Synchrony of fast-spiking interneurons interconnected by GABAergic and electrical synapses

On the Diverse Functions of Electrical Synapses

Electrical synapses are the neurophysiological product of gap junctional pores between neurons that allow bidirectional flow of current between neurons. They are expressed throughout the mammalian nervous system, including cortex, hippocampus, thalamus, retina, cerebellum, and inferior olive. Classically, the function of electrical synapses has been associated with synchrony, logically following that continuous conductance provided by gap junctions facilitates the reduction of voltage differences between coupled neurons. Indeed, electrical synapses promote synchrony at many anatomical and frequency ranges across the brain. However, a growing body of literature shows there is greater complexity to the computational function of electrical synapses. The paired membranes that embed electrical synapses act as low-pass filters, and as such, electrical synapses can preferentially transfer spike after hyperpolarizations, effectively providing spike-dependent inhibition. Other functions include driving asynchronous firing, improving signal to noise ratio, aiding in discrimination of dissimilar inputs, or dampening signals by shunting current. The diverse ways by which electrical synapses contribute to neuronal integration merits furthers study. Here we review how functions of electrical synapses vary across circuits and brain regions and depend critically on the context of the neurons and brain circuits involved. Computational modeling of electrical synapses embedded in multi-cellular models and experiments utilizing optical control and measurement of cellular activity will be essential in determining the specific roles performed by electrical synapses in varying contexts.

Neuromorphic Dynamical Synapses With Reconfigurable Voltage-Gated Kinetics

OBJECTIVE

Although biological synapses express a large variety of receptors in neuronal membranes, the current hardware implementation of neuromorphic synapses often rely on simple models ignoring the heterogeneity of synaptic transmission. Our objective is to emulate different types of synapses with distinct properties.

METHODS

Conductance-based chemical and electrical synapses were implemented between silicon neurons on a fully programmable and reconfigurable, biophysically realistic neuromorphic VLSI chip. Different synaptic properties were achieved by configuring on-chip digital parameters for the conductances, reversal potentials, and voltage dependence of the channel kinetics. The measured I-V characteristics of the artificial synapses were compared with biological data.

RESULTS

We reproduced the response properties of five different types of chemical synapses, including both excitatory ( AMPA, NMDA) and inhibitory ( GABA_A, GABA_C, glycine) ionotropic receptors. In addition, electrical synapses were implemented in a small network of four silicon neurons.

CONCLUSION

Our work extends the repertoire of synapse types between silicon neurons, providing greater flexibility for the design and implementation of biologically realistic neural networks on neuromorphic chips.

SIGNIFICANCE

A higher synaptic heterogeneity in neuromorphic chips is relevant for the hardware implementation of energy-efficient population codes as well as for dynamic clamp applications where neural models are implemented in neuromorphic VLSI hardware.

A Role for Electrotonic Coupling Between Cortical Pyramidal Cells

Many brain regions communicate information through synchronized network activity. Electrical coupling among the dendrites of interneurons in the cortex has been implicated in forming and sustaining such activity in the cortex. Evidence for the existence of electrical coupling among cortical pyramidal cells, however, has been largely absent. A recent experimental study measured properties of electrical connections between pyramidal cells in the cortex deemed “electrotonic couplings.” These junctions were seen to occur pair-wise, sparsely, and often coexist with electrically-coupled interneurons. Here, we construct a network model to investigate possible roles for these rare, electrotonically-coupled pyramidal-cell pairs. Through simulations, we show that electrical coupling among pyramidal-cell pairs significantly enhances coincidence-detection capabilities and increases network spike-timing precision. Further, a network containing multiple pairs exhibits large variability in its firing pattern, possessing a rich coding structure.

Bayesian Estimation of Phase Dynamics Based on Partially Sampled Spikes Generated by Realistic Model Neurons

A dynamic system showing stable rhythmic activity can be represented by the dynamics of phase oscillators. This would provide a useful mathematical framework through which one can understand the system's dynamic properties. A recent study proposed a Bayesian approach capable of extracting the underlying phase dynamics directly from time-series data of a system showing rhythmic activity. Here we extended this method to spike data that otherwise provide only limited phase information. To determine how this method performs with spike data, we applied it to simulated spike data generated by a realistic neuronal network model. We then compared the estimated dynamics obtained based on the spike data with the dynamics theoretically derived from the model. The method successfully extracted the modeled phase dynamics, particularly the interaction function, when the amount of available data was sufficiently large. Furthermore, the method was able to infer synaptic connections based on the estimated interaction function. Thus, the method was found to be applicable to spike data and practical for understanding the dynamic properties of rhythmic neural systems.

Collective behavior of large-scale neural networks with GPU acceleration

In this paper, the collective behaviors of a small-world neuronal network motivated by the anatomy of a mammalian cortex based on both Izhikevich model and Rulkov model are studied. The Izhikevich model can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. Rulkov model is in the form of difference equations that generate a sequence of membrane potential samples in discrete moments of time to improve computational efficiency. These two models are suitable for the construction of large scale neural networks. By varying some key parameters, such as the connection probability and the number of nearest neighbor of each node, the coupled neurons will exhibit types of temporal and spatial characteristics. It is demonstrated that the implementation of GPU can achieve more and more acceleration than CPU with the increasing of neuron number and iterations. These two small-world network models and GPU acceleration give us a new opportunity to reproduce the real biological network containing a large number of neurons.

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.

Cooperation and competition of gamma oscillation mechanisms

Oscillations of neuronal activity in different frequency ranges are thought to reflect important aspects of cortical network dynamics. Here we investigate how various mechanisms that contribute to oscillations in neuronal networks may interact. We focus on networks with inhibitory, excitatory, and electrical synapses, where the subnetwork of inhibitory interneurons alone can generate interneuron gamma (ING) oscillations and the interactions between interneurons and pyramidal cells allow for pyramidal-interneuron gamma (PING) oscillations. What type of oscillation will such a network generate? We find that ING and PING oscillations compete: The mechanism generating the higher oscillation frequency "wins"; it determines the frequency of the network oscillation and suppresses the other mechanism. For type I interneurons, the network oscillation frequency is equal to or slightly above the higher of the ING and PING frequencies in corresponding reduced networks that can generate only either of them; if the interneurons belong to the type II class, it is in between. In contrast to ING and PING, oscillations mediated by gap junctions and oscillations mediated by inhibitory synapses may cooperate or compete, depending on the type (I or II) of interneurons and the strengths of the electrical and chemical synapses. We support our computer simulations by a theoretical model that allows a full theoretical analysis of the main results. Our study suggests experimental approaches to deciding to what extent oscillatory activity in networks of interacting excitatory and inhibitory neurons is dominated by ING or PING oscillations and of which class the participating interneurons are.

Spatial and feature-based attention in a layered cortical microcircuit model

Directing attention to the spatial location or the distinguishing feature of a visual object modulates neuronal responses in the visual cortex and the stimulus discriminability of subjects. However, the spatial and feature-based modes of attention differently influence visual processing by changing the tuning properties of neurons. Intriguingly, neurons' tuning curves are modulated similarly across different visual areas under both these modes of attention. Here, we explored the mechanism underlying the effects of these two modes of visual attention on the orientation selectivity of visual cortical neurons. To do this, we developed a layered microcircuit model. This model describes multiple orientation-specific microcircuits sharing their receptive fields and consisting of layers 2/3, 4, 5, and 6. These microcircuits represent a functional grouping of cortical neurons and mutually interact via lateral inhibition and excitatory connections between groups with similar selectivity. The individual microcircuits receive bottom-up visual stimuli and top-down attention in different layers. A crucial assumption of the model is that feature-based attention activates orientation-specific microcircuits for the relevant feature selectively, whereas spatial attention activates all microcircuits homogeneously, irrespective of their orientation selectivity. Consequently, our model simultaneously accounts for the multiplicative scaling of neuronal responses in spatial attention and the additive modulations of orientation tuning curves in feature-based attention, which have been observed widely in various visual cortical areas. Simulations of the model predict contrasting differences between excitatory and inhibitory neurons in the two modes of attentional modulations. Furthermore, the model replicates the modulation of the psychophysical discriminability of visual stimuli in the presence of external noise. Our layered model with a biologically suggested laminar structure describes the basic circuit mechanism underlying the attention-mode specific modulations of neuronal responses and visual perception.

Dynamics of action potential firing in electrically connected striatal fast-spiking interneurons

Fast-spiking interneurons (FSIs) play a central role in organizing the output of striatal neural circuits, yet functional interactions between these cells are still largely unknown. Here we investigated the interplay of action potential (AP) firing between electrically connected pairs of identified FSIs in mouse striatal slices. In addition to a loose coordination of firing activity mediated by membrane potential coupling, gap junctions (GJ) induced a frequency-dependent inhibition of spike discharge in coupled cells. At relatively low firing rates (2–20 Hz), some APs were tightly synchronized whereas others were inhibited. However, burst firing at intermediate frequencies (25–60 Hz) mostly induced spike inhibition, while at frequencies >50–60 Hz FSI pairs tended to synchronize. Spike silencing occurred even in the absence of GABAergic synapses or persisted after a complete block of GABA_A receptors. Pharmacological suppression of presynaptic spike afterhyperpolarization (AHP) caused postsynaptic spikelets to become more prone to trigger spikes at near-threshold potentials, leading to a mostly synchronous firing activity. The complex pattern of functional coordination mediated by GJ endows FSIs with peculiar dynamic properties that may be critical in controlling striatal-dependent behavior.

Interaction function of oscillating coupled neurons

Large scale simulations of electrically coupled neuronal oscillators often employ the phase coupled oscillator paradigm to understand and predict network behavior. We study the nature of the interaction between such coupled oscillators using weakly coupled oscillator theory. By employing piecewise linear approximations for phase response curves and voltage time courses and parametrizing their shapes, we compute the interaction function for all such possible shapes and express it in terms of discrete Fourier modes. We find that reasonably good approximation is achieved with four Fourier modes that comprise of both sine and cosine terms.

Oscillations and synchrony in a cortical neural network

In this paper, the oscillations and synchronization status of two different network connectivity patterns based on Izhikevich model are studied. One of the connectivity patterns is a randomly connected neuronal network, the other one is a small-world neuronal network. This Izhikevich model is a simple model which can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. Detailed investigations reveal that by varying some key parameters, such as the connection weights of neurons, the external current injection, the noise of intensity and the neuron number, this neuronal network will exhibit various collective behaviors in randomly coupled neuronal network. In addition, we show that by changing the number of nearest neighbor and connection probability in small-world topology can also affect the collective dynamics of neuronal activity. These results may be instructive in understanding the collective dynamics of mammalian cortex.

Effect of phase response curve skewness on synchronization of electrically coupled neuronal oscillators

We investigate why electrically coupled neuronal oscillators synchronize or fail to synchronize using the theory of weakly coupled oscillators. Stability of synchrony and antisynchrony is predicted analytically and verified using numerical bifurcation diagrams. The shape of the phase response curve (PRC), the shape of the voltage time course, and the frequency of spiking are freely varied to map out regions of parameter spaces that hold stable solutions. We find that type 1 and type 2 PRCs can hold both synchronous and antisynchronous solutions, but the shape of the PRC and the voltage determine the extent of their stability. This is achieved by introducing a five-piecewise linear model to the PRC and a three-piecewise linear model to the voltage time course, and then analyzing the resultant eigenvalue equations that determine the stability of the phase-locked solutions. A single time parameter defines the skewness of the PRC, and another single time parameter defines the spike width and frequency. Our approach gives a comprehensive picture of the relation of the PRC shape, voltage time course, and stability of the resultant synchronous and antisynchronous solutions.

Spike width and frequency alter stability of phase-locking in electrically coupled neurons

The stability of phase-locked states of electrically coupled type-1 phase response curve neurons is studied using piecewise linear formulations for their voltage profile and phase response curves. We find that at low frequency and/or small spike width, synchrony is stable, and antisynchrony unstable. At high frequency and/or large spike width, these phase-locked states switch their stability. Increasing the ratio of spike width to spike height causes the antisynchronous state to transition into a stable synchronous state. We compute the interaction function and the boundaries of stability of both these phase-locked states, and present analytical expressions for them. We also study the effect of phase response curve skewness on the boundaries of synchrony and antisynchrony.

Gap junctions facilitate propagation of synchronous firing in the cortical neural population: a numerical simulation study

This study investigates the effect of gap junctions on firing propagation in a feedforward neural network by a numerical simulation with biologically plausible parameters. Gap junctions are electrical couplings between two cells connected by a binding protein, connexin. Recent electrophysiological studies have reported that a large number of inhibitory neurons in the mammalian cortex are mutually connected by gap junctions, and synchronization of gap junctions, spread over several hundred microns, suggests that these have a strong effect on the dynamics of the cortical network. However, the effect of gap junctions on firing propagation in cortical circuits has not been examined systematically. In this study, we perform numerical simulations using biologically plausible parameters to clarify this effect on population firing in a feedforward neural network. The results suggest that gap junctions switch the temporally uniform firing in a layer to temporally clustered firing in subsequent layers, resulting in an enhancement in the propagation of population firing in the feedforward network. Because gap junctions are often modulated in physiological conditions, we speculate that gap junctions could be related to a gating function of population firing in the brain.

Neural dynamics and information representation in microcircuits of motor cortex

The brain has to analyze and respond to external events that can change rapidly from time to time, suggesting that information processing by the brain may be essentially dynamic rather than static. The dynamical features of neural computation are of significant importance in motor cortex that governs the process of movement generation and learning. In this paper, we discuss these features based primarily on our recent findings on neural dynamics and information coding in the microcircuit of rat motor cortex. In fact, cortical neurons show a variety of dynamical behavior from rhythmic activity in various frequency bands to highly irregular spike firing. Of particular interest are the similarity and dissimilarity of the neuronal response properties in different layers of motor cortex. By conducting electrophysiological recordings in slice preparation, we report the phase response curves (PRCs) of neurons in different cortical layers to demonstrate their layer-dependent synchronization properties. We then study how motor cortex recruits task-related neurons in different layers for voluntary arm movements by simultaneous juxtacellular and multiunit recordings from behaving rats. The results suggest an interesting difference in the spectrum of functional activity between the superficial and deep layers. Furthermore, the task-related activities recorded from various layers exhibited power law distributions of inter-spike intervals (ISIs), in contrast to a general belief that ISIs obey Poisson or Gamma distributions in cortical neurons. We present a theoretical argument that this power law of in vivo neurons may represent the maximization of the entropy of firing rate with limited energy consumption of spike generation. Though further studies are required to fully clarify the functional implications of this coding principle, it may shed new light on information representations by neurons and circuits in motor cortex.

Rewiring-induced chaos in pulse-coupled neural networks

The dependence of the dynamics of pulse-coupled neural networks on random rewiring of excitatory and inhibitory connections is examined. When both excitatory and inhibitory connections are rewired, periodic synchronization emerges with a Hopf-like bifurcation and a subsequent period-doubling bifurcation; chaotic synchronization is also observed. When only excitatory connections are rewired, periodic synchronization emerges with a saddle node-like bifurcation, and chaotic synchronization is also observed. This result suggests that randomness in the system does not necessarily contaminate the system, and sometimes it even introduces rich dynamics to the system such as chaos.

Influences of membrane properties on phase response curve and synchronization stability in a model globus pallidus neuron

The activity patterns of the globus pallidus (GPe) and subthalamic nucleus (STN) are closely associated with motor function and dysfunction in the basal ganglia. In the pathological state caused by dopamine depletion, the STN-GPe network exhibits rhythmic synchronous activity accompanied by rebound bursts in the STN. Therefore, the mechanism of activity transition is a key to understand basal ganglia functions. As synchronization in GPe neurons could induce pathological STN rebound bursts, it is important to study how synchrony is generated in the GPe. To clarify this issue, we applied the phase-reduction technique to a conductance-based GPe neuronal model in order to derive the phase response curve (PRC) and interaction function between coupled GPe neurons. Using the PRC and interaction function, we studied how the steady-state activity of the GPe network depends on intrinsic membrane properties, varying ionic conductances on the membrane. We noted that a change in persistent sodium current, fast delayed rectifier Kv3 potassium current, M-type potassium current and small conductance calcium-dependent potassium current influenced the PRC shape and the steady state. The effect of those currents on the PRC shape could be attributed to extension of the firing period and reduction of the phase response immediately after an action potential. In particular, the slow potassium current arising from the M-type potassium and the SK current was responsible for the reduction of the phase response. These results suggest that the membrane property modulation controls synchronization/asynchronization in the GPe and the pathological pattern of STN-GPe activity.

Synchronization study in ring-like and grid-like neuronal networks

In this paper, we study the synchronization status of both two gap-junction coupled neurons and neuronal network with two different network connectivity patterns. One of the network connectivity patterns is a ring-like neuronal network, which only considers nearest-neighbor neurons. The other is a grid-like neuronal network, with all nearest neighbor couplings. We show that by varying some key parameters, such as the coupling strength and the external current injection, the neuronal network will exhibit various patterns of firing synchronization. Different types of firing synchronization are diagnosed by means of a mean field potential, a bifurcation diagram, a correlation coefficient and the ISI-distance method. Numerical simulations demonstrate that the synchronization status of multiple neurons is much dependent on the network patters, when the number of neurons is the same. It is also demonstrated that the synchronization status of two coupled neurons is similar with the grid-like neuronal network, but differs radically from that of the ring-like neuronal network. These results may be instructive in understanding synchronization transitions in neuronal systems.

Striatal fast-spiking interneurons: from firing patterns to postsynaptic impact

In the striatal microcircuit, fast-spiking (FS) interneurons have an important role in mediating inhibition onto neighboring medium spiny (MS) projection neurons. In this study, we combined computational modeling with in vitro and in vivo electrophysiological measurements to investigate FS cells in terms of their discharge properties and their synaptic efficacies onto MS neurons. In vivo firing of striatal FS interneurons is characterized by a high firing variability. It is not known, however, if this variability results from the input that FS cells receive, or if it is promoted by the stuttering spike behavior of these neurons. Both our model and measurements in vitro show that FS neurons that exhibit random stuttering discharge in response to steady depolarization do not show the typical stuttering behavior when they receive fluctuating input. Importantly, our model predicts that electrically coupled FS cells show substantial spike synchronization only when they are in the stuttering regime. Therefore, together with the lack of synchronized firing of striatal FS interneurons that has been reported in vivo, these results suggest that neighboring FS neurons are not in the stuttering regime simultaneously and that in vivo FS firing variability is more likely determined by the input fluctuations. Furthermore, the variability in FS firing is translated to variability in the postsynaptic amplitudes in MS neurons due to the strong synaptic depression of the FS-to-MS synapse. Our results support the idea that these synapses operate over a wide range from strongly depressed to almost fully recovered. The strong inhibitory effects that FS cells can impose on their postsynaptic targets, and the fact that the FS-to-MS synapse model showed substantial depression over extended periods of time might indicate the importance of cooperative effects of multiple presynaptic FS interneurons and the precise orchestration of their activity.

Layer-Dependent Attentional Processing by Top-down Signals in a Visual Cortical Microcircuit Model

A vast amount of information about the external world continuously flows into the brain, whereas its capacity to process such information is limited. Attention enables the brain to allocate its resources of information processing to selected sensory inputs for reducing its computational load, and effects of attention have been extensively studied in visual information processing. However, how the microcircuit of the visual cortex processes attentional information from higher areas remains largely unknown. Here, we explore the complex interactions between visual inputs and an attentional signal in a computational model of the visual cortical microcircuit. Our model not only successfully accounts for previous experimental observations of attentional effects on visual neuronal responses, but also predicts contrasting differences in the attentional effects of top-down signals between cortical layers: attention to a preferred stimulus of a column enhances neuronal responses of layers 2/3 and 5, the output stations of cortical microcircuits, whereas attention suppresses neuronal responses of layer 4, the input station of cortical microcircuits. We demonstrate that the specific modulation pattern of layer-4 activity, which emerges from inter-laminar synaptic connections, is crucial for a rapid shift of attention to a currently unattended stimulus. Our results suggest that top-down signals act differently on different layers of the cortical microcircuit.

Phase-response curves and synchronized neural networks

We review the principal assumptions underlying the application of phase-response curves (PRCs) to synchronization in neuronal networks. The PRC measures how much a given synaptic input perturbs spike timing in a neural oscillator. Among other applications, PRCs make explicit predictions about whether a given network of interconnected neurons will synchronize, as is often observed in cortical structures. Regarding the assumptions of the PRC theory, we conclude: (i) The assumption of noise-tolerant cellular oscillations at or near the network frequency holds in some but not all cases. (ii) Reduced models for PRC-based analysis can be formally related to more realistic models. (iii) Spike-rate adaptation limits PRC-based analysis but does not invalidate it. (iv) The dependence of PRCs on synaptic location emphasizes the importance of improving methods of synaptic stimulation. (v) New methods can distinguish between oscillations that derive from mutual connections and those arising from common drive. (vi) It is helpful to assume linear summation of effects of synaptic inputs; experiments with trains of inputs call this assumption into question. (vii) Relatively subtle changes in network structure can invalidate PRC-based predictions. (viii) Heterogeneity in the preferred frequencies of component neurons does not invalidate PRC analysis, but can annihilate synchronous activity.

Neurophysiological and computational principles of cortical rhythms in cognition

Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.

Roles of inhibitory neurons in rewiring-induced synchronization in pulse-coupled neural networks

The roles of inhibitory neurons in synchronous firing are examined in a network of excitatory and inhibitory neurons with Watts and Strogatz's rewiring. By examining the persistence of the synchronous firing that exists in the random network, it was found that there is a probability of rewiring at which a transition between the synchronous state and the asynchronous state takes place, and the dynamics of the inhibitory neurons play an important role in determining this probability.

Bidirectional plasticity in fast-spiking GABA circuits by visual experience

Experience-dependent plasticity in the brain requires balanced excitation-inhibition. How individual circuit elements contribute to plasticity outcome in complex neocortical networks remains unknown. Here we report an intracellular analysis of ocular dominance plasticity-the loss of acuity and cortical responsiveness for an eye deprived of vision in early life. Unlike the typical progressive loss of pyramidal-cell bias, direct recording from fast-spiking cells in vivo reveals a counterintuitive initial shift towards the occluded eye followed by a late preference for the open eye, consistent with a spike-timing-dependent plasticity rule for these inhibitory neurons. Intracellular pharmacology confirms a dynamic switch of GABA (gamma-aminobutyric acid) impact to pyramidal cells following deprivation in juvenile mice only. Together these results suggest that the bidirectional recruitment of an initially binocular GABA circuit may contribute to experience-dependent plasticity in the developing visual cortex.

Gap junctions between striatal fast-spiking interneurons regulate spiking activity and synchronization as a function of cortical activity

Striatal fast-spiking (FS) interneurons are interconnected by gap junctions into sparsely connected networks. As demonstrated for cortical FS interneurons, these gap junctions in the striatum may cause synchronized spiking, which would increase the influence that FS neurons have on spiking by the striatal medium spiny (MS) neurons. Dysfunction of the basal ganglia is characterized by changes in synchrony or periodicity, thus gap junctions between FS interneurons may modulate synchrony and thereby influence behavior such as reward learning and motor control. To explore the roles of gap junctions on activity and spike synchronization in a striatal FS population, we built a network model of FS interneurons. Each FS connects to 30-40% of its neighbors, as found experimentally, and each FS interneuron in the network is activated by simulated corticostriatal synaptic inputs. Our simulations show that the proportion of synchronous spikes in FS networks with gap junctions increases with increased conductance of the electrical synapse; however, the synchronization effects are moderate for experimentally estimated conductances. Instead, the main tendency is that the presence of gap junctions reduces the total number of spikes generated in response to synaptic inputs in the network. The reduction in spike firing is due to shunting through the gap junctions; which is minimized or absent when the neurons receive coincident inputs. Together these findings suggest that a population of electrically coupled FS interneurons may function collectively as input detectors that are especially sensitive to synchronized synaptic inputs received from the cortex.

Relationship between spontaneous and evoked spike-time correlations in primate visual cortex

Coincident spikes have been implicated in vision-related processes such as feature binding, gain modulation, and long-distance communication. The source of these spike-time correlations is unknown. Although several studies have proposed that cortical spikes are correlated based on stimulus structure, others have suggested that spike-time correlations reflect ongoing cortical activity present even in the absence of a coherent visual stimulus. To examine this issue, we collected single-unit recordings from primary visual cortex (V1) of the anesthetized and paralyzed prosimian bush baby using a 100-electrode array. Spike-time correlations for pairs of cells were compared under three conditions: a moving grating at the cells' preferred orientation, an equiluminant blank screen, and a dark condition with eyes covered. The amplitudes, lags, and widths of cross-correlation histograms (CCHs) were strongly correlated between these conditions although for the blank stimulus and dark condition, the CCHs were broader with peaks lower in amplitude. In both preferred stimulus and blank conditions, the CCH amplitudes were greater when the cells within the pair had overlapping receptive fields and preferred similar orientations rather than nonoverlapping receptive fields and different orientations. These data suggest that spike-time correlations present in evoked activity are generated by mechanisms common to those operating in spontaneous conditions.

Temporal information coding properties of a network of inhibitory interneurons

Inhibitory interneurons are coupled by electrical and inhibitory synapses and exert a powerful control of the discharges of principal cells. In this paper, the transmission properties of excitatory synaptic inputs by a network of interneurons, are studied by using a computational approach. It is shown that both the rise and decay time constants, describing the time course of the excitatory synaptic inputs, have a strong effect on the output jitter of the fired spikes. Similar results were found by changing the values of the other parameters describing the network. Lastly, it is shown that the presence of the electrical coupling between interneurons confers to the network the capability of transmitting, with less temporal spread, the timing information contained in its inputs.

Brain coordination dynamics: true and false faces of phase synchrony and metastability

Understanding the coordination of multiple parts in a complex system such as the brain is a fundamental challenge. We present a theoretical model of cortical coordination dynamics that shows how brain areas may cooperate (integration) and at the same time retain their functional specificity (segregation). This model expresses a range of desirable properties that the brain is known to exhibit, including self-organization, multi-functionality, metastability and switching. Empirically, the model motivates a thorough investigation of collective phase relationships among brain oscillations in neurophysiological data. The most serious obstacle to interpreting coupled oscillations as genuine evidence of inter-areal coordination in the brain stems from volume conduction of electrical fields. Spurious coupling due to volume conduction gives rise to zero-lag (inphase) and antiphase synchronization whose magnitude and persistence obscure the subtle expression of real synchrony. Through forward modeling and the help of a novel colorimetric method, we show how true synchronization can be deciphered from continuous EEG patterns. Developing empirical efforts along the lines of continuous EEG analysis constitutes a major response to the challenge of understanding how different brain areas work together. Key predictions of cortical coordination dynamics can now be tested thereby revealing the essential modus operandi of the intact living brain.

Role of interneuron diversity in the cortical microcircuit for attention

Receptive fields of neurons in cortical area V4 are large enough to fit multiple stimuli, making V4 the ideal place to study the effects of selective attention at the single-neuron level. Experiments have revealed evidence for stimulus competition and have characterized the effect thereon of spatial and feature-based attention. We developed a biophysical model with spiking neurons and conductance-based synapses. To account for the comprehensive set of experimental results, it was necessary to include in the model, in addition to regular spiking excitatory (E) cells, two types of interneurons: feedforward interneurons (FFI) and top-down interneurons (TDI). Feature-based attention was mediated by a projection of the TDI to the FFI, stimulus competition was mediated by a cross-columnar excitatory connection to the FFI, whereas spatial attention was mediated by an increase in activity of the feedforward inputs from cortical area V2. The model predicts that spatial attention increases the FFI firing rate, whereas feature-based attention decreases the FFI firing rate and increases the TDI firing rate. During strong stimulus competition, the E cells were synchronous in the beta frequency range (15-35 Hz), but with feature-based attention, they became synchronous in the gamma frequency range (35-50 Hz). We propose that the FFI correspond to fast-spiking, parvalbumin-positive basket cells and that the TDI correspond to cells with a double-bouquet morphology that are immunoreactive to calbindin or calretinin. Taken together, the model results provide an experimentally testable hypothesis for the behavior of two interneuron types under attentional modulation.

Inhibition potentiates the synchronizing action of electrical synapses

In vivo and in vitro experimental studies have found that blocking electrical interactions connecting GABAergic interneurons reduces oscillatory activity in the gamma range in cortex. However, recent theoretical works have shown that the ability of electrical synapses to promote or impede synchrony, when alone, depends on their location on the dendritic tree of the neurons, the intrinsic properties of the neurons and the connectivity of the network. The goal of the present paper is to show that this versatility in the synchronizing ability of electrical synapses is greatly reduced when the neurons also interact via inhibition. To this end, we study a model network comprising two-compartment conductance-based neurons interacting with both types of synapses. We investigate the effect of electrical synapses on the dynamical state of the network as a function of the strength of the inhibition. We find that for weak inhibition, electrical synapses reinforce inhibition-generated synchrony only if they promote synchrony when they are alone. In contrast, when inhibition is sufficiently strong, electrical synapses improve synchrony even if when acting alone they would stabilize asynchronous firing. We clarify the mechanism underlying this cooperative interplay between electrical and inhibitory synapses. We show that it is relevant in two physiologically observed regimes: spike-to-spike synchrony, where neurons fire at almost every cycle of the population oscillations, and stochastic synchrony, where neurons fire irregularly and at a rate which is substantially lower than the frequency of the global population rhythm.

Synchrony-Induced Attractor Transition in Cortical Neural Networks Organized by Spike-Timing Dependent Plasticity

Recent studies have shown that synchronous neural activity in the cortex area occurs related to behavior or recognition of animals, which suggests that such neural activity involves in information processing. Functions enabled by synchronous firing, however, are still unknown. Results reporting that a transition between recall states of associative memory is induced by external synchronous spikes in a neural network formed by spike-timing dependent plasticity indicate the possibility of a function of synchronous neural activity as a transition signal, requiring further examination using detailed cortical neuron models (AokiAoyagi). We introduced a mathematical model of pyramidal and fast-spiking cortical neurons based on Hodgkin-Huxley, and confirmed the transition between recall states through synchronous spike inputs in detailed neuron models.

Layer and frequency dependencies of phase response properties of pyramidal neurons in rat motor cortex

It is postulated that synchronous firing of cortical neurons plays an active role in cognitive functions of the brain. An important issue is whether pyramidal neurons in different cortical layers exhibit similar tendencies to synchronise. To address this issue, we performed intracellular and whole-cell recordings of regular-spiking pyramidal neurons in slice preparations of the rat motor cortex (18-45 days old) and analysed the phase response curves of these pyramidal neurons in layers 2/3 and 5. The phase response curve represents how an external stimulus affects the timing of spikes immediately after the stimulus in repetitively firing neurons. The phase response curve can be classified into two categories, type 1 (the spike is always advanced) and type 2 (the spike is advanced or delayed depending on the stimulus phase), and are important determinants of whether or not rhythmic synchronization of neuron pairs occurs. We found that pyramidal neurons in layer 2/3 tend to display type-2 phase response curves whereas those in layer 5 tend to exhibit type-1 phase response curves. The differences were prominent particularly in the gamma-frequency range (20-45 Hz). Our results imply that the layer-2/3 pyramidal neurons, when coupled mutually through fast excitatory synapses, may exhibit a much stronger tendency for rhythmic synchronization than layer-5 neurons in the gamma-frequency range.

Neural networks a century after Cajal

At the time of Golgi and Cajal's reception of the Nobel Prize in 1906 most scientists had accepted the notion that neurons are independent units. Although neuroscientists today still believe that neurons are independent anatomical units, functionally, it is thought that some sort of population coding occurs. Throughout this essay, we provide evidence that suggests that populations of neurons can code information through the synchronization of their responses. This synchronization occurs at several levels in the brain. Whereas spike synchrony refers to the correlation between spikes of different neurons' spike trains, oscillatory synchrony refers to the synchronization of oscillatory responses, generally among large groups of neurons. In the first section of this essay we describe the dependence of the brain's developmental processes on synchronous firing and how these processes form a brain that supports and is sensitive to synchronous spikes. Data are then presented that suggest that spike and oscillatory synchrony may serve as useful neural codes. Examples from sensory (auditory, olfactory and somatosensory), motor and higher cognitive (attention, memory) systems are then presented to illustrate potential roles for these synchronous codes in normal brain function. Results from these studies collectively suggest that spike synchrony in sensory and motor systems may provide detail information not available from changes in firing rate. Oscillatory synchrony, on the other hand, may be globally involved in the coordination of long-distance neuronal communication during higher cognitive processes. These concepts represent a dramatic shift in direction since the times of Golgi and Cajal.

Variability v.s. synchronicity of neuronal activity in local cortical network models with different wiring topologies

Dynamical behavior of a biological neuronal network depends significantly on the spatial pattern of synaptic connections among neurons. While neuronal network dynamics has extensively been studied with simple wiring patterns, such as all-to-all or random synaptic connections, not much is known about the activity of networks with more complicated wiring topologies. Here, we examined how different wiring topologies may influence the response properties of neuronal networks, paying attention to irregular spike firing, which is known as a characteristic of in vivo cortical neurons, and spike synchronicity. We constructed a recurrent network model of realistic neurons and systematically rewired the recurrent synapses to change the network topology, from a localized regular and a "small-world" network topology to a distributed random network topology. Regular and small-world wiring patterns greatly increased the irregularity or the coefficient of variation (Cv) of output spike trains, whereas such an increase was small in random connectivity patterns. For given strength of recurrent synapses, the firing irregularity exhibited monotonous decreases from the regular to the random network topology. By contrast, the spike coherence between an arbitrary neuron pair exhibited a non-monotonous dependence on the topological wiring pattern. More precisely, the wiring pattern to maximize the spike coherence varied with the strength of recurrent synapses. In a certain range of the synaptic strength, the spike coherence was maximal in the small-world network topology, and the long-range connections introduced in this wiring changed the dependence of spike synchrony on the synaptic strength moderately. However, the effects of this network topology were not really special in other properties of network activity.

Synchronization of electrically coupled pairs of inhibitory interneurons in neocortex

We performed a systematic analysis of phase locking in pairs of electrically coupled neocortical fast-spiking (FS) and low-threshold-spiking (LTS) interneurons and in a conductance-based model of a pair of FS cells. Phase-response curves (PRCs) were obtained for real interneurons and the model cells. We used PRCs and the theory of weakly coupled oscillators to make predictions about phase-locking characteristics of cell pairs. Phase locking and the robustness of phase-locked states to differences in intrinsic frequencies of cells were directly examined by driving interneuron pairs through a wide range of firing frequencies. Calculations using PRCs accurately predicted that electrical coupling robustly synchronized the firing of interneurons over all frequencies studied (FS, approximately 25-80 Hz; LTS, approximately 10-30 Hz). The synchronizing ability of electrical coupling and the robustness of the phase-locked states were directly dependent on the strength of coupling but not on firing frequency. The FS cell model also predicted the existence of stable antiphase firing at frequencies below approximately 30 Hz, but no evidence for stable antiphase firing was found using the experimentally determined PRCs or in direct measures of phase locking in pairs of interneurons. Despite significant differences in biophysical properties of FS and LTS cells, their phase-locking behavior was remarkably similar. The wide spikes and shallow action potential afterhyperpolarizations of interneurons, compared with the model, prohibited antiphase behavior. Electrical coupling between cortical interneurons of the same type maintained robust synchronous firing of cell pairs for up to approximately 10% heterogeneity in their intrinsic frequencies.

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.

Generalization of coupled spiking models and effects of the width of an action potential on synchronization phenomena

The integrate-and-fire (IF) neuron model and the piecewise-linear version of FitzHugh-Nagumo (PL) neuron model with a time scale parameter mu are frequently being used in the study of synchronization phenomena. Although the two models are regarded to be different type, we show a certain equivalence between them by deriving the coupled IF model of an improved version with a firing duration from the recovery variable coupled system of the PL model, under taking the limit of mu-->0 without a loss of any coupling properties. In the coupled IF model with the duration time, the synchronization behavior of a pair of neurons with excitatory or inhibitory synaptic coupling can be systematically explored in terms of three parameters in the model (synaptic strength, decaying relaxation rate of the synaptic coupling, and the parameter exhibiting the firing duration). We find some irregularly synchronous behavior with or without constant firing order alternations. We show that the duration of an impulse plays an important role in synchronization phenomena.

Analysis of Synchronization Between Two Modules of Pulse Neural Networks with Excitatory and Inhibitory Connections

To study the synchronized oscillations among distant neurons in the visual cortex, we analyzed the synchronization between two modules of pulse neural networks using the phase response function. It was found that the intermodule connections from excitatory to excitatory ensembles tend to stabilize the antiphase synchronization and that the intermodule connections from excitatory to inhibitory ensembles tend to stabilize the in-phase synchronization. It was also found that the intermodule synchronization was more noticeable when the inner-module synchronization was weak.

Bistable network behavior of layer I interneurons in auditory cortex

GABAergic interneurons in many areas of the neocortex are mutually connected via chemical and electrical synapses. Previous computational studies have explored how these coupling parameters influence the firing patterns of interneuronal networks. These models have predicted that the stable states of such interneuronal networks will be either synchrony (near zero phase lag) or antisynchrony (phase lag near one-half of the interspike interval), depending on network connectivity and firing rates. In certain parameter regimens, the network can be bistable, settling into either stable state depending on the initial conditions. Here, we investigated how connectivity parameters influence spike patterns in paired recordings from layer I interneurons in brain slices from juvenile mice. Observed properties of chemical and electrical synapses were used to simulate connections between uncoupled cells via dynamic clamp. In uncoupled pairs, action potentials induced by constant depolarizing currents had randomly distributed phase differences between the two cells. When coupled with simulated chemical (inhibitory) synapses, however, these pairs exhibited a bimodal firing pattern, tending to fire either in synchrony or in antisynchrony. Combining electrical with chemical synapses, prolonging tau(Decay) of inhibitory connections, or increasing the firing rate of the network all resulted in enhanced stability of the synchronous state. Thus, electrical and inhibitory synaptic coupling constrain the relative timing of spikes in a two-cell network to, at most, two stable states, the stability and precision of which depend on the exact parameters of coupling.

Electrical coupling induces bistability of rhythms in networks of inhibitory spiking neurons

Information processing in higher brain structures is thought to rely on the synchronization of spiking neurons. Increasing evidence indicates that, within these structures, inhibitory neurons are linked by both chemical and electrical synapses. However, how synchronized states may emerge from such circuits is not fully understood. Using snail neurons interconnected through a dynamic-clamp system, we show that networks of spiking neurons linked by both reciprocal inhibition and electrical coupling can express two coexisting coordination patterns of different rhythms. One of these patterns consists of antiphase firing of the network partners whereas, in the other, neurons fire synchronously. Switching between patterns may be evoked immediately by transient stimuli, demonstrating bistability of the network. Thus electrical coupling can provide a potent way for instantaneous reconfiguration of activity patterns in inhibitory spiking networks without alteration of intrinsic network properties by modulatory processes.

Contributions of intrinsic membrane dynamics to fast network oscillations with irregular neuronal discharges

During fast oscillations in the local field potential (40-100 Hz gamma, 100-200 Hz sharp-wave ripples) single cortical neurons typically fire irregularly at rates that are much lower than the oscillation frequency. Recent computational studies have provided a mathematical description of such fast oscillations, using the leaky integrate-and-fire (LIF) neuron model. Here, we extend this theoretical framework to populations of more realistic Hodgkin-Huxley-type conductance-based neurons. In a noisy network of GABAergic neurons that are connected randomly and sparsely by chemical synapses, coherent oscillations emerge with a frequency that depends sensitively on the single cell's membrane dynamics. The population frequency can be predicted analytically from the synaptic time constants and the preferred phase of discharge during the oscillatory cycle of a single cell subjected to noisy sinusoidal input. The latter depends significantly on the single cell's membrane properties and can be understood in the context of the simplified exponential integrate-and-fire (EIF) neuron. We find that 200-Hz oscillations can be generated, provided the effective input conductance of single cells is large, so that the single neuron's phase shift is sufficiently small. In a two-population network of excitatory pyramidal cells and inhibitory neurons, recurrent excitation can either decrease or increase the population rhythmic frequency, depending on whether in a neuron the excitatory synaptic current follows or precedes the inhibitory synaptic current in an oscillatory cycle. Detailed single-cell properties have a substantial impact on population oscillations, even though rhythmicity does not originate from pacemaker neurons and is an emergent network phenomenon.

The combined effects of inhibitory and electrical synapses in synchrony

Recent experimental results have shown that GABAergic interneurons in the central nervous system are frequently connected via electrical synapses. Hence, depending on the area or the subpopulation, interneurons interact via inhibitory synapses or electrical synapses alone or via both types of interactions. The theoretical work presented here addresses the significance of these different modes of interactions for the interneuron networks dynamics. We consider the simplest system in which this issue can be investigated in models or in experiments: a pair of neurons, interacting via electrical synapses, inhibitory synapses, or both, and activated by the injection of a noisy external current. Assuming that the couplings and the noise are weak, we derive an analytical expression relating the cross-correlation (CC) of the activity of the two neurons to the phase response function of the neurons. When electrical and inhibitory interactions are not too strong, they combine their effect in a linear manner. In this regime, the effect of electrical and inhibitory interactions when combined can be deduced knowing the effects of each of the interactions separately. As a consequence, depending on intrinsic neuronal properties, electrical and inhibitory synapses may cooperate, both promoting synchrony, or may compete, with one promoting synchrony while the other impedes it. In contrast, for sufficiently strong couplings, the two types of synapses combine in a nonlinear fashion. Remarkably, we find that in this regime, combining electrical synapses with inhibition amplifies synchrony, whereas electrical synapses alone would desynchronize the activity of the neurons. We apply our theory to predict how the shape of the CC of two neurons changes as a function of ionic channel conductances, focusing on the effect of persistent sodium conductance, of the firing rate of the neurons and the nature and the strength of their interactions. These predictions may be tested using dynamic clamp techniques.

Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks

Electrical and chemical synapses exist within the same networks of inhibitory cells, and each kind of synapse is known to be able to foster synchrony among oscillating neurons. Using numerical and analytical techniques, we show here that the electrical and inhibitory coupling play different roles in the synchronization of rhythms in inhibitory networks. The parameter range chosen is motivated by gamma rhythms, in which the gamma-aminobutyric acid type A (GABAA)-mediated inhibition is relatively strong. Under this condition, addition of a small electrical conductance can increase the degree of synchronization far more than a much larger increase in inhibitory conductance. The inhibitory synapses act to eliminate the effects of different initial conditions, whereas the electrical synapses mitigate suppression of firing due to heterogeneity in the network. Analytical techniques include tracking trajectories of coupled cells between spikes; the analysis shows that, in networks in which the degree of excitability is heterogeneous, inhibition can increase the dispersion of the voltages between spikes, whereas electrical coupling reduces such dispersion.