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.

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.

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.

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.

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.

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.

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 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.

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

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.

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, 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.

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 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.

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 activators, even with delayed treatment initiation. We present a simple, versatile computational model of bioelectrical signaling upstream of key patterning genes such as OTX2 and XBF1, which predicts long-range repair induced by ion channel activity, and experimentally validate the predictions of this model. Our results and quantitative model identify a powerful morphogenetic control mechanism that could be targeted by future regenerative medicine exploiting ion channel modulating drugs approved for human use.

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 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.

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 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.

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 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.

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.

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 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.

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 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.

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, 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.

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 way, the short-range interactions of the cells within the patch favor the depolarized membrane potential state, whereas the long-range interaction of the patch with the rest of the ensemble promotes the polarized state. The coupling between the local and long-range bioelectric signals allows a binary control of the patch membrane potentials, and alternating cell polarization and depolarization states can be maintained for optimal windows of the number of cells and the intercellular connectivity in the patch. The oscillatory phenomena emerge when the feedback between the single-cell bioelectric and genetic dynamics is coupled at the multicellular level. In this way, the intercellular connectivity acts as a regulatory mechanism for the bioelectrical oscillations. The simulation results are qualitatively discussed in the context of recent experimental studies.