The response of a classical Hodgkin–Huxley neuron to an inhibitory input pulse

A population of uncoupled neurons can often be brought close to synchrony by a single strong inhibitory input pulse affecting all neurons equally. This mechanism is thought to underlie some brain rhythms, in particular gamma frequency (30–80 Hz) oscillations in the hippocampus and neocortex. Here we show that synchronization by an inhibitory input pulse often fails for populations of classical Hodgkin–Huxley neurons. Our reasoning suggests that in general, synchronization by inhibitory input pulses can fail when the transition of the target neurons from rest to spiking involves a Hopf bifurcation, especially when inhibition is shunting, not hyperpolarizing. Surprisingly, synchronization is more likely to fail when the inhibitory pulse is stronger or longer-lasting. These findings have potential implications for the question which neurons participate in brain rhythms, in particular in gamma oscillations.     

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.     

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.     

Synaptic Plasticity Controls Sensory Responses through Frequency-Dependent Gamma Oscillation Resonance

Synchronized gamma frequency oscillations in neural networks are thought to be important to sensory information processing, and their effects have been intensively studied. Here we describe a mechanism by which the nervous system can readily control gamma oscillation effects, depending selectively on visual stimuli. Using a model neural network simulation, we found that sensory response in the primary visual cortex is significantly modulated by the resonance between “spontaneous” and “stimulus-driven” oscillations. This gamma resonance can be precisely controlled by the synaptic plasticity of thalamocortical connections, and cortical response is regulated differentially according to the resonance condition. The mechanism produces a selective synchronization between the afferent and downstream neural population. Our simulation results explain experimental observations such as stimulus-dependent synchronization between the thalamus and the cortex at different oscillation frequencies. The model generally shows how sensory information can be selectively routed depending on its frequency components.     

New roles for the gamma rhythm: population tuning and preprocessing for the Beta rhythm

Gamma (30–80 Hz) and beta (12–30 Hz) oscillations such as those displayed by in vitro hippocampal (CA1) slice preparations and by in vivo neocortical EEGs often occur successively, with a spontaneous transition between them. In the gamma rhythm, pyramidal cells fire together with the interneurons, while in the beta rhythm, pyramidal cells fire on a subset of cycles of the interneurons. It is shown that gamma and beta rhythms have different properties with respect to creation of cell assemblies. In the presence of heterogeneous inputs to the pyramidal cells, the gamma rhythm creates an assembly of firing pyramidal cells from cells whose drive exceeds a threshold. During the gamma to beta transition, a slow outward potassium current is activated, and as a result the cell assembly vanishes. The slow currents make each of the pyramidal cells fire with a beta rhythm, but the field potential of the network still displays a gamma rhythm. Hebbian changes of connections among the pyramidal cells give rise to a beta rhythm, and the cell assemblies are recovered with a temporal separation between cells firing in different cycles. We present experimental evidence showing that such a separation can occur in hippocampal slices.     

Dopamine D4 receptor activation increases hippocampal gamma oscillations by enhancing synchronization of fast-spiking interneurons

Background

Gamma oscillations are electric activity patterns of the mammalian brain hypothesized to serve attention, sensory perception, working memory and memory encoding. They are disrupted or altered in schizophrenic patients with associated cognitive deficits, which persist in spite of treatment with antipsychotics. Because cognitive symptoms are a core feature of schizophrenia it is relevant to explore signaling pathways that potentially regulate gamma oscillations. Dopamine has been reported to decrease gamma oscillation power via D1-like receptors. Based on the expression pattern of D4 receptors (D4R) in hippocampus, and pharmacological effects of D4R ligands in animals, we hypothesize that they are in a position to regulate gamma oscillations as well.

Methodology/Principal Findings

To address this hypothesis we use rat hippocampal slices and kainate-induced gamma oscillations. Local field potential recordings as well as intracellular recordings of pyramidal cells, fast-spiking and non-fast-spiking interneurons were carried out. We show that D4R activation with the selective ligand PD168077 increases gamma oscillation power, which can be blocked by the D4R-specific antagonist L745,870 as well as by the antipsychotic drug Clozapine. Pyramidal cells did not exhibit changes in excitatory or inhibitory synaptic current amplitudes, but inhibitory currents became more coherent with the oscillations after application of PD168077. Fast-spiking, but not non-fast spiking, interneurons, increase their action potential phase-coupling and coherence with regard to ongoing gamma oscillations in response to D4R activation. Among several possible mechanisms we found that the NMDA receptor antagonist AP5 also blocks the D4R mediated increase in gamma oscillation power.

Conclusions/Significance

We conclude that D4R activation affects fast-spiking interneuron synchronization and thereby increases gamma power by an NMDA receptor-dependent mechanism. This suggests that converging deficits on fast-spiking interneurons may lead to decreased network function and thus aberrant gamma oscillations and cognitive decline in schizophrenia.     

Perisomatic inhibition and cortical circuit dysfunction in schizophrenia

Deficits of cognitive control in schizophrenia are associated with altered gamma oscillations in the prefrontal cortex. Paralbumin basket interneurons, which innervate the perisomatic region of pyramidal neurons, appear to play a key role in generating cortical gamma oscillations. In the prefrontal cortex of subjects with schizophrenia, alterations are present in both pre- and post-synaptic markers of the strength of GABA inputs from parvalbumin basket neurons to pyramidal neurons. These alterations may contribute to the neural substrate for impaired gamma oscillations in schizophrenia.     

Ih Tunes Theta/Gamma Oscillations and Cross-Frequency Coupling In an In Silico CA3 Model

channels are uniquely positioned to act as neuromodulatory control points for tuning hippocampal theta (4–12 Hz) and gamma (25 Hz) oscillations, oscillations which are thought to have importance for organization of information flow. contributes to neuronal membrane resonance and resting membrane potential, and is modulated by second messengers. We investigated oscillatory control using a multiscale computer model of hippocampal CA3, where each cell class (pyramidal, basket, and oriens-lacunosum moleculare cells), contained type-appropriate isoforms of . Our model demonstrated that modulation of pyramidal and basket allows tuning theta and gamma oscillation frequency and amplitude. Pyramidal also controlled cross-frequency coupling (CFC) and allowed shifting gamma generation towards particular phases of the theta cycle, effected via ''s ability to set pyramidal excitability. Our model predicts that in vivo neuromodulatory control of allows flexibly controlling CFC and the timing of gamma discharges at particular theta phases.     

Adaptation and shunting inhibition leads to pyramidal/interneuron gamma with sparse firing of pyramidal cells

Gamma oscillations are a prominent phenomenon related to a number of brain functions. Data show that individual pyramidal neurons can fire at rate below gamma with the population showing clear gamma oscillations and synchrony. In one kind of idealized model of such weak gamma, pyramidal neurons fire in clusters. Here we provide a theory for clustered gamma PING rhythms with strong inhibition and weaker excitation. Our simulations of biophysical models show that the adaptation of pyramidal neurons coupled with their low firing rate leads to cluster formation. A partially analytic study of a canonical model shows that the phase response curves with a near zero flat region, caused by the presence of the slow adaptive current, are the key to the formation of clusters. Furthermore we examine shunting inhibition and show that clusters become robust and generic     

Computational study of hippocampal-septal theta rhythm changes due to β-amyloid-altered ionic channels

Electroencephagraphy (EEG) of many dementia patients has been characterized by an increase in low frequency field potential oscillations. One of the characteristics of early stage Alzheimer's disease (AD) is an increase in theta band power (4-7 Hz). However, the mechanism(s) underlying the changes in theta oscillations are still unclear. To address this issue, we investigate the theta band power changes associated with β-Amyloid (Aβ) peptide (one of the main markers of AD) using a computational model, and by mediating the toxicity of hippocampal pyramidal neurons. We use an established biophysical hippocampal CA1-medial septum network model to evaluate four ionic channels in pyramidal neurons, which were demonstrated to be affected by Aβ. They are the L-type Ca2? channel, delayed rectifying K? channel, A-type fast-inactivating K? channel and large-conductance Ca2?-activated K? channel. Our simulation results demonstrate that only the Aβ inhibited A-type fast-inactivating K? channel can induce an increase in hippocampo-septal theta band power, while the other channels do not affect theta rhythm. We further deduce that this increased theta band power is due to enhanced synchrony of the pyramidal neurons. Our research may elucidate potential biomarkers and therapeutics for AD. Further investigation will be helpful for better understanding of AD-induced theta rhythm abnormalities and associated cognitive deficits.     

Computational Study of Hippocampal-Septal Theta Rhythm Changes Due to Beta-Amyloid-Altered Ionic Channels

Electroencephagraphy (EEG) of many dementia patients has been characterized by an increase in low frequency field potential oscillations. One of the characteristics of early stage Alzheimer’s disease (AD) is an increase in theta band power (4–7 Hz). However, the mechanism(s) underlying the changes in theta oscillations are still unclear. To address this issue, we investigate the theta band power changes associated with β-Amyloid (Aβ) peptide (one of the main markers of AD) using a computational model, and by mediating the toxicity of hippocampal pyramidal neurons. We use an established biophysical hippocampal CA1-medial septum network model to evaluate four ionic channels in pyramidal neurons, which were demonstrated to be affected by Aβ. They are the L-type Ca²⁺ channel, delayed rectifying K⁺ channel, A-type fast-inactivating K⁺ channel and large-conductance Ca²⁺-activated K⁺ channel. Our simulation results demonstrate that only the Aβ inhibited A-type fast-inactivating K⁺ channel can induce an increase in hippocampo-septal theta band power, while the other channels do not affect theta rhythm. We further deduce that this increased theta band power is due to enhanced synchrony of the pyramidal neurons. Our research may elucidate potential biomarkers and therapeutics for AD. Further investigation will be helpful for better understanding of AD-induced theta rhythm abnormalities and associated cognitive deficits.     

Hippocampal rhythm generation: Gamma-related theta-frequency resonance in CA3 interneurons

 During different behavioral states different population activities are present in the hippocampal formation. These activities are not independent: sharp waves often occur together with high-frequency ripples, and gamma-frequency activity is usually superimposed on theta oscillations. There is both experimental and theoretical evidence supporting the notion that gamma oscillation is generated intrahippocampally, but there is no generally accepted view about the origin of theta waves. Precise timing of population bursts of pyramidal cells may be due to a synchronized external drive. Membrane potential oscillations recorded in the septum are unlikely to fulfill this purpose because they are not coherent enough. We investigated the prospects of an intrahippocampal mechanism supplying pyramidal cells with theta frequency periodic inhibition, by studying a model of a network of hippocampal inhibitory interneurons. As shown previously, interneurons are capable of generating synchronized gamma-frequency action potential oscillations. Exciting the neurons by periodic current injection, the system could either be entrained in an oscillation with the frequency of the inducing current or exhibit in-phase periodic changes at the frequency of single cell (and network) activity. Simulations that used spatially inhomogeneous stimulus currents showed anti-phase frequency changes across cells, which resulted in a periodic decrease in the synchrony of the network. As this periodic change in synchrony occurred in the theta frequency range, our network should be able to exhibit the theta-frequency weakening of inhibition of pyramidal cells, thus offering a possible mechanism for intrahippocampal theta generation. Received: 23 February 2000 / Accepted in revised form: 30 June 2000     

Hippocampal Theta Modulation of Neocortical Spike Times and Gamma Rhythm: A Biophysical Model Study

The hippocampal theta and neocortical gamma rhythms are two prominent examples of oscillatory neuronal activity. The hippocampus has often been hypothesized to influence neocortical networks by its theta rhythm, and, recently, evidence for such a direct influence has been found. We examined a possible mechanism for this influence by means of a biophysical model study using conductance-based model neurons. We found, in agreement with previous studies, that networks of fast-spiking GABA -ergic interneurons, coupled with shunting inhibition, synchronize their spike activity at a gamma frequency and are able to impose this rhythm on a network of pyramidal cells to which they are coupled. When our model was supplied with hippocampal theta-modulated input fibres, the theta rhythm biased the spike timings of both the fast-spiking and pyramidal cells. Furthermore, both the amplitude and frequency of local field potential gamma oscillations were influenced by the phase of the theta rhythm. We show that the fast-spiking cells, not pyramidal cells, are essential for this latter phenomenon, thus highlighting their crucial role in the interplay between hippocampus and neocortex.     

Cholinergic and glutamatergic agonists induce gamma frequency activity in dorsal subcoeruleus nucleus neurons

The dorsal subcoeruleus nucleus (SubCD) is involved in generating two signs of rapid eye movement (REM) sleep: muscle atonia and ponto-geniculo-occipital (PGO) waves. We tested the hypothesis that single cell and/or population responses of SubCD neurons are capable of generating gamma frequency activity in response to intracellular stimulation or receptor agonist activation. Whole cell patch clamp recordings (immersion chamber) and population responses (interface chamber) were conducted on 9- to 20-day-old rat brain stem slices. All SubCD neurons (n = 103) fired at gamma frequency when subjected to depolarizing steps. Two statistically distinct populations of neurons were observed, which were distinguished by their high (>80 Hz, n = 24) versus low (35-80 Hz, n = 16) initial firing frequencies. Both cell types exhibited subthreshold oscillations in the gamma range (n = 43), which may underlie the gamma band firing properties of these neurons. The subthreshold oscillations were blocked by the sodium channel blockers tetrodotoxin (TTX, n = 21) extracellularly and N-(2,6-dimethylphenylcarbamoylmethyl)triethylammonium bromide (QX-314) intracellularly (n = 5), indicating they were sodium channel dependent. Gamma frequency subthreshold oscillations were observed in response to the nonspecific cholinergic receptor agonist carbachol (CAR, n = 11, d = 1.08) and the glutamate receptor agonists N-methyl-d-aspartic acid (NMDA, n = 12, d = 1.09) and kainic acid (KA, n = 13, d = 0.96), indicating that cholinergic and glutamatergic inputs may be involved in the activation of these subthreshold currents. Gamma band activity also was observed in population responses following application of CAR (n = 4, P < 0.05), NMDA (n = 4, P < 0.05) and KA (n = 4, P < 0.05). Voltage-sensitive, sodium channel-dependent gamma band activity appears to be a part of the intrinsic membrane properties of SubCD neurons.     

Muscarinic induction of hippocampal gamma oscillations requires coupling of the M1 receptor to two mixed cation currents

Oscillatory network activity at gamma frequencies is assumed to be of major importance in cortical information processing. Whereas the synaptic mechanisms of gamma oscillations have been studied in detail, the ionic currents involved at the cellular level remain to be elucidated. Here we show that in vitro gamma oscillations induced by muscarine require activation of M1 receptors on hippocampal CA3 pyramidal neurons and are absent in M1 receptor-deficient mice. M1 receptor activation depolarizes pyramidal neurons by increasing the mixed Na(+)/K(+) current I(h) and the Ca(2+)-dependent nonspecific cation current I(cat), but not by modulation of I(M). Our data provide important insight into the molecular basis of gamma oscillations by unequivocally establishing a novel role for muscarinic modulation of I(h) and I(cat) in rhythmic network activity.     

Activation of a cGMP-sensitive calcium-dependent chloride channel may cause transition from calcium waves to whole cell oscillations in smooth muscle cells

In vitro, alpha-adrenoreceptor stimulation of rat mesenteric small arteries often leads to a rhythmic change in wall tension, i.e., vasomotion. Within the individual smooth muscle cells of the vascular wall, vasomotion is often preceded by a period of asynchronous calcium waves. Abruptly, these low-frequency waves may transform into high-frequency whole cell calcium oscillations. Simultaneously, multiple cells synchronize, leading to rhythmic generation of tension. We present a mathematical model of vascular smooth muscle cells that aims at characterizing this sudden transition. Simulations show calcium waves sweeping through the cytoplasm when the sarcoplasmic reticulum (SR) is stimulated to release calcium. A rise in cGMP leads to the experimentally observed transition from waves to whole cell calcium oscillations. At the same time, membrane potential starts to oscillate and the frequency approximately doubles. In this transition, the simulated results point to a key role for a recently discovered cGMP-sensitive calcium-dependent chloride channel. This channel depolarizes the membrane in response to calcium released from the SR. In turn, depolarization causes a uniform opening of L-type calcium channels on the cell surface, stimulating a synchronized release of SR calcium and inducing the shift from waves to whole cell oscillations. The effect of the channel is therefore to couple the processes of the SR with those of the membrane. We hypothesize that the shift in oscillatory mode and the associated onset of oscillations in membrane potential within the individual cell may underlie sudden intercellular synchronization and the appearance of vasomotion.     

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.     

Mechanisms of gamma oscillations in the hippocampus of the behaving rat

Gamma frequency oscillations (30-100 Hz) have been suggested to underlie various cognitive and motor functions. Here, we examine the generation of gamma oscillation currents in the hippocampus, using two-dimensional, 96-site silicon probes. Two gamma generators were identified, one in the dentate gyrus and another in the CA3-CA1 regions. The coupling strength between the two oscillators varied during both theta and nontheta states. Both pyramidal cells and interneurons were phase-locked to gamma waves. Anatomical connectivity, rather than physical distance, determined the coupling strength of the oscillating neurons. CA3 pyramidal neurons discharged CA3 and CA1 interneurons at latencies indicative of monosynaptic connections. Intrahippocampal gamma oscillation emerges in the CA3 recurrent system, which entrains the CA1 region via its interneurons.     

Cell-type-specific synchronization of neural activity in FEF with V4 during attention

Shifts of gaze and shifts of attention are closely linked and it is debated whether they result from the same neural mechanisms. Both processes involve the frontal eye fields (FEF), an area which is also a source of top-down feedback to area V4 during covert attention. To test the relative contributions of oculomotor and attention-related FEF signals to such feedback, we recorded simultaneously from both areas in a covert attention task and in a saccade task. In the attention task, only visual and visuomovement FEF neurons showed enhanced responses, whereas movement cells were unchanged. Importantly, visual, but not movement or visuomovement cells, showed enhanced gamma frequency synchronization with activity in V4 during attention. Within FEF, beta synchronization was increased for movement cells during attention but was suppressed in the saccade task. These findings support the idea that the attentional modulation of visual processing is not mediated by movement neurons.