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.

A Mean Field to Capture Asynchronous Irregular Dynamics of Conductance-Based Networks of Adaptive Quadratic Integrate-and-Fire Neuron Models.

Mean-field models are a class of models used in computational neuroscience to study the behavior of large populations of neurons. These models are based on the idea of representing the activity of a large number of neurons as the average behavior of mean-field variables. This abstraction allows the study of large-scale neural dynamics in a computationally efficient and mathematically tractable manner. One of these methods, based on a semianalytical approach, has previously been applied to different types of single-neuron models, but never to models based on a quadratic form. In this work, we adapted this method to quadratic integrate-and-fire neuron models with adaptation and conductance-based synaptic interactions. We validated the mean-field model by comparing it to the spiking network model. This mean-field model should be useful to model large-scale activity based on quadratic neurons interacting with conductance-based synapses.

A multi-layer mean-field model of the cerebellum embedding microstructure and population-specific dynamics.

Mean-field (MF) models are computational formalism used to summarize in a few statistical parameters the salient biophysical properties of an inter-wired neuronal network. Their formalism normally incorporates different types of neurons and synapses along with their topological organization. MFs are crucial to efficiently implement the computational modules of large-scale models of brain function, maintaining the specificity of local cortical microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar microcircuit (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF reproduced the average dynamics of different neuronal populations in response to various input patterns and predicted the modulation of the Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool for future investigations of the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions.

Extracellular and intracellular components of the impedance of neural tissue.

Electric phenomena in brain tissue can be measured using extracellular potentials, such as the local field potential, or the electro-encephalogram. The interpretation of these signals depends on the electric structure and properties of extracellular media, but the measurements of these electric properties are still debated. Some measurements point to a model in which the extracellular medium is purely resistive, and thus parameters such as electric conductivity and permittivity should be independent of frequency. Other measurements point to a pronounced frequency dependence of these parameters, with scaling laws that are consistent with capacitive or diffusive effects. However, these experiments correspond to different preparations, and it is unclear how to correctly compare them. Here, we provide for the first time, impedance measurements (in the 1-10 kHz frequency range) using the same setup in various preparations, from primary cell cultures to acute brain slices, and a comparison with similar measurements performed in artificial cerebrospinal fluid with no biological material. The measurements show that when the current flows across a cell membrane, the frequency dependence of the macroscopic impedance between intracellular and extracellular electrodes is significant, and cannot be captured by a model with resistive media. Fitting a mean-field model to the data shows that this frequency dependence could be explained by the ionic diffusion mainly associated with Debye layers surrounding the membranes. We conclude that neuronal membranes and their ionic environment induce strong deviations to resistivity that should be taken into account to correctly interpret extracellular potentials generated by neurons.

An Anatomically Constrained Model of V1 Simple Cells Predicts the Coexistence of Push-Pull and Broad Inhibition.

The spatial organization and dynamic interactions between excitatory and inhibitory synaptic inputs that define the receptive field (RF) of simple cells in the cat primary visual cortex (V1) still raise the following paradoxical issues: (1) stimulation of simple cells in V1 with drifting gratings supports a wiring schema of spatially segregated sets of excitatory and inhibitory inputs activated in an opponent way by stimulus contrast polarity and (2) in contrast, intracellular studies using flashed bars suggest that although ON and OFF excitatory inputs are indeed segregated, inhibitory inputs span the entire RF regardless of input contrast polarity. Here, we propose a biologically detailed computational model of simple cells embedded in a V1-like network that resolves this seeming contradiction. We varied parametrically the RF-correlation-based bias for excitatory and inhibitory synapses and found that a moderate bias of excitatory neurons to synapse onto other neurons with correlated receptive fields and a weaker bias of inhibitory neurons to synapse onto other neurons with anticorrelated receptive fields can explain the conductance input, the postsynaptic membrane potential, and the spike train dynamics under both stimulation paradigms. This computational study shows that the same structural model can reproduce the functional diversity of visual processing observed during different visual contexts.SIGNIFICANCE STATEMENT Identifying generic connectivity motives in cortical circuitry encoding for specific functions is crucial for understanding the computations implemented in the cortex. Indirect evidence points to correlation-based biases in the connectivity pattern in V1 of higher mammals, whereby excitatory and inhibitory neurons preferentially synapse onto neurons respectively with correlated and anticorrelated receptive fields. A recent intracellular study questions this push-pull hypothesis, failing to find spatial anticorrelation patterns between excitation and inhibition across the receptive field. We present here a spiking model of V1 that integrates relevant anatomic and physiological constraints and shows that a more versatile motif of correlation-based connectivity with selectively tuned excitation and broadened inhibition is sufficient to account for the diversity of functional descriptions obtained for different classes of stimuli.

The Human Brain Project-Synergy between neuroscience, computing, informatics, and brain-inspired technologies.

The Human Brain Project (HBP) is a European flagship project with a 10-year horizon aiming to understand the human brain and to translate neuroscience knowledge into medicine and technology. To achieve such aims, the HBP explores the multilevel complexity of the brain in space and time; transfers the acquired knowledge to brain-derived applications in health, computing, and technology; and provides shared and open computing tools and data through the HBP European brain research infrastructure. We discuss how the HBP creates a transdisciplinary community of researchers united by the quest to understand the brain, with fascinating perspectives on societal benefits.

Integration, coincidence detection and resonance in networks of spiking neurons expressing Gamma oscillations and asynchronous states.

Gamma oscillations are widely seen in the awake and sleeping cerebral cortex, but the exact role of these oscillations is still debated. Here, we used biophysical models to examine how Gamma oscillations may participate to the processing of afferent stimuli. We constructed conductance-based network models of Gamma oscillations, based on different cell types found in cerebral cortex. The models were adjusted to extracellular unit recordings in humans, where Gamma oscillations always coexist with the asynchronous firing mode. We considered three different mechanisms to generate Gamma, first a mechanism based on the interaction between pyramidal neurons and interneurons (PING), second a mechanism in which Gamma is generated by interneuron networks (ING) and third, a mechanism which relies on Gamma oscillations generated by pacemaker chattering neurons (CHING). We find that all three mechanisms generate features consistent with human recordings, but that the ING mechanism is most consistent with the firing rate change inside Gamma bursts seen in the human data. We next evaluated the responsiveness and resonant properties of these networks, contrasting Gamma oscillations with the asynchronous mode. We find that for both slowly-varying stimuli and precisely-timed stimuli, the responsiveness is generally lower during Gamma compared to asynchronous states, while resonant properties are similar around the Gamma band. We could not find conditions where Gamma oscillations were more responsive. We therefore predict that asynchronous states provide the highest responsiveness to external stimuli, while Gamma oscillations tend to overall diminish responsiveness.

A method to convert neural signals into sound sequences.

We present a method to convert neural signals into sound sequences, with the constraint that the sound sequences precisely reflect the sequences of events in the neural signal. The method consists in quantifying the wave motifs in the signal and using these parameters to generate sound envelopes. We illustrate the procedure for sleep delta waves in the human electro-encephalogram (EEG), which are converted into sound sequences that encode the time structure of the original EEG waves. This procedure can be applied to synthesize personalized sound sequences specific to the EEG of a given subject.

Noise Enhancement of Neural Information Processing.

Cortical neurons in vivo function in highly fluctuating and seemingly noisy conditions, and the understanding of how information is processed in such complex states is still incomplete. In this perspective article, we first overview that an intense "synaptic noise" was measured first in single neurons, and computational models were built based on such measurements. Recent progress in recording techniques has enabled the measurement of highly complex activity in large numbers of neurons in animals and human subjects, and models were also built to account for these complex dynamics. Here, we attempt to link these two cellular and population aspects, where the complexity of network dynamics in awake cortex seems to link to the synaptic noise seen in single cells. We show that noise in single cells, in networks, or structural noise, all participate to enhance responsiveness and boost the propagation of information. We propose that such noisy states are fundamental to providing favorable conditions for information processing at large-scale levels in the brain, and may be involved in sensory perception.

Conductance-Based Adaptive Exponential Integrate-and-Fire Model.

The intrinsic electrophysiological properties of single neurons can be described by a broad spectrum of models, from realistic Hodgkin-Huxley-type models with numerous detailed mechanisms to the phenomenological models. The adaptive exponential integrate-and-fire (AdEx) model has emerged as a convenient middle-ground model. With a low computational cost but keeping biophysical interpretation of the parameters, it has been extensively used for simulations of large neural networks. However, because of its current-based adaptation, it can generate unrealistic behaviors. We show the limitations of the AdEx model, and to avoid them, we introduce the conductance-based adaptive exponential integrate-and-fire model (CAdEx). We give an analysis of the dynamics of the CAdEx model and show the variety of firing patterns it can produce. We propose the CAdEx model as a richer alternative to perform network simulations with simplified models reproducing neuronal intrinsic properties.

Cholinergic Switch between Two Types of Slow Waves in Cerebral Cortex.

Sleep slow waves are known to participate in memory consolidation, yet slow waves occurring under anesthesia present no positive effects on memory. Here, we shed light onto this paradox, based on a combination of extracellular recordings in vivo, in vitro, and computational models. We find two types of slow waves, based on analyzing the temporal patterns of successive slow-wave events. The first type is consistently observed in natural slow-wave sleep, while the second is shown to be ubiquitous under anesthesia. Network models of spiking neurons predict that the two slow wave types emerge due to a different gain on inhibitory versus excitatory cells and that different levels of spike-frequency adaptation in excitatory cells can account for dynamical distinctions between the two types. This prediction was tested in vitro by varying adaptation strength using an agonist of acetylcholine receptors, which demonstrated a neuromodulatory switch between the two types of slow waves. Finally, we show that the first type of slow-wave dynamics is more sensitive to external stimuli, which can explain how slow waves in sleep and anesthesia differentially affect memory consolidation, as well as provide a link between slow-wave dynamics and memory diseases.

Suppressive Traveling Waves Shape Representations of Illusory Motion in Primary Visual Cortex of Awake Primate.

How does the brain link visual stimuli across space and time? Visual illusions provide an experimental paradigm to study these processes. When two stationary dots are flashed in close spatial and temporal succession, human observers experience a percept of apparent motion. Large spatiotemporal separation challenges the visual system to keep track of object identity along the apparent motion path, the so-called "correspondence problem." Here, we use voltage-sensitive dye imaging in primary visual cortex (V1) of awake monkeys to show that intracortical connections within V1 can solve this issue by shaping cortical dynamics to represent the illusory motion. We find that the appearance of the second stimulus in V1 creates a systematic suppressive wave traveling toward the retinotopic representation of the first. Using a computational model, we show that the suppressive wave is the emergent property of a recurrent gain control fed by the intracortical network. This suppressive wave acts to explain away ambiguous correspondence problems and contributes to precisely encode the expected motion velocity at the surface of V1. Together, these results demonstrate that the nonlinear dynamics within retinotopic maps can shape cortical representations of illusory motion. Understanding these dynamics will shed light on how the brain links sensory stimuli across space and time, by preformatting population responses for a straightforward read-out by downstream areas.SIGNIFICANCE STATEMENT Traveling waves have recently been observed in different animal species, brain areas, and behavioral states. However, it is still unclear what are their functional roles. In the case of cortical visual processing, waves propagate across retinotopic maps and can hereby generate interactions between spatially and temporally separated instances of feedforward driven activity. Such interactions could participate in processing long-range apparent motion stimuli, an illusion for which no clear neuronal mechanisms have yet been proposed. Using this paradigm in awake monkeys, we show that suppressive traveling waves produce a spatiotemporal normalization of apparent motion stimuli. Our study suggests that cortical waves shape the representation of illusory moving stimulus within retinotopic maps for a straightforward read-out by downstream areas.

Modelling unitary fields and the single-neuron contribution to local field potentials in the hippocampus.

KEY POINTS: We simulate the unitary local field potential (uLFP) generated in the hippocampus CA3, using morphologically detailed models. The model suggests that cancelling effects between apical and basal dendritic synapses explain the low amplitude of excitatory uLFPs. Inhibitory synapses around the soma do not cancel and could explain the high-amplitude inhibitory uLFPs. These results suggest that somatic inhibition constitutes a strong component of LFPs, which may explain a number of experimental observations. ABSTRACT: Synaptic currents represent a major contribution to the local field potential (LFP) in brain tissue, but the respective contribution of excitatory and inhibitory synapses is not known. Here, we provide estimates of this contribution by using computational models of hippocampal pyramidal neurons, constrained by in vitro recordings. We focus on the unitary LFP (uLFP) generated by single neurons in the CA3 region of the hippocampus. We first reproduce experimental results for hippocampal basket cells, and in particular how inhibitory uLFP are distributed within hippocampal layers. Next, we calculate the uLFP generated by pyramidal neurons, using morphologically reconstructed CA3 pyramidal cells. The model shows that the excitatory uLFP is of small amplitude, smaller than inhibitory uLFPs. Indeed, when the two are simulated together, inhibitory uLFPs mask excitatory uLFPs, which might create the illusion that the inhibitory field is generated by pyramidal cells. These results provide an explanation for the observation that excitatory and inhibitory uLFPs are of the same polarity, in vivo and in vitro. These results suggest that somatic inhibitory currents are large contributors to the LFP, which is important information for interpreting this signal. Finally, the results of our model might form the basis of a simple method to compute the LFP, which could be applied to point neurons for each cell type, thus providing a simple biologically grounded method for calculating LFPs from neural networks. In conclusion, computational models constrained by in vitro recordings suggest that: (1) Excitatory uLFPs are of smaller amplitude than inhibitory uLFPs. (2) Inhibitory uLFPs form the major contribution to LFPs. (3) uLFPs can be used as a simple model to generate LFPs from spiking networks.

Electrophysiological monitoring of inhibition in mammalian species, from rodents to humans.

GABAergic interneurons constitute a highly diverse family of neurons that play a critical role in cortical functions. Due to their prominent role in cortical network dynamics, genetic, developmental, or other dysfunctions in GABAergic neurons have been linked to neurological disorders such as epilepsy. Thus, it is crucial to investigate the interaction of these various neurons and to develop methods to specifically and directly monitor inhibitory activity in vivo. While research in small mammals has benefited from a wealth of recent technological development, bridging the gap to large mammals and humans remains a challenge. This is of particular interest since single neuron monitoring with intracranial electrodes in epileptic patients is developing quickly, opening new avenues for understanding the role of different cell types in epilepsy. Here, we review currently available techniques that monitor inhibitory activity in the brain and the respective validations in rodents. Finally, we discuss the future developments of these techniques and how knowledge from animal research can be translated to the study of neuronal circuit dynamics in the human brain.

Biologically Realistic Mean-Field Models of Conductance-Based Networks of Spiking Neurons with Adaptation.

Accurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas.

High-frequency oscillations in human and monkey neocortex during the wake-sleep cycle.

Beta (ß)- and gamma (γ)-oscillations are present in different cortical areas and are thought to be inhibition-driven, but it is not known if these properties also apply to γ-oscillations in humans. Here, we analyze such oscillations in high-density microelectrode array recordings in human and monkey during the wake-sleep cycle. In these recordings, units were classified as excitatory and inhibitory cells. We find that γ-oscillations in human and ß-oscillations in monkey are characterized by a strong implication of inhibitory neurons, both in terms of their firing rate and their phasic firing with the oscillation cycle. The ß- and γ-waves systematically propagate across the array, with similar velocities, during both wake and sleep. However, only in slow-wave sleep (SWS) ß- and γ-oscillations are associated with highly coherent and functional interactions across several millimeters of the neocortex. This interaction is specifically pronounced between inhibitory cells. These results suggest that inhibitory cells are dominantly involved in the genesis of ß- and γ-oscillations, as well as in the organization of their large-scale coherence in the awake and sleeping brain. The highest oscillation coherence found during SWS suggests that fast oscillations implement a highly coherent reactivation of wake patterns that may support memory consolidation during SWS.

Modeling mesoscopic cortical dynamics using a mean-field model of conductance-based networks of adaptive exponential integrate-and-fire neurons.

Voltage-sensitive dye imaging (VSDi) has revealed fundamental properties of neocortical processing at macroscopic scales. Since for each pixel VSDi signals report the average membrane potential over hundreds of neurons, it seems natural to use a mean-field formalism to model such signals. Here, we present a mean-field model of networks of Adaptive Exponential (AdEx) integrate-and-fire neurons, with conductance-based synaptic interactions. We study a network of regular-spiking (RS) excitatory neurons and fast-spiking (FS) inhibitory neurons. We use a Master Equation formalism, together with a semi-analytic approach to the transfer function of AdEx neurons to describe the average dynamics of the coupled populations. We compare the predictions of this mean-field model to simulated networks of RS-FS cells, first at the level of the spontaneous activity of the network, which is well predicted by the analytical description. Second, we investigate the response of the network to time-varying external input, and show that the mean-field model predicts the response time course of the population. Finally, to model VSDi signals, we consider a one-dimensional ring model made of interconnected RS-FS mean-field units. We found that this model can reproduce the spatio-temporal patterns seen in VSDi of awake monkey visual cortex as a response to local and transient visual stimuli. Conversely, we show that the model allows one to infer physiological parameters from the experimentally-recorded spatio-temporal patterns.

Dendritic sodium spikes endow neurons with inverse firing rate response to correlated synaptic activity.

Many neurons possess dendrites enriched with sodium channels and are capable of generating action potentials. However, the role of dendritic sodium spikes remain unclear. Here, we study computational models of neurons to investigate the functional effects of dendritic spikes. In agreement with previous studies, we found that point neurons or neurons with passive dendrites increase their somatic firing rate in response to the correlation of synaptic bombardment for a wide range of input conditions, i.e. input firing rates, synaptic conductances, or refractory periods. However, neurons with active dendrites show the opposite behavior: for a wide range of conditions the firing rate decreases as a function of correlation. We found this property in three types of models of dendritic excitability: a Hodgkin-Huxley model of dendritic spikes, a model with integrate and fire dendrites, and a discrete-state dendritic model. We conclude that fast dendritic spikes confer much broader computational properties to neurons, sometimes opposite to that of point neurons.

Heterogeneous firing responses predict diverse couplings to presynaptic activity in mice layer V pyramidal neurons.

In this study, we present a theoretical framework combining experimental characterizations and analytical calculus to capture the firing rate input-output properties of single neurons in the fluctuation-driven regime. Our framework consists of a two-step procedure to treat independently how the dendritic input translates into somatic fluctuation variables, and how the latter determine action potential firing. We use this framework to investigate the functional impact of the heterogeneity in firing responses found experimentally in young mice layer V pyramidal cells. We first design and calibrate in vitro a simplified morphological model of layer V pyramidal neurons with a dendritic tree following Rall's branching rule. Then, we propose an analytical derivation for the membrane potential fluctuations at the soma as a function of the properties of the synaptic input in dendrites. This mathematical description allows us to easily emulate various forms of synaptic input: either balanced, unbalanced, synchronized, purely proximal or purely distal synaptic activity. We find that those different forms of dendritic input activity lead to various impact on the somatic membrane potential fluctuations properties, thus raising the possibility that individual neurons will differentially couple to specific forms of activity as a result of their different firing response. We indeed found such a heterogeneous coupling between synaptic input and firing response for all types of presynaptic activity. This heterogeneity can be explained by different levels of cellular excitability in the case of the balanced, unbalanced, synchronized and purely distal activity. A notable exception appears for proximal dendritic inputs: increasing the input level can either promote firing response in some cells, or suppress it in some other cells whatever their individual excitability. This behavior can be explained by different sensitivities to the speed of the fluctuations, which was previously associated to different levels of sodium channel inactivation and density. Because local network connectivity rather targets proximal dendrites, our results suggest that this aspect of biophysical heterogeneity might be relevant to neocortical processing by controlling how individual neurons couple to local network activity.