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

Existence and stability criteria for global synchrony and for synchrony in two alternating clusters of pulse-coupled oscillators updated to include conduction delays

Phase Response Curves (PRCs) have been useful in determining and analyzing various phase-locking modes in networks of oscillators under pulse-coupling assumptions, as reviewed in Mathematical Biosciences, 226:77-96, 2010. Here, we update that review to include progress since 2010 on pulse coupled oscillators with conduction delays. We then present original results that extend the derivation of the criteria for stability of global synchrony in networks of pulse-coupled oscillators to include conduction delays. We also incorporate conduction delays to extend previous studies that showed how an alternating firing pattern between two synchronized clusters could enforce within-cluster synchrony, even for clusters unable to synchronize themselves in isolation. To obtain these results, we used self-connected neurons to represent clusters. These results greatly extend the applicability of the stability analyses to networks of pulse-coupled oscillators since conduction delays are ubiquitous and strongly impact the stability of synchrony. Although these analyses only strictly apply to identical oscillators with identical connections to other oscillators, the principles are general and suggest how to promote or impede synchrony in physiological networks of neurons, for example. Heterogeneity can be interpreted as a form of frozen noise, and approximate synchrony can be sustained despite heterogeneity. The pulse-coupled oscillator model can not only be used to describe biological neuronal networks but also cardiac pacemakers, lasers, fireflies, artificial neural networks, social self-organization, and wireless sensor networks.

Firing rate models for gamma oscillations in I-I and E-I networks

Firing rate models for describing the mean-field activities of neuronal ensembles can be used effectively to study network function and dynamics, including synchronization and rhythmicity of excitatory-inhibitory populations. However, traditional Wilson-Cowan-like models, even when extended to include an explicit dynamic synaptic activation variable, are found unable to capture some dynamics such as Interneuronal Network Gamma oscillations (ING). Use of an explicit delay is helpful in simulations at the expense of complicating mathematical analysis. We resolve this issue by introducing a dynamic variable, u, that acts as an effective delay in the negative feedback loop between firing rate (r) and synaptic gating of inhibition (s). In effect, u endows synaptic activation with second order dynamics. With linear stability analysis, numerical branch-tracking and simulations, we show that our r-u-s rate model captures some key qualitative features of spiking network models for ING. We also propose an alternative formulation, a v-u-s model, in which mean membrane potential v satisfies an averaged current-balance equation. Furthermore, we extend the framework to E-I networks. With our six-variable v-u-s model, we demonstrate in firing rate models the transition from Pyramidal-Interneuronal Network Gamma (PING) to ING by increasing the external drive to the inhibitory population without adjusting synaptic weights. Having PING and ING available in a single network, without invoking synaptic blockers, is plausible and natural for explaining the emergence and transition of two different types of gamma oscillations.

Analyzing top-down visual attention in the context of gamma oscillations: a layer- dependent network-of- networks approach

Top-down visual attention is a fundamental cognitive process that allows individuals to selectively attend to salient visual stimuli in the environment. Recent empirical findings have revealed that gamma oscillations participate in the modulation of visual attention. However, computational studies face challenges when analyzing the attentional process in the context of gamma oscillation due to the unstable nature of gamma oscillations and the complexity induced by the layered fashion in the visual cortex. In this study, we propose a layer-dependent network-of-networks approach to analyze such attention with gamma oscillations. The model is validated by reproducing empirical findings on orientation preference and the enhancement of neuronal response due to top-down attention. We perform parameter plane analysis to classify neuronal responses into several patterns and find that the neuronal response to sensory and attention signals was modulated by the heterogeneity of the neuronal population. Furthermore, we revealed a counter-intuitive scenario that the excitatory populations in layer 2/3 and layer 5 exhibit opposite responses to the attentional input. By modification of the original model, we confirmed layer 6 plays an indispensable role in such cases. Our findings uncover the layer-dependent dynamics in the cortical processing of visual attention and open up new possibilities for further research on layer-dependent properties in the cerebral cortex.

Existence and Stability Criteria for Global Synchrony and for Synchrony in two Alternating Clusters of Pulse-Coupled Oscillators Updated to Include Conduction Delays

Phase Response Curves (PRCs) have been useful in determining and analyzing various phase-locking modes in networks of oscillators under pulse-coupling assumptions, as reviewed in Mathematical Biosciences, 226:77-96, 2010. Here, we update that review to include progress since 2010 on pulse coupled oscillators with conduction delays. We then present original results that extend the derivation of the criteria for stability of global synchrony in networks of pulse-coupled oscillators to include conduction delays. We also incorporate conduction delays to extend previous studies that showed how an alternating firing pattern between two synchronized clusters could enforce within cluster synchrony, even for clusters unable to synchronize themselves in isolation. To obtain these results, we used self-connected neurons to represent clusters. These results greatly extend the applicability of the stability analyses to networks of pulse-coupled oscillators since conduction delays are ubiquitous and strongly impact the stability of synchrony. Although these analyses only strictly apply to identical oscillators with identical connections to other oscillators, the principles are general and suggest how to promote or impede synchrony in physiological networks of neurons, for example. Heterogeneity can be interpreted as a form of frozen noise, and approximate synchrony can be sustained despite heterogeneity. The pulse-coupled oscillator model can not only be used to describe biological neuronal networks but also cardiac pacemakers, lasers, fireflies, artificial neural networks, social self-organization, and wireless sensor networks.

AMS Subject Classification

37N25, 39A06, 39A30, 92B25, 92C20.

Dynamic assemblies of parvalbumin interneurons in brain oscillations

Brain oscillations are crucial for perception, memory, and behavior. Parvalbumin-expressing (PV) interneurons are critical for these oscillations, but their population dynamics remain unclear. Using voltage imaging, we simultaneously recorded membrane potentials in up to 26 PV interneurons in vivo during hippocampal ripple oscillations in mice. We found that PV cells generate ripple-frequency rhythms by forming highly dynamic cell assemblies. These assemblies exhibit rapid and significant changes from cycle to cycle, varying greatly in both size and membership. Importantly, this variability is not just random spiking failures of individual neurons. Rather, the activities of other PV cells contain significant information about whether a PV cell spikes or not in a given cycle. This coordination persists without network oscillations, and it exists in subthreshold potentials even when the cells are not spiking. Dynamic assemblies of interneurons may provide a new mechanism to modulate postsynaptic dynamics and impact cognitive functions flexibly and rapidly.

Dynamics of spike transmission and suppression between principal cells and interneurons in the hippocampus and entorhinal cortex

Synaptic excitation and inhibition are essential for neuronal communication. However, the variables that regulate synaptic excitation and inhibition in the intact brain remain largely unknown. Here, we examined how spike transmission and suppression between principal cells (PCs) and interneurons (INTs) are modulated by activity history, brain state, cell type, and somatic distance between presynaptic and postsynaptic neurons by applying cross-correlogram analyses to datasets recorded from the dorsal hippocampus and medial entorhinal cortex (MEC) of 11 male behaving and sleeping Long Evans rats. The strength, temporal delay, and brain-state dependency of the spike transmission and suppression depended on the subregions/layers. The spike transmission probability of PC-INT excitatory pairs that showed short-term depression versus short-term facilitation was higher in CA1 and lower in CA3. Likewise, the intersomatic distance affected the proportion of PC-INT excitatory pairs that showed short-term depression and facilitation in the opposite manner in CA1 compared with CA3. The time constant of depression was longer, while that of facilitation was shorter in MEC than in CA1 and CA3. During sharp-wave ripples, spike transmission showed a larger gain in the MEC than in CA1 and CA3. The intersomatic distance affected the spike transmission gain during sharp-wave ripples differently in CA1 versus CA3. A subgroup of MEC layer 3 (EC3) INTs preferentially received excitatory inputs from and inhibited MEC layer 2 (EC2) PCs. The EC2 PC-EC3 INT excitatory pairs, most of which showed short-term depression, exhibited higher spike transmission probabilities than the EC2 PC-EC2 INT and EC3 PC-EC3 INT excitatory pairs. EC2 putative stellate cells exhibited stronger spike transmission to and received weaker spike suppression from EC3 INTs than EC2 putative pyramidal cells. This study provides detailed comparisons of monosynaptic interaction dynamics in the hippocampal-entorhinal loop, which may help to elucidate circuit operations.

The Na+/K+-ATPase generically enables deterministic bursting in class I neurons by shearing the spike-onset bifurcation structure

Slow brain rhythms, for example during slow-wave sleep or pathological conditions like seizures and spreading depolarization, can be accompanied by oscillations in extracellular potassium concentration. Such slow brain rhythms typically have a lower frequency than tonic action-potential firing. They are assumed to arise from network-level mechanisms, involving synaptic interactions and delays, or from intrinsically bursting neurons. Neuronal burst generation is commonly attributed to ion channels with slow kinetics. Here, we explore an alternative mechanism generically available to all neurons with class I excitability. It is based on the interplay of fast-spiking voltage dynamics with a one-dimensional slow dynamics of the extracellular potassium concentration, mediated by the activity of the Na+/K+-ATPase. We use bifurcation analysis of the complete system as well as the slow-fast method to reveal that this coupling suffices to generate a hysteresis loop organized around a bistable region that emerges from a saddle-node loop bifurcation-a common feature of class I excitable neurons. Depending on the strength of the Na+/K+-ATPase, bursts are generated from pump-induced shearing the bifurcation structure, spiking is tonic, or cells are silenced via depolarization block. We suggest that transitions between these dynamics can result from disturbances in extracellular potassium regulation, such as glial malfunction or hypoxia affecting the Na+/K+-ATPase activity. The identified minimal mechanistic model outlining the sodium-potassium pump's generic contribution to burst dynamics can, therefore, contribute to a better mechanistic understanding of pathologies such as epilepsy syndromes and, potentially, inform therapeutic strategies.

Pulse Shape and Voltage-Dependent Synchronization in Spiking Neuron Networks

Pulse-coupled spiking neural networks are a powerful tool to gain mechanistic insights into how neurons self-organize to produce coherent collective behavior. These networks use simple spiking neuron models, such as the θ-neuron or the quadratic integrate-and-fire (QIF) neuron, that replicate the essential features of real neural dynamics. Interactions between neurons are modeled with infinitely narrow pulses, or spikes, rather than the more complex dynamics of real synapses. To make these networks biologically more plausible, it has been proposed that they must also account for the finite width of the pulses, which can have a significant impact on the network dynamics. However, the derivation and interpretation of these pulses are contradictory, and the impact of the pulse shape on the network dynamics is largely unexplored. Here, I take a comprehensive approach to pulse coupling in networks of QIF and θ-neurons. I argue that narrow pulses activate voltage-dependent synaptic conductances and show how to implement them in QIF neurons such that their effect can last through the phase after the spike. Using an exact low-dimensional description for networks of globally coupled spiking neurons, I prove for instantaneous interactions that collective oscillations emerge due to an effective coupling through the mean voltage. I analyze the impact of the pulse shape by means of a family of smooth pulse functions with arbitrary finite width and symmetric or asymmetric shapes. For symmetric pulses, the resulting voltage coupling is not very effective in synchronizing neurons, but pulses that are slightly skewed to the phase after the spike readily generate collective oscillations. The results unveil a voltage-dependent spike synchronization mechanism at the heart of emergent collective behavior, which is facilitated by pulses of finite width and complementary to traditional synaptic transmission in spiking neuron networks.

Modeling the impact of neuromorphological alterations in Down syndrome on fast neural oscillations

Cognitive disorders, including Down syndrome (DS), present significant morphological alterations in neuron architectural complexity. However, the relationship between neuromorphological alterations and impaired brain function is not fully understood. To address this gap, we propose a novel computational model that accounts for the observed cell deformations in DS. The model consists of a cross-sectional layer of the mouse motor cortex, composed of 3000 neurons. The network connectivity is obtained by accounting explicitly for two single-neuron morphological parameters: the mean dendritic tree radius and the spine density in excitatory pyramidal cells. We obtained these values by fitting reconstructed neuron data corresponding to three mouse models: wild-type (WT), transgenic (TgDyrk1A), and trisomic (Ts65Dn). Our findings reveal a dynamic interplay between pyramidal and fast-spiking interneurons leading to the emergence of gamma activity (∼40 Hz). In the DS models this gamma activity is diminished, corroborating experimental observations and validating our computational methodology. We further explore the impact of disrupted excitation-inhibition balance by mimicking the reduction recurrent inhibition present in DS. In this case, gamma power exhibits variable responses as a function of the external input to the network. Finally, we perform a numerical exploration of the morphological parameter space, unveiling the direct influence of each structural parameter on gamma frequency and power. Our research demonstrates a clear link between changes in morphology and the disruption of gamma oscillations in DS. This work underscores the potential of computational modeling to elucidate the relationship between neuron architecture and brain function, and ultimately improve our understanding of cognitive disorders.

Nondifferentiable activity in the brain

Spike raster plots of numerous neurons show vertical stripes, indicating that neurons exhibit synchronous activity in the brain. We seek to determine whether these coherent dynamics are caused by smooth brainwave activity or by something else. By analyzing biological data, we find that their cross-correlograms exhibit not only slow undulation but also a cusp at the origin, in addition to possible signs of monosynaptic connectivity. Here we show that undulation emerges if neurons are subject to smooth brainwave oscillations while a cusp results from nondifferentiable fluctuations. While modern analysis methods have achieved good connectivity estimation by adapting the models to slow undulation, they still make false inferences due to the cusp. We devise a new analysis method that may solve both problems. We also demonstrate that oscillations and nondifferentiable fluctuations may emerge in simulations of large-scale neural networks.

Transcranial alternating current stimulation (tACS) at gamma frequency: an up-and-coming tool to modify the progression of Alzheimer's Disease

The last decades have witnessed huge efforts devoted to deciphering the pathological mechanisms underlying Alzheimer's Disease (AD) and to testing new drugs, with the recent FDA approval of two anti-amyloid monoclonal antibodies for AD treatment. Beyond these drug-based experimentations, a number of pre-clinical and clinical trials are exploring the benefits of alternative treatments, such as non-invasive stimulation techniques on AD neuropathology and symptoms. Among the different non-invasive brain stimulation approaches, transcranial alternating current stimulation (tACS) is gaining particular attention due to its ability to externally control gamma oscillations. Here, we outline the current knowledge concerning the clinical efficacy, safety, ease-of-use and cost-effectiveness of tACS on early and advanced AD, applied specifically at 40 Hz frequency, and also summarise pre-clinical results on validated models of AD and ongoing patient-centred trials.

Neuronal avalanche dynamics regulated by spike-timing-dependent plasticity under different topologies and heterogeneities

Neuronal avalanches, a critical state of network self-organization, have been widely observed in electrophysiological records at different signal levels and spatial scales of the brain, which has significant influence on information transmission and processing in the brain. In this paper, the collective behavior of neuron firing is studied based on Leaky Integrate-and-Fire model and we induce spike-timing-dependent plasticity (STDP) to update the connection weight through competition between adjacent neurons in different network topologies. The result shows that STDP can facilitate the synchronization of the network and increase the probability of large-scale neuron avalanche obviously. Moreover, both the structure of STDP and network connection density can affect the generation of avalanche critical states, specifically, learning rate has positive correlation effect on the slope of power-law distribution and time constant has negative correction on it. However, when we the increase of heterogeneity in network, STDP can only has obvious promotion in synchrony under suitable level of heterogeneity. And we find that the process of long-term potentiation is sensitive to the adjustment of time constant and learning rate, unlike long-term depression, which is only sensitive to learning rate in heterogeneity network. It is suggested that presented results could facilitate our understanding on synchronization in various neural networks under the effect of STDP learning rules.

The stabilized supralinear network accounts for the contrast dependence of visual cortical gamma oscillations

When stimulated, neural populations in the visual cortex exhibit fast rhythmic activity with frequencies in the gamma band (30-80 Hz). The gamma rhythm manifests as a broad resonance peak in the power-spectrum of recorded local field potentials, which exhibits various stimulus dependencies. In particular, in macaque primary visual cortex (V1), the gamma peak frequency increases with increasing stimulus contrast. Moreover, this contrast dependence is local: when contrast varies smoothly over visual space, the gamma peak frequency in each cortical column is controlled by the local contrast in that column's receptive field. No parsimonious mechanistic explanation for these contrast dependencies of V1 gamma oscillations has been proposed. The stabilized supralinear network (SSN) is a mechanistic model of cortical circuits that has accounted for a range of visual cortical response nonlinearities and contextual modulations, as well as their contrast dependence. Here, we begin by showing that a reduced SSN model without retinotopy robustly captures the contrast dependence of gamma peak frequency, and provides a mechanistic explanation for this effect based on the observed non-saturating and supralinear input-output function of V1 neurons. Given this result, the local dependence on contrast can trivially be captured in a retinotopic SSN which however lacks horizontal synaptic connections between its cortical columns. However, long-range horizontal connections in V1 are in fact strong, and underlie contextual modulation effects such as surround suppression. We thus explored whether a retinotopically organized SSN model of V1 with strong excitatory horizontal connections can exhibit both surround suppression and the local contrast dependence of gamma peak frequency. We found that retinotopic SSNs can account for both effects, but only when the horizontal excitatory projections are composed of two components with different patterns of spatial fall-off with distance: a short-range component that only targets the source column, combined with a long-range component that targets columns neighboring the source column. We thus make a specific qualitative prediction for the spatial structure of horizontal connections in macaque V1, consistent with the columnar structure of cortex.

Differences in the consolidation by spontaneous and evoked ripples in the presence of active dendrites

Ripples are a typical form of neural activity in hippocampal neural networks associated with the replay of episodic memories during sleep as well as sleep-related plasticity and memory consolidation. The emergence of ripples has been observed both dependent as well as independent of input from other brain areas and often coincides with dendritic spikes. Yet, it is unclear how input-evoked and spontaneous ripples as well as dendritic excitability affect plasticity and consolidation. Here, we use mathematical modeling to compare these cases. We find that consolidation as well as the emergence of spontaneous ripples depends on a reliable propagation of activity in feed-forward structures which constitute memory representations. This propagation is facilitated by excitable dendrites, which entail that a few strong synapses are sufficient to trigger neuronal firing. In this situation, stimulation-evoked ripples lead to the potentiation of weak synapses within the feed-forward structure and, thus, to a consolidation of a more general sequence memory. However, spontaneous ripples that occur without stimulation, only consolidate a sparse backbone of the existing strong feed-forward structure. Based on this, we test a recently hypothesized scenario in which the excitability of dendrites is transiently enhanced after learning, and show that such a transient increase can strengthen, restructure and consolidate even weak hippocampal memories, which would be forgotten otherwise. Hence, a transient increase in dendritic excitability would indeed provide a mechanism for stabilizing memories.

Simulated dynamical transitions in a heterogeneous marmoset pFC cluster

Network analysis of the marmoset cortical connectivity data indicates a significant 3D cluster in and around the pre-frontal cortex. A multi-node, heterogeneous neural mass model of this six-node cluster was constructed. Its parameters were informed by available experimental and simulation data so that each neural mass oscillated in a characteristic frequency band. Nodes were connected with directed, weighted links derived from the marmoset structural connectivity data. Heterogeneity arose from the different link weights and model parameters for each node. Stimulation of the cluster with an incident pulse train modulated in the standard frequency bands induced a variety of dynamical state transitions that lasted in the range of 5-10 s, suggestive of timescales relevant to short-term memory. A short gamma burst rapidly reset the beta-induced transition. The theta-induced transition state showed a spontaneous, delayed reset to the resting state. An additional, continuous gamma wave stimulus induced a new beating oscillatory state. Longer or repeated gamma bursts were phase-aligned with the beta oscillation, delivering increasing energy input and causing shorter transition times. The relevance of these results to working memory is yet to be established, but they suggest interesting opportunities.

A mean-field model of gamma-frequency oscillations in networks of excitatory and inhibitory neurons

Gamma oscillations are widely seen in the cerebral cortex in different states of the wake-sleep cycle and are thought to play a role in sensory processing and cognition. Here, we study the emergence of gamma oscillations at two levels, in networks of spiking neurons, and a mean-field model. At the network level, we consider two different mechanisms to generate gamma oscillations and show that they are best seen if one takes into account the synaptic delay between neurons. At the mean-field level, we show that, by introducing delays, the mean-field can also produce gamma oscillations. The mean-field matches the mean activity of excitatory and inhibitory populations of the spiking network, as well as their oscillation frequencies, for both mechanisms. This mean-field model of gamma oscillations should be a useful tool to investigate large-scale interactions through gamma oscillations in the brain.

Emergence of complex oscillatory dynamics in the neuronal networks with long activity time of inhibitory synapses

The brain displays complex dynamics, including collective oscillations, and extensive research has been conducted to understand their generation. However, our understanding of how biological constraints influence these oscillations is incomplete. This study investigates the essential properties of neuronal networks needed to generate oscillations resembling those in the brain. A simple discrete-time model of interconnected excitable elements is developed, capable of closely resembling the complex oscillations observed in biological neural networks. In the model, synaptic connections remain active for a duration exceeding individual neuron activity. We show that the inhibitory synapses must exhibit longer activity than excitatory synapses to produce a diverse range of the dynamical states, including biologically plausible oscillations. Upon meeting this condition, the transition between different dynamical states can be controlled by external stochastic input to the neurons. The study provides a comprehensive explanation for the emergence of distinct dynamical states in neural networks based on specific parameters.

Dynamic Gain Decomposition Reveals Functional Effects of Dendrites, Ion Channels, and Input Statistics in Population Coding

Modern, high-density neuronal recordings reveal at ever higher precision how information is represented by neural populations. Still, we lack the tools to understand these processes bottom-up, emerging from the biophysical properties of neurons, synapses, and network structure. The concept of the dynamic gain function, a spectrally resolved approximation of a population's coding capability, has the potential to link cell-level properties to network-level performance. However, the concept is not only useful but also very complex because the dynamic gain's shape is co-determined by axonal and somato-dendritic parameters and the population's operating regime. Previously, this complexity precluded an understanding of any individual parameter's impact. Here, we decomposed the dynamic gain function into three components corresponding to separate signal transformations. This allowed attribution of network-level encoding features to specific cell-level parameters. Applying the method to data from real neurons and biophysically plausible models, we found: (1) The encoding bandwidth of real neurons, approximately 400 Hz, is constrained by the voltage dependence of axonal currents during early action potential initiation. (2) State-of-the-art models only achieve encoding bandwidths around 100 Hz and are limited mainly by subthreshold processes instead. (3) Large dendrites and low-threshold potassium currents modulate the bandwidth by shaping the subthreshold stimulus-to-voltage transformation. Our decomposition provides physiological interpretations when the dynamic gain curve changes, for instance during spectrinopathies and neurodegeneration. By pinpointing shortcomings of current models, it also guides inference of neuron models best suited for large-scale network simulations.

Rodents' visual gamma as a biomarker of pathological neural conditions

Neural gamma oscillations (indicatively 30-100 Hz) are ubiquitous: they are associated with a broad range of functions in multiple cortical areas and across many animal species. Experimental and computational works established gamma rhythms as a global emergent property of neuronal networks generated by the balanced and coordinated interaction of excitation and inhibition. Coherently, gamma activity is strongly influenced by the alterations of synaptic dynamics which are often associated with pathological neural dysfunctions. We argue therefore that these oscillations are an optimal biomarker for probing the mechanism of cortical dysfunctions. Gamma oscillations are also highly sensitive to external stimuli in sensory cortices, especially the primary visual cortex (V1), where the stimulus dependence of gamma oscillations has been thoroughly investigated. Gamma manipulation by visual stimuli tuning is particularly easy in rodents, which have become a standard animal model for investigating the effects of network alterations on gamma oscillations. Overall, gamma in the rodents' visual cortex offers an accessible probe on dysfunctional information processing in pathological conditions. Beyond vision-related dysfunctions, alterations of gamma oscillations in rodents were indeed also reported in neural deficits such as migraine, epilepsy and neurodegenerative or neuropsychiatric conditions such as Alzheimer's, schizophrenia and autism spectrum disorders. Altogether, the connections between visual cortical gamma activity and physio-pathological conditions in rodent models underscore the potential of gamma oscillations as markers of neuronal (dys)functioning.

Cortical cell assemblies and their underlying connectivity: An in silico study

Recent developments in experimental techniques have enabled simultaneous recordings from thousands of neurons, enabling the study of functional cell assemblies. However, determining the patterns of synaptic connectivity giving rise to these assemblies remains challenging. To address this, we developed a complementary, simulation-based approach, using a detailed, large-scale cortical network model. Using a combination of established methods we detected functional cell assemblies from the stimulus-evoked spiking activity of 186,665 neurons. We studied how the structure of synaptic connectivity underlies assembly composition, quantifying the effects of thalamic innervation, recurrent connectivity, and the spatial arrangement of synapses on dendrites. We determined that these features reduce up to 30%, 22%, and 10% of the uncertainty of a neuron belonging to an assembly. The detected assemblies were activated in a stimulus-specific sequence and were grouped based on their position in the sequence. We found that the different groups were affected to different degrees by the structural features we considered. Additionally, connectivity was more predictive of assembly membership if its direction aligned with the temporal order of assembly activation, if it originated from strongly interconnected populations, and if synapses clustered on dendritic branches. In summary, reversing Hebb's postulate, we showed how cells that are wired together, fire together, quantifying how connectivity patterns interact to shape the emergence of assemblies. This includes a qualitative aspect of connectivity: not just the amount, but also the local structure matters; from the subcellular level in the form of dendritic clustering to the presence of specific network motifs.

A prefrontal network model operating near steady and oscillatory states links spike desynchronization and synaptic deficits in schizophrenia

Schizophrenia results in part from a failure of prefrontal networks but we lack full understanding of how disruptions at a synaptic level cause failures at the network level. This is a crucial gap in our understanding because it prevents us from discovering how genetic mutations and environmental risks that alter synaptic function cause prefrontal network to fail in schizophrenia. To address that question, we developed a recurrent spiking network model of prefrontal local circuits that can explain the link between NMDAR synaptic and 0-lag spike synchrony deficits we recently observed in a pharmacological monkey model of prefrontal network failure in schizophrenia. We analyze how the balance between AMPA and NMDA components of recurrent excitation and GABA inhibition in the network influence oscillatory spike synchrony to inform the biological data. We show that reducing recurrent NMDAR synaptic currents prevents the network from shifting from a steady to oscillatory state in response to extrinsic inputs such as might occur during behavior. These findings strongly parallel dynamic modulation of 0-lag spike synchrony we observed between neurons in monkey prefrontal cortex during behavior, as well as the suppression of this 0-lag spiking by administration of NMDAR antagonists. As such, our cortical network model provides a plausible mechanism explaining the link between NMDAR synaptic and 0-lag spike synchrony deficits observed in a pharmacological monkey model of prefrontal network failure in schizophrenia.

Intra-ripple frequency accommodation in an inhibitory network model for hippocampal ripple oscillations

Hippocampal ripple oscillations have been implicated in important cognitive functions such as memory consolidation and planning. Multiple computational models have been proposed to explain the emergence of ripple oscillations, relying either on excitation or inhibition as the main pacemaker. Nevertheless, the generating mechanism of ripples remains unclear. An interesting dynamical feature of experimentally measured ripples, which may advance model selection, is intra-ripple frequency accommodation (IFA): a decay of the instantaneous ripple frequency over the course of a ripple event. So far, only a feedback-based inhibition-first model, which relies on delayed inhibitory synaptic coupling, has been shown to reproduce IFA. Here we use an analytical mean-field approach and numerical simulations of a leaky integrate-and-fire spiking network to explain the mechanism of IFA. We develop a drift-based approximation for the oscillation dynamics of the population rate and the mean membrane potential of interneurons under strong excitatory drive and strong inhibitory coupling. For IFA, the speed at which the excitatory drive changes is critical. We demonstrate that IFA arises due to a speed-dependent hysteresis effect in the dynamics of the mean membrane potential, when the interneurons receive transient, sharp wave-associated excitation. We thus predict that the IFA asymmetry vanishes in the limit of slowly changing drive, but is otherwise a robust feature of the feedback-based inhibition-first ripple model.

Excitation-Inhibition Balance, Neural Criticality, and Activities in Neuronal Circuits

Neural activities in local circuits exhibit complex and multilevel dynamic features. Individual neurons spike irregularly, which is believed to originate from receiving balanced amounts of excitatory and inhibitory inputs, known as the excitation-inhibition balance. The spatial-temporal cascades of clustered neuronal spikes occur in variable sizes and durations, manifested as neural avalanches with scale-free features. These may be explained by the neural criticality hypothesis, which posits that neural systems operate around the transition between distinct dynamic states. Here, we summarize the experimental evidence for and the underlying theory of excitation-inhibition balance and neural criticality. Furthermore, we review recent studies of excitatory-inhibitory networks with synaptic kinetics as a simple solution to reconcile these two apparently distinct theories in a single circuit model. This provides a more unified understanding of multilevel neural activities in local circuits, from spontaneous to stimulus-response dynamics.

GABAergic inhibition shapes behavior and neural dynamics in human visual working memory

Neuronal inhibition, primarily mediated by GABAergic neurotransmission, is crucial for brain development and healthy cognition. Gamma-aminobutyric acid concentration levels in sensory areas have been shown to correlate with hemodynamic and oscillatory neuronal responses. How these measures relate to one another during working memory, a higher-order cognitive process, is still poorly understood. We address this gap by collecting magnetoencephalography, functional magnetic resonance imaging, and Flumazenil positron emission tomography data within the same subject cohort using an n-back working-memory paradigm. By probing the relationship between GABAA receptor distribution, neural oscillations, and Blood Oxygen Level Dependent (BOLD) modulations, we found that GABAA receptor density in higher-order cortical areas predicted the reaction times on the working-memory task and correlated positively with the peak frequency of gamma power modulations and negatively with BOLD amplitude. These findings support and extend theories linking gamma oscillations and hemodynamic responses to gamma-aminobutyric acid neurotransmission and to the excitation-inhibition balance and cognitive performance in humans. Considering the small sample size of the study, future studies should test whether these findings also hold for other, larger cohorts as well as to examine in detail how the GABAergic system and neural fluctuations jointly support working-memory task performance.

A developmental increase of inhibition promotes the emergence of hippocampal ripples

Sharp wave-ripples (SPW-Rs) are a hippocampal network phenomenon critical for memory consolidation and planning. SPW-Rs have been extensively studied in the adult brain, yet their developmental trajectory is poorly understood. While SPWs have been recorded in rodents shortly after birth, the time point and mechanisms of ripple emergence are still unclear. Here, we combine in vivo electrophysiology with optogenetics and chemogenetics in 4 to 12-day-old mice to address this knowledge gap. We show that ripples are robustly detected and induced by light stimulation of channelrhodopsin-2-transfected CA1 pyramidal neurons only from postnatal day 10 onwards. Leveraging a spiking neural network model, we mechanistically link the maturation of inhibition and ripple emergence. We corroborate these findings by reducing ripple rate upon chemogenetic silencing of CA1 interneurons. Finally, we show that early SPW-Rs elicit a more robust prefrontal cortex response than SPWs lacking ripples. Thus, development of inhibition promotes ripples emergence.

Exact low-dimensional description for fast neural oscillations with low firing rates

Recently, low-dimensional models of neuronal activity have been exactly derived for large networks of deterministic, quadratic integrate-and-fire (QIF) neurons. Such firing rate models (FRM) describe the emergence of fast collective oscillations (>30 Hz) via the frequency locking of a subset of neurons to the global oscillation frequency. However, the suitability of such models to describe realistic neuronal states is seriously challenged by the fact that during episodes of fast collective oscillations, neuronal discharges are often very irregular and have low firing rates compared to the global oscillation frequency. Here we extend the theory to derive exact FRM for QIF neurons to include noise and show that networks of stochastic neurons displaying irregular discharges at low firing rates during episodes of fast oscillations are governed by exactly the same evolution equations as deterministic networks. Our results reconcile two traditionally confronted views on neuronal synchronization and upgrade the applicability of exact FRM to describe a broad range of biologically realistic neuronal states.

Atypical cortical networks in children at high-genetic risk of psychiatric and neurodevelopmental disorders

Although many genetic risk factors for psychiatric and neurodevelopmental disorders have been identified, the neurobiological route from genetic risk to neuropsychiatric outcome remains unclear. 22q11.2 deletion syndrome (22q11.2DS) is a copy number variant (CNV) syndrome associated with high rates of neurodevelopmental and psychiatric disorders including autism spectrum disorder (ASD), attention deficit hyperactivity disorder (ADHD) and schizophrenia. Alterations in neural integration and cortical connectivity have been linked to the spectrum of neuropsychiatric disorders seen in 22q11.2DS and may be a mechanism by which the CNV acts to increase risk. In this study, magnetoencephalography (MEG) was used to investigate electrophysiological markers of local and global network function in 34 children with 22q11.2DS and 25 controls aged 10-17 years old. Resting-state oscillatory activity and functional connectivity across six frequency bands were compared between groups. Regression analyses were used to explore the relationships between these measures, neurodevelopmental symptoms and IQ. Children with 22q11.2DS had altered network activity and connectivity in high and low frequency bands, reflecting modified local and long-range cortical circuitry. Alpha and theta band connectivity were negatively associated with ASD symptoms while frontal high frequency (gamma band) activity was positively associated with ASD symptoms. Alpha band activity was positively associated with cognitive ability. These findings suggest that haploinsufficiency at the 22q11.2 locus impacts short and long-range cortical circuits, which could be a mechanism underlying neurodevelopmental and psychiatric vulnerability in this high-risk group.

Precision data-driven modeling of cortical dynamics reveals idiosyncratic mechanisms underlying canonical oscillations

Task-free brain activity affords unique insight into the functional structure of brain network dynamics and is a strong marker of individual differences. In this work, we present an algorithmic optimization framework that makes it possible to directly invert and parameterize brain-wide dynamical-systems models involving hundreds of interacting brain areas, from single-subject time-series recordings. This technique provides a powerful neurocomputational tool for interrogating mechanisms underlying individual brain dynamics ("precision brain models") and making quantitative predictions. We extensively validate the models' performance in forecasting future brain activity and predicting individual variability in key M/EEG markers. Lastly, we demonstrate the power of our technique in resolving individual differences in the generation of alpha and beta-frequency oscillations. We characterize subjects based upon model attractor topology and a dynamical-systems mechanism by which these topologies generate individual variation in the expression of alpha vs. beta rhythms. We trace these phenomena back to global variation in excitation-inhibition balance, highlighting the explanatory power of our framework in generating mechanistic insights.

Multilevel and multifaceted brain response features in spiking, ERP and ERD: experimental observation and simultaneous generation in a neuronal network model with excitation-inhibition balance

Brain as a dynamic system responds to stimulations with specific patterns affected by its inherent ongoing dynamics. The patterns are manifested across different levels of organization-from spiking activity of neurons to collective oscillations in local field potential (LFP) and electroencephalogram (EEG). The multilevel and multifaceted response activities show patterns seemingly distinct and non-comparable from each other, but they should be coherently related because they are generated from the same underlying neural dynamic system. A coherent understanding of the interrelationships between different levels/aspects of activity features is important for understanding the complex brain functions. Here, based on analysis of data from human EEG, monkey LFP and neuronal spiking, we demonstrated that the brain response activities from different levels of neural system are highly coherent: the external stimulus simultaneously generated event-related potentials, event-related desynchronization, and variation in neuronal spiking activities that precisely match with each other in the temporal unfolding. Based on a biologically plausible but generic network of conductance-based integrate-and-fire excitatory and inhibitory neurons with dense connections, we showed that the multiple key features can be simultaneously produced at critical dynamical regimes supported by excitation-inhibition (E-I) balance. The elucidation of the inherent coherency of various neural response activities and demonstration of a simple dynamical neural circuit system having the ability to simultaneously produce multiple features suggest the plausibility of understanding high-level brain function and cognition from elementary and generic neuronal dynamics.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09889-w.

Human NMDAR autoantibodies disrupt excitatory-inhibitory balance, leading to hippocampal network hypersynchrony

Anti-NMDA receptor autoantibodies (NMDAR-Abs) in patients with NMDAR encephalitis cause severe disease symptoms resembling psychosis and cause cognitive dysfunction. After passive transfer of patients' cerebrospinal fluid or human monoclonal anti-GluN1-autoantibodies in mice, we find a disrupted excitatory-inhibitory balance resulting from CA1 neuronal hypoexcitability, reduced AMPA receptor (AMPAR) signaling, and faster synaptic inhibition in acute hippocampal slices. Functional alterations are also reflected in widespread remodeling of the hippocampal proteome, including changes in glutamatergic and GABAergic neurotransmission. NMDAR-Abs amplify network γ oscillations and disrupt θ-γ coupling. A data-informed network model reveals that lower AMPAR strength and faster GABAA receptor current kinetics chiefly account for these abnormal oscillations. As predicted in silico and evidenced ex vivo, positive allosteric modulation of AMPARs alleviates aberrant γ activity, reinforcing the causative effects of the excitatory-inhibitory imbalance. Collectively, NMDAR-Ab-induced aberrant synaptic, cellular, and network dynamics provide conceptual insights into NMDAR-Ab-mediated pathomechanisms and reveal promising therapeutic targets that merit future in vivo validation.

Neuronal connected burst cascades bridge macroscale adaptive signatures across arousal states

The human brain displays a rich repertoire of states that emerge from the microscopic interactions of cortical and subcortical neurons. Difficulties inherent within large-scale simultaneous neuronal recording limit our ability to link biophysical processes at the microscale to emergent macroscopic brain states. Here we introduce a microscale biophysical network model of layer-5 pyramidal neurons that display graded coarse-sampled dynamics matching those observed in macroscale electrophysiological recordings from macaques and humans. We invert our model to identify the neuronal spike and burst dynamics that differentiate unconscious, dreaming, and awake arousal states and provide insights into their functional signatures. We further show that neuromodulatory arousal can mediate different modes of neuronal dynamics around a low-dimensional energy landscape, which in turn changes the response of the model to external stimuli. Our results highlight the promise of multiscale modelling to bridge theories of consciousness across spatiotemporal scales.

Co-evolving dynamics and topology in a coupled oscillator model of resting brain function

Dynamic models of ongoing BOLD fMRI brain dynamics and models of communication strategies have been two important approaches to understanding how brain network structure constrains function. However, dynamic models have yet to widely incorporate one of the most important insights from communication models: the brain may not use all of its connections in the same way or at the same time. Here we present a variation of a phase delayed Kuramoto coupled oscillator model that dynamically limits communication between nodes on each time step. An active subgraph of the empirically derived anatomical brain network is chosen in accordance with the local dynamic state on every time step, thus coupling dynamics and network structure in a novel way. We analyze this model with respect to its fit to empirical time-averaged functional connectivity, finding that, with the addition of only one parameter, it significantly outperforms standard Kuramoto models with phase delays. We also perform analyses on the novel time series of active edges it produces, demonstrating a slowly evolving topology moving through intermittent episodes of integration and segregation. We hope to demonstrate that the exploration of novel modeling mechanisms and the investigation of dynamics of networks in addition to dynamics on networks may advance our understanding of the relationship between brain structure and function.

Offline memory replay in recurrent neuronal networks emerges from constraints on online dynamics

During spatial exploration, neural circuits in the hippocampus store memories of sequences of sensory events encountered in the environment. When sensory information is absent during 'offline' resting periods, brief neuronal population bursts can 'replay' sequences of activity that resemble bouts of sensory experience. These sequences can occur in either forward or reverse order, and can even include spatial trajectories that have not been experienced, but are consistent with the topology of the environment. The neural circuit mechanisms underlying this variable and flexible sequence generation are unknown. Here we demonstrate in a recurrent spiking network model of hippocampal area CA3 that experimental constraints on network dynamics such as population sparsity, stimulus selectivity, rhythmicity and spike rate adaptation, as well as associative synaptic connectivity, enable additional emergent properties, including variable offline memory replay. In an online stimulus-driven state, we observed the emergence of neuronal sequences that swept from representations of past to future stimuli on the timescale of the theta rhythm. In an offline state driven only by noise, the network generated both forward and reverse neuronal sequences, and recapitulated the experimental observation that offline memory replay events tend to include salient locations like the site of a reward. These results demonstrate that biological constraints on the dynamics of recurrent neural circuits are sufficient to enable memories of sensory events stored in the strengths of synaptic connections to be flexibly read out during rest and sleep, which is thought to be important for memory consolidation and planning of future behaviour. KEY POINTS: A recurrent spiking network model of hippocampal area CA3 was optimized to recapitulate experimentally observed network dynamics during simulated spatial exploration. During simulated offline rest, the network exhibited the emergent property of generating flexible forward, reverse and mixed direction memory replay events. Network perturbations and analysis of model diversity and degeneracy identified associative synaptic connectivity and key features of network dynamics as important for offline sequence generation. Network simulations demonstrate that population over-representation of salient positions like the site of reward results in biased memory replay.

How to incorporate biological insights into network models and why it matters

Due to the staggering complexity of the brain and its neural circuitry, neuroscientists rely on the analysis of mathematical models to elucidate its function. From Hodgkin and Huxley's detailed description of the action potential in 1952 to today, new theories and increasing computational power have opened up novel avenues to study how neural circuits implement the computations that underlie behaviour. Computational neuroscientists have developed many models of neural circuits that differ in complexity, biological realism or emergent network properties. With recent advances in experimental techniques for detailed anatomical reconstructions or large-scale activity recordings, rich biological data have become more available. The challenge when building network models is to reflect experimental results, either through a high level of detail or by finding an appropriate level of abstraction. Meanwhile, machine learning has facilitated the development of artificial neural networks, which are trained to perform specific tasks. While they have proven successful at achieving task-oriented behaviour, they are often abstract constructs that differ in many features from the physiology of brain circuits. Thus, it is unclear whether the mechanisms underlying computation in biological circuits can be investigated by analysing artificial networks that accomplish the same function but differ in their mechanisms. Here, we argue that building biologically realistic network models is crucial to establishing causal relationships between neurons, synapses, circuits and behaviour. More specifically, we advocate for network models that consider the connectivity structure and the recorded activity dynamics while evaluating task performance.

Combining aperiodic 1/f slopes and brain simulation: An EEG/MEG proxy marker of excitation/inhibition imbalance in Alzheimer's disease

INTRODUCTION

Accumulation and interaction of amyloid-beta (Aβ) and tau proteins during progression of Alzheimer's disease (AD) are shown to tilt neuronal circuits away from balanced excitation/inhibition (E/I). Current available techniques for noninvasive interrogation of E/I in the intact human brain, for example, magnetic resonance spectroscopy (MRS), are highly restrictive (i.e., limited spatial extent), have low temporal and spatial resolution and suffer from the limited ability to distinguish accurately between different neurotransmitters complicating its interpretation. As such, these methods alone offer an incomplete explanation of E/I. Recently, the aperiodic component of neural power spectrum, often referred to in the literature as the '1/f slope', has been described as a promising and scalable biomarker that can track disruptions in E/I potentially underlying a spectrum of clinical conditions, such as autism, schizophrenia, or epilepsy, as well as developmental E/I changes as seen in aging.

METHODS

Using 1/f slopes from resting-state spectral data and computational modeling, we developed a new method for inferring E/I alterations in AD.

RESULTS

We tested our method on recent freely and publicly available electroencephalography (EEG) and magnetoencephalography (MEG) datasets of patients with AD or prodromal disease and demonstrated the method's potential for uncovering regional patterns of abnormal excitatory and inhibitory parameters.

DISCUSSION

Our results provide a general framework for investigating circuit-level disorders in AD and developing therapeutic interventions that aim to restore the balance between excitation and inhibition.

Mechanisms regulating the properties of inhibition-based gamma oscillations in primate prefrontal and parietal cortices

In primates, the dorsolateral prefrontal (DLPFC) and posterior parietal (PPC) cortices are key nodes in the working memory network. The working memory-related gamma oscillations induced in these areas, predominantly in layer 3, exhibit higher frequency in DLPFC. Although these regional differences in oscillation frequency are likely essential for information transfer between DLPFC and PPC, the mechanisms underlying these differences remain poorly understood. We investigated, in rhesus monkey, the DLPFC and PPC layer 3 pyramidal neuron (L3PN) properties that might regulate oscillation frequency and assessed the effects of these properties simulating oscillations in computational models. We found that GABAAR-mediated synaptic inhibition synchronizes L3PNs in both areas, but analysis of GABAAR mRNA levels and inhibitory synaptic currents suggested similar mechanisms of inhibition-mediated synchrony in DLPFC and PPC. Basal dendrite spine density and AMPAR/NMDAR mRNA levels were higher in DLPFC L3PNs, whereas excitatory synaptic currents were similar between areas. Therefore, synaptically evoked excitation might be stronger in DLPFC L3PNs due to a greater quantity of synapses in basal dendrites, a main target of recurrent excitation. Simulations in computational networks showed that oscillation frequency and power increased with increasing recurrent excitation, suggesting a mechanism by which the DLPFC-PPC differences in oscillation properties are generated.

Synchronization and oscillation behaviors of excitatory and inhibitory populations with spike-timing-dependent plasticity

The effect of synaptic plasticity on the synchronization mechanism of the cerebral cortex has been a hot research topic over the past two decades. There are a great deal of literatures on excitatory pyramidal neurons, but the mechanism of interaction between the inhibitory interneurons is still under exploration. In this study, we consider a complex network consisting of excitatory (E) pyramidal neurons and inhibitory (I) interneurons interacting with chemical synapses through spike-timing-dependent plasticity (STDP). To study the effects of eSTDP and iSTDP on synchronization and oscillation behaviors emerged in an excitatory-inhibitory balanced network, we analyzed three different cases, a small-world network of purely excitatory neurons with eSTDP, a small-world network of purely inhibitory neurons with iSTDP and a small-world network with excitatory-inhibitory balanced neurons. By varying the number of inhibitory interneurons, and that of connected edges in a small-world network, and the coupling strength, these networks exhibit different synchronization and oscillation behaviors. We found that the eSTDP facilitates synchronization effectively, while iSTDP has no significant impact on it. In addition, eSTDP and iSTDP restrict the balance of the excitatory-inhibitory balanced neuronal network together and play a fundamental role in maintaining network stability and synchronization. They also can be used to guide the treatment and further research of neurodegenerative diseases.

Constructive role of shot noise in the collective dynamics of neural networks

Finite-size effects may significantly influence the collective dynamics of large populations of neurons. Recently, we have shown that in globally coupled networks these effects can be interpreted as additional common noise term, the so-called shot noise, to the macroscopic dynamics unfolding in the thermodynamic limit. Here, we continue to explore the role of the shot noise in the collective dynamics of globally coupled neural networks. Namely, we study the noise-induced switching between different macroscopic regimes. We show that shot noise can turn attractors of the infinitely large network into metastable states whose lifetimes smoothly depend on the system parameters. A surprising effect is that the shot noise modifies the region where a certain macroscopic regime exists compared to the thermodynamic limit. This may be interpreted as a constructive role of the shot noise since a certain macroscopic state appears in a parameter region where it does not exist in an infinite network.

Individual/Peak Gamma Frequency: What Do We Know?

In recent years, the concept of individualized measures of electroencephalographic (EEG) activity has emerged. Gamma-band activity plays an important role in many sensory and cognitive processes. Thus, peak frequency in the gamma range has received considerable attention. However, peak or individual gamma frequency (IGF) is rarely used as a primary measure of interest; consequently, little is known about its nature and functional significance. With this review, we attempt to comprehensively overview available information on the functional properties of peak gamma frequency, addressing its relationship with certain processes and/or modulation by various factors. Here, we show that IGFs seem to be related to various endogenous and exogenous factors. Broad functional aspects that are related to IGF might point to the differences in underlying mechanisms. Therefore, research utilizing different types of stimulation for IGF estimation and covering several functional aspects in the same population is required. Moreover, IGFs span a wide range of frequencies (30-100 Hz). This could be partly due to the variability of methods used to extract the measures of IGF. In order to overcome this issue, further studies aiming at the optimization of IGF extraction would be greatly beneficial.

The stabilized supralinear network accounts for the contrast dependence of visual cortical gamma oscillations

When stimulated, neural populations in the visual cortex exhibit fast rhythmic activity with frequencies in the gamma band (30-80 Hz). The gamma rhythm manifests as a broad resonance peak in the power-spectrum of recorded local field potentials, which exhibits various stimulus dependencies. In particular, in macaque primary visual cortex (V1), the gamma peak frequency increases with increasing stimulus contrast. Moreover, this contrast dependence is local: when contrast varies smoothly over visual space, the gamma peak frequency in each cortical column is controlled by the local contrast in that column's receptive field. No parsimonious mechanistic explanation for these contrast dependencies of V1 gamma oscillations has been proposed. The stabilized supralinear network (SSN) is a mechanistic model of cortical circuits that has accounted for a range of visual cortical response nonlinearities and contextual modulations, as well as their contrast dependence. Here, we begin by showing that a reduced SSN model without retinotopy robustly captures the contrast dependence of gamma peak frequency, and provides a mechanistic explanation for this effect based on the observed non-saturating and supralinear input-output function of V1 neurons. Given this result, the local dependence on contrast can trivially be captured in a retinotopic SSN which however lacks horizontal synaptic connections between its cortical columns. However, long-range horizontal connections in V1 are in fact strong, and underlie contextual modulation effects such as surround suppression. We thus explored whether a retinotopically organized SSN model of V1 with strong excitatory horizontal connections can exhibit both surround suppression and the local contrast dependence of gamma peak frequency. We found that retinotopic SSNs can account for both effects, but only when the horizontal excitatory projections are composed of two components with different patterns of spatial fall-off with distance: a short-range component that only targets the source column, combined with a long-range component that targets columns neighboring the source column. We thus make a specific qualitative prediction for the spatial structure of horizontal connections in macaque V1, consistent with the columnar structure of cortex.

Local field potentials in major depressive and obsessive-compulsive disorder: a frequency-based review

Objectives

The purpose of this paper is to provide a mini-review covering the recent progress in human and animal studies on local field potentials (LFPs) of major depressive disorder (MDD) and obsessive-compulsive disorder (OCD).

Materials and methods

PubMed and EMBASE were searched to identify related studies. Inclusion criteria were (1) reported the LFPs on OCD or MDD, (2) published in English, and (3) human or animal studies. Exclusion criteria were (1) review or meta-analysis or other literature types without original data and (2) conference abstract without full text. Descriptive synthesis of data was performed.

Results

Eight studies on LFPs of OCD containing 22 patients and 32 rats were included: seven were observational studies with no controls, and one animal study included a randomized and controlled phase. Ten studies on LFPs of MDD containing 71 patients and 52 rats were included: seven were observational studies with no controls, one study with control, and two animal studies included a randomized and controlled phase.

Conclusion

The available studies revealed that different frequency bands were associated with specific symptoms. Low frequency activity seemed to be closely related to OCD symptoms, whereas LFPs findings in patients with MDD were more complicated. However, limitations of recent studies restrict the drawing of definite conclusions. Combined with other measures such as Electroencephalogram, Electrocorticography, or Magnetoencephalography and long-term recordings in various physiological states (rest state, sleep state, task state) could help to improve the understanding of potential mechanisms.

Over and above frequency: Gamma oscillations as units of neural circuit operations

Gamma oscillations (∼30-150 Hz) are widespread correlates of neural circuit functions. These network activity patterns have been described across multiple animal species, brain structures, and behaviors, and are usually identified based on their spectral peak frequency. Yet, despite intensive investigation, whether gamma oscillations implement causal mechanisms of specific brain functions or represent a general dynamic mode of neural circuit operation remains unclear. In this perspective, we review recent advances in the study of gamma oscillations toward a deeper understanding of their cellular mechanisms, neural pathways, and functional roles. We discuss that a given gamma rhythm does not per se implement any specific cognitive function but rather constitutes an activity motif reporting the cellular substrates, communication channels, and computational operations underlying information processing in its generating brain circuit. Accordingly, we propose shifting the attention from a frequency-based to a circuit-level definition of gamma oscillations.

Uncovering the organization of neural circuits with Generalized Phase Locking Analysis

Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high dimensional functional connectivity measures to mechanistic models of network activity. We address this issue by investigating spike-field coupling (SFC) measurements, which quantify the synchronization between, on the one hand, the action potentials produced by neurons, and on the other hand mesoscopic "field" signals, reflecting subthreshold activities at possibly multiple recording sites. As the number of recording sites gets large, the amount of pairwise SFC measurements becomes overwhelmingly challenging to interpret. We develop Generalized Phase Locking Analysis (GPLA) as an interpretable dimensionality reduction of this multivariate SFC. GPLA describes the dominant coupling between field activity and neural ensembles across space and frequencies. We show that GPLA features are biophysically interpretable when used in conjunction with appropriate network models, such that we can identify the influence of underlying circuit properties on these features. We demonstrate the statistical benefits and interpretability of this approach in various computational models and Utah array recordings. The results suggest that GPLA, used jointly with biophysical modeling, can help uncover the contribution of recurrent microcircuits to the spatio-temporal dynamics observed in multi-channel experimental recordings.

Dopamine depletion leads to pathological synchronization of distinct basal ganglia loops in the beta band

Motor symptoms of Parkinson's Disease (PD) are associated with dopamine deficits and pathological oscillation of basal ganglia (BG) neurons in the β range ([12-30] Hz). However, how dopamine depletion affects the oscillation dynamics of BG nuclei is still unclear. With a spiking neurons model, we here capture the features of BG nuclei interactions leading to oscillations in dopamine-depleted condition. We highlight that both the loop between subthalamic nucleus (STN) and Globus Pallidus pars externa (GPe) and the loop between striatal fast spiking and medium spiny neurons and GPe display resonances in the β range, and synchronize to a common β frequency through interaction. Crucially, the synchronization depends on dopamine depletion: the two loops are largely independent for high levels of dopamine, but progressively synchronize as dopamine is depleted due to the increased strength of the striatal loop. The model is validated against recent experimental reports on the role of cortical inputs, STN and GPe activity in the generation of β oscillations. Our results highlight the role of the interplay between the GPe-STN and the GPe-striatum loop in generating sustained β oscillations in PD subjects, and explain how this interplay depends on the level of dopamine. This paves the way to the design of therapies specifically addressing the onset of pathological β oscillations.

Macroscopic Gamma Oscillation With Bursting Neuron Model Under Stochastic Fluctuation

Gamma oscillations are thought to play a role in information processing in the brain. Bursting neurons, which exhibit periodic clusters of spiking activity, are a type of neuron that are thought to contribute largely to gamma oscillations. However, little is known about how the properties of bursting neurons affect the emergence of gamma oscillation, its waveforms, and its synchronized characteristics, especially when subjected to stochastic fluctuations. In this study, we proposed a bursting neuron model that can analyze the bursting ratio and the phase response function. Then we theoretically analyzed the neuronal population dynamics composed of bursting excitatory neurons, mixed with inhibitory neurons. The bifurcation analysis of the equivalent Fokker-Planck equation exhibits three types of gamma oscillations of unimodal firing, bimodal firing in the inhibitory population, and bimodal firing in the excitatory population under different interaction strengths. The analyses of the macroscopic phase response function by the adjoint method of the Fokker-Planck equation revealed that the inhibitory doublet facilitates synchronization of the high-frequency oscillations. When we keep the strength of interactions constant, decreasing the bursting ratio of the individual neurons increases the relative high-gamma component of the populational phase-coupling functions. This also improves the ability of the neuronal population model to synchronize with faster oscillatory input. The analytical frameworks in this study provide insight into nontrivial dynamics of the population of bursting neurons, which further suggest that bursting neurons have an important role in rhythmic activities.

Beta oscillations and waves in motor cortex can be accounted for by the interplay of spatially structured connectivity and fluctuating inputs

The beta rhythm (13-30 Hz) is a prominent brain rhythm. Recordings in primates during instructed-delay reaching tasks have shown that different types of traveling waves of oscillatory activity are associated with episodes of beta oscillations in motor cortex during movement preparation. We propose here a simple model of motor cortex based on local excitatory-inhibitory neuronal populations coupled by long-range excitation, where additionally inputs to the motor cortex from other neural structures are represented by stochastic inputs on the different model populations. We show that the model accurately reproduces the statistics of recording data when these external inputs are correlated on a short time scale (25 ms) and have two different components, one that targets the motor cortex locally and another one that targets it in a global and synchronized way. The model reproduces the distribution of beta burst durations, the proportion of the different observed wave types, and wave speeds, which we show not to be linked to axonal propagation speed. When the long-range connectivity or the local input targets are anisotropic, traveling waves are found to preferentially propagate along the axis where connectivity decays the fastest. Different from previously proposed mechanistic explanations, the model suggests that traveling waves in motor cortex are the reflection of the dephasing by external inputs, putatively of thalamic origin, of an oscillatory activity that would otherwise be spatially synchronized by recurrent connectivity.

Decoupling of interacting neuronal populations by time-shifted stimulation through spike-timing-dependent plasticity

The synaptic organization of the brain is constantly modified by activity-dependent synaptic plasticity. In several neurological disorders, abnormal neuronal activity and pathological synaptic connectivity may significantly impair normal brain function. Reorganization of neuronal circuits by therapeutic stimulation has the potential to restore normal brain dynamics. Increasing evidence suggests that the temporal stimulation pattern crucially determines the long-lasting therapeutic effects of stimulation. Here, we tested whether a specific pattern of brain stimulation can enable the suppression of pathologically strong inter-population synaptic connectivity through spike-timing-dependent plasticity (STDP). More specifically, we tested how introducing a time shift between stimuli delivered to two interacting populations of neurons can effectively decouple them. To that end, we first used a tractable model, i.e., two bidirectionally coupled leaky integrate-and-fire (LIF) neurons, to theoretically analyze the optimal range of stimulation frequency and time shift for decoupling. We then extended our results to two reciprocally connected neuronal populations (modules) where inter-population delayed connections were modified by STDP. As predicted by the theoretical results, appropriately time-shifted stimulation causes a decoupling of the two-module system through STDP, i.e., by unlearning pathologically strong synaptic interactions between the two populations. Based on the overall topology of the connections, the decoupling of the two modules, in turn, causes a desynchronization of the populations that outlasts the cessation of stimulation. Decoupling effects of the time-shifted stimulation can be realized by time-shifted burst stimulation as well as time-shifted continuous simulation. Our results provide insight into the further optimization of a variety of multichannel stimulation protocols aiming at a therapeutic reshaping of diseased brain networks.

Creation of Neuronal Ensembles and Cell-Specific Homeostatic Plasticity through Chronic Sparse Optogenetic Stimulation

Cortical computations emerge from the dynamics of neurons embedded in complex cortical circuits. Within these circuits, neuronal ensembles, which represent subnetworks with shared functional connectivity, emerge in an experience-dependent manner. Here we induced ensembles in ex vivo cortical circuits from mice of either sex by differentially activating subpopulations through chronic optogenetic stimulation. We observed a decrease in voltage correlation, and importantly a synaptic decoupling between the stimulated and nonstimulated populations. We also observed a decrease in firing rate during Up-states in the stimulated population. These ensemble-specific changes were accompanied by decreases in intrinsic excitability in the stimulated population, and a decrease in connectivity between stimulated and nonstimulated pyramidal neurons. By incorporating the empirically observed changes in intrinsic excitability and connectivity into a spiking neural network model, we were able to demonstrate that changes in both intrinsic excitability and connectivity accounted for the decreased firing rate, but only changes in connectivity accounted for the observed decorrelation. Our findings help ascertain the mechanisms underlying the ability of chronic patterned stimulation to create ensembles within cortical circuits and, importantly, show that while Up-states are a global network-wide phenomenon, functionally distinct ensembles can preserve their identity during Up-states through differential firing rates and correlations.SIGNIFICANCE STATEMENT The connectivity and activity patterns of local cortical circuits are shaped by experience. This experience-dependent reorganization of cortical circuits is driven by complex interactions between different local learning rules, external input, and reciprocal feedback between many distinct brain areas. Here we used an ex vivo approach to demonstrate how simple forms of chronic external stimulation can shape local cortical circuits in terms of their correlated activity and functional connectivity. The absence of feedback between different brain areas and full control of external input allowed for a tractable system to study the underlying mechanisms and development of a computational model. Results show that differential stimulation of subpopulations of neurons significantly reshapes cortical circuits and forms subnetworks referred to as neuronal ensembles.

Alpha transcranial alternating current stimulation reduces depressive symptoms in people with schizophrenia and auditory hallucinations: a double-blind, randomized pilot clinical trial

People with schizophrenia exhibit reduced alpha oscillations and frontotemporal coordination of brain activity. Alpha oscillations are associated with top-down inhibition. Reduced alpha oscillations may fail to censor spurious endogenous activity, leading to auditory hallucinations. Transcranial alternating current stimulation (tACS) at the alpha frequency was shown to enhance alpha oscillations in people with schizophrenia and may thus be a network-based treatment for auditory hallucinations. We conducted a double-blind, randomized, placebo-controlled pilot clinical trial to examine the efficacy of 10-Hz tACS in treating auditory hallucinations in people with schizophrenia. 10-Hz tACS was administered in phase at the dorsolateral prefrontal cortex and the temporoparietal junction with a return current at Cz. Patients were randomized to receive tACS or sham for five consecutive days during the treatment week (40 min/day), followed by a maintenance period, during which participants received weekly tACS (40 min/visit) or sham. tACS treatment reduced general psychopathology (p < 0.05, Cohen's d = -0.690), especially depression (p < 0.005, Cohen's d = -0.806), but not auditory hallucinations. tACS treatment increased alpha power in the target region (p < 0.05), increased the frequency of peak global functional connectivity towards 10 Hz (p < 0.05), and reduced left-right frontal functional connectivity (p < 0.005). Importantly, changes in brain functional connectivity significantly correlated with symptom improvement (p < 0.05). Daily 10 Hz-tACS increased alpha power and altered alpha-band functional connectivity. Successful target engagement reduced depression and other general psychopathology symptoms, but not auditory hallucinations. Considering existing research of 10Hz tACS as a treatment for major depressive disorder, our study demonstrates its transdiagnostic potential for treating depression.

Disynaptic effect of hilar cells on pattern separation in a spiking neural network of hippocampal dentate gyrus

We study the disynaptic effect of the hilar cells on pattern separation in a spiking neural network of the hippocampal dentate gyrus (DG). The principal granule cells (GCs) in the DG perform pattern separation, transforming similar input patterns into less-similar output patterns. In our DG network, the hilus consists of excitatory mossy cells (MCs) and inhibitory HIPP (hilar perforant path-associated) cells. Here, we consider the disynaptic effects of the MCs and the HIPP cells on the GCs, mediated by the inhibitory basket cells (BCs) in the granular layer; MC → BC → GC and HIPP → BC → GC. The MCs provide disynaptic inhibitory input (mediated by the intermediate BCs) to the GCs, which decreases the firing activity of the GCs. On the other hand, the HIPP cells disinhibit the intermediate BCs, which leads to increasing the firing activity of the GCs. In this way, the disynaptic effects of the MCs and the HIPP cells are opposite. We investigate change in the pattern separation efficacy by varying the synaptic strength K ( BC , X ) [from the pre-synaptic X (= MC or HIPP) to the post-synaptic BC]. Thus, sparsity for the firing activity of the GCs is found to improve the efficacy of pattern separation, and hence the disynaptic effects of the MCs and the HIPP cells on the pattern separation become opposite ones. In the combined case when simultaneously changing both K ( BC , MC ) and K ( BC , HIPP ) , as a result of balance between the two competing disynaptic effects of the MCs and the HIPP cells, the efficacy of pattern separation is found to become the highest at their original default values where the activation degree of the GCs is the lowest. We also note that, while the GCs perform pattern separation, sparsely synchronized rhythm is found to appear in the population of the GCs. Hence, we examine quantitative association between population and individual firing behaviors in the sparsely synchronized rhythm and pattern separation. They are found to be strongly correlated. Consequently, the better the population and individual firing behaviors in the sparsely synchronized rhythm are, the more pattern separation efficacy becomes enhanced.