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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 suggestive of a mixed pore surface and bulk conduction regime. Thus, we propose a two-region conductance model where the mobile cations in the vicinity of the negative pore charges are responsible for the surface conductance, while the bulk solution conductance is assumed for the pore center region.

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.

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.

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 describe the physicochemical effects resulting from the nanostructure asymmetry, (iii) to develop a theoretical model for multi-ionic systems, and (iv) to quantify the contributions of the liquid junction potentials established in the salt bridges to the total cell membrane potential.

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 incorporates effective conductances ultimately related to specific ion channel and junction proteins that are amenable to external regulation. We also consider a bioelectrical relationship between the connexin composition of the intercellular gap junction and different stages of cancer. Abstract Electric potential distributions can act as instructive pre-patterns for development, regeneration, and tumorigenesis in cell systems. The biophysical states influence transcription, proliferation, cell shape, migration, and differentiation through biochemical and biomechanical downstream transduction processes. A major knowledge gap is the origin of spatial patterns in vivo, and their relationship to the ion channels and the electrical synapses known as gap junctions. Understanding this is critical for basic evolutionary developmental biology as well as for regenerative medicine. We computationally show that cells may express connexin proteins with different voltage-gated gap junction conductances as a way to maintain multicellular regions at distinct membrane potentials. We show that increasing the multicellular connectivity via enhanced junction function does not always contribute to the bioelectrical normalization of abnormally depolarized multicellular patches. From a purely electrical junction view, this result suggests that the reduction rather than the increase of specific connexin levels can also be a suitable bioelectrical approach in some cases and time stages. We offer a minimum model that incorporates effective conductances ultimately related to specific ion channel and junction proteins that are amenable to external regulation. We suggest that the bioelectrical patterns and their encoded instructive information can be externally modulated by acting on the mean fields of cell systems, a complementary approach to that of acting on the molecular characteristics of individual cells. We believe that despite the limitations of a biophysically focused model, our approach can offer useful qualitative insights into the collective dynamics of cell system bioelectricity.

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, uncoupled morphogen concentration along an orthogonal direction, constitute the instructive patterns that modulate the morphological outcomes, and (ii) the addition of an external agent partially blocks the intercellular GJs between neighboring cells and modifies thus the establishment of these patterns. As an illustrative example, we study how the different connectivity and morphogen patterns obtained in presence of a GJ blocker can give rise to novel head morphologies in regenerating planaria. We note that the ability of GJs to regulate the permeability of morphogens post-translationally suggests a mechanism by which different anatomies can be produced from the same genome without the modification of gene-regulatory networks. Conceptually, our model biosystem constitutes a reaction-diffusion information processing mechanism that allows reprogramming of biological morphologies through the external manipulation of the intercellular GJs and the resulting changes in instructive biochemical signals.

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 with the mobile ions present at electrochemically and biologically relevant concentrations. The different pores and electrolytes studied, together with the abundant experimental data provided, can be useful to develop new theoretical simulations of transport phenomena in nanoscale solutions that are confined within charged surfaces.

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 pore surface with the mobile ions in solution over nanoscale volumes. In particular, we describe the effects due to (i) the relative orientation of the axial charge distribution along the pore and the externally imposed concentration gradient, (ii) the different screening of the pore negative charges by the monovalent and divalent cations, and (iii) the non-zero bi-ionic potential arising between two salts of distinct cations with a common anion at the same concentration. We have also given a quantitative description of the experimental data obtained with monovalent cations on the basis of the Poisson-Nernst-Planck formalism. In the case of the divalent cations, however, we could give only a qualitative description of the observed phenomena. Taken together, the results can contribute to the understanding of electrochemical and bioelectrical membrane processes which are regulated by the interplay between the membrane asymmetry and the ionic concentration and electrical potential gradients.

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.

Advanced materials interfaces 8(6), 2001766 (2021). doi:10.1002/admi.202001766, Published by Wiley-VCH, Weinheim

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 different cell polarization states. The multicellular community effects obtained are regulated both at the single-cell and intercellular levels, and emerge from a delicate balance between the degrees of intercellular coupling in: (i) the small patch, (ii) the surrounding bulk, and (iii) the interface that separates these two regions. The model is experimentally motivated and consists of two generic voltage-gated ion channels that attempt to establish the depolarized and polarized cell states together with coupling conductances whose individual and intercellular different states permit a dynamic multicellular connectivity. The simulations suggest that community effects may allow the reprogramming of single-cell bioelectrical states, in agreement with recent experimental data. A better understanding of the resulting electrical regionalization can assist the electroceutical correction of abnormally depolarized regions initiated in the bulk of normal tissues as well as suggest new biophysical mechanisms for the establishment of target patterns in multicellular engineering.

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 depolarized cell states, (ii) a feedback mechanism for the transcriptional and bioelectrical regulations, and (iii) voltage-gated intercellular conductances that allow a dynamic intercellular connectivity. The simulations provide steady-state and oscillatory multicellular states that help explain aspects of development and guide experimental procedures attempting to establish instructive bioelectrical patterns based on electric potentials and currents to regulate cell behavior and morphogenesis.

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 ensemble. We provide qualitative insights into recent experiments concerning planarian anterior/posterior polarity by showing that: (i) bioelectrical signals can help separated cell domains to know their relative position after injury and contribute to the transitions between the abnormal double-head state and the normal head tail state; (ii) the bioelectrical phase-space of the system shows a bi-stability region that can be interpreted as the cryptic system state; and (iii) context-dependent responses are obtained depending on the cutting plane position, the initial bioelectrical state of the multicellular system, and the intercellular connectivity. The model reveals how simple bioelectric circuits can exhibit complex tissue-level patterning and suggests strategies for regenerative control in vivo and in synthetic biology contexts. (C) 2019 Elsevier B.V. All rights reserved.

[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 of the inputs of the AND gate, giving an Enabled-OR logic function. Also, the operation of the OR gate connected with a solid-state transistor, working as a signal inverter, gives a NOR gate. These hybrid electrochemical circuits allow a variety of real time logic functions because of the robust electrical coupling between ionic solutions and electronic elements., P.R., J.C., and S.M. acknowledge the support from the Ministry of Economic Affairs and Competitiveness and FEDER (project MAT2015-65011-P). M.A., S.N. and W.E. acknowledge the funding from the Hessen State Ministry of Higher Education, Research and the Arts, Germany, under the LOEWE project iNAPO.

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 in aprotic electrolyte solutions with different water mole fractions reveal that the solvated metal ion (M) species [M−(solvent)4]+ formed in acetonitrile solvent are more tightly bounded to the pore walls compared with the cationic chelates obtained in propylene carbonate solvent. The basic findings reported here should be of interest for ionic/molecular nanofiltration processes in non-aqueous conditions as well as for moisture sensitive and energy storage nanofluidic devices.

We 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 case of the addition of a constant potential to the codified potential to scale it up to the supra-threshold regime.

[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 functionalization. Upon exposing the modified pore to solutions of hydrogen peroxide (oxidizing agent) and sodium dithionite (reducing agent) the surface charge is reversibly modulated from positive to neutral, leading to measurable changes in the electronic readout of ion current passing through the nanopore. On oxidation, the quaternary nicotinamide units impart positive charge to the pore surface, resulting in the ion current rectification (anion-selective pore). On the contrary, the complementary reduced dihydronicotinamide moieties resulted in the loss of surface charge and ohmic behaviour (non-selective pore). The experimental results are further theoretically described by using Poisson-Nernst-Planck, M.A., S.N. and W.E. acknowledge the funding from the Hessen State Ministry of Higher Education, Research and the Arts, Germany, under the LOEWE project iNAPO. P. R. and S. M. acknowledge financial support by the Generalitat Valenciana (Program of Excellence Prometeo/GV/0069), the Spanish Ministry of Economic Affairs and Competitiveness (MAT2015-65011-P), and FEDER. I.A. and C.M.N. acknowledge financial support through the Helmholtz programme BioInterfaces in Technology and Medicine. The authors are also thankful to Prof. C. Trautmann, Department of Materials Research from GSI, for support with irradiation experiments.

[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 chemical modification of the nanopore. The sensing mechanism is based on the displacement of the metal ion from the NTA-Ni2+ chelates. When the modified pore is exposed to histamine solution, the Ni2+ ion in NTA-Ni2+ chelate recognizes histamine through a metal ion coordination displacement process and formation of stable Ni-histamine complexes, leading to the regeneration of metal-free NTA groups on the pore surface, as shown in the current-voltage characteristics. Nanomolar concentrations of the histamine in the working electrolyte can be detected. On the contrary, other neurotransmitters such as glycine, serotonin, gamma-aminobutyric acid, and dopamine do not provoke significant changes in the nanopore electronic signal due to their inability to displace the metal ion and form a stable complex with Ni2+ ion. The nanofluidic sensor exhibits high sensitivity, specificity and reusability towards histamine detection and can then be used to monitor the concentration of biological important neurotransmitters., M.A., I.D., S.N. and W.E. acknowledge the funding from the Hessen State Ministry of Higher Education, Research and the Arts, Germany, under the LOEWE project iNAPO. P. R. and S. M. acknowledge financial support by the Spanish Ministry of Economic Affairs and Competitiveness (MAT2015-65011-P) and FEDER. The authors are also thankful to Prof. C. Trautmann, Department of Materials Research from GSI, for support with irradiation experiments.

[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 channels operating simultaneously. The results also suggest signal transduction schemes with bio-electronic interfaces and ionic circuits where soft matter nanodiodes can be coupled to conventional electronic elements., We acknowledge the support from the Ministry of Economic Affairs and Competitiveness and FEDER (project MAT2015-65011-P) and the Generalitat Valenciana (project Prometeo/GV/0069). We thank Profs. A. Alcaraz and V. M. Aguilella for fruitful suggestions. This paper is devoted to the memory of Professor Kyosti Kontturi, Aalto University, Finland.

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 electrical potentials in aggregates of non-excitable cells. The model is of biological interest because modern techniques allow to associate bioelectrical signals with specific ion channel proteins in the cell membrane that are central to embryogenesis, regeneration, and tumorigenesis. As a complementary approach to the usual biochemical description, we have studied four biophysical questions: (i) how can single-cell bioelectrical states be established; (ii) how can a change in the cell potential caused by a transient perturbation of the cell state be maintained after the stimulus is gone (bioelectrical memory); (iii) how can a single-cell contribute to the control of multicellular ensembles based on the spatio-temporal pattern of electrical potentials; and (iv) how can oscillatory patterns arise from the single-cell bioelectrical dynamics. Experimentally, endogenous bioelectric gradients have emerged as instructive agents for morphogenetic processes. In this context, the simulations can guide new procedures that may allow a distributed control of the multicellular ensemble.

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, we explore the interplay between transcriptional and translational dynamics and membrane potential dynamics in a model multicellular ensemble, describe the spatiotemporal patterns that arise when the average electric potential allows groups of cells to act as a coordinated multicellular patch, and characterize the resulting synchronization phenomena. The simulations concern bioelectric networks and collective communication across different scales based on oscillatory and synchronization phenomena, thus shedding light on the physiological dynamics of a wide range of endogenous contexts across embryogenesis and regeneration.

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 included.

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 metals, divalent metals, and organic cations under symmetric and asymmetric electrolyte conditions. Under symmetric conditions, the pores exhibit ohmic behavior when exposed to alkali metal chlorides and ammonium chloride solutions while divalent cations cannot pass through the pores as evidenced from the current-voltage curves. For the case of asymmetric electrolyte conditions, current rectification suggests pore blockage from the side of membrane exposed to divalent cations and tetraalkylammonium (TAA) cations. The experimental data show that the SE-PI membranes efficiently discriminate alkali cations from divalent metal cations and ammonium cation from TAA cations. The ionic conduction of the membranes is also sensitive to the mole fraction of Ca2+ in multi-ionic solutions. The ionic transport experiments further confirm that the nanopores allow significant alkali cation fluxes while rejecting divalent cations. Based on the good stability and high selectivity, the solvent treated PI membranes constitute remarkable candidates to be employed in applications concerning a wide range of electrolyte solutions.

[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 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., M.A., S.N., and W.E. acknowledge the funding from the Hessen State Ministry of Higher Education, Research and the Arts, Germany, under the LOEWE project iNAPO. P.R. and S.M. acknowledge financial support by the Generalitat Valenciana (Program of Excellence Prometeo/GV/0069), the Spanish Ministry of Economic Affairs and Competitiveness (MAT2015-65011-P), and FEDER. I. A. and C.M.N. acknowledge financial support through the Helmholtz programme BioInterfaces in Technology and Medicine. The authors are also thankful to Prof. C. Trautmann, Department of Materials Research from GSI, for support with irradiation experiments.

[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 (electronics). Remarkably, these electrical characteristics do not result from slow ionic redistributions within the nanopores, which should be difficult to control and would give only small conductance changes, but arise from the robust collective response of equivalent circuits. Coupling nanoscale diodes with conventional electronic elements allows interconverting ionic and electronic currents, which should be useful for electrochemical signal processing and energy conversion based on charge transport., Support from the Ministry of Economic Affairs and Competitiveness and FEDER (project MAT2015-65011-P), the Generalitat Valenciana (project Prometeo/GV/0069 for Groups of Excellence). M. A, S. N. and W. E acknowledge the funding from the Hessen State Ministry of Higher Education, Research and the Arts, Germany, in the frame of LOEWE project iNAPO. Z. S. acknowledges the funding from the National Science Foundation (CHE 1306058).

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 polarity in biological model systems. In particular, we show that simple bioelectric circuits can exhibit complex multicellular patterning, suggesting strategies to establish axial polarity in synthetic biology and regeneration.

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

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.

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 biophysical problem suggests that the spatio-temporal map of single-cell potentials can influence downstream patterning processes by means of the voltage-gated gap junction interconnectivity, much as in the case of electronic devices where the control of electric potentials and currents allows the local modulation of the circuitry to achieve full functionality. An alternative theoretical approach, the BioElectrical Tissue Simulation Engine (BETSE), is also presented. The BETSE modeling environment utilizes finite volume techniques to simulate bioelectric states from the perspective of ion concentrations and fluxes. This model has been successfully applied to make predictions and explain experimental observations in a variety of embryonic, regenerative, and oncogenic contexts.

[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 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., P.R., J.C., V.G., and S.M. acknowledge the financial support from the Ministry of Economy and Competitiveness of Spain, (Materials Program, project No. MAT2015-65011-P), and FEDER. M.A., S.N., and W.E. acknowledge the funding from the Hessen State Ministry of Higher Education, Research and the Arts, Germany, under the LOEWE project iNAPO.

[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 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., M.A., S.N., and W.E. acknowledge the funding from the Hessen State Ministry of Higher Education, Research and the Arts, Germany, under the LOEWE Project iNAPO. P.R and S.M. acknowledge financial support by the Spanish Ministry of Economic Affairs and Competitiveness (Grant MAT2015-65011-P) and FEDER. I.A. and C.M.N. acknowledge financial support through the Helmholtz Programme BioInterfaces in Technology and Medicine. The authors are thankful to Prof. Christina Trautmann from GSI (Department of Material Research) for support with the heavy ion irradiation experiments.

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., MA, S.N. and W.E. acknowledge the funding from the Hessen State Ministry of Higher Education, Research and the Arts, Germany, under the LOEWE project iNAPO. P.R and S.M. acknowledge the support from the Ministry of Economic Affairs and Competitiveness and FEDER (project MAT2012-32084) and the Generalitat Valenciana (project Prometeo/GV/0069 for Groups of Excellence). I.A. and C.M.N. acknowledge financial support through the Helmholtz programme Bio-Interfaces in Technology and Medicine. The authors are thankful to Prof. C. Trautmann, Department of Materials Research from GSI, for support with irradiation experiments.

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 channels show also a high heterogeneity, making it possible to analyze the effects of diversity in the electrical responses of channels localized on spatial domains. We use a phenomenological approach of voltage gating that reproduces the observed rectification characteristics of inward rectifying potassium channels and relate the threshold voltage heterogeneity of the channels to the establishment of spatial domains with different electrical sensitivities. Although our model is only a limited picture of the whole cell membrane, it shows that domains with different ion channels may permit or suppress steady state bioelectrical signals over the cell surface according to their particular voltage sensitivity. Also, the nonlinear electrical coupling of channels with different threshold potentials can lead to a rich variety of bioelectrical phenomena, including regions of membrane potential bi-stability.

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 analyzed. The results suggest that simple coupling mechanisms can be significant for the biophysical chemistry of model biomolecular ensembles. In particular, the spatiotemporal map of single cell potentials should be relevant for the uptake and distribution of charged nanoparticles over model cell ensembles and the collective properties of droplet networks incorporating protein ion channels inserted in lipid bilayers.

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 multicellular domains because of the ensemble average nature of the electrical potential. The simulations allow a qualitative understanding of the context-dependent nature of the effects observed when specific signaling molecules are transferred through gap junctions. The results suggest that an efficient miRNA intercellular transfer could permit the spatiotemporal control of small cellular domains by the conversion of single-cell genetic and bioelectric states into multicellular states regulated by the gap junction interconnectivity.

[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 over a wide range of membrane resistances, electrical capacitances, and solution pH values. The model simulations are based on empirical equations that have a solid physical basis and provide a convenient description of the electrical circuit operation. The results should contribute to advance signal transduction and processing using nanoporebased biosensors and bioelectronic interfaces., We acknowledge the support from the Ministry of Economic Affairs and Competitiveness and FEDER (Project No. MAT2015-65011-P). M. A., S. N., and W. E. acknowledge the funding from the Hessen State Ministry of Higher Education, Research and the Arts, Germany, under the LOEWE project iNAPO.

[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 relatively low rectified ion currents because the cation hydrophobicity increases with the alkyl chain. At low concentrations and acidic conditions, an inversion in the current rectification characteristics is observed, which is attributed to the adsorption of the organic cations on the pore surfaces. The experimental results can be analyzed in terms of the Poisson-Nernst-Planck equations and the geometrical and electrical single pore characteristics for the different ions, pH values, and salt concentrations employed. This theoretical approach is qualitative and could be extended further to include a self-consistent theoretical treatment of the ionic adsorption and surface charge equilibria, M. A., S. N., and W. E. acknowledge the funding from the Hessen State Ministry of Higher Education, Research and the Arts, Germany, under the LOEWE project iNAPO. P. R., J. C., and S. M. acknowledge financial support by the Spanish Ministry of Economic Affairs and Competitiveness (MAT2015-65011-P) and FEDER. The authors are also thankful to Prof. C. Trautmann, Department of Materials Research from GSI, for support with irradiation experiments.

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. However, they face a number of problems before they can be considered as a technological viable option. To be used at room temperatures, NPs radii need to be in the nanometer range, and then fabrication processes lead to significant variability in the NPs physical properties. We use here two systems, a XOR gate and a R-SET model which mimics some characteristics of neurons, to show strategies that may be used to cope with the variability problem so that a robust information processing can be achieved despite using nominally different components.

[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 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., M.A., S.N., and W.E. acknowledge funding from the Hessen State Ministry of Higher Education, Research and the Arts, Germany, under LOEWE project iNAPO. P.R., J.C., and S.M. acknowledge financial support by the Spanish Ministry of Economic Affairs and Competitiveness (MAT2015-65011-P) and FEDER. I.A. and C.M.N. acknowledge financial support through the Helmholtz programme Biolnterfaces in Technology and Medicine. The authors are thankful to Prof. Christina Trautmann from GSI (Department of Material Research) for support with the heavy ion irradiation experiments and Dr. M. Nawaz Tahir (Johannes Gutenberg University Mainz) for help with contact angle measurements.

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 conversion modules based on electrochemical signals.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 conversion modules based on electrochemical signals.

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 that incorporate the basic threshold characteristics observed in the respective experimental current-voltage curves. In each case, the different shape, size, and charge distributions of the nanostructures result in statistical distributions for the individual threshold potentials, characterized by experimental average and width distribution values, rather than in identical replicates of the same unit. Despite the significant variability, the simulations suggest that useful average responses can still be achieved with summing networks of heterogeneous nanostructures because the collective behavior may compensate for individual failures and variability. Since threshold potential systems are commonplace in biology, the results obtained are also significant for understanding the role of diversity in biologically inspired networks.

Bioelectrical 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 in small multicellular ensembles, ignoring slow diffusional processes. The spatio-temporal patterns obtained for the local map of cell electric potentials illustrate the normalization of regions with abnormal cell electrical states. The effects of intercellular coupling and blocking of specific channels on the electrical patterns are described. These patterns can regulate the electrically-induced redistribution of charged nanoparticles over small regions of a model tissue. The inclusion of bioelectrical signals provides new insights for the modeling of cancer biophysics because collective multicellular states show electrical coupling mechanisms that are not readily deduced from biochemical descriptions at the individual cell level.

[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 amplitudes, and solid-state capacitances). The designed voltage multipliers operate in the liquid state and can be used in sensing devices because different electrical, optical, and chemical inputs are known to modulate the individual nanofluidic diode resistances in the electrical network., We acknowledge the support of the Ministry of Economic Affairs and Competitiveness and FEDER (project MAT2015-65011-P) and the Generalitat Valenciana (project Prometeo/GV/0069 for Groups of Excellence). M. A., S. N. and W. E. acknowledge the funding from the Hessen State Ministry of Higher Education, Research and the Arts, Germany (LOEWE project iNAPO).