Rhythmogenesis, amplitude modulation, and multiplexing in a cortical architecture

Effects of N-Methyl-d-Aspartate Receptor Antagonists on Gamma-Band Activity During Auditory Stimulation Compared With Electro/Magneto-encephalographic Data in Schizophrenia and Early-Stage Psychosis: A Systematic Review and Perspective

BACKGROUND AND HYPOTHESIS

N-Methyl-d-aspartate receptor (NMDA-R) hypofunctioning has been hypothesized to be involved in circuit dysfunctions in schizophrenia (ScZ). Yet, it remains to be determined whether the physiological changes observed following NMDA-R antagonist administration are consistent with auditory gamma-band activity in ScZ which is dependent on NMDA-R activity.

STUDY DESIGN

This systematic review investigated the effects of NMDA-R antagonists on auditory gamma-band activity in preclinical (n = 15) and human (n = 3) studies and compared these data to electro/magneto-encephalographic measurements in ScZ patients (n = 37) and 9 studies in early-stage psychosis. The following gamma-band parameters were examined: (1) evoked spectral power, (2) intertrial phase coherence (ITPC), (3) induced spectral power, and (4) baseline power.

STUDY RESULTS

Animal and human pharmacological data reported a reduction, especially for evoked gamma-band power and ITPC, as well as an increase and biphasic effects of gamma-band activity following NMDA-R antagonist administration. In addition, NMDA-R antagonists increased baseline gamma-band activity in preclinical studies. Reductions in ITPC and evoked gamma-band power were broadly compatible with findings observed in ScZ and early-stage psychosis patients where the majority of studies observed decreased gamma-band spectral power and ITPC. In regard to baseline gamma-band power, there were inconsistent findings. Finally, a publication bias was observed in studies investigating auditory gamma-band activity in ScZ patients.

CONCLUSIONS

Our systematic review indicates that NMDA-R antagonists may partially recreate reductions in gamma-band spectral power and ITPC during auditory stimulation in ScZ. These findings are discussed in the context of current theories involving alteration in E/I balance and the role of NMDA hypofunction in the pathophysiology of ScZ.

Site-dependent shaping of field potential waveforms

The activity of neuron populations gives rise to field potentials (FPs) that extend beyond the sources. Their mixing in the volume dilutes the original temporal motifs in a site-dependent manner, a fact that has received little attention. And yet, it potentially rids of physiological significance the time-frequency parameters of individual waves (amplitude, phase, duration). This is most likely to happen when a single source or a local origin is erroneously assumed. Recent studies using spatial treatment of these signals and anatomically realistic modeling of neuron aggregates provide convincing evidence for the multisource origin and site-dependent blend of FPs. Thus, FPs generated in primary structures like the neocortex and hippocampus reach far and cross-contaminate each other but also, they add and even impose their temporal traits on distant regions. Furthermore, both structures house neurons that act as spatially distinct (but overlapped) FP sources whose activation is state, region, and time dependent, making the composition of so-called local FPs highly volatile and strongly site dependent. Since the spatial reach cannot be predicted without source geometry, it is important to assess whether waveforms and temporal motifs arise from a single source; otherwise, those from each of the co-active sources should be sought.

Time Is of the Essence: Neural Codes, Synchronies, Oscillations, Architectures

Time is of the essence in how neural codes, synchronies, and oscillations might function in encoding, representation, transmission, integration, storage, and retrieval of information in brains. This Hypothesis and Theory article examines observed and possible relations between codes, synchronies, oscillations, and types of neural networks they require. Toward reverse-engineering informational functions in brains, prospective, alternative neural architectures incorporating principles from radio modulation and demodulation, active reverberant circuits, distributed content-addressable memory, signal-signal time-domain correlation and convolution operations, spike-correlation-based holography, and self-organizing, autoencoding anticipatory systems are outlined. Synchronies and oscillations are thought to subserve many possible functions: sensation, perception, action, cognition, motivation, affect, memory, attention, anticipation, and imagination. These include direct involvement in coding attributes of events and objects through phase-locking as well as characteristic patterns of spike latency and oscillatory response. They are thought to be involved in segmentation and binding, working memory, attention, gating and routing of signals, temporal reset mechanisms, inter-regional coordination, time discretization, time-warping transformations, and support for temporal wave-interference based operations. A high level, partial taxonomy of neural codes consists of channel, temporal pattern, and spike latency codes. The functional roles of synchronies and oscillations in candidate neural codes, including oscillatory phase-offset codes, are outlined. Various forms of multiplexing neural signals are considered: time-division, frequency-division, code-division, oscillatory-phase, synchronized channels, oscillatory hierarchies, polychronous ensembles. An expandable, annotative neural spike train framework for encoding low- and high-level attributes of events and objects is proposed. Coding schemes require appropriate neural architectures for their interpretation. Time-delay, oscillatory, wave-interference, synfire chain, polychronous, and neural timing networks are discussed. Some novel concepts for formulating an alternative, more time-centric theory of brain function are discussed. As in radio communication systems, brains can be regarded as networks of dynamic, adaptive transceivers that broadcast and selectively receive multiplexed temporally-patterned pulse signals. These signals enable complex signal interactions that select, reinforce, and bind common subpatterns and create emergent lower dimensional signals that propagate through spreading activation interference networks. If memory traces share the same kind of temporal pattern forms as do active neuronal representations, then distributed, holograph-like content-addressable memories are made possible via temporal pattern resonances.

Role of Interaction Delays in the Synchronization of Inhibitory Networks

Neural oscillations provide a means for efficient and flexible communication among different brain areas. Understanding the mechanisms of the generation of brain oscillations is crucial to determine principles of communication and information transfer in the brain circuits. It is well known that the inhibitory neurons play a major role in the generation of oscillations in the gamma range, in pure inhibitory networks, or in the networks composed of excitatory and inhibitory neurons. In this study, we explore the impact of different parameters and, in particular, the delay in the transmission of the signals between the neurons, on the dynamics of inhibitory networks. We show that increasing delay in a reasonable range increases the synchrony and stabilizes the oscillations. Unstable gamma oscillations characterized by a highly variable amplitude of oscillations can be observed in an intermediate range of delays. We show that in this range of delays, other experimentally observed phenomena such as sparse firing, variable amplitude and period, and the correlation between the instantaneous amplitude and period could be observed. The results broaden our understanding of the mechanism of the generation of the gamma oscillations in the inhibitory networks, known as the ING (interneuron-gamma) mechanism.

Synchronized Cardiac Impulses Emerge From Heterogeneous Local Calcium Signals Within and Among Cells of Pacemaker Tissue

OBJECTIVES

This study sought to identify subcellular Ca²⁺ signals within and among cells comprising the sinoatrial node (SAN) tissue.

BACKGROUND

The current paradigm of SAN impulse generation: 1) is that full-scale action potentials (APs) of a common frequency are initiated at 1 site and are conducted within the SAN along smooth isochrones; and 2) does not feature fine details of Ca²⁺ signaling present in isolated SAN cells, in which small subcellular, subthreshold local Ca²⁺ releases (LCRs) self-organize to generate cell-wide APs.

METHODS

Immunolabeling was combined with a novel technique to detect the occurrence of LCRs and AP-induced Ca²⁺ transients (APCTs) in individual pixels (chronopix) across the entire mouse SAN images.

RESULTS

At high magnification, Ca²⁺ signals appeared markedly heterogeneous in space, amplitude, frequency, and phase among cells comprising an HCN4⁺/CX43^- cell meshwork. The signaling exhibited several distinguishable patterns of LCR/APCT interactions within and among cells. Rhythmic APCTs that were apparently conducted within the meshwork were transferred to a truly conducting HCN4^-/CX43⁺ network of striated cells via narrow functional interfaces where different cell types intertwine, that is, the SAN anatomic/functional unit. At low magnification, the earliest APCT of each cycle occurred within a small area of the HCN4 meshwork, and subsequent APCT appearance throughout SAN pixels was discontinuous and asynchronous.

CONCLUSIONS

The study has discovered a novel, microscopic Ca²⁺ signaling paradigm of SAN operation that has escaped detection using low-resolution, macroscopic tissue isochrones employed in prior studies: synchronized APs emerge from heterogeneous subcellular subthreshold Ca²⁺ signals, resembling multiscale complex processes of impulse generation within clusters of neurons in neuronal networks.

Long range temporal correlations (LRTCs) in MEG-data during emerging psychosis: Relationship to symptoms, medication-status and clinical trajectory

Long-Range Temporal Correlations (LRTCs) index the capacity of the brain to optimally process information. Previous research has shown that patients with chronic schizophrenia present altered LRTCs at alpha and beta oscillations. However, it is currently unclear at which stage of schizophrenia aberrant LRTCs emerge. To address this question, we investigated LRTCs in resting-state magnetoencephalographic (MEG) recordings obtained from patients with affective disorders and substance abuse (clinically at low-risk of psychosis, CHR-N), patients at clinical high-risk of psychosis (CHR-P) (n = 115), as well as patients with a first episode (FEP) (n = 25). Matched healthy controls (n = 47) served as comparison group. LRTCs were obtained for frequencies from 4 to 40 Hz and correlated with clinical and neuropsychological data. In addition, we examined the relationship between LRTCs and transition to psychosis in CHR-P participants, and the relationship between LRTC and antipsychotic medication in FEP participants. Our results show that participants from the clinical groups have similar LRTCs to controls. In addition, LRTCs did not correlate with clinical and neurocognitive variables across participants nor did LRTCs predict transition to psychosis. Therefore, impaired LRTCs do not reflect a feature in the clinical trajectory of psychosis. Nevertheless, reduced LRTCs in the beta-band over posterior sensors of medicated FEP participants indicate that altered LRTCs may appear at the onset of the illness. Future studies are needed to elucidate the role of anti-psychotic medication in altered LRTCs.

Do NMDA-R antagonists re-create patterns of spontaneous gamma-band activity in schizophrenia? A systematic review and perspective

NMDA-R hypofunctioninig is a core pathophysiological mechanism in schizophrenia. However, it is unclear whether the physiological changes observed following NMDA-R antagonist administration are consistent with gamma-band alterations in schizophrenia. This systematic review examined the effects of NMDA-R antagonists on the amplitude of spontaneous gamma-band activity and functional connectivity obtained from preclinical (n = 24) and human (n = 9) studies and compared these data to resting-state EEG/MEG-measurements in schizophrenia patients (n = 27). Overall, the majority of preclinical and human studies observed increased gamma-band power following acute administration of NMDA-R antagonists. However, the direction of gamma-band power alterations in schizophrenia were inconsistent, which involved upregulation (n = 10), decreases (n = 7), and no changes (n = 8) in spectral power. Five out of 6 preclinical studies observed increased connectivity, while in healthy controls receiving Ketamine and in schizophrenia patients the direction of connectivity results was also inconsistent. Accordingly, the effects of NMDA-R hypofunctioning on gamma-band oscillations are different than pathophysiological signatures observed in schizophrenia. The implications of these findings for current E/I balance models of schizophrenia are discussed.

Ultra-slow Oscillations in fMRI and Resting-State Connectivity: Neuronal and Vascular Contributions and Technical Confounds

Ultra-slow, ∼0.1-Hz variations in the oxygenation level of brain blood are widely used as an fMRI-based surrogate of "resting-state" neuronal activity. The temporal correlations among these fluctuations across the brain are interpreted as "functional connections" for maps and neurological diagnostics. Ultra-slow variations in oxygenation follow a cascade. First, they closely track changes in arteriole diameter. Second, interpretable functional connections arise when the ultra-slow changes in amplitude of γ-band neuronal oscillations, which are shared across even far-flung but synaptically connected brain regions, entrain the ∼0.1-Hz vasomotor oscillation in diameter of local arterioles. Significant confounds to estimates of functional connectivity arise from residual vasomotor activity as well as arteriole dynamics driven by self-generated movements and subcortical common modulatory inputs. Last, methodological limitations of fMRI can lead to spurious functional connections. The neuronal generator of ultra-slow variations in γ-band amplitude, including that associated with self-generated movements, remains an open issue.

What is the true discharge rate and pattern of the striatal projection neurons in Parkinson's disease and Dystonia?

Dopamine and striatal dysfunctions play a key role in the pathophysiology of Parkinson's disease (PD) and Dystonia, but our understanding of the changes in the discharge rate and pattern of striatal projection neurons (SPNs) remains limited. Here, we recorded and examined multi-unit signals from the striatum of PD and dystonic patients undergoing deep brain stimulation surgeries. Contrary to earlier human findings, we found no drastic changes in the spontaneous discharge of the well-isolated and stationary SPNs of the PD patients compared to the dystonic patients or to the normal levels of striatal activity reported in healthy animals. Moreover, cluster analysis using SPN discharge properties did not characterize two well-separated SPN subpopulations, indicating no SPN subpopulation-specific (D1 or D2 SPNs) discharge alterations in the pathological state. Our results imply that small to moderate changes in spontaneous SPN discharge related to PD and Dystonia are likely amplified by basal ganglia downstream structures.

Geometric analysis of synchronization in neuronal networks with global inhibition and coupling delays

We study synaptically coupled neuronal networks to identify the role of coupling delays in network synchronized behaviour. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory and one inhibitory, are coupled with time-delayed synapses. The excitatory population is uncoupled, while the inhibitory population is tightly coupled without time delay. A geometric singular perturbation analysis yields existence and stability conditions for periodic solutions where the excitatory cells are synchronized and different phase relationships between the excitatory and inhibitory populations can occur, along with formulae for the periods of such solutions. In particular, we show that if there are no delays in the coupling, oscillations where the excitatory population is synchronized cannot occur. Numerical simulations are conducted to supplement and validate the analytical results. The analysis helps to explain how coupling delays in either excitatory or inhibitory synapses contribute to producing synchronized rhythms. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Resting-state gamma-band power alterations in schizophrenia reveal E/I-balance abnormalities across illness-stages

We examined alterations in E/I-balance in schizophrenia (ScZ) through measurements of resting-state gamma-band activity in participants meeting clinical high-risk (CHR) criteria (n = 88), 21 first episode (FEP) patients and 34 chronic ScZ-patients. Furthermore, MRS-data were obtained in CHR-participants and matched controls. Magnetoencephalographic (MEG) resting-state activity was examined at source level and MEG-data were correlated with neuropsychological scores and clinical symptoms. CHR-participants were characterized by increased 64–90 Hz power. In contrast, FEP- and ScZ-patients showed aberrant spectral power at both low- and high gamma-band frequencies. MRS-data showed a shift in E/I-balance toward increased excitation in CHR-participants, which correlated with increased occipital gamma-band power. Finally, neuropsychological deficits and clinical symptoms in FEP and ScZ-patients were correlated with reduced gamma band-activity, while elevated psychotic symptoms in the CHR group showed the opposite relationship. The current study suggests that resting-state gamma-band power and altered Glx/GABA ratio indicate changes in E/I-balance parameters across illness stages in ScZ.

On Rhythms in Neuronal Networks with Recurrent Excitation

We investigate rhythms in networks of neurons with recurrent excitation, that is, with excitatory cells exciting each other. Recurrent excitation can sustain activity even when the cells in the network are driven below threshold, too weak to fire on their own. This sort of "reverberating" activity is often thought to be the basis of working memory. Recurrent excitation can also lead to "runaway" transitions, sudden transitions to high-frequency firing; this may be related to epileptic seizures. Not all fundamental questions about these phenomena have been answered with clarity in the literature. We focus on three questions here: (1) How much recurrent excitation is needed to sustain reverberating activity? How does the answer depend on parameters? (2) Is there a positive minimum frequency of reverberating activity, a positive "onset frequency"? How does it depend on parameters? (3) When do runaway transitions occur? For reduced models, we give mathematical answers to these questions. We also examine computationally to which extent our findings are reflected in the behavior of biophysically more realistic model networks. Our main results can be summarized as follows. (1) Reverberating activity can be fueled by extremely weak slow recurrent excitation, but only by sufficiently strong fast recurrent excitation. (2) The onset of reverberating activity, as recurrent excitation is strengthened or external drive is raised, occurs at a positive frequency. It is faster when the external drive is weaker (and the recurrent excitation stronger). It is slower when the recurrent excitation has a longer decay time constant. (3) Runaway transitions occur only with fast, not with slow, recurrent excitation. We also demonstrate that the relation between reverberating activity fueled by recurrent excitation and runaway transitions can be visualized in an instructive way by a (generalized) cusp catastrophe surface.

Subthalamic, not striatal, activity correlates with basal ganglia downstream activity in normal and parkinsonian monkeys

The striatum and the subthalamic nucleus (STN) constitute the input stage of the basal ganglia (BG) network and together innervate BG downstream structures using GABA and glutamate, respectively. Comparison of the neuronal activity in BG input and downstream structures reveals that subthalamic, not striatal, activity fluctuations correlate with modulations in the increase/decrease discharge balance of BG downstream neurons during temporal discounting classical condition task. After induction of parkinsonism with 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP), abnormal low beta (8-15 Hz) spiking and local field potential (LFP) oscillations resonate across the BG network. Nevertheless, LFP beta oscillations entrain spiking activity of STN, striatal cholinergic interneurons and BG downstream structures, but do not entrain spiking activity of striatal projection neurons. Our results highlight the pivotal role of STN divergent projections in BG physiology and pathophysiology and may explain why STN is such an effective site for invasive treatment of advanced Parkinson's disease and other BG-related disorders.

DOI:http://dx.doi.org/10.7554/eLife.16443.001

The symptoms of Parkinson’s disease include tremor and slow movement, as well as loss of balance, depression and problems with sleep and memory. The death of neurons in a region of the brain called the substantia nigra pars compacta is one of the major hallmarks of Parkinson’s disease. These neurons produce a chemical called dopamine, and their death reduces dopamine levels in another area of the brain called the striatum. This structure is one of five brain regions known collectively as the basal ganglia, which form a circuit that helps to control movement.

The most effective treatment currently available for advanced Parkinson’s disease entails lowering electrodes deep into the brain in order to shut down the activity of part of the basal ganglia. However, the target is not the striatum; instead it is a structure called the subthalamic nucleus. The striatum and the subthalamic nucleus are the two input regions of the basal ganglia: each sends signals to the other three structures downstream. So why does targeting the subthalamic nucleus, but not the striatum, reduce the symptoms of Parkinson’s disease?

To shed some light on this issue, Deffains et al. recorded the activity of neurons in the basal ganglia before and after injecting two monkeys with a drug called MPTP. Related to heroin, MPTP produces symptoms in animals that resemble those of Parkinson’s disease. Before the injections, spontaneous fluctuations in the activity of the subthalamic nucleus produced matching changes in the activity of the three downstream basal ganglia structures. Fluctuations in the activity of the striatum, by contrast, had no such effect. Moreover, injecting the monkeys with MPTP caused the basal ganglia to fire in an abnormal highly synchronized rhythm, similar to that seen in Parkinson’s disease. Crucially, the subthalamic nucleus contributed to this abnormal rhythm, whereas the striatum did not.

The results presented by Deffains et al. provide a concrete explanation for why inactivating the subthalamic nucleus, but not the striatum, reduces the symptoms of Parkinson’s disease. Further research is now needed to explore how the striatum controls the activity of downstream regions of the basal ganglia, both in healthy people and in those with Parkinson's disease.

DOI:http://dx.doi.org/10.7554/eLife.16443.002

Cooperation and competition of gamma oscillation mechanisms

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

Reduced gamma frequency in the medial frontal cortex of aged rats during behavior and rest: implications for age-related behavioral slowing

Age-related cognitive and behavioral slowing may be caused by changes in the speed of neural signaling or by changes in the number of signaling steps necessary to achieve a given function. In the mammalian cortex, neural communication is organized by a 30-100 Hz "gamma" oscillation. There is a putative link between the gamma frequency and the speed of processing in a neural network: the dynamics of pyramidal neuron membrane time constants suggest that synaptic integration is framed by the gamma cycle, and pharmacological slowing of gamma also slows reaction times on behavioral tasks. The present experiments identify reductions in a robust 40-70 Hz gamma oscillation in the aged rat medial frontal cortex. The reductions were observed in the form of local field potentials, later peaks in fast-spiking neuron autocorrelations, and delays in the spiking of inhibitory neurons following local excitatory signals. Gamma frequency did not vary with movement speed, but rats with slower gamma also moved more slowly. Gamma frequency age differences were not observed in hippocampus. Hippocampal CA1 fast-spiking neurons exhibited interspike intervals consistent with a fast (70-100 Hz) gamma frequency, a pattern maintained across theta phases and theta frequencies independent of fluctuations in the average firing rates of the neurons. We propose that an average lengthening of the cortical 15-25 ms gamma cycle is one factor contributing to age-related slowing and that future attempts to offset cognitive declines will find a target in the response of fast-spiking inhibitory neurons to excitatory inputs.

Linking speech perception and neurophysiology: speech decoding guided by cascaded oscillators locked to the input rhythm

The premise of this study is that current models of speech perception, which are driven by acoustic features alone, are incomplete, and that the role of decoding time during memory access must be incorporated to account for the patterns of observed recognition phenomena. It is postulated that decoding time is governed by a cascade of neuronal oscillators, which guide template-matching operations at a hierarchy of temporal scales. Cascaded cortical oscillations in the theta, beta, and gamma frequency bands are argued to be crucial for speech intelligibility. Intelligibility is high so long as these oscillations remain phase locked to the auditory input rhythm. A model (Tempo) is presented which is capable of emulating recent psychophysical data on the intelligibility of speech sentences as a function of “packaging” rate (Ghitza and Greenberg, 2009). The data show that intelligibility of speech that is time-compressed by a factor of 3 (i.e., a high syllabic rate) is poor (above 50% word error rate), but is substantially restored when the information stream is re-packaged by the insertion of silent gaps in between successive compressed-signal intervals – a counterintuitive finding, difficult to explain using classical models of speech perception, but emerging naturally from the Tempo architecture.

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.

Searching for autocoherence in the cortical network with a time-frequency analysis of the local field potential

Gamma-band peaks in the power spectrum of local field potentials (LFP) are found in multiple brain regions. It has been theorized that gamma oscillations may serve as a 'clock' signal for the purposes of precise temporal encoding of information and 'binding' of stimulus features across regions of the brain. Neurons in model networks may exhibit periodic spike firing or synchronized membrane potentials that give rise to a gamma-band oscillation that could operate as a 'clock'. The phase of the oscillation in such models is conserved over the length of the stimulus. We define these types of oscillations to be 'autocoherent'. We investigated the hypothesis that autocoherent oscillations are the basis of the experimentally observed gamma-band peaks: the autocoherent oscillator (ACO) hypothesis. To test the ACO hypothesis, we developed a new technique to analyze the autocoherence of a time-varying signal. This analysis used the continuous Gabor transform to examine the time evolution of the phase of each frequency component in the power spectrum. Using this analysis method, we formulated a statistical test to compare the ACO hypothesis with measurements of the LFP in macaque primary visual cortex, V1. The experimental data were not consistent with the ACO hypothesis. Gamma-band activity recorded in V1 did not have the properties of a 'clock' signal during visual stimulation. We propose instead that the source of the gamma-band spectral peak is the resonant V1 network driven by random inputs.

Analyzing Neuronal Networks Using Discrete-Time Dynamics

We develop mathematical techniques for analyzing detailed Hodgkin-Huxley like models for excitatory-inhibitory neuronal networks. Our strategy for studying a given network is to first reduce it to a discrete-time dynamical system. The discrete model is considerably easier to analyze, both mathematically and computationally, and parameters in the discrete model correspond directly to parameters in the original system of differential equations. While these networks arise in many important applications, a primary focus of this paper is to better understand mechanisms that underlie temporally dynamic responses in early processing of olfactory sensory information. The models presented here exhibit several properties that have been described for olfactory codes in an insect's Antennal Lobe. These include transient patterns of synchronization and decorrelation of sensory inputs. By reducing the model to a discrete system, we are able to systematically study how properties of the dynamics, including the complex structure of the transients and attractors, depend on factors related to connectivity and the intrinsic and synaptic properties of cells within the network.

Dominant ionic mechanisms explored in spiking and bursting using local low-dimensional reductions of a biophysically realistic model neuron

The large number of variables involved in many biophysical models can conceal potentially simple dynamical mechanisms governing the properties of its solutions and the transitions between them as parameters are varied. To address this issue, we extend a novel model reduction method, based on "scales of dominance," to multi-compartment models. We use this method to systematically reduce the dimension of a two-compartment conductance-based model of a crustacean pyloric dilator (PD) neuron that exhibits distinct modes of oscillation--tonic spiking, intermediate bursting and strong bursting. We divide trajectories into intervals dominated by a smaller number of variables, resulting in a locally reduced hybrid model whose dimension varies between two and six in different temporal regimes. The reduced model exhibits the same modes of oscillation as the 16 dimensional model over a comparable parameter range, and requires fewer ad hoc simplifications than a more traditional reduction to a single, globally valid model. The hybrid model highlights low-dimensional organizing structure in the dynamics of the PD neuron, and the dependence of its oscillations on parameters such as the maximal conductances of calcium currents. Our technique could be used to build hybrid low-dimensional models from any large multi-compartment conductance-based model in order to analyze the interactions between different modes of activity.

Ketamine increases the frequency of electroencephalographic bicoherence peak on the alpha spindle area induced with propofol

BACKGROUND

The reticular and thalamocortical system is known to play a prominent role in spindle wave activity, and the spindle wave is related to the sedative effects of anaesthetics. Recently, bispectral analysis of the EEG has been developed as a better method to indicate nonlinear regulation including the thalamocortical system linking to the cortical area. In the present study, in order to explore the interference of ketamine with the nonlinear regulation of the sub-cortical system, we examined the effect of ketamine on spindle alpha waves through the bispectral analysis.

METHODS

The study included 21 patients. Anaesthesia was induced and maintained using a propofol-TCI system (target-controlled infusion, with target concentration 3.5 microg ml(-1)). An A-2000 BIS monitor was used and the raw EEG signals were collected via an RS232 interface on a personal computer. Bicoherence, the normalized bispectrum, and power spectrum were analysed before and after i.v. administration of 1 mg kg(-1) racemic ketamine.

RESULTS

Propofol caused alpha peaks in both power and bicoherence spectra, with average frequencies of 10.6 (SD 0.9) Hz and 10.7 (1.0) Hz, respectively. The addition of ketamine significantly shifted each peak to frequencies of 14.4 (1.4) Hz and 13.6 (1.5) Hz, respectively [P < 0.05, mean (SD)].

CONCLUSIONS

Ketamine shifted the alpha peaks of bicoherence induced by propofol to higher frequencies. This suggests that ketamine changes the alpha spindle rhythms through the modulation of the nonlinear sub-cortical reverberating network.

The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells

Medial entorhinal cortex layer II stellate cells display subthreshold oscillations (STOs). We study a single compartment biophysical model of such cells which qualitatively reproduces these STOs. We argue that in the subthreshold interval (STI) the seven-dimensional model can be reduced to a three-dimensional system of equations with well differentiated times scales. Using dynamical systems arguments we provide a mechanism for generations of STOs. This mechanism is based on the "canard structure," in which relevant trajectories stay close to repelling manifolds for a significant interval of time. We also show that the transition from subthreshold oscillatory activity to spiking ("canard explosion") is controlled in the STI by the same structure. A similar mechanism is invoked to explain why noise increases the robustness of the STO regime. Taking advantage of the reduction of the dimensionality of the full stellate cell system, we propose a nonlinear artificially spiking (NAS) model in which the STI reduced system is supplemented with a threshold for spiking and a reset voltage. We show that the synchronization properties in networks made up of the NAS cells are similar to those of networks using the full stellate cell models.

Optical recording from respiratory pattern generator of fetal mouse brainstem reveals a distributed network

Unfailing respiration depends on neural mechanisms already present in mammals before birth. Experiments were made to determine how inspiratory and expiratory neurons are grouped in the brainstem of fetal mice. A further aim was to assess whether rhythmicity arises from a single pacemaker or is generated by multiple sites in the brainstem. To measure neuronal firing, a fluorescent calcium indicator dye was applied to embryonic central nervous systems isolated from mice. While respiratory commands were monitored electrically from third to fifth cervical ventral roots, activity was measured optically over areas containing groups of respiratory neurones, or single neurones, along the medulla from the facial nucleus to the pre-Bötzinger complex. Large optical signals allowed recordings to be made during individual respiratory cycles. Inspiratory and expiratory neurones were intermingled. A novel finding was that bursts of activity arose in a discrete area intermittently, occurring during some breaths, but failing in others. Raised CO2 partial pressure or lowered pH increased the frequency of respiration; neurons then fired reliably with every cycle. Movies of activity revealed patterns of activation of inspiratory and expiratory neurones during successive respiratory cycles; there was no evidence for waves spreading systematically from region to region. Our results suggest that firing of neurons in immature respiratory circuits is a stochastic process, and that the rhythm does not depend on a single pacemaker. Respiratory circuits in fetal mouse brainstem appear to possess a high safety factor for generating rhythmicity, which may or may not persist as development proceeds.

Genetic dissection of theta rhythm heterogeneity in mice

Rhythmic oscillatory activities at the theta frequency (4-12 Hz) in the hippocampus have long-attracted attention because they have been implicated in diverse brain functions, including spatial cognition. Although studies based on pharmacology and lesion experiments suggested heterogeneity of these rhythms and their behavioral correlates, controversies are abundant on these issues. Here we show that mice harboring a phospholipase C (PLC)-beta1(-/-) mutation (PLC-beta1(-/-) mice) lack one subset of theta rhythms normally observed during urethane anesthesia, alert immobility, and passive whole-body rotation. In contrast, the other subset of theta rhythms observed during walking or running was intact in these mutant mice. PLC-beta1(-/-) mice also have somewhat disrupted theta activity during paradoxical sleep but do have an atropine-resistant component of theta rhythm. In addition, carbachol-induced oscillations were obliterated in hippocampal slices of PLC-beta1(-/-) mice. Interestingly, PLC-beta1(-/-) mice showed deficits in a hidden platform version of the Morris water maze yet performed well in motor coordination tests and a visual platform version of the Morris water maze. The results genetically define the existence of at least two subtypes of theta rhythms and reveal their association with different behaviors.

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

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

Slow and Fast Inhibition and an H-Current Interact to Create a Theta Rhythm in a Model of CA1 Interneuron Network

The oriens-lacunosum moleculare (O-LM) subtype of interneuron is a key component in the formation of the theta rhythm (8–12 Hz) in the hippocampus. It is known that the CA1 region of the hippocampus can produce theta rhythms in vitro with all ionotropic excitation blocked, but the mechanisms by which this rhythmicity happens were previously unknown. Here we present a model suggesting that individual O-LM cells, by themselves, are capable of producing a single-cell theta-frequency firing, but coupled O-LM cells are not capable of producing a coherent population theta. By including in the model fast-spiking (FS) interneurons, which give rise to IPSPs that decay faster than those of the O-LM cells, coherent theta rhythms are produced. The inhibition to O-LM cells from the FS cells synchronizes the O-LM cells, but only when the FS cells themselves fire at a theta frequency. Reciprocal connections from the O-LM cells to the FS cells serve to parse the FS cell firing into theta bursts, which can then synchronize the O-LM cells. A component of the model O-LM cell critical to the synchronization mechanism is the hyperpolarization-activated h-current. The model can robustly reproduce relative phases of theta frequency activity in O-LM and FS cells.

In vivo contribution of h-channels in the septal pacemaker to theta rhythm generation

One of the most intriguing network-level inferences made on the basis of in vitro and modelling data regarding the role of Ih current was that they participate in rhythmogenesis in different parts of the brain. The nature of Ih contribution to various neuronal oscillations is far from uniform however, and the proper evaluation of the role of Ih in each particular structure requires in situ investigations in the intact brain. In this study we tested the effect of Ih blockade in the medial septum on hippocampal theta rhythm in anaesthetized and freely behaving rats. We could not confirm the recent report of elimination of theta by septal injection of ZD7288 [C. Xu et al. (2004) Eur. J. Neurosci., 19, 2299-2309]; the observed effects were more subtle and more specific. We found that Ih blockade in the medial septum substantially decreased the frequency of hippocampal oscillations without changing the context in which theta occurred, i.e. specific behaviours in freely moving rats and spontaneous switching and brainstem stimulation under anaesthesia. Septal injection of ZD7288 eliminated atropine-resistant theta elicited by high intensity electrical stimulation of the reticular formation in anaesthetized rats but was ineffective in combination with the muscarinic agonist, carbachol. Thus, functional Ih was necessary for the septum to generate or transmit high frequency theta rhythm elicited by strong ascending activation, whereas low frequency theta persisted after Ih blockade. These results suggest that Ih plays a specific role in septal theta generation by promoting fast oscillations during exploratory behaviour and rapid eye movement sleep.

Hippocampal gamma-frequency oscillations: from interneurones to pyramidal cells, and back

GABAergic interneurones are necessary for the emergence of hippocampal gamma-frequency network oscillations, during which they play a key role in the synchronization of pyramidal cell firing. However, it remains to be resolved how distinct interneurone subtypes contribute to gamma-frequency oscillations, in what way the spatiotemporal pattern of interneuronal input affects principal cell activity, and by which mechanisms the interneurones themselves are synchronized. Here we summarize recent evidence from cholinergically induced gamma-frequency network oscillations in vitro, showing that perisomatic-targeting GABAergic interneurones provide prominent rhythmic inhibition in pyramidal cells, and that these interneurones are synchronized by recurrent excitation. We conclude by presenting a minimal integrate-and-fire network model which demonstrates that this excitatory-inhibitory feedback loop is sufficient to explain the generation of intrahippocampal gamma-frequency oscillations.

Rapid temporal modulation of synchrony by competition in cortical interneuron networks

The synchrony of neurons in extrastriate visual cortex is modulated by selective attention even when there are only small changes in firing rate (Fries, Reynolds, Rorie, & Desimone, 2001). We used Hodgkin-Huxley type models of cortical neurons to investigate the mechanism by which the degree of synchrony can be modulated independently of changes in firing rates. The synchrony of local networks of model cortical interneurons interacting through GABA(A) synapses was modulated on a fast timescale by selectively activating a fraction of the interneurons. The activated interneurons became rapidly synchronized and suppressed the activity of the other neurons in the network but only if the network was in a restricted range of balanced synaptic background activity. During stronger background activity, the network did not synchronize, and for weaker background activity, the network synchronized but did not return to an asynchronous state after synchronizing. The inhibitory output of the network blocked the activity of pyramidal neurons during asynchronous network activity, and during synchronous network activity, it enhanced the impact of the stimulus-related activity of pyramidal cells on receiving cortical areas (Salinas & Sejnowski, 2001). Synchrony by competition provides a mechanism for controlling synchrony with minor alterations in rate, which could be useful for information processing. Because traditional methods such as cross-correlation and the spike field coherence require several hundred milliseconds of recordings and cannot measure rapid changes in the degree of synchrony, we introduced a new method to detect rapid changes in the degree of coincidence and precision of spike timing.

Interactions between membrane conductances underlying thalamocortical slow-wave oscillations

Neurons of the central nervous system display a broad spectrum of intrinsic electrophysiological properties that are absent in the traditional "integrate-and-fire" model. A network of neurons with these properties interacting through synaptic receptors with many time scales can produce complex patterns of activity that cannot be intuitively predicted. Computational methods, tightly linked to experimental data, provide insights into the dynamics of neural networks. We review this approach for the case of bursting neurons of the thalamus, with a focus on thalamic and thalamocortical slow-wave oscillations. At the single-cell level, intrinsic bursting or oscillations can be explained by interactions between calcium- and voltage-dependent channels. At the network level, the genesis of oscillations, their initiation, propagation, termination, and large-scale synchrony can be explained by interactions between neurons with a variety of intrinsic cellular properties through different types of synaptic receptors. These interactions can be altered by neuromodulators, which can dramatically shift the large-scale behavior of the network, and can also be disrupted in many ways, resulting in pathological patterns of activity, such as seizures. We suggest a coherent framework that accounts for a large body of experimental data at the ion-channel, single-cell, and network levels. This framework suggests physiological roles for the highly synchronized oscillations of slow-wave sleep.

What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance

When the local field potential of a cortical network displays coherent fast oscillations ( approximately 40-Hz gamma or approximately 200-Hz sharp-wave ripples), the spike trains of constituent neurons are typically irregular and sparse. The dichotomy between rhythmic local field and stochastic spike trains presents a challenge to the theory of brain rhythms in the framework of coupled oscillators. Previous studies have shown that when noise is large and recurrent inhibition is strong, a coherent network rhythm can be generated while single neurons fire intermittently at low rates compared to the frequency of the oscillation. However, these studies used too simplified synaptic kinetics to allow quantitative predictions of the population rhythmic frequency. Here we show how to derive quantitatively the coherent oscillation frequency for a randomly connected network of leaky integrate-and-fire neurons with realistic synaptic parameters. In a noise-dominated interneuronal network, the oscillation frequency depends much more on the shortest synaptic time constants (delay and rise time) than on the longer synaptic decay time, and approximately 200-Hz frequency can be realized with synaptic time constants taken from slice data. In a network composed of both interneurons and excitatory cells, the rhythmogenesis is a compromise between two scenarios: the fast purely interneuronal mechanism, and the slower feedback mechanism (relying on the excitatory-inhibitory loop). The properties of the rhythm are determined essentially by the ratio of time scales of excitatory and inhibitory currents and by the balance between the mean recurrent excitation and inhibition. Faster excitation than inhibition, or a higher excitation/inhibition ratio, favors the feedback loop and a much slower oscillation (typically in the gamma range).

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.

The generation of oscillations in networks of electrically coupled cells

In several biological systems, the electrical coupling of nonoscillating cells generates synchronized membrane potential oscillations. Because the isolated cell is nonoscillating and electrical coupling tends to equalize the membrane potentials of the coupled cells, the mechanism underlying these oscillations is unclear. Here we present a dynamic mechanism by which the electrical coupling of identical nonoscillating cells can generate synchronous membrane potential oscillations. We demonstrate this mechanism by constructing a biologically feasible model of electrically coupled cells, characterized by an excitable membrane and calcium dynamics. We show that strong electrical coupling in this network generates multiple oscillatory states with different spatio-temporal patterns and discuss their possible role in the cooperative computations performed by the system.

Synchronous clusters in a noisy inhibitory neural network

We study the stability and information encoding capacity of synchronized states in a neuronal network model that represents part of thalamic circuitry. Our model neurons have a Hodgkin-Huxley-type low-threshold calcium channel, display postinhibitory rebound, and are connected via GABAergic inhibitory synapses. We find that there is a threshold in synaptic strength, tau(c), below which there are no stable spiking network states. Above threshold the stable spiking state is a cluster state, where different groups of neurons fire consecutively, and each neuron fires with the same cluster each time. Weak noise destabilizes this state, but stronger noise drives the system into a different, self-organized, stochastically synchronized state. Neuronal firing is still organized in clusters, but individual neurons can hop from cluster to cluster. Noise can actually induce and sustain such a state below the threshold of synaptic strength. We do find a qualitative difference in the firing patterns between small (approximately 10 neurons) and large (approximately 1000 neurons) networks. We determine the information content of the spike trains in terms of two separate contributions: the spike-time jitter around cluster firing times, and the hopping from cluster to cluster. We quantify the information loss due to temporally correlated interspike intervals. Recent experiments on the locust olfactory system and striatal neurons suggest that the nervous system may actually use these two channels to encode separate and unique information.

Geometric analysis of population rhythms in synaptically coupled neuronal networks

We develop geometric dynamical systems methods to determine how various components contribute to a neuronal network's emergent population behaviors. The results clarify the multiple roles inhibition can play in producing different rhythms. Which rhythms arise depends on how inhibition interacts with intrinsic properties of the neurons; the nature of these interactions depends on the underlying architecture of the network. Our analysis demonstrates that fast inhibitory coupling may lead to synchronized rhythms if either the cells within the network or the architecture of the network is sufficiently complicated. This cannot occur in mutually coupled networks with basic cells; the geometric approach helps explain how additional network complexity allows for synchronized rhythms in the presence of fast inhibitory coupling. The networks and issues considered are motivated by recent models for thalamic oscillations. The analysis helps clarify the roles of various biophysical features, such as fast and slow inhibition, cortical inputs, and ionic conductances, in producing network behavior associated with the spindle sleep rhythm and with paroxysmal discharge rhythms. Transitions between these rhythms are also discussed.

Hyperpolarization-activated current, Ih, in inspiratory brainstem neurons and its inhibition by hypoxia

A hyperpolarization-activated current, Ih, is often implied in pacemaker-like depolarizations during rhythmic oscillatory activity. We describe Ih in the isolated respiratory centre of immature mice (P6-P11). Ih was recorded in 15% (22/146) of all inspiratory neurons examined. The mean half-maximal Ih activation occurred at -78 mV and the reversal potential was -40 mV. Ih was inhibited by Cs+ (1-5 mM) and by organic blockers N-ethyl-1,6-dihydro-1, 2-dimethyl-6-(methylimino)-N-phenyl-4-pyrimidinamine (ZD 7288; 0.3-3 microM) and N,N'-bis-(3,4-dimethylphenylethyl)-N-methylamine (YS 035, 3-30 microM), but not by Ba2+ (0.5 mM). The organic Ih blockers did not change the inspiratory bursts recorded from the XIIth nerve and synaptic drives in inspiratory neurons. Hypoxia reversibly inhibited Ih but, in the presence of organic blockers, the hypoxic reaction remained unchanged. We conclude that although Ih channels are functional in a minority of inspiratory neurons, Ih does not contribute to respiratory rhythm generation or its modulation by hypoxia.

Fast global oscillations in networks of integrate-and-fire neurons with low firing rates

We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons --> infinity, the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized. The activity becomes oscillatory when the inhibitory feedback is strong enough. The period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input. In large but finite networks, the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold. Their characteristics are determined as functions of systems parameters in these two different regions. The results are found to be in good agreement with numerical simulations.

Frequency control in synchronized networks of inhibitory neurons

We analyze the control of frequency for a synchronized inhibitory neuronal network. The analysis is done for a reduced membrane model with a biophysically based synaptic influence. We argue that such a reduced model can quantitatively capture the frequency behavior of a larger class of neuronal models. We show that in different parameter regimes, the network frequency depends in different ways on the intrinsic and synaptic time constants. Only in one portion of the parameter space, called phasic, is the network period proportional to the synaptic decay time. These results are discussed in connection with previous work of the authors, which showed that for mildly heterogeneous networks, the synchrony breaks down, but coherence is preserved much more for systems in the phasic regime than in the other regimes. These results imply that for mildly heterogeneous networks, the existence of a coherent rhythm implies a linear dependence of the network period on synaptic decay time and a much weaker dependence on the drive to the cells. We give experimental evidence for this conclusion.

Synaptic origin and stimulus dependency of neuronal oscillatory activity in the primary visual cortex of the cat

1. We have studied the oscillatory activity of single neurons (91 recorded extracellularly and 76 intracellularly) in the primary visual cortex of cats and kittens to characterize its origins and its stimulus dependency. A new method for the detection of oscillations was developed in order to maximize the range of detectable frequencies in both types of recordings. Three types of activity were examined: spontaneous background activity, responses to intracellular current steps and visual responses. 2. During spontaneous activity, persistent oscillatory activity was very rare in both types of recordings. However, when intracellular records were made using KCl-filled micropipettes, spontaneous activity appeared rhythmic and contained repeated depolarizing events at a variety of frequencies, suggestive of tonic periodic inhibitory input normally masked at resting potential. 3. Patterns of firing activity in response to intracellular current steps allowed us to classify neurons as regular spiking, intrinsically bursting, and fast-spiking types, as described in vitro. In the case of rhythmically firing cells, the spike frequency increased with the amount of injected current. Subthreshold current-induced oscillations were rarely observed (2 out of 76 cells). 4. Visual stimulation elicited oscillations in one-third of the neurons (55 out of 167), predominantly in the 7-20 Hz frequency range in 93% of the cases. Rhythmicity was observed in both simple and complex cells, and appeared to be more prominent at 5 and 6 weeks of age. 5. Intracellular recordings in bridge mode and voltage clamp revealed that visually evoked oscillations were driven by synaptic activity and did not depend primarily on the intrinsic properties of recorded neurons. Hyperpolarizing the membrane led to an increase in the size of the rhythmic depolarizing events without a change in frequency. In voltage-clamped cells, current responses showed large oscillations at the same frequency as in bridge mode, independently of the actual value of the holding potential. 6. In fourteen intracellularly recorded neurons, oscillations consisted of excitatory events that could be superimposed on a depolarizing or a hyperpolarizing slow wave. In two other neurons, visual responses consisted of excitatory and inhibitory events, alternating with a constant phase shift. 7. Drifting bars were much more efficient in evoking oscillatory responses than flashed bars. Except in three cells, the frequency of the oscillation did not depend on the physical characteristics of the stimulus that were tested (contrast, orientation, direction, ocularity and position in the receptive field). No significant correlation was found between the intensity of the visual response and the strength of the rhythmic component. 8. Although it cannot be excluded that the dominant frequency of oscillations might be related to the type of anaesthetics used, no correlation was found between local EEG and the oscillatory activity elicited by visual stimulation. 9. We conclude that the oscillations observed in the present work are generated by synaptic activity. It is likely that they represent an important mode of transmission in sensory processing, resulting from periodic packets of synchronized activity propagated across recurrent circuits. Their relevance to perceptual binding is further discussed.

Oscillatory mechanisms in pairs of neurons connected with fast inhibitory synapses

We study dynamical mechanisms underlying oscillatory behavior in reciprocal inhibitory pairs of neurons, using a two-dimensional cell model. We introduce one-and-two dimensional phase portraits to illustrate the behaviors, thus reducing the study of dynamical mechanisms to planar geometrical properties. We examined whether other mechanisms besides the escape and release mechanisms (Wang and Rinzel, 1992) might be needed for some cases of reciprocal inhibition, and show that, within the confines of a simple two-dimensional cell model, escape and release are sufficient for all cases. We divided the behaviors of a single cell into six different types and examined the joint behaviors arising from every combination of pairs of cells with behaviors drawn from these six types. For the case of two quiescent cells or two cells each having plateau potentials, bifurcation diagrams demonstrate the relations between synaptic threshold and synaptic strength necessary for oscillations by escape, oscillations by release, or network-generated plateau potentials. Thus we clarify the relationship between plateau potentials and oscillations in a cell. Using the two dimensional cell model we examine 1:N beating between cells and find that our simple model displays many of the essential dynamical properties displayed by more sophisticated models, some of which relate to thalamocortical spindling.

Functional reorganization in thalamocortical networks: transition between spindling and delta sleep rhythms

Thalamic reticularis, thalamocortical, and cortical cells participate in the 7-14-hz spindling rhythm of early sleep and the slower delta rhythms of deeper sleep, with different firing patterns. In this case study, showing the interactions of intrinsic and synaptic properties, a change in the conductance of one kind of cell effectively rewires the thalamocortical circuit, leading to the transition from the spindling to the delta rhythm. The two rhythms make different uses of the fast (GABAA) and slow (GABAB) inhibition generated by the thalamic reticularis cells.

Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model

Fast neuronal oscillations (gamma, 20-80 Hz) have been observed in the neocortex and hippocampus during behavioral arousal. Using computer simulations, we investigated the hypothesis that such rhythmic activity can emerge in a random network of interconnected GABAergic fast-spiking interneurons. Specific conditions for the population synchronization, on properties of single cells and the circuit, were identified. These include the following: (1) that the amplitude of spike afterhyperpolarization be above the GABAA synaptic reversal potential; (2) that the ratio between the synaptic decay time constant and the oscillation period be sufficiently large; (3) that the effects of heterogeneities be modest because of a steep frequency-current relationship of fast-spiking neurons. Furthermore, using a population coherence measure, based on coincident firings of neural pairs, it is demonstrated that large-scale network synchronization requires a critical (minimal) average number of synaptic contacts per cell, which is not sensitive to the network size. By changing the GABAA synaptic maximal conductance, synaptic decay time constant, or the mean external excitatory drive to the network, the neuronal firing frequencies were gradually and monotonically varied. By contrast, the network synchronization was found to be high only within a frequency band coinciding with the gamma (20-80 Hz) range. We conclude that the GABAA synaptic transmission provides a suitable mechanism for synchronized gamma oscillations in a sparsely connected network of fast-spiking interneurons. In turn, the interneuronal network can presumably maintain subthreshold oscillations in principal cell populations and serve to synchronize discharges of spatially distributed neurons.

Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model

Fast neuronal oscillations (gamma, 20-80 Hz) have been observed in the neocortex and hippocampus during behavioral arousal. Using computer simulations, we investigated the hypothesis that such rhythmic activity can emerge in a random network of interconnected GABAergic fast-spiking interneurons. Specific conditions for the population synchronization, on properties of single cells and the circuit, were identified. These include the following: (1) that the amplitude of spike afterhyperpolarization be above the GABAA synaptic reversal potential; (2) that the ratio between the synaptic decay time constant and the oscillation period be sufficiently large; (3) that the effects of heterogeneities be modest because of a steep frequency-current relationship of fast-spiking neurons. Furthermore, using a population coherence measure, based on coincident firings of neural pairs, it is demonstrated that large-scale network synchronization requires a critical (minimal) average number of synaptic contacts per cell, which is not sensitive to the network size. By changing the GABAA synaptic maximal conductance, synaptic decay time constant, or the mean external excitatory drive to the network, the neuronal firing frequencies were gradually and monotonically varied. By contrast, the network synchronization was found to be high only within a frequency band coinciding with the gamma (20-80 Hz) range. We conclude that the GABAA synaptic transmission provides a suitable mechanism for synchronized gamma oscillations in a sparsely connected network of fast-spiking interneurons. In turn, the interneuronal network can presumably maintain subthreshold oscillations in principal cell populations and serve to synchronize discharges of spatially distributed neurons.

Inhibition synchronizes sparsely connected cortical neurons within and between columns in realistic network models

Networks of compartmental model neurons were used to investigate the biophysical basis of the synchronization observed between sparsely-connected neurons in neocortex. A model of a single column in layer 5 consisted of 100 model neurons: 80 pyramidal and 20 inhibitory. The pyramidal cells had conductances that caused intrinsic repetitive bursting at different frequencies when driven with the same input. When connected randomly with a connection density of 10%, a single model column displayed synchronous oscillatory action potentials in response to stationary, uncorrelated Poisson spike-train inputs. Synchrony required a high ratio of inhibitory to excitatory synaptic strength; the optimal ratio was 4 : 1, within the range observed in cortex. The synchrony was insensitive to variation in amplitudes of postsynaptic potentials and synaptic delay times, even when the mean synaptic delay times were varied over the range 1 to 7 ms. Synchrony was found to be sensitive to the strength of reciprocal inhibition between the inhibitory neurons in one column: Too weak or too strong reciprocal inhibition degraded intra-columnar synchrony. The only parameter that affected the oscillation frequency of the network was the strength of the external driving input which could shift the frequency between 35 to 60 Hz. The same results were obtained using a model column of 1000 neurons with a connection density of 5%, except that the oscillation became more regular. Synchronization between cortical columns was studied in a model consisting of two columns with 100 model neurons each. When connections were made with a density of 3% between the pyramidal cells of each column there was no inter-columnar synchrony and in some cases the columns oscillated 180 degrees out of phase with each other. Only when connections from the pyramidal cells in each column to the inhibitory cells in the other column were added was synchrony between the columns observed. This synchrony was established within one or two cycles of the oscillation and there was on average less than 1 ms phase difference between the two columns. Unlike the intra-columnar synchronization, the inter-columnar synchronization was found to be sensitive to the synaptic delay: A mean delay of greater than 5 ms virtually abolished synchronization between columns.