Weak Electrical Coupling Research Articles

Analysis of dynamical robustness of multilayer neuronal networks with inter-layer ephaptic coupling at different scales

In nervous system, a non-synaptic communication between neurons, known as the ephaptic coupling, emerges depending on electromagnetic induction which is induced by extracellular electric fields. In this paper, a multilayer neuronal network is constructed by adopting ephaptic coupling between layers, and dynamical robustness of multilayer neuronal networks with inter-layer ephaptic coupling is analyzed at different scales. The macroscopic oscillation of the whole network occupies the middle ground between mesoscopic oscillation of intermediate layer and that of the top (or bottom) layer. Strong inter-layer ephaptic coupling is capable of suppressing the resonance like phenomena of oscillation at mesoscale and macroscale. At weak electrical coupling, dynamical robustness of intermediate layer is stronger than that of top and bottom layers, and is even stronger than that of the whole network. While at strong electrical coupling, dynamical robustness of each layer is comparable to that of the whole network. The inter-layer ephaptic coupling could enhance dynamical robustness of each layer and the entire multilayer neuronal network, which is in stark contrast to electrical coupling with the tendency to spoil the dynamical robustness. Dynamical robustness of the whole network is always weaker than that of intermediate layer, but is stronger than that of top and bottom layers with increasing inter-layer ephaptic coupling. The firing modes of neurons before the critical ratio is analyzed at microscale. The ratio of inactive neurons switches the firing patterns of the active neuron among different firing patterns in multilayer neuronal network. The dynamics of multilayer neuronal network with inter-layer ephaptic coupling is verified in the analog circuit built on Multisim. This study provides new clues to understand mechanism of collective phenomenon in realistic neuronal systems.

Network Properties of Electrically Coupled Bursting Pituitary Cells.

The endocrine cells of the anterior pituitary gland are electrically active when stimulated or, in some cases, when not inhibited. The activity pattern thought to be most effective in releasing hormones is bursting, which consists of depolarization with small spikes that are much longer than single spikes. Although a majority of the research on cellular activity patterns has been performed on dispersed cells, the environment in situ is characterized by networks of coupled cells of the same type, at least in the case of somatotrophs and lactotrophs. This produces some degree of synchronization of their activity, which can be greatly increased by hormones and changes in the physiological state. In this computational study, we examine how electrical coupling among model cells influences synchronization of bursting oscillations among the population. We focus primarily on weak electrical coupling, since strong coupling leads to complete synchronization that is not characteristic of pituitary cell networks. We first look at small networks to point out several unexpected behaviors of the coupled system, and then consider a larger random scale-free network to determine what features of the structural network formed through gap junctional coupling among cells produce a high degree of functional coupling, i.e., clusters of synchronized cells. We employ several network centrality measures, and find that cells that are closely related in terms of their closeness centrality are most likely to be synchronized. We also find that structural hubs (cells with extensive coupling to other cells) are typically not functional hubs (cells synchronized with many other cells). Overall, in the case of weak electrical coupling, it is hard to predict the functional network that arises from a structural network, or to use a functional network as a means for determining the structural network that gives rise to it.

Synchronization mode transitions induced by chaos in modified Morris–Lecar neural systems with weak coupling

Based on a modified Morris–Lecar neural model, the synchronization modes transitions between two coupled neurons or star-coupled neural network connected by weak electrical and chemical coupling are, respectively, investigated. For the two coupled neurons, by increasing the calcium conductivity, it is found that the period-2 synchronization of the action potential is transformed to desynchronization first, and then to period-3 synchronization. By increasing the potassium conductivity, however, the synchronization mode transition is a reversal direction process as mentioned above. The corresponding inter-spike interval shows the synchronization modes transition is induced by the chaos. The stronger the coupling strength is, the smaller the period-2 synchronization region in the parameters plane is, while the larger the period-3 synchronization region will be. For the star-coupled neural network, in the presence of weak electrical coupling, it can exhibit the completely synchronized mode, desynchronized mode, and drum head mode under different parameter values, respectively. In the presence of chemical synapse, however, the completely synchronized mode cannot be observed. Our results might provide novel insights into synchronization modes transition and related biological experiments.

A Simulation Study on the Pacing and Driving of the Biological Pacemaker.

The research on the biological pacemaker has been very active in recent years. And turning nonautomatic ventricular cells into pacemaking cells is believed to hold the key to making a biological pacemaker. In the study, the inward-rectifier K+ current (IK1) is depressed to induce the automaticity of the ventricular myocyte, and then, the effects of the other membrane ion currents on the automaticity are analyzed. It is discovered that the L-type calcium current (ICaL) plays a major part in the rapid depolarization of the action potential (AP). A small enough ICaL would lead to the failure of the automaticity of the ventricular myocyte. Meanwhile, the background sodium current (IbNa), the background calcium current (IbCa), and the Na+/Ca2+ exchanger current (INaCa) contribute significantly to the slow depolarization, indicating that these currents are the main supplementary power of the pacing induced by depressing IK1, while in the 2D simulation, we find that the weak electrical coupling plays a more important role in the driving of a biological pacemaker.

NMDA Receptor Activation Strengthens Weak Electrical Coupling in Mammalian Brain

NMDA Receptor Activation Strengthens Weak Electrical Coupling in Mammalian Brain

NMDA Receptor Activation Strengthens Weak Electrical Coupling in Mammalian Brain

Electrical synapses are formed by gap junctions and permit electrical coupling, which shapes the synchrony of neuronal ensembles. Here, we provide a direct demonstration of receptor-mediated strengthening of electrical coupling in mammalian brain. Electrical coupling in the inferior olive of rats was strengthened by activation of NMDA-type glutamate receptors (NMDARs), which were found at synaptic loci and at extrasynaptic loci 20-100nm proximal to gap junctions. Electrical coupling was strengthened by pharmacological and synaptic activation of NMDARs, whereas costimulation of ionotropic non-NMDAR glutamate receptors transiently antagonized the effect of NMDAR activation. NMDAR-dependent strengthening (1) occurred despite increased input conductance, (2) induced Ca(2+)-influx microdomains near dendritic spines, (3) required activation of the Ca(2+)/calmodulin-dependent protein-kinase II, (4) was restricted to neurons that were weakly coupled, and (5) thus strengthened coupling, mainly between nonadjacent neurons. This provided a mechanism to expand the synchronization of rhythmic membrane potential oscillations by chemical neurotransmitter input.

Differing synaptic strengths between homologous mechanosensory neurons

Leeches have four mechanosensory pressure neurons (P cells) in each midbody ganglion. Within a ganglion, P cells show complex electrical and chemical connections that vary between species. In Hirudo verbana, stimulating one P cell causes a weak depolarization followed by a strong hyperpolarization in the other P cells; however, stimulating a P cell in Erpobdella obscura produces strong depolarizations in the other P cells. In this study, we examined interactions between P cells in the American medicinal leech Macrobdella decora. Not only is Macrobdella more closely related to Hirudo than to Erpobdella, but Hirudo and Macrobdella also have very similar behavioral responses to mechanical stimulation. Despite the phylogenetic relationship and behavioral similarities between the two species, we found that intracellular stimulation of one P cell in Macrobdella causes a depolarization in the other P cells, rather than the hyperpolarization seen in Hirudo. Experiments performed in a high Mg(2+), 0 Ca(2+) saline solution and a high Mg(2+), high Ca(2+) saline solution suggest that the P cells in Macrobdella have a monosynaptic excitatory connection, a polysynaptic inhibitory connection, and a weak electrical coupling, similar to the connections between P cells in Hirudo. The difference in net response of P cells between these two species seems to be based on differences in the strengths of the chemical connections. These results demonstrate that even when behavioral patterns are conserved in closely related species, the underlying neural circuitry is not necessarily tightly constrained.

Spatial Profiles of Electrical Mismatch Determine Vulnerability to Conduction Failure Across a Host–Donor Cell Interface

Electrophysiological mismatch between host cardiomyocytes and donor cells can directly affect the electrical safety of cardiac cell therapies; however, the ability to study host-donor interactions at the microscopic scale in situ is severely limited. We systematically explored how action potential (AP) differences between cardiomyocytes and other excitable cells modulate vulnerability to conduction failure in vitro. AP propagation was optically mapped at 75 μm resolution in micropatterned strands (n=152) in which host neonatal rat ventricular myocytes (AP duration=153.2±2.3 ms, conduction velocity=22.3±0.3 cm/s) seamlessly interfaced with genetically engineered excitable donor cells expressing inward rectifier potassium (Kir2.1) and cardiac sodium (Na(v)1.5) channels with either weak (conduction velocity=3.1±0.1 cm/s) or strong (conduction velocity=22.1±0.4 cm/s) electrical coupling. Selective prolongation of engineered donor cell AP duration (31.9-139.1 ms) by low-dose BaCl2 generated a wide range of host-donor repolarization time (RT) profiles with maximum gradients (∇RT(max)) of 5.5 to 257 ms/mm. During programmed stimulation of donor cells, the vulnerable time window for conduction block across the host-donor interface most strongly correlated with ∇RT(max). Compared with well-coupled donor cells, the interface composed of poorly coupled cells significantly shortened the RT profile width by 19.7% and increased ∇RT(max) and vulnerable time window by 22.2% and 19%, respectively. Flattening the RT profile by perfusion of 50 μmol/L BaCl2 eliminated coupling-induced differences in vulnerability to block. Our results quantify how the degree of electrical mismatch across a cardiomyocyte-donor cell interface affects vulnerability to conduction block, with important implications for the design of safe cardiac cell and gene therapies.

Stable Antiphase Oscillations in a Network of Electrically Coupled Model Neurons

We consider a model of two identical neurons with electrical coupling and give a rigorous analysis for when the network exhibits stable antiphase behavior. Each neuron is modeled as a relaxation oscillator, and the main technique used in the analysis is geometric singular perturbation theory. Using fast/slow analysis, we derive a one-dimensional map; the antiphase solution corresponds to a fixed point of this map. Detailed analysis of the map, along with its derivative, leads to precise conditions on the duty cycle of an individual cell for when there exists an antiphase solution and when it is stable, for sufficiently weak electrical coupling. The results presented here extend our previous analysis [D. Terman et al., SIAM J. Appl. Dyn. Syst., 10 (2011), pp. 1127--1153] to more biophysical neuronal models.

Bursting synchronization dynamics of pancreatic β-cells with electrical and chemical coupling

Based on bifurcation analysis, the synchronization behaviors of two identical pancreatic β-cells connected by electrical and chemical coupling are investigated, respectively. Various firing patterns are produced in coupled cells when a single cell exhibits tonic spiking or square-wave bursting individually, irrespectively of what the cells are connected by electrical or chemical coupling. On the one hand, cells can burst synchronously for both weak electrical and chemical coupling when an isolated cell exhibits tonic spiking itself. In particular, for electrically coupled cells, under the variation of the coupling strength there exist complex transition processes of synchronous firing patterns such as "fold/limit cycle" type of bursting, then anti-phase continuous spiking, followed by the "fold/torus" type of bursting, and finally in-phase tonic spiking. On the other hand, it is shown that when the individual cell exhibits square-wave bursting, suitable coupling strength can make the electrically coupled system generate "fold/Hopf" bursting via "fold/fold" hysteresis loop; whereas, the chemically coupled cells generate "fold/subHopf" bursting. Especially, chemically coupled bursters can exhibit inverse period-adding bursting sequence. Fast-slow dynamics analysis is applied to explore the generation mechanism of these bursting oscillations. The above analysis of bursting types and the transition may provide us with better insight into understanding the role of coupling in the dynamic behaviors of pancreatic β-cells.

State Estimation for Smart Distribution Substations

In the upcoming smart grid environment many more measurements will be available, which can be locally processed by the so-called substation state estimator (SSE). Distribution substations serve energy to a large set of feeders, each one delivering power to a certain number of secondary transformers. In this context, the SSE may have to deal with a huge network model, comprising several hundred or even thousand buses. Taking advantage of the weak electrical coupling existing among the set of feeders connected to the same or adjacent substations, a two-stage procedure is proposed in this paper to efficiently solve the SSE. In the first stage the overall SE is decomposed into <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> + <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> WLS subproblems ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> being the total number of feeders and substations, respectively), which are then solved in a decoupled manner. The second stage, involving a linear WLS problem, consists of coordinating the solution provided by each subsystem (feeder or substation). The proposed solution scheme has a number of advantages, as shown by the case studies.

Stability of Anti-Phase and In-Phase Locking by Electrical Coupling but Not Fast Inhibition Alone

We consider a model network consisting of two identical neurons with inhibitory and electrical coupling and find conditions under which a particular type of coupling promotes stable in-phase locking, anti-phase behavior, or some other type of firing pattern. A traditional view is that fast inhibition leads to stable anti-phase behavior, while electrical coupling leads to stable in-phase locking. Here, we follow up with rigorous analysis our previous computational demonstration [T. Bem and J. Rinzel, J. Neurophysiol., 91 (2004), pp. 693–703] that this is not always the case. We give precise conditions, which depend on the intrinsic properties of the cells involved, for when this traditional view is not valid. In particular, if the cells have short duty cycles, then fast inhibitory coupling leads to an almost-in-phase solution in which short active phases of the two cells occur subsequently, one immediately after the other. Moreover, if the cells have short duty cycles, then a network with weak electrical coupling exhibits bistability of in-phase and anti-phase behavior. The cells are modeled as relaxation oscillators, and we analyze the network using geometric singular perturbation methods. This allows us to construct maps, fixed points of which correspond to a particular type of solution. Rigorous analysis of these maps leads to precise conditions for when a particular type of solution exists and when it is stable for either pure electrical or pure inhibitory coupling. We also demonstrate how adding the other type of coupling may change the network behavior.

Spine-shaped gold protrusions improve the adherence and electrical coupling of neurons with the surface of micro-electronic devices

Interfacing neurons with micro- and nano-electronic devices has been a subject of intense study over the last decade. One of the major problems in assembling efficient neuro-electronic hybrid systems is the weak electrical coupling between the components. This is mainly attributed to the fundamental property of living cells to form and maintain an extracellular cleft between the plasma membrane and any substrate to which they adhere. This cleft shunts the current generated by propagating action potentials and thus reduces the signal-to-noise ratio. Reducing the cleft thickness, and thereby increasing the seal resistance formed between the neurons and the sensing surface, is thus a challenge and could improve the electrical coupling coefficient. Using electron microscopic analysis and field potential recordings, we examined here the use of gold micro-structures that mimic dendritic spines in their shape and dimensions to improve the adhesion and electrical coupling between neurons and micro-electronic devices. We found that neurons cultured on a gold-spine matrix, functionalized by a cysteine-terminated peptide with a number of RGD repeats, readily engulf the spines, forming tight apposition. The recorded field potentials of cultured Aplysia neurons are significantly larger using gold-spine electrodes in comparison with flat electrodes.

Innexins in the lobster stomatogastric nervous system: cloning, phylogenetic analysis, developmental changes and expression within adult identified dye and electrically coupled neurons

Gap junctions play a key role in the operation of neuronal networks by enabling direct electrical and metabolic communication between neurons. Suitable models to investigate their role in network operation and plasticity are invertebrate motor networks, which are built of comparatively few identified neurons, and can be examined throughout development; an excellent example is the lobster stomatogastric nervous system. In invertebrates, gap junctions are formed by proteins that belong to the innexin family. Here, we report the first molecular characterization of two crustacean innexins: the lobster Homarus gammarus innexin 1 (Hg-inx1) and 2 (Hg-inx2). Phylogenetic analysis reveals that innexin gene duplication occurred within the arthropod clade before the separation of insect and crustacean lineages. Using in situ hybridization, we find that each innexin is expressed within the adult and developing lobster stomatogastric nervous system and undergoes a marked down-regulation throughout development within the stomatogastric ganglion (STG). The number of innexin expressing neurons is significantly higher in the embryo than in the adult. By combining in situ hybridization, dye and electrical coupling experiments on identified neurons, we demonstrate that adult neurons that express at least one innexin are dye and electrically coupled with at least one other STG neuron. Finally, two STG neurons display no detectable amount of either innexin mRNAs but may express weak electrical coupling with other STG neurons, suggesting the existence of other forms of innexins. Altogether, we provide evidence that innexins are expressed within small neuronal networks built of dye and electrically coupled neurons and may be developmentally regulated.

An Electrically Coupled Network of Skeletal Muscle in Zebrafish Distributes Synaptic Current

Fast and slow skeletal muscle types are readily distinguished in larval zebrafish on the basis of differences in location and orientation. Additionally, both muscle types are compact, rendering them amenable to in vivo patch clamp study of synaptic function. Slow muscle mediates rhythmic swimming, but it does so purely through synaptic drive, as these cells are unable to generate action potentials. Our patch clamp recordings from muscle pairs of zebrafish reveal a network of electrical coupling in slow muscle that allows sharing of synaptic current within and between segmental boundaries of the tail. The synaptic current exhibits slow kinetics (τdecay ∼4 ms), which further facilitates passage through the low pass filter, a consequence of the electrically coupled network. In contrast to slow muscle, fast skeletal muscle generates action potentials to mediate the initial rapid component of the escape response. The combination of very weak electrical coupling and synaptic kinetics (τdecay <1 ms) too fast for the network low pass filter minimizes intercellular sharing of synaptic current in fast muscle. These differences between muscle types provide insights into the physiological role(s) of electrical coupling in skeletal muscle. First, intrasegmental coupling among slow muscle cells allows effective transfer of synaptic currents within tail segments, thereby minimizing differences in synaptic depolarization. Second, a fixed intersegmental delay in synaptic current transit, resulting from the low pass filter properties of the slow muscle network, helps coordinate the rostral–caudal wave of contraction.

Exploring gap junction location and density in electrically coupled hippocampal oriens interneurons

Interneuronal networks, connected by chemical and electrical (gap junctions) synapses, are important for shaping population field rhythms in the hippocampus. Recently, weak electrical coupling has been found between oriens interneurons in the CA1 region of the hippocampus. Action potentials in one cell produced spikelets in the connected cell. We use a two-cell model network of oriens interneurons to determine the dendritic location and strength of gap junctions needed to match experimentally measured spikelet characteristics. The location of the gap junctions is predicted to be 150–200 μm from the soma, corresponding to electrotonic lengths of 0.17–0.23 as measured from the soma to the dendrite location and 0.71–1.04 as measured from the dendritic location to the soma, with a conductance of 500–800 pS.

Dendritic effects in networks of electrically coupled fast-spiking interneurons

We examine how the location of weak electrical coupling affects phase-locking in a pair of model fast-spiking interneurons. Each model neuron consists of a somatic compartment and a passive dendritic compartment. At relatively low frequencies, the phase-locking structure for somatic and dendritic coupling is qualitatively the same: below a critical frequency, stable synchronous and anti-phase activity co-exist, and only synchrony is stable above this critical frequency. At higher frequencies, the synchronous state remains stable for somatic coupling, but for dendritic coupling, the synchronous state becomes unstable and anti-phase oscillations become stable.

Dendritic effects in networks of electrically coupled fast-spiking interneurons

We examine how the location of weak electrical coupling affects phase-locking in a pair of model fast-spiking interneurons. Each model neuron consists of a somatic compartment and a passive dendritic compartment. At relatively low frequencies, the phase-locking structure for somatic and dendritic coupling is qualitatively the same: below a critical frequency, stable synchronous and anti-phase activity co-exist, and only synchrony is stable above this critical frequency. At higher frequencies, the synchronous state remains stable for somatic coupling, but for dendritic coupling, the synchronous state becomes unstable and anti-phase oscillations become stable.

Suppression of superconductor quasiparticle tunneling into single-walled carbon nanotubes

Electrical transport through single-walled carbon nanotubes with weak electrical coupling to superconducting leads has been studied theoretically and experimentally. A simple model is considered to describe single-particle tunneling into a Luttinger-liquid-like state from electrically weak connected superconducting electrodes. This involves the superconductor's quasiparticle and the Luttinger liquid's excitation density of states. Experimentally, the suppression of quasiparticle tunneling induced current peaks was observed at temperatures below 0.1 K, which we attributed to the Luttinger-liquid-like excitation spectrum of the single-walled carbon nanotube.

Dynamics of spiking neurons connected by both inhibitory and electrical coupling.

We study the dynamics of a pair of intrinsically oscillating leaky integrate-and-fire neurons (identical and noise-free) connected by combinations of electrical and inhibitory coupling. We use the theory of weakly coupled oscillators to examine how synchronization patterns are influenced by cellular properties (intrinsic frequency and the strength of spikes) and coupling parameters (speed of synapses and coupling strengths). We find that, when inhibitory synapses are fast and the electrotonic effect of the suprathreshold portion of the spike is large, increasing the strength of weak electrical coupling promotes synchrony. Conversely, when inhibitory synapses are slow and the electrotonic effect of the suprathreshold portion of the spike is small, increasing the strength of weak electrical coupling promotes antisynchrony (see Fig. 10). Furthermore, our results indicate that, given a fixed total coupling strength, either electrical coupling alone or inhibition alone is better at enhancing neural synchrony than a combination of electrical and inhibitory coupling. We also show that these results extend to moderate coupling strengths.