Spindle rhythmicity in the reticularis thalami nucleus: synchronization among mutually inhibitory neurons

Spindle oscillations emerge at the critical state of electrically coupled networks in the thalamic reticular nucleus

Spindle oscillation is a waxing-and-waning neural oscillation observed in the brain, initiated at the thalamic reticular nucleus (TRN) and typically occurring at 7-15 Hz. Experiments have shown that in the adult brain, electrical synapses, rather than chemical synapses, dominate between TRN neurons, suggesting that the traditional view of spindle generation via chemical synapses may need reconsideration. Based on known experimental data, we develop a computational model of the TRN network, where heterogeneous neurons are connected by electrical synapses. The model shows that the interplay between synchronizing electrical synapses and desynchronizing heterogeneity leads to multiple synchronized clusters with slightly different oscillation frequencies whose summed-up activity produces spindle oscillation as seen in local field potentials. Our results suggest that during spindle oscillation, the network operates at the critical state, which is known for facilitating efficient information processing. This study provides insights into the underlying mechanism of spindle oscillation and its functional significance.

A Computational Model of Deep Brain Stimulation for Parkinson's Disease Tremor and Bradykinesia

Parkinson's disease (PD) is a progressive neurological disorder that is typically characterized by a range of motor dysfunctions, and its impact extends beyond physical abnormalities into emotional well-being and cognitive symptoms. The loss of dopaminergic neurons in the substantia nigra pars compacta (SNc) leads to an array of dysfunctions in the functioning of the basal ganglia (BG) circuitry that manifests into PD. While active research is being carried out to find the root cause of SNc cell death, various therapeutic techniques are used to manage the symptoms of PD. The most common approach in managing the symptoms is replenishing the lost dopamine in the form of taking dopaminergic medications such as levodopa, despite its long-term complications. Another commonly used intervention for PD is deep brain stimulation (DBS). DBS is most commonly used when levodopa medication efficacy is reduced, and, in combination with levodopa medication, it helps reduce the required dosage of medication, prolonging the therapeutic effect. DBS is also a first choice option when motor complications such as dyskinesia emerge as a side effect of medication. Several studies have also reported that though DBS is found to be effective in suppressing severe motor symptoms such as tremors and rigidity, it has an adverse effect on cognitive capabilities. Henceforth, it is important to understand the exact mechanism of DBS in alleviating motor symptoms. A computational model of DBS stimulation for motor symptoms will offer great insights into understanding the mechanisms underlying DBS, and, along this line, in our current study, we modeled a cortico-basal ganglia circuitry of arm reaching, where we simulated healthy control (HC) and PD symptoms as well as the DBS effect on PD tremor and bradykinesia. Our modeling results reveal that PD tremors are more correlated with the theta band, while bradykinesia is more correlated with the beta band of the frequency spectrum of the local field potential (LFP) of the subthalamic nucleus (STN) neurons. With a DBS current of 220 pA, 130 Hz, and a 100 microsecond pulse-width, we could found the maximum therapeutic effect for the pathological dynamics simulated using our model using a set of parameter values. However, the exact DBS characteristics vary from patient to patient, and this can be further studied by exploring the model parameter space. This model can be extended to study different DBS targets and accommodate cognitive dynamics in the future to study the impact of DBS on cognitive symptoms and thereby optimize the parameters to produce optimal performance effects across modalities. Combining DBS with rehabilitation is another frontier where DBS can reduce symptoms such as tremors and rigidity, enabling patients to participate in their therapy. With DBS providing instant relief to patients, a combination of DBS and rehabilitation can enhance neural plasticity. One of the key motivations behind combining DBS with rehabilitation is to expect comparable results in motor performance even with milder DBS currents.

The neuronal and synaptic dynamics underlying post-inhibitory rebound burst related to major depressive disorder in the lateral habenula neuron model

A burst behavior observed in the lateral habenula (LHb) neuron related to major depressive disorder has attracted much attention. The burst is induced from silence by the excitatory N-methyl-D-aspartate (NMDA) synapse or by the inhibitory stimulation, i.e., a post-inhibitory rebound (PIR) burst, which has not been explained clearly. In the present paper, the neuronal and synaptic dynamics for the PIR burst are acquired in a theoretical neuron model. At first, dynamic cooperations between the fast rise of inhibitory γ-aminobutyric acid (GABA) synapse, slow rise of NMDA synapse, and T-type calcium current to evoke the PIR burst are obtained. Similar to the inhibitory pulse stimulation, fast rising GABA current can reduce the membrane potential to a level low enough to de-inactivate the low threshold T-type calcium current to evoke a PIR spike, which can enhance the slow rising NMDA current activated at a time before or after the PIR spike. The NMDA current following the PIR spike exhibits slow decay to induce multiple spikes to form the PIR burst. Such results present a theoretical explanation and a candidate for the PIR burst in real LHb neurons. Then, the dynamical mechanism for the PIR spike mediated by the T-type calcium channel is obtained. At large conductance of T-type calcium channel, the resting state corresponds to a stable focus near Hopf bifurcation and exhibits an "uncommon" threshold curve with membrane potential much lower than the resting membrane potential. Inhibitory modulation induces membrane potential decreased to run across the threshold curve to evoke the PIR spike. At small conductance of the T-type calcium channel, a stable node appears and manifests a common threshold curve with higher membrane potential, resulting in non-PIR phenomenon. The results present the dynamic cooperations between neuronal dynamics and fast/slow dynamics of different synapses for the PIR burst observed in the LHb neuron, which is helpful for the modulations to major depressive disorder.

Synchrony in Networks of Type 2 Interneurons Is More Robust to Noise with Hyperpolarizing Inhibition Compared to Shunting Inhibition in Both the Stochastic Population Oscillator and the Coupled Oscillator Regimes

Synchronization in the gamma band (25-150 Hz) is mediated by PV+ inhibitory interneurons, and evidence is accumulating for the essential role of gamma oscillations in cognition. Oscillations can arise in inhibitory networks via synaptic interactions between individual oscillatory neurons (mean-driven) or via strong recurrent inhibition that destabilizes the stationary background firing rate in the fluctuation-driven balanced state, causing an oscillation in the population firing rate. Previous theoretical work focused on model neurons with Hodgkin's Type 1 excitability (integrators) connected by current-based synapses. Here we show that networks comprised of simple Type 2 oscillators (resonators) exhibit a supercritical Hopf bifurcation between synchrony and asynchrony and a gradual transition via cycle skipping from coupled oscillators to stochastic population oscillator (SPO), as previously shown for Type 1. We extended our analysis to homogeneous networks with conductance rather than current based synapses and found that networks with hyperpolarizing inhibitory synapses were more robust to noise than those with shunting synapses, both in the coupled oscillator and SPO regime. Assuming that reversal potentials are uniformly distributed between shunting and hyperpolarized values, as observed in one experimental study, converting synapses to purely hyperpolarizing favored synchrony in all cases, whereas conversion to purely shunting synapses made synchrony less robust except at very high conductance strengths. In mature neurons the synaptic reversal potential is controlled by chloride cotransporters that control the intracellular concentrations of chloride and bicarbonate ions, suggesting these transporters as a potential therapeutic target to enhance gamma synchrony and cognition.

Synchrony in Networks of Type 2 Interneurons is More Robust to Noise with Hyperpolarizing Inhibition Compared to Shunting Inhibition in Both the Stochastic Population Oscillator and the Coupled Oscillator Regimes

Synchronization in the gamma band (30-80 Hz) is mediated by PV+ inhibitory interneurons, and evidence is accumulating for the essential role of gamma oscillations in cognition. Oscillations can arise in inhibitory networks via synaptic interactions between individual oscillatory neurons (mean-driven) or via strong recurrent inhibition that destabilizes the stationary background firing rate in the fluctuation-driven balanced state, causing an oscillation in the population firing rate. Previous theoretical work focused on model neurons with Hodgkin's type 1 excitability (integrators) connected by current-based synapses. Here we show that networks comprised of simple type 2 oscillators (resonators) exhibit a supercritical Hopf bifurcation between synchrony and asynchrony and a gradual transition via cycle skipping from coupled oscillators to stochastic population oscillator, as previously shown for type 1. We extended our analysis to homogeneous networks with conductance rather than current based synapses and found that networks with hyperpolarizing inhibitory synapses were more robust to noise than those with shunting synapses, both in the coupled oscillator and stochastic population oscillator regime. Assuming that reversal potentials are uniformly distributed between shunting and hyperpolarized values, as observed in one experimental study, converting synapses to purely hyperpolarizing favored synchrony in all cases, whereas conversion to purely shunting synapses made synchrony less robust except at very high conductance strengths. In mature neurons the synaptic reversal potential is controlled by chloride cotransporters that control the intracellular concentrations of chloride and bicarbonate ions, suggesting these transporters as a potential therapeutic target to enhance gamma synchrony and cognition.

Significance Statement

Brain rhythms in the gamma frequency band (30-80 Hz) depend on the activity of inhibitory interneurons and evidence for a causal role for gamma oscillations in cognitive functions is accumulating. Here we extend previous studies on synchronization mechanisms to interneurons that have an abrupt threshold frequency below which they cannot sustain firing. In addition to current based synapses, we examined inhibitory networks with conductance based synapses. We found that if the reversal potential for inhibition was below the average membrane potential (hyperpolarizing), synchrony was more robust to noise than if the reversal potential was very close to the average potential (shunting). These results have implications for therapies to ameliorate cognitive deficits.

The Feature of Sleep Spindle Deficits in Patients With Schizophrenia With and Without Auditory Verbal Hallucinations

BACKGROUND

Previous sleep electroencephalography studies have detected abnormalities in sleep architecture and sleep spindle deficits in schizophrenia (SCZ), but the consistency of these results was not robust, which might be due to the small sample size and the influence of clinical factors such as the various medication therapies and symptom heterogeneity. This study aimed to regard auditory verbal hallucinations (AVHs) as a pointcut to downscale the heterogeneity of SCZ and explore whether some sleep architecture and spindle parameters were more severely impaired in SCZ patients with AVHs compared with those without AVHs.

METHODS

A total of 90 SCZ patients with AVHs, 92 SCZ patients without AVHs, and 91 healthy control subjects were recruited, and parameters of sleep architecture and spindle activities were compared between groups. The correlation between significant sleep parameters and clinical indicators was analyzed.

RESULTS

Deficits of sleep spindle activities at prefrontal electrodes and intrahemispheric spindle coherence were observed in both AVH and non-AVH groups, several of which were more serious in the AVH group. In addition, deficits of spindle activities at central and occipital electrodes and interhemispheric spindle coherence mainly manifested accompanying AVH symptoms, most of which were retained in the medication-naive first-episode patients, and were associated with Auditory Hallucination Rating Scale scores.

CONCLUSIONS

Our results suggest that the underlying mechanism of spindle deficits might be different between SCZ patients with and without AVHs. In the future, the sleep feature of SCZ patients with different symptoms and the influence of clinical factors, such as medication therapy, should be further illustrated.

Activity-dependent long-term potentiation of electrical synapses in the mammalian thalamus

Activity-dependent changes of synapse strength have been extensively characterized at chemical synapses, but the relationship between physiological forms of activity and strength at electrical synapses remains poorly characterized and understood. For mammalian electrical synapses comprising hexamers of connexin36, physiological forms of neuronal activity in coupled pairs have thus far only been linked to long-term depression; activity that results in strengthening of electrical synapses has not yet been identified. Here, we performed dual whole-cell current-clamp recordings in acute slices of P11-P15 Sprague-Dawley rats of electrically coupled neurons of the thalamic reticular nucleus (TRN), a central brain area that regulates cortical input from and attention to the sensory surround. Using TTA-A2 to limit bursting, we show that tonic spiking in one neuron of a pair results in long-term potentiation of electrical synapses. We use experiments and computational modeling to show that the magnitude of plasticity expressed alters the functionality of the synapse. Potentiation is expressed asymmetrically, indicating that regulation of connectivity depends on the direction of use. Furthermore, calcium pharmacology and imaging indicate that potentiation depends on calcium flux. We thus propose a calcium-based activity rule for bidirectional plasticity of electrical synapse strength. Because electrical synapses dominate intra-TRN connectivity, these synapses and their activity-dependent modifications are key dynamic regulators of thalamic attention circuitry. More broadly, we speculate that bidirectional modifications of electrical synapses may be a widespread and powerful principle for ongoing, dynamic reorganization of neuronal circuitry across the brain.NEW & NOTEWORTHY This work reveals a physiologically relevant form of activity pairing in coupled neurons that results in long-term potentiation of mammalian electrical synapses. These findings, in combination with previous work, allow the authors to propose a bidirectional calcium-based rule for plasticity of electrical synapses, similar to those demonstrated for chemical synapses. These new insights inform the field on how electrical synapse plasticity may modify the neural circuits that incorporate them.

A Computational Model of Loss of Dopaminergic Cells in Parkinson's Disease Due to Glutamate-Induced Excitotoxicity

Parkinson's disease (PD) is a neurodegenerative disease associated with progressive and inexorable loss of dopaminergic cells in Substantia Nigra pars compacta (SNc). Although many mechanisms have been suggested, a decisive root cause of this cell loss is unknown. A couple of the proposed mechanisms, however, show potential for the development of a novel line of PD therapeutics. One of these mechanisms is the peculiar metabolic vulnerability of SNc cells compared to other dopaminergic clusters; the other is the SubThalamic Nucleus (STN)-induced excitotoxicity in SNc. To investigate the latter hypothesis computationally, we developed a spiking neuron network-model of SNc-STN-GPe system. In the model, prolonged stimulation of SNc cells by an overactive STN leads to an increase in ‘stress' variable; when the stress in a SNc neuron exceeds a stress threshold, the neuron dies. The model shows that the interaction between SNc and STN involves a positive-feedback due to which, an initial loss of SNc cells that crosses a threshold causes a runaway-effect, leading to an inexorable loss of SNc cells, strongly resembling the process of neurodegeneration. The model further suggests a link between the two aforementioned mechanisms of SNc cell loss. Our simulation results show that the excitotoxic cause of SNc cell loss might initiate by weak-excitotoxicity mediated by energy deficit, followed by strong-excitotoxicity, mediated by a disinhibited STN. A variety of conventional therapies were simulated to test their efficacy in slowing down SNc cell loss. Among them, glutamate inhibition, dopamine restoration, subthalamotomy and deep brain stimulation showed superior neuroprotective-effects in the proposed model.

Electrical synapses regulate both subthreshold integration and population activity of principal cells in response to transient inputs within canonical feedforward circuits

As information about the world traverses the brain, the signals exchanged between neurons are passed and modulated by synapses, or specialized contacts between neurons. While neurotransmitter-based synapses tend to exert either excitatory or inhibitory pulses of influence on the postsynaptic neuron, electrical synapses, composed of plaques of gap junction channels, continuously transmit signals that can either excite or inhibit a coupled neighbor. A growing body of evidence indicates that electrical synapses, similar to their chemical counterparts, are modified in strength during physiological neuronal activity. The synchronizing role of electrical synapses in neuronal oscillations has been well established, but their impact on transient signal processing in the brain is much less understood. Here we constructed computational models based on the canonical feedforward neuronal circuit and included electrical synapses between inhibitory interneurons. We provided discrete closely-timed inputs to the circuits, and characterize the influence of electrical synapse strength on both subthreshold summation and spike trains in the output neuron. Our simulations highlight the diverse and powerful roles that electrical synapses play even in simple circuits. Because these canonical circuits are represented widely throughout the brain, we expect that these are general principles for the influence of electrical synapses on transient signal processing across the brain.

The roles that electrical synapses play in neural oscillations, network synchronization and rhythmicity are well established, but their roles in neuronal processing of transient inputs are much less understood. Here, we used computational models of canonical feedforward circuits and networks to investigate how electrical synapses regulate the flow of transient signals passing through those circuits. We show that because the influence of electrical synapses on coupled neighbors can be either inhibitory or excitatory, their role in network information processing is heterogeneous, and powerful. Because electrical synapses between interneurons are widespread across the brain, and in addition to a growing body of evidence for their activity-dependent plasticity, we expect the effects we describe here to play a substantial role in how the brain processes incoming sensory inputs.

Impact of sex steroids and reproductive stage on sleep-dependent memory consolidation in women

Age and sex are two of the three major risk factors for Alzheimer's disease (ApoE-e4 allele is the third), with women having a twofold greater risk for Alzheimer's disease after the age of 75 years. Sex differences have been shown across a wide range of cognitive skills in young and older adults, and evidence supports a role for sex steroids, especially estradiol, in protecting against the development of cognitive decline in women. Sleep may also be a protective factor against age-related cognitive decline, since specific electrophysiological sleep events (e.g. sleep spindle/slow oscillation coupling) are critical for offline memory consolidation. Furthermore, studies in young women have shown fluctuations in sleep events and sleep-dependent memory consolidation during different phases of the menstrual cycle that are associated with the levels of sex steroids. An under-appreciated possibility is that there may be an important interaction between these two protective factors (sex steroids and sleep) that may play a role in daily fluctuations in cognitive processing, in particular memory, across a woman's lifespan. Here, we summarize the current knowledge of sex steroid-dependent influences on sleep and cognition across the lifespan in women, with special emphasis on sleep-dependent memory processing. We further indicate gaps in knowledge that require further experimental examination in order to fully appreciate the complex and changing landscape of sex steroids and cognition. Lastly, we propose a series of testable predictions for how sex steroids impact sleep events and sleep-dependent cognition across the three major reproductive stages in women (reproductive years, menopause transition, and post-menopause).

Robust and tunable bursting requires slow positive feedback

We highlight that the robustness and tunability of a bursting model critically rely on currents that provide slow positive feedback to the membrane potential. Such currents have the ability to make the total conductance of the circuit negative in a timescale that is termed "slow" because it is intermediate between the fast timescale of the spike upstroke and the ultraslow timescale of even slower adaptation currents. We discuss how such currents can be assessed either in voltage-clamp experiments or in computational models. We show that, while frequent in the literature, mathematical and computational models of bursting that lack the slow negative conductance are fragile and rigid. Our results suggest that modeling the slow negative conductance of cellular models is important when studying the neuromodulation of rhythmic circuits at any broader scale. NEW & NOTEWORTHY Nervous system functions rely on the modulation of neuronal activity between different rhythmic patterns. The mechanisms of this modulation are still poorly understood. Using computational modeling, we show the critical role of currents that provide slow negative conductance, distinct from the fast negative conductance necessary for spike generation. The significance of the slow negative conductance for neuromodulation is often overlooked, leading to computational models that are rigid and fragile.

GABAB receptors suppress burst-firing in reticular thalamic neurons

Burst-firing in thalamic neurons is known to play a key role in mediating thalamocortical (TC) oscillations that are associated with non-REM sleep and some types of epileptic seizure. Within the TC system the primary output of GABAergic neurons in the reticular thalamic nucleus (RTN) is thought to induce the de-inactivation of T-type calcium channels in thalamic relay (TR) neurons, promoting burst-firing drive to the cortex and the propagation of TC network activity. However, RTN neurons also project back onto other neurons within the RTN. The role of this putative negative feedback upon the RTN itself is less well understood, although is hypothesized to induce de-synchronization of RTN neuron firing leading to the suppression of TC oscillations. Here we tested two hypotheses concerning possible mechanisms underlying TC oscillation modulation. Firstly, we assessed the burst-firing behavior of RTN neurons in response to GABA_B receptor activation using acute brain slices. The selective GABA_B receptor agonist baclofen was found to induce suppression of burst-firing concurrent with effects on membrane input resistance. Secondly, RTN neurons express Ca_V3.2 and Ca_V3.3 T-type calcium channel isoforms known to contribute toward TC burst-firing and we examined the modulation of these channels by GABA_B receptor activation. Utilizing exogenously expressed T-type channels we assessed whether GABA_B receptor activation could directly alter T-type calcium channel properties. Overall, GABA_B receptor activation had only modest effects on Ca_V3.2 and Ca_V3.3 isoforms. The only effect that could be predicted to suppress burst-firing was a hyperpolarized shift in the voltage-dependence of inactivation, potentially causing lower channel availability at membrane potentials critical for burst-firing. Conversely, other effects observed such as a hyperpolarized shift in the voltage-dependence of activation of both Ca_V3.2 and Ca_V3.3 as well as increased time constant of activation of the Ca_V3.3 isoform would be expected to enhance burst-firing. Together, we hypothesize that GABA_B receptor activation mediates multiple downstream effectors that combined act to suppress burst-firing within the RTN. It appears unlikely that direct GABA_B receptor-mediated modulation of T-type calcium channels is the major mechanistic contributor to this suppression.

The Potential Role of Gap Junctional Plasticity in the Regulation of State

Electrical synapses are the functional correlate of gap junctions and allow transmission of small molecules and electrical current between coupled neurons. Instead of static pores, electrical synapses are actually plastic, similar to chemical synapses. In the thalamocortical system, gap junctions couple inhibitory neurons that are similar in their biochemical profile, morphology, and electrophysiological properties. We postulate that electrical synaptic plasticity among inhibitory neurons directly interacts with the switching between different firing patterns in a state-dependent and type-dependent manner. In neuronal networks, electrical synapses may function as a modifiable resonance feedback system that enables stable oscillations. Furthermore, the plasticity of electrical synapses may play an important role in regulation of state, synchrony, and rhythmogenesis in the mammalian thalamocortical system, similar to chemical synaptic plasticity. Based on their plasticity, rich diversity, and specificity, electrical synapses are thus likely to participate in the control of consciousness and attention.

Reduced sleep spindle activity point to a TRN-MD thalamus-PFC circuit dysfunction in schizophrenia

Sleep disturbances have been reliably reported in patients with schizophrenia, thus suggesting that abnormal sleep may represent a core feature of this disorder. Traditional electroencephalographic studies investigating sleep architecture have found reduced deep non-rapid eye movement (NREM) sleep, or slow wave sleep (SWS), and increased REM density. However, these findings have been inconsistently observed, and have not survived meta-analysis. By contrast, several recent EEG studies exploring brain activity during sleep have established marked deficits in sleep spindles in schizophrenia, including first-episode and early-onset patients, compared to both healthy and psychiatric comparison subjects. Spindles are waxing and waning, 12-16Hz NREM sleep oscillations that are generated within the thalamus by the thalamic reticular nucleus (TRN), and are then synchronized and sustained in the cortex. While the functional role of sleep spindles still needs to be fully established, increasing evidence has shown that sleep spindles are implicated in learning and memory, including sleep dependent memory consolidation, and spindle parameters have been associated to general cognitive ability and IQ. In this article we will review the EEG studies demonstrating sleep spindle deficits in patients with schizophrenia, and show that spindle deficits can predict their reduced cognitive performance. We will then present data indicating that spindle impairments point to a TRN-MD thalamus-prefrontal cortex circuit deficit, and discuss about the possible molecular mechanisms underlying thalamo-cortical sleep spindle abnormalities in schizophrenia.

Rhythm generation, coordination, and initiation in the vocal pathways of male African clawed frogs

Central pattern generators (CPGs) in the brain stem are considered to underlie vocalizations in many vertebrate species, but the detailed mechanisms underlying how motor rhythms are generated, coordinated, and initiated remain unclear. We addressed these issues using isolated brain preparations of Xenopus laevis from which fictive vocalizations can be elicited. Advertisement calls of male X. laevis that consist of fast and slow trills are generated by vocal CPGs contained in the brain stem. Brain stem central vocal pathways consist of a premotor nucleus [dorsal tegmental area of medulla (DTAM)] and a laryngeal motor nucleus [a homologue of nucleus ambiguus (n.IX-X)] with extensive reciprocal connections between the nuclei. In addition, DTAM receives descending inputs from the extended amygdala. We found that unilateral transection of the projections between DTAM and n.IX-X eliminated premotor fictive fast trill patterns but did not affect fictive slow trills, suggesting that the fast and slow trill CPGs are distinct; the slow trill CPG is contained in n.IX-X, and the fast trill CPG spans DTAM and n.IX-X. Midline transections that eliminated the anterior, posterior, or both commissures caused no change in the temporal structure of fictive calls, but bilateral synchrony was lost, indicating that the vocal CPGs are contained in the lateral halves of the brain stem and that the commissures synchronize the two oscillators. Furthermore, the elimination of the inputs from extended amygdala to DTAM, in addition to the anterior commissure, resulted in autonomous initiation of fictive fast but not slow trills by each hemibrain stem, indicating that the extended amygdala provides a bilateral signal to initiate fast trills.

NEW & NOTEWORTHY

Central pattern generators (CPGs) are considered to underlie vocalizations in many vertebrate species, but the detailed mechanisms underlying their functions remain unclear. We addressed this question using an isolated brain preparation of African clawed frogs. We discovered that two vocal phases are mediated by anatomically distinct CPGs, that there are a pair of CPGs contained in the left and right half of the brain stem, and that mechanisms underlying initiation of the two vocal phases are distinct.

Linking dynamics of the inhibitory network to the input structure

Networks of inhibitory interneurons are found in many distinct classes of biological systems. Inhibitory interneurons govern the dynamics of principal cells and are likely to be critically involved in the coding of information. In this theoretical study, we describe the dynamics of a generic inhibitory network in terms of low-dimensional, simplified rate models. We study the relationship between the structure of external input applied to the network and the patterns of activity arising in response to that stimulation. We found that even a minimal inhibitory network can generate a great diversity of spatio-temporal patterning including complex bursting regimes with non-trivial ratios of burst firing. Despite the complexity of these dynamics, the network's response patterns can be predicted from the rankings of the magnitudes of external inputs to the inhibitory neurons. This type of invariant dynamics is robust to noise and stable in densely connected networks with strong inhibitory coupling. Our study predicts that the response dynamics generated by an inhibitory network may provide critical insights about the temporal structure of the sensory input it receives.

Resonant Interneurons Can Increase Robustness of Gamma Oscillations

Gamma oscillations are believed to play a critical role in in information processing, encoding, and retrieval. Inhibitory interneuronal network gamma (ING) oscillations may arise from a coupled oscillator mechanism in which individual neurons oscillate or from a population oscillator in which individual neurons fire sparsely and stochastically. All ING mechanisms, including the one proposed herein, rely on alternating waves of inhibition and windows of opportunity for spiking. The coupled oscillator model implemented with Wang-Buzsáki model neurons is not sufficiently robust to heterogeneity in excitatory drive, and therefore intrinsic frequency, to account for in vitro models of ING. Similarly, in a tightly synchronized regime, the stochastic population oscillator model is often characterized by sparse firing, whereas interneurons both in vivo and in vitro do not fire sparsely during gamma, but rather on average every other cycle. We substituted so-called resonator neural models, which exhibit class 2 excitability and postinhibitory rebound (PIR), for the integrators that are typically used. This results in much greater robustness to heterogeneity that actually increases as the average participation in spikes per cycle approximates physiological levels. Moreover, dynamic clamp experiments that show autapse-induced firing in entorhinal cortical interneurons support the idea that PIR can serve as a network gamma mechanism. Furthermore, parvalbumin-positive (PV(+)) cells were much more likely to display both PIR and autapse-induced firing than GAD2(+) cells, supporting the view that PV(+) fast-firing basket cells are more likely to exhibit class 2 excitability than other types of inhibitory interneurons.

SIGNIFICANCE STATEMENT

Gamma oscillations are believed to play a critical role in information processing, encoding, and retrieval. Networks of inhibitory interneurons are thought to be essential for these oscillations. We show that one class of interneurons with an abrupt onset of firing at a threshold frequency may allow more robust synchronization in the presence of noise and heterogeneity. The mechanism for this robustness depends on the intrinsic resonance at this threshold frequency. Moreover, we show experimentally the feasibility of the proposed mechanism and suggest a way to distinguish between this mechanism and another proposed mechanism: that of a stochastic population oscillator independent of the dynamics of individual neurons.

Effects of self-coupling and asymmetric output on metastable dynamical transient firing patterns in arrays of neurons with bidirectional inhibitory coupling

Metastable dynamical transient patterns in arrays of bidirectionally coupled neurons with self-coupling and asymmetric output were studied. First, an array of asymmetric sigmoidal neurons with symmetric inhibitory bidirectional coupling and self-coupling was considered and the bifurcations of its steady solutions were shown. Metastable dynamical transient spatially nonuniform states existed in the presence of a pair of spatially symmetric stable solutions as well as unstable spatially nonuniform solutions in a restricted range of the output gain of a neuron. The duration of the transients increased exponentially with the number of neurons up to the maximum number at which the spatially nonuniform steady solutions were stabilized. The range of the output gain for which they existed reduced as asymmetry in a sigmoidal output function of a neuron increased, while the existence range expanded as the strength of inhibitory self-coupling increased. Next, arrays of spiking neuron models with slow synaptic inhibitory bidirectional coupling and self-coupling were considered with computer simulation. In an array of Class 1 Hindmarsh-Rose type models, in which each neuron showed a graded firing rate, metastable dynamical transient firing patterns were observed in the presence of inhibitory self-coupling. This agreed with the condition for the existence of metastable dynamical transients in an array of sigmoidal neurons. In an array of Class 2 Bonhoeffer-van der Pol models, in which each neuron had a clear threshold between firing and resting, long-lasting transient firing patterns with bursting and irregular motion were observed.

Dynamics of Time Delay-Induced Multiple Synchronous Behaviors in Inhibitory Coupled Neurons

The inhibitory synapse can induce synchronous behaviors different from the anti-phase synchronous behaviors, which have been reported in recent studies. In the present paper, synchronous behaviors are investigated in the motif model composed of reciprocal inhibitory coupled neurons with endogenous bursting and time delay. When coupling strength is weak, synchronous behavior appears at a single interval of time delay within a bursting period. When coupling strength is strong, multiple synchronous behaviors appear at different intervals of time delay within a bursting period. The different bursting patterns of synchronous behaviors, and time delays and coupling strengths that can induce the synchronous bursting patterns can be well interpreted by the dynamics of the endogenous bursting pattern of isolated neuron, which is acquired by the fast-slow dissection method, combined with the inhibitory coupling current. For an isolated neuron, when a negative impulsive current with suitable strength is applied at different phases of the bursting, multiple different bursting patterns can be induced. For a neuron in the motif, the inhibitory coupling current, of which the application time and strength is modulated by time delay and coupling strength, can cause single or multiple synchronous firing patterns like the negative impulsive current when time delay and coupling strength is suitable. The difference compared to the previously reported multiple synchronous behaviors that appear at time delays wider than a period of the endogenous firing is discussed. The results present novel examples of synchronous behaviors in the neuronal network with inhibitory synapses and provide a reasonable explanation.

A positive feedback at the cellular level promotes robustness and modulation at the circuit level

This article highlights the role of a positive feedback gating mechanism at the cellular level in the robustness and modulation properties of rhythmic activities at the circuit level. The results are presented in the context of half-center oscillators, which are simple rhythmic circuits composed of two reciprocally connected inhibitory neuronal populations. Specifically, we focus on rhythms that rely on a particular excitability property, the postinhibitory rebound, an intrinsic cellular property that elicits transient membrane depolarization when released from hyperpolarization. Two distinct ionic currents can evoke this transient depolarization: a hyperpolarization-activated cation current and a low-threshold T-type calcium current. The presence of a slow activation is specific to the T-type calcium current and provides a slow positive feedback at the cellular level that is absent in the cation current. We show that this slow positive feedback is required to endow the network rhythm with physiological modulation and robustness properties. This study thereby identifies an essential cellular property to be retained at the network level in modeling network robustness and modulation.

A spiking Basal Ganglia model of synchrony, exploration and decision making

To make an optimal decision we need to weigh all the available options, compare them with the current goal, and choose the most rewarding one. Depending on the situation an optimal decision could be to either “explore” or “exploit” or “not to take any action” for which the Basal Ganglia (BG) is considered to be a key neural substrate. In an attempt to expand this classical picture of BG function, we had earlier hypothesized that the Indirect Pathway (IP) of the BG could be the subcortical substrate for exploration. In this study we build a spiking network model to relate exploration to synchrony levels in the BG (which are a neural marker for tremor in Parkinson's disease). Key BG nuclei such as the Sub Thalamic Nucleus (STN), Globus Pallidus externus (GPe) and Globus Pallidus internus (GPi) were modeled as Izhikevich spiking neurons whereas the Striatal output was modeled as Poisson spikes. The model is cast in reinforcement learning framework with the dopamine signal representing reward prediction error. We apply the model to two decision making tasks: a binary action selection task (similar to one used by Humphries et al., 2006) and an n-armed bandit task (Bourdaud et al., 2008). The model shows that exploration levels could be controlled by STN's lateral connection strength which also influenced the synchrony levels in the STN-GPe circuit. An increase in STN's lateral strength led to a decrease in exploration which can be thought as the possible explanation for reduced exploratory levels in Parkinson's patients. Our simulations also show that on complete removal of IP, the model exhibits only Go and No-Go behaviors, thereby demonstrating the crucial role of IP in exploration. Our model provides a unified account for synchronization, action section, and explorative behavior.

Grid cell firing patterns may arise from feedback interaction between intrinsic rebound spiking and transverse traveling waves with multiple heading angles

This article presents a model using cellular resonance and rebound properties to model grid cells in medial entorhinal cortex. The model simulates the intrinsic resonance properties of single layer II stellate cells with different frequencies due to the hyperpolarization activated cation current (h current). The stellate cells generate rebound spikes after a delay interval that differs for neurons with different resonance frequency. Stellate cells drive inhibitory interneurons to cause rebound from inhibition in an alternate set of stellate cells that drive interneurons to activate the first set of cells. This allows maintenance of activity with cycle skipping of the spiking of cells that matches recent physiological data on theta cycle skipping. The rebound spiking interacts with subthreshold oscillatory input to stellate cells or interneurons regulated by medial septal input and defined relative to the spatial location coded by neurons. The timing of rebound determines whether the network maintains the activity for the same location or shifts to phases of activity representing a different location. Simulations show that spatial firing patterns similar to grid cells can be generated with a range of different resonance frequencies, indicating how grid cells could be generated with low frequencies present in bats and in mice with knockout of the HCN1 subunit of the h current.

Associative learning beyond the medial temporal lobe: many actors on the memory stage

Decades of research have established a model that includes the medial temporal lobe, and particularly the hippocampus, as a critical node for episodic memory. Neuroimaging and clinical studies have shown the involvement of additional cortical and subcortical regions. Among these areas, the thalamus, the retrosplenial cortex, and the prefrontal cortices have been consistently related to episodic memory performance. This article provides evidences that these areas are in different forms and degrees critical for human memory function rather than playing only an ancillary role. First we briefly summarize the functional architecture of the medial temporal lobe with respect to recognition memory and recall. We then focus on the clinical and neuroimaging evidence available on thalamo-prefrontal and thalamo-retrosplenial networks. The role of these networks in episodic memory has been considered secondary, partly because disruption of these areas does not always lead to severe impairments; to account for this evidence, we discuss methodological issues related to the investigation of these regions. We propose that these networks contribute differently to recognition memory and recall, and also that the memory stage of their contribution shows specificity to encoding or retrieval in recall tasks. We note that the same mechanisms may be in force when humans perform non-episodic tasks, e.g., semantic retrieval and mental time travel. Functional disturbance of these networks is related to cognitive impairments not only in neurological disorders, but also in psychiatric medical conditions, such as schizophrenia. Finally we discuss possible mechanisms for the contribution of these areas to memory, including regulation of oscillatory rhythms and long-term potentiation. We conclude that integrity of the thalamo-frontal and the thalamo-retrosplenial networks is necessary for the manifold features of episodic memory.

The cellular building blocks of breathing

Respiratory brainstem neurons fulfill critical roles in controlling breathing: they generate the activity patterns for breathing and contribute to various sensory responses including changes in O2 and CO2. These complex sensorimotor tasks depend on the dynamic interplay between numerous cellular building blocks that consist of voltage-, calcium-, and ATP-dependent ionic conductances, various ionotropic and metabotropic synaptic mechanisms, as well as neuromodulators acting on G-protein coupled receptors and second messenger systems. As described in this review, the sensorimotor responses of the respiratory network emerge through the state-dependent integration of all these building blocks. There is no known respiratory function that involves only a small number of intrinsic, synaptic, or modulatory properties. Because of the complex integration of numerous intrinsic, synaptic, and modulatory mechanisms, the respiratory network is capable of continuously adapting to changes in the external and internal environment, which makes breathing one of the most integrated behaviors. Not surprisingly, inspiration is critical not only in the control of ventilation, but also in the context of "inspiring behaviors" such as arousal of the mind and even creativity. Far-reaching implications apply also to the underlying network mechanisms, as lessons learned from the respiratory network apply to network functions in general.

The calcium-binding protein parvalbumin modulates the firing 1 properties of the reticular thalamic nucleus bursting neurons

The reticular thalamic nucleus (RTN) of the mouse is characterized by an overwhelming majority of GABAergic neurons receiving afferences from both the thalamus and the cerebral cortex and sending projections mainly on thalamocortical neurons. The RTN neurons express high levels of the "slow Ca(2+) buffer" parvalbumin (PV) and are characterized by low-threshold Ca(2+) currents, I(T). We performed extracellular recordings in ketamine/xylazine anesthetized mice in the rostromedial portion of the RTN. In the RTN of wild-type and PV knockout (PVKO) mice we distinguished four types of neurons characterized on the basis of their firing pattern: irregular firing (type I), medium bursting (type II), long bursting (type III), and tonically firing (type IV). Compared with wild-type mice, we observed in the PVKOs the medium bursting (type II) more frequently than the long bursting type and longer interspike intervals within the burst without affecting the number of spikes. This suggests that PV may affect the firing properties of RTN neurons via a mechanism associated with the kinetics of burst discharges. Ca(v)3.2 channels, which mediate the I(T) currents, were more localized to the somatic plasma membrane of RTN neurons in PVKO mice, whereas Ca(v)3.3 expression was similar in both genotypes. The immunoelectron microscopy analysis showed that Ca(v)3.2 channels were localized at active axosomatic synapses, thus suggesting that the differential localization of Ca(v)3.2 in the PVKOs may affect bursting dynamics. Cross-correlation analysis of simultaneously recorded neurons from the same electrode tip showed that about one-third of the cell pairs tended to fire synchronously in both genotypes, independent of PV expression. In summary, PV deficiency does not affect the functional connectivity between RTN neurons but affects the distribution of Ca(v)3.2 channels and the dynamics of burst discharges of RTN cells, which in turn regulate the activity in the thalamocortical circuit.

Stochastic generation of gamma-band activity in primary visual cortex of awake and anesthetized monkeys

Oscillatory neural activity within the gamma band (25-90 Hz) is generally thought to be able to provide a timing signal for harmonizing neural computations across different brain regions. Using time-frequency analyses of the dynamics of gamma-band activity in the local field potentials recorded from monkey primary visual cortex, we found identical temporal characteristics of gamma activity in both awake and anesthetized brain states, including large variability of peak frequency, brief oscillatory epochs (<100 ms on average), and stochastic statistics of the incidence and duration of oscillatory events. These findings indicate that gamma-band activity is temporally unstructured and is inherently a stochastic signal generated by neural networks. This idea was corroborated further by our neural-network simulations. Our results suggest that gamma-band activity is too random to serve as a clock signal for synchronizing neuronal responses in awake as in anesthetized monkeys. Instead, gamma-band activity is more likely to be filtered neuronal network noise. Its mean frequency changes with global state and is reduced under anesthesia.

Synchronization of neuron population subject to steady DC electric field induced by magnetic stimulation

Electric fields, which are ubiquitous in the context of neurons, are induced either by external electromagnetic fields or by endogenous electric activities. Clinical evidences point out that magnetic stimulation can induce an electric field that modulates rhythmic activity of special brain tissue, which are associated with most brain functions, including normal and pathological physiological mechanisms. Recently, the studies about the relationship between clinical treatment for psychiatric disorders and magnetic stimulation have been investigated extensively. However, further development of these techniques is limited due to the lack of understanding of the underlying mechanisms supporting the interaction between the electric field induced by magnetic stimulus and brain tissue. In this paper, the effects of steady DC electric field induced by magnetic stimulation on the coherence of an interneuronal network are investigated. Different behaviors have been observed in the network with different topologies (i.e., random and small-world network, modular network). It is found that the coherence displays a peak or a plateau when the induced electric field varies between the parameter range we defined. The coherence of the neuronal systems depends extensively on the network structure and parameters. All these parameters play a key role in determining the range for the induced electric field to synchronize network activities. The presented results could have important implications for the scientific theoretical studies regarding the effects of magnetic stimulation on human brain.

Phase-locked cluster oscillations in periodically forced integrate-and-fire-or-burst neuronal populations

The minimal integrate-and-fire-or-burst neuron model succinctly describes both tonic firing and postinhibitory rebound bursting of thalamocortical cells in the sensory relay. Networks of integrate-and-fire-or-burst (IFB) neurons with slow inhibitory synaptic interactions have been shown to support stable rhythmic states, including globally synchronous and cluster oscillations, in which network-mediated inhibition cyclically generates bursting in coherent subgroups of neurons. In this paper, we introduce a reduced IFB neuronal population model to study synchronization of inhibition-mediated oscillatory bursting states to periodic excitatory input. Using numeric methods, we demonstrate the existence and stability of 1:1 phase-locked bursting oscillations in the sinusoidally forced IFB neuronal population model. Phase locking is shown to arise when periodic excitation is sufficient to pace the onset of bursting in an IFB cluster without counteracting the inhibitory interactions necessary for burst generation. Phase-locked bursting states are thus found to destabilize when periodic excitation increases in strength or frequency. Further study of the IFB neuronal population model with pulse-like periodic excitatory input illustrates that this synchronization mechanism generalizes to a broad range of n:m phase-locked bursting states across both globally synchronous and clustered oscillatory regimes.

Exponential transient propagating oscillations in a ring of spiking neurons with unidirectional slow inhibitory synaptic coupling

Transient oscillations in a ring of spiking neuron models unidirectionally coupled with slow inhibitory synapses are studied. There are stable spatially fixed steady firing-resting states and unstable symmetric propagating firing-resting states. In transients, firing-resting patterns rotate in the direction of coupling (propagating oscillations), the duration of which increases exponentially with the number of neurons (exponential transients). Further, the duration of randomly generated transient propagating oscillations is distributed in a power law form and spatiotemporal noise of intermediate strength sustains propagating oscillations. These properties agree with those of transient propagating waves in a ring of sigmoidal neuron models.

Glutamate and nicotinic receptor interactions in working memory: importance for the cognitive impairment of schizophrenia

This article reaches across disciplines to correlate results in molecular, cellular, behavioral, and clinical research to develop a more complete picture of how working memory (WM) functions. It identifies a new idea that deserves further investigation. NMDA glutamate receptors (NMDAR) are critical for memory function. NMDAR inhibition effectively reproduces principal manifestations of schizophrenia (SP), such as WM impairment and GABAergic deficit (mainly reduction of glutamic acid decarboxylase 67 (GAD67) and parvalbumin (PV) content). Nicotine and selective α7 nicotinic acetylcholine receptor (nAChR) agonists reduce WM impairments in patients with SP and reverse WM deficits in animals treated with NMDAR antagonists. The mechanism of this effect is unknown. Importantly, WM recovery occurs even before restoration of NMDAR blockade-induced molecular alterations, including reduced GAD67 in interneurons. Our insight into the cognitive-enhancing effect of α7 nAChR agonists, particularly in the animal models of SP, combines reviews of recent findings on glutamate and nicotinic receptor expression in the neuronal circuits involved in WM, the properties of these receptors, their implication in WM regulation, generation of rhythmic neuronal activity, resulting in a proposed hypothesis for further investigations. We suggest that (1) cortical/hippocampal interneurons, particularly PV positive, play a crucial role in WM and that impairment of these cells in SP could be behind the WM deficit; (2) activation of α7 nAChRs could restore calcium signaling and intrinsic properties of these interneurons, and associated with these events, computational capacity, gamma rhythmic activity, and WM would also be restored.

Network reconfiguration and neuronal plasticity in rhythm-generating networks

Neuronal networks are highly plastic and reconfigure in a state-dependent manner. The plasticity at the network level emerges through multiple intrinsic and synaptic membrane properties that imbue neurons and their interactions with numerous nonlinear properties. These properties are continuously regulated by neuromodulators and homeostatic mechanisms that are critical to maintain not only network stability and also adapt networks in a short- and long-term manner to changes in behavioral, developmental, metabolic, and environmental conditions. This review provides concrete examples from neuronal networks in invertebrates and vertebrates, and illustrates that the concepts and rules that govern neuronal networks and behaviors are universal.

Impact of noise structure and network topology on tracking speed of neural networks

Understanding why neural systems can process information extremely fast is a fundamental question in theoretical neuroscience. The present study investigates the effect of noise on accelerating neural computation. To evaluate the speed of network response, we consider a computational task in which the network tracks time-varying stimuli. Two noise structures are compared, namely, the stimulus-dependent and stimulus-independent noises. Based on a simple linear integrate-and-fire model, we theoretically analyze the network dynamics, and find that the stimulus-dependent noise, whose variance is proportional to the mean of external inputs, has better effect on speeding up network computation. This is due to two good properties in the transient network dynamics: (1) the instant firing rate of the network is proportional to the mean of external inputs, and (2) the stationary state of the network is robust to stimulus changes. We investigate two network models with varying recurrent interactions, and find that recurrent interactions tend to slow down the tracking speed of the network. When the biologically plausible Hodgkin-Huxley model is considered, we also observe that the stimulus-dependent noise accelerates neural computation, although the improvement is smaller than that in the case of linear integrate-and-fire model.

The function of the sleep spindle: a physiological index of intelligence and a mechanism for sleep-dependent memory consolidation

Until recently, the electrophysiological mechanisms involved in strengthening new memories into a more permanent form during sleep have been largely unknown. The sleep spindle is an event in the electroencephalogram (EEG) characterizing Stage 2 sleep. Sleep spindles may reflect, at the electrophysiological level, an ideal mechanism for inducing long-term synaptic changes in the neocortex. Recent evidence suggests the spindle is highly correlated with tests of intellectual ability (e.g.; IQ tests) and may serve as a physiological index of intelligence. Further, spindles increase in number and duration in sleep following new learning and are correlated with performance improvements. Spindle density and sigma (14-16Hz) spectral power have been found to be positively correlated with performance following a daytime nap, and animal studies suggest the spindle is involved in a hippocampal-neocortical dialogue necessary for memory consolidation. The findings reviewed here collectively provide a compelling body of evidence that the function of the sleep spindle is related to intellectual ability and memory consolidation.

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.

EEG generator--a model of potentials in a volume conductor

EEG generator-a model of potentials in a volume conductor. The potential recorded over the cortex electro-corticogram (ECoG) or over the scalp [electroencephalograph (EEG)] derives from the activity of many sources known as "EEG generators." The recorded amplitude is basically a function of the unitary potential of a generator and the statistical relationship between different EEG generators in the recorded population. In this study, we first suggest a new definition of the EEG generator. We use the theory of potentials in a volume conductor and model the contribution of a single synapse activated to the surface potential. We then model the contribution of the generator to the surface potential. Once the generator and its contribution are well defined, we can quantitatively assess the degree of synchronization among generators. The measures obtained by the model for a real life scenario of a group of generators organized in a specific statistical way were consistent with the expected values that were reported experimentally. The study sheds new light on macroscopic modeling approaches which make use of mean soma membrane potential. We showed major contribution of activity of superficial apical synapses to the ECoG signal recorded relative to lower somatic or basal synapses activity.

Neural mechanisms of interstimulus interval-dependent responses in the primary auditory cortex of awake cats

Background

Primary auditory cortex (AI) neurons show qualitatively distinct response features to successive acoustic signals depending on the inter-stimulus intervals (ISI). Such ISI-dependent AI responses are believed to underlie, at least partially, categorical perception of click trains (elemental vs. fused quality) and stop consonant-vowel syllables (eg.,/da/-/ta/continuum).

Methods

Single unit recordings were conducted on 116 AI neurons in awake cats. Rectangular clicks were presented either alone (single click paradigm) or in a train fashion with variable ISI (2–480 ms) (click-train paradigm). Response features of AI neurons were quantified as a function of ISI: one measure was related to the degree of stimulus locking (temporal modulation transfer function [tMTF]) and another measure was based on firing rate (rate modulation transfer function [rMTF]). An additional modeling study was performed to gain insight into neurophysiological bases of the observed responses.

Results

In the click-train paradigm, the majority of the AI neurons ("synchronization type"; n = 72) showed stimulus-locking responses at long ISIs. The shorter cutoff ISI for stimulus-locking responses was on average ~30 ms and was level tolerant in accordance with the perceptual boundary of click trains and of consonant-vowel syllables. The shape of tMTF of those neurons was either band-pass or low-pass. The single click paradigm revealed, at maximum, four response periods in the following order: 1st excitation, 1st suppression, 2nd excitation then 2nd suppression. The 1st excitation and 1st suppression was found exclusively in the synchronization type, implying that the temporal interplay between excitation and suppression underlies stimulus-locking responses. Among these neurons, those showing the 2nd suppression had band-pass tMTF whereas those with low-pass tMTF never showed the 2nd suppression, implying that tMTF shape is mediated through the 2nd suppression. The recovery time course of excitability suggested the involvement of short-term plasticity. The observed phenomena were well captured by a single cell model which incorporated AMPA, GABA_A, NMDA and GABA_B receptors as well as short-term plasticity of thalamocortical synaptic connections.

Conclusion

Overall, it was suggested that ISI-dependent responses of the majority of AI neurons are configured through the temporal interplay of excitation and suppression (inhibition) along with short-term plasticity.

GABA neurons and the mechanisms of network oscillations: implications for understanding cortical dysfunction in schizophrenia

Synchronization of neuronal activity in the neocortex may underlie the coordination of neural representations and thus is critical for optimal cognitive function. Because cognitive deficits are the major determinant of functional outcome in schizophrenia, identifying their neural basis is important for the development of new therapeutic interventions. Here we review the data suggesting that phasic synaptic inhibition mediated by specific subtypes of cortical gamma-aminobutyric acid (GABA) neurons is essential for the production of synchronized network oscillations. We also discuss evidence indicating that GABA neurotransmission is altered in schizophrenia and propose mechanisms by which such alterations can decrease the strength of inhibitory connections in a cell-type-specific manner. We suggest that some alterations observed in the neocortex of schizophrenia subjects may be compensatory responses that partially restore inhibitory synaptic efficacy. The findings of altered neural synchrony and impaired cognitive function in schizophrenia suggest that such compensatory responses are insufficient and that interventions aimed at augmenting the efficacy of GABA neurotransmission might be of therapeutic value.

The properties of reticular thalamic neuron GABA(A) IPSCs of absence epilepsy rats lead to enhanced network excitability

Both human investigations and studies in animal models have suggested that abnormalities in GABA(A) receptor function have a potential role in the pathophysiology of absence seizures. Recently we showed that, prior to seizure onset, GABA(A) IPSCs in thalamic reticular (NRT) neurons of genetic absence epilepsy rats from Strasbourg (GAERS) had a 25% larger amplitude, a 40% faster decay and a 45% smaller paired-pulse depression than those of nonepileptic control (NEC) rats. By means of a novel mathematical description, the properties of both GAERS and NEC GABAergic synapses can be mimicked. These model synapses were then used in an NRT network model in order to investigate their potential impact on the neuronal firing patterns. Compared to NEC, GAERS NRT neurons show an overall increase in excitability and a higher frequency and regularity of firing in response to periodic input signals. Moreover, in response to randomly distributed stimuli, the GAERS but not the NEC model produces resonance between 7 and 9 Hz, the frequency range of spike-wave discharges in GAERS. The implications of these results for the epileptogenesis of absence seizures are discussed.

Transitions between irregular and rhythmic firing patterns in excitatory-inhibitory neuronal networks

Changes in firing patterns are an important hallmark of the functional status of neuronal networks. We apply dynamical systems methods to understand transitions between irregular and rhythmic firing in an excitatory-inhibitory neuronal network model. Using the geometric theory of singular perturbations, we systematically reduce the full model to a simpler set of equations, one that can be studied analytically. The analytic tools are used to understand how an excitatory-inhibitory network with a fixed architecture can generate both activity patterns for possibly different values of the intrinsic and synaptic parameters. These results are applied to a recently developed model for the subthalamopallidal network of the basal ganglia. The results suggest that an increase in correlated activity, corresponding to a pathological state, may be due to an increased level of inhibition from the striatum to the inhibitory GPe cells along with an increased ability of the excitatory STN neurons to generate rebound bursts.

Capturing the bursting dynamics of a two-cell inhibitory network using a one-dimensional map

Out-of-phase bursting is a functionally important behavior displayed by central pattern generators and other neural circuits. Understanding this complex activity requires the knowledge of the interplay between the intrinsic cell properties and the properties of synaptic coupling between the cells. Here we describe a simple method that allows us to investigate the existence and stability of anti-phase bursting solutions in a network of two spiking neurons, each possessing a T-type calcium current and coupled by reciprocal inhibition. We derive a one-dimensional map which fully characterizes the genesis and regulation of anti-phase bursting arising from the interaction of the T-current properties with the properties of synaptic inhibition. This map is the burst length return map formed as the composition of two distinct one-dimensional maps that are each regulated by a different set of model parameters. Although each map is constructed using the properties of a single isolated model neuron, the composition of the two maps accurately captures the behavior of the full network. We analyze the parameter sensitivity of these maps to determine the influence of both the intrinsic cell properties and the synaptic properties on the burst length, and to find the conditions under which multistability of several bursting solutions is achieved. Although the derivation of the map relies on a number of simplifying assumptions, we discuss how the principle features of this dimensional reduction method could be extended to more realistic model networks.

Intrinsic and Synaptic Mechanisms Determining the Timing of Neuron Population Activity During Hippocampal Theta Oscillation

Hippocampal theta (3–8 Hz) is a major electrophysiological activity in rodents, which can be found in primates and humans as well. During theta activity, pyramidal cells and different classes of interneurons were shown to discharge at different phases of the extracellular theta. A recent in vitro study has shown that theta-frequency oscillation can be elicited in a hippocampal CA1 slice by the activation of metabotropic glutamate receptors with similar pharmacological and physiological profile that was found in vivo. We constructed a conductance based three-population network model of the hippocampal CA1 region to study the specific roles of neuron types in the generation of the in vitro theta oscillation and the emergent network properties. Interactions between pairs of neuron populations were studied systematically to assess synchronization and delay properties. We showed that the circuitry consisting of pyramidal cells and two types of hippocampal interneurons [basket and oriens lacunosum-moleculare (O-LM) neurons] was able to generate coherent theta-frequency population oscillation. Furthermore, we found that hyperpolarization-activated nonspecific cation current in pyramidal cells, but not in O-LM neurons, plays an important role in the timing of spike generation, and thus synchronization of pyramidal cells. The model was shown to exhibit the same phase differences between neuron population activities found in vivo, supporting the idea that these patterns of activity are determined internal to the hippocampus.

Distinct electrical and chemical connectivity maps in the thalamic reticular nucleus: potential roles in synchronization and sensation

GABAergic neurons of the thalamic reticular nucleus (nRt) provide thalamocortical relay neurons with feedback inhibition that influences sensory processing and thalamocortical rhythm generation. Mutual interactions between reticular neurons coordinate oscillatory activities developed within the network during normal sleep and in absence epilepsy, but the chemical versus electrical nature of these connections and their functional influence remain controversial. Here, we investigated the incidence and spatial extent of intra-nRt connectivity in vitro in horizontal and coronal thalamic slices from rat. Laser scanning photostimulation activated presynaptic nRt cells during patch-clamp recordings of postsynaptic neurons. Photolysis of caged glutamate evoked GABAergic IPSCs and/or depolarizing events (spikelets, mediated via electrical coupling) in a large proportion of neurons, thus indicating connectivity with presynaptic cell(s). Synaptic inputs were organized along the major axis of the nucleus in the same orientation as, but commonly exceeding the extent of, dendritic arborization of the postsynaptic neuron. In the anteroposterior (horizontal) plane, chemical connectivity had higher incidence (60% of recorded neurons vs 40% in vertical plane) and longer spatial extent, whereas in the dorsoventral (vertical) plane, electrical coupling dominated (47% incidence vs 37% in horizontal plane) and was more widely distributed. These data demonstrate that both electrical and chemical synapses are prominent within nRt and suggest different roles for the two types of connections. We thus propose that, along the vertical plane, electrical connectivity will promote coordinated rhythmic activity of sleep and/or thalamocortical epilepsy, whereas along the horizontal plane, chemical connectivity will oppose widespread thalamocortical synchronization and modulate sensory throughput.

Spontaneous rhythmic field potentials of isolated mouse hippocampal-subicular-entorhinal cortices in vitro

The rodent hippocampal circuit is capable of exhibiting in vitro spontaneous rhythmic field potentials (SRFPs) of 1-4 Hz that originate from the CA3 area and spread to the CA1 area. These SRFPs are largely correlated with GABA-A IPSPs in pyramidal neurons and repetitive discharges in inhibitory interneurons. As such, their generation is thought to result from cooperative network activities involving both pyramidal neurons and GABAergic interneurons. Considering that the hippocampus, subiculum and entorhinal cortex function as an integrated system crucial for memory and cognition, it is of interest to know whether similar SRFPs occur in hippocampal output structures (that is, the subiculum and entorhinal cortex), and if so, to understand the cellular basis of these subicular and entorhinal SRFPs as well as their temporal relation to hippocampal SRFPs. We explored these issues in the present study using thick hippocampal-subicular-entorhinal cortical slices prepared from adult mice. SRFPs were found to spread from the CA1 area to the subicular and entorhinal cortical areas. Subicular and entorhinal cortical SRFPs were correlated with mixed IPSPs/EPSPs in local pyramidal neurons, and their generation was dependent upon the activities of GABA-A and AMPA glutamate receptors. In addition, the isolated subicular circuit could elicit SRFPs independent of CA3 inputs. We hypothesize that the SRFPs represent a basal oscillatory activity of the hippocampal-subicular-entorhinal cortices and that the subiculum functions as both a relay and an amplifier, spreading the SRFPs from the hippocampus to the entorhinal cortex.

Hyperpolarization-activated cation channels in fast-spiking interneurons of rat hippocampus

Hyperpolarization-activated channels (Ih or HCN channels) are widely expressed in principal neurons in the central nervous system. However, Ih in inhibitory GABAergic interneurons is less well characterized. We examined the functional properties of Ih in fast-spiking basket cells (BCs) of the dentate gyrus, using hippocampal slices from 17- to 21-day-old rats. Bath application of the Ih channel blocker ZD 7288 at a concentration of 30 microm induced a hyperpolarization of 5.7 +/- 1.5 mV, an increase in input resistance and a correlated increase in apparent membrane time constant. ZD 7288 blocked a hyperpolarization-activated current in a concentration-dependent manner (IC50, 1.4 microm). The effects of ZD 7288 were mimicked by external Cs+. The reversal potential of Ih was -27.4 mV, corresponding to a Na+ to K+ permeability ratio (PNa/PK) of 0.36. The midpoint potential of the activation curve of Ih was -83.9 mV, and the activation time constant at -120 mV was 190 ms. Single-cell expression analysis using reverse transcription followed by quantitative polymerase chain reaction revealed that BCs coexpress HCN1 and HCN2 subunit mRNA, suggesting the formation of heteromeric HCN1/2 channels. ZD 7288 increased the current threshold for evoking antidromic action potentials by extracellular stimulation, consistent with the expression of Ih in BC axons. Finally, ZD 7288 decreased the frequency of miniature inhibitory postsynaptic currents (mIPSCs) in hippocampal granule cells, the main target cells of BCs, to 70 +/- 4% of the control value. In contrast, the amplitude of mIPSCs was unchanged, consistent with the presence of Ih in inhibitory terminals. In conclusion, our results suggest that Ih channels are expressed in the somatodendritic region, axon and presynaptic elements of fast-spiking BCs in the hippocampus.

The Blue Brain Project

IBM's Blue Gene supercomputer allows a quantum leap in the level of detail at which the brain can be modelled. I argue that the time is right to begin assimilating the wealth of data that has been accumulated over the past century and start building biologically accurate models of the brain from first principles to aid our understanding of brain function and dysfunction.

Persistent Synchronized Bursting Activity in Cortical Tissues With Low Magnesium Concentration: A Modeling Study

We explore the mechanism of synchronized bursting activity with frequency of ∼10 Hz that appears in cortical tissues at low extracellular magnesium concentration [Mg2+]o. We hypothesize that this activity is persistent, namely coexists with the quiescent state and depends on slow N-methyl-d-aspartate (NMDA) conductances. To explore this hypothesis, we construct and investigate a conductance-based model of excitatory cortical networks. Population bursting activity can persist for physiological values of the NMDA decay time constant (∼100 ms). Neurons are synchronized at the time scale of bursts but not of single spikes. A reduced model of a cell coupled to itself can encompass most of this highly synchronized network behavior and is analyzed using the fast-slow method. Synchronized bursts appear for intermediate values of the NMDA conductance gNMDA if NMDA conductances are not too fast. Regular spiking activity appears for larger gNMDA. If the single cell is a conditional burster, persistent synchronized bursts become more robust. Weakly synchronized states appear for zero AMPA conductance gAMPA. Enhancing gAMPA increases both synchrony and the number of spikes within bursts and decreases the bursting frequency. Too strong gAMPA, however, prevents the activity because it enhances neuronal intrinsic adaptation. When [Mg2+]o is increased, higher gNMDA values are needed to maintain bursting activity. Bursting frequency decreases with [Mg2+]o, and the network is silent with physiological [Mg2+]o. Inhibition weakly decreases the bursting frequency if inhibitory cells receive enough NMDA-mediated excitation. This study explains the importance of conditional bursters in layer V in supporting epileptiform activity at low [Mg2+]o.