The generation of oscillations in networks of electrically coupled cells

The voltage and spiking responses of subthreshold resonant neurons to structured and fluctuating inputs: persistence and loss of resonance and variability

We systematically investigate the response of neurons to oscillatory currents and synaptic-like inputs and we extend our investigation to non-structured synaptic-like spiking inputs with more realistic distributions of presynaptic spike times. We use two types of chirp-like inputs consisting of (i) a sequence of cycles with discretely increasing frequencies over time, and (ii) a sequence having the same cycles arranged in an arbitrary order. We develop and use a number of frequency-dependent voltage response metrics to capture the different aspects of the voltage response, including the standard impedance (Z) and the peak-to-trough amplitude envelope ([Formula: see text]) profiles. We show that Z-resonant cells (cells that exhibit subthreshold resonance in response to sinusoidal inputs) also show [Formula: see text]-resonance in response to sinusoidal inputs, but generally do not (or do it very mildly) in response to square-wave and synaptic-like inputs. In the latter cases the resonant response using Z is not predictive of the preferred frequencies at which the neurons spike when the input amplitude is increased above subthreshold levels. We also show that responses to conductance-based synaptic-like inputs are attenuated as compared to the response to current-based synaptic-like inputs, thus providing an explanation to previous experimental results. These response patterns were strongly dependent on the intrinsic properties of the participating neurons, in particular whether the unperturbed Z-resonant cells had a stable node or a focus. In addition, we show that variability emerges in response to chirp-like inputs with arbitrarily ordered patterns where all signals (trials) in a given protocol have the same frequency content and the only source of uncertainty is the subset of all possible permutations of cycles chosen for a given protocol. This variability is the result of the multiple different ways in which the autonomous transient dynamics is activated across cycles in each signal (different cycle orderings) and across trials. We extend our results to include high-rate Poisson distributed current- and conductance-based synaptic inputs and compare them with similar results using additive Gaussian white noise. We show that the responses to both Poisson-distributed synaptic inputs are attenuated with respect to the responses to Gaussian white noise. For cells that exhibit oscillatory responses to Gaussian white noise (band-pass filters), the response to conductance-based synaptic inputs are low-pass filters, while the response to current-based synaptic inputs may remain band-pass filters, consistent with experimental findings. Our results shed light on the mechanisms of communication of oscillatory activity among neurons in a network via subthreshold oscillations and resonance and the generation of network resonance.

Spontaneous Calcium Oscillations through Differentiation: A Calcium Imaging Analysis of Rat Cochlear Nucleus Neural Stem Cells

Causal therapies for the auditory-pathway and inner-ear diseases are still not yet available for clinical application. Regenerative medicine approaches are discussed and examined as possible therapy options. Neural stem cells could play a role in the regeneration of the auditory pathway. In recent years, neural stem and progenitor cells have been identified in the cochlear nucleus, the second nucleus of the auditory pathway. The current investigation aimed to analyze cell maturation concerning cellular calcium activity. Cochlear nuclei from PND9 CD rats were microscopically dissected and propagated as neurospheres in free-floating cultures in stem-cell medium (Neurobasal, B27, GlutaMAX, EGF, bFGF). After 30 days, the dissociation and plating of these cells took place under withdrawal of the growth factors and the addition of retinoic acid, which induces neural cell differentiation. Calcium imaging analysis with BAPTA-1/Oregon Green was carried out at different times during the differentiation phase. In addition, the influence of different voltage-dependent calcium channels was analyzed through the targeted application of inhibitors of the L-, N-, R- and T-type calcium channels. For this purpose, comparative examinations were performed on CN NSCs, and primary CN neurons. As the cells differentiated, a significant increase in spontaneous neuronal calcium activity was demonstrated. In the differentiation stage, specific frequencies of the spontaneous calcium oscillations were measured in different regions of the individual cells. Initially, the highest frequency of spontaneous calcium oscillations was ascertainable in the maturing somata. Over time, these were overtaken by calcium oscillations in the axons and dendrites. Additionally, in the area of the growth cones, an increasing activity was determined. By inhibiting voltage-dependent calcium channels, their expression and function in the differentiation process were confirmed. A comparable pattern of maturation of these channels was found in CN NSCs and primary CN neurons. The present results show that neural stem cells of the rat cochlear nucleus differentiated not only morphologically but also functionally. Spontaneous calcium activities are of great relevance in terms of neurogenesis and integration into existing neuronal structures. These functional aspects of neurogenesis within the auditory pathway could serve as future targets for the exogenous control of neuronal regeneration.

Imaging Subthreshold Voltage Oscillation With Cellular Resolution in the Inferior Olive in vitro

Voltage imaging with cellular resolution in mammalian brain slices is still a challenging task. Here, we describe and validate a method for delivery of the voltage-sensitive dye ANNINE-6plus (A6+) into tissue for voltage imaging that results in higher signal-to-noise ratio (SNR) than conventional bath application methods. The not fully dissolved dye was injected into the inferior olive (IO) 0, 1, or 7 days prior to acute slice preparation using stereotactic surgery. We find that the voltage imaging improves after an extended incubation period in vivo in terms of labeled volume, homogeneous neuropil labeling with saliently labeled somata, and SNR. Preparing acute slices 7 days after the dye injection, the SNR is high enough to allow single-trial recording of IO subthreshold oscillations using wide-field (network-level) as well as high-magnification (single-cell level) voltage imaging with a CMOS camera. This method is easily adaptable to other brain regions where genetically-encoded voltage sensors are prohibitively difficult to use and where an ultrafast, pure electrochromic sensor, like A6+, is required. Due to the long-lasting staining demonstrated here, the method can be combined, for example, with deep-brain imaging using implantable GRIN lenses.

Using subthreshold events to characterize the functional architecture of the electrically coupled inferior olive network

The electrical connectivity in the inferior olive (IO) nucleus plays an important role in generating well-timed spiking activity. Here we combined electrophysiological and computational approaches to assess the functional organization of the IO nucleus in mice. Spontaneous fast and slow subthreshold events were commonly encountered during in vitro recordings. We show that whereas the fast events represent intrinsic regenerative activity, the slow events reflect the electrical connectivity between neurons (‘spikelets’). Recordings from cell pairs revealed the synchronized occurrence of distinct groups of spikelets; their rate and distribution enabled an accurate estimation of the number of connected cells and is suggestive of a clustered organization. This study thus provides a new perspective on the functional and structural organization of the olivary nucleus and a novel experimental and theoretical approach to study electrically coupled networks.

Variability and directionality of inferior olive neuron dendrites revealed by detailed 3D characterization of an extensive morphological library

The inferior olive (IO) is an evolutionarily conserved brain stem structure and its output activity plays a major role in the cerebellar computation necessary for controlling the temporal accuracy of motor behavior. The precise timing and synchronization of IO network activity has been attributed to the dendro-dendritic gap junctions mediating electrical coupling within the IO nucleus. Thus, the dendritic morphology and spatial arrangement of IO neurons governs how synchronized activity emerges in this nucleus. To date, IO neuron structural properties have been characterized in few studies and with small numbers of neurons; these investigations have described IO neurons as belonging to two morphologically distinct types, “curly” and “straight”. In this work we collect a large number of individual IO neuron morphologies visualized using different labeling techniques and present a thorough examination of their morphological properties and spatial arrangement within the olivary neuropil. Our results show that the extensive heterogeneity in IO neuron dendritic morphologies occupies a continuous range between the classically described “curly” and “straight” types, and that this continuum is well represented by a relatively simple measure of “straightness”. Furthermore, we find that IO neuron dendritic trees are often directionally oriented. Combined with an examination of cell body density distributions and dendritic orientation of adjacent IO neurons, our results suggest that the IO network may be organized into groups of densely coupled neurons interspersed with areas of weaker coupling.

Membrane potential resonance in non-oscillatory neurons interacts with synaptic connectivity to produce network oscillations

Several neuron types have been shown to exhibit (subthreshold) membrane potential resonance (MPR), defined as the occurrence of a peak in their voltage amplitude response to oscillatory input currents at a preferred (resonant) frequency. MPR has been investigated both experimentally and theoretically. However, whether MPR is simply an epiphenomenon or it plays a functional role for the generation of neuronal network oscillations and how the latent time scales present in individual, non-oscillatory cells affect the properties of the oscillatory networks in which they are embedded are open questions. We address these issues by investigating a minimal network model consisting of (i) a non-oscillatory linear resonator (band-pass filter) with 2D dynamics, (ii) a passive cell (low-pass filter) with 1D linear dynamics, and (iii) nonlinear graded synaptic connections (excitatory or inhibitory) with instantaneous dynamics. We demonstrate that (i) the network oscillations crucially depend on the presence of MPR in the resonator, (ii) they are amplified by the network connectivity, (iii) they develop relaxation oscillations for high enough levels of mutual inhibition/excitation, and (iv) the network frequency monotonically depends on the resonators resonant frequency. We explain these phenomena using a reduced adapted version of the classical phase-plane analysis that helps uncovering the type of effective network nonlinearities that contribute to the generation of network oscillations. We extend our results to networks having cells with 2D dynamics. Our results have direct implications for network models of firing rate type and other biological oscillatory networks (e.g, biochemical, genetic).

Synchrony and so much more: Diverse roles for electrical synapses in neural circuits

Electrical synapses are neuronal gap junctions that are ubiquitous across brain regions and species. The biophysical properties of most electrical synapses are relatively simple-transcellular channels allow nearly ohmic, bidirectional flow of ionic current. Yet these connections can play remarkably diverse roles in different neural circuit contexts. Recent findings illustrate how electrical synapses may excite or inhibit, synchronize or desynchronize, augment or diminish rhythms, phase-shift, detect coincidences, enhance signals relative to noise, adapt, and interact with nonlinear membrane and transmitter-release mechanisms. Most of these functions are likely to be widespread in central nervous systems. © 2016 Wiley Periodicals, Inc. Develop Neurobiol 77: 610-624, 2017.

The shaping of intrinsic membrane potential oscillations: positive/negative feedback, ionic resonance/amplification, nonlinearities and time scales

The generation of intrinsic subthreshold (membrane potential) oscillations (STOs) in neuronal models requires the interaction between two processes: a relatively fast positive feedback that favors changes in voltage and a slower negative feedback that opposes these changes. These are provided by the so-called resonant and amplifying gating variables associated to the participating ionic currents. We investigate both the biophysical and dynamic mechanisms of generation of STOs and how their attributes (frequency and amplitude) depend on the model parameters for biophysical (conductance-based) models having qualitatively different types of resonant currents (activating and inactivating) and an amplifying current. Combinations of the same types of ionic currents (same models) in different parameter regimes give rise to different types of nonlinearities in the voltage equation: quasi-linear, parabolic-like and cubic-like. On the other hand, combinations of different types of ionic currents (different models) may give rise to the same type of nonlinearities. We examine how the attributes of the resulting STOs depend on the combined effect of these resonant and amplifying ionic processes, operating at different effective time scales, and the various types of nonlinearities. We find that, while some STO properties and attribute dependencies on the model parameters are determined by the specific combinations of ionic currents (biophysical properties), and are different for models with different such combinations, others are determined by the type of nonlinearities and are common for models with different types of ionic currents. Our results highlight the richness of STO behavior in single cells as the result of the various ways in which resonant and amplifying currents interact and affect the generation and termination of STOs as control parameters change. We make predictions that can be tested experimentally and are expected to contribute to the understanding of how rhythmic activity in neuronal networks emerge from the interplay of the intrinsic properties of the participating neurons and the network connectivity.

Environmental coupling in ecosystems: From oscillation quenching to rhythmogenesis

How landscape fragmentation affects ecosystems diversity and stability is an important and complex question in ecology with no simple answer, as spatially separated habitats where species live are highly dynamic rather than just static. Taking into account the species dispersal among nearby connected habitats (or patches) through a common dynamic environment, we model the consumer-resource interactions with a ring type coupled network. By characterizing the dynamics of consumer-resource interactions in a coupled ecological system with three fundamental mechanisms such as the interaction within the patch, the interaction between the patches, and the interaction through a common dynamic environment, we report the occurrence of various collective behaviors. We show that the interplay between the dynamic environment and the dispersal among connected patches exhibits the mechanism of generation of oscillations, i.e., rhythmogenesis, as well as suppression of oscillations, i.e., amplitude death and oscillation death. Also, the transition from homogeneous steady state to inhomogeneous steady state occurs through a codimension-2 bifurcation. Emphasizing a network of a spatially extended system, the coupled model exposes the collective behavior of a synchrony-stability relationship with various synchronization occurrences such as in-phase and out-of-phase.

Cellular Architecture Regulates Collective Calcium Signaling and Cell Contractility

A key feature of multicellular systems is the ability of cells to function collectively in response to external stimuli. However, the mechanisms of intercellular cell signaling and their functional implications in diverse vascular structures are poorly understood. Using a combination of computational modeling and plasma lithography micropatterning, we investigate the roles of structural arrangement of endothelial cells in collective calcium signaling and cell contractility. Under histamine stimulation, endothelial cells in self-assembled and microengineered networks, but not individual cells and monolayers, exhibit calcium oscillations. Micropatterning, pharmacological inhibition, and computational modeling reveal that the calcium oscillation depends on the number of neighboring cells coupled via gap junctional intercellular communication, providing a mechanistic basis of the architecture-dependent calcium signaling. Furthermore, the calcium oscillation attenuates the histamine-induced cytoskeletal reorganization and cell contraction, resulting in differential cell responses in an architecture-dependent manner. Taken together, our results suggest that endothelial cells can sense and respond to chemical stimuli according to the vascular architecture via collective calcium signaling.

Effects of extracellular potassium diffusion on electrically coupled neuron networks

Potassium accumulation and diffusion during neuronal epileptiform activity have been observed experimentally, and potassium lateral diffusion has been suggested to play an important role in nonsynaptic neuron networks. We adopt a hippocampal CA1 pyramidal neuron network in a zero-calcium condition to better understand the influence of extracellular potassium dynamics on the stimulus-induced activity. The potassium concentration in the interstitial space for each neuron is regulated by potassium currents, Na(+)-K(+) pumps, glial buffering, and ion diffusion. In addition to potassium diffusion, nearby neurons are also coupled through gap junctions. Our results reveal that the latency of the first spike responding to stimulus monotonically decreases with increasing gap-junction conductance but is insensitive to potassium diffusive coupling. The duration of network oscillations shows a bell-like shape with increasing potassium diffusive coupling at weak gap-junction coupling. For modest electrical coupling, there is an optimal K(+) diffusion strength, at which the flow of potassium ions among the network neurons appropriately modulates interstitial potassium concentrations in a degree that provides the most favorable environment for the generation and continuance of the action potential waves in the network.

Oscillations emerging from noise-driven steady state in networks with electrical synapses and subthreshold resonance

Oscillations play a critical role in cognitive phenomena and have been observed in many brain regions. Experimental evidence indicates that classes of neurons exhibit properties that could promote oscillations, such as subthreshold resonance and electrical gap junctions. Typically, these two properties are studied separately but it is not clear which is the dominant determinant of global network rhythms. Our aim is to provide an analytical understanding of how these two effects destabilize the fluctuation-driven state, in which neurons fire irregularly, and lead to an emergence of global synchronous oscillations. Here we show how the oscillation frequency is shaped by single neuron resonance, electrical and chemical synapses.The presence of both gap junctions and subthreshold resonance are necessary for the emergence of oscillations. Our results are in agreement with several experimental observations such as network responses to oscillatory inputs and offer a much-needed conceptual link connecting a collection of disparate effects observed in networks.

Cerebellar inhibitory input to the inferior olive decreases electrical coupling and blocks subthreshold oscillations

GABAergic projection neurons in the cerebellar nuclei (CN) innervate the inferior olive (IO) that in turn is the source of climbing fibers targeting Purkinje neurons in the cerebellar cortex. Anatomical evidence suggests that CN synapses modulate electrical coupling between IO neurons. In vivo studies indicate that they are also involved in controlling synchrony and rhythmicity of IO neurons. Here, we demonstrate using virally targeted channelrhodopsin in the cerebellar nucleo-olivary neurons that synaptic input can indeed modulate both the strength and symmetry of electrical coupling between IO neurons and alter network activity. Similar synaptic modifications of electrical coupling are likely to occur in other brain regions, where rapid modification of the spatiotemporal features of the coupled networks is needed to adequately respond to behavioral demands.

Network oscillations drive correlated spiking of ON and OFF ganglion cells in the rd1 mouse model of retinal degeneration

Following photoreceptor degeneration, ON and OFF retinal ganglion cells (RGCs) in the rd-1/rd-1 mouse receive rhythmic synaptic input that elicits bursts of action potentials at ∼ 10 Hz. To characterize the properties of this activity, RGCs were targeted for paired recording and morphological classification as either ON alpha, OFF alpha or non-alpha RGCs using two-photon imaging. Identified cell types exhibited rhythmic spike activity. Cross-correlation of spike trains recorded simultaneously from pairs of RGCs revealed that activity was correlated more strongly between alpha RGCs than between alpha and non-alpha cell pairs. Bursts of action potentials in alpha RGC pairs of the same type, i.e. two ON or two OFF cells, were in phase, while bursts in dissimilar alpha cell types, i.e. an ON and an OFF RGC, were 180 degrees out of phase. This result is consistent with RGC activity being driven by an input that provides correlated excitation to ON cells and inhibition to OFF cells. A2 amacrine cells were investigated as a candidate cellular mechanism and found to display 10 Hz oscillations in membrane voltage and current that persisted in the presence of antagonists of fast synaptic transmission and were eliminated by tetrodotoxin. Results support the conclusion that the rhythmic RGC activity originates in a presynaptic network of electrically coupled cells including A2s via a Na(+)-channel dependent mechanism. Network activity drives out of phase oscillations in ON and OFF cone bipolar cells, entraining similar frequency fluctuations in RGC spike activity over an area of retina that migrates with changes in the spatial locus of the cellular oscillator.

Oscillatory activity, phase differences, and phase resetting in the inferior olivary nucleus

The generation of temporal patterns is one of the most fascinating functions of the brain. Unlike the response to external stimuli temporal patterns are generated within the system and recalled for a specific use. To generate temporal patterns one needs a timing machine, a “master clock” that determines the temporal framework within which temporal patterns can be generated and implemented. Here we present the concept that in this putative “master clock” phase and frequency interact to generate temporal patterns. We define the requirements for a neuronal “master clock” to be both reliable and versatile. We introduce this concept within the inferior olive nucleus which at least by some scientists is regarded as the source of timing for cerebellar function. We review the basic properties of the subthreshold oscillation recorded from olivary neurons, analyze the phase relationships between neurons and demonstrate that the phase and onset of oscillation is tightly controlled by synaptic input. These properties endowed the olivary nucleus with the ability to act as a “master clock.”

[Cellularity and extracellularity: the multi-fibrillar system: from cytoskeleton to connective tissue]

This brief text aims at illustrating the interactions between connective tissue fibers and cell cytoskeleton fibers. These two networks are connected by molecular bridges at the level of the cell membrane of the cells of the connective and vascular tissues, allowing functional adjustments across the two domains, but also the transduction of forces and tensions into a biochemical alphabet. The signaling between the cell kern and its environment, but equally the other way round, from the environment to the core of the cell, depends on it.

The generation of phase differences and frequency changes in a network model of inferior olive subthreshold oscillations

It is commonly accepted that the Inferior Olive (IO) provides a timing signal to the cerebellum. Stable subthreshold oscillations in the IO can facilitate accurate timing by phase-locking spikes to the peaks of the oscillation. Several theoretical models accounting for the synchronized subthreshold oscillations have been proposed, however, two experimental observations remain an enigma. The first is the observation of frequent alterations in the frequency of the oscillations. The second is the observation of constant phase differences between simultaneously recorded neurons. In order to account for these two observations we constructed a canonical network model based on anatomical and physiological data from the IO. The constructed network is characterized by clustering of neurons with similar conductance densities, and by electrical coupling between neurons. Neurons inside a cluster are densely connected with weak strengths, while neurons belonging to different clusters are sparsely connected with stronger connections. We found that this type of network can robustly display stable subthreshold oscillations. The overall frequency of the network changes with the strength of the inter-cluster connections, and phase differences occur between neurons of different clusters. Moreover, the phase differences provide a mechanistic explanation for the experimentally observed propagating waves of activity in the IO. We conclude that the architecture of the network of electrically coupled neurons in combination with modulation of the inter-cluster coupling strengths can account for the experimentally observed frequency changes and the phase differences.

There is a profound interest in the dynamics of neuronal networks and the simulation of network models is a prevalent approach to study these dynamics. Generally, network models contain neurons that are connected mostly through chemical synapses to form either a completely regular topology (such as nearest neighbor connections), a completely random topology, small-world networks or scale-free networks. We investigate the dynamics of an atypical network, inspired by the Inferior Olive (IO) network, a brain structure located at the end of the brainstem that is responsible for timely execution of motor commands. This network is atypical in the sense that it has neurons in a clustered topology, which are connected solely by electrical synapses. The dynamics in the IO are enigmatic as the membrane voltage of some neurons can oscillate at the same frequency while maintaining phase difference with other neurons. It has also been demonstrated that propagating waves of activity occur spontaneously in this network. Using computer simulations we unraveled the mechanism underlying these previously enigmatic experimental observations. In so doing, we stress the importance of investigating more realistic network topologies to explore complex brain dynamics.

Mathematical models for insulin secretion in pancreatic β-cells

Insulin secretion is one of the most characteristic features of β-cell physiology. As it plays a central role in glucose regulation, a number of experimental and theoretical studies have been performed since the discovery of the pancreatic β-cell. This review article aims to give an overview of the mathematical approaches to insulin secretion. Beginning with the bursting electrical activity in pancreatic β-cells, we describe effects of the gap-junction coupling between β-cells on the dynamics of insulin secretion. Then, implications of paracrine interactions among such islet cells as α-, β-, and δ-cells are discussed. Finally, we present mathematical models which incorporate effects of glycolysis and mitochondrial glucose metabolism on the control of insulin secretion.

Phase precession through acceleration of local theta rhythm: a biophysical model for the interaction between place cells and local inhibitory neurons

Phase precession is one of the most well known examples within the temporal coding hypothesis. Here we present a biophysical spiking model for phase precession in hippocampal CA1 which focuses on the interaction between place cells and local inhibitory interneurons. The model's functional block is composed of a place cell (PC) connected with a local inhibitory cell (IC) which is modulated by the population theta rhythm. Both cells receive excitatory inputs from the entorhinal cortex (EC). These inputs are both theta modulated and space modulated. The dynamics of the two neuron types are described by integrate-and-fire models with conductance synapses, and the EC inputs are described using non-homogeneous Poisson processes. Phase precession in our model is caused by increased drive to specific PC/IC pairs when the animal is in their place field. The excitation increases the IC's firing rate, and this modulates the PC's firing rate such that both cells precess relative to theta. Our model implies that phase coding in place cells may not be independent from rate coding. The absence of restrictive connectivity constraints in this model predicts the generation of phase precession in any network with similar architecture and subject to a clocking rhythm, independently of the involvement in spatial tasks.

An intrinsic neural oscillator in the degenerating mouse retina

The loss of photoreceptors during retinal degeneration (RD) is known to lead to an increase in basal activity in remnant neural networks. To identify the source of activity, we combined two-photon imaging with patch-clamp techniques to examine the physiological properties of morphologically identified retinal neurons in a mouse model of RD (rd1). Analysis of activity in rd1 ganglion cells revealed sustained oscillatory (∼10 Hz) synaptic activity in ∼30% of all classes of cells. Oscillatory activity persisted after putative inputs from residual photoreceptor, rod bipolar cell, and inhibitory amacrine cell synapses were pharmacologically blocked, suggesting that presynaptic cone bipolar cells were intrinsically active. Examination of presynaptic rd1 ON and OFF bipolar cells indicated that they rested at relatively negative potentials (less than -50 mV). However, in approximately half the cone bipolar cells, low-amplitude membrane oscillation (∼5 mV, ∼10 Hz) were apparent. Such oscillations were also observed in AII amacrine cells. Oscillations in ON cone bipolar and AII amacrine cells exhibited a weak apparent voltage dependence and were resistant to blockade of synaptic receptors, suggesting that, as in wild-type retina, they form an electrically coupled network. In addition, oscillations were insensitive to blockers of voltage-gated Ca(2+) channels (0.5 mm Cd(2+) and 0.5 mm Ni(2+)), ruling out known mechanisms that underlie oscillatory behavior in bipolar cells. Together, these results indicate that an electrically coupled network of ON cone bipolar/AII amacrine cells constitutes an intrinsic oscillator in the rd1 retina that is likely to drive synaptic activity in downstream circuits.

Primary culture of the isolated terminal nerve-gonadotrophin-releasing hormone neurones derived from adult teleost (dwarf gourami, Colisa lalia) brain for the study of peptide release mechanisms

Terminal nerve (TN)-gonadotrophin-releasing hormone (GnRH) neurones are suggested to release GnRH peptides from widely-branched neural processes and the somatodendritic regions, depending on their firing activities. The released GnRH may exert its neuromodulatory actions on GnRH receptors located on various target neurones. The electrophysiological and morphological characteristics of TN-GnRH neurones, which are shared with other peptidergic neurones of vertebrate brains, are thought to represent general features of neuromodulatory and ⁄ or neurosecretory neurones. To address questions concerning the ways in which the electrical activities of peptidergic (TN-GnRH) neuronal somata affect GnRH release from different neuronal compartments, we established a primary culture system of TN-GnRH neurones, which will facilitate simultaneous recordings of various physiological signals from different compartments of a single TN-GnRH neurone cultured in a flat plane. The whole brain of an adult freshwater teleost, the dwarf gourami, was dissected out. The TN-GnRH neurones were then isolated and plated on a coverslip in culture medium. The isolated TN-GnRH neurones could be cultured for up to 2 weeks. In culture, the neurones grew both axon- and dendrite-like neurites, and these processes were phenotypically similar to those found in situ. Unlike the neurones in situ, the cultured neurones had somewhat depolarised resting membrane potentials and showed no spontaneous discharge, which, however, should not be considered to comprise unhealthy culture conditions. Instead, they showed subthreshold spontaneous membrane potential oscillations and could be induced to fire in phasic or tonic patterns. In addition, stimulus-induced exocytotic events could be demonstrated in the soma and neurites using a fluorescent dye, FM1-43. Thus, the present isolated culture of TN-GnRH neurones will open up a wide range of possibilities for studying cellular mechanism of exocytosis, generation of spontaneous firing activity, and neurite outgrowth in peptidergic neurones.

Electrical coupling between hippocampal astrocytes in rat brain slices

Gap junctions in astrocytes play a crucial role in intercellular communication by supporting both biochemical and electrical coupling between adjacent cells. Despite the critical role of electrical coupling in the network organization of these glial cells, the electrophysiological properties of gap junctions have been characterized in cultures while no direct evidence has been sought in situ. In the present study, gap-junctional currents were investigated using simultaneous dual whole-cell patch-clamp recordings between astrocytes from rat hippocampal slices. Bidirectional electrotonic coupling was observed in 82% of the cell pairs with an average coupling coefficient of 5.1%. Double patch-clamp analysis indicated that junctional currents were independent of the transjunctional voltage over a range from -100 to +110 mV. Interestingly, astrocytic electrical coupling displayed weak low-pass filtering properties compared to neuronal electrical synapses. Finally, during uncoupling processes triggered by either the gap-junction inhibitor carbenoxolone or endothelin-1, an increase in the input resistance in the injected cell paralleled the decrease in the coupling coefficient. Altogether, these results demonstrate that hippocampal astrocytes are electrically coupled through gap-junction channels characterized by properties that are distinct from those of electrical synapses between neurons. In addition, gap-junctional communication is efficiently regulated by endogenous compounds. This is taken to represent a mode of communication that may have important implications for the functional role of astrocyte networks in situ.

Exploiting dynamical symmetry in coupled nonlinear elements for efficient frequency down-conversion

The rich dynamical behavior stemming from unidirectional coupling in a single array of overdamped nonlinear elements has, recently, been extensively studied. By adjusting control parameters, one obtains regimes of oscillations with a frequency that scales in a characteristic way with the control parameter. With an external time-sinusoidal driving signal, a richness of synchronized (to the drive frequency or its subharmonics depending on the control parameter) dynamical behavior ensues. Including M > or = 2 arrays with a suitably chosen cross coupling has also been shown to lead to multifrequency patterns in the emergent dynamics. Here, we consider this arrangement and demonstrate that, under the appropriate conditions, the oscillation frequency of each successive array decreases by a rational factor with increasing M . This frequency down-conversion, obtainable without a heterodyning signal, affords the promise of very efficient signal processing in a variety of applications wherein, currently, the frequency down-conversion stage typically involves multistep processes with complicated and (often) noisy circuitry.

A Parturition-Associated Nonsynaptic Coherent Activity Pattern in the Developing Hippocampus

Correlated neuronal activity is instrumental in the formation of networks, but its emergence during maturation is poorly understood. We have used multibeam two-photon calcium microscopy combined with targeted electrophysiological recordings in order to determine the development of population coherence from embryonic to postnatal stages in the hippocampus. At embryonic stages (E16-E19), synchronized activity is absent, and neurons are intrinsically active and generate L-type channel-mediated calcium spikes. At birth, small cell assemblies coupled by gap junctions spontaneously generate synchronous nonsynaptic calcium plateaus associated to recurrent burst discharges. The emergence of coherent calcium plateaus at birth is controlled by oxytocin, a maternal hormone initiating labour, and progressively shut down a few days later by the synapse-driven giant depolarizing potentials (GDPs) that synchronize the entire network. Therefore, in the developing hippocampus, delivery is an important signal that triggers the first coherent activity pattern, which is silenced by the emergence of synaptic transmission.

Gap junctions between accessory medulla neurons appear to synchronize circadian clock cells of the cockroach Leucophaea maderae

The temporal organization of physiological and behavioral states is controlled by circadian clocks in apparently all eukaryotic organisms. In the cockroach Leucophaea maderae lesion and transplantation studies located the circadian pacemaker in the accessory medulla (AMe). The AMe is densely innervated by gamma-aminobutyric acid (GABA)-immunoreactive and peptidergic neurons, among them the pigment-dispersing factor immunoreactive circadian pacemaker candidates. The large majority of cells of the cockroach AMe spike regularly and synchronously in the gamma frequency range of 25-70 Hz as a result of synaptic and nonsynaptic coupling. Although GABAergic coupling forms assemblies of phase-locked cells, in the absence of synaptic release the cells remain synchronized but fire now at a stable phase difference. To determine whether these coupling mechanisms of AMe neurons, which are independent of synaptic release, are based on electrical synapses between the circadian pacemaker cells the gap-junction blockers halothane, octanol, and carbenoxolone were used in the presence and absence of synaptic transmission. Here, we show that different populations of AMe neurons appear to be coupled by gap junctions to maintain synchrony at a stable phase difference. This synchronization by gap junctions is a prerequisite to phase-locked assembly formation by synaptic interactions and to synchronous gamma-type action potential oscillations within the circadian clock.

Stabilizing role of calcium store-dependent plasma membrane calcium channels in action-potential firing and intracellular calcium oscillations

In many biological systems, cells display spontaneous calcium oscillations (CaOs) and repetitive action-potential firing. These phenomena have been described separately by models for intracellular inositol trisphosphate (IP3)-mediated CaOs and for plasma membrane excitability. In this study, we present an integrated model that combines an excitable membrane with an IP3-mediated intracellular calcium oscillator. The IP3 receptor is described as an endoplasmic reticulum (ER) calcium channel with open and close probabilities that depend on the cytoplasmic concentration of IP3 and Ca2+. We show that simply combining this ER model for intracellular CaOs with a model for membrane excitability of normal rat kidney (NRK) fibroblasts leads to instability of intracellular calcium dynamics. To ensure stable long-term periodic firing of action potentials and CaOs, it is essential to incorporate calcium transporters controlled by feedback of the ER store filling, for example, store-operated calcium channels in the plasma membrane. For low IP3 concentrations, our integrated NRK cell model is at rest at -70 mV. For higher IP3 concentrations, the CaOs become activated and trigger repetitive firing of action potentials. At high IP3 concentrations, the basal intracellular calcium concentration becomes elevated and the cell is depolarized near -20 mV. These predictions are in agreement with the different proliferative states of cultures of NRK fibroblasts. We postulate that the stabilizing role of calcium channels and/or other calcium transporters controlled by feedback from the ER store is essential for any cell in which calcium signaling by intracellular CaOs involves both ER and plasma membrane calcium fluxes.

Role of gap junctions in synchronized neuronal oscillations in the inferior olive

Inferior olivary (IO) neurons are electrically coupled through gap junctions and generate synchronous subthreshold oscillations of their membrane potential at a frequency of 1-10 Hz. Whereas the ionic mechanisms of these oscillatory responses are well understood, their origin and ensemble properties remain controversial. Here, the role of gap junctions in generating and synchronizing IO oscillations was examined by combining intracellular recordings with high-speed voltage-sensitive dye imaging in rat brain stem slices. Single cell responses and ensemble synchronized responses of IO neurons were compared in control conditions and in the presence of 18beta-glycyrrhetinic acid (18beta-GA), a pharmacological gap junction blocker. Under our experimental conditions, 18beta-GA had no adverse effects on intrinsic electroresponsive properties of IO neurons, other than the block of gap junction-dependent dye coupling and the resulting change in cells' passive properties. Application of 18beta-GA did not abolish single cell oscillations. Pharmacologically uncoupled IO neurons continued to oscillate with a frequency and amplitude that were similar to those recorded in control conditions. However, these oscillations were no longer synchronized across a population of IO neurons. Our optical recordings did not detect any clusters of synchronous oscillatory activity in the presence of the blocker. These results indicate that gap junctions are not necessary for generating subthreshold oscillations, rather, they are required for clustering of coherent oscillatory activity in the IO. The findings support the view that oscillatory properties of single IO neurons endow the system with important reset dynamics, while gap junctions are mainly required for synchronized neuronal ensemble activity.

Gap junctional regulatory mechanisms in the AII amacrine cell of the rabbit retina

Gap junctions are commonplace in retina, often between cells of the same morphological type, but sometimes linking different cell types. The strength of coupling between cells derives from the properties of the connexins, but also is regulated by the intracellular environment of each cell. We measured the relative coupling of two different gap junctions made by AII amacrine cells of the rabbit retina. Permeability to the tracer Neurobiotin was measured at different concentrations of the neuromodulators dopamine, nitric oxide, or cyclic adenosine monophosphate (cAMP) analogs. Diffusion coefficients were calculated separately for the gap junctions between pairs of AII amacrine cells and for those connecting AII amacrine cells with ON cone bipolar cells. Increased dopamine caused diffusion rates to decline more rapidly across the AII-AII gap junctions than across the AII-bipolar cell gap junctions. The rate of decline at these sites was well fit by a model proposing that dopamine modulates two independent gates in AII-AII channels, but only a single gate on the AII side of the AII-bipolar channel. However, a membrane-permeant cAMP agonist modulated both types of channel equally. Therefore, the major regulator of channel closure in this network is the local cAMP concentration within each cell, as regulated by dopamine, rather than different cAMP sensitivity of their respective gates. In contrast, nitric oxide preferentially reduced AII-bipolar cell permeabilities. Coupling from AII amacrine cells to the different bipolar cell subtypes was differentially affected by dopamine, indicating that light adaptation acting via dopamine release alters network coupling properties in multiple ways.

Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons

The dynamics of two coupled piece-wise linear one-dimensional monostable maps is investigated. The single map is associated with Poincare section of the FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to the appearance of chaotic attractor. The attractor exists in an invariant region of phase space bounded by the manifolds of the saddle fixed point and the saddle periodic point. The oscillations from the chaotic attractor have a spike-burst shape with anti-phase synchronized spiking.

Experimental evidence and modeling studies support a synchronizing role for electrical coupling in the cat thalamic reticular neurons in vivo

Thalamic reticular (RE) neurons are crucially implicated in brain rhythms. Here, we report that RE neurons of adult cats, recorded and stained intracellularly in vivo, displayed spontaneously occurring spikelets, which are characteristic of central neurons that are coupled electrotonically via gap junctions. Spikelets occurred spontaneously during spindles, an oscillation in which RE neurons play a leading role, as well as during interspindle lulls. They were significantly different from excitatory postsynaptic potentials and also distinct from fast prepotentials that are presumably dendritic spikes generated synaptically. Spikelets were strongly reduced by halothane, a blocker of gap junctions. Multi-site extracellular recordings performed before, during and after administration of halothane demonstrated a role for electrical coupling in the synchronization of spindling activity within the RE nucleus. Finally, computational models of RE neurons predicted that gap junctions between these neurons could mediate the spread of low-frequency activity at great distances. These experimental and modeling data suggest that electrotonic coupling within the RE nucleus plays an important role in the generation and synchronization of low-frequency (spindling) activities in the thalamus.

Analysis of the noise-induced bursting-spiking transition in a pancreatic beta-cell model

A stochastic model of the electrophysiological behavior of the pancreatic beta cell is studied, as a paradigmatic example of a bursting biological cell embedded in a noisy environment. The analysis is focused on the distortion that a growing noise causes to the basic properties of the membrane potential signals, such as their periodic or chaotic nature, and their bursting or spiking behavior. We present effective computational tools to obtain as much information as possible from these signals, and we suggest that the methods could be applied to real time series. Finally, a universal dependence of the main characteristics of the membrane potential on the size of the considered cell cluster is presented.

Deformation of network connectivity in the inferior olive of connexin 36-deficient mice is compensated by morphological and electrophysiological changes at the single neuron level

Compensatory mechanisms after genetic manipulations have been documented extensively for the nervous system. In many cases, these mechanisms involve genetic regulation at the transcription or expression level of existing isoforms. We report a novel mechanism by which single neurons compensate for changes in network connectivity by retuning their intrinsic electrical properties. We demonstrate this mechanism in the inferior olive, in which widespread electrical coupling is mediated by abundant gap junctions formed by connexin 36 (Cx36). It has been shown in various mammals that this electrical coupling supports the generation of subthreshold oscillations, but recent work revealed that rhythmic activity is sustained in knock-outs of Cx36. Thus, these results raise the question of whether the olivary oscillations in Cx36 knock-outs simply reflect the status of wild-type neurons without gap junctions or the outcome of compensatory mechanisms. Here, we demonstrate that the absence of Cx36 results in thicker dendrites with gap-junction-like structures with an abnormally wide interneuronal gap that prevents electrotonic coupling. The mutant olivary neurons show unusual voltage-dependent oscillations and an increased excitability that is attributable to a combined decrease in leak conductance and an increase in voltage-dependent calcium conductance. Using dynamic-clamp techniques, we demonstrated that these changes are sufficient to transform a wild-type neuron into a knock-out-like neuron. We conclude that the absence of Cx36 in the inferior olive is not compensated by the formation of other gap-junction channels but instead by changes in the cytological and electroresponsive properties of its neurons, such that the capability to produce rhythmic activity is maintained.

Deformation of network connectivity in the inferior olive of connexin 36-deficient mice is compensated by morphological and electrophysiological changes at the single neuron level

Compensatory mechanisms after genetic manipulations have been documented extensively for the nervous system. In many cases, these mechanisms involve genetic regulation at the transcription or expression level of existing isoforms. We report a novel mechanism by which single neurons compensate for changes in network connectivity by retuning their intrinsic electrical properties. We demonstrate this mechanism in the inferior olive, in which widespread electrical coupling is mediated by abundant gap junctions formed by connexin 36 (Cx36). It has been shown in various mammals that this electrical coupling supports the generation of subthreshold oscillations, but recent work revealed that rhythmic activity is sustained in knock-outs of Cx36. Thus, these results raise the question of whether the olivary oscillations in Cx36 knock-outs simply reflect the status of wild-type neurons without gap junctions or the outcome of compensatory mechanisms. Here, we demonstrate that the absence of Cx36 results in thicker dendrites with gap-junction-like structures with an abnormally wide interneuronal gap that prevents electrotonic coupling. The mutant olivary neurons show unusual voltage-dependent oscillations and an increased excitability that is attributable to a combined decrease in leak conductance and an increase in voltage-dependent calcium conductance. Using dynamic-clamp techniques, we demonstrated that these changes are sufficient to transform a wild-type neuron into a knock-out-like neuron. We conclude that the absence of Cx36 in the inferior olive is not compensated by the formation of other gap-junction channels but instead by changes in the cytological and electroresponsive properties of its neurons, such that the capability to produce rhythmic activity is maintained.

Addition of inhibition in the olivocerebellar system and the ontogeny of a motor memory

The developmental emergence of learning has traditionally been attributed to the maturation of single brain regions necessary for learning in adults, rather than to the maturation of synaptic interactions within neural systems. Acquisition and retention of a simple form of motor learning, classical conditioning of the eyeblink reflex, depends on the cerebellum and interconnected brainstem structures, including the inferior olive. Here, we combined unit recordings from Purkinje cells in eye regions of the cerebellar cortex and quantitative electron microscopy of the inferior olive to show that the developmental emergence of eyeblink conditioning in rats is associated with the maturation of inhibitory feedback from the cerebellum to the inferior olive. The results are consistent with previous work in adult animals and indicate that the maturation of cerebellar inhibition within the inferior olive may be a critical factor for the formation and retention of learning-specific cerebellar plasticity and eyeblink conditioning.

Rhythmicity without synchrony in the electrically uncoupled inferior olive

Neurons of the inferior olivary nucleus (IO) form the climbing fibers that excite Purkinje cells of the cerebellar cortex. IO neurons are electrically coupled through gap junctions, and they generate synchronous, subthreshold oscillations of membrane potential at approximately 5-10 Hz. Experimental and theoretical studies have suggested that both the rhythmicity and synchrony of IO neurons require electrical coupling. We recorded from pairs of IO neurons in slices of mouse brainstem in vitro. Most pairs of neurons from wild-type (WT) mice were electrically coupled, but coupling was rare and weak between neurons of knock-out (KO) mice for connexin36, a neuronal gap junction protein. IO cells in both WT and KO mice generated rhythmic membrane fluctuations of similar frequency and amplitude. Oscillations in neighboring pairs of WT neurons were strongly synchronized, whereas the oscillations of KO pairs were uncorrelated. Spontaneous oscillations in KO neurons were not blocked by tetrodotoxin. Spontaneously oscillating neurons of both WT and KO mice generated occasional action potentials in phase with their membrane rhythms, but only the action potentials of WT neuron pairs were synchronous. Harmaline, a beta-carboline derivative thought to induce tremor by facilitating rhythmogenesis in the IO, was injected systemically into WT and KO mice. Harmaline-induced tremors were robust and indistinguishable in the two genotypes, suggesting that gap junction-mediated synchrony does not play a role in harmaline-induced tremor. We conclude that electrical coupling is not necessary for the generation of spontaneous subthreshold oscillations in single IO neurons, but that coupling can serve to synchronize rhythmic activity among IO neurons.

Rhythmicity without synchrony in the electrically uncoupled inferior olive

Neurons of the inferior olivary nucleus (IO) form the climbing fibers that excite Purkinje cells of the cerebellar cortex. IO neurons are electrically coupled through gap junctions, and they generate synchronous, subthreshold oscillations of membrane potential at approximately 5-10 Hz. Experimental and theoretical studies have suggested that both the rhythmicity and synchrony of IO neurons require electrical coupling. We recorded from pairs of IO neurons in slices of mouse brainstem in vitro. Most pairs of neurons from wild-type (WT) mice were electrically coupled, but coupling was rare and weak between neurons of knock-out (KO) mice for connexin36, a neuronal gap junction protein. IO cells in both WT and KO mice generated rhythmic membrane fluctuations of similar frequency and amplitude. Oscillations in neighboring pairs of WT neurons were strongly synchronized, whereas the oscillations of KO pairs were uncorrelated. Spontaneous oscillations in KO neurons were not blocked by tetrodotoxin. Spontaneously oscillating neurons of both WT and KO mice generated occasional action potentials in phase with their membrane rhythms, but only the action potentials of WT neuron pairs were synchronous. Harmaline, a beta-carboline derivative thought to induce tremor by facilitating rhythmogenesis in the IO, was injected systemically into WT and KO mice. Harmaline-induced tremors were robust and indistinguishable in the two genotypes, suggesting that gap junction-mediated synchrony does not play a role in harmaline-induced tremor. We conclude that electrical coupling is not necessary for the generation of spontaneous subthreshold oscillations in single IO neurons, but that coupling can serve to synchronize rhythmic activity among IO neurons.

The olivocerebellar system as a generator of temporal patterns

The large number of diverse functions attributed to the cerebellum appears to be inconsistent with its simple, homogeneous and evolutionary preserved structure. A homogeneous structure that participates in a variety of functions implies that a common denominator underlies all of them. Since the concept of precise timing can be recognized in almost all cerebellar functions, it is likely, therefore, that the basic cerebellar circuit is capable of generating temporal patterns. Of the different mechanisms that can generate temporal patterns, two are suggested by the functional anatomy of the cerbellum: transmission lines or oscillators. Our recent experimental observations indicate that the olivary oscillatory property is more likely to serve this function. We propose that interactions between the cerebellum and the inferior olive endow the system with the ability to generate complex temporal patterns. These temporal patterns can be used for fine adjustment of motor output, sensory expectation, or shifting attentions.

Electrotonic coupling in the inferior olivary nucleus revealed by simultaneous double patch recordings

Electrotonic coupling in the inferior olivary (IO) nucleus is assumed to play a crucial role in generating the subthreshold membrane potential oscillations in olivary neurons and in synchronizing climbing fiber input into the cerebellar cortex. We studied the strength and spatial distribution of the coupling by simultaneous double patch recordings from olivary neurons in the brain slice preparation. Electrotonic coupling was observed in 50% of the cell pairs. The coupling coefficient (CC), defined as the ratio between voltage responses of the post- and the prejunctional cell, varied between 0.002 and 0.17; most of the pairs were weakly coupled. In more than 75% of the pairs, the CC was <0.05. The coupling resistance varied between 0.7 to 19.8 G(Omega), and 68% of the values fell between 0.7 to 8 G(Omega). The difference between the coupling coefficient measured on stimulation of cell 1 or cell 2 of a coupled pair was 27 +/- 16%. Direct calculation of the coupling resistance revealed an asymmetry of 24 +/- 12%, suggesting a directional preference of coupling. The coupling was voltage independent, although depolarization of either the pre- or the postjunctional neuron reduced the CC. The chance of a cell pair being coupled was 80% in immediate neighboring cells, but dropped to about 30% at a distance of 40 microm. No coupled pairs were observed at distances larger than 70 microm. In 52% of staining experiments neurobiotin injection into an olivary neuron produced indirect labeling of 1-11 nearby cells with an average of 3.8 +/- 2.9. All indirectly labeled cells were found in, or immediately adjacent, to the dendritic field of the directly stained neuron. Two distinct morphological types of olivary neurons, "curly" and "straight" cells, were found. In each case all neurons stained indirectly by dye passage through gap junctions belonged to the same type. Using the physiological data we estimated that each olivary neuron is directly coupled to about 50 neurons. Since somatic recordings may not reveal coupling through remote dendrites, we conclude that each neuron is directly connected to > or =50 neurons forming two distinct networks of curly and straight cells.

Generation and propagation of subthreshold waves in a network of inferior olivary neurons

The cells of the inferior olivary (IO) nucleus generate a large repertoire of electrical signals, among them subthreshold oscillations of the membrane potential (STO). To date, subthreshold oscillations have been studied at the level of single-cell recordings, from which network properties were inferred. In this study we used whole cell patch recordings and optical imaging to address the following issues: 1) synchrony of STO in neighboring neurons; 2) stability of the oscillatory activity in the temporal and spatial domain; and 3) the size of the oscillating network. Recordings were made from 126 pairs of IO neurons in 13- to 30-day-old rats. An additional 262 neurons were recorded individually. The frequency of STO varied from 0.8 to 8.6 Hz. The frequency distribution revealed two subpopulations with peaks at about 3 and 6 Hz. The maximum amplitude among the cells varied from 2 to 25 mV. Oscillations in most neurons showed ongoing modulations in both frequency and amplitude. These modulations were largely abolished following bath application of 40 microM 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX), a competitive non-N-methyl-D-aspartate (non-NMDA) receptor antagonist, suggesting that they were caused by glutamatergic action. In 35 of 61 recorded pairs at least one neuron exhibited STO permitting us to compare frequency and phase relations. In 22 pairs there was coherent activity with zero phase difference between oscillations in the 2 cells. In these pairs, frequency and amplitude modulation occurred simultaneously in both neurons. Electrotonic coupling was tested in 13 pairs, that had coherent STO, and it was detected in 12. An additional seven pairs showed coherent oscillations but with a phase difference of 20-50 ms. Electrotonic coupling was observed in three of these pairs. Electrotonic coupling was also observed in two of five pairs in which only one neuron oscillated. No coupling was detected in one pair where both neurons oscillated but at different frequencies. Optical imaging using a voltage-sensitive dye (RH 414) was performed on 40 IO slices using an array of 128 photodiodes. Patches of oscillatory activity were observed in 10 slices. Among them six showed spontaneous oscillations, and four exhibited oscillations following extracellular stimulation. In agreement with cell pair recording, optical imaging demonstrated phase-shifted activity in the form of propagating waves of activity within an oscillating patch. We conclude that 1) STO exhibit ongoing modulations of frequency and amplitude that are probably caused by extrinsic inputs to the IO nucleus; 2) electrotonically coupled neurons show a high level of STO synchrony; and 3) the oscillatory activity can propagate within a network of coupled olivary neurons.

Oscillations by symmetry breaking in homogeneous networks with electrical coupling

In many biological systems, the electrical coupling of nonoscillating cells generates synchronized membrane potential oscillations. This work describes a dynamical mechanism in which the electrical coupling of identical nonoscillating cells destabilizes the homogeneous fixed point and leads to network oscillations via a Hopf bifurcation. Each cell is described by a passive membrane potential and additional internal variables. The dynamics of the internal variables, in isolation, is oscillatory, but their interaction with the membrane potential damps the oscillations and therefore constructs nonoscillatory cells. The electrical coupling reveals the oscillatory nature of the internal variables and generates network oscillations. This mechanism is analyzed near the bifurcation point, where the spatial structure of the membrane potential oscillations is determined by the network architecture and in the limit of strong coupling, where the membrane potentials of all cells oscillate in-phase and multiple cluster states dominate the dynamics. In particular, we have derived an asymptotic behavior for the spatial fluctuations in the limit of strong coupling in fully connected networks and in a one-dimensional lattice architecture.

AII (Rod) amacrine cells form a network of electrically coupled interneurons in the mammalian retina

AII (rod) amacrine cells in the mammalian retina are reciprocally connected via gap junctions, but there is no physiological evidence that demonstrates a proposed function as electrical synapses. In whole-cell recordings from pairs of AII amacrine cells in a slice preparation of the rat retina, bidirectional, nonrectifying electrical coupling was observed in all pairs with overlapping dendritic trees (average conductance approximately 700 pS). Coupling displayed characteristics of a low-pass filter, with no evidence for amplification of spike-evoked electrical postsynaptic potentials by active conductances. Coincidence detection, as well as precise temporal synchronization of subthreshold membrane potential oscillations and TTX-sensitive spiking, was commonly observed. These results indicate a unique mode of operation and integrative capability of the network of AII amacrine cells.

Bursting as an emergent phenomenon in coupled chaotic maps

A two-dimensional map exhibiting chaotic bursting behavior similar to the bursting electrical activity observed in biological neurons and endocrine cells is examined. Model parameters are changed so that the bursting behavior is destroyed. We show that bursting can be recovered in a population of such nonbursting cells when they are coupled via the mean field. The phenomenon is explained with a geometric bifurcation analysis. The analysis reveals that emergent bursting in the network is due to coupling alone and is very robust to changes in the coupling strength, and that heterogeneity in the model parameters does not play a role.