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1.  Interplay of Intrinsic and Synaptic Conductances in the Generation of High-Frequency Oscillations in Interneuronal Networks with Irregular Spiking 
PLoS Computational Biology  2014;10(5):e1003574.
High-frequency oscillations (above 30 Hz) have been observed in sensory and higher-order brain areas, and are believed to constitute a general hallmark of functional neuronal activation. Fast inhibition in interneuronal networks has been suggested as a general mechanism for the generation of high-frequency oscillations. Certain classes of interneurons exhibit subthreshold oscillations, but the effect of this intrinsic neuronal property on the population rhythm is not completely understood. We study the influence of intrinsic damped subthreshold oscillations in the emergence of collective high-frequency oscillations, and elucidate the dynamical mechanisms that underlie this phenomenon. We simulate neuronal networks composed of either Integrate-and-Fire (IF) or Generalized Integrate-and-Fire (GIF) neurons. The IF model displays purely passive subthreshold dynamics, while the GIF model exhibits subthreshold damped oscillations. Individual neurons receive inhibitory synaptic currents mediated by spiking activity in their neighbors as well as noisy synaptic bombardment, and fire irregularly at a lower rate than population frequency. We identify three factors that affect the influence of single-neuron properties on synchronization mediated by inhibition: i) the firing rate response to the noisy background input, ii) the membrane potential distribution, and iii) the shape of Inhibitory Post-Synaptic Potentials (IPSPs). For hyperpolarizing inhibition, the GIF IPSP profile (factor iii)) exhibits post-inhibitory rebound, which induces a coherent spike-mediated depolarization across cells that greatly facilitates synchronous oscillations. This effect dominates the network dynamics, hence GIF networks display stronger oscillations than IF networks. However, the restorative current in the GIF neuron lowers firing rates and narrows the membrane potential distribution (factors i) and ii), respectively), which tend to decrease synchrony. If inhibition is shunting instead of hyperpolarizing, post-inhibitory rebound is not elicited and factors i) and ii) dominate, yielding lower synchrony in GIF networks than in IF networks.
Author Summary
Neurons in the brain engage in collective oscillations at different frequencies. Gamma and high-gamma oscillations (30–100 Hz and higher) have been associated with cognitive functions, and are altered in psychiatric disorders such as schizophrenia and autism. Our understanding of how high-frequency oscillations are orchestrated in the brain is still limited, but it is necessary for the development of effective clinical approaches to the treatment of these disorders. Some neuron types exhibit dynamical properties that can favour synchronization. The theory of weakly coupled oscillators showed how the phase response of individual neurons can predict the patterns of phase relationships that are observed at the network level. However, neurons in vivo do not behave like regular oscillators, but fire irregularly in a regime dominated by fluctuations. Hence, which intrinsic dynamical properties matter for synchronization, and in which regime, is still an open question. Here, we show how single-cell damped subthreshold oscillations enhance synchrony in interneuronal networks by introducing a depolarizing component, mediated by post-inhibitory rebound, that is correlated among neurons due to common inhibitory input.
PMCID: PMC4006709  PMID: 24784237
2.  Cell-Type-Specific Recruitment of Amygdala Interneurons to Hippocampal Theta Rhythm and Noxious Stimuli In Vivo 
Neuron  2012;74-20(6):1059-1074.
Neuronal synchrony in the basolateral amygdala (BLA) is critical for emotional behavior. Coordinated theta-frequency oscillations between the BLA and the hippocampus and precisely timed integration of salient sensory stimuli in the BLA are involved in fear conditioning. We characterized GABAergic interneuron types of the BLA and determined their contribution to shaping these network activities. Using in vivo recordings in rats combined with the anatomical identification of neurons, we found that the firing of BLA interneurons associated with network activities was cell type specific. The firing of calbindin-positive interneurons targeting dendrites was precisely theta-modulated, but other cell types were heterogeneously modulated, including parvalbumin-positive basket cells. Salient sensory stimuli selectively triggered axo-axonic cells firing and inhibited firing of a disctinct projecting interneuron type. Thus, GABA is released onto BLA principal neurons in a time-, domain-, and sensory-specific manner. These specific synaptic actions likely cooperate to promote amygdalo-hippocampal synchrony involved in emotional memory formation.
► Comprehensive definition of interneuron types of the basolateral amygdala ► Identification of the target subcellular domains of each cell type ► GABAergic cell-type-specific coding of hippocampal theta rhythm and sensory stimuli ► Axo-axonic interneurons are excited by salient sensory stimuli
Bienvenu et al. provide a comprehensive characterization and in vivo recordings of basolateral amygdala interneurons. Their findings suggest that GABA is released onto BLA principal neurons in a time-, subcellular domain-, and sensory-dependent manner.
PMCID: PMC3391683  PMID: 22726836
3.  Purkinje neuron synchrony elicits time-locked spiking in the cerebellar nuclei 
Nature  2011;481(7382):502-505.
An unusual feature of the cerebellar cortex is that its output neurons, Purkinje cells, are GABAergic. Their high intrinsic firing rates1 (50 Hz) and extensive convergence2,3 predict that that target neurons in the cerebellar nuclei would be largely inhibited unless Purkinje cells pause their spiking, yet Purkinje and nuclear neuron firing rates do not always vary inversely4. A potential clue to how these synapses transmit information is that populations of Purkinje neurons synchronize their spikes during cerebellar behaviors5–11. If nuclear neurons respond to Purkinje synchrony, they may encode signals from subsets of inhibitory inputs7,12–14. Here we show in weanling and adult mice that nuclear neurons transmit the timing of synchronous Purkinje afferent spikes, owing to modest Purkinje-to-nuclear convergence ratios (~40:1), fast IPSC kinetics (τdecay=2.5 ms), and high intrinsic firing rates (~90 Hz). In vitro, dynamically clamped asynchronous IPSPs mimicking Purkinje afferents suppress nuclear cell spiking, whereas synchronous IPSPs entrain nuclear cell spiking. With partial synchrony, nuclear neurons time-lock their spikes to the synchronous subpopulation of inputs, even when only 2 of 40 afferents synchronize. In vivo, nuclear neurons reliably phase-lock to regular trains of molecular layer stimulation. Thus, cerebellar nuclear neurons can preferentially relay the spike timing of synchronized Purkinje cells to downstream premotor areas.
PMCID: PMC3268051  PMID: 22198670
4.  Membrane Potential-Dependent Modulation of Recurrent Inhibition in Rat Neocortex 
PLoS Biology  2011;9(3):e1001032.
Dynamic balance of excitation and inhibition is crucial for network stability and cortical processing, but it is unclear how this balance is achieved at different membrane potentials (Vm) of cortical neurons, as found during persistent activity or slow Vm oscillation. Here we report that a Vm-dependent modulation of recurrent inhibition between pyramidal cells (PCs) contributes to the excitation-inhibition balance. Whole-cell recording from paired layer-5 PCs in rat somatosensory cortical slices revealed that both the slow and the fast disynaptic IPSPs, presumably mediated by low-threshold spiking and fast spiking interneurons, respectively, were modulated by changes in presynaptic Vm. Somatic depolarization (>5 mV) of the presynaptic PC substantially increased the amplitude and shortened the onset latency of the slow disynaptic IPSPs in neighboring PCs, leading to a narrowed time window for EPSP integration. A similar increase in the amplitude of the fast disynaptic IPSPs in response to presynaptic depolarization was also observed. Further paired recording from PCs and interneurons revealed that PC depolarization increases EPSP amplitude and thus elevates interneuronal firing and inhibition of neighboring PCs, a reflection of the analog mode of excitatory synaptic transmission between PCs and interneurons. Together, these results revealed an immediate Vm-dependent modulation of cortical inhibition, a key strategy through which the cortex dynamically maintains the balance of excitation and inhibition at different states of cortical activity.
Author Summary
Proper functioning of the neocortex requires a balance between excitation and inhibition. This balance can be achieved through the operation of cortical microcircuits interweaved by excitatory and inhibitory neurons. Since the membrane potentials (Vm) of cortical neurons fluctuate at different levels during cortical activities, it is important to know how the balance of excitation and inhibition is dynamically maintained at different Vm. Recurrent inhibition between excitatory pyramidal cells is mediated by two distinct types of inhibitory interneurons. Here, we show that the amount of recurrent inhibition depends on the Vm levels of presynaptic pyramidal cells. Modest depolarization of a pyramidal cell substantially increases, and sometimes turns on, disynaptic inhibition on its neighboring pyramidal cells. We find that this effect is due to an increase in the strength of synaptic connections from the pyramidal cell to inhibitory interneurons and a consequent elevation of interneuronal firing. The depolarization-induced increase in synaptic strength from the pyramidal cell therefore reflects “analog-mode” signaling in cortical excitatory synapses. We thus reveal a profound impact of analog-mode signaling on the operation of cortical microcircuits and provide a new mechanism for dynamic control of the balance of cortical excitation and inhibition.
PMCID: PMC3062529  PMID: 21445327
5.  GABAergic Projections from the Medial Septum Selectively Inhibit Interneurons in the Medial Entorhinal Cortex 
The Journal of Neuroscience  2014;34(50):16739-16743.
The medial septum (MS) is required for theta rhythmic oscillations and grid cell firing in the medial entorhinal cortex (MEC). While GABAergic, glutamatergic, and cholinergic neurons project from the MS to the MEC, their synaptic targets are unknown. To investigate whether MS neurons innervate specific layers and cell types in the MEC, we expressed channelrhodopsin-2 in mouse MS neurons and used patch-clamp recording in brain slices to determine the response to light activation of identified cells in the MEC. Following activation of MS axons, we observed fast monosynaptic GABAergic IPSPs in the majority (>60%) of fast-spiking (FS) and low-threshold-spiking (LTS) interneurons in all layers of the MEC, but in only 1.5% of nonstellate principal cells (NSPCs) and in no stellate cells. We also observed fast glutamatergic responses to MS activation in a minority (<5%) of NSPCs, FS, and LTS interneurons. During stimulation of MS inputs at theta frequency (10 Hz), the amplitude of GABAergic IPSPs was maintained, and spike output from LTS and FS interneurons was entrained at low (25–60 Hz) and high (60–180 Hz) gamma frequencies, respectively. By demonstrating cell type-specific targeting of the GABAergic projection from the MS to the MEC, our results support the idea that the MS controls theta frequency activity in the MEC through coordination of inhibitory circuits.
PMCID: PMC4261098  PMID: 25505326
gamma; interneuron; lamina organization; medial entorhinal cortex; medial septum; theta
6.  The Electrocortical Effects of Enflurane: Experiment and Theory 
Anesthesia and analgesia  2009;109(4):1253-1262.
High concentrations of enflurane will induce a characteristic electroencephalogram pattern consisting of periods of suppression alternating with large short paroxysmal epileptiform discharges (PEDs). In this study, we compared a theoretical computer model of this activity with real local field potential data obtained from anesthetized rats.
After implantation of a high-density 8x8 electrode array in the visual cortex, the patterns of local field potential and multiunit spike activity were recorded in rats during 0.5, 1.0, 1.5 and 2.0 minimum alveolar anesthetic concentration (MAC) enflurane anesthesia. These recordings were compared with computer simulations from a mean field model of neocortical dynamics. The neuronal effect of increasing enflurane concentration was simulated by prolonging the decay time constant of the inhibitory postsynaptic potential (IPSP). The amplitude of the excitatory postsynaptic potential (EPSP) was modulated, inverse to the neocortical firing rate.
In the anesthetized rats, increasing enflurane concentrations consistently caused the appearance of suppression pattern (>1.5MAC) in the local field potential recordings. The mean rate of multiunit spike activity decreased from 2.54/s (0.5MAC) to 0.19/s (2.0MAC). At high MAC the majority of the multiunit action potential events became synchronous with the PED. In the theoretical model, prolongation of the IPSP decay time and activity-dependent EPSP modulation resulted in output that was similar in morphology to that obtained from the experimental data. The propensity for rhythmic seizure-like activity in the model could be determined by analysis of the eigenvalues of the equations.
It is possible to use a mean field theory of neocortical dynamics to replicate the PED pattern observed in local field potentials in rats under enflurane anesthesia. This pattern requires a combination of a moderately increased total area under the IPSP, prolonged IPSP decay time, and also activity-dependent modulation of EPSP amplitude.
PMCID: PMC2747102  PMID: 19762755
7.  Desynchronization of Neocortical Networks by Asynchronous Release of GABA at Autaptic and Synaptic Contacts from Fast-Spiking Interneurons 
PLoS Biology  2010;8(9):e1000492.
An activity-dependent long-lasting asynchronous release of GABA from identified fast-spiking inhibitory neurons in the neocortex can impair the reliability and temporal precision of activity in a cortical network.
Networks of specific inhibitory interneurons regulate principal cell firing in several forms of neocortical activity. Fast-spiking (FS) interneurons are potently self-inhibited by GABAergic autaptic transmission, allowing them to precisely control their own firing dynamics and timing. Here we show that in FS interneurons, high-frequency trains of action potentials can generate a delayed and prolonged GABAergic self-inhibition due to sustained asynchronous release at FS-cell autapses. Asynchronous release of GABA is simultaneously recorded in connected pyramidal (P) neurons. Asynchronous and synchronous autaptic release show differential presynaptic Ca2+ sensitivity, suggesting that they rely on different Ca2+ sensors and/or involve distinct pools of vesicles. In addition, asynchronous release is modulated by the endogenous Ca2+ buffer parvalbumin. Functionally, asynchronous release decreases FS-cell spike reliability and reduces the ability of P neurons to integrate incoming stimuli into precise firing. Since each FS cell contacts many P neurons, asynchronous release from a single interneuron may desynchronize a large portion of the local network and disrupt cortical information processing.
Author Summary
In the cerebral cortex (neocortex) of the brain, fast-spiking (FS) inhibitory cells contact many principal pyramidal (P) neurons on their cell bodies, which allows the FS cells to control the generation of action potentials (neuronal output). FS-cell-mediated rhythmic and synchronous inhibition drives coherent network oscillations of large ensembles of P neurons, indicating that FS interneurons are needed for the precise timing of cortical circuits. Interestingly, FS cells are self-innervated by GABAergic autaptic contacts, whose synchronous activation regulates FS-cell precise firing. Here we report that high-frequency firing in FS interneurons results in a massive (>10-fold), delayed, and prolonged (for seconds) increase in inhibitory events, occurring at both autaptic (FS–FS) and synaptic (FS–P) sites. This increased inhibition is due to asynchronous release of GABA from presynaptic FS cells. Delayed and disorganized asynchronous inhibitory responses significantly affected the input–output properties of both FS and P neurons, suggesting that asynchronous release of GABA might promote network desynchronization. FS interneurons can fire at high frequency (>100 Hz) in vitro and in vivo, and are known for their reliable and precise signaling. Our results show an unprecedented action of these cells, by which their tight temporal control of cortical circuits can be broken when they are driven to fire above certain frequencies.
PMCID: PMC2946936  PMID: 20927409
8.  Synaptic Plasticity in Medial Vestibular Nucleus Neurons: Comparison with Computational Requirements of VOR Adaptation 
PLoS ONE  2010;5(10):e13182.
Vestibulo-ocular reflex (VOR) gain adaptation, a longstanding experimental model of cerebellar learning, utilizes sites of plasticity in both cerebellar cortex and brainstem. However, the mechanisms by which the activity of cortical Purkinje cells may guide synaptic plasticity in brainstem vestibular neurons are unclear. Theoretical analyses indicate that vestibular plasticity should depend upon the correlation between Purkinje cell and vestibular afferent inputs, so that, in gain-down learning for example, increased cortical activity should induce long-term depression (LTD) at vestibular synapses.
Methodology/Principal Findings
Here we expressed this correlational learning rule in its simplest form, as an anti-Hebbian, heterosynaptic spike-timing dependent plasticity interaction between excitatory (vestibular) and inhibitory (floccular) inputs converging on medial vestibular nucleus (MVN) neurons (input-spike-timing dependent plasticity, iSTDP). To test this rule, we stimulated vestibular afferents to evoke EPSCs in rat MVN neurons in vitro. Control EPSC recordings were followed by an induction protocol where membrane hyperpolarizing pulses, mimicking IPSPs evoked by flocculus inputs, were paired with single vestibular nerve stimuli. A robust LTD developed at vestibular synapses when the afferent EPSPs coincided with membrane hyperpolarisation, while EPSPs occurring before or after the simulated IPSPs induced no lasting change. Furthermore, the iSTDP rule also successfully predicted the effects of a complex protocol using EPSP trains designed to mimic classical conditioning.
These results, in strong support of theoretical predictions, suggest that the cerebellum alters the strength of vestibular synapses on MVN neurons through hetero-synaptic, anti-Hebbian iSTDP. Since the iSTDP rule does not depend on post-synaptic firing, it suggests a possible mechanism for VOR adaptation without compromising gaze-holding and VOR performance in vivo.
PMCID: PMC2950150  PMID: 20957149
9.  Amplification of Asynchronous Inhibition-Mediated Synchronization by Feedback in Recurrent Networks 
PLoS Computational Biology  2010;6(2):e1000679.
Synchronization of 30–80 Hz oscillatory activity of the principle neurons in the olfactory bulb (mitral cells) is believed to be important for odor discrimination. Previous theoretical studies of these fast rhythms in other brain areas have proposed that principle neuron synchrony can be mediated by short-latency, rapidly decaying inhibition. This phasic inhibition provides a narrow time window for the principle neurons to fire, thus promoting synchrony. However, in the olfactory bulb, the inhibitory granule cells produce long lasting, small amplitude, asynchronous and aperiodic inhibitory input and thus the narrow time window that is required to synchronize spiking does not exist. Instead, it has been suggested that correlated output of the granule cells could serve to synchronize uncoupled mitral cells through a mechanism called “stochastic synchronization”, wherein the synchronization arises through correlation of inputs to two neural oscillators. Almost all work on synchrony due to correlations presumes that the correlation is imposed and fixed. Building on theory and experiments that we and others have developed, we show that increased synchrony in the mitral cells could produce an increase in granule cell activity for those granule cells that share a synchronous group of mitral cells. Common granule cell input increases the input correlation to the mitral cells and hence their synchrony by providing a positive feedback loop in correlation. Thus we demonstrate the emergence and temporal evolution of input correlation in recurrent networks with feedback. We explore several theoretical models of this idea, ranging from spiking models to an analytically tractable model.
Author Summary
Neurons in many parts of the brain fire spikes rhythmically and synchronously in many behaviorally and functionally relevant contexts. There are many mechanisms for producing oscillatory synchronization between populations of biological oscillators. One way to produce synchrony is that the population of oscillators receives common correlated input. In this paper, we study a population of oscillating neurons (mitral cells) that are not directly coupled to each other but receive broadband correlated input from a second population of neurons (granule cells). The granule cell population, in turn, receives inputs from the mitral cells; hence, the mitral and granule cells are reciprocally connected. Correlated input to the oscillating mitral cells produces tighter synchrony in the activity of the mitral cell population. We hypothesize that this increased mitral cell synchrony will evoke greater activity in specific groups of granule cells and that these specific granule cells, in turn, become the source of the correlated input to the mitral cells. That is, the synchronous input from the mitral cells increases the fraction of correlated feedback. Thus, we close the correlation loop. We show through analysis and simulations that this feedback mechanism can lead to the spontaneous appearance of highly synchronous activity within the mitral cells. We show that there is good experimental support for this mechanism in the circuitry of the olfactory bulb. We speculate that such mechanisms could also arise in other parts of the brain.
PMCID: PMC2824757  PMID: 20174555
10.  Impact of Adaptation Currents on Synchronization of Coupled Exponential Integrate-and-Fire Neurons 
PLoS Computational Biology  2012;8(4):e1002478.
The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies.
Author Summary
Synchronization of neuronal spiking in the brain is related to cognitive functions, such as perception, attention, and memory. It is therefore important to determine which properties of neurons influence their collective behavior in a network and to understand how. A prominent feature of many cortical neurons is spike frequency adaptation, which is caused by slow transmembrane currents. We investigated how these adaptation currents affect the synchronization tendency of coupled model neurons. Using the efficient adaptive exponential integrate-and-fire (aEIF) model and a biophysically detailed neuron model for validation, we found that increased adaptation currents promote synchronization of coupled excitatory neurons at lower spike frequencies, as long as the conduction delays between the neurons are negligible. Inhibitory neurons on the other hand synchronize in presence of conduction delays, with or without adaptation currents. Our results emphasize the utility of the aEIF model for computational studies of neuronal network dynamics. We conclude that adaptation currents provide a mechanism to generate low frequency oscillations in local populations of excitatory neurons, while faster rhythms seem to be caused by inhibition rather than excitation.
PMCID: PMC3325187  PMID: 22511861
11.  L-Type Calcium Channel-Mediated Plateau Potentials in Barrelette Cells During Structural Plasticity 
Journal of neurophysiology  2002;88(2):794-801.
Development and maintenance of whisker-specific patterns along the rodent trigeminal pathway depends on an intact sensory periphery during the sensitive/critical period in development. Barrelette cells of the brain stem trigeminal nuclei are the first set of neurons to develop whisker-specific patterns. Those in the principal sensory nucleus (PrV) relay these patterns to the ventrobasal thalamus, and consequently, to the somatosensory cortex. Thus PrV barrelette cells are among the first group of central neurons susceptible to the effects of peripheral damage. Previously we showed that membrane properties of barrelette cells are distinct as early as postnatal day 1 (PND 1) and remain unchanged following peripheral denervation in newborn rat pups (Lo and Erzurumlu 2001). In the present study, we investigated the changes in synaptic transmission. In barrelette cells of normal PND 1 rats, weak stimulation of the trigeminal tract (TrV) that was subthreshold for inducing Na+ spikes evoked an excitatory postsynaptic potential–inhibitory postsynaptic potential (EPSP-IPSP) sequence that was similar to the responses seen in older rats (Lo et al. 1999). Infraorbital nerve transection at birth did not alter excitatory and inhibitory synaptic connections of the barrelette cells. These observations suggested that local neuronal circuits are already established in PrV at birth and remain intact after deafferentation. Strong stimulation of the TrV induced a sustained depolarization (plateau potential) in denervated but not in normal barrelette neurons. The plateau potential was distinct from the EPSP-IPSP sequence by 1) a sustained (>80 ms) depolarization above −40 mV; 2) a slow decline slope (<0.1 mV/ms); 3) partially or totally inactivated Na+ spikes on the plateau; and 4) a termination by a steep decay (> 1 mV/ms) to a hyperpolarizing membrane level. The plateau potential was mediated by L-type Ca2+ channels and triggered by a N-methyl-d-aspartate (NMDA) receptor-mediated EPSP. γ-aminobutyric acid-A (GABAA) receptor-mediated IPSP dynamically regulated the latency and duration of the plateau potential. These results indicate that after neonatal peripheral damage, central trigeminal inputs cause a large and longlasting Ca2+ influx through L-type Ca2+ channels in barrelette neurons. Increased Ca2+ entry may play a key role in injury-induced structural remodeling, and/or transsynaptic cell death.
PMCID: PMC3686508  PMID: 12163531
12.  Spike Firing and IPSPs in Layer V Pyramidal Neurons during Beta Oscillations in Rat Primary Motor Cortex (M1) In Vitro 
PLoS ONE  2014;9(1):e85109.
Beta frequency oscillations (10–35 Hz) in motor regions of cerebral cortex play an important role in stabilising and suppressing unwanted movements, and become intensified during the pathological akinesia of Parkinson's Disease. We have used a cortical slice preparation of rat brain, combined with concurrent intracellular and field recordings from the primary motor cortex (M1), to explore the cellular basis of the persistent beta frequency (27–30 Hz) oscillations manifest in local field potentials (LFP) in layers II and V of M1 produced by continuous perfusion of kainic acid (100 nM) and carbachol (5 µM). Spontaneous depolarizing GABA-ergic IPSPs in layer V cells, intracellularly dialyzed with KCl and IEM1460 (to block glutamatergic EPSCs), were recorded at −80 mV. IPSPs showed a highly significant (P< 0.01) beta frequency component, which was highly significantly coherent with both the Layer II and V LFP oscillation (which were in antiphase to each other). Both IPSPs and the LFP beta oscillations were abolished by the GABAA antagonist bicuculline. Layer V cells at rest fired spontaneous action potentials at sub-beta frequencies (mean of 7.1+1.2 Hz; n = 27) which were phase-locked to the layer V LFP beta oscillation, preceding the peak of the LFP beta oscillation by some 20 ms. We propose that M1 beta oscillations, in common with other oscillations in other brain regions, can arise from synchronous hyperpolarization of pyramidal cells driven by synaptic inputs from a GABA-ergic interneuronal network (or networks) entrained by recurrent excitation derived from pyramidal cells. This mechanism plays an important role in both the physiology and pathophysiology of control of voluntary movement generation.
PMCID: PMC3896371  PMID: 24465488
13.  Submillisecond firing synchrony between different subtypes of cortical interneurons connected chemically but not electrically 
Synchronous firing is commonly observed in the brain, but its underlying mechanisms and neurobiological meaning remain debated. Most commonly, synchrony is attributed either to electrical coupling by gap junctions or to shared excitatory inputs. In the cerebral cortex and hippocampus, fast-spiking (FS) or somatostatin–containing (SOM) inhibitory interneurons are electrically coupled to same-type neighbors, and each subtype-specific network tends to fire in synchrony. Electrical coupling across subtypes is weak or absent, but SOM-FS and FS-FS pairs are often connected by inhibitory synapses. Theoretical studies suggest that purely inhibitory coupling can also promote synchrony; however, this has not been confirmed experimentally. We recorded from 74 pairs of electrically non-coupled layer 4 interneurons in mouse somatosensory cortex in vitro, and found that tonically depolarized FS-FS and SOM-FS pairs connected by uni- or bidirectional inhibitory synapses often fired within one millisecond of each other. Using a novel, jitter-based measure of synchrony, we found that synchrony correlated with inhibitory coupling strength. Importantly, synchrony was resistant to ionotropic glutamate receptors antagonists but was strongly reduced when GABAA receptors were blocked, confirming that in our experimental system IPSPs were both necessary and sufficient for synchrony. Submillisecond firing lags emerged in a computer simulation of pairs of spiking neurons, in which the only assumed interaction between neurons was by inhibitory synapses. We conclude that cortical interneurons are capable of synchronizing both within and across subtypes, and that submillisecond coordination of firing can arise by mutual synaptic inhibition alone, with neither shared inputs nor electrical coupling.
PMCID: PMC3076707  PMID: 21368047
14.  Inhibitory synchrony as a mechanism for attentional gain modulation☆ 
Journal of physiology, Paris  2005;98(4-6):296-314.
Recordings from area V4 of monkeys have revealed that when the focus of attention is on a visual stimulus within the receptive field of a cortical neuron, two distinct changes can occur: The firing rate of the neuron can change and there can be an increase in the coherence between spikes and the local field potential (LFP) in the gamma-frequency range (30–50 Hz). The hypothesis explored here is that these observed effects of attention could be a consequence of changes in the synchrony of local interneuron networks. We performed computer simulations of a Hodgkin-Huxley type neuron driven by a constant depolarizing current, I, representing visual stimulation and a modulatory inhibitory input representing the effects of attention via local interneuron networks. We observed that the neuron’s firing rate and the coherence of its output spike train with the synaptic inputs was modulated by the degree of synchrony of the inhibitory inputs. When inhibitory synchrony increased, the coherence of spiking model neurons with the synaptic input increased, but the firing rate either increased or remained the same. The mean number of synchronous inhibitory inputs was a key determinant of the shape of the firing rate versus current (f–I) curves. For a large number of inhibitory inputs (~50), the f–I curve saturated for large I and an increase in input synchrony resulted in a shift of sensitivity—the model neuron responded to weaker inputs I. For a small number (~10), the f–I curves were non-saturating and an increase in input synchrony led to an increase in the gain of the response—the firing rate in response to the same input was multiplied by an approximately constant factor. The firing rate modulation with inhibitory synchrony was highest when the input network oscillated in the gamma frequency range. Thus, the observed changes in firing rate and coherence of neurons in the visual cortex could be controlled by top-down inputs that regulated the coherence in the activity of a local inhibitory network discharging at gamma frequencies.
PMCID: PMC2872773  PMID: 16274973
Selective attention; Synchrony; Noise; Gamma oscillation; Gain modulation; Computer model
15.  Cellular Correlates of Enhanced Anxiety Caused by Acute Treatment with the Selective Serotonin Reuptake Inhibitor Fluoxetine in Rats 
Selective serotonin reuptake inhibitors (SSRIs) are used extensively in the treatment of depression and anxiety disorders. The therapeutic benefits of SSRIs typically require several weeks of continuous treatment. Intriguingly, according to clinical reports, symptoms of anxiety may actually increase during the early stages of treatment although more prolonged treatment alleviates affective symptoms. Consistent with earlier studies that have used animal models to capture this paradoxical effect of SSRIs, we find that rats exhibit enhanced anxiety-like behavior on the elevated plus-maze 1 h after a single injection of the SSRI fluoxetine. Next we investigated the potential neural substrates underlying the acute anxiogenic effects by analyzing the morphological and physiological impact of acute fluoxetine treatment on principal neurons of the basolateral amygdala (BLA), a brain area that plays a pivotal role in fear and anxiety. Although earlier studies have shown that behavioral or genetic perturbations that are anxiogenic for rodents also increase dendritic spine density in the BLA, we find that a single injection of fluoxetine does not cause spinogenesis on proximal apical dendritic segments on BLA principal neurons an hour later. However, at the same time point when a single dose of fluoxetine caused enhanced anxiety, it also enhanced action potential firing in BLA neurons in ex vivo slices. Consistent with this finding, in vitro bath application of fluoxetine caused higher spiking frequency and this increase in excitability was correlated with an increase in the input resistance of these neurons. Our results suggest that enhanced excitability of amygdala neurons may contribute to the increase in anxiety-like behavior observed following acute fluoxetine treatment.
PMCID: PMC3246766  PMID: 22232580
amygdala; anxiety; neuronal excitability; SSRI; fluoxetine; dendritic spines
16.  Endocannabinoid Release Modulates Electrical Coupling between CCK Cells Connected via Chemical and Electrical Synapses in CA1 
Electrical coupling between some subclasses of interneurons is thought to promote coordinated firing that generates rhythmic synchronous activity in cortical regions. Synaptic activity of cholecystokinin (CCK) interneurons which co-express cannabinoid type-1 (CB1) receptors are powerful modulators of network activity via the actions of endocannabinoids. We investigated the modulatory actions of endocannabinoids between chemically and electrically connected synapses of CCK cells using paired whole-cell recordings combined with biocytin and double immunofluorescence labeling in acute slices of rat hippocampus at P18–20 days. CA1 stratum radiatum CCK Schaffer collateral-associated cells were coupled electrically with each other as well as CCK basket cells and CCK cells with axonal projections expanding to dentate gyrus. Approximately 50% of electrically coupled cells received facilitating, asynchronously released inhibitory postsynaptic potential (IPSPs) that curtailed the steady-state coupling coefficient by 57%. Tonic CB1 receptor activity which reduces inhibition enhanced electrical coupling between cells that were connected via chemical and electrical synapses. Blocking CB1 receptors with antagonist, AM-251 (5 μM) resulted in the synchronized release of larger IPSPs and this enhanced inhibition further reduced the steady-state coupling coefficient by 85%. Depolarization induced suppression of inhibition (DSI), maintained the asynchronicity of IPSP latency, but reduced IPSP amplitudes by 95% and enhanced the steady-state coupling coefficient by 104% and IPSP duration by 200%. However, DSI did not did not enhance electrical coupling at purely electrical synapses. These data suggest that different morphological subclasses of CCK interneurons are interconnected via gap junctions. The synergy between the chemical and electrical coupling between CCK cells probably plays a role in activity-dependent endocannabinoid modulation of rhythmic synchronization.
PMCID: PMC3222094  PMID: 22125513
CA1; CB1; CCK; DSI; electrically coupled; endocannabinoids; interneurons
17.  A Model of Stimulus-Specific Neural Assemblies in the Insect Antennal Lobe 
PLoS Computational Biology  2008;4(8):e1000139.
It has been proposed that synchronized neural assemblies in the antennal lobe of insects encode the identity of olfactory stimuli. In response to an odor, some projection neurons exhibit synchronous firing, phase-locked to the oscillations of the field potential, whereas others do not. Experimental data indicate that neural synchronization and field oscillations are induced by fast GABAA-type inhibition, but it remains unclear how desynchronization occurs. We hypothesize that slow inhibition plays a key role in desynchronizing projection neurons. Because synaptic noise is believed to be the dominant factor that limits neuronal reliability, we consider a computational model of the antennal lobe in which a population of oscillatory neurons interact through unreliable GABAA and GABAB inhibitory synapses. From theoretical analysis and extensive computer simulations, we show that transmission failures at slow GABAB synapses make the neural response unpredictable. Depending on the balance between GABAA and GABAB inputs, particular neurons may either synchronize or desynchronize. These findings suggest a wiring scheme that triggers stimulus-specific synchronized assemblies. Inhibitory connections are set by Hebbian learning and selectively activated by stimulus patterns to form a spiking associative memory whose storage capacity is comparable to that of classical binary-coded models. We conclude that fast inhibition acts in concert with slow inhibition to reformat the glomerular input into odor-specific synchronized neural assemblies.
Author Summary
A fundamental question in computational neuroscience is to understand how interactions between neurons underlie sensory coding and information storage. In the first relay of the insect olfactory system, odorant stimuli trigger synchronized activities in neuron populations. Synchronized assemblies may arise as a consequence of inhibitory coupling, because they are disrupted when inhibition is pharmacologically blocked. Using computational modelling, we studied the role of inhibitory, noisy interactions in producing stimulus-specific synchrony. So far, experimental data and modelling studies indicate that fast inhibition induces neural synchrony, but it remains unclear how desynchronization occurs. From theoretical analysis and computer simulations, we found that slow inhibition plays a key role in desynchronizing neurons. Depending on the balance between fast and slow inhibitory inputs, particular neurons may either synchronize or desynchronize. The complementary roles of the two synaptic time scales in the formation of neural assemblies suggest a wiring scheme that produces stimulus-specific inhibitory interactions and endows inhibitory sub-circuits with properties of binary memories.
PMCID: PMC2536510  PMID: 18795147
18.  Spike-Timing Dependent Plasticity and Feed-Forward Input Oscillations Produce Precise and Invariant Spike Phase-Locking 
In the hippocampus and the neocortex, the coupling between local field potential (LFP) oscillations and the spiking of single neurons can be highly precise, across neuronal populations and cell types. Spike phase (i.e., the spike time with respect to a reference oscillation) is known to carry reliable information, both with phase-locking behavior and with more complex phase relationships, such as phase precession. How this precision is achieved by neuronal populations, whose membrane properties and total input may be quite heterogeneous, is nevertheless unknown. In this note, we investigate a simple mechanism for learning precise LFP-to-spike coupling in feed-forward networks – the reliable, periodic modulation of presynaptic firing rates during oscillations, coupled with spike-timing dependent plasticity. When oscillations are within the biological range (2–150 Hz), firing rates of the inputs change on a timescale highly relevant to spike-timing dependent plasticity (STDP). Through analytic and computational methods, we find points of stable phase-locking for a neuron with plastic input synapses. These points correspond to precise phase-locking behavior in the feed-forward network. The location of these points depends on the oscillation frequency of the inputs, the STDP time constants, and the balance of potentiation and de-potentiation in the STDP rule. For a given input oscillation, the balance of potentiation and de-potentiation in the STDP rule is the critical parameter that determines the phase at which an output neuron will learn to spike. These findings are robust to changes in intrinsic post-synaptic properties. Finally, we discuss implications of this mechanism for stable learning of spike-timing in the hippocampus.
PMCID: PMC3216007  PMID: 22110429
spike-timing dependent plasticity; oscillations; phase-locking; stable learning; stability of neuronal plasticity; place fields
19.  Cannabinoids attenuate hippocampal gamma oscillations by suppressing excitatory synaptic input onto CA3 pyramidal neurons and fast spiking basket cells 
The Journal of Physiology  2011;589(20):4921-4934.
Non-Technical Summary
Administration of cannabinoids can impair several cognitive functions, including memory by altering synchronous activities in cortical networks. We show that the gamma frequency (40 Hz) oscillations in hippocampal slices, that are prominent oscillations in electroencephalogram during awake states in vivo, are reduced by cannabinoids. This effect can be explained by the suppression of the excitatory synaptic transmission onto fast spiking basket cells, GABAergic cells that are key players in oscillogenesis. The reduced excitatory drive onto these interneurons leads to a reduction in neuronal firing frequency and precision, and thus to smaller field potentials. Our data further our understanding of the synaptic mechanisms of how cannabinoids alter neuronal operation.
CB1 cannabinoid receptor (CB1R) activation by exogenous ligands can impair memory processes, which critically depend on synchronous neuronal activities that are temporarily structured by oscillations. In this study, we aimed to reveal the mechanisms underlying the cannabinoid-induced decrease in gamma oscillations. We first verified that cannabinoids (CP55,940 and WIN55,212-2) readily suppressed carbachol-induced gamma oscillations in the CA3 region of hippocampal slices via activation of CB1Rs. The cannabinoid-induced decrease in the peak power of oscillations was accompanied by reduced and less precise firing activity in CA3 pyramidal cells and fast spiking basket cells. By examining the cannabinoid sensitivity of synaptic inputs we found that the amplitude of evoked excitatory postsynaptic currents was significantly suppressed upon CB1R activation in both CA3 pyramidal cells and fast spiking basket cells. In contrast, evoked inhibitory postsynaptic currents in CA3 pyramidal cells were unaltered. Furthermore, we observed that a CB1R agonist-induced decrease in the oscillation power at the beginning of the drug application was accompanied primarily by the reduced discharge of fast spiking basket cells, while pyramidal cell firing was unaltered. This result implies that the dampening of cholinergically induced gamma oscillations in the hippocampus by cannabinoids can be explained by a reduced excitatory input predominantly onto fast spiking basket cells, which leads to a reduction in neuronal firing frequency and precision, and thus to smaller field potentials. In addition, we uncovered that the spontaneously occurring sharp wave-ripple activities in hippocampal slices could also be suppressed by CB1R activation suggesting that cannabinoids profoundly reduce the intrinsically generated oscillatory activities at distinct frequencies in CA3 networks by reducing synaptic neurotransmission.
PMCID: PMC3224883  PMID: 21859823
20.  Cannabinoids attenuate hippocampal gamma oscillations by suppressing excitatory synaptic input onto CA3 pyramidal neurons and fast spiking basket cells 
The Journal of Physiology  2011;589(Pt 20):4921-4934.
Non-technical summary
Administration of cannabinoids can impair several cognitive functions, including memory by altering synchronous activities in cortical networks. We show that the gamma frequency (40 Hz) oscillations in hippocampal slices, that are prominent oscillations in electroencephalogram during awake states in vivo, are reduced by cannabinoids. This effect can be explained by the suppression of the excitatory synaptic transmission onto fast spiking basket cells, GABAergic cells that are key players in oscillogenesis. The reduced excitatory drive onto these interneurons leads to a reduction in neuronal firing frequency and precision, and thus to smaller field potentials. Our data further our understanding of the synaptic mechanisms of how cannabinoids alter neuronal operation.
CB1 cannabinoid receptor (CB1R) activation by exogenous ligands can impair memory processes, which critically depend on synchronous neuronal activities that are temporarily structured by oscillations. In this study, we aimed to reveal the mechanisms underlying the cannabinoid-induced decrease in gamma oscillations. We first verified that cannabinoids (CP55,940 and WIN55,212-2) readily suppressed carbachol-induced gamma oscillations in the CA3 region of hippocampal slices via activation of CB1Rs. The cannabinoid-induced decrease in the peak power of oscillations was accompanied by reduced and less precise firing activity in CA3 pyramidal cells and fast spiking basket cells. By examining the cannabinoid sensitivity of synaptic inputs we found that the amplitude of evoked excitatory postsynaptic currents was significantly suppressed upon CB1R activation in both CA3 pyramidal cells and fast spiking basket cells. In contrast, evoked inhibitory postsynaptic currents in CA3 pyramidal cells were unaltered. Furthermore, we observed that a CB1R agonist-induced decrease in the oscillation power at the beginning of the drug application was accompanied primarily by the reduced discharge of fast spiking basket cells, while pyramidal cell firing was unaltered. This result implies that the dampening of cholinergically induced gamma oscillations in the hippocampus by cannabinoids can be explained by a reduced excitatory input predominantly onto fast spiking basket cells, which leads to a reduction in neuronal firing frequency and precision, and thus to smaller field potentials. In addition, we uncovered that the spontaneously occurring sharp wave-ripple activities in hippocampal slices could also be suppressed by CB1R activation suggesting that cannabinoids profoundly reduce the intrinsically generated oscillatory activities at distinct frequencies in CA3 networks by reducing synaptic neurotransmission.
PMCID: PMC3224883  PMID: 21859823
21.  Noise Suppression and Surplus Synchrony by Coincidence Detection 
PLoS Computational Biology  2013;9(4):e1002904.
The functional significance of correlations between action potentials of neurons is still a matter of vivid debate. In particular, it is presently unclear how much synchrony is caused by afferent synchronized events and how much is intrinsic due to the connectivity structure of cortex. The available analytical approaches based on the diffusion approximation do not allow to model spike synchrony, preventing a thorough analysis. Here we theoretically investigate to what extent common synaptic afferents and synchronized inputs each contribute to correlated spiking on a fine temporal scale between pairs of neurons. We employ direct simulation and extend earlier analytical methods based on the diffusion approximation to pulse-coupling, allowing us to introduce precisely timed correlations in the spiking activity of the synaptic afferents. We investigate the transmission of correlated synaptic input currents by pairs of integrate-and-fire model neurons, so that the same input covariance can be realized by common inputs or by spiking synchrony. We identify two distinct regimes: In the limit of low correlation linear perturbation theory accurately determines the correlation transmission coefficient, which is typically smaller than unity, but increases sensitively even for weakly synchronous inputs. In the limit of high input correlation, in the presence of synchrony, a qualitatively new picture arises. As the non-linear neuronal response becomes dominant, the output correlation becomes higher than the total correlation in the input. This transmission coefficient larger unity is a direct consequence of non-linear neural processing in the presence of noise, elucidating how synchrony-coded signals benefit from these generic properties present in cortical networks.
Author Summary
Whether spike timing conveys information in cortical networks or whether the firing rate alone is sufficient is a matter of controversial debate, touching the fundamental question of how the brain processes, stores, and conveys information. If the firing rate alone is the decisive signal used in the brain, correlations between action potentials are just an epiphenomenon of cortical connectivity, where pairs of neurons share a considerable fraction of common afferents. Due to membrane leakage, small synaptic amplitudes and the non-linear threshold, nerve cells exhibit lossy transmission of correlation originating from shared synaptic inputs. However, the membrane potential of cortical neurons often displays non-Gaussian fluctuations, caused by synchronized synaptic inputs. Moreover, synchronously active neurons have been found to reflect behavior in primates. In this work we therefore contrast the transmission of correlation due to shared afferents and due to synchronously arriving synaptic impulses for leaky neuron models. We not only find that neurons are highly sensitive to synchronous afferents, but that they can suppress noise on signals transmitted by synchrony, a computational advantage over rate signals.
PMCID: PMC3617020  PMID: 23592953
22.  Neuroadaptation of GABAergic Transmission in the Central Amygdala During Chronic Morphine Treatment 
Addiction biology  2010;16(4):551-564.
We investigated possible alterations of pharmacologically-isolated, evoked GABAA inhibitory postsynaptic potentials (eIPSPs) and miniature GABAA inhibitory postsynaptic currents (mIPSCs) in the rat central amygdala (CeA) elicited by acute application of μ-opioid receptor (MOR) agonists (DAMGO and morphine; 1 μM) and by chronic morphine treatment with morphine pellets. The acute activation of MORs decreased the amplitudes of eIPSPs, increased paired-pulse facilitation (PPF) of eIPSPs and decreased the frequency (but not the amplitude) of mIPSCs in a majority of CeA neurons, suggesting that acute MOR-dependent modulation of this GABAergic transmission is mediated predominantly via presynaptic inhibition of GABA release. We observed no significant changes in the membrane properties, eIPSPs, PPF or mIPSCs of CeA neurons during chronic morphine treatment compared to CeA of naïve or sham rats. Superfusion of the MOR antagonist CTOP (1 μM) increased the mean amplitude of eIPSPs in a majority of CeA neurons to the same degree in both naïve/sham and morphine-treated rats, suggesting a tonic activation of MORs in both conditions. Superfusion of DAMGO decreased eIPSP amplitudes and the frequency of mIPSCs equally in both naïve/sham and morphine-treated rats but decreased the amplitude of mIPSCs only in morphine treated rats, an apparent postsynaptic action. Our combined findings suggest the development of tolerance of the CeA GABAergic system to inhibitory effects of acute activation of MORs on presynaptic GABA release and possible alteration of MOR-dependent postsynaptic mechanisms that may represent important neuroadaptations of the GABAergic and MOR systems during chronic morphine treatment.
PMCID: PMC3117063  PMID: 21182569
addiction; drug abuse; electrophysiology; extended amygdala; opiate; tolerance
23.  Electrophysiological Properties and Synaptic Responses of Cells in the Trigeminal Principal Sensory Nucleus of Postnatal Rats 
Journal of neurophysiology  1999;82(5):2765-2775.
In the rodent brain stem trigeminal complex, select sets of neurons form modular arrays or “barrelettes,” that replicate the patterned distribution of whiskers and sinus hairs on the ipsilateral snout. These cells detect the patterned input from the trigeminal axons that innervate the whiskers and sinus hairs. Other brain stem trigeminal cells, interbarrelette neurons, do not form patterns and respond to multiple whiskers. We examined the membrane properties and synaptic responses of morphologically identified barrelette and interbarrelette neurons in the principal sensory nucleus (PrV) of the trigeminal nerve in early postnatal rats shortly after whisker-related patterns are established. Barrelette cell dendritic trees are confined to a single barrelette, whereas the dendrites of interbarrelette cells span wider territories. These two cell types are distinct from smaller GABAergic interneurons. Barrelette cells can be distinguished by a prominent transient A-type K+ current (IA) and higher input resistance. On the other hand, interbarrelette cells display a prominent low-threshold T-type Ca2+ current (IT) and lower input resistance. Both classes of neurons respond differently to electrical stimulation of the trigeminal tract. Barrelette cells show either a monosynaptic excitatory postsynaptic potential (EPSP) followed by a large disynaptic inhibitory postsynaptic potential (IPSP) or just simply a disynaptic IPSP. Increasing stimulus intensity produces little change in EPSP amplitude but leads to a stepwise increase in IPSP amplitude, suggesting that barrelette cells receive more inhibitory input than excitatory input. This pattern of excitation and inhibition indicates that barrelette cells receive both feed-forward and lateral inhibition. Interbarrelette cells show a large monosynaptic EPSP followed by a small disynaptic IPSP. Increasing stimulus intensity leads to a stepwise increase in EPSP amplitude and the appearance of polysynaptic EPSPs, suggesting that interbarrelette cells receive excitatory inputs from multiple sources. Taken together, these results indicate that barrelette and interbarrelette neurons can be identified by their morphological and functional attributes soon after whisker-related pattern formation in the PrV.
PMCID: PMC3677564  PMID: 10561443
24.  Membrane Properties and the Balance between Excitation and Inhibition Control Gamma-Frequency Oscillations Arising from Feedback Inhibition 
PLoS Computational Biology  2012;8(1):e1002354.
Computational studies as well as in vivo and in vitro results have shown that many cortical neurons fire in a highly irregular manner and at low average firing rates. These patterns seem to persist even when highly rhythmic signals are recorded by local field potential electrodes or other methods that quantify the summed behavior of a local population. Models of the 30–80 Hz gamma rhythm in which network oscillations arise through ‘stochastic synchrony’ capture the variability observed in the spike output of single cells while preserving network-level organization. We extend upon these results by constructing model networks constrained by experimental measurements and using them to probe the effect of biophysical parameters on network-level activity. We find in simulations that gamma-frequency oscillations are enabled by a high level of incoherent synaptic conductance input, similar to the barrage of noisy synaptic input that cortical neurons have been shown to receive in vivo. This incoherent synaptic input increases the emergent network frequency by shortening the time scale of the membrane in excitatory neurons and by reducing the temporal separation between excitation and inhibition due to decreased spike latency in inhibitory neurons. These mechanisms are demonstrated in simulations and in vitro current-clamp and dynamic-clamp experiments. Simulation results further indicate that the membrane potential noise amplitude has a large impact on network frequency and that the balance between excitatory and inhibitory currents controls network stability and sensitivity to external inputs.
Author Summary
The gamma rhythm is a prominent, 30–80-Hz EEG signal that is associated with cognition. Several classes of computational models have been posited to explain the gamma rhythm mechanistically. We study a particular class in which the gamma rhythm arises from delayed negative feedback. Our study is unique in that we calibrate the model from direct measurements. We also test the model's most critical predictions directly in experiments that take advantage of cutting-edge computer technologies able to simulate ion channels in real time. Our major findings are that a large amount of “background” synaptic input to neurons is necessary to promote the gamma rhythm; that inhibitory neurons are specially tuned to keep the gamma rhythm stable; that noise has a strong effect on network frequency; and that incoming sensory input can be represented with sensitivity that depends on the strength of excitatory-excitatory synapses and the number of neurons receiving the input. Overall, our results support the hypothesis that the gamma rhythm reflects the presence of delayed feedback that controls overall cortical activity on a cycle-by-cycle basis. Furthermore, its frequency range mainly reflects the timescale of synaptic inhibition, the degree of background activity, and noise levels in the network.
PMCID: PMC3261914  PMID: 22275859
25.  Short Conduction Delays Cause Inhibition Rather than Excitation to Favor Synchrony in Hybrid Neuronal Networks of the Entorhinal Cortex 
PLoS Computational Biology  2012;8(1):e1002306.
How stable synchrony in neuronal networks is sustained in the presence of conduction delays is an open question. The Dynamic Clamp was used to measure phase resetting curves (PRCs) for entorhinal cortical cells, and then to construct networks of two such neurons. PRCs were in general Type I (all advances or all delays) or weakly type II with a small region at early phases with the opposite type of resetting. We used previously developed theoretical methods based on PRCs under the assumption of pulsatile coupling to predict the delays that synchronize these hybrid circuits. For excitatory coupling, synchrony was predicted and observed only with no delay and for delays greater than half a network period that cause each neuron to receive an input late in its firing cycle and almost immediately fire an action potential. Synchronization for these long delays was surprisingly tight and robust to the noise and heterogeneity inherent in a biological system. In contrast to excitatory coupling, inhibitory coupling led to antiphase for no delay, very short delays and delays close to a network period, but to near-synchrony for a wide range of relatively short delays. PRC-based methods show that conduction delays can stabilize synchrony in several ways, including neutralizing a discontinuity introduced by strong inhibition, favoring synchrony in the case of noisy bistability, and avoiding an initial destabilizing region of a weakly type II PRC. PRCs can identify optimal conduction delays favoring synchronization at a given frequency, and also predict robustness to noise and heterogeneity.
Author Summary
Individual oscillators, such as pendulum-based clocks and fireflies, can spontaneously organize into a coherent, synchronized entity with a common frequency. Neurons can oscillate under some circumstances, and can synchronize their firing both within and across brain regions. Synchronized assemblies of neurons are thought to underlie cognitive functions such as recognition, recall, perception and attention. Pathological synchrony can lead to epilepsy, tremor and other dynamical diseases, and synchronization is altered in most mental disorders. Biological neurons synchronize despite conduction delays, heterogeneous circuit composition, and noise. In biological experiments, we built simple networks in which two living neurons could interact via a computer in real time. The computer precisely controlled the nature of the connectivity and the length of the communication delays. We characterized the synchronization tendencies of individual, isolated oscillators by measuring how much a single input delivered by the computer transiently shortened or lengthened the cycle period of the oscillation. We then used this information to correctly predict the strong dependence of the coordination pattern of the firing of the component neurons on the length of the communication delays. Upon this foundation, we can begin to build a theory of the basic principles of synchronization in more complex brain circuits.
PMCID: PMC3252263  PMID: 22241969

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