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1.  Entorhinal stellate cells show preferred spike phase-locking to theta inputs that is enhanced by correlations in synaptic activity 
In active networks, excitatory and inhibitory synaptic inputs generate membrane voltage fluctuations that drive spike activity in a probabilistic manner. Despite this, some cells in vivo show a strong propensity to precisely lock to the local field potential and maintain a specific spike-phase relationship relative to other cells. In recordings from rat medial entorhinal cortical stellate cells, we measured spike phase-locking in response to sinusoidal “test” inputs in the presence of different forms of background membrane voltage fluctuations, generated via dynamic clamp. We find that stellate cells show strong and robust spike phase-locking to theta (4–12 Hz) inputs. This response occurs under a wide variety of background membrane voltage fluctuation conditions that include a substantial increase in overall membrane conductance. Furthermore, the IH current present in stellate cells is critical to the enhanced spike phase-locking response at theta. Finally, we show that correlations between inhibitory and excitatory conductance fluctuations, which can arise through feed-back and feed-forward inhibition, can substantially enhance the spike phase-locking response. The enhancement in locking is a result of a selective reduction in the size of low frequency membrane voltage fluctuations due to cancelation of inhibitory and excitatory current fluctuations with correlations. Hence, our results demonstrate that stellate cells have a strong preference for spike phase-locking to theta band inputs and that the absolute magnitude of locking to theta can be modulated by the properties of background membrane voltage fluctuations.
doi:10.1523/JNEUROSCI.3892-12.2013
PMCID: PMC3680114  PMID: 23554484
synaptic correlations; high conductance; theta; IH; voltage fluctuations; balanced excitation and inhibition; spike phase-locking
2.  Fluctuating Inhibitory Inputs Promote Reliable Spiking at Theta Frequencies in Hippocampal Interneurons 
Theta-frequency (4–12 Hz) rhythms in the hippocampus play important roles in learning and memory. CA1 interneurons located at the stratum lacunosum-moleculare and radiatum junction (LM/RAD) are thought to contribute to hippocampal theta population activities by rhythmically pacing pyramidal cells with inhibitory postsynaptic potentials. This implies that LM/RAD cells need to fire reliably at theta frequencies in vivo. To determine whether this could occur, we use biophysically based LM/RAD model cells and apply different cholinergic and synaptic inputs to simulate in vivo-like network environments. We assess spike reliabilities and spiking frequencies, identifying biophysical properties and network conditions that best promote reliable theta spiking. We find that synaptic background activities that feature large inhibitory, but not excitatory, fluctuations are essential. This suggests that strong inhibitory input to these cells is vital for them to be able to contribute to population theta activities. Furthermore, we find that Type I-like oscillator models produced by augmented persistent sodium currents (INaP) or diminished A-type potassium currents (IA) enhance reliable spiking at lower theta frequencies. These Type I-like models are also the most responsive to large inhibitory fluctuations and can fire more reliably under such conditions. In previous work, we showed that INaP and IA are largely responsible for establishing LM/RAD cells’ subthreshold activities. Taken together with this study, we see that while both these currents are important for subthreshold theta fluctuations and reliable theta spiking, they contribute in different ways – INaP to reliable theta spiking and subthreshold activity generation, and IA to subthreshold activities at theta frequencies. This suggests that linking subthreshold and suprathreshold activities should be done with consideration of both in vivo contexts and biophysical specifics.
doi:10.3389/fncom.2012.00030
PMCID: PMC3359426  PMID: 22654751
spike reliability; inhibition; noise; subthreshold oscillations; theta rhythm; interneuron; hippocampus; biophysical model
3.  Comparison of Sleep Spindles and Theta Oscillations in the Hippocampus 
The Journal of Neuroscience  2014;34(2):662-674.
Several network patterns allow for information exchange between the neocortex and the entorhinal–hippocampal complex, including theta oscillations and sleep spindles. How neurons are organized in these respective patterns is not well understood. We examined the cellular–synaptic generation of sleep spindles and theta oscillations in the waking rat and during rapid eye movement (REM) sleep by simultaneously recording local field and spikes in the regions and layers of the hippocampus and entorhinal cortex (EC). We show the following: (1) current source density analysis reveals that similar anatomical substrates underlie spindles and theta in the hippocampus, although the hippocampal subregions are more synchronized during spindles than theta; (2) the spiking of putative principal cells and interneurons in the CA1, CA3, and dentate gyrus subregions of the hippocampus, as well as layers 2, 3, and 5 of medial EC, are significantly phase locked to spindles detected in CA1; (3) the relationship between local field potential (LFP) phase and unit spiking differs between spindles and theta; (4) individual hippocampal principal cells generally do not fire in a rhythmic manner during spindles; (5) power in gamma (30–90 Hz) and epsilon (>90 Hz) bands of hippocampal LFP is modulated by the phase of spindle oscillations; and (6) unit firing rates during spindles were not significantly affected by whether spindles occurred during non-REM or transitions between non-REM and REM sleep. Thus, despite the similar current generator inputs and macroscopic appearance of the LFP, the organization of neuronal firing patterns during spindles bears little resemblance to that of theta oscillations.
doi:10.1523/JNEUROSCI.0552-13.2014
PMCID: PMC3870943  PMID: 24403164
entorhinal cortex; gamma; hippocampus; sleep; spindle; theta
4.  Ketamine disrupts theta modulation of gamma in a computer model of hippocampus 
Abnormalities in oscillations have been suggested to play a role in schizophrenia. We studied theta-modulated gamma oscillations in a computer model of hippocampal CA3 in vivo with and without simulated application of ketamine, an NMDA receptor antagonist and psychotomimetic. Networks of 1200 multi-compartment neurons (pyramidal, basket and oriens-lacunosum moleculare, OLM, cells) generated theta and gamma oscillations from intrinsic network dynamics: basket cells primarily generated gamma and amplified theta, while OLM cells strongly contributed to theta. Extrinsic medial septal inputs paced theta and amplified both theta and gamma oscillations. Exploration of NMDA receptor reduction across all location combinations demonstrated that the experimentally-observed ketamine effect occurred only with isolated reduction of NMDA receptors on OLMs. In the ketamine simulations, lower OLM activity reduced theta power and disinhibited pyramidal cells, resulting in increased basket cell activation and gamma power. Our simulations predict:
ketamine increases firing rates;oscillations can be generated by intrinsic hippocampal circuits;medial septum inputs pace and augment oscillations;pyramidal cells lead basket cells at the gamma peak but lag at trough;basket cells amplify theta rhythms;ketamine alters oscillations due to primary blockade at OLM NMDA receptors;ketamine alters phase relationships of cell firing;ketamine reduces network responsivity to the environmentketamine effect could be reversed by providing a continuous inward current to OLM cells.
We suggest that this last prediction has implications for a possible novel treatment for cognitive deficits of schizophrenia by targeting OLM cells.
doi:10.1523/JNEUROSCI.0501-11.2011
PMCID: PMC3177405  PMID: 21832203
5.  Long-Term Plasticity Is Proportional to Theta-Activity 
PLoS ONE  2009;4(6):e5850.
Background
Theta rhythm in the hippocampal formation is a main feature of exploratory behaviour and is believed to enable the encoding of new spatial information and the modification of synaptic weights. Cyclic changes of dentate gyrus excitability during theta rhythm are related to its function, but whether theta epochs per se are able to alter network properties of dentate gyrus for long time-periods is still poorly understood.
Methodology/Principal Findings
We used low-frequency stimulation protocols that amplify the power of endogenous theta oscillations, in order to estimate the plasticity effect of endogenous theta oscillations on a population level. We found that stimulation-induced augmentation of the theta rhythm is linked to a subsequent increase of neuronal excitability and decrease of the synaptic response. This EPSP-to-Spike uncoupling is related to an increased postsynaptic spiking on the positive phases of theta frequency oscillations. Parallel increase of the field EPSP slope and the population spike occurs only after concurrent pre- and postsynaptic activation. Furthermore, we observed that long-term potentiation (>24 h) occurs in the dentate gyrus of freely behaving adult rats after phasic activity of entorhinal afferents in the theta-frequency range. This plasticity is proportional to the field bursting activity of granule cells during the stimulation, and may comprise a key step in spatial information transfer. Long-term potentiation of the synaptic component occurs only when the afferent stimulus precedes the evoked population burst, and is input-specific.
Conclusions/Significance
Our data confirm the role of the dentate gyrus in filtering information to the subsequent network during the activated state of the hippocampus.
doi:10.1371/journal.pone.0005850
PMCID: PMC2688745  PMID: 19513114
6.  Effects of nicotine stimulation on spikes, theta frequency oscillations, and spike-theta oscillation relationship in rat medial septum diagonal band Broca slices 
Acta Pharmacologica Sinica  2013;34(4):464-472.
Aim:
Spiking activities and neuronal network oscillations in the theta frequency range have been found in many cortical areas during information processing. The aim of this study is to determine whether nicotinic acetylcholine receptors (nAChRs) mediate neuronal network activity in rat medial septum diagonal band Broca (MSDB) slices.
Methods:
Extracellular field potentials were recorded in the slices using an Axoprobe 1A amplifier. Data analysis was performed off-line. Spike sorting and local field potential (LFP) analyses were performed using Spike2 software. The role of spiking activity in the generation of LFP oscillations in the slices was determined by analyzing the phase-time relationship between the spikes and LFP oscillations. Circular statistic analysis based on the Rayleigh test was used to determine the significance of phase relationships between the spikes and LFP oscillations. The timing relationship was examined by quantifying the spike-field coherence (SFC).
Results:
Application of nicotine (250 nmol/L) induced prominent LFP oscillations in the theta frequency band and both small- and large-amplitude population spiking activity in the slices. These spikes were phase-locked to theta oscillations at specific phases. The Rayleigh test showed a statistically significant relationship in phase-locking between the spikes and theta oscillations. Larger changes in the SFC were observed for large-amplitude spikes, indicating an accurate timing relationship between this type of spike and LFP oscillations. The nicotine-induced spiking activity (large-amplitude population spikes) was suppressed by the nAChR antagonist dihydro-β-erythroidine (0.3 μmol/L).
Conclusion:
The results demonstrate that large-amplitude spikes are phase-locked to theta oscillations and have a high spike-timing accuracy, which are likely a main contributor to the theta oscillations generated in MSDB during nicotine receptor activation.
doi:10.1038/aps.2012.180
PMCID: PMC4002786  PMID: 23474704
medial septum diagonal band of Broca; theta oscillations; spike; LFP; nicotinic acetylcholine receptor; nicotine; dihydro-β-erythroidine; brain slice; electrophysiology
7.  Learning alters theta amplitude, theta-gamma coupling and neuronal synchronization in inferotemporal cortex 
BMC Neuroscience  2011;12:55.
Background
How oscillatory brain rhythms alone, or in combination, influence cortical information processing to support learning has yet to be fully established. Local field potential and multi-unit neuronal activity recordings were made from 64-electrode arrays in the inferotemporal cortex of conscious sheep during and after visual discrimination learning of face or object pairs. A neural network model has been developed to simulate and aid functional interpretation of learning-evoked changes.
Results
Following learning the amplitude of theta (4-8 Hz), but not gamma (30-70 Hz) oscillations was increased, as was the ratio of theta to gamma. Over 75% of electrodes showed significant coupling between theta phase and gamma amplitude (theta-nested gamma). The strength of this coupling was also increased following learning and this was not simply a consequence of increased theta amplitude. Actual discrimination performance was significantly correlated with theta and theta-gamma coupling changes. Neuronal activity was phase-locked with theta but learning had no effect on firing rates or the magnitude or latencies of visual evoked potentials during stimuli. The neural network model developed showed that a combination of fast and slow inhibitory interneurons could generate theta-nested gamma. By increasing N-methyl-D-aspartate receptor sensitivity in the model similar changes were produced as in inferotemporal cortex after learning. The model showed that these changes could potentiate the firing of downstream neurons by a temporal desynchronization of excitatory neuron output without increasing the firing frequencies of the latter. This desynchronization effect was confirmed in IT neuronal activity following learning and its magnitude was correlated with discrimination performance.
Conclusions
Face discrimination learning produces significant increases in both theta amplitude and the strength of theta-gamma coupling in the inferotemporal cortex which are correlated with behavioral performance. A network model which can reproduce these changes suggests that a key function of such learning-evoked alterations in theta and theta-nested gamma activity may be increased temporal desynchronization in neuronal firing leading to optimal timing of inputs to downstream neural networks potentiating their responses. In this way learning can produce potentiation in neural networks simply through altering the temporal pattern of their inputs.
doi:10.1186/1471-2202-12-55
PMCID: PMC3123243  PMID: 21658251
8.  Dynamic Changes in Phase-Amplitude Coupling Facilitate Spatial Attention Control in Fronto-Parietal Cortex 
PLoS Biology  2014;12(8):e1001936.
Electrocorticography reveals how coupling between two frequencies of neuronal oscillation allows the frontal and parietal areas of the cortex to control visual attention from moment to moment in the human brain.
Attention is a core cognitive mechanism that allows the brain to allocate limited resources depending on current task demands. A number of frontal and posterior parietal cortical areas, referred to collectively as the fronto-parietal attentional control network, are engaged during attentional allocation in both humans and non-human primates. Numerous studies have examined this network in the human brain using various neuroimaging and scalp electrophysiological techniques. However, little is known about how these frontal and parietal areas interact dynamically to produce behavior on a fine temporal (sub-second) and spatial (sub-centimeter) scale. We addressed how human fronto-parietal regions control visuospatial attention on a fine spatiotemporal scale by recording electrocorticography (ECoG) signals measured directly from subdural electrode arrays that were implanted in patients undergoing intracranial monitoring for localization of epileptic foci. Subjects (n = 8) performed a spatial-cuing task, in which they allocated visuospatial attention to either the right or left visual field and detected the appearance of a target. We found increases in high gamma (HG) power (70–250 Hz) time-locked to trial onset that remained elevated throughout the attentional allocation period over frontal, parietal, and visual areas. These HG power increases were modulated by the phase of the ongoing delta/theta (2–5 Hz) oscillation during attentional allocation. Critically, we found that the strength of this delta/theta phase-HG amplitude coupling predicted reaction times to detected targets on a trial-by-trial basis. These results highlight the role of delta/theta phase-HG amplitude coupling as a mechanism for sub-second facilitation and coordination within human fronto-parietal cortex that is guided by momentary attentional demands.
Author Summary
The frontal and parietal areas of the cortex control the ability to focus visuospatial attention, and damage to these areas results in profound attentional disturbances. Although much research has concentrated on where these areas are located, little is known about how these areas may function in humans. Previous studies have demonstrated that neuronal spiking is more likely to occur in specific time windows based upon the phase of lower frequency neural oscillations – rhythmic or repetitive neuronal activity. These low-frequency rhythms are hypothesized to coordinate the timing of neuronal firing within local and across network regions. Here, we investigated how human frontal and parietal cortices use neural oscillations to control visuospatial attention. We identified a high-frequency component of electrical brain activity, broadband high gamma (70–250 Hz) amplitude, that became phase-locked to a slower rhythm, delta/theta (2–5 Hz), over frontal, parietal, and visual areas while the study subjects paid attention to the peripheral visual field. Changes in the strength of the coupling between delta/theta phase and high gamma amplitude predicted the attentional behavior of the subjects across single trials. From these results, we conclude that coupling between delta/theta phase and high gamma amplitude serves to coordinate information within – and perhaps between – frontal and parietal areas during allocation of visuospatial attention.
doi:10.1371/journal.pbio.1001936
PMCID: PMC4144794  PMID: 25157678
9.  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.
doi:10.1371/journal.pcbi.1002478
PMCID: PMC3325187  PMID: 22511861
10.  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.
doi:10.3389/fncom.2011.00045
PMCID: PMC3216007  PMID: 22110429
spike-timing dependent plasticity; oscillations; phase-locking; stable learning; stability of neuronal plasticity; place fields
11.  Modulation of hippocampal rhythms by subthreshold electric fields and network topology 
Journal of computational neuroscience  2012;34(3):10.1007/s10827-012-0426-4.
Theta (4–12 Hz) and gamma (30–80 Hz) rhythms are considered important for cortical and hippocampal function. Although several neuron types are implicated in rhythmogenesis, the exact cellular mechanisms remain unknown. Subthreshold electric fields provide a flexible, area-specific tool to modulate neural activity and directly test functional hypotheses. Here we present experimental and computational evidence of the interplay among hippocampal synaptic circuitry, neuronal morphology, external electric fields, and network activity. Electrophysiological data are used to constrain and validate an anatomically and biophysically realistic model of area CA1 containing pyramidal cells and two interneuron types: dendritic- and perisomatic-targeting. We report two lines of results: addressing the network structure capable of generating theta-modulated gamma rhythms, and demonstrating electric field effects on those rhythms. First, theta-modulated gamma rhythms require specific inhibitory connectivity. In one configuration, GABAergic axo-dendritic feedback on pyramidal cells is only effective in proximal but not distal layers. An alternative configuration requires two distinct perisomatic interneuron classes, one exclusively receiving excitatory contacts, the other additionally targeted by inhibition. These observations suggest novel roles for particular classes of oriens and basket cells. The second major finding is that subthreshold electric fields robustly alter the balance between different rhythms. Independent of network configuration, positive electric fields decrease, while negative fields increase the theta/gamma ratio. Moreover, electric fields differentially affect average theta frequency depending on specific synaptic connectivity. These results support the testable prediction that subthreshold electric fields can alter hippocampal rhythms, suggesting new approaches to explore their cognitive functions and underlying circuitry.
doi:10.1007/s10827-012-0426-4
PMCID: PMC3549326  PMID: 23053863
Pyramidal; Interneuron; theta-rhythm; gamma-rhythm
12.  Hippocampal Theta Modulation of Neocortical Spike Times and Gamma Rhythm: A Biophysical Model Study 
PLoS ONE  2012;7(10):e45688.
The hippocampal theta and neocortical gamma rhythms are two prominent examples of oscillatory neuronal activity. The hippocampus has often been hypothesized to influence neocortical networks by its theta rhythm, and, recently, evidence for such a direct influence has been found. We examined a possible mechanism for this influence by means of a biophysical model study using conductance-based model neurons. We found, in agreement with previous studies, that networks of fast-spiking GABA -ergic interneurons, coupled with shunting inhibition, synchronize their spike activity at a gamma frequency and are able to impose this rhythm on a network of pyramidal cells to which they are coupled. When our model was supplied with hippocampal theta-modulated input fibres, the theta rhythm biased the spike timings of both the fast-spiking and pyramidal cells. Furthermore, both the amplitude and frequency of local field potential gamma oscillations were influenced by the phase of the theta rhythm. We show that the fast-spiking cells, not pyramidal cells, are essential for this latter phenomenon, thus highlighting their crucial role in the interplay between hippocampus and neocortex.
doi:10.1371/journal.pone.0045688
PMCID: PMC3462809  PMID: 23056213
13.  Frequency dependence of CA3 spike phase response arising from h-current properties 
The phase of firing of hippocampal neurons during theta oscillations encodes spatial information. Moreover, the spike phase response to synaptic inputs in individual cells depends on the expression of the hyperpolarization-activated mixed cation current (Ih), which differs between CA3 and CA1 pyramidal neurons. Here, we compared the phase response of these two cell types, as well as their intrinsic membrane properties. We found that both CA3 and CA1 pyramidal neurons show a voltage sag in response to negative current steps but that this voltage sag is significantly smaller in CA3 cells. Moreover, CA3 pyramidal neurons have less prominent resonance properties compared to CA1 pyramidal neurons. This is consistent with differential expression of Ih by the two cell types. Despite their distinct intrinsic membrane properties, both CA3 and CA1 pyramidal neurons displayed bidirectional spike phase control by excitatory conductance inputs during theta oscillations. In particular, excitatory inputs delivered at the descending phase of a dynamic clamp-induced membrane potential oscillation delayed the subsequent spike by nearly 50 mrad. The effect was shown to be mediated by Ih and was counteracted by increasing inhibitory conductance driving the membrane potential oscillation. Using our experimental data to feed a computational model, we showed that differences in Ih between CA3 and CA1 pyramidal neurons could predict frequency-dependent differences in phase response properties between these cell types. We confirmed experimentally such frequency-dependent spike phase control in CA3 neurons. Therefore, a decrease in theta frequency, which is observed in intact animals during novelty, might switch the CA3 spike phase response from unidirectional to bidirectional and thereby promote encoding of the new context.
doi:10.3389/fncel.2013.00263
PMCID: PMC3872302  PMID: 24399930
theta oscillation; phase response; Ih; resonance; hippocampus; CA3; CA1
14.  Directional Theta Coherence in Prefrontal Cortical to Amygdalo-Hippocampal Pathways Signals Fear Extinction 
PLoS ONE  2013;8(10):e77707.
Theta oscillations are considered crucial mechanisms in neuronal communication across brain areas, required for consolidation and retrieval of fear memories. One form of inhibitory learning allowing adaptive control of fear memory is extinction, a deficit of which leads to maladaptive fear expression potentially leading to anxiety disorders. Behavioral responses after extinction training are thought to reflect a balance of recall from extinction memory and initial fear memory traces. Therefore, we hypothesized that the initial fear memory circuits impact behavioral fear after extinction, and more specifically, that the dynamics of theta synchrony in these pathways signal the individual fear response. Simultaneous multi-channel local field and unit recordings were obtained from the infralimbic prefrontal cortex, the hippocampal CA1 and the lateral amygdala in mice. Data revealed that the pattern of theta coherence and directionality within and across regions correlated with individual behavioral responses. Upon conditioned freezing, units were phase-locked to synchronized theta oscillations in these pathways, characterizing states of fear memory retrieval. When the conditioned stimulus evoked no fear during extinction recall, theta interactions were directional with prefrontal cortical spike firing leading hippocampal and amygdalar theta oscillations. These results indicate that the directional dynamics of theta-entrained activity across these areas guide changes in appraisal of threatening stimuli during fear memory and extinction retrieval. Given that exposure therapy involves procedures and pathways similar to those during extinction of conditioned fear, one therapeutical extension might be useful that imposes artificial theta activity to prefrontal cortical-amygdalo-hippocampal pathways that mimics the directionality signaling successful extinction recall.
doi:10.1371/journal.pone.0077707
PMCID: PMC3812006  PMID: 24204927
15.  Theta-Gamma-Modulated Synaptic Currents in Hippocampal Granule Cells In Vivo Define a Mechanism for Network Oscillations 
Neuron  2014;81(1):140-152.
Summary
Theta-gamma network oscillations are thought to represent key reference signals for information processing in neuronal ensembles, but the underlying synaptic mechanisms remain unclear. To address this question, we performed whole-cell (WC) patch-clamp recordings from mature hippocampal granule cells (GCs) in vivo in the dentate gyrus of anesthetized and awake rats. GCs in vivo fired action potentials at low frequency, consistent with sparse coding in the dentate gyrus. GCs were exposed to barrages of fast AMPAR-mediated excitatory postsynaptic currents (EPSCs), primarily relayed from the entorhinal cortex, and inhibitory postsynaptic currents (IPSCs), presumably generated by local interneurons. EPSCs exhibited coherence with the field potential predominantly in the theta frequency band, whereas IPSCs showed coherence primarily in the gamma range. Action potentials in GCs were phase locked to network oscillations. Thus, theta-gamma-modulated synaptic currents may provide a framework for sparse temporal coding of information in the dentate gyrus.
Highlights
•Granule cells in vivo fire action potentials sparsely but often in bursts•Granule cells are exposed to barrages of fast excitatory postsynaptic currents•Granule cells receive theta-coherent excitation but gamma-coherent inhibition
Pernía-Andrade and Jonas characterize the synaptic mechanisms underlying network oscillations and temporal coding in the dorsal hippocampus in awake rats. Theta-gamma-modulated synaptic currents may provide a framework for sparse temporal coding of information in the dentate gyrus.
doi:10.1016/j.neuron.2013.09.046
PMCID: PMC3909463  PMID: 24333053
16.  Theta Frequency Background Tunes Transmission but Not Summation of Spiking Responses 
PLoS ONE  2013;8(1):e55607.
Hippocampal neurons are known to fire as a function of frequency and phase of spontaneous network rhythms, associated with the animal's behaviour. This dependence is believed to give rise to precise rate and temporal codes. However, it is not well understood how these periodic membrane potential fluctuations affect the integration of synaptic inputs. Here we used sinusoidal current injection to the soma of CA1 pyramidal neurons in the rat brain slice to simulate background oscillations in the physiologically relevant theta and gamma frequency range. We used a detailed compartmental model to show that somatic current injection gave comparable results to more physiological synaptically driven theta rhythms incorporating excitatory input in the dendrites, and inhibitory input near the soma. We systematically varied the phase of synaptic inputs with respect to this background, and recorded changes in response and summation properties of CA1 neurons using whole-cell patch recordings. The response of the cell was dependent on both the phase of synaptic inputs and frequency of the background input. The probability of the cell spiking for a given synaptic input was up to 40% greater during the depolarized phases between 30–135 degrees of theta frequency current injection. Summation gain on the other hand, was not affected either by the background frequency or the phasic afferent inputs. This flat summation gain, coupled with the enhanced spiking probability during depolarized phases of the theta cycle, resulted in enhanced transmission of summed inputs during the same phase window of 30–135 degrees. Overall, our study suggests that although oscillations provide windows of opportunity to selectively boost transmission and EPSP size, summation of synaptic inputs remains unaffected during membrane oscillations.
doi:10.1371/journal.pone.0055607
PMCID: PMC3561309  PMID: 23383242
17.  Hippocampal CA1 Circuitry Dynamically Gates Direct Cortical Inputs Preferentially at Theta Frequencies 
Hippocampal CA1 pyramidal neurons receive intrahippocampal and extrahipppocampal inputs during theta cycle, whose relative timing and magnitude regulate the probability of CA1 pyramidal cell spiking. Extrahippocampal inputs, giving rise to the primary theta dipole in CA1 stratum lacunosum moleculare, are conveyed by the temporoammonic pathway. The temporoammonic pathway impinging onto the CA1 distal apical dendritic tuft is the most electrotonically distant from the perisomatic region yet is critical in regulating CA1 place cell activity during theta cycles. How does local hippocampal circuitry regulate the integration of this essential, but electrotonically distant, input within the theta period? Using whole-cell somatic recording and voltage-sensitive dye imaging with simultaneous dendritic recording of CA1 pyramidal cell responses, we demonstrate that temporoammonic EPSPs are normally compartmentalized to the apical dendritic tuft by feedforward inhibition. However, when this input is preceded at a one-half theta cycle interval by proximally targeted Schaffer collateral activity, temporoammonic EPSPs propagate to thesomathrough a joint, codependent mechanism involving activation of Schaffer-specific NMDA receptors and presynaptic inhibition of GABAergic terminals. These afferent interactions, tuned for synaptic inputs arriving one-half theta interval apart, are in turn modulated by feedback inhibition initiated via axon collaterals of pyramidal cells. Therefore, CA1 circuit integration of excitatory inputs endows the CA1 principal cell with a novel property: the ability to function as a temporally specific “AND” gate that provides for sequence-dependent readout of distal inputs.
doi:10.1523/JNEUROSCI.2992-05.2005
PMCID: PMC2048747  PMID: 16237162
voltage-sensitive dye imaging; circuit integration; temporoammonic; inhibition; gating; theta cycle
18.  The Role of Ongoing Dendritic Oscillations in Single-Neuron Dynamics 
PLoS Computational Biology  2009;5(9):e1000493.
The dendritic tree contributes significantly to the elementary computations a neuron performs while converting its synaptic inputs into action potential output. Traditionally, these computations have been characterized as both temporally and spatially localized. Under this localist account, neurons compute near-instantaneous mappings from their current input to their current output, brought about by somatic summation of dendritic contributions that are generated in functionally segregated compartments. However, recent evidence about the presence of oscillations in dendrites suggests a qualitatively different mode of operation: the instantaneous phase of such oscillations can depend on a long history of inputs, and under appropriate conditions, even dendritic oscillators that are remote may interact through synchronization. Here, we develop a mathematical framework to analyze the interactions of local dendritic oscillations and the way these interactions influence single cell computations. Combining weakly coupled oscillator methods with cable theoretic arguments, we derive phase-locking states for multiple oscillating dendritic compartments. We characterize how the phase-locking properties depend on key parameters of the oscillating dendrite: the electrotonic properties of the (active) dendritic segment, and the intrinsic properties of the dendritic oscillators. As a direct consequence, we show how input to the dendrites can modulate phase-locking behavior and hence global dendritic coherence. In turn, dendritic coherence is able to gate the integration and propagation of synaptic signals to the soma, ultimately leading to an effective control of somatic spike generation. Our results suggest that dendritic oscillations enable the dendritic tree to operate on more global temporal and spatial scales than previously thought; notably that local dendritic activity may be a mechanism for generating on-going whole-cell voltage oscillations.
Author Summary
A central issue in biology is how local processes yield global consequences. This is especially relevant for neurons since these spatially extended cells process local synaptic inputs to generate global action potential output. The dendritic tree of a neuron, which receives most of the inputs, expresses ion channels that can generate nonlinear dynamics. A prominent phenomenon resulting from such ion channels are voltage oscillations. The distribution of the active membrane channels throughout the cell is often highly non-uniform. This can turn the dendritic tree into a network of sparsely spaced local oscillators. Here we analyze whether local dendritic oscillators can produce cell-wide voltage oscillations. Our mathematical theory shows that indeed even when the dendritic oscillators are weakly coupled, they lock their phases and give global oscillations. We show how the biophysical properties of the dendrites determine the global locking and how it can be controlled by synaptic inputs. As a consequence of global locking, even individual synaptic inputs can affect the timing of action potentials. In fact, dendrites locking in synchrony can lead to sustained firing of the cell. We show that dendritic trees can be bistable, with dendrites locking in either synchrony or asynchrony, which may provide a novel mechanism for single cell-based memory.
doi:10.1371/journal.pcbi.1000493
PMCID: PMC2725317  PMID: 19730677
19.  Spike-Timing Precision and Neuronal Synchrony Are Enhanced by an Interaction between Synaptic Inhibition and Membrane Oscillations in the Amygdala 
PLoS ONE  2012;7(4):e35320.
The basolateral complex of the amygdala (BLA) is a critical component of the neural circuit regulating fear learning. During fear learning and recall, the amygdala and other brain regions, including the hippocampus and prefrontal cortex, exhibit phase-locked oscillations in the high delta/low theta frequency band (∼2–6 Hz) that have been shown to contribute to the learning process. Network oscillations are commonly generated by inhibitory synaptic input that coordinates action potentials in groups of neurons. In the rat BLA, principal neurons spontaneously receive synchronized, inhibitory input in the form of compound, rhythmic, inhibitory postsynaptic potentials (IPSPs), likely originating from burst-firing parvalbumin interneurons. Here we investigated the role of compound IPSPs in the rat and rhesus macaque BLA in regulating action potential synchrony and spike-timing precision. Furthermore, because principal neurons exhibit intrinsic oscillatory properties and resonance between 4 and 5 Hz, in the same frequency band observed during fear, we investigated whether compound IPSPs and intrinsic oscillations interact to promote rhythmic activity in the BLA at this frequency. Using whole-cell patch clamp in brain slices, we demonstrate that compound IPSPs, which occur spontaneously and are synchronized across principal neurons in both the rat and primate BLA, significantly improve spike-timing precision in BLA principal neurons for a window of ∼300 ms following each IPSP. We also show that compound IPSPs coordinate the firing of pairs of BLA principal neurons, and significantly improve spike synchrony for a window of ∼130 ms. Compound IPSPs enhance a 5 Hz calcium-dependent membrane potential oscillation (MPO) in these neurons, likely contributing to the improvement in spike-timing precision and synchronization of spiking. Activation of the cAMP-PKA signaling cascade enhanced the MPO, and inhibition of this cascade blocked the MPO. We discuss these results in the context of spike-timing dependent plasticity and modulation by neurotransmitters important for fear learning, such as dopamine.
doi:10.1371/journal.pone.0035320
PMCID: PMC3338510  PMID: 22563382
20.  Locomotion-Related Oscillatory Body Movements at 6–12 Hz Modulate the Hippocampal Theta Rhythm 
PLoS ONE  2011;6(11):e27575.
The hippocampal theta rhythm is required for accurate navigation and spatial memory but its relation to the dynamics of locomotion is poorly understood. We used miniature accelerometers to quantify with high temporal and spatial resolution the oscillatory movements associated with running in rats. Simultaneously, we recorded local field potentials in the CA1 area of the hippocampus. We report that when rats run their heads display prominent vertical oscillations with frequencies in the same range as the hippocampal theta rhythm (i.e., 6–12 Hz). In our behavioral set-up, rats run mainly with speeds between 50 and 100 cm/s. In this range of speeds, both the amplitude and frequency of the “theta” head oscillations were increasing functions of running speed, demonstrating that the head oscillations are part of the locomotion dynamics. We found evidence that these rhythmical locomotor dynamics interact with the neuronal activity in the hippocampus. The amplitude of the hippocampal theta rhythm depended on the relative phase shift with the head oscillations, being maximal when the two signals were in phase. Despite similarity in frequency, the head movements and LFP oscillations only displayed weak phase and frequency locking. Our results are consistent with that neurons in the CA1 region receive inputs that are phase locked to the head acceleration signal and that these inputs are integrated with the ongoing theta rhythm.
doi:10.1371/journal.pone.0027575
PMCID: PMC3216955  PMID: 22102910
21.  Mu opioid receptor activation normalizes temporo-ammonic pathway driven inhibition in hippocampal CA1 
Neuropharmacology  2010;60(2-3):472-479.
The hippocampus of the mammalian brain is important for the formation of long term memories. Hippocampal-dependent learning can be affected by a number of neurotransmitters including the activation of μ-opioid receptors (MOR). It has been shown that MOR activation can alter synaptic plasticity and network oscillations in the hippocampus, both of which are thought to be important for the encoding of information and formation of memories. One hippocampal oscillation that has been correlated with learning and memory formation is the 4-10 Hz theta rhythm. During theta rhythms, inputs to hippocampal CA1 from CA3 (Schaffer collaterals, SC) and the entorhinal cortex (perforant path) can integrate at different times within an individual theta cycle. Consequently, when excitatory inputs in the stratum lacunosum-moleculare (the temporo-ammonic pathway (TA), which includes the perforant path) are stimulated approximately one theta period before SC inputs, the TA can indirectly inhibit SC inputs. This inhibition is due to the activation of postsynaptic GABAB receptors on CA1 pyramidal neurons. Importantly, MOR activation has been shown to suppress GABAB inhibitory postsynaptic potentials in CA1 pyramidal neurons. Therefore, we examined how MOR activation affects the integration between TA inputs and SC inputs in hippocampal CA1. To do this we used voltage-sensitive dye imaging and whole cell patch clamping from acute hippocampal slices taken from young adult rats. Here we show that MOR activation has no effect on the integration between TA and SC inputs when activation of the TA precedes SC by less than one half of a theta cycle (< 75 ms). However, MOR activation completely blocked the inhibitory action of TA on SC inputs when TA stimulation occurred approximately one theta cycle before SC activation (> 150 ms). This MOR suppression of TA driven inhibition occurred in both the SC input layer of hippocampal CA1 (stratum radiatum) and the output layer of CA1 pyramidal neurons (stratum pyramidale). Thus MOR activation can have profound effects on the temporal integration between two primary excitatory pathways to hippocampal CA1 and subsequently the resultant output from CA1 pyramidal neurons. These data provide important information for understanding how acute or chronic MOR activation may affect the integration of activity within hippocampal CA1 during theta rhythm.
doi:10.1016/j.neuropharm.2010.10.029
PMCID: PMC3014450  PMID: 21056047
voltage-sensitive dye; integration; interneuron; feed forward; theta
22.  Ih Tunes Theta/Gamma Oscillations and Cross-Frequency Coupling In an In Silico CA3 Model 
PLoS ONE  2013;8(10):e76285.
channels are uniquely positioned to act as neuromodulatory control points for tuning hippocampal theta (4–12 Hz) and gamma (25 Hz) oscillations, oscillations which are thought to have importance for organization of information flow. contributes to neuronal membrane resonance and resting membrane potential, and is modulated by second messengers. We investigated oscillatory control using a multiscale computer model of hippocampal CA3, where each cell class (pyramidal, basket, and oriens-lacunosum moleculare cells), contained type-appropriate isoforms of . Our model demonstrated that modulation of pyramidal and basket allows tuning theta and gamma oscillation frequency and amplitude. Pyramidal also controlled cross-frequency coupling (CFC) and allowed shifting gamma generation towards particular phases of the theta cycle, effected via 's ability to set pyramidal excitability. Our model predicts that in vivo neuromodulatory control of allows flexibly controlling CFC and the timing of gamma discharges at particular theta phases.
doi:10.1371/journal.pone.0076285
PMCID: PMC3799898  PMID: 24204609
23.  Cortical Pyramidal Cells as Non-Linear Oscillators: Experiment and Spike-Generation Theory 
Brain research  2007;1171:122-137.
Cortical neurons are capable of generating trains of action potentials in response to current injections. These discharges can take different forms, e.g. repetive firing that adapts during the period of current injection or bursting behaviors. We have used a combined experimental and computational approach to characterize the dynamics leading to action potential responses in single neurons. Specifically we investigated the origin of complex firing patterns in response to sinusoidal current injections. Using a reduced model, the theta neuron, alongside recordings from cortical pyramidal cells we show that both real and simulated neurons show phase locking to sine wave stimuli up to a critical frequency, above which period skipping and 1-to-x phase locking occurs. The locking behavior follows a complex “devil’s staircase” phenomena, where locked modes are interleaved with irregular firing. We further show that the critical frequency depends on the time scale of spike generation and on the level of spike frequency adaptation. These results suggest that phase locking of neuronal responses to complex input patterns can be explained by basic properties of the spike generating machinery.
doi:10.1016/j.brainres.2007.07.028
PMCID: PMC2045506  PMID: 17716635
bifurcation theory; devil’s staircase; endogenous oscillators
24.  Auditory Nerve Spike Generator Modeled as a Variable Attenuator Based on a Saddle Node on Invariant Circle Bifurcation 
PLoS ONE  2012;7(9):e45326.
Mammalian inner hair cells transduce the sound waves amplified by the cochlear amplifier (CA) into a graded neurotransmitter release that activates channels on auditory nerve fibers (ANF). These synaptic channels then charge its dendritic spike generator. While the outer hair cells of the CA employ positive feedback, poising on Andronov-Hopf type instabilities which make them extremely sensitive to faint sounds and make CA output strongly nonlinear, the ANF appears to be based on different principles and a different type of dynamical instability. Its spike generator “digitizes” CA output into trains of action potentials and behaves as a linear filter, rate-coding sound intensity across a wide dynamic range. Here we model the spike generator as a 3 dimensional version of a saddle node on invariant circle (SNIC) bifurcation. The generic 2d SNIC increases its spike rate as the square root of the input current above its spiking threshold. We add negative feedback in the form of a low voltage-threshold potassium conductance that slows down the generator’s rate of increase of its spike rate. A Poisson random source simulates an inner hair cell, outputting a series of noisy periodic current pulses to the model ANF whose spikes phase lock to these pulses and have a linear frequency to current relation with a wide dynamic range. Also, the spike generator compartment has a cholinergic feedback connection from the olive and experiments show that such feedback is able to alter the amount of H conductance inside the generator compartment. We show that an olive able to decrease H would be able to shift the spike generator’s dynamic range to higher sound intensities. In a quiet environment by increasing H the olive would be able to make spike trains similar to those caused by synaptic input.
doi:10.1371/journal.pone.0045326
PMCID: PMC3445452  PMID: 23028935
25.  A Computational Predictor of Human Episodic Memory Based on a Theta Phase Precession Network 
PLoS ONE  2009;4(10):e7536.
In the rodent hippocampus, a phase precession phenomena of place cell firing with the local field potential (LFP) theta is called “theta phase precession” and is considered to contribute to memory formation with spike time dependent plasticity (STDP). On the other hand, in the primate hippocampus, the existence of theta phase precession is unclear. Our computational studies have demonstrated that theta phase precession dynamics could contribute to primate–hippocampal dependent memory formation, such as object–place association memory. In this paper, we evaluate human theta phase precession by using a theory–experiment combined analysis. Human memory recall of object–place associations was analyzed by an individual hippocampal network simulated by theta phase precession dynamics of human eye movement and EEG data during memory encoding. It was found that the computational recall of the resultant network is significantly correlated with human memory recall performance, while other computational predictors without theta phase precession are not significantly correlated with subsequent memory recall. Moreover the correlation is larger than the correlation between human recall and traditional experimental predictors. These results indicate that theta phase precession dynamics are necessary for the better prediction of human recall performance with eye movement and EEG data. In this analysis, theta phase precession dynamics appear useful for the extraction of memory-dependent components from the spatio–temporal pattern of eye movement and EEG data as an associative network. Theta phase precession may be a common neural dynamic between rodents and humans for the formation of environmental memories.
doi:10.1371/journal.pone.0007536
PMCID: PMC2762313  PMID: 19851508

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