane fixed charge concentration; and amino acid membrane/solution partition coefficients) under different experimental conditions (symport vs antiport transport, uphill transport, etc.). The theoretical approach employed is based on the Nernst–Planck flux equations in the (Goldman) constant electric field assumption and considers all the species present in the system…

Fluoride-Induced Negative Differential Resistance in Nanopores: Experimental and Theoretical Characterization

We describe experimentally and theoretically the fluoride-induced negative differential resistance (NDR) phenomena observed in conical nanopores operating in aqueous electrolyte solutions. The threshold voltage switching occurs around 1 V and leads to sharp current drops in the nA range with a peak-to-valley ratio close to 10. The experimental characterization of the NDR effect with single pore and multipore samples concern different pore radii, charge concentrations, scan rates, salt concentrations, solvents, and cations. The experimental fact that the effective radius of the pore tip zone is of the same order of magnitude as the Debye length for the low salt concentrations used here is su…

Entropy–enthalpy compensation at the single protein level: pH sensing in the bacterial channel OmpF

The pH sensing mechanism of the OmpF channel operates via ligand modification: increasing acidity induces the replacement of cations with protons in critical binding sites decreasing the channel conductance. Aside from the change in enthalpy associated with the binding, there is also a change in the microscopic arrangements of ligands, receptors and the surrounding solvent. We show that the pH-modulation of the single channel conduction involves small free energy changes because large enthalpic and entropic contributions change in opposite ways, demonstrating an approximate enthalpy–entropy compensation for different salts and concentrations. We wish to acknowledge the support from the Span…

HCN2 Channel-Induced Rescue of Brain Teratogenesis via Local and Long-Range Bioelectric Repair

Embryonic exposure to the teratogen nicotine results in brain defects, by disrupting endogenous spatial pre patterns necessary for normal brain size and patterning. Extending prior work in Xenopus laevis that showed that misexpression of ion channels can rescue morphogenesis, we demonstrate and characterize a novel aspect of developmental bioelectricity: channel-dependent repair signals propagate long-range across the embryo. We show that distal HCN2 channel misexpression and distal transplants of HCN2-expressing tissue, non-cell-autonomously reverse profound defects, rescuing brain anatomy, gene expression, and learning. Moreover, such rescue can be induced by small-molecule HCN2 channel a…

Cell-cell bioelectrical interactions and local heterogeneities in genetic networks: a model for the stabilization of single-cell states and multicellular oscillations.

Genetic networks operate in the presence of local heterogeneities in single-cell transcription and translation rates. Bioelectrical networks and spatio-temporal maps of cell electric potentials can influence multicellular ensembles. Could cell-cell bioelectrical interactions mediated by intercellular gap junctions contribute to the stabilization of multicellular states against local genetic heterogeneities? We theoretically analyze this question on the basis of two well-established experimental facts: (i) the membrane potential is a reliable read-out of the single-cell electrical state and (ii) when the cells are coupled together, their individual cell potentials can be influenced by ensemb…

From non-excitable single-cell to multicellular bioelectrical states supported by ion channels and gap junction proteins: Electrical potentials as distributed controllers.

Endogenous bioelectric patterns within tissues are an important driver of morphogenesis and a tractable component of a number of disease states. Developing system-level understanding of the dynamics by which non-neural bioelectric circuits regulate complex downstream cascades is a key step towards both, an evolutionary understanding of ion channel genes, and novel strategies in regenerative medicine. An important capability gap is deriving rational modulation strategies targeting individual cells' bioelectric states to achieve global (tissue- or organ-level) outcomes. Here, we develop an ion channel-based model that describes multicellular states on the basis of spatio-temporal patterns of …

Kinetic modeling of ion conduction in KcsA potassium channel.

KcsA constitutes a potassium channel of known structure that shows both high conduction rates and selectivity among monovalent cations. A kinetic model for ion conduction through this channel that assumes rapid ion transport within the filter has recently been presented by Nelson. In a recent, brief communication, we used the model to provide preliminary explanations to the experimental current-voltage J-V and conductance-concentration g-S curves obtained for a series of monovalent ions (K(+),Tl(+), and Rb(+)). We did not assume rapid ion transport in the calculations, since ion transport within the selectivity filter could be rate limiting for ions other than native K(+). This previous wor…

A signal processing scheme based on high-frequency electromechanical oscillations in nanostructures

We explore the characteristics of a new signal processing scheme based on the high-frequency electromechanical oscillations of a nanostructure formed by an oscillating metallic nanoparticle connected to the left and right electrodes by soft links. Because this system shows resonant behavior when the frequency of the applied electric potential is close to the characteristic natural frequency of the oscillating nanoparticle, a parallel arrangement of nanostructures with different frequencies can be excited selectively by an external time-dependent electrical signal with the appropriate resonant frequencies. The highly nonlinear system response makes it possible to devise a signal processing s…

Membrane potential of single asymmetric nanopores: Divalent cations and salt mixtures

We study the electric potential difference (membrane potential) that arises across a single-pore membrane which separates two aqueous solutions at different salt concentrations. This potential difference is obtained here as the reversal potential of a conical nanopore, defined as the applied voltage needed to obtain a zero current through the membrane. To this end, different monovalent (LiCl, NaCl, KCl, and CsCl) and divalent (CaCl2, MgCl2, and BaCl2) cations are considered over a wide range of concentrations and salt mixtures for the two asymmetric nanostructure directionalities. The experimental data allows discussing fundamental questions on the interaction of the charges fixed to the po…

Net currents obtained from zero-average potentials in single amphoteric nanopores

We have studied experimentally and theoretically the rectifying properties of a single asymmetric nanopore functionalized with amphoteric lysine groups and characterized the net current obtained with zero-average time dependent potentials. The pH-controlled rectification phenomena may be relevant to bio-electrochemistry, pH sensing and regulation, and energy conversion. (C) 2013 Elsevier B.V. All rights reserved.

Ionic conduction, rectification, and selectivity in single conical nanopores

Modern track-etching methods allow the preparation of membranes containing a single charged conical nanopore that shows high ionic permselectivity due to the electrical interactions of the surface pore charges with the mobile ions in the aqueous solution. The nanopore has potential applications in electrically assisted single-particle detection, analysis, and separation of biomolecules. We present a detailed theoretical and experimental account of the effects of pore radii and electrolyte concentration on the current-voltage and current-concentration curves. The physical model used is based on the Nernst-Planck and Poisson equations. Since the validity of continuum models for the descriptio…

Synchronization of Bioelectric Oscillations in Networks of Nonexcitable Cells: From Single-Cell to Multicellular States.

Biological networks use collective oscillations for information processing tasks. In particular, oscillatory membrane potentials have been observed in nonexcitable cells and bacterial communities where specific ion channel proteins contribute to the bioelectric coordination of large populations. We aim at describing theoretically the oscillatory spatiotemporal patterns that emerge at the multicellular level from the single-cell bioelectric dynamics. To this end, we focus on two key questions: (i) What single-cell properties are relevant to multicellular behavior? (ii) What properties defined at the multicellular level can allow an external control of the bioelectric dynamics? In particular,…

Synchronization of coupled single-electron circuits based on nanoparticles and tunneling junctions

We explore theoretically the synchronization properties of a device composed of coupled single-electron circuits whose building blocks are nanoparticles interconnected with tunneling junctions. Elementary nanoscillators can be achieved by a single-electron tunneling cell where the relaxation oscillation is induced by the tunneling. We develop a model to describe the synchronization of the nanoscillators and present sample calculations to demonstrate that the idea is feasible and could readily find applications. Instead of considering a particular system, we analyze the general properties of the device making use of an ideal model that emphasizes the essential characteristics of the concept.…

A finite-difference method for numerical solution of the steady-state nernst—planck equations with non-zero convection and electric current density

Abstract A computer algorithm has been developed for digital simulation of ionic transport through membranes obeying the Nernst—Planck and Poisson equations. The method of computation is quite general and allows the treatment of steady-state electrodiffusion equations for multiionic environments, the ionic species having arbitrary valences and mobilities, when convection and electric current are involved. The procedure provides a great flexibility in the choice of suitable boundary conditions and avoids numerical instabilities which are so frequent in numerical methods. Numerical results for concentration and electric potential gradient profiles are presented in the particular case of the t…

MicroRNA Intercellular Transfer and Bioelectrical Regulation of Model Multicellular Ensembles by the Gap Junction Connectivity.

We have studied theoretically the microRNA (miRNA) intercellular transfer through voltage-gated gap junctions in terms of a biophysically grounded system of coupled differential equations. Instead of modeling a specific system, we use a general approach describing the interplay between the genetic mechanisms and the single-cell electric potentials. The dynamics of the multicellular ensemble are simulated under different conditions including spatially inhomogeneous transcription rates and local intercellular transfer of miRNAs. These processes result in spatiotemporal changes of miRNA, mRNA, and ion channel protein concentrations that eventually modify the bioelectrical states of small multi…