Generating oscillatory bursts from a network of regular spiking neurons without inhibition

Avian nucleus isthmi pars parvocellularis (Ipc) neurons are reciprocally connected with the layer 10 (L10) neurons in the optic tectum and respond with oscillatory bursts to visual stimulation. Our in vitro experiments show that both neuron types respond with regular spiking to somatic current injection and that the feedforward and feedback synaptic connections are excitatory, but of different strength and time course. To elucidate mechanisms of oscillatory bursting in this network of regularly spiking neurons, we investigated an experimentally constrained model of coupled leaky integrate-and-fire neurons with spike-rate adaptation. The model reproduces the observed Ipc oscillatory bursting in response to simulated visual stimulation. A scan through the model parameter volume reveals that Ipc oscillatory burst generation can be caused by strong and brief feedforward synaptic conductance changes. The mechanism is sensitive to the parameter values of spike-rate adaptation. In conclusion, we show that a network of regular-spiking neurons with feedforward excitation and spike-rate adaptation can generate oscillatory bursting in response to a constant input.     

Directed Communication between Nucleus Accumbens and Neocortex in Humans Is Differentially Supported by Synchronization in the Theta and Alpha Band

Here, we report evidence for oscillatory bi-directional interactions between the nucleus accumbens and the neocortex in humans. Six patients performed a demanding covert visual attention task while we simultaneously recorded brain activity from deep-brain electrodes implanted in the nucleus accumbens and the surface electroencephalogram (EEG). Both theta and alpha oscillations were strongly coherent with the frontal and parietal EEG during the task. Theta-band coherence increased during processing of the visual stimuli. Granger causality analysis revealed that the nucleus accumbens was communicating with the neocortex primarily in the theta-band, while the cortex was communicating the nucleus accumbens in the alpha-band. These data are consistent with a model, in which theta- and alpha-band oscillations serve dissociable roles: Prior to stimulus processing, the cortex might suppress ongoing processing in the nucleus accumbens by modulating alpha-band activity. Subsequently, upon stimulus presentation, theta oscillations might facilitate the active exchange of stimulus information from the nucleus accumbens to the cortex.     

Six types of multistability in a neuronal model based on slow calcium current

Background

Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified.

Methodology/Principal Findings

Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics of a single leech heart interneuron. We carry out a bifurcation analysis of the model and show that it possesses six different types of multistability of dynamical regimes. These types are the co-existence of 1) bursting and silence, 2) tonic spiking and silence, 3) tonic spiking and subthreshold oscillations, 4) bursting and subthreshold oscillations, 5) bursting, subthreshold oscillations and silence, and 6) bursting and tonic spiking. These first five types of multistability occur due to the presence of a separating regime that is either a saddle periodic orbit or a saddle equilibrium. We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate.

Conclusions

We developed a neuronal model which exhibits a rich variety of different types of multistability. We described a novel mechanism supporting the bistability of bursting and silence. This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability.     

An integrate-and-fire model for synchronized bursting in a network of cultured cortical neurons

It has been suggested that spontaneous synchronous neuronal activity is an essential step in the formation of functional networks in the central nervous system. The key features of this type of activity consist of bursts of action potentials with associated spikes of elevated cytoplasmic calcium. These features are also observed in networks of rat cortical neurons that have been formed in culture. Experimental studies of these cultured networks have led to several hypotheses for the mechanisms underlying the observed synchronized oscillations. In this paper, bursting integrate-and-fire type mathematical models for regular spiking (RS) and intrinsic bursting (IB) neurons are introduced and incorporated through a small-world connection scheme into a two-dimensional excitatory network similar to those in the cultured network. This computer model exhibits spontaneous synchronous activity through mechanisms similar to those hypothesized for the cultured experimental networks. Traces of the membrane potential and cytoplasmic calcium from the model closely match those obtained from experiments. We also consider the impact on network behavior of the IB neurons, the geometry and the small world connection scheme. Action Editor: David Golomb     

Two types of independent bursting mechanisms in inspiratory neurons: an integrative model

The network of coupled neurons in the pre-Bötzinger complex (pBC) of the medulla generates a bursting rhythm, which underlies the inspiratory phase of respiration. In some of these neurons, bursting persists even when synaptic coupling in the network is blocked and respiratory rhythmic discharge stops. Bursting in inspiratory neurons has been extensively studied, and two classes of bursting neurons have been identified, with bursting mechanism depends on either persistent sodium current or changes in intracellular Ca²⁺, respectively. Motivated by experimental evidence from these intrinsically bursting neurons, we present a two-compartment mathematical model of an isolated pBC neuron with two independent bursting mechanisms. Bursting in the somatic compartment is modeled via inactivation of a persistent sodium current, whereas bursting in the dendritic compartment relies on Ca²⁺ oscillations, which are determined by the neuromodulatory tone. The model explains a number of conflicting experimental results and is able to generate a robust bursting rhythm, over a large range of parameters, with a frequency adjusted by neuromodulators.     

Synchronous and asynchronous bursting states: role of intrinsic neural dynamics

Brain signals such as local field potentials often display gamma-band oscillations (30-70 Hz) in a variety of cognitive tasks. These oscillatory activities possibly reflect synchronization of cell assemblies that are engaged in a cognitive function. A type of pyramidal neurons, i.e., chattering neurons, show fast rhythmic bursting (FRB) in the gamma frequency range, and may play an active role in generating the gamma-band oscillations in the cerebral cortex. Our previous phase response analyses have revealed that the synchronization between the coupled bursting neurons significantly depends on the bursting mode that is defined as the number of spikes in each burst. Namely, a network of neurons bursting through a Ca(2+)-dependent mechanism exhibited sharp transitions between synchronous and asynchronous firing states when the neurons exchanged the bursting mode between singlet, doublet and so on. However, whether a broad class of bursting neuron models commonly show such a network behavior remains unclear. Here, we analyze the mechanism underlying this network behavior using a mathematically tractable neuron model. Then we extend our results to a multi-compartment version of the NaP current-based neuron model and prove a similar tight relationship between the bursting mode changes and the network state changes in this model. Thus, the synchronization behavior couples tightly to the bursting mode in a wide class of networks of bursting neurons.     

Cell Type-Specific Properties of Subicular GABAergic Currents Shape Hippocampal Output Firing Mode

GABAergic function of the subiculum is central to the regulation of hippocampal output activity. Subicular neuronal networks are indeed under potent control by local inhibition. However, information about the properties of GABAergic currents generated by neurons of this parahippocampal area in normal tissue is still missing. Here, we describe GABA_A receptor (GABA_AR)-mediated phasic and tonic currents generated by principal cells (PCs) and interneurons (INs) of the rat subiculum. We show that in spite of similar synaptic current densities, INs generate spontaneous IPSCs (sIPSCs) that occur less frequently and exhibit smaller charge transfer, thus receiving less synaptic total current than PCs. Further distinction of PCs between intrinsically bursting (IB) and regular-spiking (RS) neurons suggested that sIPSCs generated by the two PC sub-types are likely to be similar. PCs and INs are also controlled by a similar tonic inhibition. However, whereas a comparable tonic current density is found in RS cells and INs, IB neurons are constrained by a greater inhibitory tone. Finally, pharmacological blockade of GABA_AR did not promote functional switch of RS neurons to IB mode, but influenced the bursting propensity of IB cells and released fast spiking activity in INs. Our findings reveal differences in GABAergic currents between PCs and INs as well as within PC sub-types. We propose that GABAergic inhibition may shape hippocampal output activity by providing cell type-specific fine-tuning of subicular excitatory and inhibitory drives.     

Synchronization without oscillatory neurons

Experimental results suggest that neurons in the cortex synchronize their action potentials on the millisecond time scale. More importantly this binding expresses functional relationships between the neurons. A model of neuronal interactions is proposed in which simultaneous discharges of neurons develop through specialized synaptic circuits. As an important prerequisite for this synchronization it is demonstrated that SynFire chains, generating different levels of excitation, propagate their activity waves at distinct velocities. Two chains were coupled by excitatory synapses and their activity was initiated at different times. Due to synaptic interactions, activity in the earlier-initiated chain accelerates propagation in the other chain until the two activity waves are synchronized. Compared with several neural network models with oscillatory units, physiologically more plausible neurons are simulated. It is still under debate whether neurons in the cortex show oscillatory dischargesper se. In particular, a high rate of noise relative to very weak synaptic gains cannot impair our results in the neural network simulations.     

Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons

The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous states in which neurons fire regularly; asynchronous states with stationary global activity and very irregular individual cell activity; and states in which the global activity oscillates but individual cells fire irregularly, typically at rates lower than the global oscillation frequency. The network can switch between these states, provided the external frequency, or the balance between excitation and inhibition, is varied. Two types of network oscillations are observed. In the fast oscillatory state, the network frequency is almost fully controlled by the synaptic time scale. In the slow oscillatory state, the network frequency depends mostly on the membrane time constant. Finite size effects in the asynchronous state are also discussed.     

A Phantom Bursting Mechanism for Episodic Bursting

We describe a novel dynamic mechanism for episodic or compound bursting oscillations, in which bursts of electrical impulses are clustered together into episodes, separated by long silent phases. We demonstrate the mechanism for episodic bursting using a minimal mathematical model for “phantom bursting.” Depending on the location in parameter space, this model can produce fast, medium, or slow bursting, or in the present case, fast, slow, and episodic bursting. The episodic bursting is modestly robust to noise and to parameter variation, and the effect that noise has on the episodic bursting pattern is quite different from that of an alternate episodic burst mechanism in which the slow envelope is produced by metabolic oscillations. This mechanism could account for episodic bursting produced in endocrine cells or neurons, such as pancreatic islets or gonadotropin releasing neurons of the hypothalamus.     

Perisomatic feedback inhibition underlies cholinergically induced fast network oscillations in the rat hippocampus in vitro

Gamma frequency network oscillations are assumed to be important in cognitive processes, including hippocampal memory operations, but the precise functions of these oscillations remain unknown. Here, we examine the cellular and network mechanisms underlying carbachol-induced fast network oscillations in the hippocampus in vitro, which closely resemble hippocampal gamma oscillations in the behaving rat. Using a combination of planar multielectrode array recordings, imaging with voltage-sensitive dyes, and recordings from single hippocampal neurons within the CA3 gamma generator, active current sinks and sources were localized to the stratum pyramidale. These proximal currents were driven by phase-locked rhythmic inhibitory inputs to pyramidal cells from identified perisomatic-targeting interneurons. AMPA receptor-mediated recurrent excitation was necessary for the synchronization of interneuronal discharge, which strongly supports a synaptic feedback model for the generation of hippocampal gamma oscillations.     

Cell Type-Specific Separation of Subicular Principal Neurons during Network Activities

The hippocampal output structure, the subiculum, expresses two major memory relevant network rhythms, sharp wave ripple and gamma frequency oscillations. To this date, it remains unclear how the two distinct types of subicular principal cells, intrinsically bursting and regular spiking neurons, participate in these two network rhythms. Using concomitant local field potential and intracellular recordings in an in vitro mouse model that allows the investigation of both network rhythms, we found a cell type-specific segregation of principal neurons into participating intrinsically bursting and non-participating regular spiking cells. However, if regular spiking cells were kept at a more depolarized level, they did participate in a specific manner, suggesting a potential bimodal working model dependent on the level of excitation. Furthermore, intrinsically bursting and regular spiking cells exhibited divergent intrinsic membrane and synaptic properties in the active network. Thus, our results suggest a cell-type-specific segregation of principal cells into two separate groups during network activities, supporting the idea of two parallel streams of information processing within the subiculum.     

Nonlinear dynamics and information processing in pacemaker neurons

The paper treats some nonlinear dynamic phenomena in oscillatory activity of a single nerve cell. Based on experiments with CNS bursting pacemaker neurons ofHelix pomatia snail, a mathematical model was studied. The model demonstrates the majority of experimentally observable phenomena and allows one to investigate the role of its separate components. The phenomena demonstrated by model neuron (chaotic behavior, bistability, and sensitivity to parameter variations, initial conditions, and stimuli) may be relevant to information processing in nerve cells. The complexity of [Ca²⁺] _in −V phase diagrams of initial conditions depends on parameters. Transient synaptic impulse produces stable parameter-independent changes in activity of model neuron. These results indicate that a single bursting neuron can work in the neuronal ensemble as a dynamic switch. The sensitivity of this switch is regulated by a neurotransmitter.     

Efficient “Communication through Coherence” Requires Oscillations Structured to Minimize Interference between Signals

The ‘communication through coherence’ (CTC) hypothesis proposes that selective communication among neural networks is achieved by coherence between firing rate oscillation in a sending region and gain modulation in a receiving region. Although this hypothesis has stimulated extensive work, it remains unclear whether the mechanism can in principle allow reliable and selective information transfer. Here we use a simple mathematical model to investigate how accurately coherent gain modulation can filter a population-coded target signal from task-irrelevant distracting inputs. We show that selective communication can indeed be achieved, although the structure of oscillatory activity in the target and distracting networks must satisfy certain previously unrecognized constraints. Firstly, the target input must be differentiated from distractors by the amplitude, phase or frequency of its oscillatory modulation. When distracting inputs oscillate incoherently in the same frequency band as the target, communication accuracy is severely degraded because of varying overlap between the firing rate oscillations of distracting inputs and the gain modulation in the receiving region. Secondly, the oscillatory modulation of the target input must be strong in order to achieve a high signal-to-noise ratio relative to stochastic spiking of individual neurons. Thus, whilst providing a quantitative demonstration of the power of coherent oscillatory gain modulation to flexibly control information flow, our results identify constraints imposed by the need to avoid interference between signals, and reveal a likely organizing principle for the structure of neural oscillations in the brain.     

Effects of transition metal ions on spontaneous electrical activity and chemical synaptic transmission of neurons in the medicinal leech

Leech neurons exposed to salines containing inorganic Ca²⁺-channel blockers generate rhythmic bursts of impulses. According to an earlier model, these blockers unmask persistent Na⁺ currents that generate plateau-like depolarizations, each triggering a burst of impulses. The resulting increase in intracellular Na⁺ activates an outward Na⁺/K⁺ pump current that contributes to burst termination. We tested this model by examining systematically the effects of six transition metal ions (Co²⁺, Ni²⁺, Mn²⁺, Cd²⁺, La³⁺, and Zn²⁺) on the electrical activity of neurons in isolated leech ganglia. Each ion induced bursting activity, but the amplitude, form, and persistence of bursting differed with the ion used and its concentration relative to Ca²⁺. All ions tested suppressed chemical synaptic transmission between identified motor neurons, consistent with block of voltage-dependent Ca²⁺ currents in these cells. In addition, a strong correlation between suppression of synaptic transmission and burst amplitudes was obtained. Finally, burst duration was increased and the rate of repolarization decreased in reduced K⁺ saline, as expected for pump-dependent repolarization. These results provide further support for the hypothesis that a novel form of oscillatory electrical activity driven by persistent Na⁺ currents and the Na⁺/K⁺ pump occurs in leech ganglia exposed to Ca²⁺-channel blockers. Accepted: 15 May 1997     

Rhythmic cortical neurons increase their oscillations and sculpt basal ganglia signaling during motor learning

The function and modulation of neural circuits underlying motor skill may involve rhythmic oscillations (Feller, 1999 ; Marder and Goaillard, 2006 ; Churchland et al., 2012 ). In the proposed pattern generator for birdsong, the cortical nucleus HVC, the frequency and power of oscillatory bursting during singing increases with development (Crandall et al., 2007 ; Day et al., 2009 ). We examined the maturation of cellular activity patterns that underlie these changes. Single unit ensemble recording combined with antidromic identification (Day et al., 2011 ) was used to study network development in anesthetized zebra finches. Autocovariance quantified oscillations within single units. A subset of neurons oscillated in the theta/alpha/mu/beta range (8–20 Hz), with greater power in adults compared to juveniles. Across the network, the normalized oscillatory power in the 8–20 Hz range was greater in adults than juveniles. In addition, the correlated activity between rhythmic neuron pairs increased with development. We next examined the functional impact of the oscillators on the output neurons of HVC. We found that the firing of oscillatory neurons negatively correlated with the activity of cortico‐basal ganglia neurons (HVC_Xs), which project to Area X (the song basal ganglia). If groups of oscillators work together to tonically inhibit and precisely control the spike timing of adult HVC_Xs with coordinated release from inhibition, then the activity of HVC_Xs in juveniles should be decreased relative to adults due to uncorrelated, tonic inhibition. Consistent with this hypothesis, HVC_Xs had lower activity in juveniles. These data reveal network changes that shape cortical‐to‐basal ganglia signaling during motor learning. © 2013 Wiley Periodicals, Inc. Develop Neurobiol 73: 754–768, 2013     

Modeling of Rhythmogenesis in an Ensemble of Cortical Neurons Connected with Electrical Synapses

Based on our own data on generation of spindle-like field electrical activity in neuronal barrels of the rat somatic cortex and also on the published data on the properties of voltage-dependent channels in the membranes of cortical cells, we developed a model of the ensemble (simple network) of neurons connected by electrical synapses. Such connections were found earlier in neurophysiological and ultramicroscopic studies. Model neurons with membranes having sodium, potassium, and calcium channels described in the literature were capable of generating bursting rhythmic impulse activity under conditions of switching off of synaptic connections between cells (isolation). With switching on of electrical synapses, spiking generated by separate neurons, which initially was nonsynchronous, became synchronized in time. Ipso facto, we demonstrated the ability of pacemaker oscillatory activity to be electrotonically synchronized in ensembles of neurons connected with electrical synapses.     

Intrinsic bursting enhances the robustness of a neural network model of sequence generation by avian brain area HVC

Avian brain area HVC is known to be important for the production of birdsong. In zebra finches, each RA-projecting neuron in HVC emits a single burst of spikes during a song motif. The population of neurons is activated in a precisely timed, stereotyped sequence. We propose a model of these burst sequences that relies on two hypotheses. First, we hypothesize that the sequential order of bursting is reflected in the excitatory synaptic connections between neurons. Second, we propose that the neurons are intrinsically bursting, so that burst duration is set by cellular properties. Our model generates burst sequences similar to those observed in HVC. If intrinsic bursting is removed from the model, burst sequences can also be produced. However, they require more fine-tuning of synaptic strengths, and are therefore less robust. In our model, intrinsic bursting is caused by dendritic calcium spikes, and strong spike frequency adaptation in the soma contributes to burst termination.     

Brain-derived neurotrophic factor-induced potentiation of Ca(2+) oscillations in developing cortical neurons.

Brain-derived neurotrophic factor (BDNF) has been reported to exert an acute potentiation of synaptic activity. Here we examined the action of BDNF on synchronous spontaneous Ca(2+) oscillations in cultured cerebral cortical neurons prepared from postnatal 2-3-day-old rats. The synchronous spontaneous Ca(2+) oscillations began at approximately DIV 5. It was revealed that voltage-dependent Ca(2+) channels and ionotropic glutamate receptors were involved in the synchronous spontaneous oscillatory activity. BDNF potentiated the frequency of these oscillations. The BDNF-potentiated activity reached 207 +/- 20.1% of basal oscillatory activity. NT-3 and NT-4/5 also induced the potentiation. However, nerve growth factor did not. We examined the correlation between BDNF-induced glutamate release and the BDNF-potentiated oscillatory activity. Both up-regulation of phospholipase C-gamma (PLC-gamma) expression and the BDNF-induced glutamate release occurred at approximately DIV 5 when the BDNF-potentiated oscillations appeared. We confirmed that the BDNF-induced glutamate release occurred through a glutamate transporter that was dependent on the PLC-gamma/IP(3)/Ca(2+) pathway. Transporter inhibitors blocked the BDNF-potentiated oscillations, demonstrating that BDNF enhanced the glutamatergic transmissions in the developing cortical network by inducing glutamate release via a glutamate transporter.     

Long-term Relationships between Cholinergic Tone, Synchronous Bursting and Synaptic Remodeling

Cholinergic neuromodulation plays key roles in the regulation of neuronal excitability, network activity, arousal, and behavior. On longer time scales, cholinergic systems play essential roles in cortical development, maturation, and plasticity. Presumably, these processes are associated with substantial synaptic remodeling, yet to date, long-term relationships between cholinergic tone and synaptic remodeling remain largely unknown. Here we used automated microscopy combined with multielectrode array recordings to study long-term relationships between cholinergic tone, excitatory synapse remodeling, and network activity characteristics in networks of cortical neurons grown on multielectrode array substrates. Experimental elevations of cholinergic tone led to the abrupt suppression of episodic synchronous bursting activity (but not of general activity), followed by a gradual growth of excitatory synapses over hours. Subsequent blockage of cholinergic receptors led to an immediate restoration of synchronous bursting and the gradual reversal of synaptic growth. Neither synaptic growth nor downsizing was governed by multiplicative scaling rules. Instead, these occurred in a subset of synapses, irrespective of initial synaptic size. Synaptic growth seemed to depend on intrinsic network activity, but not on the degree to which bursting was suppressed. Intriguingly, sustained elevations of cholinergic tone were associated with a gradual recovery of synchronous bursting but not with a reversal of synaptic growth. These findings show that cholinergic tone can strongly affect synaptic remodeling and synchronous bursting activity, but do not support a strict coupling between the two. Finally, the reemergence of synchronous bursting in the presence of elevated cholinergic tone indicates that the capacity of cholinergic neuromodulation to indefinitely suppress synchronous bursting might be inherently limited.