Synchronous chaos and broad band gamma rhythm in a minimal multi-layer model of primary visual cortex

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.

Decomposing Neural Circuit Function into Information Processing Primitives

It is challenging to measure how specific aspects of coordinated neural dynamics translate into operations of information processing and, ultimately, cognitive functions. An obstacle is that simple circuit mechanisms-such as self-sustained or propagating activity and nonlinear summation of inputs-do not directly give rise to high-level functions. Nevertheless, they already implement simple the information carried by neural activity. Here, we propose that distinct functions, such as stimulus representation, working memory, or selective attention, stem from different combinations and types of low-level manipulations of information or information processing primitives. To test this hypothesis, we combine approaches from information theory with simulations of multi-scale neural circuits involving interacting brain regions that emulate well-defined cognitive functions. Specifically, we track the information dynamics emergent from patterns of neural dynamics, using quantitative metrics to detect where and when information is actively buffered, transferred or nonlinearly merged, as possible modes of low-level processing (storage, transfer and modification). We find that neuronal subsets maintaining representations in working memory or performing attentional gain modulation are signaled by their boosted involvement in operations of information storage or modification, respectively. Thus, information dynamic metrics, beyond detecting which network units participate in cognitive processing, also promise to specify how and when they do it, that is, through which type of primitive computation, a capability that may be exploited for the analysis of experimental recordings.

Baclofen-associated neurophysiologic target engagement across species in fragile X syndrome

BACKGROUND

Fragile X syndrome (FXS) is the most common inherited form of neurodevelopmental disability. It is often characterized, especially in males, by intellectual disability, anxiety, repetitive behavior, social communication deficits, delayed language development, and abnormal sensory processing. Recently, we identified electroencephalographic (EEG) biomarkers that are conserved between the mouse model of FXS (Fmr1 KO mice) and humans with FXS.

METHODS

In this report, we evaluate small molecule target engagement utilizing multielectrode array electrophysiology in the Fmr1 KO mouse and in humans with FXS. Neurophysiologic target engagement was evaluated using single doses of the GABA_B selective agonist racemic baclofen (RBAC).

RESULTS

In Fmr1 KO mice and in humans with FXS, baclofen use was associated with suppression of elevated gamma power and increase in low-frequency power at rest. In the Fmr1 KO mice, a baclofen-associated improvement in auditory chirp synchronization was also noted.

CONCLUSIONS

Overall, we noted synchronized target engagement of RBAC on resting state electrophysiology, in particular the reduction of aberrant high frequency gamma activity, across species in FXS. This finding holds promise for translational medicine approaches to drug development for FXS, synchronizing treatment study across species using well-established EEG biological markers in this field.

TRIAL REGISTRATION

The human experiments are registered under NCT02998151.

Neocortical localization and thalamocortical modulation of neuronal hyperexcitability contribute to Fragile X Syndrome

Fragile X Syndrome (FXS) is a monogenetic form of intellectual disability and autism in which well-established knockout (KO) animal models point to neuronal hyperexcitability and abnormal gamma-frequency physiology as a basis for key disorder features. Translating these findings into patients may identify tractable treatment targets. Using source modeling of resting-state electroencephalography data, we report findings in FXS, including 1) increases in localized gamma activity, 2) pervasive changes of theta/alpha activity, indicative of disrupted thalamocortical modulation coupled with elevated gamma power, 3) stepwise moderation of low and high-frequency abnormalities based on female sex, and 4) relationship of this physiology to intellectual disability and neuropsychiatric symptoms. Our observations extend findings in Fmr1-/- KO mice to patients with FXS and raise a key role for disrupted thalamocortical modulation in local hyperexcitability. This systems-level mechanism has received limited preclinical attention but has implications for understanding fundamental disease mechanisms.

Narrow and Broad γ Bands Process Complementary Visual Information in Mouse Primary Visual Cortex

γ Band plays a key role in the encoding of visual features in the primary visual cortex (V1). In rodents V1 two ranges within the γ band are sensitive to contrast: a broad γ band (BB) increasing with contrast, and a narrow γ band (NB), peaking at ∼60 Hz, decreasing with contrast. The functional roles of the two bands and the neural circuits originating them are not completely clear yet. Here, we show, combining experimental and simulated data, that in mice V1 (1) BB carries information about high contrast and NB about low contrast; (2) BB modulation depends on excitatory-inhibitory interplay in the cortex, while NB modulation is because of entrainment to the thalamic drive. In awake mice presented with alternating gratings, NB power progressively decreased from low to intermediate levels of contrast where it reached a plateau. Conversely, BB power was constant across low levels of contrast, but it progressively increased from intermediate to high levels of contrast. Furthermore, BB response was stronger immediately after contrast reversal, while the opposite held for NB. These complementary modulations were reproduced by a recurrent excitatory-inhibitory leaky integrate-and-fire network provided that the thalamic inputs were composed of a sustained and a periodic component having complementary sensitivity ranges. These results show that in rodents the thalamic-driven NB plays a specific key role in encoding visual contrast. Moreover, we propose a simple and effective network model of response to visual stimuli in rodents that might help in investigating network dysfunctions of pathologic visual information processing.

Robust rhythmogenesis via spike-timing-dependent plasticity

Rhythmic activity has been observed in numerous animal species ranging from insects to humans, and in relation to a wide range of cognitive tasks. Various experimental and theoretical studies have investigated rhythmic activity. The theoretical efforts have mainly been focused on the neuronal dynamics, under the assumption that network connectivity satisfies certain fine-tuning conditions required to generate oscillations. However, it remains unclear how this fine-tuning is achieved. Here we investigated the hypothesis that spike-timing-dependent plasticity (STDP) can provide the underlying mechanism for tuning synaptic connectivity to generate rhythmic activity. We addressed this question in a modeling study. We examined STDP dynamics in the framework of a network of excitatory and inhibitory neuronal populations that has been suggested to underlie the generation of oscillations in the gamma range. Mean-field Fokker-Planck equations for the synaptic weight dynamics are derived in the limit of slow learning. We drew on this approximation to determine which types of STDP rules drive the system to exhibit rhythmic activity, and we demonstrate how the parameters that characterize the plasticity rule govern the rhythmic activity. Finally, we propose a mechanism that can ensure the robustness of self-developing processes in general, and for rhythmogenesis in particular.

Collective firing patterns of neuronal networks with short-term synaptic plasticity

We investigate the occurrence of synchronous population activities in a neuronal network composed of both excitatory and inhibitory neurons and equipped with short-term synaptic plasticity. The collective firing patterns with different macroscopic properties emerge visually with the change of system parameters, and most long-time collective evolution also shows periodic-like characteristics. We systematically discuss the pattern-formation dynamics on a microscopic level and find a lot of hidden features of the population activities. The bursty phase with power-law distributed avalanches is observed in which the population activity can be either entire or local periodic-like. In the purely spike-to-spike synchronous regime, the periodic-like phase emerges from the synchronous chaos after the backward period-doubling transition. The local periodic-like population activity and the synchronous chaotic activity show substantial trial-to-trial variability, which is unfavorable for neural code, while they are contrary to the stable periodic-like phases. We also show that the inhibitory neurons can promote the generation of cluster firing behavior and strong bursty collective firing activity by depressing the activities of postsynaptic neurons partially or wholly.

Synchronization, Stochasticity, and Phase Waves in Neuronal Networks With Spatially-Structured Connectivity

Oscillations in the beta/low gamma range (10–45 Hz) are recorded in diverse neural structures. They have successfully been modeled as sparsely synchronized oscillations arising from reciprocal interactions between randomly connected excitatory (E) pyramidal cells and local interneurons (I). The synchronization of spatially distant oscillatory spiking E–I modules has been well-studied in the rate model framework but less so for modules of spiking neurons. Here, we first show that previously proposed modifications of rate models provide a quantitative description of spiking E–I modules of Exponential Integrate-and-Fire (EIF) neurons. This allows us to analyze the dynamical regimes of sparsely synchronized oscillatory E–I modules connected by long-range excitatory interactions, for two modules, as well as for a chain of such modules. For modules with a large number of neurons (> 10⁵), we obtain results similar to previously obtained ones based on the classic deterministic Wilson-Cowan rate model, with the added bonus that the results quantitatively describe simulations of spiking EIF neurons. However, for modules with a moderate (~ 10⁴) number of neurons, stochastic variations in the spike emission of neurons are important and need to be taken into account. On the one hand, they modify the oscillations in a way that tends to promote synchronization between different modules. On the other hand, independent fluctuations on different modules tend to disrupt synchronization. The correlations between distant oscillatory modules can be described by stochastic equations for the oscillator phases that have been intensely studied in other contexts. On shorter distances, we develop a description that also takes into account amplitude modes and that quantitatively accounts for our simulation data. Stochastic dephasing of neighboring modules produces transient phase gradients and the transient appearance of phase waves. We propose that these stochastically-induced phase waves provide an explanative framework for the observations of traveling waves in the cortex during beta oscillations.

Dimensional reduction of emergent spatiotemporal cortical dynamics via a maximum entropy moment closure

Modern electrophysiological recordings and optical imaging techniques have revealed a diverse spectrum of spatiotemporal neural activities underlying fundamental cognitive processing. Oscillations, traveling waves and other complex population dynamical patterns are often concomitant with sensory processing, information transfer, decision making and memory consolidation. While neural population models such as neural mass, population density and kinetic theoretical models have been used to capture a wide range of the experimentally observed dynamics, a full account of how the multi-scale dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Here we apply a recently developed coarse-graining framework for reduced-dimensional descriptions of neuronal networks to model visual cortical dynamics. We show that, without introducing any new parameters, how a sequence of models culminating in an augmented system of spatially-coupled ODEs can effectively model a wide range of the observed cortical dynamics, ranging from visual stimulus orientation dynamics to traveling waves induced by visual illusory stimuli. In addition to an efficient simulation method, this framework also offers an analytic approach to studying large-scale network dynamics. As such, the dimensional reduction naturally leads to mesoscopic variables that capture the interplay between neuronal population stochasticity and network architecture that we believe to underlie many emergent cortical phenomena.

Determinants of Brain Rhythm Burst Statistics

Brain rhythms recorded in vivo, such as gamma oscillations, are notoriously variable both in amplitude and frequency. They are characterized by transient epochs of higher amplitude known as bursts. It has been suggested that, despite their short-life and random occurrence, bursts in gamma and other rhythms can efficiently contribute to working memory or communication tasks. Abnormalities in bursts have also been associated with e.g. motor and psychiatric disorders. It is thus crucial to understand how single cell and connectivity parameters influence burst statistics and the corresponding brain states. To address this problem, we consider a generic stochastic recurrent network of Pyramidal Interneuron Network Gamma (PING) type. Using the stochastic averaging method, we derive dynamics for the phase and envelope of the amplitude process, and find that they depend on only two meta-parameters that combine all the model parameters. This allows us to identify an optimal parameter regime of healthy variability with similar statistics to those seen in vivo; in this regime, oscillations and bursts are supported by synaptic noise. The probability density for the rhythm’s envelope as well as the mean burst duration are then derived using first passage time analysis. Our analysis enables us to link burst attributes, such as duration and frequency content, to system parameters. Our general approach can be extended to different frequency bands, network topologies and extra populations. It provides the much needed insight into the biophysical determinants of rhythm burst statistics, and into what needs to be changed to correct rhythms with pathological statistics.

A coarse-graining framework for spiking neuronal networks: from strongly-coupled conductance-based integrate-and-fire neurons to augmented systems of ODEs

Homogeneously structured, fluctuation-driven networks of spiking neurons can exhibit a wide variety of dynamical behaviors, ranging from homogeneity to synchrony. We extend our partitioned-ensemble average (PEA) formalism proposed in Zhang et al. (Journal of Computational Neuroscience, 37(1), 81-104, 2014a) to systematically coarse grain the heterogeneous dynamics of strongly coupled, conductance-based integrate-and-fire neuronal networks. The population dynamics models derived here successfully capture the so-called multiple-firing events (MFEs), which emerge naturally in fluctuation-driven networks of strongly coupled neurons. Although these MFEs likely play a crucial role in the generation of the neuronal avalanches observed in vitro and in vivo, the mechanisms underlying these MFEs cannot easily be understood using standard population dynamic models. Using our PEA formalism, we systematically generate a sequence of model reductions, going from Master equations, to Fokker-Planck equations, and finally, to an augmented system of ordinary differential equations. Furthermore, we show that these reductions can faithfully describe the heterogeneous dynamic regimes underlying the generation of MFEs in strongly coupled conductance-based integrate-and-fire neuronal networks.

Synchronization transition in neuronal networks composed of chaotic or non-chaotic oscillators

Chaotic dynamics has been shown in the dynamics of neurons and neural networks, in experimental data and numerical simulations. Theoretical studies have proposed an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to network behaviour and whether the dynamical richness of neural networks is sensitive to the dynamics of isolated neurons, still remain open questions. We investigated synchronization transitions in heterogeneous neural networks of neurons connected by electrical coupling in a small world topology. The nodes in our model are oscillatory neurons that – when isolated – can exhibit either chaotic or non-chaotic behaviour, depending on conductance parameters. We found that the heterogeneity of firing rates and firing patterns make a greater contribution than chaos to the steepness of the synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in the transition to full synchrony. Moreover, macroscopic chaos is observed regardless of the dynamics nature of the neurons. However, performing a Functional Connectivity Dynamics analysis, we show that chaotic nodes can promote what is known as multi-stable behaviour, where the network dynamically switches between a number of different semi-synchronized, metastable states.

Disrupted cholinergic modulation can underlie abnormal gamma rhythms in schizophrenia and auditory hallucination

The pathophysiology of auditory hallucination, a common symptom of schizophrenia, has yet been understood, but during auditory hallucination, primary auditory cortex (A1) shows paradoxical responses. When auditory stimuli are absent, A1 becomes hyperactive, while A1 responses to auditory stimuli are reduced. Such activation pattern of A1 responses during auditory hallucination is consistent with aberrant gamma rhythms in schizophrenia observed during auditory tasks, raising the possibility that the pathology underlying abnormal gamma rhythms can account for auditory hallucination. Moreover, A1 receives top-down signals in the gamma frequency band from an adjacent association area (Par2), and cholinergic modulation regulates interactions between A1 and Par2. In this study, we utilized a computational model of A1 to ask if disrupted cholinergic modulation could underlie abnormal gamma rhythms in schizophrenia. Furthermore, based on our simulation results, we propose potential pathology by which A1 can directly contribute to auditory hallucination.

Transition between Functional Regimes in an Integrate-And-Fire Network Model of the Thalamus

The thalamus is a key brain element in the processing of sensory information. During the sleep and awake states, this brain area is characterized by the presence of two distinct dynamical regimes: in the sleep state activity is dominated by spindle oscillations (7 − 15 Hz) weakly affected by external stimuli, while in the awake state the activity is primarily driven by external stimuli. Here we develop a simple and computationally efficient model of the thalamus that exhibits two dynamical regimes with different information-processing capabilities, and study the transition between them. The network model includes glutamatergic thalamocortical (TC) relay neurons and GABAergic reticular (RE) neurons described by adaptive integrate-and-fire models in which spikes are induced by either depolarization or hyperpolarization rebound. We found a range of connectivity conditions under which the thalamic network composed by these neurons displays the two aforementioned dynamical regimes. Our results show that TC-RE loops generate spindle-like oscillations and that a minimum level of clustering (i.e. local connectivity density) in the RE-RE connections is necessary for the coexistence of the two regimes. We also observe that the transition between the two regimes occurs when the external excitatory input on TC neurons (mimicking sensory stimulation) is large enough to cause a significant fraction of them to switch from hyperpolarization-rebound-driven firing to depolarization-driven firing. Overall, our model gives a novel and clear description of the role that the two types of neurons and their connectivity play in the dynamical regimes observed in the thalamus, and in the transition between them. These results pave the way for the development of efficient models of the transmission of sensory information from periphery to cortex.

Model-Free Estimation of Tuning Curves and Their Attentional Modulation, Based on Sparse and Noisy Data

Tuning curves are the functions that relate the responses of sensory neurons to various values within one continuous stimulus dimension (such as the orientation of a bar in the visual domain or the frequency of a tone in the auditory domain). They are commonly determined by fitting a model e.g. a Gaussian or other bell-shaped curves to the measured responses to a small subset of discrete stimuli in the relevant dimension. However, as neuronal responses are irregular and experimental measurements noisy, it is often difficult to determine reliably the appropriate model from the data. We illustrate this general problem by fitting diverse models to representative recordings from area MT in rhesus monkey visual cortex during multiple attentional tasks involving complex composite stimuli. We find that all models can be well-fitted, that the best model generally varies between neurons and that statistical comparisons between neuronal responses across different experimental conditions are affected quantitatively and qualitatively by specific model choices. As a robust alternative to an often arbitrary model selection, we introduce a model-free approach, in which features of interest are extracted directly from the measured response data without the need of fitting any model. In our attentional datasets, we demonstrate that data-driven methods provide descriptions of tuning curve features such as preferred stimulus direction or attentional gain modulations which are in agreement with fit-based approaches when a good fit exists. Furthermore, these methods naturally extend to the frequent cases of uncertain model selection. We show that model-free approaches can identify attentional modulation patterns, such as general alterations of the irregular shape of tuning curves, which cannot be captured by fitting stereotyped conventional models. Finally, by comparing datasets across different conditions, we demonstrate effects of attention that are cell- and even stimulus-specific. Based on these proofs-of-concept, we conclude that our data-driven methods can reliably extract relevant tuning information from neuronal recordings, including cells whose seemingly haphazard response curves defy conventional fitting approaches.

Quantifying Neural Oscillatory Synchronization: A Comparison between Spectral Coherence and Phase-Locking Value Approaches

Synchronization or phase-locking between oscillating neuronal groups is considered to be important for coordination of information among cortical networks. Spectral coherence is a commonly used approach to quantify phase locking between neural signals. We systematically explored the validity of spectral coherence measures for quantifying synchronization among neural oscillators. To that aim, we simulated coupled oscillatory signals that exhibited synchronization dynamics using an abstract phase-oscillator model as well as interacting gamma-generating spiking neural networks. We found that, within a large parameter range, the spectral coherence measure deviated substantially from the expected phase-locking. Moreover, spectral coherence did not converge to the expected value with increasing signal-to-noise ratio. We found that spectral coherence particularly failed when oscillators were in the partially (intermittent) synchronized state, which we expect to be the most likely state for neural synchronization. The failure was due to the fast frequency and amplitude changes induced by synchronization forces. We then investigated whether spectral coherence reflected the information flow among networks measured by transfer entropy (TE) of spike trains. We found that spectral coherence failed to robustly reflect changes in synchrony-mediated information flow between neural networks in many instances. As an alternative approach we explored a phase-locking value (PLV) method based on the reconstruction of the instantaneous phase. As one approach for reconstructing instantaneous phase, we used the Hilbert Transform (HT) preceded by Singular Spectrum Decomposition (SSD) of the signal. PLV estimates have broad applicability as they do not rely on stationarity, and, unlike spectral coherence, they enable more accurate estimations of oscillatory synchronization across a wide range of different synchronization regimes, and better tracking of synchronization-mediated information flow among networks.

Oscillatorylike behavior in feedforward neuronal networks

We demonstrate how rhythmic activity can arise in neural networks from feedforward rather than recurrent circuitry and, in so doing, we provide a mechanism capable of explaining the temporal decorrelation of γ-band oscillations. We compare the spiking activity of a delayed recurrent network of inhibitory neurons with that of a feedforward network with the same neural properties and axonal delays. Paradoxically, these very different connectivities can yield very similar spike-train statistics in response to correlated input. This happens when neurons are noisy and axonal delays are short. A Taylor expansion of the feedback network's susceptibility-or frequency-dependent gain function-can then be stopped at first order to a good approximation, thus matching the feedforward net's susceptibility. The feedback network is known to display oscillations; these oscillations imply that the spiking activity of the population is felt by all neurons within the network, leading to direct spike correlations in a given neuron. On the other hand, in the output layer of the feedforward net, the interaction between the external drive and the delayed feedforward projection of this drive by the input layer causes indirect spike correlations: spikes fired by a given output layer neuron are correlated only through the activity of the input layer neurons. High noise and short delays partially bridge the gap between these two types of correlation, yielding similar spike-train statistics for both networks. This similarity is even stronger when the delay is distributed, as confirmed by linear response theory.

Asynchronous Rate Chaos in Spiking Neuronal Circuits

The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI) spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results.

Cross-frequency transfer in a stochastically driven mesoscopic neuronal model

The brain is known to operate in multiple coexisting frequency bands. Increasing experimental evidence suggests that interactions between those distinct bands play a crucial role in brain processes, but the dynamical mechanisms underlying this cross-frequency coupling are still under investigation. Two approaches have been proposed to address this issue. In the first one distinct nonlinear oscillators representing the brain rhythms involved are coupled actively (bidirectionally), whereas in the second one the oscillators are coupled unidirectionally and thus the driving between them is passive. Here we elaborate the latter approach by implementing a stochastically driven network of coupled neural mass models that operate in the alpha range. This model exhibits a broadband power spectrum with 1/f^b form, similar to those observed experimentally. Our results show that such a model is able to reproduce recent experimental observations on the effect of slow rocking on the alpha activity associated with sleep. This suggests that passive driving can account for cross-frequency transfer in the brain, as a result of the complex nonlinear dynamics of its underlying oscillators.

A reduction for spiking integrate-and-fire network dynamics ranging from homogeneity to synchrony

In this paper we provide a general methodology for systematically reducing the dynamics of a class of integrate-and-fire networks down to an augmented 4-dimensional system of ordinary-differential-equations. The class of integrate-and-fire networks we focus on are homogeneously-structured, strongly coupled, and fluctuation-driven. Our reduction succeeds where most current firing-rate and population-dynamics models fail because we account for the emergence of 'multiple-firing-events' involving the semi-synchronous firing of many neurons. These multiple-firing-events are largely responsible for the fluctuations generated by the network and, as a result, our reduction faithfully describes many dynamic regimes ranging from homogeneous to synchronous. Our reduction is based on first principles, and provides an analyzable link between the integrate-and-fire network parameters and the relatively low-dimensional dynamics underlying the 4-dimensional augmented ODE.

Stimulus dependence of local field potential spectra: experiment versus theory

The local field potential (LFP) captures different neural processes, including integrative synaptic dynamics that cannot be observed by measuring only the spiking activity of small populations. Therefore, investigating how LFP power is modulated by external stimuli can offer important insights into sensory neural representations. However, gaining such insight requires developing data-driven computational models that can identify and disambiguate the neural contributions to the LFP. Here, we investigated how networks of excitatory and inhibitory integrate-and-fire neurons responding to time-dependent inputs can be used to interpret sensory modulations of LFP spectra. We computed analytically from such models the LFP spectra and the information that they convey about input and used these analytical expressions to fit the model to LFPs recorded in V1 of anesthetized macaques (Macaca mulatta) during the presentation of color movies. Our expressions explain 60%-98% of the variance of the LFP spectrum shape and its dependency upon movie scenes and we achieved this with realistic values for the best-fit parameters. In particular, synaptic best-fit parameters were compatible with experimental measurements and the predictions of firing rates, based only on the fit of LFP data, correlated with the multiunit spike rate recorded from the same location. Moreover, the parameters characterizing the input to the network across different movie scenes correlated with cross-scene changes of several image features. Our findings suggest that analytical descriptions of spiking neuron networks may become a crucial tool for the interpretation of field recordings.

Emergent spike patterns in neuronal populations

This numerical study documents and analyzes emergent spiking behavior in local neuronal populations. Emphasis is given to a phenomenon we call clustering, by which we refer to a tendency of random groups of neurons large and small to spontaneously coordinate their spiking activity in some fashion. Using a sparsely connected network of integrate-and-fire neurons, we demonstrate that spike clustering occurs ubiquitously in both high firing and low firing regimes. As a practical tool for quantifying such spike patterns, we propose a simple scheme with two parameters, one setting the temporal scale and the other the amount of deviation from the mean to be regarded as significant. Viewing population activity as a sequence of events, meaning relatively brief durations of elevated spiking, separated by inter-event times, we observe that background activity tends to give rise to extremely broad distributions of event sizes and inter-event times, while driving a system imposes a certain regularity on its inter-event times, producing a rhythm consistent with broad-band gamma oscillations. We note also that event sizes and inter-event times decorrelate very quickly. Dynamical analyses supported by numerical evidence are offered.

Non-linear dynamics in parkinsonism

Over the last 30 years, the functions (and dysfunctions) of the sensory-motor circuitry have been mostly conceptualized using linear modelizations which have resulted in two main models: the “rate hypothesis” and the “oscillatory hypothesis.” In these two models, the basal ganglia data stream is envisaged as a random temporal combination of independent simple patterns issued from its probability distribution of interval interspikes or its spectrum of frequencies respectively. More recently, non-linear analyses have been introduced in the modelization of motor circuitry activities, and they have provided evidences that complex temporal organizations exist in basal ganglia neuronal activities. Regarding movement disorders, these complex temporal organizations in the basal ganglia data stream differ between conditions (i.e., parkinsonism, dyskinesia, healthy control) and are responsive to treatments (i.e., l-DOPA, deep brain stimulation). A body of evidence has reported that basal ganglia neuronal entropy (a marker for complexity/irregularity in time series) is higher in hypokinetic state. In line with these findings, an entropy-based model has been recently formulated to introduce basal ganglia entropy as a marker for the alteration of motor processing and a factor of motor inhibition. Importantly, non-linear features have also been identified as a marker of condition and/or treatment effects in brain global signals (EEG), muscular activities (EMG), or kinetic of motor symptoms (tremor, gait) of patients with movement disorders. It is therefore warranted that the non-linear dynamics of motor circuitry will contribute to a better understanding of the neuronal dysfunctions underlying the spectrum of parkinsonian motor symptoms including tremor, rigidity, and hypokinesia.

Neuroscience, quantum indeterminism and the Cartesian soul

Quantum indeterminism is frequently invoked as a solution to the problem of how a disembodied soul might interact with the brain (as Descartes proposed), and is sometimes invoked in theories of libertarian free will even when they do not involve dualistic assumptions. Taking as example the Eccles-Beck model of interaction between self (or soul) and brain at the level of synaptic exocytosis, I here evaluate the plausibility of these approaches. I conclude that Heisenbergian uncertainty is too small to affect synaptic function, and that amplification by chaos or by other means does not provide a solution to this problem. Furthermore, even if Heisenbergian effects did modify brain functioning, the changes would be swamped by those due to thermal noise. Cells and neural circuits have powerful noise-resistance mechanisms, that are adequate protection against thermal noise and must therefore be more than sufficient to buffer against Heisenbergian effects. Other forms of quantum indeterminism must be considered, because these can be much greater than Heisenbergian uncertainty, but these have not so far been shown to play a role in the brain.

Distribution of correlated spiking events in a population-based approach for Integrate-and-Fire networks

Randomly connected populations of spiking neurons display a rich variety of dynamics. However, much of the current modeling and theoretical work has focused on two dynamical extremes: on one hand homogeneous dynamics characterized by weak correlations between neurons, and on the other hand total synchrony characterized by large populations firing in unison. In this paper we address the conceptual issue of how to mathematically characterize the partially synchronous "multiple firing events" (MFEs) which manifest in between these two dynamical extremes. We further develop a geometric method for obtaining the distribution of magnitudes of these MFEs by recasting the cascading firing event process as a first-passage time problem, and deriving an analytical approximation of the first passage time density valid for large neuron populations. Thus, we establish a direct link between the voltage distributions of excitatory and inhibitory neurons and the number of neurons firing in an MFE that can be easily integrated into population-based computational methods, thereby bridging the gap between homogeneous firing regimes and total synchrony.

Basal forebrain activation controls contrast sensitivity in primary visual cortex

BACKGROUND

The basal forebrain (BF) regulates cortical activity by the action of cholinergic projections to the cortex. At the same time, it also sends substantial GABAergic projections to both cortex and thalamus, whose functional role has received far less attention. We used deep brain stimulation (DBS) in the BF, which is thought to activate both types of projections, to investigate the impact of BF activation on V1 neural activity.

RESULTS

BF stimulation robustly increased V1 single and multi-unit activity, led to moderate decreases in orientation selectivity and a remarkable increase in contrast sensitivity as demonstrated by a reduced semi-saturation contrast. The spontaneous V1 local field potential often exhibited spectral peaks centered at 40 and 70 Hz as well as reliably showed a broad γ-band (30-90 Hz) increase following BF stimulation, whereas effects in a low frequency band (1-10 Hz) were less consistent. The broad γ-band, rather than low frequency activity or spectral peaks was the best predictor of both the firing rate increase and contrast sensitivity increase of V1 unit activity.

CONCLUSIONS

We conclude that BF activation has a strong influence on contrast sensitivity in V1. We suggest that, in addition to cholinergic modulation, the BF GABAergic projections play a crucial role in the impact of BF DBS on cortical activity.

Controlling the oscillation phase through precisely timed closed-loop optogenetic stimulation: a computational study

Dynamic oscillatory coherence is believed to play a central role in flexible communication between brain circuits. To test this communication-through-coherence hypothesis, experimental protocols that allow a reliable control of phase-relations between neuronal populations are needed. In this modeling study, we explore the potential of closed-loop optogenetic stimulation for the control of functional interactions mediated by oscillatory coherence. The theory of non-linear oscillators predicts that the efficacy of local stimulation will depend not only on the stimulation intensity but also on its timing relative to the ongoing oscillation in the target area. Induced phase-shifts are expected to be stronger when the stimulation is applied within specific narrow phase intervals. Conversely, stimulations with the same or even stronger intensity are less effective when timed randomly. Stimulation should thus be properly phased with respect to ongoing oscillations (in order to optimally perturb them) and the timing of the stimulation onset must be determined by a real-time phase analysis of simultaneously recorded local field potentials (LFPs). Here, we introduce an electrophysiologically calibrated model of Channelrhodopsin 2 (ChR2)-induced photocurrents, based on fits holding over two decades of light intensity. Through simulations of a neural population which undergoes coherent gamma oscillations—either spontaneously or as an effect of continuous optogenetic driving—we show that precisely-timed photostimulation pulses can be used to shift the phase of oscillation, even at transduction rates smaller than 25%. We consider then a canonic circuit with two inter-connected neural populations oscillating with gamma frequency in a phase-locked manner. We demonstrate that photostimulation pulses applied locally to a single population can induce, if precisely phased, a lasting reorganization of the phase-locking pattern and hence modify functional interactions between the two populations.

Emergent dynamics in a model of visual cortex

This paper proposes that the network dynamics of the mammalian visual cortex are highly structured and strongly shaped by temporally localized barrages of excitatory and inhibitory firing we call ‘multiple-firing events’ (MFEs). Our proposal is based on careful study of a network of spiking neurons built to reflect the coarse physiology of a small patch of layer 2/3 of V1. When appropriately benchmarked this network is capable of reproducing the qualitative features of a range of phenomena observed in the real visual cortex, including spontaneous background patterns, orientation-specific responses, surround suppression and gamma-band oscillations. Detailed investigation into the relevant regimes reveals causal relationships among dynamical events driven by a strong competition between the excitatory and inhibitory populations. It suggests that along with firing rates, MFE characteristics can be a powerful signature of a regime. Testable predictions based on model observations and dynamical analysis are proposed.

Dynamics of spiking neurons: between homogeneity and synchrony

Randomly connected networks of neurons driven by Poisson inputs are often assumed to produce "homogeneous" dynamics, characterized by largely independent firing and approximable by diffusion processes. At the same time, it is well known that such networks can fire synchronously. Between these two much studied scenarios lies a vastly complex dynamical landscape that is relatively unexplored. In this paper, we discuss a phenomenon which commonly manifests in these intermediate regimes, namely brief spurts of spiking activity which we call multiple firing events (MFE). These events do not depend on structured network architecture nor on structured input; they are an emergent property of the system. We came upon them in an earlier modeling paper, in which we discovered, through a careful benchmarking process, that MFEs are the single most important dynamical mechanism behind many of the V1 phenomena we were able to replicate. In this paper we explain in a simpler setting how MFEs come about, as well as their potential dynamic consequences. Although the mechanism underlying MFEs cannot easily be captured by current population dynamics models, this phenomena should not be ignored during analysis; there is a growing body of evidence that such collaborative activity may be a key towards unlocking the possible functional properties of many neuronal networks.

Dynamic effective connectivity of inter-areal brain circuits

Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity (or, more precisely, causal connectivity), related to the elusive question “Which areas cause the present activity of which others?”. Effective connectivity is directed and depends flexibly on contexts and tasks. Here we show that dynamic effective connectivity can emerge from transitions in the collective organization of coherent neural activity. Integrating simulation and semi-analytic approaches, we study mesoscale network motifs of interacting cortical areas, modeled as large random networks of spiking neurons or as simple rate units. Through a causal analysis of time-series of model neural activity, we show that different dynamical states generated by a same structural connectivity motif correspond to distinct effective connectivity motifs. Such effective motifs can display a dominant directionality, due to spontaneous symmetry breaking and effective entrainment between local brain rhythms, although all connections in the considered structural motifs are reciprocal. We show then that transitions between effective connectivity configurations (like, for instance, reversal in the direction of inter-areal interactions) can be triggered reliably by brief perturbation inputs, properly timed with respect to an ongoing local oscillation, without the need for plastic synaptic changes. Finally, we analyze how the information encoded in spiking patterns of a local neuronal population is propagated across a fixed structural connectivity motif, demonstrating that changes in the active effective connectivity regulate both the efficiency and the directionality of information transfer. Previous studies stressed the role played by coherent oscillations in establishing efficient communication between distant areas. Going beyond these early proposals, we advance here that dynamic interactions between brain rhythms provide as well the basis for the self-organized control of this “communication-through-coherence”, making thus possible a fast “on-demand” reconfiguration of global information routing modalities.

The circuits of the brain must perform a daunting amount of functions. But how can “brain states” be flexibly controlled, given that anatomic inter-areal connections can be considered as fixed, on timescales relevant for behavior? We hypothesize that, thanks to the nonlinear interaction between brain rhythms, even a simple circuit involving few brain areas can originate a multitude of effective circuits, associated with alternative functions selectable “on demand”. A distinction is usually made between structural connectivity, which describes actual synaptic connections, and effective connectivity, quantifying, beyond correlation, directed inter-areal causal influences. In our study, we measure effective connectivity based on time-series of neural activity generated by model inter-areal circuits. We find that “causality follows dynamics”. We show indeed that different effective networks correspond to different dynamical states associated to a same structural network (in particular, different phase-locking patterns between local neuronal oscillations). We then find that “information follows causality” (and thus, again, dynamics). We demonstrate that different effective networks give rise to alternative modalities of information routing between brain areas wired together in a fixed structural network. In particular, we show that the self-organization of interacting “analog” rate oscillations control the flow of “digital-like” information encoded in complex spiking patterns.