Neuromorphic responses of nanofluidic memristors in symmetric and asymmetric ionic solutions.

We show that ionic conduction properties of a multipore nanofluidic memristor can be controlled not only by the amplitude and frequency of an external driving signal but also by chemical gating based on the electrolyte concentration, presence of divalent and trivalent cations, and multi-ionic systems in single and mixed electrolytes. In addition, we describe the modulation of current rectification and hysteresis phenomena, together with neuromorphic conductance responses to voltage pulses, in symmetric and asymmetric external solutions. In our case, memristor conical pores act as nanofluidic diodes modulated by ionic solution characteristics due to the surface charge-regulated ionic transport. The above facts suggest potential sensing and actuating applications based on the conversion between ionic and electronic signals in bioelectrochemical hybrid circuits.

Transplantation of fragments from different planaria: A bioelectrical model for head regeneration.

Head-tail planaria morphologies are influenced by the electric potential differences across the animal's primary axis, as evidenced e.g. by voltage-sensitive dyes and functional experiments that create permanent lines of 2-headed but genetically wild-type animals. However, bioelectrical and biochemical models that make predictions on what would happen in the case of spatial chimeras made by tissue transplantation from different planaria (different species and head shapes) are lacking. Here, we use a bioelectrical model to qualitatively describe the effects of tissue transplantation on the shape of the regenerated head. To this end, we assume that the cells may have distinct sets of ion channels and ascribe the system outcome to the axial distributions of average cell potentials over morphologically relevant regions. Our rationale is that the distributions of signaling ions and molecules are spatially coupled with multicellular electric potentials. Thus, long-time downstream transcriptional events should be triggered by short-time bioelectrical processes. We show that relatively small differences between the ion channel characteristics of the cells could eventually give noticeable changes in the electric potential profiles and the expected morphological deviations, which suggests that small but timely bioelectrical actions may have significant morphological effects. Our approach is based on the observed relationships between bioelectrical regionalization and biochemical gradients in body-plan studies. Such models are relevant to regenerative, developmental, and cancer biology in which cells with distinct properties and morphogenetic target states confront each other in the same tissue.

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

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

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, showing that single-pore membranes can be used efficiently in ionic circuitry with distinct ionic environments.

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

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 known to specifically bind with lithium ions and when the modified pore is exposed to different alkali metal chloride solutions separately, significant changes in the ion current and rectification are only observed for lithium chloride. This fact suggests the generation of positively charged B12C4-Li+ complexes on the pore surface. Furthermore, the nanofluidic diode is able to recognize the lithium ion even in the presence of high concentrations of potassium ions in the external electrolyte solution. Thus, this nanodevice suggests a strategy to miniaturize nanofluidic porous systems for efficient recognition, extraction, and separation of lithium from raw materials.

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

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 scale up the transduction between ionic and electronic signals. The network designs discussed here should be useful to convert the weak signals characteristic of the micro and nanoscale into robust electronic responses by interconnecting iontronics and electronic elements.

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 ensemble-averaged electrical potentials. We propose a minimal biophysical model for the coupling between genetic and bioelectrical networks that associates the local changes occurring in the transcription and translation rates of an ion channel protein with abnormally low (depolarized) cell potentials. We then analyze the conditions under which the depolarization of a small region (patch) in a multicellular ensemble can be reverted by its bioelectrical coupling with the (normally polarized) neighboring cells. We show also that the coupling between genetic and bioelectric networks of non-excitable cells, modulated by average electric potentials at the multicellular ensemble level, can produce oscillatory phenomena. The simulations show the importance of single-cell potentials characteristic of polarized and depolarized states, the relative sizes of the abnormally polarized patch and the rest of the normally polarized ensemble, and intercellular coupling.

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

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 (t-BuC[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 these groups along the conical nanopore leads to the electrical rectification observed in the current-voltage (I-V) curve. On the contrary, other alkali cations are not able to induce any significant change in the rectification characteristics of the nanopore. The success of the chemical modification is monitored from the changes in the electrical readout of the nanopore. Theoretical results based on the Nernst-Planck and Poisson equations further demonstrate the validity of the experimental approach to the cesium-induced ionic conduction of the nanopore.

Label-Free Pyrophosphate Recognition with Functionalized Asymmetric Nanopores.

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 (Zn(2+) ) ion is achieved by exposing the modified pore to a solution of zinc chloride to form bis(Zn(2+) -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(Zn(2+) -DPA) complexes on the pore walls serve as recognition sites for pyrophosphate anion. The experimental results show that the proposed nanofluidic sensor has the ability to sense picomolar concentrations of PPi anion in the surrounding environment. On the contrary, it does not respond to other phosphate anions, including monohydrogen phosphate, dihydrogen phosphate, adenosine monophosphate, adenosine diphosphate, and adenosine triphosphate. The experimental results are described theoretically by using a model based on the Poisson-Nernst-Planck equations.

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

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 charged pore 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 the transport even at the isoelectric point of the protein. Surprisingly, even at pore sizes 100 times larger than the protein, the electrostatic hindrance still plays a major role in the transport. The experimental data are qualitatively explained using a two-region model for the membrane pore and approximated equations for the pH dependence of the protein and pore charges. The experimental and theoretical results should be useful for designing protein separation processes based on nanoporous charged membranes.

Oscillatory phenomena in electrophysiological networks: The coupling between cell bioelectricity and transcription.

Morphogenetic regulation during embryogenesis and regeneration rely on information transfer and coordination between different regions. Here, we explore theoretically the coupling between bioelectrical and transcriptional oscillations at the individual cell and multicellular levels. The simulations, based on a set of ion channels and intercellular gap junctions, show that bioelectrical and transcriptional waves can electrophysiologically couple distant regions of a model network in phase and antiphase oscillatory states that include synchronization phenomena. In this way, different multicellular regionalizations can be encoded by cell potentials that oscillate between depolarized and polarized states, thus allowing a spatio-temporal coding. Because the electric potential patterns characteristic of development and regeneration are correlated with the spatial distributions of signaling ions and molecules, bioelectricity can act as a template for slow biochemical signals following a hierarchy of experimental times. In particular, bioelectrical gradients that couple cell potentials to transcription rates give to each single cell a rough idea of its location in the multicellular ensemble, thus controlling local differentiation processes that switch on and off crucial parts of the genome.

Memristive arrangements of nanofluidic pores.

We demonstrate that nanofluidic diodes in multipore membranes show a memristive behavior that can be controlled not only by the amplitude and frequency of the external signal but also by series and parallel arrangements of the membranes. Each memristor consists of a polymeric membrane with conical nanopores that allow current rectification due to the electrical interaction between the ionic solution and the pore surface charges. This surface charge-regulated ionic transport shows a rich nonlinear physics, including memory and inductive effects, which are characterized here by the current-voltage curves and electrical impedance spectroscopy. Also, neuromorphiclike potentiation of the membrane conductance following voltage pulses (spikes) is observed. The multipore membrane with nanofluidic diodes shows physical concepts that should have application for information processing and signal conversion in iontronics hybrid devices.

pH-Dependent Effects in Nanofluidic Memristors.

Multipore membranes with nanofluidic diodes show memristive and current rectifying effects that can be controlled by the nanostructure asymmetry and ionic solution characteristics in addition to the frequency and amplitude of the electrical driving signal. Here, we show that the electrical conduction phenomena, which are modulated by the interaction between the pore surface charges and the solution mobile ions, allow for a pH-dependent neuromorphic-like potentiation of the membrane conductance by voltage pulses. Also, we demonstrate that arrangements of memristors can be employed in the design of electrochemical circuits for implementing logic functions and information processing in iontronics.

Nernst-Planck model of photo-triggered, pH-tunable ionic transport through nanopores functionalized with "caged" lysine chains.

We describe the fabrication of asymmetric nanopores sensitive to ultraviolet (UV) light, and give a detailed account of the divalent ionic transport through these pores using a theoretical model based on the Nernst-Planck equations. The pore surface is decorated with lysine chains having pH-sensitive (amine and carboxylic acid) moieties that are caged with photo-labile 4,5-dimethoxy-2-nitrobenzyl (NVOC) groups. The uncharged hydrophobic NVOC groups are removed using UV irradiation, leading to the generation of hydrophilic "uncaged" amphoteric groups on the pore surface. We demonstrate experimentally that polymer membranes containing single pore and arrays of asymmetric nanopores can be employed for the pH-controlled transport of ionic and molecular analytes. Comparison between theory and experiment allows for understanding the individual properties of the phototriggered nanopores, and provides also useful clues for the design and fabrication of multipore membranes to be used in practical applications.

Correcting instructive electric potential patterns in multicellular systems: External actions and endogenous processes.

BACKGROUND: Transmembrane electrical potential differences in cells modulate the spatio-temporal distribution of signaling ions and molecules that are instructive for downstream signaling pathways in multicellular systems. The local coupling between bioelectricity and protein transcription patterns allows dynamic subsystems (modules) of cells that share the same bioelectrical state to show similar biochemical downstream processes. METHODS: We simulate theoretically how the integration-segregation pattern formed by the different multicellular modules that define a biosystem can be controlled by multicellular potentials. To this end, we couple together the model equations of the bioelectrical network to those of the genetic network. RESULTS: The coupling provided by the intercellular junctions and the external microenvironment allows the restoration of the target bioelectrical pattern by changing the transcription rate of specific ion channels, the post-translational blocking of these channels, and changes in the environmental ionic concentrations. CONCLUSIONS: The simulations show that the single-cell feedback between bioelectrical and transcriptional processes, together with the coupling provided by the intercellular junctions and the environment, can correct large-scale patterns by means of suitable external actions. GENERAL SIGNIFICANCE: This study provides a theoretical advancement in the understanding of how the multicellular bioelectric coupling may guide repolarizing interventions for regenerating a tissue, with potential implications in biomedicine.

Synaptical Tunability of Multipore Nanofluidic Memristors.

We demonstrate a multipore nanofluidic memristor with conical pores showcasing a wide range of hysteresis and memristor properties that provide functionalities for brainlike computation in neuromorphic applications. Leveraging the interplay between the charged functional groups on the pore surfaces and the confined ionic solution, the memristor characteristics are modulated through the electrolyte type, ionic concentrations, and pH levels of the aqueous solution. The multipore membrane mimics the functional characteristics of biological ion channels and displays synaptical potentiation and depression. Furthermore, this property can be inverted in polarity by chemically varying the pH level. The ability to modulate memory effects by ionic conductivity holds promise for enhancing signal information processing capabilities.

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

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

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 a diversity-induced static noise should be considered together with the dynamic noise caused by thermal fluctuations. This static noise originates from the hardware variability and produces fluctuations in the threshold potential of the individual nanoparticles arranged in a parallel array. The correlation between different input (potential) and output (current) signals in the array is analyzed as a function of temperature, applied voltage, and the variability in the electrical properties of the nanostructures. Extensive kinetic Monte Carlo simulations with nanostructures whose basic properties have been demonstrated experimentally show that variability can enhance the correlation, even for the case of weak signals and high variability, provided that the signal is processed by a sufficiently high number of nanostructures. Moderate redundancy permits us not only to minimize the adverse effects of the hardware variability but also to take advantage of the nanoparticles' threshold fluctuations to increase the detection range at low temperatures. This conclusion holds for the average behavior of a moderately large statistical ensemble of non-identical nanostructures processing different types of input signals and suggests that variability could be beneficial for signal processing. We demonstrate also that circuits composed of coupled non-identical nanoparticles can act as elementary nano-oscillators that show synchronization properties for sub-threshold stimuli. The results obtained should be of conceptual interest for the design of reliable signal processing schemes with non-identical nanostructures.

Divalent cations reduce the pH sensitivity of OmpF channel inducing the pK(a) 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 based on the available structural data suggest that the binding of divalent cations has two main effects: (i) the pK(a) values of key ionizable groups differ significantly from those of the isolated groups in solution and (ii) the cation binding has a decisive impact on the effective electric charge regulating the channel selectivity. A simple molecular model based on statistical thermodynamics provides additional qualitative explanations to the experimental findings that could also be useful for other related systems like synthetic nanopores, ion exchange membranes, and polyelectrolyte multilayers.

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 demonstrated and theoretically described electrical characteristics of these nanostructures. In particular, we make use of the tunnelling current through a metallic nanocluster attached to the electrodes by ligands. The nanostructure is described as a single electron transistor (SET) that can be gated by an external potential. This fact permits exploiting information processing schemes in approximately defined arrays of MPCs. These schemes include: (i) binary, multivalued, and reversible logic gates; (ii) an associative memory and a synchronization circuit; and (iii) two signal processing nanodevices based on parallel arrays of MPCs and nanoswitches. In each case, the practical operation of the nanodevice is based on the SET properties of MPCs reported experimentally. We examine also some of the practical problems that should be addressed in future experimental realizations: the stochastic nature of the electron tunnelling, the relatively low operation temperatures, and the limited reliability caused by the weak signals involved and the nanostructure variability. The perspectives to solve these problems are based on the potentially high degree of scalability of the nanostructures.