Electrical synapses and synchrony: the role of intrinsic currents

Intrinsic heterogeneity in oscillatory dynamics limits correlation-induced neural synchronization

Synchronous neural oscillations are found throughout the brain and are thought to contribute to neural coding and the propagation of activity. Several proposed mechanisms of synchronization have gained support through combined theoretical and experimental investigation, including mechanisms based on coupling and correlated input. Here, we ask how correlation-induced synchrony is affected by physiological heterogeneity across neurons. To address this question, we examined cell-to-cell differences in phase-response curves (PRCs), which characterize the response of periodically firing neurons to weak perturbations. Using acute slice electrophysiology, we measured PRCs across a single class of principal neurons capable of sensory-evoked oscillations in vivo: the olfactory bulb mitral cells (MCs). Periodically firing MCs displayed a broad range of PRCs, each of which was well fit by a simple three-parameter model. MCs also displayed differences in firing rate-current relationships and in preferred firing rate ranges. Both the observed PRC heterogeneity and moderate firing rate differences (∼10 Hz) separately reduced the maximum correlation-induced synchrony between MCs by up to 25-30%. Simulations further demonstrated that these components of heterogeneity alone were sufficient to account for the difference in synchronization among heterogeneous vs. homogeneous populations in vitro. Within this simulation framework, independent modulation of specific PRC features additionally revealed which aspects of PRC heterogeneity most strongly impact correlation-induced synchronization. Finally, we demonstrated good agreement of novel mathematical theory with our experimental and simulation results, providing a theoretical basis for the influence of heterogeneity on correlation-induced neural synchronization.

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.

Formation of antiwaves in gap-junction-coupled chains of neurons

Using network models consisting of gap-junction-coupled Wang-Buszaki neurons, we demonstrate that it is possible to obtain not only synchronous activity between neurons but also a variety of constant phase shifts between 0 and π. We call these phase shifts intermediate stable phase-locked states. These phase shifts can produce a large variety of wavelike activity patterns in one-dimensional chains and two-dimensional arrays of neurons, which can be studied by reducing the system of equations to a phase model. The 2π periodic coupling functions of these models are characterized by prominent higher order terms in their Fourier expansion, which can be varied by changing model parameters. We study how the relative contribution of the odd and even terms affects what solutions are possible, the basin of attraction of those solutions, and their stability. These models may be applicable to the spinal central pattern generators of the dogfish and also to the developing neocortex of the neonatal rat.

A dynamical pattern recognition model of γ activity in auditory cortex

This paper describes a dynamical process which serves both as a model of temporal pattern recognition in the brain and as a forward model of neuroimaging data. This process is considered at two separate levels of analysis: the algorithmic and implementation levels. At an algorithmic level, recognition is based on the use of Occurrence Time features. Using a speech digit database we show that for noisy recognition environments, these features rival standard cepstral coefficient features. At an implementation level, the model is defined using a Weakly Coupled Oscillator (WCO) framework and uses a transient synchronization mechanism to signal a recognition event. In a second set of experiments, we use the strength of the synchronization event to predict the high gamma (75–150 Hz) activity produced by the brain in response to word versus non-word stimuli. Quantitative model fits allow us to make inferences about parameters governing pattern recognition dynamics in the brain.

Shaping bursting by electrical coupling and noise

Gap-junctional coupling is an important way of communication between neurons and other excitable cells. Strong electrical coupling synchronizes activity across cell ensembles. Surprisingly, in the presence of noise synchronous oscillations generated by an electrically coupled network may differ qualitatively from the oscillations produced by uncoupled individual cells forming the network. A prominent example of such behavior is the synchronized bursting in islets of Langerhans formed by pancreatic β-cells, which in isolation are known to exhibit irregular spiking (Sherman and Rinzel, Biophys J 54:411-425, 1988; Sherman and Rinzel, Biophys J 59:547-559, 1991). At the heart of this intriguing phenomenon lies denoising, a remarkable ability of electrical coupling to diminish the effects of noise acting on individual cells. In this paper, building on an earlier analysis of denoising in networks of integrate-and-fire neurons (Medvedev, Neural Comput 21 (11):3057-3078, 2009) and our recent study of spontaneous activity in a closely related model of the Locus Coeruleus network (Medvedev and Zhuravytska, The geometry of spontaneous spiking in neuronal networks, submitted, 2012), we derive quantitative estimates characterizing denoising in electrically coupled networks of conductance-based models of square wave bursting cells. Our analysis reveals the interplay of the intrinsic properties of the individual cells and network topology and their respective contributions to this important effect. In particular, we show that networks on graphs with large algebraic connectivity (Fiedler, Czech Math J 23(98):298-305, 1973) or small total effective resistance (Bollobas, Modern graph theory, Graduate Texts in Mathematics, vol. 184, Springer, New York, 1998) are better equipped for implementing denoising. As a by-product of the analysis of denoising, we analytically estimate the rate with which trajectories converge to the synchronization subspace and the stability of the latter to random perturbations. These estimates reveal the role of the network topology in synchronization. The analysis is complemented by numerical simulations of electrically coupled conductance-based networks. Taken together, these results explain the mechanisms underlying synchronization and denoising in an important class of biological models.

Expression of gap junction protein connexin36 in multiple subtypes of GABAergic neurons in adult rat somatosensory cortex

To characterize connexin36 (Cx36)-expressing neurons of the adult rat somatosensory cortex, we examined fluorescence signals for Cx36 messenger RNA (mRNA) in 3 nonoverlapping subpopulations of γ-aminobutyric acid (GABA)ergic interneurons, which showed immunoreactivity for 1) parvalbumin (PV); 2) somatostatin (SOM); and 3) either calretinin (CR), vasoactive intestinal polypeptide (VIP), cholecystokinin (CCK), or choline acetyltransferase (ChAT). About 80% of PV-, 52% of SOM-, 37% of CR/VIP/CCK/ChAT-immunoreactive cells displayed Cx36 signals across all cortical layers, and inversely 64%, 25%, and 9% of Cx36-expressing neurons were positive for PV, SOM, or CR/VIP/CCK/ChAT, respectively. Notably, although almost all Cx36-expressing neurons in layer (L) 4, L5, and L6 were positive for one of these markers, a substantial proportion of those in L1 (91%) and L2/3 (10%) were negative for the markers tested, suggesting that other types of neurons might express Cx36. We further investigated the colocalization of Cx36 mRNA and α-actinin2 immunoreactivity, as a marker for late-spiking GABAergic neurons, by using mirror-image sections. Surprisingly, more than 77% of α-actinin2-positive cells displayed Cx36 signals in L1-L3, and about 49% and 13% of Cx36-expressing neurons were positive for α-actinin2 in L1 and L2/3, respectively. These findings suggest that all the subtypes of GABAergic interneurons might form gap junctions in the neocortex.

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.

Robust entrainment of circadian oscillators requires specific phase response curves

The circadian clocks keeping time in many living organisms rely on self-sustained biochemical oscillations entrained by external cues, such as light, to the 24-h cycle induced by Earth's rotation. However, environmental cues are unreliable due to the variability of habitats, weather conditions, or cue-sensing mechanisms among individuals. A tempting hypothesis is that circadian clocks have evolved so as to be robust to fluctuations in the signal that entrains them. To support this hypothesis, we analyze the synchronization behavior of weakly and periodically forced oscillators in terms of their phase response curve (PRC), which measures phase changes induced by a perturbation applied at different times of the cycle. We establish a general relationship between the robustness of key entrainment properties, such as stability and oscillator phase, on the one hand, and the shape of the PRC as characterized by a specific curvature or the existence of a dead zone, on the other hand. The criteria obtained are applied to computational models of circadian clocks and account for the disparate robustness properties of various forcing schemes. Finally, the analysis of PRCs measured experimentally in several organisms strongly suggests a case of convergent evolution toward an optimal strategy for maintaining a clock that is accurate and robust to environmental fluctuations.

Spike-timing-dependent plasticity and reliability optimization: the role of neuron dynamics

Plastic changes in synaptic efficacy can depend on the time ordering of presynaptic and postsynaptic spikes. This phenomenon is called spike-timing-dependent plasticity (STDP). One of the most striking aspects of this plasticity mechanism is that the STDP windows display a great variety of forms in different parts of the nervous system. We explore this issue from a theoretical point of view. We choose as the optimization principle the minimization of conditional entropy or maximization of reliability in the transmission of information. We apply this principle to two types of postsynaptic dynamics, designated type I and type II. The first is characterized as being an integrator, while the second is a resonator. We find that, depending on the parameters of the models, the optimization principle can give rise to a wide variety of STDP windows, such as antisymmetric Hebbian, predominantly depressing or symmetric with one positive region and two lateral negative regions. We can relate each of these forms to the dynamical behavior of the different models. We also propose experimental tests to assess the validity of the optimization principle.

Effects of dendritic load on the firing frequency of oscillating neurons

We study the effects of passive dendritic properties on the dynamics of neuronal oscillators. We find that the addition of a passive dendrite can sometimes have counterintuitive effects on firing frequency. Specifically, the addition of a hyperpolarized passive dendritic load can either increase, decrease, or have negligible effects on firing frequency. We use the theory of weak coupling to derive phase equations for "ball-and-stick" model neurons and two-compartment model neurons. We then develop a framework for understanding how the addition of passive dendrites modulates the frequency of neuronal oscillators. We show that the average value of the neuronal oscillator's phase response curves measures the sensitivity of the neuron's firing rate to the dendritic load, including whether the addition of the dendrite causes an increase or decrease in firing frequency. We interpret this finding in terms of to the slope of the neuronal oscillator's frequency-applied current curve. We also show that equivalent results exist for constant and noisy point-source input to the dendrite. We note that the results are not specific to neurons but are applicable to any oscillator subject to a passive load.

Non-weak inhibition and phase resetting at negative values of phase in cells with fast-slow dynamics at hyperpolarized potentials

Phase response is a powerful concept in the analysis of both weakly and non-weakly perturbed oscillators such as regularly spiking neurons, and is applicable if the oscillator returns to its limit cycle trajectory between successive perturbations. When the latter condition is violated, a formal application of the phase return map may yield phase values outside of its definition domain; in particular, strong synaptic inhibition may result in negative values of phase. The effect of a second perturbation arriving close to the first one is undetermined in this case. However, here we show that for a Morris-Lecar model of a spiking cell with strong time scale separation, extending the phase response function definition domain to an additional negative value branch allows to retain the accuracy of the phase response approach in the face of such strong inhibitory coupling. We use the resulting extended phase response function to accurately describe the response of a Morris-Lecar oscillator to consecutive non-weak synaptic inputs. This method is particularly useful when analyzing the dynamics of three or more non-weakly coupled cells, whereby more than one synaptic perturbation arrives per oscillation cycle into each cell. The method of perturbation prediction based on the negative-phase extension of the phase response function may be applicable to other excitable cell models characterized by slow voltage dynamics at hyperpolarized potentials.

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.

Signal transmission, conversion and multiplication by polar molecules confined in nanochannels

The mechanism of signal transmission, conversion and multiplication at molecular level has been of great interest lately, due to its wide applications in nanoscience and nanotechnology. The interferences between authentic signals and thermal noises at the nanoscale make it difficult for molecular signal transduction. Here we review some of our recent progress on the signal transduction mediated by water and other polar molecules confined in nanochannels, such as Y-shaped carbon nanotubes. We also explore possible future directions in this emerging field. These studies on molecular signal conduction might have significance in future designs and applications of nanoscale electronic devices, and might also provide useful insights for a better understanding of signal conduction in both physical and biological systems.

Rapid desynchronization of an electrically coupled interneuron network with sparse excitatory synaptic input

Electrical synapses between interneurons contribute to synchronized firing and network oscillations in the brain. However, little is known about how such networks respond to excitatory synaptic input. To investigate this, we studied electrically coupled Golgi cells (GoC) in the cerebellar input layer. We show with immunohistochemistry, electron microscopy, and electrophysiology that Connexin-36 is necessary for functional gap junctions (GJs) between GoC dendrites. In the absence of coincident synaptic input, GoCs synchronize their firing. In contrast, sparse, coincident mossy fiber input triggered a mixture of excitation and inhibition of GoC firing and spike desynchronization. Inhibition is caused by propagation of the spike afterhyperpolarization through GJs. This triggers network desynchronization because heterogeneous coupling to surrounding cells causes spike-phase dispersion. Detailed network models predict that desynchronization is robust, local, and dependent on synaptic input properties. Our results show that GJ coupling can be inhibitory and either promote network synchronization or trigger rapid network desynchronization depending on the synaptic input.

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.

Enhanced functions of electrical junctions

Electrical synapses and synchrony are nearly synonymous. In this issue of Neuron, Vervaeke et al. broaden this longstanding association. They found that in the Golgi cell network of the cerebellum, electrical synapses synchronize resting activity, and cause surround inhibition and desynchronization in response to excitatory input.

Phase-resetting curve determines how BK currents affect neuronal firing

BK channels are large conductance potassium channels gated by calcium and voltage. Paradoxically, blocking these channels has been shown experimentally to increase or decrease the firing rate of neurons, depending on the neural subtype and brain region. The mechanism for how this current can alter the firing rates of different neurons remains poorly understood. Using phase-resetting curve (PRC) theory, we determine when BK channels increase or decrease the firing rates in neural models. The addition of BK currents always decreases the firing rate when the PRC has only a positive region. When the PRC has a negative region (type II), BK currents can increase the firing rate. The influence of BK channels on firing rate in the presence of other conductances, such as I(m) and I(h), as well as with different amplitudes of depolarizing input, were also investigated. These results provide a formal explanation for the apparently contradictory effects of BK channel antagonists on firing rates.

Pulse coupled oscillators and the phase resetting curve

Limit cycle oscillators that are coupled in a pulsatile manner are referred to as pulse coupled oscillators. In these oscillators, the interactions take the form of brief pulses such that the effect of one input dies out before the next is received. A phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike in an oscillatory neuron depending upon where in the cycle the input is applied. PRCs can be used to predict phase locking in networks of pulse coupled oscillators. In some studies of pulse coupled oscillators, a specific form is assumed for the interactions between oscillators, but a more general approach is to formulate the problem assuming a PRC that is generated using a perturbation that approximates the input received in the real biological network. In general, this approach requires that circuit architecture and a specific firing pattern be assumed. This allows the construction of discrete maps from one event to the next. The fixed points of these maps correspond to periodic firing modes and are easier to locate and analyze for stability compared to locating and analyzing periodic modes in the original network directly. Alternatively, maps based on the PRC have been constructed that do not presuppose a firing order. Specific circuits that have been analyzed under the assumption of pulsatile coupling include one to one lockings in a periodically forced oscillator or an oscillator forced at a fixed delay after a threshold event, two bidirectionally coupled oscillators with and without delays, a unidirectional N-ring of oscillators, and N all-to-all networks.

Electrical coupling promotes fidelity of responses in the networks of model neurons

We consider an integrate-and-fire element subject to randomly perturbed synaptic input and an electrically coupled ensemble of such elements. The latter is interpreted as either a model of electrically coupled population of neurons or a multicompartment model of a dendrite. Random fluctuations blur the input signal and cause false responses in the system dynamics. For instance, under the influence of noise, the system may respond with an action potential to a subthreshold stimulus. We show that the responses of the elements within the network are more reliable than the responses of the same elements in isolation. Specifically, we show that the variances of the stochastic processes generated by the coupled model can be made arbitrarily small (i.e., the network responses can be made arbitrarily accurate) by increasing the number of elements in the network and the strength of electrical coupling. Our results suggest that the organization of cells in electrically coupled groups on the network level, or the dendritic morphology on the cellular level, may be involved in the filtering noise and therefore may play an important role in the information processing mechanisms operating on the network or cellular level respectively.

Firing patterns and synchronization in nonsynaptic epileptiform activity: the effect of gap junctions modulated by potassium accumulation

Several lines of evidence point to the modification of firing patterns and of synchronization due to gap junctions (GJs) as having a role in the establishment of epileptiform activity (EA). However, previous studies consider GJs as ohmic resistors, ignoring the effects of intense variations in ionic concentration known to occur during seizures. In addition to GJs, extracellular potassium is regarded as a further important factor involved in seizure initiation and sustainment. To analyze how these two mechanisms act together to shape firing and synchronization, we use a detailed computational model for in vitro high-K(+) and low-Ca(2+) nonsynaptic EA. The model permits us to explore the modulation of electrotonic interactions under ionic concentration changes caused by electrodiffusion in the extracellular space, altered by tortuosity. In addition, we investigate the special case of null GJ current. Increased electrotonic interaction alters bursts and action potential frequencies, favoring synchronization. The particularities of pattern changes depend on the tortuosity and array size. Extracellular potassium accumulation alone modifies firing and synchronization when the GJ coupling is null.

A novel role of dendritic gap junction and mechanisms underlying its interaction with thalamocortical conductance in fast spiking inhibitory neurons

BACKGROUND

Little is known about the roles of dendritic gap junctions (GJs) of inhibitory interneurons in modulating temporal properties of sensory induced responses in sensory cortices. Electrophysiological dual patch-clamp recording and computational simulation methods were used in combination to examine a novel role of GJs in sensory mediated feed-forward inhibitory responses in barrel cortex layer IV and its underlying mechanisms.

RESULTS

Under physiological conditions, excitatory post-junctional potentials (EPJPs) interact with thalamocortical (TC) inputs within an unprecedented few milliseconds (i.e. over 200 Hz) to enhance the firing probability and synchrony of coupled fast-spiking (FS) cells. Dendritic GJ coupling allows fourfold increase in synchrony and a significant enhancement in spike transmission efficacy in excitatory spiny stellate cells. The model revealed the following novel mechanisms: 1) rapid capacitive current (Icap) underlies the activation of voltage-gated sodium channels; 2) there was less than 2 milliseconds in which the Icap underlying TC input and EPJP was coupled effectively; 3) cells with dendritic GJs had larger input conductance and smaller membrane response to weaker inputs; 4) synchrony in inhibitory networks by GJ coupling leads to reduced sporadic lateral inhibition and increased TC transmission efficacy.

CONCLUSION

Dendritic GJs of neocortical inhibitory networks can have very powerful effects in modulating the strength and the temporal properties of sensory induced feed-forward inhibitory and excitatory responses at a very high frequency band (>200 Hz). Rapid capacitive currents are identified as main mechanisms underlying interaction between two transient synaptic conductances.

Electrical coupling mediates tunable low-frequency oscillations and resonance in the cerebellar Golgi cell network

Tonic motor control involves oscillatory synchronization of activity at low frequency (5-30 Hz) throughout the sensorimotor system, including cerebellar areas. We investigated the mechanisms underpinning cerebellar oscillations. We found that Golgi interneurons, which gate information transfer in the cerebellar cortex input layer, are extensively coupled through electrical synapses. When depolarized in vitro, these neurons displayed low-frequency oscillatory synchronization, imposing rhythmic inhibition onto granule cells. Combining experiments and modeling, we show that electrical transmission of the spike afterhyperpolarization is the essential component for oscillatory population synchronization. Rhythmic firing arises in spite of strong heterogeneities, is frequency tuned by the mean excitatory input to Golgi cells, and displays pronounced resonance when the modeled network is driven by oscillating inputs. In vivo, unitary Golgi cell activity was found to synchronize with low-frequency LFP oscillations occurring during quiet waking. These results suggest a major role for Golgi cells in coordinating cerebellar sensorimotor integration during oscillatory interactions.

Predicting synchronous and asynchronous network groupings of hippocampal interneurons coupled with dendritic gap junctions

Direct electrical communication between central nervous system (CNS) neurons including those in the hippocampus is well-established. This form of communication is mediated by gap junctions and it is known that this coupling is important for brain rhythms such as gamma (20-80 Hz) which occur during active behavioural states. It is also known that gap junctions are present at several locations along the dendrites of hippocampal interneurons including parvalbumin-positive basket cell types. Weakly coupled oscillator theory, which uses phase response curves (PRCs), has been used to understand and predict the dynamics of electrically coupled networks. Here we use compartmental models of hippocampal basket cells with different levels of basal and apical spike attenuation together with the theory to show that network output can be broken down into three groupings: synchronous, asynchronous and antiphase-like patterns. Moreover, quantified PRCs can be used as a rule of thumb to determine the occurrence of a particular grouping under weak coupling conditions, which in turn implies that spike delays are critical factors in determining network output. In moving beyond weak coupling to encompass the full physiological regime of coupling strengths with network simulations, we note that it is important to be able to differentiate between these different groupings as it affects how the network responds with modulation. Specifically, an asynchronous grouping provides more dynamic richness as a larger range of phase-locked states can be expressed with strength changes. From a functional viewpoint it may be that modulation of electrically coupled networks are key to controlling cell assemblies that contribute to information coding brain substrates.

Electrical Synapses Between AII Amacrine Cells: Dynamic Range and Functional Consequences of Variation in Junctional Conductance

AII amacrine cells form a network of electrically coupled interneurons in the mammalian retina and tracer coupling studies suggest that the junctional conductance ( Gj) can be modulated. However, the dynamic range of Gjand the functional consequences of varying Gjover the dynamic range are unknown. Here we use whole cell recordings from pairs of coupled AII amacrine cells in rat retinal slices to provide direct evidence for physiological modulation of Gj, appearing as a time-dependent increase from about 500 pS to a maximum of about 3,000 pS after 30–90 min of recording. The increase occurred in recordings with low- but not high-resistance pipettes, suggesting that it was related to intracellular washout and perturbation of a modulatory system. Computer simulations of a network of electrically coupled cells verified that our recordings were able to detect and quantify changes in Gjover a large range. Dynamic-clamp electrophysiology, with insertion of electrical synapses between AII amacrine cells, allowed us to finely and reversibly control Gjwithin the same range observed for physiologically coupled cells and to examine the quantitative relationship between Gjand steady-state coupling coefficient, synchronization of subthreshold membrane potential fluctuations, synchronization and transmission of action potentials, and low-pass filter characteristics. The range of Gjvalues over which signal transmission was modulated depended strongly on the specific functional parameter examined, with the largest range observed for action potential transmission and synchronization, suggesting that the full range of Gjvalues observed during spontaneous run-up of coupling could represent a physiologically relevant dynamic range.

Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities

We investigate how synchrony can be generated or induced in networks of electrically coupled integrate-and-fire neurons subject to noisy and heterogeneous inputs. Using analytical tools, we find that in a network under constant external inputs, synchrony can appear via a Hopf bifurcation from the asynchronous state to an oscillatory state. In a homogeneous net work, in the oscillatory state all neurons fire in synchrony, while in a heterogeneous network synchrony is looser, many neurons skipping cycles of the oscillation. If the transmission of action potentials via the electrical synapses is effectively excitatory, the Hopf bifurcation is supercritical, while effectively inhibitory transmission due to pronounced hyperpolarization leads to a subcritical bifurcation. In the latter case, the network exhibits bistability between an asynchronous state and an oscillatory state where all the neurons fire in synchrony. Finally we show that for time-varying external inputs, electrical coupling enhances the synchronization in an asynchronous network via a resonance at the firing-rate frequency.

Pyramidal neurons switch from integrators in vitro to resonators under in vivo-like conditions

During wakefulness, pyramidal neurons in the intact brain are bombarded by synaptic input that causes tonic depolarization, increased membrane conductance (i.e., shunting), and noisy fluctuations in membrane potential; by comparison, pyramidal neurons in acute slices typically experience little background input. Such differences in operating conditions can compromise extrapolation of in vitro data to explain neuronal operation in vivo. For instance, pyramidal neurons have been identified as integrators (i.e., class 1 neurons according to Hodgkin's classification of intrinsic excitability) based on in vitro experiments but that classification is inconsistent with the ability of hippocampal pyramidal neurons to oscillate/resonate at theta frequency since intrinsic oscillatory behavior is limited to class 2 neurons. Using long depolarizing stimuli and dynamic clamp to reproduce in vivo-like conditions in slice experiments, we show that CA1 hippocampal pyramidal cells switch from integrators to resonators, i.e., from class 1 to class 2 excitability. The switch is explained by increased outward current contributed by the M-type potassium current I(M), which shifts the balance of inward and outward currents active at perithreshold potentials and thereby converts the spike-initiating mechanism as predicted by dynamical analysis of our computational model. Perithreshold activation of I(M) is enhanced by the depolarizing shift in spike threshold caused by shunting and/or sodium channel inactivation secondary to tonic depolarization. Our conclusions were validated by multiple comparisons between simulation and experimental data. Thus even so-called "intrinsic" properties may differ qualitatively between in vitro and in vivo conditions.

Multifunctional pattern-generating circuits

The ability of distinct anatomical circuits to generate multiple behavioral patterns is widespread among vertebrate and invertebrate species. These multifunctional neuronal circuits are the result of multistable neural dynamics and modular organization. The evidence suggests multifunctional circuits can be classified by distinct architectures, yet the activity patterns of individual neurons involved in more than one behavior can vary dramatically. Several mechanisms, including sensory input, the parallel activity of projection neurons, neuromodulation, and biomechanics, are responsible for the switching between patterns. Recent advances in both analytical and experimental tools have aided the study of these complex circuits.

Chemical transmission between dopaminergic neuron pairs

Midbrain dopaminergic (DAergic) neurons play a major regulatory role in in goal-directed behavior and reinforcement learning. DAergic neuron activity, and therefore spatiotemporal properties of dopamine release, precisely encodes reward signals. Neuronal activity is shaped both by external afferences and local interactions (chemical and electrical transmissions). Numerous hints suggest the existence of chemical interactions between DAergic neurons, but direct evidence and characterization are still lacking. Here, we show, using dual patch-clamp recordings in rat brain slices, a widespread bidirectional chemical transmission between DAergic neuron pairs. Hyperpolarizing postsynaptic potentials were partially mediated by D2-like receptors, and entirely resulted from the inhibition of the hyperpolarization-activated depolarizing current (Ih). These results constitute the first evidence in paired recordings of a chemical transmission relying on conductance decrease in mammals. In addition, we show that chemical transmission and electrical synapses frequently coexist within the same neuron pair and dynamically interact to shape DAergic neuron activity.

Sustained rhythmic activity in gap-junctionally coupled networks of model neurons depends on the diameter of coupled dendrites

Gap junctions are known to be important for many network functions such as synchronization of activity and the generation of waves and oscillations. Gap junctions have also been proposed to be essential for the generation of early embryonic activity. We have previously shown that the amplitude of electrical signals propagating across gap-junctionally coupled passive cables is maximized at a unique diameter. This suggests that threshold-dependent signals may propagate through gap junctions for a finite range of diameters around this optimal value. Here we examine the diameter dependence of action potential propagation across model networks of dendro-dendritically coupled neurons. The neurons in these models have passive soma and dendrites and an action potential-generating axon. We show that propagation of action potentials across gap junctions occurs only over a finite range of dendritic diameters and that propagation delay depends on this diameter. Additionally, in networks of gap-junctionally coupled neurons, rhythmic activity can emerge when closed loops (re-entrant paths) occur but again only for a finite range of dendrite diameters. The frequency of such rhythmic activity depends on the length of the path and the dendrite diameter. For large networks of randomly coupled neurons, we find that the re-entrant paths that underlie rhythmic activity also depend on dendrite diameter. These results underline the potential importance of dendrite diameter as a determinant of network activity in gap-junctionally coupled networks, such as network rhythms that are observed during early nervous system development.

Mechanisms of firing patterns in fast-spiking cortical interneurons

Cortical fast-spiking (FS) interneurons display highly variable electrophysiological properties. Their spike responses to step currents occur almost immediately following the step onset or after a substantial delay, during which subthreshold oscillations are frequently observed. Their firing patterns include high-frequency tonic firing and rhythmic or irregular bursting (stuttering). What is the origin of this variability? In the present paper, we hypothesize that it emerges naturally if one assumes a continuous distribution of properties in a small set of active channels. To test this hypothesis, we construct a minimal, single-compartment conductance-based model of FS cells that includes transient Na⁺, delayed-rectifier K⁺, and slowly inactivating d-type K⁺ conductances. The model is analyzed using nonlinear dynamical system theory. For small Na⁺ window current, the neuron exhibits high-frequency tonic firing. At current threshold, the spike response is almost instantaneous for small d-current conductance, g_d, and it is delayed for larger g_d. As g_d further increases, the neuron stutters. Noise substantially reduces the delay duration and induces subthreshold oscillations. In contrast, when the Na⁺ window current is large, the neuron always fires tonically. Near threshold, the firing rates are low, and the delay to firing is only weakly sensitive to noise; subthreshold oscillations are not observed. We propose that the variability in the response of cortical FS neurons is a consequence of heterogeneities in their g_d and in the strength of their Na⁺ window current. We predict the existence of two types of firing patterns in FS neurons, differing in the sensitivity of the delay duration to noise, in the minimal firing rate of the tonic discharge, and in the existence of subthreshold oscillations. We report experimental results from intracellular recordings supporting this prediction.

About 25% of the neurons in the mammalian neocortex are inhibitory, namely reduce the activity of neurons they contact. These inhibitory neurons exhibit diversity of morphological, chemical, and biophysical properties, and their classification has recently been the focus of much debate. Even neurons belonging to a single class of “fast-spiking” (FS) display a large variety of firing patterns in response to standard square current pulses. Previous works proposed that this class is in fact a discrete set of neuronal subtypes with biophysical properties differing in a discontinuous way. In this work, we propose an alternative theory, according to which the biophysical properties of FS neurons are continuously distributed, but distinct firing patterns emerge due to highly nonlinear dynamics of these neurons. We ascertain this theory by exploring with mathematical techniques a biophysically based model of FS neurons. We demonstrate that variable firing responses of cortical FS neurons can be accounted for if one assumes heterogeneity in the strength of some of the ionic conductances underlying neuronal activity. Our theory predicts the existence of two main firing patterns of FS neurons. This prediction is verified by direct recordings in cortical slices.

Electrical synapses in basal ganglia

The basal ganglia (BG) provide a major integrative system of the forebrain involved in the organization of goal-directed behaviour. Pathological alteration of BG function leads to major motor and cognitive impairments such as observed in Parkinson's disease. Recent advances in BG research stress the role of neural oscillations and synchronization in the normal and pathological function of BG. As demonstrated in several brain structures, these patterns of neural activity can emerge from electrically coupled neuronal networks. This review aims at addressing the presence, functionality and putative role of electrical synapses in BG, with a particular emphasis on the striatum and the substantia nigra pars compacta (SNc), two main BG nuclei in which the existence and functional properties of neuronal coupling are best documented.

Sensitivity versus resonance in two-dimensional spiking-bursting neuron models

Through phase plane analysis of a class of two-dimensional spiking and bursting neuron models, covering some of the most popular map-based neuron models, we show that there exists a trade-off between the sensitivity of the neuron to steady external stimulation and its resonance properties, and how this trade-off may be tuned by the neutral or asymptotic character of the slow variable. Implications of the results for the suprathreshold behavior of the neurons, both by themselves and as part of networks, are presented in different regimes of interest, such as the excitable, regular spiking, and bursting regimes. These results establish a consistent link between single-neuron parameters and resulting network dynamics, and will hopefully be useful as a guide for modeling.

Synaptic mechanisms of synchronized gamma oscillations in inhibitory interneuron networks

Gamma frequency oscillations are thought to provide a temporal structure for information processing in the brain. They contribute to cognitive functions, such as memory formation and sensory processing, and are disturbed in some psychiatric disorders. Fast-spiking, parvalbumin-expressing, soma-inhibiting interneurons have a key role in the generation of these oscillations. Experimental analysis in the hippocampus and the neocortex reveals that synapses among these interneurons are highly specialized. Computational analysis further suggests that synaptic specialization turns interneuron networks into robust gamma frequency oscillators.

Response Properties and Synchronization of Rhythmically Firing Dendritic Neurons

The responsiveness of rhythmically firing neurons to synaptic inputs is characterized by their phase-response curve (PRC), which relates how weak somatic perturbations affect the timing of the next action potential. The shape of the somatic PRC is an important determinant of collective network dynamics. Here we study theoretically and experimentally the impact of distally located synapses and dendritic nonlinearities on the synchronization properties of rhythmically firing neurons. By combining the theories of quasi-active cables and phase-coupled oscillators we derive an approximation for the dendritic responsiveness, captured by the neuron's dendritic PRC (dPRC). This closed-form expression indicates that the dPRCs are linearly filtered versions of the somatic PRC and that the filter characteristics are determined by the passive and active properties of the dendrite. The passive properties induce leftward shifts in the dPRCs and attenuate them. Our analysis yields a single dimensionless parameter that classifies active dendritic conductances as either regenerative conductances that counter the passive properties by boosting the dPRCs or restorative conductances that high-pass filter the dPRCs. Thus dendritic properties can generate a qualitative difference between the somatic and dendritic PRCs. As a result collective dynamics can be qualitatively different depending on the location of the synapse, the neuronal firing rates, and the dendritic nonlinearities. Finally, we use dual whole cell recordings from the soma and apical dendrite of cortical pyramidal neurons to test these predictions and find that empirical dPRCs are shifted leftward, as predicted, but may also display high-pass characteristics resulting from the restorative dendritic HCN (h) current.

The synchronization properties of a network of inhibitory interneurons depend on the biophysical model

The synchronization properties of a pair of coupled fast spiking interneurons are studied by using the theory of weakly coupled oscillators. Four different biophysical models of the single fast spiking interneuron are used and the corresponding results are compared. It is shown that for a pair of identical coupled cells, the synchronization properties are model-dependent. In particular, the firing coherence of the network is strongly affected by the reversal potential, the kinetics of the inhibitory postsynaptic current and the electrical coupling; the activation properties of the sodium and potassium currents play a significant role too.

On the dynamics of electrically-coupled neurons with inhibitory synapses

We study the dynamics and bifurcations of noise-free neurons coupled by gap junctions and inhibitory synapses, using both delayed delta functions and alpha functions to model the latter. We focus on the case of two cells, as in the studies of Chow and Kopell (2000) and Lewis and Rinzel (2003), but also show that stable asynchronous splay states exist for globally coupled networks of N cells dominated by subthreshold electrical coupling. Our results agree with those of Lewis and Rinzel (2003) in the weak coupling range, but our Poincaré map analysis yields more information about global behavior and domains of attraction, and we show that the explicit discontinuous maps derived using delayed delta functions compare well with the continuous history-dependent, implicitly-defined maps derived from alpha functions. We find that increased bias currents, super-threshold electrical coupling and synaptic delays promote synchrony, while sub-threshold electrical coupling and fast synapses promote asynchrony. We compare our analytical results with simulations of an ionic current model of spiking cells, and briefly discuss implications for stimulus response modes of locus coeruleus and for central pattern generators.

Gap junctions destroy persistent states in excitatory networks

Gap junctions between excitatory neurons are shown to disrupt the persistent state. The asynchronous state of the network loses stability via a Hopf bifurcation and then the active state is destroyed via a homoclinic bifurcation with a stationary state. A partial differential equation (PDE) is developed to analyze the Hopf and the homoclinic bifurcations. The simplified dynamics are compared to a biophysical model where similar behavior is observed. In the low noise case, the dynamics of the PDE is shown to be very complicated and includes possible chaotic behavior. The onset of synchrony is studied by the application of averaging to obtain a simple criterion for destabilization of the asynchronous persistent state.

Signal transmission between gap-junctionally coupled passive cables is most effective at an optimal diameter

We analyze simple morphological configurations that represent gap-junctional coupling between neuronal processes or between muscle fibers. Specifically, we use cable theory and simulations to examine the consequences of current flow from one cable to other gap-junctionally coupled passive cables. When the proximal end of the first cable is voltage clamped, the amplitude of the electrical signal in distal portions of the second cable depends on the cable diameter. However, this amplitude does not simply increase if cable diameter is increased, as expected from the larger length constant; instead, an optimal diameter exists. The optimal diameter arises because the dependency of voltage attenuation along the second cable on cable diameter follows two opposing rules. As cable diameter increases, the attenuation decreases because of a larger length constant yet increases because of a reduction in current density arising from the limiting effect of the gap junction on current flow into the second cable. The optimal diameter depends on the gap junction resistance and cable parameters. In branched cables, dependency on diameter is local and thus may serve to functionally compartmentalize branches that are coupled to other cells. Such compartmentalization may be important when periodic signals or action potentials cause the current flow across gap junctions.

How Noise Affects the Synchronization Properties of Recurrent Networks of Inhibitory Neurons

GABAergic interneurons play a major role in the emergence of various types of synchronous oscillatory patterns of activity in the central nervous system. Motivated by these experimental facts, modeling studies have investigated mechanisms for the emergence of coherent activity in networks of inhibitory neurons. However, most of these studies have focused either when the noise in the network is absent or weak or in the opposite situation when it is strong. Hence, a full picture of how noise affects the dynamics of such systems is still lacking. The aim of this letter is to provide a more comprehensive understanding of the mechanisms by which the asynchronous states in large, fully connected networks of inhibitory neurons are destabilized as a function of the noise level. Three types of single neuron models are considered: the leaky integrate-and-fire (LIF) model, the exponential integrate-and-fire (EIF), model and conductance-based models involving sodium and potassium Hodgkin-Huxley (HH) currents. We show that in all models, the instabilities of the asynchronous state can be classified in two classes. The first one consists of clustering instabilities, which exist in a restricted range of noise. These instabilities lead to synchronous patterns in which the population of neurons is broken into clusters of synchronously firing neurons. The irregularity of the firing patterns of the neurons is weak. The second class of instabilities, termed oscillatory firing rate instabilities, exists at any value of noise. They lead to cluster state at low noise. As the noise is increased, the instability occurs at larger coupling, and the pattern of firing that emerges becomes more irregular. In the regime of high noise and strong coupling, these instabilities lead to stochastic oscillations in which neurons fire in an approximately Poisson way with a common instantaneous probability of firing that oscillates in time.

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.

Distal gap junctions and active dendrites can tune network dynamics

Gap junctions allow direct electrical communication between CNS neurons. From theoretical and modeling studies, it is well known that although gap junctions can act to synchronize network output, they can also give rise to many other dynamic patterns including antiphase and other phase-locked states. The particular network pattern that arises depends on cellular, intrinsic properties that affect firing frequencies as well as the strength and location of the gap junctions. Interneurons or GABAergic neurons in hippocampus are diverse in their cellular characteristics and have been shown to have active dendrites. Furthermore, parvalbumin-positive GABAergic neurons, also known as basket cells, can contact one another via gap junctions on their distal dendrites. Using two-cell network models, we explore how distal electrical connections affect network output. We build multi-compartment models of hippocampal basket cells using NEURON and endow them with varying amounts of active dendrites. Two-cell networks of these model cells as well as reduced versions are explored. The relationship between intrinsic frequency and the level of active dendrites allows us to define three regions based on what sort of network dynamics occur with distal gap junction coupling. Weak coupling theory is used to predict the delineation of these regions as well as examination of phase response curves and distal dendritic polarization levels. We find that a nonmonotonic dependence of network dynamic characteristics (phase lags) on gap junction conductance occurs. This suggests that distal electrical coupling and active dendrite levels can control how sensitive network dynamics are to gap junction modulation. With the extended geometry, gap junctions located at more distal locations must have larger conductances for pure synchrony to occur. Furthermore, based on simulations with heterogeneous networks, it may be that one requires active dendrites if phase-locking is to occur in networks formed with distal gap junctions.

Quinine, a blocker of neuronal cx36 channels, suppresses seizure activity in rat neocortex in vivo

PURPOSE

The selective contribution of neuronal gap junction (GJ) communication via connexin 36 (Cx36) channels to epileptogenesis and to the maintenance and propagation of seizures was investigated in both the primary focus and the mirror focus by using pharmacologic approaches with the 4-aminopyridine in vivo epilepsy model.

METHODS

ECoG recording was performed on anesthetized adult rats, in which either quinine, a selective blocker of Cx36, or the broad-spectrum GJ blockers carbenoxolone and octanol were applied locally, before the induction or at already active epileptic foci.

RESULTS

The blockade of Cx36 channels by quinine before the induction of epileptiform activity slightly reduced the epileptogenesis. When quinine was applied after 25-30 repetitions of seizures, a new discharge pattern appeared with frequencies >15 Hz at the initiation of seizures. In spite of the increased number of seizures, the summated ictal activity decreased, because of the significant reduction in the duration of the seizures. The amplitudes of the seizure discharges of all the patterns decreased, with the exception of those with frequencies of 11-12 Hz. The blockade of Cx36 channels and the global blockade of the GJ channels resulted in qualitatively different modifications in ictogenesis.

CONCLUSIONS

The blockade of Cx36 channels at the already active epileptic focus has an anticonvulsive effect and modifies the manifestation of the 1- to 18-Hz seizure discharges. Our findings indicate that the GJ communication via Cx36 channels is differently involved in the synchronization of the activities of the networks generating seizure discharges with different frequencies. Additionally, we conclude that both neuronal and glial GJ communication contribute to the manifestation and propagation of seizures in the adult rat neocortex.

Analytical solution of the cable equation with synaptic reversal potentials for passive neurons with tip-to-tip dendrodendritic coupling

A passive cable model is presented for a pair of electrotonically coupled neurons in order to investigate the effects of tip-to-tip dendrodendritic gap junctions on the interaction between excitation and either pre or postsynaptic inhibition. The model represents each dendritic tree by a tapered equivalent cylinder attached to an isopotential soma. Analytical solution of the cable equation with synaptic reversal potentials is considered for each neuron to yield a system of Volterra integral equations for the voltage. The solution to the system of linear integral equations (expressed as a Neumann series) is used to determine the current spread within the two coupled neurons, and to re-examine the sensitivity of the soma potentials (in particular) to the coupling resistance for various loci of synaptic inputs. The model is actually posed generally, so that active as well as passive properties could be considered. In the active case, a system of non-linear integral equations is derived for the voltage.

Predicting mutual entrainment of oscillators with experiment-based phase models

We show that mutual entrainment in interacting oscillators can be characterized using phase models that are developed from direct experiments with a single oscillator. The models are used to predict order-disorder transitions in populations and the dependence of order on system parameters; the description is verified in independent experiments in sets of chemical oscillators. The experiment-based model properly describes in-phase and antiphase mutual entrainment with positive and negative interactions in small sets as well as dynamical clustering in populations of oscillators.

Gap junctions promote synchronous activities in a network of inhibitory interneurons

By using a single compartment biophysical model of a fast spiking interneuron the synchronization properties of a pair of cells, coupled by electrical and inhibitory synapses, are investigated. The inhibitory and excitatory synaptic couplings are modeled in order to reproduce the experimental time course of the corresponding currents. It is shown that increasing the conductance value of the electrical synapses enhances the synchronization between the spike trains of the two cells. Moreover, increasing either the decay time constant of the inhibitory current or the firing frequency of the cells favours the emergence of synchronous discharges.

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.

The role of distal dendritic gap junctions in synchronization of mitral cell axonal output

One of the first and most important stages of odor processing occurs in the glomerular units of the olfactory bulb and most likely involves mitral cell synchronization. Using a detailed model constrained by a number of experimental findings, we show how the intercellular coupling mediated by intraglomerular gap junctions (GJs) in the tuft dendrites could play a major role in sychronization of mitral cell action potential output in spite of their distal dendritic location. The model suggests that the high input resistance and active properties of the fine tuft dendrites are instrumental in generating local spike synchronization and an efficient forward and backpropagation of action potentials between the tuft and the soma. The model also gives insight into the physiological significance of long primary dendrites in mitral cells, and provides evidence against the use of reduced single compartmental models to investigate network properties of cortical pyramidal neurons.

Phase-response curves give the responses of neurons to transient inputs

Neuronal firing is determined largely by incoming barrages of excitatory postsynaptic potentials (EPSPs), each of which produce a transient increase in firing probability. To measure the effects of weak transient inputs on firing probability of cortical neurons, we compute phase-response curves (PRCs). PRCs, whose shape can be related to the dynamics of spike generation, document the changes in timing of spikes caused by an EPSP in a repetitively firing neuron as a function of when it arrives in the interspike interval (ISI). The PRC can be exactly related to the poststimulus time histogram (PSTH) so that knowledge of one uniquely determines the other. Typically, PRCs have zero values at the start and end of the ISI, where EPSPs have minimal effects and a peak in the middle. Where the peak occurs depends in part on the firing properties of neurons. The PRC can have regions of positivity and negativity corresponding respectively to speeding up and slowing down the time of the next spike. A simple canonical model for spike generation is introduced that shows how both the background firing rate and the degree of postspike afterhyperpolarization contribute to the shape of the PRC and thus to the PSTH. PRCs in strongly adapting neurons are highly skewed to the right (indicating a higher change in probability when the EPSPs appear late in the ISI) and can have negative regions (indicating a decrease in firing probability) early in the ISI. The PRC becomes more skewed to the right as the firing rate decreases. Thus at low firing rates, the spikes are triggered preferentially by inputs that occur only during a small time interval late in the ISI. This implies that the neuron is more of a coincidence detector at low firing frequencies and more of an integrator at high frequencies. The steady-state theory is shown to also hold for slowly varying inputs.

Effect of electrical coupling on ionic current and synaptic potential measurements

Recent studies have found electrical coupling to be more ubiquitous than previously thought, and coupling through gap junctions is known to play a crucial role in neuronal function and network output. In particular, current spread through gap junctions may affect the activation of voltage-dependent conductances as well as chemical synaptic release. Using voltage-clamp recordings of two strongly electrically coupled neurons of the lobster stomatogastric ganglion and conductance-based models of these neurons, we identified effects of electrical coupling on the measurement of leak and voltage-gated outward currents, as well as synaptic potentials. Experimental measurements showed that both leak and voltage-gated outward currents are recruited by gap junctions from neurons coupled to the clamped cell. Nevertheless, in spite of the strong coupling between these neurons, the errors made in estimating voltage-gated conductance parameters were relatively minor (<10%). Thus in many cases isolation of coupled neurons may not be required if a small degree of measurement error of the voltage-gated currents or the synaptic potentials is acceptable. Modeling results show, however, that such errors may be as high as 20% if the gap-junction position is near the recording site or as high as 90% when measuring smaller voltage-gated ionic currents. Paradoxically, improved space clamp increases the errors arising from electrical coupling because voltage control across gap junctions is poor for even the highest realistic coupling conductances. Furthermore, the common procedure of leak subtraction can add an extra error to the conductance measurement, the sign of which depends on the maximal conductance.

Connexon connexions in the thalamocortical system

Electrical synapses are composed of gap junction channels that interconnect neurons. They occur throughout the mammalian brain, although this has been appreciated only recently. Gap junction channels, which are made of proteins called connexins, allow ionic current and small organic molecules to pass directly between cells, usually with symmetrical ease. Here we review evidence that electrical synapses are a major feature of the inhibitory circuitry in the thalamocortical system. In the neocortex, pairs of neighboring inhibitory interneurons are often electrically coupled, and these electrical connections are remarkably specific. To date, there is evidence that five distinct subtypes of inhibitory interneurons in the cortex make electrical interconnections selectively with interneurons of the same subtype. Excitatory neurons (i.e., pyramidal and spiny stellate cells) of the mature cortex do not appear to make electrical synapses. Within the thalamus, electrical coupling is observed in the reticular nucleus, which is composed entirely of GABAergic neurons. Some pairs of inhibitory neurons in the cortex and reticular thalamus have mixed synaptic connections: chemical (GABAergic) inhibitory synapses operating in parallel with electrical synapses. Inhibitory neurons of the thalamus and cortex express the gap junction protein connexin 36 (C x 36), and knocking out its gene abolishes nearly all of their electrical synapses. The electrical synapses of the thalamocortical system are strong enough to mediate robust interactions between inhibitory neurons. When pairs or groups of electrically coupled cells are excited by synaptic input, receptor agonists, or injected current, they typically display strong synchrony of both subthreshold voltage fluctuations and spikes. For example, activating metabotropic glutamate receptors on coupled pairs of cortical interneurons or on thalamic reticular neurons can induce rhythmic action potentials that are synchronized with millisecond precision. Electrical synapses offer a uniquely fast, bidirectional mechanism for coordinating local neural activity. Their widespread distribution in the thalamocortical system suggests that they serve myriad functions. We are far from a complete understanding of those functions, but recent experiments suggest that electrical synapses help to coordinate the temporal and spatial features of various forms of neural activity.