Theta-nested Gamma Oscillations Research Articles

A dynamical computational model of theta generation in hippocampal circuits to study theta-gamma oscillations during neurostimulation.

Neurostimulation of the hippocampal formation has shown promising results for modulating memory but the underlying mechanisms remain unclear. In particular, the effects on hippocampal theta-nested gamma oscillations and theta phase reset, which are both crucial for memory processes, are unknown. Moreover, these effects cannot be investigated using current computational models, which consider theta oscillations with a fixed amplitude and phase velocity. Here, we developed a novel computational model that includes the medial septum, represented as a set of abstract Kuramoto oscillators producing a dynamical theta rhythm with phase reset, and the hippocampal formation, composed of biophysically realistic neurons and able to generate theta-nested gamma oscillations under theta drive. We showed that, for theta inputs just below the threshold to induce self-sustained theta-nested gamma oscillations, a single stimulation pulse could switch the network behavior from non-oscillatory to a state producing sustained oscillations. Next, we demonstrated that, for a weaker theta input, pulse train stimulation at the theta frequency could transiently restore seemingly physiological oscillations. Importantly, the presence of phase reset influenced whether these two effects depended on the phase at which stimulation onset was delivered, which has practical implications for designing neurostimulation protocols that are triggered by the phase of ongoing theta oscillations. This novel model opens new avenues for studying the effects of neurostimulation on the hippocampal formation. Furthermore, our hybrid approach that combines different levels of abstraction could be extended in future work to other neural circuits that produce dynamical brain rhythms.

Comprehensive characterization of oscillatory signatures in a model circuit with PV- and SOM-expressing interneurons

Neural circuits contain a wide variety of interneuron types, which differ in their biophysical properties and connectivity patterns. The two most common interneuron types, parvalbumin-expressing and somatostatin-expressing cells, have been shown to be differentially involved in many cognitive functions. These cell types also show different relationships with the power and phase of oscillations in local field potentials. The mechanisms that underlie the emergence of different oscillatory rhythms in neural circuits with more than one interneuron subtype, and the roles specific interneurons play in those mechanisms, are not fully understood. Here, we present a comprehensive analysis of all possible circuit motifs and input regimes that can be achieved in circuits comprised of excitatory cells, PV-like fast-spiking interneurons and SOM-like low-threshold spiking interneurons. We identify 18 unique motifs and simulate their dynamics over a range of input strengths. Using several characteristics, such as oscillation frequency, firing rates, phase of firing and burst fraction, we cluster the resulting circuit dynamics across motifs in order to identify patterns of activity and compare these patterns to behaviors that were generated in circuits with one interneuron type. In addition to the well-known PING and ING gamma oscillations and an asynchronous state, our analysis identified three oscillatory behaviors that were generated by the three-cell-type motifs only: theta-nested gamma oscillations, stable beta oscillations and theta-locked bursting behavior, which have also been observed in experiments. Our characterization provides a map to interpret experimental activity patterns and suggests pharmacological manipulations or optogenetics approaches to validate these conclusions.

Theta-Nested Gamma Oscillations in Next Generation Neural Mass Models.

Theta-nested gamma oscillations have been reported in many areas of the brain and are believed to represent a fundamental mechanism to transfer information across spatial and temporal scales. In a series of recent experiments in vitro it has been possible to replicate with an optogenetic theta frequency stimulation several features of cross-frequency coupling (CFC) among theta and gamma rhythms observed in behaving animals. In order to reproduce the main findings of these experiments we have considered a new class of neural mass models able to reproduce exactly the macroscopic dynamics of spiking neural networks. In this framework, we have examined two set-ups able to support collective gamma oscillations: namely, the pyramidal interneuronal network gamma (PING) and the interneuronal network gamma (ING). In both set-ups we observe the emergence of theta-nested gamma oscillations by driving the system with a sinusoidal theta-forcing in proximity of a Hopf bifurcation. These mixed rhythms always display phase amplitude coupling. However, two different types of nested oscillations can be identified: one characterized by a perfect phase locking between theta and gamma rhythms, corresponding to an overall periodic behavior; another one where the locking is imperfect and the dynamics is quasi-periodic or even chaotic. From our analysis it emerges that the locked states are more frequent in the ING set-up. In agreement with the experiments, we find theta-nested gamma oscillations for forcing frequencies in the range [1:10] Hz, whose amplitudes grow proportionally to the forcing intensity and which are clearly modulated by the theta phase. Furthermore, analogously to the experiments, the gamma power and the frequency of the gamma-power peak increase with the forcing amplitude. At variance with experimental findings, the gamma-power peak does not shift to higher frequencies by increasing the theta frequency. This effect can be obtained, in our model, only by incrementing, at the same time, also the stimulation power. An effect achieved by increasing the amplitude either of the noise or of the forcing term proportionally to the theta frequency. On the basis of our analysis both the PING and the ING mechanism give rise to theta-nested gamma oscillations with almost identical features.

Synchronicity of excitatory inputs drives hippocampal networks to distinct oscillatory patterns.

The rodent hippocampus expresses a variety of neuronal network oscillations depending on the behavioral state of the animal. Locomotion and active exploration are accompanied by theta-nested gamma oscillations while resting states and slow-wave sleep are dominated by intermittent sharp wave-ripple complexes. It is believed that gamma rhythms create a framework for efficient acquisition of information whereas sharp wave-ripples are thought to be involved in consolidation and retrieval of memory. While not strictly mutually exclusive, one of the two patterns usually dominates in a given behavioral state. Here we explore how different input patterns induce either of the two network states, using an optogenetic stimulation approach in hippocampal brain slices of mice. We report that the pattern of the evoked oscillation depends strongly on the initial synchrony of activation of excitatory cells within CA3. Short, synchronous activation favors the emergence of sharp wave-ripple complexes while persistent but less synchronous activity-as typical for sensory input during exploratory behavior-supports the generation of gamma oscillations. This dichotomy is reflected by different degrees of synchrony of excitatory and inhibitory synaptic currents within these two states. Importantly, the induction of these two fundamental network patterns does not depend on the presence of any neuromodulatory transmitter like acetylcholine, but is merely based on a different synchrony in the initial activation pattern.

Optogenetic activation of parvalbumin and somatostatin interneurons selectively restores theta-nested gamma oscillations and oscillation-induced spike timing-dependent\xa0long-term potentiation impaired by amyloid \u03b2 oligomers

BackgroundAbnormal accumulation of amyloid β1–42 oligomers (AβO1–42), a hallmark of Alzheimer’s disease, impairs hippocampal theta-nested gamma oscillations and long-term potentiation (LTP) that are believed to underlie learning and memory. Parvalbumin-positive (PV) and somatostatin-positive (SST) interneurons are critically involved in theta-nested gamma oscillogenesis and LTP induction. However, how AβO1–42 affects PV and SST interneuron circuits is unclear. Through optogenetic manipulation of PV and SST interneurons and computational modeling of the hippocampal neural circuits, we dissected the contributions of PV and SST interneuron circuit dysfunctions on AβO1–42-induced impairments of hippocampal theta-nested gamma oscillations and oscillation-induced LTP.ResultsTargeted whole-cell patch-clamp recordings and optogenetic manipulations of PV and SST interneurons during in vivo-like, optogenetically induced theta-nested gamma oscillations in vitro revealed that AβO1–42 causes synapse-specific dysfunction in PV and SST interneurons. AβO1–42 selectively disrupted CA1 pyramidal cells (PC)-to-PV interneuron and PV-to-PC synapses to impair theta-nested gamma oscillogenesis. In contrast, while having no effect on PC-to-SST or SST-to-PC synapses, AβO1–42 selectively disrupted SST interneuron-mediated disinhibition to CA1 PC to impair theta-nested gamma oscillation-induced spike timing-dependent LTP (tLTP). Such AβO1–42-induced impairments of gamma oscillogenesis and oscillation-induced tLTP were fully restored by optogenetic activation of PV and SST interneurons, respectively, further supporting synapse-specific dysfunctions in PV and SST interneurons. Finally, computational modeling of hippocampal neural circuits including CA1 PC, PV, and SST interneurons confirmed the experimental observations and further revealed distinct functional roles of PV and SST interneurons in theta-nested gamma oscillations and tLTP induction.ConclusionsOur results reveal that AβO1–42 causes synapse-specific dysfunctions in PV and SST interneurons and that optogenetic modulations of these interneurons present potential therapeutic targets for restoring hippocampal network oscillations and synaptic plasticity impairments in Alzheimer’s disease.

A detailed anatomical and mathematical model of the hippocampal formation for the generation of sharp-wave ripples and theta-nested gamma oscillations

The mechanisms underlying the broad variety of oscillatory rhythms measured in the hippocampus during the sleep-wake cycle are not yet fully understood. In this article, we propose a computational model of the hippocampal formation based on a realistic topology and synaptic connectivity, and we analyze the effect of different changes on the network, namely the variation of synaptic conductances, the variations of the CAN channel conductance and the variation of inputs. By using a detailed simulation of intracerebral recordings, we show that this is able to reproduce both the theta-nested gamma oscillations that are seen in awake brains and the sharp-wave ripple complexes measured during slow-wave sleep. The results of our simulations support the idea that the functional connectivity of the hippocampus, modulated by the sleep-wake variations in Acetylcholine concentration, is a key factor in controlling its rhythms.

Intrinsic Cornu Ammonis Area 1 Theta-Nested Gamma Oscillations Induced by Optogenetic Theta Frequency Stimulation.

This study demonstrates that the cornu ammonis area 1 (CA1) is capable of generating intrinsic gamma oscillations in response to theta input. This gamma generator is independent of activity in the upstream regions, highlighting that CA1 can produce its own gamma oscillation in addition to inheriting activity from the upstream regions. This supports the theory that gamma oscillations predominantly function to achieve local synchrony, and that a local gamma generated in each area conducts the signal to the downstream region.

Noise promotes independent control of gamma oscillations and grid firing within recurrent attractor networks.

Neural computations underlying cognitive functions require calibration of the strength of excitatory and inhibitory synaptic connections and are associated with modulation of gamma frequency oscillations in network activity. However, principles relating gamma oscillations, synaptic strength and circuit computations are unclear. We address this in attractor network models that account for grid firing and theta-nested gamma oscillations in the medial entorhinal cortex. We show that moderate intrinsic noise massively increases the range of synaptic strengths supporting gamma oscillations and grid computation. With moderate noise, variation in excitatory or inhibitory synaptic strength tunes the amplitude and frequency of gamma activity without disrupting grid firing. This beneficial role for noise results from disruption of epileptic-like network states. Thus, moderate noise promotes independent control of multiplexed firing rate- and gamma-based computational mechanisms. Our results have implications for tuning of normal circuit function and for disorders associated with changes in gamma oscillations and synaptic strength.

Impact of noise on theta-nested gamma oscillations in a spiking continuous attractor model of grid cells

Grid cells in the medial entorhinal cortex (MEC) encode location through firing fields that form grid-like maps of the environment. At the same time network activity in the MEC is dominated by oscillations in the theta (4-12 Hz) and gamma (30-100 Hz) bands. Our recent experimental data established that feedback inhibition between excitatory stellate cells and inhibitory fast spiking interneurons dominates the synaptic connectivity in layer II of the MEC, and that continuous attractor models derived from these properties are sufficient to explain both the network oscillations and grid firing fields [1]. Here we use a spiking continuous attractor network model of layer II stellate cells and fast spiking interneurons to examine the effect of intrinsic noise on the emergence of theta nested-gamma oscillations. In this model, stellate cells connect exclusively to interneurons, while interneurons contact only stellate cells. When driven with a theta (8 Hz) modulated external input, we observed network synchronization in the gamma range during the trough of the theta signal, which depended on the amount of intrinsic Gaussian noise generated independently at each neuron. Without noise, the network exhibited aberrant hyper-synchronous firing of a subpopulation of stellate cells at the beginning of each theta cycle. The stellate cell firing resulted in a strong feedback inhibitory postsynaptic currents from fast spiking interneurons that had an additional synchronizing effect. The strong inhibitory feedback abolished nested gamma oscillations. With increasing noise, the network entered an intermediate state in which we observed theta nested-gamma oscillations [1]. When noise level was set even higher, the nested gamma oscillations disappeared without increasing the amount of inhibitory coupling. We also present the impact of noise on bump attractor formation and gridness score of the grid-like receptive fields. Together, these results show that the presence of noise may have profound implications on the stability of theta-nested gamma oscillations in attractor neural circuits with feedback inhibition.

Feedback Inhibition Enables Theta-Nested Gamma Oscillations and Grid Firing Fields

Cortical circuits are thought to multiplex firing rate codes with temporal codes that rely on oscillatory network activity, but the circuit mechanisms that combine these coding schemes are unclear. We establish with optogenetic activation of layer II of the medial entorhinal cortex that theta frequency drive to this circuit is sufficient to generate nested gamma frequency oscillations in synaptic activity. These nested gamma oscillations closely resemble activity during spatial exploration, are generated by local feedback inhibition without recurrent excitation, and have clock-like features suitable as reference signals for multiplexing temporal codes within rate-coded grid firing fields. In network models deduced from our data, feedback inhibition supports coexistence of theta-nested gamma oscillations with attractor states that generate grid firing fields. These results indicate that grid cells communicate primarily via inhibitory interneurons. This circuit mechanism enables multiplexing of oscillation-based temporal codes with rate-coded attractor states.

Multiplexing of theta-nested gamma oscillations and grid firing fields in an attractor network model of layer II of the medial entorhinal cortex

Multiplexing of theta-nested gamma oscillations and grid firing fields in an attractor network model of layer II of the medial entorhinal cortex

Sequence generation in arbitrary temporal patterns from theta-nested gamma oscillations: a model of the basal ganglia–thalamo-cortical loops

A computational model that is able to generate sequences at arbitrary rates in a given serial order is presented for the cortico-basal ganglia (BG)–thalamic neural circuitry. Upon generating a sequence, this model stores information on the serial order of components in a cortical buffer by means of theta-nested gamma frequency oscillations observed experimentally in cortico-striatal neurons. This model assumes the existence of at least two functionally different classes of striatal spiny neurons. One class of striatal projection neurons (S-cells) select the first component in the cortical buffer through a temporal winner-take-all mechanism implemented by lateral inhibition. The inhibition should last for at least a few hundred milliseconds. In reality, it may be mediated by GABA B receptors at the presynaptic terminals of the cortico-striatal projection. The other class of striatal projection neurons (M-cells) retain the currently executed component in a cortico-BG–thalamic loop, for which the strong nonlinearity in transitions between up and down states of striatal neurons is crucial. For sequence generation at the level of striatum, the cortical neurons encoding the component selected for execution are inactivated by the feedback from the activated cortico-BG–thalamic loop. This model predicts that the transition to next component is triggered by a single external signal, i.e. the subthalamic input to the globus pallidum. This input gives a neural substrate for adjusting the rate of sequence generation.